DCE screen output is being saved to: C:\Users\Katarzyna\Desktop\TPN_substitutes\coding\replication package (2)\replication package\CDM_results\CDM_loop_log.txt
 
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Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.71 -0.55 0.33 -0.13 0.0032 0.043 -0.013 -0.048 0.16 0.2 -0.06 -0.16 0.061 0.091 0.24 -0.37 0.044 0.064 -0.021 0.018 -0.029 0.034 0.032 0.13 0.061 0.0096 0.0037 0.021 0.18 0.44 0.29 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3916.9325470606             NaN     3332.7412793110     0.0006   2026-09-08 10:27:26
     1      4    0.0397632437    0.1466492624     3216.9197811866  700.0127658740      663.5496082322     0.0190   2026-09-08 10:27:26
     2      5    0.0065178725    0.0181524938     3192.2632863078   24.6564948789      441.0858128729     0.0111   2026-09-08 10:27:26
     3      6    0.0101406409    0.0246528071     3174.8236770362   17.4396092715      377.7819332547     0.0050   2026-09-08 10:27:26
     4      7    0.0151630122    0.0318165403     3157.2051799541   17.6184970822      390.2159486572     0.0036   2026-09-08 10:27:26
     5      8    0.0378322884    0.0754426372     3125.7760196485   31.4291603056      411.0352209418     0.0032   2026-09-08 10:27:26
     6      9    0.0278198749    0.0510898330     3108.7644941678   17.0115254807      313.5045828503     0.0029   2026-09-08 10:27:26
     7     10    0.0205766307    0.0322929962     3100.3683435098    8.3961506580      337.4510230912     0.0026   2026-09-08 10:27:26
     8     11    0.0167653454    0.0217190430     3095.4251344707    4.9432090390      352.7074059148     0.0023   2026-09-08 10:27:26
     9     12    0.0449200854    0.0543866209     3083.4526235746   11.9725108961      371.8649598597     0.0022   2026-09-08 10:27:26
    10     13    0.1065008268    0.1258629479     3056.9601877889   26.4924357857      470.2203576102     0.0023   2026-09-08 10:27:26
    11     14    0.2447121147    0.2866861649     3000.2041769175   56.7560108714      633.6142315926     0.0026   2026-09-08 10:27:26
    12     15    0.4421429265    0.5164862956     2908.9112260065   91.2929509110      670.8349164183     0.0024   2026-09-08 10:27:26
    13     16    0.5019436067    0.5867935169     2827.4055371294   81.5056888771      511.9661593159     0.0024   2026-09-08 10:27:26
    14     17    0.2043562318    0.2412194859     2798.8242284983   28.5813086311      288.8190472281     0.0024   2026-09-08 10:27:26
    15     18    0.0223756605    0.0338685720     2790.1379699300    8.6862585683      121.0841689351     0.0024   2026-09-08 10:27:26
    16     19    0.0887082308    0.1045534056     2787.3010867617    2.8368831683       73.9104611437     0.0022   2026-09-08 10:27:26
    17     20    0.0346589405    0.0408536626     2786.7346068732    0.5664798885       74.6290597784     0.0024   2026-09-08 10:27:26
    18     21    0.0307940268    0.0369083898     2785.9313186362    0.8032882370       66.0275616059     0.0024   2026-09-08 10:27:26
    19     22    0.0291903545    0.0381802190     2784.3381832709    1.5931353653       48.5553925732     0.0025   2026-09-08 10:27:26
    20     23    0.0100881152    0.0293238091     2781.9329834810    2.4051997899       34.2261821926     0.0026   2026-09-08 10:27:26
    21     24    0.0453643003    0.0596576903     2780.0076799796    1.9253035014       31.5316740855     0.0023   2026-09-08 10:27:26
    22     25    0.0501114700    0.0594663927     2779.3658943334    0.6417856463       27.3721252400     0.0023   2026-09-08 10:27:26
    23     26    0.0171813078    0.0203335815     2779.2745174447    0.0913768886       23.6140837701     0.0022   2026-09-08 10:27:26
    24     27    0.0048417807    0.0060046868     2779.2361279893    0.0383894554       21.8080181836     0.0024   2026-09-08 10:27:26
    25     28    0.0082735372    0.0109528805     2779.1209026214    0.1152253679       18.1181653360     0.0027   2026-09-08 10:27:26
    26     29    0.0108884814    0.0166593173     2778.8596885847    0.2612140367       19.1699258317     0.0023   2026-09-08 10:27:26
    27     30    0.0160824143    0.0331556811     2778.1998835372    0.6598050474       29.0594949021     0.0023   2026-09-08 10:27:26
    28     31    0.0301385945    0.0646329535     2776.7923147065    1.4075688308       39.3536975431     0.0022   2026-09-08 10:27:26
    29     32    0.0533920847    0.1122270779     2774.4057387290    2.3865759774       42.4635463981     0.0020   2026-09-08 10:27:26
    30     33    0.0570591833    0.1263946459     2771.9926177581    2.4131209709       31.9743834733     0.0022   2026-09-08 10:27:26
    31     34    0.0298918008    0.0623467861     2770.9571298444    1.0354879138       16.5319980062     0.0038   2026-09-08 10:27:26
    32     35    0.0141218567    0.0208623497     2770.8039077076    0.1532221367       12.2344228062     0.0022   2026-09-08 10:27:26
    33     36    0.0040900597    0.0090742736     2770.7844761213    0.0194315864       12.2381967506     0.0021   2026-09-08 10:27:26
    34     37    0.0033622259    0.0076722205     2770.7602371903    0.0242389310       12.2370805320     0.0022   2026-09-08 10:27:26
    35     38    0.0056821561    0.0140027825     2770.6863906101    0.0738465802       12.2231025776     0.0022   2026-09-08 10:27:26
    36     39    0.0081095410    0.0195018134     2770.5104563787    0.1759342314       12.1738800122     0.0025   2026-09-08 10:27:26
    37     40    0.0136287113    0.0316609161     2770.0728305713    0.4376258074       12.0244560376     0.0028   2026-09-08 10:27:26
    38     41    0.0239358226    0.0604832617     2769.1354529510    0.9373776204       15.1346638712     0.0027   2026-09-08 10:27:26
    39     42    0.0567646531    0.1200419264     2767.5767487194    1.5587042316       15.6988034731     0.0022   2026-09-08 10:27:26
    40     43    0.0756543941    0.1607198174     2766.0529455962    1.5238031232       17.2361775129     0.0022   2026-09-08 10:27:26
    41     44    0.0483661238    0.1030827840     2765.3885772127    0.6643683835       19.8941784242     0.0023   2026-09-08 10:27:26
    42     45    0.0104330218    0.0268578869     2765.2807525575    0.1078246552       18.5421948590     0.0022   2026-09-08 10:27:26
    43     46    0.0027885951    0.0074573577     2765.2631845035    0.0175680541       17.7699100357     0.0024   2026-09-08 10:27:26
    44     47    0.0039117312    0.0091926552     2765.2303982798    0.0327862237       16.7420498881     0.0023   2026-09-08 10:27:26
    45     48    0.0067702737    0.0135410130     2765.1443311985    0.0860670813       14.9745919194     0.0022   2026-09-08 10:27:26
    46     49    0.0114346830    0.0193850182     2764.9253525170    0.2189786815       11.9986630232     0.0021   2026-09-08 10:27:26
    47     50    0.0193837190    0.0362186470     2764.3792396179    0.5461128990       12.2006466267     0.0022   2026-09-08 10:27:26
    48     51    0.0456472591    0.0921706714     2763.1246786324    1.2545609855       17.4244080510     0.0023   2026-09-08 10:27:26
    49     52    0.1198223809    0.2174971802     2760.7324579578    2.3922206746       21.9489297175     0.0024   2026-09-08 10:27:26
    50     53    0.1991442654    0.3527221397     2757.7083482177    3.0241097401       20.3127048558     0.0024   2026-09-08 10:27:26
    51     54    0.1575220080    0.2814974284     2755.8616006939    1.8467475238       19.8760812092     0.0023   2026-09-08 10:27:26
    52     55    0.0300934798    0.0688461577     2755.4190360552    0.4425646388       19.2234419352     0.0022   2026-09-08 10:27:26
    53     56    0.0121089404    0.0254819263     2755.3753964003    0.0436396548       17.9801755388     0.0022   2026-09-08 10:27:26
    54     57    0.0053523294    0.0099676922     2755.3639898692    0.0114065312       17.5132751798     0.0024   2026-09-08 10:27:26
    55     58    0.0124166942    0.0234445065     2755.3214314746    0.0425583946       16.2703707185     0.0021   2026-09-08 10:27:26
    56     59    0.0140769254    0.0279353215     2755.2289361265    0.0924953480       14.4017751244     0.0023   2026-09-08 10:27:26
    57     60    0.0161414068    0.0371081983     2754.9865379281    0.2423981984       10.8262672910     0.0025   2026-09-08 10:27:26
    58     61    0.0272697516    0.0407893552     2754.4582656289    0.5282722992        8.7841881592     0.0021   2026-09-08 10:27:26
    59     62    0.0411910684    0.0909903039     2753.5076659673    0.9505996617        7.4163670907     0.0021   2026-09-08 10:27:26
    60     63    0.1034737823    0.1860631637     2752.4500361628    1.0576298045        9.5273839027     0.0021   2026-09-08 10:27:26
    61     64    0.1016548033    0.1784631810     2751.9092320790    0.5408040838        9.2405999520     0.0021   2026-09-08 10:27:26
    62     65    0.0340222805    0.0629337896     2751.8102716834    0.0989603956        6.5144614802     0.0024   2026-09-08 10:27:26
    63     66    0.0051420615    0.0077658786     2751.8030495019    0.0072221815        5.4724422030     0.0021   2026-09-08 10:27:26
    64     67    0.0013148016    0.0026028378     2751.8012968808    0.0017526211        5.2233218521     0.0023   2026-09-08 10:27:26
    65     68    0.0030822718    0.0061481290     2751.7950973945    0.0061994863        4.6423002926     0.0022   2026-09-08 10:27:26
    66     69    0.0044772542    0.0079742244     2751.7813186093    0.0137787852        4.2493788021     0.0022   2026-09-08 10:27:26
    67     70    0.0080769754    0.0123183837     2751.7446663703    0.0366522390        4.4388704160     0.0024   2026-09-08 10:27:26
    68     71    0.0127996033    0.0178520987     2751.6605432534    0.0841231169        4.7546280090     0.0027   2026-09-08 10:27:26
    69     72    0.0177764754    0.0325446157     2751.4911541940    0.1693890595        5.2074849588     0.0026   2026-09-08 10:27:26
    70     73    0.0218136584    0.0593982553     2751.2547501454    0.2364040486        6.9384500167     0.0023   2026-09-08 10:27:26
    71     74    0.0275288972    0.0679997635     2751.0809129417    0.1738372037        7.0417333166     0.0023   2026-09-08 10:27:26
    72     75    0.0156406607    0.0345733367     2751.0303402050    0.0505727367        5.4510365606     0.0022   2026-09-08 10:27:26
    73     76    0.0053904529    0.0077391239     2751.0242923210    0.0060478840        5.3379630685     0.0022   2026-09-08 10:27:26
    74     77    0.0015872928    0.0024189715     2751.0225483938    0.0017439272        5.3132313748     0.0025   2026-09-08 10:27:26
    75     78    0.0029553259    0.0045162567     2751.0174117194    0.0051366744        5.2674250000     0.0025   2026-09-08 10:27:26
    76     79    0.0043009269    0.0059722578     2751.0053314434    0.0120802759        5.1890106034     0.0023   2026-09-08 10:27:26
    77     80    0.0072957863    0.0092755448     2750.9727740669    0.0325573766        5.0261296404     0.0025   2026-09-08 10:27:26
    78     81    0.0115444301    0.0170623407     2750.8910171335    0.0817569333        4.6996990317     0.0020   2026-09-08 10:27:26
    79     82    0.0240619255    0.0434882562     2750.6901906333    0.2008265002        4.9717394260     0.0020   2026-09-08 10:27:26
    80     83    0.0669774295    0.1107795684     2750.2504108096    0.4397798238        9.4985222795     0.0023   2026-09-08 10:27:26
    81     84    0.1382563133    0.2252853940     2749.4980588480    0.7523519615       12.9811812000     0.0021   2026-09-08 10:27:26
    82     85    0.1725524555    0.2834378595     2748.7232168251    0.7748420229       11.3351283994     0.0024   2026-09-08 10:27:26
    83     86    0.0876474695    0.1512312579     2748.3689451931    0.3542716320        5.5524045197     0.0021   2026-09-08 10:27:26
    84     87    0.0168796956    0.0214056806     2748.3122085744    0.0567366187        6.2833681511     0.0023   2026-09-08 10:27:26
    85     88    0.0095290918    0.0157719185     2748.3086777975    0.0035307769        6.2941529896     0.0020   2026-09-08 10:27:26
    86     89    0.0035029171    0.0057592093     2748.3074412366    0.0012365609        6.2607643732     0.0020   2026-09-08 10:27:26
    87     90    0.0093701442    0.0153906255     2748.3022194409    0.0052217957        6.1408267576     0.0022   2026-09-08 10:27:26
    88     91    0.0116387248    0.0190856468     2748.2909440335    0.0112754075        5.9319736379     0.0023   2026-09-08 10:27:26
    89     92    0.0172041979    0.0283492325     2748.2605429676    0.0304010659        5.4459766414     0.0021   2026-09-08 10:27:26
    90     93    0.0179071275    0.0315164887     2748.1908810839    0.0696618837        4.4302598976     0.0019   2026-09-08 10:27:26
    91     94    0.0215679408    0.0324369166     2748.0492935998    0.1415874841        2.4523822391     0.0022   2026-09-08 10:27:26
    92     95    0.0351028218    0.0808487331     2747.8488225047    0.2004710951        2.6205804575     0.0021   2026-09-08 10:27:26
    93     96    0.0725954261    0.1309011424     2747.6978398384    0.1509826663        2.3152844749     0.0020   2026-09-08 10:27:26
    94     97    0.0492512146    0.0824428082     2747.6534646835    0.0443751549        2.4933751605     0.0022   2026-09-08 10:27:26
    95     98    0.0095818292    0.0160440836     2747.6490227373    0.0044419462        2.5559604817     0.0021   2026-09-08 10:27:26
    96     99    0.0012608075    0.0019005461     2747.6484842924    0.0005384448        2.5640943450     0.0021   2026-09-08 10:27:26
    97    100    0.0017375751    0.0027335004     2747.6473559558    0.0011283366        2.5729443825     0.0020   2026-09-08 10:27:26
    98    101    0.0027522377    0.0041508312     2747.6444347578    0.0029211980        2.5847831691     0.0023   2026-09-08 10:27:26
    99    102    0.0043308326    0.0061305735     2747.6368310693    0.0076036885        2.5984820424     0.0023   2026-09-08 10:27:26
   100    103    0.0065837320    0.0094302974     2747.6173102324    0.0195208369        2.6923159282     0.0021   2026-09-08 10:27:26
   101    104    0.0092753935    0.0186354381     2747.5686246579    0.0486855745        2.8220849856     0.0022   2026-09-08 10:27:26
   102    105    0.0168956388    0.0462434293     2747.4560398787    0.1125847792        2.8795571200     0.0020   2026-09-08 10:27:26
   103    106    0.0429434763    0.1058197343     2747.2385189961    0.2175208826        3.6146608444     0.0019   2026-09-08 10:27:26
   104    107    0.0718147009    0.1717941266     2746.9513192026    0.2871997936        5.0786970686     0.0021   2026-09-08 10:27:26
   105    108    0.0615125460    0.1474382470     2746.7559352948    0.1953839078        5.0661722844     0.0020   2026-09-08 10:27:26
   106    109    0.0208824869    0.0427698358     2746.7044794173    0.0514558775        4.6005007630     0.0021   2026-09-08 10:27:26
   107    110    0.0044695788    0.0130196531     2746.6994363106    0.0050431067        4.2542153713     0.0023   2026-09-08 10:27:26
   108    111    0.0024865305    0.0061012083     2746.6982757035    0.0011606071        4.1487736318     0.0020   2026-09-08 10:27:26
   109    112    0.0047206125    0.0114596578     2746.6949183560    0.0033573475        3.9450089796     0.0022   2026-09-08 10:27:26
   110    113    0.0062302625    0.0150795843     2746.6870833819    0.0078349742        3.9301243992     0.0020   2026-09-08 10:27:26
   111    114    0.0084172909    0.0204967881     2746.6665444749    0.0205389070        3.8915104063     0.0020   2026-09-08 10:27:26
   112    115    0.0080558732    0.0204008690     2746.6184184800    0.0481259949        3.6708449207     0.0022   2026-09-08 10:27:26
   113    116    0.0113350552    0.0258978249     2746.5188561718    0.0995623082        3.0115361174     0.0020   2026-09-08 10:27:26
   114    117    0.0305902733    0.0831707818     2746.3712265627    0.1476296091        2.1403170801     0.0020   2026-09-08 10:27:26
   115    118    0.0504661490    0.1311754420     2746.2513976416    0.1198289211        2.6520409471     0.0020   2026-09-08 10:27:26
   116    119    0.0330601067    0.0820586788     2746.2119454418    0.0394521997        1.9202938618     0.0022   2026-09-08 10:27:26
   117    120    0.0058726740    0.0146009279     2746.2077443066    0.0042011352        1.3981277492     0.0020   2026-09-08 10:27:26
   118    121    0.0007816658    0.0020950537     2746.2074862820    0.0002580246        1.2940259015     0.0021   2026-09-08 10:27:26
   119    122    0.0006454061    0.0016548287     2746.2072538435    0.0002324385        1.2678847621     0.0020   2026-09-08 10:27:26
   120    123    0.0014303926    0.0036078117     2746.2064419300    0.0008119134        1.3309758799     0.0021   2026-09-08 10:27:26
   121    124    0.0019638584    0.0048246119     2746.2045626235    0.0018793065        1.3972760139     0.0022   2026-09-08 10:27:26
   122    125    0.0029399111    0.0070476396     2746.1996583056    0.0049043179        1.4417301435     0.0021   2026-09-08 10:27:26
   123    126    0.0039189693    0.0089167445     2746.1883978885    0.0112604171        1.3936476791     0.0021   2026-09-08 10:27:26
   124    127    0.0057121257    0.0137556252     2746.1660652968    0.0223325917        1.4310348396     0.0023   2026-09-08 10:27:26
   125    128    0.0103719218    0.0274021799     2746.1355058796    0.0305594172        1.9172145715     0.0024   2026-09-08 10:27:26
   126    129    0.0129023602    0.0348348345     2746.1134994665    0.0220064132        1.9622540991     0.0022   2026-09-08 10:27:26
   127    130    0.0068352351    0.0187267438     2746.1073252706    0.0061741959        1.8438497535     0.0024   2026-09-08 10:27:26
   128    131    0.0014741110    0.0036428080     2746.1066501001    0.0006751705        1.8421099126     0.0020   2026-09-08 10:27:26
   129    132    0.0004469620    0.0009524087     2746.1064450813    0.0002050188        1.8104024765     0.0021   2026-09-08 10:27:26
   130    133    0.0009001070    0.0018824585     2746.1057946264    0.0006504549        1.7363569429     0.0020   2026-09-08 10:27:26
   131    134    0.0012925772    0.0024923753     2746.1042813650    0.0015132613        1.6278920963     0.0020   2026-09-08 10:27:26
   132    135    0.0022055587    0.0040646829     2746.1001626051    0.0041187600        1.4431076868     0.0023   2026-09-08 10:27:26
   133    136    0.0035072623    0.0077868183     2746.0897217583    0.0104408467        1.1515048664     0.0020   2026-09-08 10:27:26
   134    137    0.0095120991    0.0198843366     2746.0632707115    0.0264510468        1.1474188741     0.0023   2026-09-08 10:27:26
   135    138    0.0249646656    0.0521780559     2746.0007787178    0.0624919938        2.2870585631     0.0021   2026-09-08 10:27:26
   136    139    0.0558497032    0.1202384891     2745.8729639002    0.1278148175        3.6983269728     0.0021   2026-09-08 10:27:26
   137    140    0.0919840545    0.2035860106     2745.6845902129    0.1883736874        4.2391359268     0.0020   2026-09-08 10:27:26
   138    141    0.0853318254    0.1900578274     2745.5333304125    0.1512598004        2.8890376072     0.0020   2026-09-08 10:27:26
   139    142    0.0232846681    0.0561959108     2745.4844155715    0.0489148410        2.7885835092     0.0020   2026-09-08 10:27:26
   140    143    0.0091016715    0.0188803923     2745.4791256415    0.0052899300        2.8712667581     0.0021   2026-09-08 10:27:26
   141    144    0.0038736949    0.0084759899     2745.4787701771    0.0003554644        2.8376170837     0.0021   2026-09-08 10:27:26
   142    145    0.0024083602    0.0053130632     2745.4784486196    0.0003215575        2.8042728582     0.0020   2026-09-08 10:27:26
   143    146    0.0051447031    0.0113218965     2745.4773229168    0.0011257028        2.7073276233     0.0021   2026-09-08 10:27:26
   144    147    0.0066455615    0.0145454883     2745.4747703007    0.0025526161        2.5217263865     0.0024   2026-09-08 10:27:26
   145    148    0.0086669355    0.0188360457     2745.4683968930    0.0063734077        2.1117928666     0.0021   2026-09-08 10:27:26
   146    149    0.0062861390    0.0142127436     2745.4553067999    0.0130900931        1.3364695268     0.0021   2026-09-08 10:27:26
   147    150    0.0093990163    0.0189560054     2745.4349969722    0.0203098277        0.7860463991     0.0023   2026-09-08 10:27:26
   148    151    0.0264991589    0.0544832263     2745.4175513899    0.0174455822        0.8941253411     0.0020   2026-09-08 10:27:26
   149    152    0.0225542485    0.0485498569     2745.4113723649    0.0061790251        0.9396480885     0.0025   2026-09-08 10:27:26
   150    153    0.0063615121    0.0139548044     2745.4106172322    0.0007551327        0.9313422739     0.0020   2026-09-08 10:27:26
   151    154    0.0004376526    0.0009448477     2745.4105529500    0.0000642821        0.9258999057     0.0022   2026-09-08 10:27:26
   152    155    0.0003070966    0.0004334184     2745.4104875288    0.0000654212        0.9222659847     0.0021   2026-09-08 10:27:26
   153    156    0.0006420072    0.0008775950     2745.4102709756    0.0002165533        0.9148047785     0.0020   2026-09-08 10:27:26
   154    157    0.0009524303    0.0013134810     2745.4097520245    0.0005189511        0.9034038497     0.0022   2026-09-08 10:27:26
   155    158    0.0016063194    0.0024961876     2745.4083518630    0.0014001614        0.8826228638     0.0021   2026-09-08 10:27:26
   156    159    0.0025673889    0.0053832968     2745.4047717537    0.0035801093        0.8447748968     0.0020   2026-09-08 10:27:26
   157    160    0.0076379120    0.0133597011     2745.3956127316    0.0091590221        1.0475822824     0.0020   2026-09-08 10:27:26
   158    161    0.0204100258    0.0333746415     2745.3733559080    0.0222568236        2.0250201762     0.0021   2026-09-08 10:27:26
   159    162    0.0480674188    0.0766443895     2745.3248124433    0.0485434647        3.2769120563     0.0022   2026-09-08 10:27:26
   160    163    0.0884929619    0.1397069811     2745.2429141575    0.0818982859        4.2008256993     0.0022   2026-09-08 10:27:26
   161    164    0.0991950977    0.1561626721     2745.1600933615    0.0828207959        3.6879817637     0.0024   2026-09-08 10:27:26
   162    165    0.0413326440    0.0662498050     2745.1235201574    0.0365732041        2.1051895155     0.0022   2026-09-08 10:27:26
   163    166    0.0065448011    0.0129751272     2745.1178516795    0.0056684779        1.5246330534     0.0021   2026-09-08 10:27:26
   164    167    0.0065047405    0.0103664463     2745.1173969236    0.0004547558        1.4644819891     0.0022   2026-09-08 10:27:26
   165    168    0.0032802572    0.0052118649     2745.1171136437    0.0002832799        1.4360833542     0.0021   2026-09-08 10:27:26
   166    169    0.0074234199    0.0118557217     2745.1160575901    0.0010560536        1.3613967150     0.0021   2026-09-08 10:27:26
   167    170    0.0090064707    0.0145726162     2745.1137069852    0.0023506049        1.2409716544     0.0023   2026-09-08 10:27:26
   168    171    0.0109739617    0.0184163066     2745.1076897854    0.0060171999        1.1030138499     0.0022   2026-09-08 10:27:26
   169    172    0.0054006469    0.0122857603     2745.0949338021    0.0127559833        0.8894342156     0.0021   2026-09-08 10:27:26
   170    173    0.0159322159    0.0244626301     2745.0735630482    0.0213707539        0.6804121030     0.0022   2026-09-08 10:27:26
   171    174    0.0459243296    0.0697444100     2745.0525873055    0.0209757427        0.7776246042     0.0022   2026-09-08 10:27:26
   172    175    0.0434834611    0.0673037869     2745.0435968796    0.0089904259        0.7079698458     0.0022   2026-09-08 10:27:26
   173    176    0.0132202125    0.0211908291     2745.0422755277    0.0013213519        0.6771025355     0.0024   2026-09-08 10:27:26
   174    177    0.0003678020    0.0010742887     2745.0421951053    0.0000804224        0.6687387753     0.0021   2026-09-08 10:27:26
   175    178    0.0002837626    0.0004678062     2745.0421651908    0.0000299145        0.6701831798     0.0022   2026-09-08 10:27:26
   176    179    0.0008173979    0.0013791437     2745.0420348568    0.0001303341        0.6740336028     0.0021   2026-09-08 10:27:26
   177    180    0.0009171579    0.0017200738     2745.0417491238    0.0002857330        0.6788279360     0.0021   2026-09-08 10:27:26
   178    181    0.0011890667    0.0026596502     2745.0409475838    0.0008015400        0.6865854873     0.0021   2026-09-08 10:27:26
   179    182    0.0017890728    0.0037752944     2745.0389169702    0.0020306136        0.6977391282     0.0022   2026-09-08 10:27:26
   180    183    0.0035710214    0.0075122749     2745.0336322098    0.0052847604        0.7136912165     0.0022   2026-09-08 10:27:26
   181    184    0.0143560132    0.0205540903     2745.0204183547    0.0132138551        0.7624749714     0.0022   2026-09-08 10:27:26
   182    185    0.0439713718    0.0565160174     2744.9893064772    0.0311118775        1.2307500832     0.0022   2026-09-08 10:27:26
   183    186    0.1052257856    0.1310542174     2744.9269496147    0.0623568626        1.6785022233     0.0021   2026-09-08 10:27:26
   184    187    0.1764099404    0.2172136656     2744.8386871242    0.0882624905        1.6725687684     0.0022   2026-09-08 10:27:26
   185    188    0.1554578577    0.1908821639     2744.7729325506    0.0657545736        1.1094845798     0.0023   2026-09-08 10:27:26
   186    189    0.0376572390    0.0487678230     2744.7538427669    0.0190897837        0.8677685858     0.0022   2026-09-08 10:27:26
   187    190    0.0139091879    0.0184676069     2744.7520476848    0.0017950822        0.7575428208     0.0022   2026-09-08 10:27:26
   188    191    0.0058398354    0.0072369551     2744.7519685320    0.0000791527        0.7465950668     0.0022   2026-09-08 10:27:26
   189    192    0.0023436255    0.0028999326     2744.7519252350    0.0000432971        0.7444727663     0.0021   2026-09-08 10:27:26
   190    193    0.0064957054    0.0080672374     2744.7517332763    0.0001919586        0.7388706105     0.0020   2026-09-08 10:27:26
   191    194    0.0083910611    0.0105023943     2744.7513108148    0.0004224615        0.7307854226     0.0021   2026-09-08 10:27:26
   192    195    0.0135746490    0.0172395964     2744.7501295745    0.0011812403        0.7149658836     0.0023   2026-09-08 10:27:26
   193    196    0.0185715631    0.0243525464     2744.7471466914    0.0029828830        0.6857684209     0.0024   2026-09-08 10:27:26
   194    197    0.0226351158    0.0324501324     2744.7394632406    0.0076834508        0.6277522300     0.0024   2026-09-08 10:27:26
   195    198    0.0156771241    0.0356821599     2744.7207413956    0.0187218450        0.5800496568     0.0023   2026-09-08 10:27:26
   196    199    0.0254467380    0.0536014290     2744.6793992530    0.0413421426        0.6042699527     0.0021   2026-09-08 10:27:26
   197    200    0.1309482172    0.1590658025     2744.6078040570    0.0715951959        0.5962051845     0.0024   2026-09-08 10:27:26
   198    201    0.2487614250    0.2890495685     2744.5316216432    0.0761824139        0.6307742676     0.0022   2026-09-08 10:27:26
   199    202    0.2008496306    0.2354374955     2744.4954472997    0.0361743434        0.5202040737     0.0026   2026-09-08 10:27:26
   200    203    0.0472918265    0.0616350571     2744.4895412650    0.0059060347        0.4593140576     0.0020   2026-09-08 10:27:26
   201    204    0.0052041918    0.0087988637     2744.4892301884    0.0003110766        0.4647339874     0.0021   2026-09-08 10:27:26
   202    205    0.0025499130    0.0030064493     2744.4892055373    0.0000246511        0.4656496553     0.0027   2026-09-08 10:27:26
   203    206    0.0044395812    0.0052201087     2744.4891413874    0.0000641499        0.4661183674     0.0023   2026-09-08 10:27:26
   204    207    0.0065959144    0.0077798929     2744.4889837466    0.0001576408        0.4650028488     0.0024   2026-09-08 10:27:26
   205    208    0.0105124555    0.0124783720     2744.4885619157    0.0004218309        0.4607162955     0.0026   2026-09-08 10:27:26
   206    209    0.0156660383    0.0188297447     2744.4874729109    0.0010890048        0.4506039644     0.0023   2026-09-08 10:27:26
   207    210    0.0221621837    0.0273934033     2744.4846488638    0.0028240472        0.4459420224     0.0021   2026-09-08 10:27:26
   208    211    0.0266733623    0.0357903613     2744.4775106495    0.0071382143        0.4392098743     0.0026   2026-09-08 10:27:26
   209    212    0.0183712093    0.0389495811     2744.4603719785    0.0171386710        0.4385683713     0.0022   2026-09-08 10:27:26
   210    213    0.0296399200    0.0606063487     2744.4243048795    0.0360670990        0.4950486186     0.0021   2026-09-08 10:27:26
   211    214    0.1422182493    0.1700778135     2744.3678616716    0.0564432079        0.7042089748     0.0026   2026-09-08 10:27:26
   212    215    0.2367198088    0.2684448588     2744.3179472970    0.0499143746        0.6363620730     0.0020   2026-09-08 10:27:26
   213    216    0.1560244533    0.1778599985     2744.2996362141    0.0183110829        0.4797319296     0.0020   2026-09-08 10:27:26
   214    217    0.0265579100    0.0356263945     2744.2974104974    0.0022257167        0.4129026513     0.0026   2026-09-08 10:27:26
   215    218    0.0042978665    0.0062811105     2744.2973199206    0.0000905768        0.4023566228     0.0020   2026-09-08 10:27:26
   216    219    0.0015765230    0.0018482330     2744.2973065752    0.0000133453        0.4021809951     0.0022   2026-09-08 10:27:26
   217    220    0.0047143366    0.0055109171     2744.2972461939    0.0000603814        0.4020956672     0.0023   2026-09-08 10:27:26
   218    221    0.0060319069    0.0070783528     2744.2971168306    0.0001293632        0.4016425315     0.0021   2026-09-08 10:27:26
   219    222    0.0101594339    0.0120137457     2744.2967509371    0.0003658935        0.3998241163     0.0022   2026-09-08 10:27:26
   220    223    0.0146110112    0.0175496639     2744.2958305683    0.0009203688        0.3947102718     0.0021   2026-09-08 10:27:26
   221    224    0.0201577171    0.0251176438     2744.2934543862    0.0023761821        0.3810505988     0.0022   2026-09-08 10:27:26
   222    225    0.0217229525    0.0306279896     2744.2876579853    0.0057964009        0.3472642994     0.0024   2026-09-08 10:27:26
   223    226    0.0133339669    0.0303339934     2744.2748021610    0.0128558243        0.4263761579     0.0025   2026-09-08 10:27:26
   224    227    0.0471409636    0.0640997739     2744.2523489298    0.0224532312        0.4800284393     0.0023   2026-09-08 10:27:26
   225    228    0.1249274745    0.1418614967     2744.2280904205    0.0242585093        0.4901747209     0.0023   2026-09-08 10:27:26
   226    229    0.1224375335    0.1379338597     2744.2162631541    0.0118272664        0.3829560220     0.0020   2026-09-08 10:27:26
   227    230    0.0394730291    0.0470850298     2744.2142510826    0.0020120715        0.3881706736     0.0022   2026-09-08 10:27:26
   228    231    0.0020155859    0.0045892761     2744.2141401715    0.0001109110        0.3820595974     0.0022   2026-09-08 10:27:26
   229    232    0.0011731247    0.0014187231     2744.2141299294    0.0000102421        0.3791065382     0.0023   2026-09-08 10:27:26
   230    233    0.0022974736    0.0027313496     2744.2141010514    0.0000288780        0.3735128760     0.0022   2026-09-08 10:27:26
   231    234    0.0033261639    0.0039612872     2744.2140318091    0.0000692423        0.3654109227     0.0024   2026-09-08 10:27:26
   232    235    0.0053250215    0.0063816723     2744.2138447332    0.0001870759        0.3519317428     0.0021   2026-09-08 10:27:26
   233    236    0.0078067600    0.0094847652     2744.2133639786    0.0004807546        0.3301509696     0.0021   2026-09-08 10:27:26
   234    237    0.0107711535    0.0135502480     2744.2121183070    0.0012456716        0.2936574020     0.0021   2026-09-08 10:27:26
   235    238    0.0120632469    0.0171951760     2744.2089895661    0.0031287409        0.2403429813     0.0024   2026-09-08 10:27:26
   236    239    0.0088072171    0.0200290904     2744.2015837736    0.0074057925        0.2530481502     0.0022   2026-09-08 10:27:26
   237    240    0.0236991713    0.0429419130     2744.1865245786    0.0150591950        0.2753497033     0.0022   2026-09-08 10:27:26
   238    241    0.0823097382    0.1044399870     2744.1646060508    0.0219185278        0.2948191270     0.0020   2026-09-08 10:27:26
   239    242    0.1159015226    0.1370894416     2744.1475317774    0.0170742734        0.1928387740     0.0021   2026-09-08 10:27:26
   240    243    0.0621663915    0.0726515218     2744.1422611859    0.0052705916        0.1922058402     0.0021   2026-09-08 10:27:26
   241    244    0.0064416130    0.0109592899     2744.1417337031    0.0005274828        0.1959471267     0.0020   2026-09-08 10:27:26
   242    245    0.0021836196    0.0031216055     2744.1417167047    0.0000169984        0.1913651051     0.0023   2026-09-08 10:27:26
   243    246    0.0005618692    0.0006974251     2744.1417142781    0.0000024266        0.1904788127     0.0021   2026-09-08 10:27:26
   244    247    0.0019463488    0.0024086994     2744.1417014490    0.0000128291        0.1879408758     0.0021   2026-09-08 10:27:26
   245    248    0.0024298217    0.0030153753     2744.1416747389    0.0000267100        0.1852773044     0.0022   2026-09-08 10:27:26
   246    249    0.0042169765    0.0052621760     2744.1415980024    0.0000767365        0.1811143446     0.0022   2026-09-08 10:27:26
   247    250    0.0062414277    0.0078767495     2744.1414046276    0.0001933748        0.1751120293     0.0021   2026-09-08 10:27:26
   248    251    0.0093139172    0.0120613177     2744.1408959050    0.0005087227        0.1654840781     0.0022   2026-09-08 10:27:26
   249    252    0.0123912423    0.0172457214     2744.1396002880    0.0012956169        0.1686550565     0.0028   2026-09-08 10:27:26
   250    253    0.0128329231    0.0234606883     2744.1363932237    0.0032070643        0.1978591361     0.0021   2026-09-08 10:27:26
   251    254    0.0159156450    0.0353025149     2744.1291527634    0.0072404603        0.2286885114     0.0023   2026-09-08 10:27:26
   252    255    0.0359994530    0.0744331671     2744.1159011091    0.0132516543        0.2354315834     0.0022   2026-09-08 10:27:26
   253    256    0.0935159199    0.1321689355     2744.1002819047    0.0156192044        0.1974130575     0.0021   2026-09-08 10:27:26
   254    257    0.0974675170    0.1219128303     2744.0915791334    0.0087027713        0.1173190890     0.0021   2026-09-08 10:27:26
   255    258    0.0343287068    0.0429108463     2744.0898378879    0.0017412455        0.0740602679     0.0024   2026-09-08 10:27:26
   256    259    0.0033700075    0.0075079990     2744.0897316309    0.0001062570        0.0735774448     0.0021   2026-09-08 10:27:26
   257    260    0.0012107703    0.0018728413     2744.0897295054    0.0000021255        0.0729844329     0.0021   2026-09-08 10:27:26
   258    261    0.0002336527    0.0003187238     2744.0897291461    0.0000003593        0.0729541223     0.0021   2026-09-08 10:27:26
   259    262    0.0010546796    0.0014310589     2744.0897266603    0.0000024858        0.0731437458     0.0021   2026-09-08 10:27:26
   260    263    0.0012703159    0.0017203564     2744.0897217055    0.0000049548        0.0736804538     0.0021   2026-09-08 10:27:26
   261    264    0.0022910050    0.0030948387     2744.0897072095    0.0000144961        0.0749545973     0.0022   2026-09-08 10:27:26
   262    265    0.0034659454    0.0046657187     2744.0896710529    0.0000361566        0.0770632849     0.0024   2026-09-08 10:27:26
   263    266    0.0054354291    0.0072949912     2744.0895764966    0.0000945563        0.0802188875     0.0020   2026-09-08 10:27:26
   264    267    0.0078139812    0.0105384626     2744.0893412613    0.0002352353        0.0837109671     0.0021   2026-09-08 10:27:26
   265    268    0.0095649836    0.0136384048     2744.0887908038    0.0005504575        0.0845232026     0.0021   2026-09-08 10:27:26
   266    269    0.0065847001    0.0151287837     2744.0877060829    0.0010847209        0.0825320416     0.0020   2026-09-08 10:27:26
   267    270    0.0088608206    0.0243826998     2744.0862221762    0.0014839067        0.0744935884     0.0022   2026-09-08 10:27:26
   268    271    0.0231343652    0.0369913425     2744.0851775381    0.0010446380        0.0494514734     0.0023   2026-09-08 10:27:26
   269    272    0.0174287228    0.0240280798     2744.0848959650    0.0002815732        0.0187786100     0.0022   2026-09-08 10:27:26
   270    273    0.0039141227    0.0054105007     2744.0848719954    0.0000239696        0.0183382472     0.0020   2026-09-08 10:27:26
   271    274    0.0002604348    0.0005988836     2744.0848713979    0.0000005975        0.0188836419     0.0020   2026-09-08 10:27:26
   272    275    0.0000521075    0.0000936195     2744.0848713784    0.0000000195        0.0189019643     0.0020   2026-09-08 10:27:26
   273    276    0.0000900650    0.0001571078     2744.0848713283    0.0000000501        0.0189300272     0.0020   2026-09-08 10:27:26
   274    277    0.0001398742    0.0002430627     2744.0848712025    0.0000001258        0.0189718910     0.0022   2026-09-08 10:27:26
   275    278    0.0002299917    0.0003982493     2744.0848708683    0.0000003343        0.0190346572     0.0021   2026-09-08 10:27:26
   276    279    0.0003686725    0.0006352101     2744.0848700005    0.0000008678        0.0191193246     0.0020   2026-09-08 10:27:26
   277    280    0.0005928486    0.0010149699     2744.0848677370    0.0000022635        0.0192145605     0.0020   2026-09-08 10:27:26
   278    281    0.0009354829    0.0015926278     2744.0848619088    0.0000058282        0.0192593050     0.0020   2026-09-08 10:27:26
   279    282    0.0014171916    0.0024252551     2744.0848472566    0.0000146522        0.0190534553     0.0020   2026-09-08 10:27:26
   280    283    0.0019108158    0.0034685389     2744.0848127158    0.0000345408        0.0180667601     0.0020   2026-09-08 10:27:26
   281    284    0.0020782938    0.0045752692     2744.0847429809    0.0000697349        0.0201183450     0.0021   2026-09-08 10:27:26
   282    285    0.0033789331    0.0062940023     2744.0846429700    0.0001000110        0.0205654124     0.0021   2026-09-08 10:27:26
   283    286    0.0032540609    0.0081468325     2744.0845667717    0.0000761983        0.0152600788     0.0020   2026-09-08 10:27:26
   284    287    0.0031165310    0.0056656033     2744.0845439816    0.0000227900        0.0095161247     0.0021   2026-09-08 10:27:26
   285    288    0.0009287433    0.0016152717     2744.0845417967    0.0000021849        0.0077284177     0.0020   2026-09-08 10:27:26
   286    289    0.0001186887    0.0002248731     2744.0845417324    0.0000000643        0.0076187616     0.0020   2026-09-08 10:27:26
   287    290    0.0000144891    0.0000307609     2744.0845417277    0.0000000047        0.0076303667     0.0020   2026-09-08 10:27:26
   288    291    0.0000381301    0.0000834360     2744.0845417083    0.0000000194        0.0076653380     0.0021   2026-09-08 10:27:26
   289    292    0.0000500030    0.0001106901     2744.0845416658    0.0000000425        0.0077111592     0.0020   2026-09-08 10:27:26
   290    293    0.0000849624    0.0001911857     2744.0845415463    0.0000001195        0.0077877461     0.0020   2026-09-08 10:27:26
   291    294    0.0001269497    0.0002942793     2744.0845412428    0.0000003035        0.0078989426     0.0020   2026-09-08 10:27:26
   292    295    0.0001893819    0.0004648267     2744.0845404459    0.0000007969        0.0080562126     0.0020   2026-09-08 10:27:26
   293    296    0.0002799967    0.0007059082     2744.0845384099    0.0000020360        0.0082431869     0.0020   2026-09-08 10:27:26
   294    297    0.0004320470    0.0010441023     2744.0845333454    0.0000050645        0.0083688574     0.0022   2026-09-08 10:27:26
   295    298    0.0007097773    0.0015355737     2744.0845217581    0.0000115872        0.0081336981     0.0023   2026-09-08 10:27:26
   296    299    0.0009946206    0.0025219294     2744.0844999082    0.0000218499        0.0069149122     0.0022   2026-09-08 10:27:26
   297    300    0.0019844225    0.0040906956     2744.0844726149    0.0000272933        0.0043499035     0.0023   2026-09-08 10:27:26
   298    301    0.0021884494    0.0041427143     2744.0844559884    0.0000166265        0.0035794022     0.0022   2026-09-08 10:27:26
   299    302    0.0008639993    0.0018755543     2744.0844522684    0.0000037200        0.0031753697     0.0022   2026-09-08 10:27:26

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.524943e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -4.4576**   1.7770   0.0121   
TC/100 EUR                        -0.8314     0.8983   0.3547   
Babiogorski                        0.1991     0.7824   0.7992   
Bialowieski                       -0.2405     0.6482   0.7106   
Biebrzanski                        0.2104     0.7098   0.7669   
Bieszczadzki                       0.3700     0.4679   0.4291   
BoryTucholskie                     0.1354     0.4197   0.7470   
Drawienski                        -0.5616     0.5933   0.3439   
Gorczanski                         0.1985     0.8591   0.8172   
GorStolowych                       1.5541***  0.4542   0.0006   
Kampinoski                        -0.6957*    0.3915   0.0756   
Karkonoski                        -1.1584***  0.3869   0.0028   
Magurski                           0.4403     0.4930   0.3718   
Narwianski                         0.1307     0.7131   0.8546   
Ojcowski                           0.6243     0.5249   0.2343   
Pieninski                         -1.6126**   0.7763   0.0378   
Poleski                            0.1961     0.4575   0.6681   
Roztoczanski                       0.0459     0.4064   0.9102   
Slowinski                         -0.4485     0.3823   0.2408   
Swietokrzyski                      0.3217     0.4300   0.4544   
UjscieWarty                       -0.7668*    0.4396   0.0811   
Wielkopolski                       0.7079     0.4407   0.1082   
Wigierski                          0.3004     0.4760   0.5279   
Wolinski                           1.3818***  0.4415   0.0017   
Household income (10k PLN)         0.2943***  0.1019   0.0039   
Male                               0.1165     0.0719   0.1052   
Higher education                   0.0152     0.0803   0.8494   
City                               0.1727**   0.0783   0.0274   
Winter                             0.8177***  0.0837   0.0000   
Hiking                             2.0910***  0.0792   0.0000   
Skiing                             1.3982***  0.2669   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2803     0.0951            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.2028     1.2997   0.3547   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2744.0845
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1763
AIC/n:                             0.9483
BIC/n:                             0.9848
n (observations):               5855
r (respondents):                5855
k (parameters):                   32
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.7225
median                           0.0000          1.7321
std                              0.7834          0.7394
min                              0.0000          0.0246
max                             20.0000          3.5357
quantile 0.025                   0.0000          0.4668
quantile 0.975                   2.0000          3.0518
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:27
Estimation took 1.2658 seconds (0 hours 0 minutes 1.2658 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.12 -0.6 0.37 -0.15 0.0091 0.03 -0.053 -0.057 0.14 0.12 0.03 -0.16 0.052 0.058 0.27 -0.38 0.009 0.019 -0.052 0.035 -0.052 0.098 -0.0019 0.082 0.18 0.0095 0.0048 0.019 0.18 0.43 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3915.7008532260             NaN     3769.9309841759     0.0004   2026-09-08 10:27:29
     1      4    0.0369197611    0.1355334728     3233.8450297457  681.8558234803      882.7973828749     0.0099   2026-09-08 10:27:29
     2      5    0.0069259681    0.0198365832     3199.1035849761   34.7414447696      445.8055586177     0.0026   2026-09-08 10:27:29
     3      6    0.0066038938    0.0182622972     3184.7114717754   14.3921132007      386.0425393673     0.0020   2026-09-08 10:27:29
     4      7    0.0095773421    0.0213962213     3171.2995795043   13.4118922712      401.5380468478     0.0022   2026-09-08 10:27:29
     5      8    0.0308744541    0.0655058012     3141.3549326306   29.9446468736      417.6057808415     0.0021   2026-09-08 10:27:29
     6      9    0.0219061093    0.0428581767     3126.0749160002   15.2800166305      342.0273790662     0.0024   2026-09-08 10:27:29
     7     10    0.0167702868    0.0280863537     3118.2626604190    7.8122555812      341.6722648602     0.0022   2026-09-08 10:27:29
     8     11    0.0118543444    0.0158261023     3114.4957943722    3.7668660468      355.8329784165     0.0024   2026-09-08 10:27:29
     9     12    0.0313430625    0.0386014699     3105.6271495145    8.8686448577      374.2926303704     0.0022   2026-09-08 10:27:29
    10     13    0.0765786156    0.0917212457     3085.4918867670   20.1352627474      475.1677544652     0.0020   2026-09-08 10:27:29
    11     14    0.1842415444    0.2184957475     3040.1202370661   45.3716497010      679.4298147884     0.0020   2026-09-08 10:27:29
    12     15    0.3664961476    0.4330796176     2957.8213673167   82.2988697494      793.0140984197     0.0021   2026-09-08 10:27:29
    13     16    0.5169304739    0.6105643912     2861.9861272232   95.8352400935      692.7472939749     0.0020   2026-09-08 10:27:29
    14     17    0.3287963803    0.3895209781     2816.0320930828   45.9540341404      430.0735734210     0.0020   2026-09-08 10:27:29
    15     18    0.0301615113    0.0410298514     2803.3196678848   12.7124251980      220.4224456838     0.0021   2026-09-08 10:27:29
    16     19    0.0793470779    0.0952339125     2797.9791641665    5.3405037182      109.3751444428     0.0020   2026-09-08 10:27:29
    17     20    0.0566453560    0.0674324884     2796.6118211461    1.3673430205      127.5339739690     0.0021   2026-09-08 10:27:29
    18     21    0.0417219377    0.0501891667     2795.1798882731    1.4319328730      122.9675347905     0.0020   2026-09-08 10:27:29
    19     22    0.0448769286    0.0571296323     2792.0598547776    3.1200334955      103.0298197020     0.0023   2026-09-08 10:27:29
    20     23    0.0121305043    0.0359993100     2787.3048354248    4.7550193528       62.1367802466     0.0020   2026-09-08 10:27:29
    21     24    0.0674887839    0.0868748974     2783.1024019417    4.2024334831       29.1146246438     0.0022   2026-09-08 10:27:29
    22     25    0.0805812092    0.0960287863     2781.6204928289    1.4819091128       27.5187396811     0.0019   2026-09-08 10:27:29
    23     26    0.0290476467    0.0345080644     2781.4424178885    0.1780749404       26.9190470526     0.0020   2026-09-08 10:27:29
    24     27    0.0054137934    0.0066997828     2781.4070690226    0.0353488659       26.5503611631     0.0022   2026-09-08 10:27:29
    25     28    0.0072139639    0.0094658212     2781.3227530168    0.0843160058       25.8624367029     0.0020   2026-09-08 10:27:29
    26     29    0.0098492900    0.0143659866     2781.1235441207    0.1992088961       24.7495352257     0.0025   2026-09-08 10:27:29
    27     30    0.0151906880    0.0273660525     2780.6049231636    0.5186209571       22.7173862815     0.0021   2026-09-08 10:27:29
    28     31    0.0274811008    0.0545746285     2779.3686691247    1.2362540390       37.5038607664     0.0020   2026-09-08 10:27:29
    29     32    0.0588942669    0.1102939476     2776.7120094318    2.6566596929       55.7968219330     0.0019   2026-09-08 10:27:29
    30     33    0.0987585582    0.1845899128     2772.3757682018    4.3362412300       64.2214827266     0.0020   2026-09-08 10:27:29
    31     34    0.0972726154    0.1918255741     2768.2435251218    4.1322430799       45.3542596880     0.0019   2026-09-08 10:27:29
    32     35    0.0426025294    0.0772820924     2766.6398240507    1.6037010711       21.1135808270     0.0019   2026-09-08 10:27:29
    33     36    0.0177593555    0.0331178481     2766.4229824157    0.2168416350       14.1572706823     0.0021   2026-09-08 10:27:29
    34     37    0.0068544781    0.0129332455     2766.4042093181    0.0187730976       13.2326782567     0.0021   2026-09-08 10:27:29
    35     38    0.0039367763    0.0075595396     2766.3878223786    0.0163869395       12.8899801935     0.0020   2026-09-08 10:27:29
    36     39    0.0084360822    0.0168588519     2766.3280562141    0.0597661645       12.0679784466     0.0020   2026-09-08 10:27:29
    37     40    0.0099696754    0.0220731024     2766.1931544146    0.1349017995       11.4734201609     0.0020   2026-09-08 10:27:29
    38     41    0.0132852997    0.0336494006     2765.8451298043    0.3480246104       11.4485853181     0.0020   2026-09-08 10:27:29
    39     42    0.0221088958    0.0506423406     2765.0829509657    0.7621788386       11.4074015325     0.0020   2026-09-08 10:27:29
    40     43    0.0387140360    0.0936619698     2763.7171635893    1.3657873763       12.2085778835     0.0021   2026-09-08 10:27:29
    41     44    0.0700862454    0.1470202793     2762.2073628451    1.5098007442       10.2604929523     0.0021   2026-09-08 10:27:29
    42     45    0.0681435503    0.1235758128     2761.4485217234    0.7588411217       12.5468483654     0.0019   2026-09-08 10:27:29
    43     46    0.0221271213    0.0433563208     2761.3054673747    0.1430543487       13.1713627115     0.0019   2026-09-08 10:27:29
    44     47    0.0041383362    0.0095251889     2761.2869891382    0.0184782366       13.1680069614     0.0020   2026-09-08 10:27:29
    45     48    0.0028272888    0.0063213514     2761.2690015146    0.0179876236       13.0037997935     0.0019   2026-09-08 10:27:29
    46     49    0.0053277997    0.0118344493     2761.2119176767    0.0570838379       12.5846214727     0.0020   2026-09-08 10:27:29
    47     50    0.0068161042    0.0158800407     2761.0774784694    0.1344392073       11.8512965903     0.0019   2026-09-08 10:27:29
    48     51    0.0094704306    0.0267894461     2760.7357083477    0.3417701217       10.7182619358     0.0020   2026-09-08 10:27:29
    49     52    0.0248876748    0.0566823596     2759.9780691156    0.7576392321       10.3048412824     0.0019   2026-09-08 10:27:29
    50     53    0.0639379158    0.1245590888     2758.6019468863    1.3761222293       13.9441614834     0.0019   2026-09-08 10:27:29
    51     54    0.0988780742    0.1896291506     2757.0143736399    1.5875732464       14.4764156069     0.0020   2026-09-08 10:27:29
    52     55    0.0702824857    0.1426143200     2756.1623199130    0.8520537269       15.2594910184     0.0020   2026-09-08 10:27:29
    53     56    0.0164538087    0.0369740740     2755.9959054780    0.1664144350       17.7107693833     0.0022   2026-09-08 10:27:29
    54     57    0.0045833708    0.0113060273     2755.9766284283    0.0192770497       17.6950401044     0.0020   2026-09-08 10:27:29
    55     58    0.0032917216    0.0071465677     2755.9629464543    0.0136819740       17.5084211801     0.0020   2026-09-08 10:27:30
    56     59    0.0062073945    0.0142643103     2755.9171309157    0.0458155387       16.9915493651     0.0023   2026-09-08 10:27:30
    57     60    0.0071323456    0.0175106006     2755.8105727910    0.1065581247       16.0686608030     0.0020   2026-09-08 10:27:30
    58     61    0.0091519408    0.0241860481     2755.5308279864    0.2797448046       15.2988610169     0.0020   2026-09-08 10:27:30
    59     62    0.0188490036    0.0457242816     2754.8766798487    0.6541481377       14.6872391420     0.0020   2026-09-08 10:27:30
    60     63    0.0635958359    0.1233817251     2753.5290077574    1.3476720913       13.0127270618     0.0021   2026-09-08 10:27:30
    61     64    0.1397121757    0.2508518818     2751.5573123115    1.9716954459       10.4319376092     0.0020   2026-09-08 10:27:30
    62     65    0.1588104169    0.2816030953     2749.9892212818    1.5680910297       13.1144861926     0.0020   2026-09-08 10:27:30
    63     66    0.0690107044    0.1278910220     2749.4728756483    0.5163456335       13.0075038925     0.0020   2026-09-08 10:27:30
    64     67    0.0071953761    0.0187835089     2749.4160778091    0.0567978392       11.4724690681     0.0021   2026-09-08 10:27:30
    65     68    0.0043642274    0.0084506931     2749.4108074980    0.0052703111       11.0026194337     0.0021   2026-09-08 10:27:30
    66     69    0.0047698656    0.0090173139     2749.4030968627    0.0077106352       10.5246217610     0.0021   2026-09-08 10:27:30
    67     70    0.0079302467    0.0151379610     2749.3814817027    0.0216151600        9.6310486424     0.0026   2026-09-08 10:27:30
    68     71    0.0105686789    0.0209126915     2749.3282607496    0.0532209531        8.5625331113     0.0027   2026-09-08 10:27:30
    69     72    0.0136241629    0.0271996879     2749.1965449093    0.1317158403        9.0451599376     0.0020   2026-09-08 10:27:30
    70     73    0.0213063905    0.0325942991     2748.9085698774    0.2879750319        9.2701513419     0.0019   2026-09-08 10:27:30
    71     74    0.0291482158    0.0652528138     2748.4127094109    0.4958604665        8.5280990906     0.0020   2026-09-08 10:27:30
    72     75    0.0604363211    0.1226159086     2747.8944972828    0.5182121281        6.7911933450     0.0021   2026-09-08 10:27:30
    73     76    0.0580291374    0.1085607196     2747.6541050970    0.2403921858        5.2762236091     0.0021   2026-09-08 10:27:30
    74     77    0.0176444437    0.0339645183     2747.6157929512    0.0383121458        3.5144241901     0.0021   2026-09-08 10:27:30
    75     78    0.0029628437    0.0044543926     2747.6132142655    0.0025786857        3.5622359485     0.0025   2026-09-08 10:27:30
    76     79    0.0008870528    0.0017682129     2747.6121286298    0.0010856357        3.6164051171     0.0022   2026-09-08 10:27:30
    77     80    0.0023527040    0.0046890016     2747.6076067914    0.0045218384        3.7710587971     0.0021   2026-09-08 10:27:30
    78     81    0.0032388466    0.0060165000     2747.5976352466    0.0099715447        3.9706864094     0.0021   2026-09-08 10:27:30
    79     82    0.0057131334    0.0098928644     2747.5701414996    0.0274937470        4.2796520200     0.0023   2026-09-08 10:27:30
    80     83    0.0090097704    0.0163534323     2747.5026026151    0.0675388845        4.6632672297     0.0022   2026-09-08 10:27:30
    81     84    0.0138592251    0.0348713508     2747.3408293658    0.1617732492        5.0053588321     0.0029   2026-09-08 10:27:30
    82     85    0.0397758263    0.0782780871     2747.0104830069    0.3303463589        8.3824061862     0.0032   2026-09-08 10:27:30
    83     86    0.0790827356    0.1399314738     2746.5199791114    0.4905038955       10.5196779541     0.0030   2026-09-08 10:27:30
    84     87    0.0842253511    0.1434714772     2746.1249759036    0.3950032079        8.5670668046     0.0026   2026-09-08 10:27:30
    85     88    0.0308317569    0.0565871862     2745.9975852673    0.1273906363        8.2510496502     0.0029   2026-09-08 10:27:30
    86     89    0.0070899054    0.0140454923     2745.9829064362    0.0146788311        7.9855235311     0.0024   2026-09-08 10:27:30
    87     90    0.0030124373    0.0058957529     2745.9805163044    0.0023901318        7.8178130761     0.0024   2026-09-08 10:27:30
    88     91    0.0047059964    0.0090153598     2745.9748832666    0.0056330378        7.5252879577     0.0023   2026-09-08 10:27:30
    89     92    0.0065141852    0.0125971139     2745.9608872463    0.0139960204        7.0355510479     0.0025   2026-09-08 10:27:30
    90     93    0.0083561752    0.0169147310     2745.9245806255    0.0363066208        6.1593345681     0.0026   2026-09-08 10:27:30
    91     94    0.0096013260    0.0191084730     2745.8357215596    0.0888590659        4.6273670425     0.0026   2026-09-08 10:27:30
    92     95    0.0160789480    0.0311435306     2745.6360716685    0.1996498911        4.1786814581     0.0023   2026-09-08 10:27:30
    93     96    0.0383342571    0.0902405478     2745.2766378045    0.3594338639        4.2085137049     0.0024   2026-09-08 10:27:30
    94     97    0.0826871491    0.1687445445     2744.8632832155    0.4133545890        4.4333948181     0.0024   2026-09-08 10:27:30
    95     98    0.0769406459    0.1487995606     2744.6413045994    0.2219786162        3.6632332787     0.0029   2026-09-08 10:27:30
    96     99    0.0231201603    0.0442327414     2744.5984182916    0.0428863078        2.6206876661     0.0033   2026-09-08 10:27:30
    97    100    0.0033034036    0.0064361819     2744.5954054268    0.0030128648        2.6019103355     0.0036   2026-09-08 10:27:30
    98    101    0.0012068794    0.0027648786     2744.5949574668    0.0004479600        2.5966701060     0.0024   2026-09-08 10:27:30
    99    102    0.0024516411    0.0055394315     2744.5936057913    0.0013516756        2.6398165014     0.0019   2026-09-08 10:27:30
   100    103    0.0033313143    0.0076127557     2744.5904465656    0.0031592257        2.6944219247     0.0019   2026-09-08 10:27:30
   101    104    0.0049511515    0.0116894781     2744.5819479956    0.0084985700        2.7703320799     0.0018   2026-09-08 10:27:30
   102    105    0.0059537186    0.0156495392     2744.5608752487    0.0210727469        2.8586982535     0.0018   2026-09-08 10:27:30
   103    106    0.0075349957    0.0201382603     2744.5106112404    0.0502640083        2.9289357645     0.0018   2026-09-08 10:27:30
   104    107    0.0148229752    0.0349679517     2744.4083156998    0.1022955405        2.8762191365     0.0018   2026-09-08 10:27:30
   105    108    0.0313646708    0.0763636122     2744.2594838559    0.1488318439        4.2511069961     0.0046   2026-09-08 10:27:30
   106    109    0.0437802614    0.1008569480     2744.1439019064    0.1155819495        4.6360136764     0.0036   2026-09-08 10:27:30
   107    110    0.0269353177    0.0588257876     2744.1061551610    0.0377467454        5.2682066216     0.0020   2026-09-08 10:27:30
   108    111    0.0045991631    0.0123995466     2744.1014243921    0.0047307689        5.0792418743     0.0049   2026-09-08 10:27:30
   109    112    0.0011028088    0.0026421239     2744.1005752947    0.0008490974        4.9665704683     0.0020   2026-09-08 10:27:30
   110    113    0.0017631087    0.0044055641     2744.0984808540    0.0020944407        4.7711570586     0.0020   2026-09-08 10:27:30
   111    114    0.0025125015    0.0060196807     2744.0933842661    0.0050965879        4.4722136853     0.0019   2026-09-08 10:27:30
   112    115    0.0042113733    0.0083294661     2744.0798627717    0.0135214944        3.9741241168     0.0034   2026-09-08 10:27:30
   113    116    0.0066967861    0.0111378409     2744.0458383918    0.0340243799        3.1891502586     0.0030   2026-09-08 10:27:30
   114    117    0.0102206217    0.0242749104     2743.9631769116    0.0826614802        2.1659341578     0.0029   2026-09-08 10:27:30
   115    118    0.0271695279    0.0683548245     2743.7859756449    0.1772012667        3.1110011661     0.0026   2026-09-08 10:27:30
   116    119    0.0618327093    0.1486237963     2743.4966031138    0.2893725311        5.0658175459     0.0027   2026-09-08 10:27:30
   117    120    0.0800328095    0.1917692472     2743.2187954623    0.2778076515        5.0748447178     0.0029   2026-09-08 10:27:30
   118    121    0.0439095306    0.1058077866     2743.1036548276    0.1151406347        3.7023016095     0.0029   2026-09-08 10:27:30
   119    122    0.0081825922    0.0139079723     2743.0882001794    0.0154546482        3.3806017933     0.0029   2026-09-08 10:27:30
   120    123    0.0031688592    0.0078217336     2743.0872371021    0.0009630772        3.2596490055     0.0028   2026-09-08 10:27:30
   121    124    0.0016261959    0.0039363601     2743.0867045145    0.0005325876        3.2062241486     0.0026   2026-09-08 10:27:30
   122    125    0.0039530328    0.0095834372     2743.0846351357    0.0020693788        3.1580588177     0.0028   2026-09-08 10:27:30
   123    126    0.0049719955    0.0121539854     2743.0800522034    0.0045829323        3.1966332630     0.0027   2026-09-08 10:27:30
   124    127    0.0070111298    0.0171617701     2743.0680744790    0.0119777244        3.1574856839     0.0030   2026-09-08 10:27:30
   125    128    0.0078135197    0.0170376214     2743.0417048616    0.0263696174        2.8576738370     0.0026   2026-09-08 10:27:30
   126    129    0.0079275129    0.0172304064     2742.9933946814    0.0483101802        1.9874564062     0.0025   2026-09-08 10:27:30
   127    130    0.0205923818    0.0497041514     2742.9372197661    0.0561749153        1.5979572983     0.0025   2026-09-08 10:27:30
   128    131    0.0261162303    0.0629957925     2742.9062715101    0.0309482560        1.1213702615     0.0027   2026-09-08 10:27:30
   129    132    0.0114832015    0.0277269079     2742.9002750513    0.0059964588        1.2040770679     0.0026   2026-09-08 10:27:30
   130    133    0.0015272962    0.0033281448     2742.8998505453    0.0004245060        1.2073305719     0.0028   2026-09-08 10:27:30
   131    134    0.0002593759    0.0005380702     2742.8997557901    0.0000947552        1.1994968308     0.0027   2026-09-08 10:27:30
   132    135    0.0006500145    0.0013180102     2742.8994036615    0.0003521286        1.1778801194     0.0026   2026-09-08 10:27:30
   133    136    0.0008977770    0.0017302590     2742.8986133251    0.0007903364        1.1460607499     0.0026   2026-09-08 10:27:30
   134    137    0.0015364570    0.0028549734     2742.8964268660    0.0021864591        1.2230854445     0.0026   2026-09-08 10:27:30
   135    138    0.0023721905    0.0048081131     2742.8909091450    0.0055177210        1.3601839979     0.0028   2026-09-08 10:27:30
   136    139    0.0039565174    0.0105655263     2742.8768543732    0.0140547718        1.5534706931     0.0025   2026-09-08 10:27:30
   137    140    0.0128145843    0.0261967080     2742.8434189269    0.0334354463        1.7674384769     0.0026   2026-09-08 10:27:30
   138    141    0.0325719307    0.0606277530     2742.7737568148    0.0696621120        1.8459500843     0.0027   2026-09-08 10:27:30
   139    142    0.0593760841    0.1065292472     2742.6672679110    0.1064889039        2.3962876111     0.0025   2026-09-08 10:27:30
   140    143    0.0605763047    0.1070112141     2742.5767128802    0.0905550308        2.2951483875     0.0025   2026-09-08 10:27:30
   141    144    0.0207605299    0.0381946351     2742.5450110364    0.0317018439        2.1418277622     0.0026   2026-09-08 10:27:30
   142    145    0.0039188505    0.0102010533     2742.5409995584    0.0040114780        2.3334369786     0.0024   2026-09-08 10:27:30
   143    146    0.0028984287    0.0053815540     2742.5405189882    0.0004805703        2.3462145868     0.0021   2026-09-08 10:27:30
   144    147    0.0030494884    0.0055825930     2742.5397817546    0.0007372336        2.3382142407     0.0028   2026-09-08 10:27:30
   145    148    0.0049955713    0.0091354131     2742.5377049562    0.0020767984        2.3072211944     0.0028   2026-09-08 10:27:30
   146    149    0.0064321961    0.0118217058     2742.5326314269    0.0050735293        2.2257769065     0.0027   2026-09-08 10:27:30
   147    150    0.0065890791    0.0126320461     2742.5202997517    0.0123316752        2.0176682817     0.0027   2026-09-08 10:27:30
   148    151    0.0030011081    0.0091781374     2742.4945264923    0.0257732594        1.5582039295     0.0027   2026-09-08 10:27:30
   149    152    0.0178972504    0.0365056303     2742.4542508417    0.0402756506        0.7917053631     0.0028   2026-09-08 10:27:30
   150    153    0.0372387715    0.0699179526     2742.4188814765    0.0353693651        0.8781249728     0.0028   2026-09-08 10:27:30
   151    154    0.0281792913    0.0517199520     2742.4060204064    0.0128610702        0.8079604768     0.0027   2026-09-08 10:27:30
   152    155    0.0063210570    0.0116422640     2742.4044531773    0.0015672291        0.7329865755     0.0026   2026-09-08 10:27:30
   153    156    0.0003166952    0.0009526225     2742.4043654819    0.0000876954        0.7048309343     0.0027   2026-09-08 10:27:30
   154    157    0.0002933917    0.0006126011     2742.4043223238    0.0000431581        0.6936218910     0.0024   2026-09-08 10:27:30
   155    158    0.0008438450    0.0016976231     2742.4041373382    0.0001849856        0.6628395781     0.0023   2026-09-08 10:27:30
   156    159    0.0011251533    0.0021772968     2742.4037287952    0.0004085430        0.6477182179     0.0021   2026-09-08 10:27:30
   157    160    0.0018725474    0.0034583220     2742.4025937395    0.0011350558        0.6382672382     0.0022   2026-09-08 10:27:30
   158    161    0.0026965216    0.0048977695     2742.3997565099    0.0028372295        0.6982230309     0.0021   2026-09-08 10:27:30
   159    162    0.0036151131    0.0081872666     2742.3926534232    0.0071030867        0.9159710670     0.0021   2026-09-08 10:27:30
   160    163    0.0065496217    0.0181513718     2742.3765263389    0.0161270843        1.1866429088     0.0027   2026-09-08 10:27:30
   161    164    0.0156549172    0.0411740295     2742.3463960733    0.0301302656        1.3785997088     0.0027   2026-09-08 10:27:30
   162    165    0.0289655546    0.0656508727     2742.3095794933    0.0368165800        1.7106976916     0.0027   2026-09-08 10:27:30
   163    166    0.0252466672    0.0529152879     2742.2878531374    0.0217263559        2.3600974004     0.0026   2026-09-08 10:27:30
   164    167    0.0070805553    0.0147485207     2742.2830785106    0.0047746268        2.4391923253     0.0022   2026-09-08 10:27:30
   165    168    0.0015693862    0.0042305251     2742.2826569476    0.0004215630        2.3736387164     0.0022   2026-09-08 10:27:30
   166    169    0.0006527894    0.0017912215     2742.2825262032    0.0001307445        2.3420568429     0.0028   2026-09-08 10:27:30
   167    170    0.0015426773    0.0041698834     2742.2820440470    0.0004821561        2.2568629269     0.0022   2026-09-08 10:27:30
   168    171    0.0018289917    0.0050856740     2742.2809750967    0.0010689503        2.1224409565     0.0020   2026-09-08 10:27:30
   169    172    0.0022567793    0.0067184893     2742.2781397669    0.0028353297        1.8551958554     0.0022   2026-09-08 10:27:30
   170    173    0.0031143553    0.0059378496     2742.2716894943    0.0064502726        1.3788442697     0.0021   2026-09-08 10:27:30
   171    174    0.0050903476    0.0110706120     2742.2589511886    0.0127383056        0.6154909254     0.0024   2026-09-08 10:27:30
   172    175    0.0135257929    0.0324588525     2742.2418641070    0.0170870817        0.4601740440     0.0021   2026-09-08 10:27:30
   173    176    0.0174872171    0.0427579639     2742.2301125869    0.0117515201        0.5301576371     0.0022   2026-09-08 10:27:30
   174    177    0.0082638912    0.0212082836     2742.2270359103    0.0030766766        0.3914641747     0.0022   2026-09-08 10:27:30
   175    178    0.0010473561    0.0025625009     2742.2267734837    0.0002624266        0.3622966749     0.0019   2026-09-08 10:27:30
   176    179    0.0002702345    0.0006607928     2742.2267604017    0.0000130820        0.3571805996     0.0022   2026-09-08 10:27:30
   177    180    0.0001856585    0.0004504962     2742.2267492627    0.0000111390        0.3541503123     0.0021   2026-09-08 10:27:30
   178    181    0.0004297517    0.0010581167     2742.2267076000    0.0000416626        0.3467248686     0.0022   2026-09-08 10:27:30
   179    182    0.0005707897    0.0014520284     2742.2266113038    0.0000962962        0.3413180330     0.0022   2026-09-08 10:27:30
   180    183    0.0008600227    0.0023457933     2742.2263477108    0.0002635930        0.3350556778     0.0020   2026-09-08 10:27:30
   181    184    0.0010648301    0.0034705584     2742.2256780117    0.0006696991        0.3243176900     0.0021   2026-09-08 10:27:30
   182    185    0.0020133426    0.0054383059     2742.2239647633    0.0017132484        0.4200624567     0.0022   2026-09-08 10:27:30
   183    186    0.0042988939    0.0099885274     2742.2198268270    0.0041379363        0.7310190611     0.0020   2026-09-08 10:27:30
   184    187    0.0095803229    0.0220059669     2742.2109119132    0.0089149138        1.0872925612     0.0019   2026-09-08 10:27:30
   185    188    0.0191925045    0.0432387976     2742.1962784503    0.0146334629        1.2493368365     0.0026   2026-09-08 10:27:30
   186    189    0.0226806799    0.0541676150     2742.1821799796    0.0140984707        0.8962435166     0.0021   2026-09-08 10:27:30
   187    190    0.0136668805    0.0303317574     2742.1763640956    0.0058158840        0.3032587390     0.0021   2026-09-08 10:27:30
   188    191    0.0021800180    0.0066040602     2742.1755546059    0.0008094897        0.2541185431     0.0022   2026-09-08 10:27:30
   189    192    0.0011503520    0.0026016829     2742.1755188036    0.0000358023        0.2446417979     0.0023   2026-09-08 10:27:30
   190    193    0.0002149617    0.0004942272     2742.1755158308    0.0000029727        0.2426053872     0.0020   2026-09-08 10:27:30
   191    194    0.0004352078    0.0010139351     2742.1755063759    0.0000094550        0.2383423712     0.0019   2026-09-08 10:27:30
   192    195    0.0006009728    0.0014242251     2742.1754844016    0.0000219742        0.2322073062     0.0026   2026-09-08 10:27:30
   193    196    0.0010252591    0.0023522404     2742.1754243085    0.0000600931        0.2215557574     0.0021   2026-09-08 10:27:30
   194    197    0.0016492159    0.0035539102     2742.1752708994    0.0001534091        0.2039224334     0.0020   2026-09-08 10:27:30
   195    198    0.0027074591    0.0053094563     2742.1748745803    0.0003963191        0.1855710524     0.0023   2026-09-08 10:27:30
   196    199    0.0042773347    0.0074131859     2742.1738920723    0.0009825080        0.2031924970     0.0021   2026-09-08 10:27:30
   197    200    0.0061593795    0.0102263905     2742.1716364857    0.0022555866        0.2205468743     0.0021   2026-09-08 10:27:30
   198    201    0.0067571056    0.0178777603     2742.1673684318    0.0042680539        0.2204245771     0.0025   2026-09-08 10:27:30
   199    202    0.0167897425    0.0327714806     2742.1619949169    0.0053735149        0.1775462955     0.0022   2026-09-08 10:27:30
   200    203    0.0180566781    0.0348338643     2742.1586845257    0.0033103912        0.1644943610     0.0023   2026-09-08 10:27:30
   201    204    0.0067384561    0.0153131080     2742.1579313443    0.0007531814        0.1713546666     0.0020   2026-09-08 10:27:30
   202    205    0.0016882685    0.0027701088     2742.1578773078    0.0000540364        0.1743524030     0.0021   2026-09-08 10:27:30
   203    206    0.0002830223    0.0006011939     2742.1578751926    0.0000021152        0.1734965749     0.0023   2026-09-08 10:27:30
   204    207    0.0001646093    0.0003327187     2742.1578735445    0.0000016481        0.1728545171     0.0022   2026-09-08 10:27:30
   205    208    0.0004100213    0.0008319837     2742.1578669861    0.0000065585        0.1710913375     0.0020   2026-09-08 10:27:30
   206    209    0.0005502795    0.0011315234     2742.1578520948    0.0000148913        0.1684363674     0.0022   2026-09-08 10:27:30
   207    210    0.0008822844    0.0018613998     2742.1578110822    0.0000410126        0.1634120087     0.0020   2026-09-08 10:27:30
   208    211    0.0012227264    0.0027285825     2742.1577074660    0.0001036161        0.1543610427     0.0022   2026-09-08 10:27:30
   209    212    0.0015039945    0.0038953178     2742.1574440967    0.0002633693        0.1371169291     0.0023   2026-09-08 10:27:30
   210    213    0.0018204513    0.0051537911     2742.1568201227    0.0006239741        0.1049045391     0.0022   2026-09-08 10:27:30
   211    214    0.0041572486    0.0079769430     2742.1555347551    0.0012853676        0.1042307128     0.0023   2026-09-08 10:27:30
   212    215    0.0072564202    0.0159927930     2742.1536178928    0.0019168623        0.0994620294     0.0020   2026-09-08 10:27:30
   213    216    0.0115999513    0.0219937727     2742.1520559852    0.0015619076        0.0845371748     0.0022   2026-09-08 10:27:30
   214    217    0.0070894376    0.0135095033     2742.1515448529    0.0005111323        0.0896362103     0.0020   2026-09-08 10:27:30
   215    218    0.0010547164    0.0030048052     2742.1514903458    0.0000545071        0.0878484912     0.0021   2026-09-08 10:27:30
   216    219    0.0002926761    0.0005757850     2742.1514883891    0.0000019567        0.0871187084     0.0026   2026-09-08 10:27:30
   217    220    0.0000622693    0.0001308651     2742.1514880725    0.0000003166        0.0869977401     0.0021   2026-09-08 10:27:30
   218    221    0.0002089590    0.0004379449     2742.1514864488    0.0000016236        0.0865505850     0.0028   2026-09-08 10:27:30
   219    222    0.0002585456    0.0005508619     2742.1514830460    0.0000034028        0.0858834841     0.0021   2026-09-08 10:27:30
   220    223    0.0004335571    0.0009529841     2742.1514733147    0.0000097313        0.0844981476     0.0021   2026-09-08 10:27:30
   221    224    0.0006044314    0.0014155119     2742.1514488618    0.0000244529        0.0819329590     0.0022   2026-09-08 10:27:30
   222    225    0.0009005422    0.0021426747     2742.1513852239    0.0000636379        0.0768285713     0.0024   2026-09-08 10:27:30
   223    226    0.0012460652    0.0030804320     2742.1512274197    0.0001578042        0.0667138749     0.0025   2026-09-08 10:27:30
   224    227    0.0023029271    0.0046936434     2742.1508623923    0.0003650275        0.0589618072     0.0023   2026-09-08 10:27:30
   225    228    0.0043208571    0.0087744598     2742.1501612232    0.0007011690        0.0569492743     0.0020   2026-09-08 10:27:30
   226    229    0.0079832574    0.0154130821     2742.1492503594    0.0009108638        0.0495441862     0.0021   2026-09-08 10:27:30
   227    230    0.0088014175    0.0158042650     2742.1486602233    0.0005901361        0.0587955023     0.0020   2026-09-08 10:27:30
   228    231    0.0034203641    0.0068451756     2742.1485172949    0.0001429284        0.0556761459     0.0022   2026-09-08 10:27:30
   229    232    0.0006543307    0.0014002827     2742.1485063966    0.0000108983        0.0512908864     0.0022   2026-09-08 10:27:30
   230    233    0.0001529847    0.0003299480     2742.1485060506    0.0000003461        0.0504805642     0.0024   2026-09-08 10:27:30
   231    234    0.0000543174    0.0001070813     2742.1485059071    0.0000001434        0.0502628328     0.0020   2026-09-08 10:27:30
   232    235    0.0001791410    0.0003534501     2742.1485051654    0.0000007417        0.0495309255     0.0021   2026-09-08 10:27:30
   233    236    0.0002257248    0.0004499663     2742.1485035906    0.0000015748        0.0485494599     0.0021   2026-09-08 10:27:30
   234    237    0.0003806536    0.0007735574     2742.1484991085    0.0000044821        0.0467429986     0.0020   2026-09-08 10:27:30
   235    238    0.0005443804    0.0011508546     2742.1484878022    0.0000113064        0.0437834947     0.0022   2026-09-08 10:27:30
   236    239    0.0007506499    0.0017387223     2742.1484582558    0.0000295463        0.0398367178     0.0020   2026-09-08 10:27:30
   237    240    0.0012357708    0.0024872895     2742.1483840363    0.0000742195        0.0378397561     0.0030   2026-09-08 10:27:30
   238    241    0.0020144212    0.0037215542     2742.1482068719    0.0001771644        0.0347991204     0.0021   2026-09-08 10:27:30
   239    242    0.0028435539    0.0070470380     2742.1478404282    0.0003664437        0.0367160415     0.0022   2026-09-08 10:27:30
   240    243    0.0062937576    0.0138091182     2742.1472866627    0.0005537654        0.0344467007     0.0024   2026-09-08 10:27:30
   241    244    0.0091383311    0.0172243705     2742.1468260375    0.0004606252        0.0277222523     0.0021   2026-09-08 10:27:30
   242    245    0.0051992104    0.0095714630     2742.1466709887    0.0001550488        0.0217482953     0.0021   2026-09-08 10:27:30
   243    246    0.0010695440    0.0020757542     2742.1466539902    0.0000169986        0.0178648744     0.0023   2026-09-08 10:27:30
   244    247    0.0002095880    0.0005452517     2742.1466534361    0.0000005541        0.0170134887     0.0023   2026-09-08 10:27:30
   245    248    0.0000412890    0.0000810543     2742.1466534172    0.0000000189        0.0169575558     0.0022   2026-09-08 10:27:30
   246    249    0.0000528111    0.0001028502     2742.1466533797    0.0000000375        0.0168877794     0.0019   2026-09-08 10:27:30
   247    250    0.0000889793    0.0001740489     2742.1466532769    0.0000001028        0.0167594154     0.0022   2026-09-08 10:27:30
   248    251    0.0001388412    0.0002739344     2742.1466530127    0.0000002642        0.0165395943     0.0020   2026-09-08 10:27:30
   249    252    0.0002195318    0.0004397984     2742.1466523180    0.0000006947        0.0161540513     0.0020   2026-09-08 10:27:30
   250    253    0.0003353421    0.0006912145     2742.1466505145    0.0000018035        0.0154794376     0.0022   2026-09-08 10:27:30
   251    254    0.0004889549    0.0010679782     2742.1466458597    0.0000046548        0.0150533171     0.0022   2026-09-08 10:27:30
   252    255    0.0006443366    0.0015861392     2742.1466341519    0.0000117078        0.0151632959     0.0019   2026-09-08 10:27:30
   253    256    0.0009363102    0.0022294324     2742.1466064612    0.0000276907        0.0148238999     0.0020   2026-09-08 10:27:30
   254    257    0.0014222995    0.0031473864     2742.1465501630    0.0000562982        0.0132205534     0.0021   2026-09-08 10:27:30
   255    258    0.0021024466    0.0051343302     2742.1464682215    0.0000819415        0.0095727227     0.0020   2026-09-08 10:27:30
   256    259    0.0036726314    0.0067190039     2742.1464042298    0.0000639916        0.0066926400     0.0021   2026-09-08 10:27:30
   257    260    0.0023375904    0.0043026616     2742.1463844469    0.0000197829        0.0056709354     0.0023   2026-09-08 10:27:30
   258    261    0.0004558292    0.0011152452     2742.1463824796    0.0000019673        0.0047461449     0.0022   2026-09-08 10:27:30
   259    262    0.0000723372    0.0001805846     2742.1463824220    0.0000000576        0.0045618209     0.0023   2026-09-08 10:27:30
   260    263    0.0000127385    0.0000245302     2742.1463824202    0.0000000018        0.0045491204     0.0019   2026-09-08 10:27:30
   261    264    0.0000167377    0.0000316675     2742.1463824167    0.0000000035        0.0045332222     0.0022   2026-09-08 10:27:30
   262    265    0.0000284683    0.0000536674     2742.1463824070    0.0000000097        0.0045054118     0.0021   2026-09-08 10:27:30
   263    266    0.0000451442    0.0000847406     2742.1463823821    0.0000000249        0.0044595074     0.0020   2026-09-08 10:27:30
   264    267    0.0000732928    0.0001367392     2742.1463823165    0.0000000656        0.0043804409     0.0024   2026-09-08 10:27:30
   265    268    0.0001172416    0.0002170008     2742.1463821460    0.0000001705        0.0042421789     0.0022   2026-09-08 10:27:30
   266    269    0.0001859336    0.0003416469     2742.1463817038    0.0000004422        0.0042766034     0.0020   2026-09-08 10:27:30
   267    270    0.0002852576    0.0005268271     2742.1463805785    0.0000011253        0.0045705139     0.0021   2026-09-08 10:27:30
   268    271    0.0004025961    0.0007924914     2742.1463778365    0.0000027420        0.0048725912     0.0020   2026-09-08 10:27:30
   269    272    0.0004461134    0.0011866650     2742.1463718495    0.0000059870        0.0049097220     0.0020   2026-09-08 10:27:30
   270    273    0.0006737762    0.0018562169     2742.1463616997    0.0000101499        0.0040925165     0.0024   2026-09-08 10:27:30
   271    274    0.0012408331    0.0025558658     2742.1463513360    0.0000103637        0.0026364255     0.0022   2026-09-08 10:27:30

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','6.991445e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -1.6713**   0.6912   0.0156   
TC/100 EUR                        -1.1297     0.8754   0.1969   
Babiogorski                        0.3928     0.6903   0.5693   
Bialowieski                       -0.3871     0.5991   0.5182   
Biebrzanski                        0.2535     0.7053   0.7193   
Bieszczadzki                       0.2872     0.4421   0.5159   
BoryTucholskie                    -0.0578     0.3920   0.8827   
Drawienski                        -0.5275     0.5646   0.3501   
Gorczanski                         0.1089     0.8577   0.8989   
GorStolowych                       1.1226***  0.4085   0.0060   
Kampinoski                        -0.2771     0.2825   0.3267   
Karkonoski                        -1.1106***  0.3471   0.0014   
Magurski                           0.4002     0.4818   0.4062   
Narwianski                        -0.0002     0.7033   0.9998   
Ojcowski                           0.8619*    0.4453   0.0529   
Pieninski                         -1.6120**   0.7620   0.0344   
Poleski                            0.0160     0.4260   0.9700   
Roztoczanski                      -0.1528     0.3772   0.6854   
Slowinski                         -0.6082     0.3718   0.1019   
Swietokrzyski                      0.3806     0.3965   0.3371   
UjscieWarty                       -0.8376**   0.4145   0.0433   
Wielkopolski                       0.9414***  0.3640   0.0097   
Wigierski                          0.1573     0.4555   0.7299   
Wolinski                           1.1182***  0.4157   0.0071   
Household income (10k PLN)         0.5958***  0.1823   0.0011   
Male                               0.1191*    0.0721   0.0984   
Higher education                   0.0247     0.0805   0.7587   
City                               0.1715**   0.0783   0.0284   
Winter                             0.8095***  0.0841   0.0000   
Hiking                             2.0840***  0.0793   0.0000   
Skiing                             1.3876***  0.2686   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2868     0.0946            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.8852     0.6860   0.1969   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2742.1464
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1769
AIC/n:                             0.9476
BIC/n:                             0.9841
n (observations):               5855
r (respondents):                5855
k (parameters):                   32
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.9364
median                           0.0000          1.9333
std                              0.7834          0.8370
min                              0.0000          0.0250
max                             20.0000          4.9654
quantile 0.025                   0.0000          0.5313
quantile 0.975                   2.0000          3.5345
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:31
Estimation took 0.8967 seconds (0 hours 0 minutes 0.8967 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.35 -0.63 0.43 -0.094 0.019 0.043 -0.04 -0.021 0.15 0.091 0.0027 -0.11 0.047 0.034 0.2 -0.31 0.013 0.0035 -0.043 0.03 -0.037 0.059 0.0085 0.074 0.24 0.01 0.0051 0.018 0.17 0.43 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3914.9625676064             NaN     4687.5512028310     0.0003   2026-09-08 10:27:31
     1      4    0.0331789704    0.1199131059     3293.3833568066  621.5792107997     1444.1096085021     0.0072   2026-09-08 10:27:31
     2      5    0.0076994338    0.0235728727     3224.1909212724   69.1924355342      597.9632354344     0.0027   2026-09-08 10:27:31
     3      6    0.0053192366    0.0150202565     3209.6018717287   14.5890495437      379.2322492250     0.0030   2026-09-08 10:27:31
     4      7    0.0037882169    0.0095817997     3201.7238780893    7.8779936394      396.5392964741     0.0028   2026-09-08 10:27:31
     5      8    0.0293331118    0.0710937933     3165.4782906940   36.2455873954      379.4066039016     0.0027   2026-09-08 10:27:31
     6      9    0.0096100202    0.0203066798     3158.7196344175    6.7586562765      331.3532407461     0.0022   2026-09-08 10:27:31
     7     10    0.0084034193    0.0138704424     3155.3628036381    3.3568307794      349.4993056531     0.0022   2026-09-08 10:27:31
     8     11    0.0090783587    0.0121869822     3152.5669527159    2.7958509223      358.5797817830     0.0022   2026-09-08 10:27:31
     9     12    0.0335755741    0.0422923161     3143.0383694252    9.5285832906      376.1546596484     0.0021   2026-09-08 10:27:31
    10     13    0.0756590095    0.0929332506     3122.8494894877   20.1888799375      592.7120736132     0.0021   2026-09-08 10:27:31
    11     14    0.1802833204    0.2194211361     3077.5674075497   45.2820819380      832.7541300638     0.0020   2026-09-08 10:27:31
    12     15    0.3367450206    0.4085358436     3000.3590063184   77.2084012313      942.4121303616     0.0019   2026-09-08 10:27:31
    13     16    0.4459057235    0.5409899979     2915.3982973874   84.9607089310      737.4424244271     0.0019   2026-09-08 10:27:31
    14     17    0.2558888993    0.3117118365     2877.4993614932   37.8989358943      459.2314972363     0.0020   2026-09-08 10:27:31
    15     18    0.0065063734    0.0178119138     2866.8391251302   10.6602363629      259.5034280655     0.0023   2026-09-08 10:27:31
    16     19    0.0783709569    0.0967683155     2860.5441623058    6.2949628245      254.8534272975     0.0022   2026-09-08 10:27:31
    17     20    0.0536826773    0.0662929953     2857.1976468250    3.3465154808      281.6783604160     0.0024   2026-09-08 10:27:31
    18     21    0.0670567204    0.0859167140     2849.7018422426    7.4958045824      286.5285712068     0.0025   2026-09-08 10:27:31
    19     22    0.0172109904    0.0480069257     2837.4437691164   12.2580731262      236.3577989196     0.0021   2026-09-08 10:27:31
    20     23    0.0998268780    0.1305560200     2822.4790979913   14.9646711252      131.0169957026     0.0018   2026-09-08 10:27:31
    21     24    0.1592459363    0.1938146094     2814.9628408464    7.5162571449       57.9713187035     0.0021   2026-09-08 10:27:31
    22     25    0.0778858761    0.0943493538     2813.7930381846    1.1698026618       47.9646525620     0.0020   2026-09-08 10:27:31
    23     26    0.0160436037    0.0196937626     2813.6845607601    0.1084774245       48.3029295242     0.0022   2026-09-08 10:27:31
    24     27    0.0082971446    0.0105091449     2813.5918974583    0.0926633018       48.1970500480     0.0019   2026-09-08 10:27:31
    25     28    0.0147413721    0.0195415374     2813.3151600291    0.2767374292       47.6953599372     0.0019   2026-09-08 10:27:31
    26     29    0.0210525642    0.0305132501     2812.6658048434    0.6493551857       46.5853738991     0.0019   2026-09-08 10:27:31
    27     30    0.0335063069    0.0574741839     2811.0058536839    1.6599511596       44.0493923466     0.0018   2026-09-08 10:27:31
    28     31    0.0554134095    0.1070607706     2807.2406639737    3.7651897102       53.4369434546     0.0019   2026-09-08 10:27:31
    29     32    0.1047824766    0.1890848707     2799.9813797387    7.2592842350       75.9517563586     0.0026   2026-09-08 10:27:31
    30     33    0.1400810684    0.2511991482     2790.4170387080    9.5643410307       79.2234987852     0.0025   2026-09-08 10:27:31
    31     34    0.0899855727    0.1828146458     2783.9413645785    6.4756741295       54.4292152180     0.0024   2026-09-08 10:27:31
    32     35    0.0553211027    0.0688262796     2782.2006295170    1.7407350614       39.8023096968     0.0018   2026-09-08 10:27:31
    33     36    0.0214569279    0.0425091164     2781.9788726887    0.2217568284       34.5416470247     0.0018   2026-09-08 10:27:31
    34     37    0.0081906588    0.0153760076     2781.9182708451    0.0606018435       32.4771957656     0.0020   2026-09-08 10:27:31
    35     38    0.0137766659    0.0264330035     2781.7528462310    0.1654246141       30.7980545039     0.0021   2026-09-08 10:27:31
    36     39    0.0171661934    0.0349585998     2781.3694728152    0.3833734158       33.1201500590     0.0021   2026-09-08 10:27:31
    37     40    0.0246471144    0.0490272372     2780.3880939388    0.9813788764       43.1146000634     0.0023   2026-09-08 10:27:31
    38     41    0.0330017371    0.0614872834     2778.2029924048    2.1851015340       54.2905681551     0.0019   2026-09-08 10:27:31
    39     42    0.0570713946    0.1089410526     2774.2342771273    3.9687152775       56.9974413288     0.0020   2026-09-08 10:27:31
    40     43    0.1270362967    0.2027172795     2769.7445724313    4.4897046960       41.6071085647     0.0018   2026-09-08 10:27:31
    41     44    0.1156735193    0.1950008469     2767.4325543730    2.3120180583       24.2367869952     0.0021   2026-09-08 10:27:31
    42     45    0.0369588218    0.0699850352     2767.0525487752    0.3800055978       15.2961496234     0.0022   2026-09-08 10:27:31
    43     46    0.0051958932    0.0094039356     2767.0288527394    0.0236960358       13.2767066298     0.0020   2026-09-08 10:27:31
    44     47    0.0012412645    0.0031055991     2767.0177304145    0.0111223248       12.6901176249     0.0021   2026-09-08 10:27:31
    45     48    0.0027018889    0.0076493770     2766.9742275167    0.0435028978       11.5702358704     0.0018   2026-09-08 10:27:31
    46     49    0.0037551120    0.0101009427     2766.8791947700    0.0950327467       11.9165160226     0.0019   2026-09-08 10:27:31
    47     50    0.0079098985    0.0180583491     2766.6256954405    0.2534993296       14.8767582857     0.0019   2026-09-08 10:27:31
    48     51    0.0150059903    0.0340245157     2766.0468386309    0.5788568096       18.3097733309     0.0018   2026-09-08 10:27:31
    49     52    0.0262342294    0.0704003149     2764.8845024331    1.1623361978       20.2991695648     0.0022   2026-09-08 10:27:31
    50     53    0.0455350128    0.1156840221     2763.2626701461    1.6218322870       16.5182957001     0.0018   2026-09-08 10:27:31
    51     54    0.0493418998    0.1100888308     2762.0572591200    1.2054110260       12.2486297712     0.0021   2026-09-08 10:27:31
    52     55    0.0182221956    0.0420604419     2761.7114986569    0.3457604632       12.7915087633     0.0019   2026-09-08 10:27:31
    53     56    0.0055296286    0.0124325764     2761.6771009105    0.0343977464       12.6700780777     0.0020   2026-09-08 10:27:31
    54     57    0.0015329970    0.0043060512     2761.6708987354    0.0062021751       12.7634130994     0.0018   2026-09-08 10:27:31
    55     58    0.0027069781    0.0076510935     2761.6537291388    0.0171695966       13.2459722470     0.0019   2026-09-08 10:27:31
    56     59    0.0038752488    0.0105360089     2761.6127084929    0.0410206459       13.9605561633     0.0025   2026-09-08 10:27:31
    57     60    0.0060857273    0.0159179159     2761.5033445665    0.1093639264       15.0767968210     0.0025   2026-09-08 10:27:31
    58     61    0.0092466092    0.0239140114     2761.2305404277    0.2728041388       16.5796331300     0.0018   2026-09-08 10:27:31
    59     62    0.0204872809    0.0472069178     2760.5763484271    0.6541920006       18.1836827988     0.0019   2026-09-08 10:27:31
    60     63    0.0487376710    0.1109611576     2759.2199411841    1.3564072429       21.7576866472     0.0018   2026-09-08 10:27:31
    61     64    0.1006865541    0.2138155859     2757.1543739939    2.0655671902       26.3386287139     0.0021   2026-09-08 10:27:31
    62     65    0.1131104352    0.2408558542     2755.4051738264    1.7492001675       22.2618778201     0.0018   2026-09-08 10:27:31
    63     66    0.0464258909    0.1105818383     2754.7941557000    0.6110181264       14.1081459369     0.0021   2026-09-08 10:27:31
    64     67    0.0088483132    0.0214119521     2754.7190674006    0.0750882993       13.8532449437     0.0025   2026-09-08 10:27:31
    65     68    0.0038222582    0.0089736964     2754.7054529919    0.0136144088       13.4148412406     0.0018   2026-09-08 10:27:31
    66     69    0.0062780501    0.0147054250     2754.6713189518    0.0341340401       12.4183419894     0.0019   2026-09-08 10:27:31
    67     70    0.0078276225    0.0194613718     2754.5889308931    0.0823880587       11.7508599096     0.0019   2026-09-08 10:27:31
    68     71    0.0097165169    0.0253335474     2754.3732776666    0.2156532265       11.6049484048     0.0020   2026-09-08 10:27:31
    69     72    0.0110293141    0.0303121945     2753.8487478775    0.5245297891       11.7062974007     0.0025   2026-09-08 10:27:31
    70     73    0.0287334084    0.0725038876     2752.6744187740    1.1743291035       11.1661438134     0.0028   2026-09-08 10:27:31
    71     74    0.0955389054    0.1980195968     2750.5833100168    2.0911087572       13.8467447937     0.0024   2026-09-08 10:27:31
    72     75    0.1646006994    0.3326963686     2748.2353989532    2.3479110636       12.3939907101     0.0020   2026-09-08 10:27:31
    73     76    0.1234916776    0.2524354911     2747.0559928018    1.1794061514        7.1079563626     0.0020   2026-09-08 10:27:31
    74     77    0.0219642461    0.0539846281     2746.8529362971    0.2030565046        6.2972547543     0.0019   2026-09-08 10:27:31
    75     78    0.0056032738    0.0134400826     2746.8405562961    0.0123800010        6.4371793578     0.0025   2026-09-08 10:27:31
    76     79    0.0019880000    0.0041620897     2746.8388099003    0.0017463958        6.4708945379     0.0027   2026-09-08 10:27:31
    77     80    0.0044238227    0.0092920563     2746.8328188011    0.0059910992        6.5360839453     0.0026   2026-09-08 10:27:31
    78     81    0.0056135827    0.0119573403     2746.8196204085    0.0131983927        6.5851385379     0.0026   2026-09-08 10:27:31
    79     82    0.0083921995    0.0185259704     2746.7838837741    0.0357366343        6.5485912022     0.0025   2026-09-08 10:27:31
    80     83    0.0095419399    0.0238503217     2746.6986272119    0.0852565622        6.1845079749     0.0026   2026-09-08 10:27:31
    81     84    0.0125281759    0.0289726508     2746.5096763679    0.1889508441        7.2513205950     0.0026   2026-09-08 10:27:31
    82     85    0.0193152453    0.0501440052     2746.1872093177    0.3224670501        8.2641804269     0.0020   2026-09-08 10:27:31
    83     86    0.0409052109    0.0935690212     2745.8521567376    0.3350525802        7.9299942016     0.0019   2026-09-08 10:27:31
    84     87    0.0418739227    0.0868253132     2745.6965662217    0.1555905159        6.1795447611     0.0022   2026-09-08 10:27:31
    85     88    0.0146131551    0.0309489376     2745.6702967779    0.0262694437        4.8817187344     0.0020   2026-09-08 10:27:31
    86     89    0.0018530832    0.0042807511     2745.6683275992    0.0019691787        4.5545497406     0.0025   2026-09-08 10:27:31
    87     90    0.0006436791    0.0015699534     2745.6675268628    0.0008007364        4.4569809131     0.0023   2026-09-08 10:27:31
    88     91    0.0016547576    0.0038511136     2745.6644558908    0.0030709720        4.2134318384     0.0026   2026-09-08 10:27:31
    89     92    0.0023319393    0.0049794674     2745.6575753786    0.0068805122        3.8673957705     0.0025   2026-09-08 10:27:31
    90     93    0.0040861040    0.0078349546     2745.6387169028    0.0188584758        3.6934474750     0.0025   2026-09-08 10:27:31
    91     94    0.0064550166    0.0118423735     2745.5922264469    0.0464904558        4.7054155748     0.0025   2026-09-08 10:27:31
    92     95    0.0105936614    0.0234479870     2745.4807801034    0.1114463435        6.0948633520     0.0022   2026-09-08 10:27:31
    93     96    0.0274493574    0.0536642689     2745.2524777696    0.2283023338        7.4268055797     0.0019   2026-09-08 10:27:31
    94     97    0.0500289700    0.1004913067     2744.9123496637    0.3401281059        7.3792339926     0.0021   2026-09-08 10:27:31
    95     98    0.0497152959    0.1090731959     2744.6391265066    0.2732231572        8.2465273614     0.0020   2026-09-08 10:27:31
    96     99    0.0190176964    0.0481615507     2744.5519660981    0.0871604085        7.7569994097     0.0019   2026-09-08 10:27:31
    97    100    0.0049899028    0.0096860669     2744.5418689978    0.0100971003        7.0162448896     0.0024   2026-09-08 10:27:31
    98    101    0.0021487635    0.0041860168     2744.5407066549    0.0011623430        6.7930124214     0.0022   2026-09-08 10:27:31
    99    102    0.0022259391    0.0044052408     2744.5389735103    0.0017331446        6.6085509895     0.0022   2026-09-08 10:27:31
   100    103    0.0036962756    0.0074580082     2744.5340438761    0.0049296341        6.4512905732     0.0025   2026-09-08 10:27:31
   101    104    0.0049085846    0.0103418914     2744.5217841883    0.0122596878        6.1724438901     0.0024   2026-09-08 10:27:31
   102    105    0.0062974299    0.0137164022     2744.4904725305    0.0313116578        5.6409821143     0.0024   2026-09-08 10:27:31
   103    106    0.0107485302    0.0163614102     2744.4166896727    0.0737828578        4.6617529714     0.0025   2026-09-08 10:27:31
   104    107    0.0162931779    0.0319346464     2744.2657826989    0.1509069738        3.0304636154     0.0022   2026-09-08 10:27:31
   105    108    0.0367090513    0.0755391270     2744.0454118755    0.2203708235        4.4412928746     0.0023   2026-09-08 10:27:31
   106    109    0.0520088606    0.0993177994     2743.8743690143    0.1710428611        5.1888655905     0.0021   2026-09-08 10:27:31
   107    110    0.0275836319    0.0524733372     2743.8224415130    0.0519275013        3.6365002378     0.0019   2026-09-08 10:27:31
   108    111    0.0047272032    0.0086801442     2743.8171777032    0.0052638098        2.6633806009     0.0018   2026-09-08 10:27:31
   109    112    0.0008566119    0.0020421585     2743.8168600102    0.0003176931        2.6055735654     0.0018   2026-09-08 10:27:31
   110    113    0.0006843463    0.0015374719     2743.8165389878    0.0003210223        2.5718237190     0.0018   2026-09-08 10:27:31
   111    114    0.0014797999    0.0032780136     2743.8154297422    0.0011092457        2.4903671341     0.0023   2026-09-08 10:27:31
   112    115    0.0020303310    0.0044735925     2743.8128278298    0.0026019124        2.3681980696     0.0020   2026-09-08 10:27:31
   113    116    0.0033179029    0.0067747783     2743.8059178428    0.0069099870        2.1639705945     0.0020   2026-09-08 10:27:31
   114    117    0.0055073016    0.0092691099     2743.7892212785    0.0166965643        1.8605093154     0.0020   2026-09-08 10:27:31
   115    118    0.0086139220    0.0144803240     2743.7519453566    0.0372759219        1.9226210879     0.0017   2026-09-08 10:27:31
   116    119    0.0152271409    0.0291811140     2743.6865926170    0.0653527396        3.4126432602     0.0019   2026-09-08 10:27:31
   117    120    0.0224357408    0.0478814190     2743.6147102907    0.0718823264        4.4536865636     0.0018   2026-09-08 10:27:31
   118    121    0.0153583570    0.0404531748     2743.5777795419    0.0369307488        3.7370278173     0.0019   2026-09-08 10:27:31
   119    122    0.0057669831    0.0130553576     2743.5709457832    0.0068337587        3.2003023421     0.0024   2026-09-08 10:27:31
   120    123    0.0014900477    0.0024727090     2743.5703546405    0.0005911426        3.1850926038     0.0024   2026-09-08 10:27:31
   121    124    0.0006271181    0.0012715764     2743.5699985458    0.0003560947        3.1538448318     0.0021   2026-09-08 10:27:31
   122    125    0.0014201881    0.0028428930     2743.5686898798    0.0013086660        3.0719597220     0.0024   2026-09-08 10:27:31
   123    126    0.0020184032    0.0035875768     2743.5656864520    0.0030034278        2.9507109871     0.0018   2026-09-08 10:27:31
   124    127    0.0034646957    0.0052439209     2743.5574997945    0.0081866575        2.7340885956     0.0020   2026-09-08 10:27:31
   125    128    0.0054531658    0.0081032723     2743.5370271573    0.0204726372        2.5397617455     0.0021   2026-09-08 10:27:31
   126    129    0.0097944219    0.0198697260     2743.4866146168    0.0504125405        2.6275187608     0.0023   2026-09-08 10:27:31
   127    130    0.0322977156    0.0535862606     2743.3758847260    0.1107298908        3.7440898749     0.0026   2026-09-08 10:27:31
   128    131    0.0729829771    0.1154907465     2743.1840974692    0.1917872568        5.4736507479     0.0024   2026-09-08 10:27:31
   129    132    0.0996933857    0.1558163957     2742.9802983770    0.2037990922        4.9852336996     0.0019   2026-09-08 10:27:31
   130    133    0.0591879727    0.0936043381     2742.8820588164    0.0982395606        2.4345799813     0.0022   2026-09-08 10:27:31
   131    134    0.0087023924    0.0134303697     2742.8652587967    0.0168000198        2.1375702140     0.0022   2026-09-08 10:27:31
   132    135    0.0054708094    0.0089543744     2742.8643028819    0.0009559148        2.0852901586     0.0019   2026-09-08 10:27:31
   133    136    0.0013998261    0.0022033922     2742.8641974088    0.0001054731        2.0708978418     0.0025   2026-09-08 10:27:31
   134    137    0.0027212709    0.0043009485     2742.8638778158    0.0003195930        2.0368575907     0.0025   2026-09-08 10:27:31
   135    138    0.0037169598    0.0059348916     2742.8631370350    0.0007407807        1.9734357207     0.0024   2026-09-08 10:27:31
   136    139    0.0056436814    0.0091944694     2742.8611696253    0.0019674097        1.8298468861     0.0022   2026-09-08 10:27:31
   137    140    0.0069671003    0.0119381460     2742.8564642497    0.0047053756        1.5236656537     0.0025   2026-09-08 10:27:31
   138    141    0.0054905809    0.0118015997     2742.8461767743    0.0102874755        1.3964308203     0.0019   2026-09-08 10:27:31
   139    142    0.0054365797    0.0105810451     2742.8289778056    0.0171989687        1.4063982365     0.0023   2026-09-08 10:27:31
   140    143    0.0206690671    0.0308310617     2742.8117472629    0.0172305427        1.2245989522     0.0025   2026-09-08 10:27:31
   141    144    0.0226331517    0.0343180435     2742.8042013531    0.0075459098        1.3260226461     0.0030   2026-09-08 10:27:31
   142    145    0.0081564608    0.0130706088     2742.8030318163    0.0011695368        1.1704955116     0.0028   2026-09-08 10:27:31
   143    146    0.0006604775    0.0014722134     2742.8029318434    0.0000999730        1.1523003906     0.0028   2026-09-08 10:27:31
   144    147    0.0002668043    0.0004900240     2742.8028604777    0.0000713656        1.1410348446     0.0030   2026-09-08 10:27:31
   145    148    0.0006120254    0.0010644244     2742.8026023459    0.0002581318        1.1130056063     0.0026   2026-09-08 10:27:31
   146    149    0.0008787543    0.0015098632     2742.8020039295    0.0005984164        1.0713313497     0.0027   2026-09-08 10:27:31
   147    150    0.0015051248    0.0027023054     2742.8003725954    0.0016313341        0.9975088046     0.0031   2026-09-08 10:27:31
   148    151    0.0023898370    0.0050793362     2742.7962506991    0.0041218962        0.8746286031     0.0028   2026-09-08 10:27:31
   149    152    0.0052344497    0.0112222453     2742.7858737824    0.0103769168        0.8613833986     0.0026   2026-09-08 10:27:31
   150    153    0.0121944875    0.0257177793     2742.7617854597    0.0240883227        1.6114454268     0.0025   2026-09-08 10:27:31
   151    154    0.0245496704    0.0531593981     2742.7145565458    0.0472289139        2.7476743543     0.0023   2026-09-08 10:27:31
   152    155    0.0349477454    0.0793666891     2742.6509090744    0.0636474714        3.2218712644     0.0027   2026-09-08 10:27:31
   153    156    0.0244133804    0.0612401673     2742.6070677112    0.0438413632        2.3598702205     0.0028   2026-09-08 10:27:31
   154    157    0.0063058338    0.0140129114     2742.5955491523    0.0115185589        1.5957719977     0.0026   2026-09-08 10:27:31
   155    158    0.0038060500    0.0079800444     2742.5945637204    0.0009854319        1.6855160783     0.0026   2026-09-08 10:27:31
   156    159    0.0010838963    0.0023604603     2742.5945080470    0.0000556734        1.6768292610     0.0029   2026-09-08 10:27:31
   157    160    0.0007158823    0.0015717913     2742.5944524253    0.0000556217        1.6659679100     0.0023   2026-09-08 10:27:31
   158    161    0.0015180545    0.0033248991     2742.5942611168    0.0001913085        1.6351736224     0.0030   2026-09-08 10:27:31
   159    162    0.0020800072    0.0045328651     2742.5938162482    0.0004448686        1.5750779677     0.0026   2026-09-08 10:27:31
   160    163    0.0030629967    0.0066346444     2742.5926626276    0.0011536205        1.4374621624     0.0025   2026-09-08 10:27:31
   161    164    0.0034503985    0.0075106945     2742.5900378509    0.0026247767        1.1488372617     0.0026   2026-09-08 10:27:31
   162    165    0.0036045790    0.0054614419     2742.5849571815    0.0050806694        0.6124214686     0.0025   2026-09-08 10:27:31
   163    166    0.0046359645    0.0129141825     2742.5783666780    0.0065905036        0.5116900694     0.0026   2026-09-08 10:27:31
   164    167    0.0096617411    0.0227108654     2742.5740809875    0.0042856905        0.4664058556     0.0024   2026-09-08 10:27:31
   165    168    0.0062285982    0.0138153812     2742.5730354768    0.0010455107        0.4325782828     0.0025   2026-09-08 10:27:31
   166    169    0.0011675818    0.0025324455     2742.5729504251    0.0000850517        0.3934533962     0.0025   2026-09-08 10:27:31
   167    170    0.0001396553    0.0001867197     2742.5729424822    0.0000079429        0.3933652511     0.0025   2026-09-08 10:27:31
   168    171    0.0001798459    0.0002583425     2742.5729267950    0.0000156872        0.3937519988     0.0027   2026-09-08 10:27:31
   169    172    0.0002974718    0.0004163390     2742.5728850796    0.0000417154        0.3944081826     0.0026   2026-09-08 10:27:31
   170    173    0.0004787905    0.0006361003     2742.5727770740    0.0001080056        0.3950767899     0.0026   2026-09-08 10:27:31
   171    174    0.0007761608    0.0009960124     2742.5724960290    0.0002810450        0.3949883630     0.0023   2026-09-08 10:27:31
   172    175    0.0012333943    0.0017383197     2742.5717780996    0.0007179294        0.3917606851     0.0026   2026-09-08 10:27:31
   173    176    0.0018688995    0.0037602655     2742.5700082670    0.0017698326        0.3857768045     0.0026   2026-09-08 10:27:32
   174    177    0.0044299391    0.0089006517     2742.5660351081    0.0039731589        0.7468182411     0.0024   2026-09-08 10:27:32
   175    178    0.0096603847    0.0182591099     2742.5588663186    0.0071687895        1.0433453540     0.0025   2026-09-08 10:27:32
   176    179    0.0134205152    0.0250361593     2742.5506383185    0.0082280001        0.9418694945     0.0022   2026-09-08 10:27:32
   177    180    0.0083503915    0.0160914539     2742.5462346435    0.0044036751        0.4406974182     0.0023   2026-09-08 10:27:32
   178    181    0.0023395480    0.0031420000     2742.5453926819    0.0008419615        0.4537706525     0.0025   2026-09-08 10:27:32
   179    182    0.0008809659    0.0017647176     2742.5453399095    0.0000527724        0.4419087510     0.0024   2026-09-08 10:27:32
   180    183    0.0002286333    0.0004301990     2742.5453348859    0.0000050237        0.4383091534     0.0023   2026-09-08 10:27:32
   181    184    0.0003800877    0.0007166579     2742.5453219070    0.0000129789        0.4320414922     0.0024   2026-09-08 10:27:32
   182    185    0.0005563346    0.0010571025     2742.5452900075    0.0000318995        0.4224344024     0.0023   2026-09-08 10:27:32
   183    186    0.0008671386    0.0016741013     2742.5452046847    0.0000853228        0.4062409103     0.0018   2026-09-08 10:27:32
   184    187    0.0012394695    0.0024831176     2742.5449845870    0.0002200978        0.3795642880     0.0024   2026-09-08 10:27:32
   185    188    0.0016031108    0.0035666103     2742.5444150933    0.0005694937        0.3345755478     0.0024   2026-09-08 10:27:32
   186    189    0.0024858307    0.0049847618     2742.5429837020    0.0014313913        0.2592278961     0.0024   2026-09-08 10:27:32
   187    190    0.0048427470    0.0085902332     2742.5395951254    0.0033885766        0.2914833796     0.0023   2026-09-08 10:27:32
   188    191    0.0099594224    0.0201359891     2742.5326985522    0.0068965732        0.3368177563     0.0020   2026-09-08 10:27:32
   189    192    0.0183564334    0.0398622754     2742.5226394228    0.0100591294        0.3404243478     0.0019   2026-09-08 10:27:32
   190    193    0.0233554311    0.0451036674     2742.5147569767    0.0078824461        0.3044752869     0.0022   2026-09-08 10:27:32
   191    194    0.0113384335    0.0207445040     2742.5123009402    0.0024560365        0.2623340878     0.0025   2026-09-08 10:27:32
   192    195    0.0020243827    0.0036623467     2742.5120524268    0.0002485134        0.2615118219     0.0023   2026-09-08 10:27:32
   193    196    0.0006565918    0.0013583995     2742.5120428300    0.0000095968        0.2583025620     0.0023   2026-09-08 10:27:32
   194    197    0.0001832151    0.0003982355     2742.5120398233    0.0000030067        0.2573002420     0.0023   2026-09-08 10:27:32
   195    198    0.0006112253    0.0013144687     2742.5120243172    0.0000155060        0.2538813336     0.0023   2026-09-08 10:27:32
   196    199    0.0007726558    0.0016498675     2742.5119915763    0.0000327410        0.2493422124     0.0024   2026-09-08 10:27:32
   197    200    0.0013186525    0.0027897012     2742.5118985068    0.0000930694        0.2409720969     0.0024   2026-09-08 10:27:32
   198    201    0.0019094095    0.0039907611     2742.5116658007    0.0002327062        0.2272030571     0.0024   2026-09-08 10:27:32
   199    202    0.0026697535    0.0055535113     2742.5110701888    0.0005956119        0.2033640936     0.0023   2026-09-08 10:27:32
   200    203    0.0029302837    0.0067482866     2742.5096524815    0.0014177073        0.1997055940     0.0023   2026-09-08 10:27:32
   201    204    0.0040707786    0.0098343641     2742.5066856062    0.0029668753        0.1918586807     0.0026   2026-09-08 10:27:32
   202    205    0.0114008505    0.0227559651     2742.5021188572    0.0045667489        0.1876386438     0.0025   2026-09-08 10:27:32
   203    206    0.0180856737    0.0347030228     2742.4981860461    0.0039328111        0.2151109345     0.0025   2026-09-08 10:27:32
   204    207    0.0112924202    0.0229210902     2742.4967974881    0.0013885581        0.2036544285     0.0023   2026-09-08 10:27:32
   205    208    0.0023947242    0.0049994950     2742.4966356010    0.0001618871        0.1904368944     0.0023   2026-09-08 10:27:32
   206    209    0.0003581421    0.0008695810     2742.4966288526    0.0000067484        0.1855754605     0.0023   2026-09-08 10:27:32
   207    210    0.0001297997    0.0002580340     2742.4966273511    0.0000015015        0.1846152569     0.0023   2026-09-08 10:27:32
   208    211    0.0004243123    0.0008443213     2742.4966198153    0.0000075358        0.1815257720     0.0019   2026-09-08 10:27:32
   209    212    0.0005268261    0.0010615085     2742.4966039002    0.0000159151        0.1774160823     0.0019   2026-09-08 10:27:32
   210    213    0.0008716302    0.0017988794     2742.4965585796    0.0000453206        0.1697114269     0.0017   2026-09-08 10:27:32
   211    214    0.0011930618    0.0025908359     2742.4964447739    0.0001138057        0.1566617739     0.0017   2026-09-08 10:27:32
   212    215    0.0015371299    0.0036845311     2742.4961502112    0.0002945627        0.1329700368     0.0017   2026-09-08 10:27:32
   213    216    0.0019218335    0.0047712152     2742.4954288841    0.0007213271        0.1101160014     0.0017   2026-09-08 10:27:32
   214    217    0.0030517229    0.0073256782     2742.4938119986    0.0016168855        0.1301703435     0.0017   2026-09-08 10:27:32
   215    218    0.0080106713    0.0168115662     2742.4909201225    0.0028918761        0.1461413649     0.0026   2026-09-08 10:27:32
   216    219    0.0162836394    0.0297481830     2742.4876498951    0.0032702273        0.1607463286     0.0026   2026-09-08 10:27:32
   217    220    0.0143725818    0.0259234697     2742.4859420137    0.0017078814        0.1594250977     0.0020   2026-09-08 10:27:32
   218    221    0.0039551634    0.0081796290     2742.4856263533    0.0003156604        0.1556000122     0.0021   2026-09-08 10:27:32
   219    222    0.0005669726    0.0013770980     2742.4856080848    0.0000182686        0.1518305948     0.0024   2026-09-08 10:27:32
   220    223    0.0001971475    0.0003765027     2742.4856072429    0.0000008419        0.1505144604     0.0023   2026-09-08 10:27:32
   221    224    0.0001819340    0.0003435210     2742.4856060957    0.0000011472        0.1493034912     0.0019   2026-09-08 10:27:32
   222    225    0.0003503101    0.0006666847     2742.4856024998    0.0000035959        0.1468917048     0.0019   2026-09-08 10:27:32
   223    226    0.0005088630    0.0009841947     2742.4855936911    0.0000088086        0.1431721706     0.0021   2026-09-08 10:27:32
   224    227    0.0007913037    0.0015763481     2742.4855700863    0.0000236048        0.1367896519     0.0023   2026-09-08 10:27:32
   225    228    0.0011205356    0.0023690398     2742.4855092585    0.0000608278        0.1260940138     0.0023   2026-09-08 10:27:32
   226    229    0.0015428991    0.0034557693     2742.4853519488    0.0001573097        0.1076654966     0.0020   2026-09-08 10:27:32
   227    230    0.0023655559    0.0047277707     2742.4849574156    0.0003945332        0.0891357157     0.0026   2026-09-08 10:27:32
   228    231    0.0039012713    0.0068315043     2742.4840282189    0.0009291966        0.0954213604     0.0025   2026-09-08 10:27:32
   229    232    0.0069924262    0.0140870518     2742.4821599784    0.0018682406        0.1008228143     0.0023   2026-09-08 10:27:32
   230    233    0.0175986710    0.0285905663     2742.4795015308    0.0026584476        0.1287686924     0.0019   2026-09-08 10:27:32
   231    234    0.0212077092    0.0337054727     2742.4775024995    0.0019990314        0.1278786654     0.0019   2026-09-08 10:27:32
   232    235    0.0095198105    0.0165097135     2742.4769150963    0.0005874031        0.0878626910     0.0018   2026-09-08 10:27:32
   233    236    0.0016312124    0.0029436630     2742.4768597500    0.0000553463        0.0784955593     0.0023   2026-09-08 10:27:32
   234    237    0.0004863611    0.0008498044     2742.4768579165    0.0000018336        0.0778915732     0.0025   2026-09-08 10:27:32
   235    238    0.0001237834    0.0002006251     2742.4768575284    0.0000003881        0.0776366947     0.0025   2026-09-08 10:27:32
   236    239    0.0004430095    0.0007196621     2742.4768553778    0.0000021506        0.0766370813     0.0023   2026-09-08 10:27:32
   237    240    0.0005456558    0.0008943477     2742.4768509165    0.0000044613        0.0753250436     0.0024   2026-09-08 10:27:32
   238    241    0.0009336646    0.0015546059     2742.4768380820    0.0000128345        0.0743670552     0.0025   2026-09-08 10:27:32
   239    242    0.0013398959    0.0023004466     2742.4768057892    0.0000322928        0.0731432938     0.0021   2026-09-08 10:27:32
   240    243    0.0018822493    0.0034518088     2742.4767210298    0.0000847594        0.0706934293     0.0020   2026-09-08 10:27:32
   241    244    0.0021614550    0.0047463188     2742.4765066118    0.0002144180        0.0661429701     0.0026   2026-09-08 10:27:32
   242    245    0.0021401857    0.0061428249     2742.4759847668    0.0005218450        0.0687431951     0.0021   2026-09-08 10:27:32
   243    246    0.0036059779    0.0101309501     2742.4748545849    0.0011301819        0.0714610283     0.0023   2026-09-08 10:27:32
   244    247    0.0148997573    0.0233499143     2742.4729690551    0.0018855297        0.0646245074     0.0024   2026-09-08 10:27:32
   245    248    0.0256174175    0.0370022873     2742.4711010222    0.0018680329        0.0661763867     0.0029   2026-09-08 10:27:32
   246    249    0.0184194694    0.0270964566     2742.4702976692    0.0008033531        0.0524686382     0.0029   2026-09-08 10:27:32
   247    250    0.0035084418    0.0068025206     2742.4701803617    0.0001173075        0.0420964668     0.0021   2026-09-08 10:27:32
   248    251    0.0006208490    0.0013233372     2742.4701752184    0.0000051433        0.0431817954     0.0020   2026-09-08 10:27:32
   249    252    0.0001962505    0.0002875312     2742.4701750875    0.0000001309        0.0432825922     0.0019   2026-09-08 10:27:32
   250    253    0.0001168615    0.0001701935     2742.4701749697    0.0000001178        0.0433397036     0.0021   2026-09-08 10:27:32
   251    254    0.0002865094    0.0004181372     2742.4701745101    0.0000004595        0.0434718849     0.0025   2026-09-08 10:27:32
   252    255    0.0003969561    0.0005818722     2742.4701734579    0.0000010522        0.0436355707     0.0026   2026-09-08 10:27:32
   253    256    0.0006635567    0.0009800708     2742.4701705583    0.0000028996        0.0438636966     0.0024   2026-09-08 10:27:32
   254    257    0.0010064229    0.0015076486     2742.4701631567    0.0000074016        0.0441011254     0.0025   2026-09-08 10:27:32
   255    258    0.0015107062    0.0023282486     2742.4701438982    0.0000192585        0.0441740505     0.0024   2026-09-08 10:27:32
   256    259    0.0020476840    0.0033732751     2742.4700954059    0.0000484923        0.0434991455     0.0025   2026-09-08 10:27:32
   257    260    0.0021740861    0.0044215484     2742.4699795410    0.0001158649        0.0405309609     0.0029   2026-09-08 10:27:32
   258    261    0.0021053734    0.0052277170     2742.4697388763    0.0002406647        0.0357473939     0.0022   2026-09-08 10:27:32
   259    262    0.0046928213    0.0088855689     2742.4693721468    0.0003667295        0.0350154702     0.0020   2026-09-08 10:27:32
   260    263    0.0102362130    0.0144965876     2742.4690625290    0.0003096178        0.0309347025     0.0019   2026-09-08 10:27:32
   261    264    0.0077209652    0.0108437942     2742.4689561382    0.0001063908        0.0231250135     0.0019   2026-09-08 10:27:32
   262    265    0.0017263099    0.0029094110     2742.4689441911    0.0000119471        0.0182308999     0.0024   2026-09-08 10:27:32
   263    266    0.0001603175    0.0003632369     2742.4689437890    0.0000004021        0.0174262980     0.0022   2026-09-08 10:27:32
   264    267    0.0000436343    0.0000651649     2742.4689437729    0.0000000161        0.0173996311     0.0019   2026-09-08 10:27:32
   265    268    0.0000659576    0.0000969504     2742.4689437365    0.0000000364        0.0173715547     0.0018   2026-09-08 10:27:32
   266    269    0.0001061609    0.0001558167     2742.4689436415    0.0000000950        0.0173246349     0.0018   2026-09-08 10:27:32
   267    270    0.0001704531    0.0002499991     2742.4689433929    0.0000002486        0.0172394921     0.0020   2026-09-08 10:27:32
   268    271    0.0002709602    0.0003972316     2742.4689427449    0.0000006480        0.0170782988     0.0021   2026-09-08 10:27:32
   269    272    0.0004233290    0.0006213078     2742.4689410656    0.0000016793        0.0167595966     0.0021   2026-09-08 10:27:32
   270    273    0.0006343267    0.0009382532     2742.4689367861    0.0000042795        0.0161060235     0.0024   2026-09-08 10:27:32
   271    274    0.0008561515    0.0013128284     2742.4689263335    0.0000104526        0.0147843280     0.0019   2026-09-08 10:27:32
   272    275    0.0008486712    0.0015851971     2742.4689033686    0.0000229649        0.0136082426     0.0018   2026-09-08 10:27:32
   273    276    0.0007075754    0.0019323334     2742.4688639022    0.0000394664        0.0128945437     0.0025   2026-09-08 10:27:32
   274    277    0.0017229763    0.0034475402     2742.4688225776    0.0000413247        0.0105169415     0.0019   2026-09-08 10:27:32
   275    278    0.0023654919    0.0036530361     2742.4688033160    0.0000192616        0.0082514588     0.0022   2026-09-08 10:27:32
   276    279    0.0010154742    0.0014904368     2742.4688002170    0.0000030990        0.0081481374     0.0026   2026-09-08 10:27:32
   277    280    0.0001008535    0.0002102238     2742.4688000656    0.0000001514        0.0081685300     0.0024   2026-09-08 10:27:32
   278    281    0.0000125125    0.0000297356     2742.4688000611    0.0000000044        0.0081491530     0.0025   2026-09-08 10:27:32
   279    282    0.0000086252    0.0000192977     2742.4688000569    0.0000000042        0.0081352991     0.0022   2026-09-08 10:27:32
   280    283    0.0000204702    0.0000459926     2742.4688000411    0.0000000158        0.0081010996     0.0018   2026-09-08 10:27:32
   281    284    0.0000283722    0.0000645919     2742.4688000045    0.0000000366        0.0080510910     0.0019   2026-09-08 10:27:32
   282    285    0.0000472535    0.0001083754     2742.4687999041    0.0000001004        0.0079622273     0.0022   2026-09-08 10:27:32
   283    286    0.0000727845    0.0001675115     2742.4687996469    0.0000002572        0.0078124224     0.0023   2026-09-08 10:27:32
   284    287    0.0001122661    0.0002623240     2742.4687989749    0.0000006720        0.0075465725     0.0019   2026-09-08 10:27:32
   285    288    0.0001619339    0.0004002332     2742.4687972621    0.0000017128        0.0070685850     0.0017   2026-09-08 10:27:32
   286    289    0.0002463899    0.0006175118     2742.4687930435    0.0000042186        0.0069011412     0.0018   2026-09-08 10:27:32
   287    290    0.0004376720    0.0010374223     2742.4687836109    0.0000094326        0.0071801843     0.0022   2026-09-08 10:27:32
   288    291    0.0008128415    0.0018972412     2742.4687667364    0.0000168745        0.0067871823     0.0021   2026-09-08 10:27:32
   289    292    0.0013006819    0.0027902178     2742.4687476942    0.0000190422        0.0055094861     0.0022   2026-09-08 10:27:32
   290    293    0.0011531195    0.0022430732     2742.4687377737    0.0000099204        0.0039346119     0.0021   2026-09-08 10:27:32

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','8.391957e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.2749***  0.3345   0.0000   
TC/100 EUR                        -1.5281*    0.8197   0.0623   
Babiogorski                        0.9130*    0.5429   0.0926   
Bialowieski                       -0.1625     0.5281   0.7583   
Biebrzanski                        0.3219     0.6954   0.6435   
Bieszczadzki                       0.2999     0.3890   0.4408   
BoryTucholskie                    -0.0179     0.3539   0.9598   
Drawienski                        -0.1723     0.4920   0.7262   
Gorczanski                         0.2080     0.8462   0.8058   
GorStolowych                       0.7863**   0.3488   0.0242   
Kampinoski                        -0.2896     0.2237   0.1955   
Karkonoski                        -0.8219***  0.2881   0.0043   
Magurski                           0.3602     0.4468   0.4201   
Narwianski                        -0.0399     0.6669   0.9523   
Ojcowski                           0.6402*    0.3658   0.0801   
Pieninski                         -1.2824*    0.7152   0.0729   
Poleski                           -0.0113     0.3777   0.9762   
Roztoczanski                      -0.2131     0.3302   0.5186   
Slowinski                         -0.5857*    0.3437   0.0884   
Swietokrzyski                      0.3108     0.3302   0.3465   
UjscieWarty                       -0.7104*    0.3743   0.0577   
Wielkopolski                       0.6285**   0.2949   0.0331   
Wigierski                          0.1036     0.4288   0.8091   
Wolinski                           0.9202**   0.3682   0.0124   
Household income (10k PLN)         0.6651***  0.1936   0.0006   
Male                               0.1223*    0.0722   0.0904   
Higher education                   0.0292     0.0806   0.7170   
City                               0.1645**   0.0783   0.0355   
Winter                             0.8058***  0.0843   0.0000   
Hiking                             2.0849***  0.0794   0.0000   
Skiing                             1.3735***  0.2708   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2940     0.0940            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.6544*    0.3510   0.0623   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2742.4687
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1768
AIC/n:                             0.9477
BIC/n:                             0.9842
n (observations):               5855
r (respondents):                5855
k (parameters):                   32
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.3643
median                           0.0000          2.3002
std                              0.7834          1.0883
min                              0.0000          0.0258
max                             20.0000          8.1215
quantile 0.025                   0.0000          0.6384
quantile 0.975                   2.0000          4.6816
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:32
Estimation took 0.92393 seconds (0 hours 0 minutes 0.92393 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [0.00037 -0.63 0.37 -0.15 0.0087 0.034 -0.054 -0.023 0.16 0.066 0.035 -0.12 0.066 0.071 0.27 -0.34 -0.0044 0.011 -0.053 0.0092 -0.048 0.098 -0.0052 0.061 0.055 0.01 0.0043 0.018 0.18 0.43 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3914.0179667229             NaN     4471.9176713932     0.0002   2026-09-08 10:27:33
     1      4    0.0352081851    0.1279527869     3235.3932354846  678.6247312383     1281.4006805383     0.0083   2026-09-08 10:27:33
     2      5    0.0077517034    0.0229695723     3177.1084226206   58.2848128640      540.4277122417     0.0033   2026-09-08 10:27:33
     3      6    0.0057222239    0.0159325581     3162.3253638407   14.7830587799      394.2910518510     0.0031   2026-09-08 10:27:33
     4      7    0.0053101905    0.0129078056     3152.4396896830    9.8856741577      425.1249277067     0.0024   2026-09-08 10:27:33
     5      8    0.0288833043    0.0669253441     3118.0668532928   34.3728363901      409.7203463607     0.0022   2026-09-08 10:27:33
     6      9    0.0142614157    0.0298566212     3107.0639513369   11.0029019560      333.7696994829     0.0024   2026-09-08 10:27:33
     7     10    0.0113246446    0.0194226720     3101.8075439772    5.2564073597      357.4920855987     0.0024   2026-09-08 10:27:33
     8     11    0.0086016873    0.0114020542     3099.1017459899    2.7057979873      367.5713515199     0.0022   2026-09-08 10:27:33
     9     12    0.0302099901    0.0370456362     3090.5496867047    8.5520592853      384.3022790444     0.0023   2026-09-08 10:27:33
    10     13    0.0698523525    0.0831957362     3072.1255247141   18.4241619906      514.7681108209     0.0022   2026-09-08 10:27:33
    11     14    0.1724077154    0.2032041003     3029.4149047422   42.7106199719      753.2054042977     0.0023   2026-09-08 10:27:33
    12     15    0.3416694010    0.4011443876     2951.8905976179   77.5243071243      899.2504958848     0.0023   2026-09-08 10:27:33
    13     16    0.4983377833    0.5847302566     2856.7216643900   95.1689332279      768.8148627771     0.0027   2026-09-08 10:27:33
    14     17    0.3530075453    0.4154174154     2805.7507059745   50.9709584155      482.2716846397     0.0023   2026-09-08 10:27:33
    15     18    0.0405310218    0.0523260527     2792.2187477759   13.5319581986      258.2863877567     0.0022   2026-09-08 10:27:33
    16     19    0.0773932291    0.0922638183     2786.6094347152    5.6093130607      123.2732069301     0.0021   2026-09-08 10:27:33
    17     20    0.0634066687    0.0749243113     2785.0649156302    1.5445190851      150.2666367984     0.0019   2026-09-08 10:27:33
    18     21    0.0379545481    0.0453336232     2783.7422790916    1.3226365385      146.6935672646     0.0020   2026-09-08 10:27:33
    19     22    0.0460338623    0.0577486752     2780.5237328453    3.2185462463      122.6786970781     0.0028   2026-09-08 10:27:33
    20     23    0.0109356839    0.0321850823     2775.7136464735    4.8100863718       78.8910492828     0.0021   2026-09-08 10:27:33
    21     24    0.0662778018    0.0829149174     2771.2328639880    4.4807824855       30.5210051557     0.0021   2026-09-08 10:27:33
    22     25    0.0820051926    0.0964384429     2769.6033762459    1.6294877421       26.6683839431     0.0021   2026-09-08 10:27:33
    23     26    0.0305570711    0.0359278452     2769.4108138695    0.1925623764       23.1224205489     0.0020   2026-09-08 10:27:33
    24     27    0.0043560699    0.0053260606     2769.3892761308    0.0215377387       21.3285693936     0.0019   2026-09-08 10:27:33
    25     28    0.0034436365    0.0044351774     2769.3565005401    0.0327755907       19.2174798237     0.0026   2026-09-08 10:27:33
    26     29    0.0053557139    0.0073613288     2769.2695514819    0.0869490582       15.8082919633     0.0028   2026-09-08 10:27:33
    27     30    0.0084002439    0.0132810377     2769.0519935655    0.2175579164       20.3946160955     0.0025   2026-09-08 10:27:33
    28     31    0.0134581632    0.0274470377     2768.5135090561    0.5384845094       30.8191975851     0.0020   2026-09-08 10:27:33
    29     32    0.0272331857    0.0575694682     2767.3120857834    1.2014232727       43.9226606998     0.0024   2026-09-08 10:27:33
    30     33    0.0503537870    0.1056542314     2765.1535814438    2.1585043397       55.5462593254     0.0027   2026-09-08 10:27:33
    31     34    0.0597971688    0.1296145623     2762.7160758554    2.4375055884       47.5994205243     0.0028   2026-09-08 10:27:33
    32     35    0.0268641412    0.0691884418     2761.4780763406    1.2379995148       21.8992738422     0.0029   2026-09-08 10:27:33
    33     36    0.0146379442    0.0198508404     2761.2526849500    0.2253913906       14.2847875926     0.0030   2026-09-08 10:27:33
    34     37    0.0051494383    0.0110444240     2761.2352070962    0.0174778538       12.9098235407     0.0028   2026-09-08 10:27:33
    35     38    0.0017158001    0.0037026315     2761.2285551193    0.0066519769       12.2925379693     0.0029   2026-09-08 10:27:33
    36     39    0.0046210899    0.0101967148     2761.1992366818    0.0293184374       11.9572327669     0.0032   2026-09-08 10:27:33
    37     40    0.0054754224    0.0128337517     2761.1358427293    0.0633939526       11.9514568897     0.0022   2026-09-08 10:27:33
    38     41    0.0075946197    0.0213313435     2760.9607882338    0.1750544955       13.1461934010     0.0025   2026-09-08 10:27:33
    39     42    0.0148744419    0.0350887186     2760.5386528401    0.4221353936       19.5062988883     0.0027   2026-09-08 10:27:33
    40     43    0.0340012205    0.0729511354     2759.5666843358    0.9719685043       27.6449885838     0.0028   2026-09-08 10:27:33
    41     44    0.0789632795    0.1517369669     2757.7692079029    1.7974764329       37.6304090950     0.0023   2026-09-08 10:27:33
    42     45    0.1226444538    0.2302557295     2755.5917444790    2.1774634239       39.6636107239     0.0024   2026-09-08 10:27:33
    43     46    0.0893815537    0.1794777166     2754.3050987775    1.2866457015       28.9222045349     0.0025   2026-09-08 10:27:33
    44     47    0.0253523223    0.0546530727     2754.0094589393    0.2956398382       24.0551844423     0.0020   2026-09-08 10:27:33
    45     48    0.0075681894    0.0158342253     2753.9728033471    0.0366555922       23.4938530913     0.0022   2026-09-08 10:27:33
    46     49    0.0051545886    0.0106403731     2753.9412965691    0.0315067780       23.0790555776     0.0030   2026-09-08 10:27:33
    47     50    0.0099085366    0.0197985074     2753.8380881145    0.1032084546       22.0662480203     0.0029   2026-09-08 10:27:33
    48     51    0.0115403071    0.0222176407     2753.6003051245    0.2377829900       22.6261472508     0.0022   2026-09-08 10:27:33
    49     52    0.0137040445    0.0291803919     2753.0051087166    0.5951964080       24.7422656804     0.0020   2026-09-08 10:27:33
    50     53    0.0367034594    0.0744818189     2751.7542715827    1.2508371338       25.6784970317     0.0020   2026-09-08 10:27:33
    51     54    0.1039986448    0.1875128906     2749.7393168849    2.0149546978       22.1201698658     0.0021   2026-09-08 10:27:33
    52     55    0.1466198172    0.2629119694     2747.9217051665    1.8176117184       13.8783701801     0.0023   2026-09-08 10:27:33
    53     56    0.0827186837    0.1539510193     2747.2226292252    0.6990759413        9.1508930378     0.0022   2026-09-08 10:27:33
    54     57    0.0134790756    0.0259858610     2747.1215181422    0.1011110830        9.0768839298     0.0022   2026-09-08 10:27:33
    55     58    0.0043268970    0.0084309129     2747.1145037417    0.0070144004        8.9464400919     0.0022   2026-09-08 10:27:33
    56     59    0.0025854387    0.0048878616     2747.1095202216    0.0049835202        8.9927464427     0.0020   2026-09-08 10:27:33
    57     60    0.0059523431    0.0115522263     2747.0902950682    0.0192251534        9.9487032436     0.0021   2026-09-08 10:27:33
    58     61    0.0068572327    0.0143222177     2747.0475444006    0.0427506676       11.1530732956     0.0022   2026-09-08 10:27:33
    59     62    0.0074771436    0.0198759752     2746.9362655768    0.1112788238       12.8509884530     0.0028   2026-09-08 10:27:33
    60     63    0.0097158745    0.0247586306     2746.6923851203    0.2438804565       14.4810791002     0.0027   2026-09-08 10:27:33
    61     64    0.0213853592    0.0499102058     2746.2520716104    0.4403135100       14.5390427879     0.0026   2026-09-08 10:27:33
    62     65    0.0528484784    0.0949024137     2745.7559806863    0.4960909241       11.0858067056     0.0020   2026-09-08 10:27:33
    63     66    0.0530396852    0.0917624056     2745.4928263177    0.2631543686        6.6505743052     0.0021   2026-09-08 10:27:33
    64     67    0.0183941167    0.0341940125     2745.4409012443    0.0519250734        6.4635179603     0.0021   2026-09-08 10:27:33
    65     68    0.0018739883    0.0050785633     2745.4359514702    0.0049497741        6.7425160741     0.0020   2026-09-08 10:27:33
    66     69    0.0008259235    0.0022034735     2745.4334580914    0.0024933788        6.7290568533     0.0021   2026-09-08 10:27:33
    67     70    0.0017318565    0.0048772194     2745.4246088643    0.0088492271        6.6248147652     0.0021   2026-09-08 10:27:33
    68     71    0.0020797962    0.0062615729     2745.4044187876    0.0201900767        6.6387427902     0.0021   2026-09-08 10:27:33
    69     72    0.0035209871    0.0099196455     2745.3501315245    0.0542872631        6.9548172131     0.0020   2026-09-08 10:27:33
    70     73    0.0059185379    0.0184522306     2745.2191654222    0.1309661023        7.2934772430     0.0020   2026-09-08 10:27:33
    71     74    0.0192849560    0.0450574345     2744.9245790677    0.2945863546        7.3613214543     0.0028   2026-09-08 10:27:33
    72     75    0.0465200218    0.0977902356     2744.4038355906    0.5207434771        6.4393026394     0.0028   2026-09-08 10:27:33
    73     76    0.0678906149    0.1391292809     2743.8354925570    0.5683430336        6.5108419641     0.0029   2026-09-08 10:27:33
    74     77    0.0440975730    0.0914972259     2743.5555984955    0.2798940615        8.6031680323     0.0033   2026-09-08 10:27:33
    75     78    0.0066178653    0.0199839884     2743.5011253070    0.0544731885        9.5718410882     0.0031   2026-09-08 10:27:33
    76     79    0.0035071094    0.0083060843     2743.4961889197    0.0049363873        9.4633572545     0.0023   2026-09-08 10:27:33
    77     80    0.0019149848    0.0039516169     2743.4940530378    0.0021358819        9.3648364733     0.0027   2026-09-08 10:27:33
    78     81    0.0047593821    0.0096768165     2743.4857750210    0.0082780168        9.0896743564     0.0027   2026-09-08 10:27:33
    79     82    0.0059687403    0.0120816297     2743.4673962511    0.0183787699        8.6821232793     0.0024   2026-09-08 10:27:33
    80     83    0.0084878350    0.0175696719     2743.4175233360    0.0498729151        7.9204166329     0.0022   2026-09-08 10:27:33
    81     84    0.0113490119    0.0217116959     2743.2982512198    0.1192721161        6.6294709203     0.0023   2026-09-08 10:27:33
    82     85    0.0182548171    0.0383736052     2743.0328602575    0.2653909624        7.5755095887     0.0026   2026-09-08 10:27:33
    83     86    0.0426310104    0.0939437929     2742.5778152869    0.4550449706        8.9043084385     0.0026   2026-09-08 10:27:33
    84     87    0.0740433241    0.1536706619     2742.1049975754    0.4728177114        7.1916784329     0.0026   2026-09-08 10:27:33
    85     88    0.0545783429    0.1152215578     2741.8869561884    0.2180413870        4.7023949384     0.0027   2026-09-08 10:27:33
    86     89    0.0139953619    0.0296552595     2741.8516858420    0.0352703464        4.4954201485     0.0028   2026-09-08 10:27:33
    87     90    0.0024852904    0.0051154403     2741.8498223794    0.0018634626        4.2839136962     0.0033   2026-09-08 10:27:33
    88     91    0.0008162695    0.0018510982     2741.8493384242    0.0004839553        4.2264448791     0.0027   2026-09-08 10:27:33
    89     92    0.0024650359    0.0055595885     2741.8471211323    0.0022172919        4.0435180815     0.0024   2026-09-08 10:27:33
    90     93    0.0029942939    0.0068898705     2741.8424244008    0.0046967315        3.7724756121     0.0026   2026-09-08 10:27:33
    91     94    0.0044793796    0.0109129341     2741.8294909568    0.0129334440        3.2159253315     0.0032   2026-09-08 10:27:33
    92     95    0.0065280254    0.0141162776     2741.7991509492    0.0303400076        3.2466248965     0.0029   2026-09-08 10:27:33
    93     96    0.0114638847    0.0190227660     2741.7332788161    0.0658721331        3.7508608850     0.0029   2026-09-08 10:27:33
    94     97    0.0153837213    0.0351237669     2741.6261151771    0.1071636390        4.0420977989     0.0025   2026-09-08 10:27:33
    95     98    0.0239021783    0.0574613869     2741.5220093795    0.1041057976        4.0360583708     0.0021   2026-09-08 10:27:33
    96     99    0.0207357124    0.0457142835     2741.4778967483    0.0441126313        3.9868427393     0.0026   2026-09-08 10:27:33
    97    100    0.0053316832    0.0130214737     2741.4716333366    0.0062634117        3.3313604937     0.0028   2026-09-08 10:27:33
    98    101    0.0013141970    0.0021019546     2741.4710776369    0.0005556997        3.1136746863     0.0029   2026-09-08 10:27:33
    99    102    0.0008605169    0.0014536893     2741.4705407369    0.0005369000        2.9692465599     0.0028   2026-09-08 10:27:33
   100    103    0.0017870336    0.0028682835     2741.4687781738    0.0017625632        2.6692357396     0.0027   2026-09-08 10:27:33
   101    104    0.0026778842    0.0038933524     2741.4645590615    0.0042191123        2.4377193018     0.0027   2026-09-08 10:27:33
   102    105    0.0045713525    0.0060377717     2741.4532406063    0.0113184552        2.3138532414     0.0029   2026-09-08 10:27:33
   103    106    0.0074001275    0.0105389188     2741.4246708968    0.0285697095        2.2477588534     0.0029   2026-09-08 10:27:33
   104    107    0.0118503826    0.0252177154     2741.3539278275    0.0707430693        2.2503689515     0.0022   2026-09-08 10:27:33
   105    108    0.0272414526    0.0641013931     2741.1951796606    0.1587481669        4.4265512795     0.0022   2026-09-08 10:27:33
   106    109    0.0592443166    0.1365664569     2740.9071250070    0.2880546537        7.1890985051     0.0022   2026-09-08 10:27:33
   107    110    0.0826208916    0.1918088390     2740.5734003719    0.3337246350        7.7128148060     0.0022   2026-09-08 10:27:33
   108    111    0.0516127989    0.1246098549     2740.3921578737    0.1812424982        5.9177072902     0.0026   2026-09-08 10:27:33
   109    112    0.0139814799    0.0205008874     2740.3557054593    0.0364524144        6.2898922558     0.0022   2026-09-08 10:27:33
   110    113    0.0058624707    0.0139565703     2740.3528720111    0.0028334482        6.1673681701     0.0023   2026-09-08 10:27:33
   111    114    0.0019536457    0.0045500260     2740.3522223673    0.0006496438        6.1060942593     0.0024   2026-09-08 10:27:33
   112    115    0.0046043737    0.0107671273     2740.3497943066    0.0024280607        5.9341407324     0.0023   2026-09-08 10:27:33
   113    116    0.0057320404    0.0135342196     2740.3444367846    0.0053575220        5.6583232335     0.0024   2026-09-08 10:27:33
   114    117    0.0080738184    0.0195333150     2740.3300781011    0.0143586835        5.0909722112     0.0024   2026-09-08 10:27:33
   115    118    0.0080033707    0.0203169504     2740.2968653450    0.0332127561        4.0353101685     0.0022   2026-09-08 10:27:33
   116    119    0.0117630418    0.0164543125     2740.2284633610    0.0684019840        2.2069711642     0.0023   2026-09-08 10:27:33
   117    120    0.0267481361    0.0561611857     2740.1285529835    0.0999103775        1.8272359143     0.0022   2026-09-08 10:27:33
   118    121    0.0435514567    0.0989245119     2740.0496645384    0.0788884452        1.6023747375     0.0023   2026-09-08 10:27:33
   119    122    0.0286638801    0.0657345222     2740.0251216750    0.0245428633        1.2049411216     0.0028   2026-09-08 10:27:33
   120    123    0.0054638810    0.0133903135     2740.0225294317    0.0025922433        1.2888986576     0.0028   2026-09-08 10:27:33
   121    124    0.0007424123    0.0012272380     2740.0223633771    0.0001660546        1.2996230275     0.0023   2026-09-08 10:27:33
   122    125    0.0004435507    0.0009582978     2740.0222283640    0.0001350131        1.3047184744     0.0023   2026-09-08 10:27:33
   123    126    0.0009800646    0.0022111528     2740.0217345200    0.0004938440        1.3148695503     0.0023   2026-09-08 10:27:33
   124    127    0.0012556561    0.0029555421     2740.0205934457    0.0011410742        1.3291281636     0.0024   2026-09-08 10:27:33
   125    128    0.0020352629    0.0045221535     2740.0175112123    0.0030822334        1.3517529949     0.0028   2026-09-08 10:27:33
   126    129    0.0028938401    0.0063519708     2740.0099088931    0.0076023191        1.3803604751     0.0028   2026-09-08 10:27:33
   127    130    0.0035853338    0.0108670763     2739.9919056034    0.0180032897        1.4032327392     0.0029   2026-09-08 10:27:33
   128    131    0.0125852481    0.0240229483     2739.9558916361    0.0360139673        1.9356140823     0.0030   2026-09-08 10:27:33
   129    132    0.0273802522    0.0455999071     2739.9049162500    0.0509753861        3.0383344397     0.0032   2026-09-08 10:27:33
   130    133    0.0300188551    0.0493067790     2739.8670133562    0.0379028937        3.2889517133     0.0036   2026-09-08 10:27:33
   131    134    0.0118907504    0.0218127512     2739.8559063502    0.0111070060        2.9218545568     0.0028   2026-09-08 10:27:33
   132    135    0.0017758303    0.0041989145     2739.8547325397    0.0011738105        2.7878637998     0.0025   2026-09-08 10:27:33
   133    136    0.0007951177    0.0015274198     2739.8545408022    0.0001917374        2.7303020743     0.0023   2026-09-08 10:27:33
   134    137    0.0013222765    0.0024771651     2739.8540741426    0.0004666597        2.6350136768     0.0028   2026-09-08 10:27:33
   135    138    0.0017870904    0.0034710313     2739.8529276821    0.0011464605        2.4883320598     0.0025   2026-09-08 10:27:33
   136    139    0.0024032498    0.0048436178     2739.8499147674    0.0030129147        2.2461609332     0.0023   2026-09-08 10:27:33
   137    140    0.0036405947    0.0057661200     2739.8424220470    0.0074927204        1.8694925503     0.0023   2026-09-08 10:27:33
   138    141    0.0051649805    0.0082333801     2739.8248160448    0.0176060022        1.3281367255     0.0022   2026-09-08 10:27:33
   139    142    0.0134088309    0.0230812882     2739.7898351946    0.0349808502        1.5428871569     0.0024   2026-09-08 10:27:33
   140    143    0.0314445115    0.0504996564     2739.7410907175    0.0487444771        3.2030905243     0.0024   2026-09-08 10:27:33
   141    144    0.0357879364    0.0577203667     2739.7056111823    0.0354795352        3.6636319535     0.0023   2026-09-08 10:27:33
   142    145    0.0148498350    0.0254189106     2739.6955187658    0.0100924166        3.0363288917     0.0021   2026-09-08 10:27:33
   143    146    0.0021434394    0.0031325398     2739.6945004933    0.0010182724        2.6220802367     0.0022   2026-09-08 10:27:33
   144    147    0.0008420056    0.0014235285     2739.6943511114    0.0001493819        2.5239359355     0.0024   2026-09-08 10:27:33
   145    148    0.0013672640    0.0022720815     2739.6940044241    0.0003466873        2.3758923409     0.0024   2026-09-08 10:27:33
   146    149    0.0019433634    0.0032564873     2739.6931401005    0.0008643237        2.1396731474     0.0030   2026-09-08 10:27:33
   147    150    0.0026051636    0.0045148402     2739.6908907959    0.0022493045        2.1897076656     0.0029   2026-09-08 10:27:33
   148    151    0.0033356839    0.0052517498     2739.6853362694    0.0055545266        2.2130519607     0.0030   2026-09-08 10:27:33
   149    152    0.0052806359    0.0066028533     2739.6725995928    0.0127366766        2.0915244256     0.0029   2026-09-08 10:27:33
   150    153    0.0088662876    0.0186711010     2739.6486360258    0.0239635669        1.6015653383     0.0029   2026-09-08 10:27:33
   151    154    0.0226141383    0.0396322855     2739.6187389620    0.0298970638        1.9315575880     0.0023   2026-09-08 10:27:33
   152    155    0.0244808769    0.0406922411     2739.6005405182    0.0181984438        1.4336482286     0.0032   2026-09-08 10:27:33
   153    156    0.0092137603    0.0151369963     2739.5964554063    0.0040851119        0.6859999573     0.0030   2026-09-08 10:27:33
   154    157    0.0013878502    0.0016830214     2739.5961489612    0.0003064451        0.6714746917     0.0022   2026-09-08 10:27:33
   155    158    0.0003736727    0.0007153805     2739.5961163755    0.0000325857        0.6643662803     0.0020   2026-09-08 10:27:33
   156    159    0.0006286655    0.0011546547     2739.5960395715    0.0000768040        0.6526316100     0.0023   2026-09-08 10:27:33
   157    160    0.0009655840    0.0017358150     2739.5958464661    0.0001931054        0.6456718909     0.0021   2026-09-08 10:27:33
   158    161    0.0015230292    0.0026650234     2739.5953358247    0.0005106414        0.6519766006     0.0021   2026-09-08 10:27:33
   159    162    0.0022656421    0.0038489257     2739.5940201655    0.0013156592        0.6589895256     0.0022   2026-09-08 10:27:33
   160    163    0.0031337106    0.0054582302     2739.5906628239    0.0033573416        0.6621265919     0.0021   2026-09-08 10:27:33
   161    164    0.0034977854    0.0089739479     2739.5824852756    0.0081775483        0.9184048398     0.0022   2026-09-08 10:27:33
   162    165    0.0079509208    0.0206026124     2739.5645987276    0.0178865480        1.4867759383     0.0020   2026-09-08 10:27:33
   163    166    0.0183289415    0.0451511096     2739.5341822792    0.0304164484        1.8381685147     0.0022   2026-09-08 10:27:33
   164    167    0.0257740433    0.0637384377     2739.5029088793    0.0312733999        2.1472655563     0.0023   2026-09-08 10:27:33
   165    168    0.0172360123    0.0414367536     2739.4886671711    0.0142417082        2.2081842763     0.0023   2026-09-08 10:27:33
   166    169    0.0051496438    0.0087554248     2739.4863962335    0.0022709376        2.0138541496     0.0021   2026-09-08 10:27:33
   167    170    0.0011821934    0.0030214106     2739.4862406993    0.0001555343        1.9362689825     0.0023   2026-09-08 10:27:33
   168    171    0.0005089682    0.0012651074     2739.4861782781    0.0000624212        1.9093995049     0.0019   2026-09-08 10:27:33
   169    172    0.0013089622    0.0032793790     2739.4859213334    0.0002569447        1.8327107337     0.0023   2026-09-08 10:27:33
   170    173    0.0015925035    0.0040592186     2739.4853604591    0.0005608743        1.7159195531     0.0027   2026-09-08 10:27:33
   171    174    0.0021778405    0.0057967070     2739.4838595218    0.0015009372        1.4851995958     0.0025   2026-09-08 10:27:33
   172    175    0.0026929438    0.0058274081     2739.4804410385    0.0034184833        1.0800915708     0.0019   2026-09-08 10:27:33
   173    176    0.0042176741    0.0056967158     2739.4736242576    0.0068167809        0.5007153222     0.0021   2026-09-08 10:27:33
   174    177    0.0076291297    0.0184342434     2739.4643238177    0.0093004398        0.3377645757     0.0019   2026-09-08 10:27:33
   175    178    0.0119197485    0.0283298003     2739.4577399866    0.0065838311        0.5137644828     0.0025   2026-09-08 10:27:33
   176    179    0.0066684484    0.0162544891     2739.4559586596    0.0017813270        0.3173173723     0.0030   2026-09-08 10:27:33
   177    180    0.0009591969    0.0026169491     2739.4558030272    0.0001556324        0.2913848533     0.0028   2026-09-08 10:27:33
   178    181    0.0001711117    0.0003468979     2739.4557948202    0.0000082071        0.2917546979     0.0029   2026-09-08 10:27:33
   179    182    0.0001010421    0.0002642474     2739.4557873972    0.0000074230        0.2921394219     0.0029   2026-09-08 10:27:33
   180    183    0.0002232364    0.0006035125     2739.4557604250    0.0000269722        0.2931037073     0.0027   2026-09-08 10:27:33
   181    184    0.0003133156    0.0008333364     2739.4556975208    0.0000629042        0.2944581926     0.0028   2026-09-08 10:27:33
   182    185    0.0005321058    0.0013406388     2739.4555258097    0.0001717111        0.2965826172     0.0023   2026-09-08 10:27:33
   183    186    0.0008411253    0.0020227185     2739.4550879922    0.0004378176        0.2994566705     0.0023   2026-09-08 10:27:33
   184    187    0.0013380497    0.0034162346     2739.4539619448    0.0011260473        0.3666479023     0.0022   2026-09-08 10:27:33
   185    188    0.0024740114    0.0070767185     2739.4512002784    0.0027616664        0.6680743619     0.0021   2026-09-08 10:27:33
   186    189    0.0066477035    0.0166142013     2739.4450263998    0.0061738786        1.0432537350     0.0023   2026-09-08 10:27:33
   187    190    0.0157131436    0.0340903379     2739.4340227492    0.0110036507        1.3015861673     0.0021   2026-09-08 10:27:33
   188    191    0.0229388851    0.0465567583     2739.4216668345    0.0123559147        1.0810390837     0.0019   2026-09-08 10:27:33
   189    192    0.0150516481    0.0297094630     2739.4152705684    0.0063962661        0.4629059392     0.0020   2026-09-08 10:27:33
   190    193    0.0024237742    0.0060195101     2739.4140990300    0.0011715384        0.2901138769     0.0025   2026-09-08 10:27:33
   191    194    0.0012546024    0.0031000993     2739.4140302013    0.0000688286        0.2768707890     0.0022   2026-09-08 10:27:33
   192    195    0.0003326786    0.0007034489     2739.4140249120    0.0000052893        0.2734419865     0.0027   2026-09-08 10:27:33
   193    196    0.0004945578    0.0010460993     2739.4140127034    0.0000122086        0.2680304788     0.0026   2026-09-08 10:27:33
   194    197    0.0007526462    0.0016145436     2739.4139815448    0.0000311586        0.2592964431     0.0021   2026-09-08 10:27:33
   195    198    0.0011513363    0.0025365219     2739.4138994619    0.0000820829        0.2475084543     0.0020   2026-09-08 10:27:33
   196    199    0.0016453559    0.0038216593     2739.4136867231    0.0002127389        0.2402112134     0.0023   2026-09-08 10:27:33
   197    200    0.0021765411    0.0054875848     2739.4131387489    0.0005479742        0.2273436463     0.0026   2026-09-08 10:27:33
   198    201    0.0027135200    0.0071880710     2739.4117686128    0.0013701361        0.2295938143     0.0029   2026-09-08 10:27:33
   199    202    0.0037679911    0.0092840857     2739.4085745897    0.0031940230        0.2462795738     0.0029   2026-09-08 10:27:33
   200    203    0.0098215086    0.0193004711     2739.4022980000    0.0062765898        0.2460303258     0.0027   2026-09-08 10:27:33
   201    204    0.0241292467    0.0413277778     2739.3937784128    0.0085195872        0.2060544753     0.0028   2026-09-08 10:27:33
   202    205    0.0275125217    0.0482367627     2739.3878558391    0.0059225737        0.2222324535     0.0029   2026-09-08 10:27:33
   203    206    0.0112881494    0.0223921393     2739.3862855605    0.0015702786        0.1700104105     0.0025   2026-09-08 10:27:33
   204    207    0.0013606742    0.0034168564     2739.3861529622    0.0001325983        0.1835876722     0.0022   2026-09-08 10:27:33
   205    208    0.0005529102    0.0009764527     2739.3861485447    0.0000044175        0.1830508044     0.0020   2026-09-08 10:27:33
   206    209    0.0001804569    0.0003108202     2739.3861469718    0.0000015730        0.1824989304     0.0019   2026-09-08 10:27:33
   207    210    0.0006139471    0.0010612857     2739.3861386111    0.0000083606        0.1804016766     0.0022   2026-09-08 10:27:33
   208    211    0.0007672461    0.0013372987     2739.3861210039    0.0000176072        0.1775711197     0.0022   2026-09-08 10:27:33
   209    212    0.0012979020    0.0022969943     2739.3860707609    0.0000502430        0.1722645480     0.0022   2026-09-08 10:27:33
   210    213    0.0018492295    0.0033802639     2739.3859444559    0.0001263050        0.1633113882     0.0021   2026-09-08 10:27:33
   211    214    0.0025295047    0.0050041884     2739.3856161070    0.0003283489        0.1540387589     0.0021   2026-09-08 10:27:33
   212    215    0.0027139894    0.0068485413     2739.3848034561    0.0008126509        0.1536934263     0.0020   2026-09-08 10:27:33
   213    216    0.0039809735    0.0097624292     2739.3829330687    0.0018703874        0.1440177493     0.0020   2026-09-08 10:27:33
   214    217    0.0078631126    0.0190417329     2739.3793806004    0.0035524684        0.1384949761     0.0020   2026-09-08 10:27:33
   215    218    0.0192970060    0.0356742305     2739.3748678043    0.0045127960        0.1743440025     0.0020   2026-09-08 10:27:33
   216    219    0.0222582997    0.0370543915     2739.3720495139    0.0028182904        0.1899561117     0.0027   2026-09-08 10:27:33
   217    220    0.0090807572    0.0154730273     2739.3713982472    0.0006512667        0.1587587752     0.0022   2026-09-08 10:27:33
   218    221    0.0011163362    0.0027138891     2739.3713505748    0.0000476723        0.1419081855     0.0020   2026-09-08 10:27:33
   219    222    0.0003236028    0.0006819113     2739.3713489811    0.0000015937        0.1394680128     0.0019   2026-09-08 10:27:33
   220    223    0.0001411208    0.0002708949     2739.3713481434    0.0000008377        0.1387378092     0.0019   2026-09-08 10:27:33
   221    224    0.0004257288    0.0008167654     2739.3713441700    0.0000039734        0.1366301438     0.0019   2026-09-08 10:27:33
   222    225    0.0005491578    0.0010623663     2739.3713355528    0.0000086172        0.1338691291     0.0020   2026-09-08 10:27:33
   223    226    0.0009173572    0.0018027878     2739.3713112703    0.0000242825        0.1289299798     0.0028   2026-09-08 10:27:33
   224    227    0.0013165339    0.0026717407     2739.3712499079    0.0000613623        0.1207687182     0.0029   2026-09-08 10:27:33
   225    228    0.0018077269    0.0039540021     2739.3710904311    0.0001594768        0.1063184090     0.0025   2026-09-08 10:27:33
   226    229    0.0021321038    0.0053721049     2739.3706939354    0.0003964957        0.0900009024     0.0024   2026-09-08 10:27:33
   227    230    0.0036097579    0.0072444848     2739.3697729696    0.0009209658        0.0864776574     0.0020   2026-09-08 10:27:33
   228    231    0.0051929134    0.0135508365     2739.3679857757    0.0017871939        0.1033631904     0.0028   2026-09-08 10:27:33
   229    232    0.0138200726    0.0269153260     2739.3656182565    0.0023675192        0.1004849684     0.0027   2026-09-08 10:27:33
   230    233    0.0169477177    0.0304238715     2739.3640363733    0.0015818832        0.1079446236     0.0025   2026-09-08 10:27:33
   231    234    0.0075251377    0.0140255370     2739.3636375888    0.0003987844        0.0861385819     0.0025   2026-09-08 10:27:33
   232    235    0.0011550774    0.0023949847     2739.3636058476    0.0000317412        0.0750851386     0.0024   2026-09-08 10:27:33
   233    236    0.0002661245    0.0005870610     2739.3636047993    0.0000010483        0.0744414605     0.0022   2026-09-08 10:27:33
   234    237    0.0001016303    0.0002017303     2739.3636043644    0.0000004349        0.0742993033     0.0027   2026-09-08 10:27:33
   235    238    0.0003328234    0.0006590996     2739.3636021438    0.0000022206        0.0738484639     0.0028   2026-09-08 10:27:33
   236    239    0.0004219811    0.0008398858     2739.3635974182    0.0000047255        0.0732287929     0.0026   2026-09-08 10:27:33
   237    240    0.0007144137    0.0014363314     2739.3635839905    0.0000134278        0.0720216919     0.0029   2026-09-08 10:27:33
   238    241    0.0010308652    0.0021172835     2739.3635501527    0.0000338378        0.0698578718     0.0027   2026-09-08 10:27:33
   239    242    0.0014429418    0.0031215872     2739.3634620610    0.0000880917        0.0656429274     0.0023   2026-09-08 10:27:33
   240    243    0.0016331420    0.0041808588     2739.3632428295    0.0002192315        0.0573715310     0.0023   2026-09-08 10:27:33
   241    244    0.0018756433    0.0054558887     2739.3627316610    0.0005111685        0.0542162949     0.0020   2026-09-08 10:27:33
   242    245    0.0031033161    0.0102844109     2739.3617311607    0.0010005004        0.0521939378     0.0022   2026-09-08 10:27:33
   243    246    0.0098352657    0.0213430905     2739.3603820052    0.0013491554        0.0524912737     0.0022   2026-09-08 10:27:33
   244    247    0.0128366874    0.0250160969     2739.3594539769    0.0009280283        0.0420144564     0.0021   2026-09-08 10:27:33
   245    248    0.0061286906    0.0119003747     2739.3592111348    0.0002428421        0.0302018218     0.0020   2026-09-08 10:27:33
   246    249    0.0006565948    0.0019641521     2739.3591911123    0.0000200225        0.0283037968     0.0022   2026-09-08 10:27:33
   247    250    0.0001971587    0.0004919616     2739.3591905958    0.0000005165        0.0283344258     0.0019   2026-09-08 10:27:33
   248    251    0.0000405156    0.0000836029     2739.3591905427    0.0000000531        0.0283256199     0.0022   2026-09-08 10:27:33
   249    252    0.0001439533    0.0002968813     2739.3591902539    0.0000002888        0.0283069527     0.0028   2026-09-08 10:27:33
   250    253    0.0001784550    0.0003713707     2739.3591896566    0.0000005973        0.0282995569     0.0028   2026-09-08 10:27:33
   251    254    0.0003109059    0.0006572185     2739.3591879351    0.0000017215        0.0282965464     0.0026   2026-09-08 10:27:33
   252    255    0.0004598937    0.0010004071     2739.3591836017    0.0000043334        0.0282781955     0.0026   2026-09-08 10:27:33
   253    256    0.0006870182    0.0015789161     2739.3591721965    0.0000114052        0.0281714968     0.0023   2026-09-08 10:27:33
   254    257    0.0009771344    0.0023702829     2739.3591431553    0.0000290412        0.0282321066     0.0023   2026-09-08 10:27:33
   255    258    0.0014714299    0.0034247598     2739.3590712725    0.0000718827        0.0298730796     0.0024   2026-09-08 10:27:33
   256    259    0.0019030460    0.0048215021     2739.3589090403    0.0001622322        0.0329998914     0.0027   2026-09-08 10:27:33
   257    260    0.0029008635    0.0078031595     2739.3586123310    0.0002967093        0.0345701822     0.0027   2026-09-08 10:27:33
   258    261    0.0068563664    0.0128601752     2739.3582631672    0.0003491638        0.0311744702     0.0025   2026-09-08 10:27:33
   259    262    0.0071386205    0.0126813053     2739.3580692934    0.0001938738        0.0240989411     0.0024   2026-09-08 10:27:33
   260    263    0.0025144137    0.0053374704     2739.3580306866    0.0000386068        0.0200214501     0.0026   2026-09-08 10:27:33
   261    264    0.0003981537    0.0010148074     2739.3580283318    0.0000023548        0.0193874495     0.0027   2026-09-08 10:27:33
   262    265    0.0000878954    0.0001821971     2739.3580282826    0.0000000492        0.0194253954     0.0022   2026-09-08 10:27:33
   263    266    0.0000193259    0.0000357242     2739.3580282721    0.0000000105        0.0194432363     0.0020   2026-09-08 10:27:33
   264    267    0.0000841910    0.0001557520     2739.3580282013    0.0000000708        0.0195240345     0.0020   2026-09-08 10:27:33
   265    268    0.0001013001    0.0001889382     2739.3580280590    0.0000001423        0.0196209774     0.0020   2026-09-08 10:27:33
   266    269    0.0001793860    0.0003393052     2739.3580276434    0.0000004156        0.0197902918     0.0028   2026-09-08 10:27:33
   267    270    0.0002652979    0.0005149847     2739.3580266016    0.0000010418        0.0200347479     0.0021   2026-09-08 10:27:33
   268    271    0.0004008938    0.0008182568     2739.3580238512    0.0000027504        0.0203885553     0.0022   2026-09-08 10:27:33
   269    272    0.0005452310    0.0012422570     2739.3580168287    0.0000070225        0.0208270629     0.0027   2026-09-08 10:27:33
   270    273    0.0006113912    0.0018497054     2739.3579992903    0.0000175384        0.0211872333     0.0026   2026-09-08 10:27:33
   271    274    0.0009133996    0.0027585389     2739.3579588517    0.0000404386        0.0208856695     0.0026   2026-09-08 10:27:33
   272    275    0.0025010988    0.0046037541     2739.3578811622    0.0000776896        0.0186278007     0.0026   2026-09-08 10:27:33
   273    276    0.0048276674    0.0075633544     2739.3577804893    0.0001006729        0.0134214772     0.0027   2026-09-08 10:27:33
   274    277    0.0047150066    0.0078630678     2739.3577154780    0.0000650113        0.0093720120     0.0027   2026-09-08 10:27:33
   275    278    0.0020570226    0.0036975146     2739.3576998137    0.0000156643        0.0093681528     0.0027   2026-09-08 10:27:33
   276    279    0.0002776994    0.0008256120     2739.3576986364    0.0000011773        0.0094867688     0.0026   2026-09-08 10:27:33
   277    280    0.0000999646    0.0001609914     2739.3576986087    0.0000000277        0.0094093033     0.0027   2026-09-08 10:27:33
   278    281    0.0000146959    0.0000233809     2739.3576986058    0.0000000030        0.0093942629     0.0020   2026-09-08 10:27:34
   279    282    0.0000556765    0.0000892058     2739.3576985884    0.0000000174        0.0093333979     0.0021   2026-09-08 10:27:34
   280    283    0.0000681810    0.0001100556     2739.3576985529    0.0000000355        0.0092537346     0.0020   2026-09-08 10:27:34
   281    284    0.0001200879    0.0001961540     2739.3576984501    0.0000001028        0.0091028295     0.0020   2026-09-08 10:27:34
   282    285    0.0001787556    0.0002983126     2739.3576981917    0.0000002584        0.0088546592     0.0021   2026-09-08 10:27:34
   283    286    0.0002716313    0.0004720495     2739.3576975104    0.0000006813        0.0084170539     0.0022   2026-09-08 10:27:34
   284    287    0.0003743970    0.0007091802     2739.3576957719    0.0000017385        0.0076495409     0.0023   2026-09-08 10:27:34
   285    288    0.0005190192    0.0010183987     2739.3576914412    0.0000043307        0.0080274232     0.0023   2026-09-08 10:27:34
   286    289    0.0008228292    0.0013753394     2739.3576815150    0.0000099261        0.0084583766     0.0023   2026-09-08 10:27:34
   287    290    0.0010612906    0.0020807361     2739.3576627083    0.0000188068        0.0078910895     0.0024   2026-09-08 10:27:34
   288    291    0.0023648253    0.0036361504     2739.3576389999    0.0000237084        0.0053573177     0.0023   2026-09-08 10:27:34
   289    292    0.0028794148    0.0040725890     2739.3576243453    0.0000146546        0.0025134240     0.0025   2026-09-08 10:27:34

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.619205e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -0.9807     0.6037   0.1043   
TC/100 EUR                        -1.2931     0.8369   0.1223   
Babiogorski                        0.4536     0.6118   0.4585   
Bialowieski                       -0.4697     0.5585   0.4003   
Biebrzanski                        0.2100     0.6984   0.7636   
Bieszczadzki                       0.2759     0.4123   0.5033   
BoryTucholskie                     0.0219     0.3773   0.9537   
Drawienski                        -0.2487     0.5383   0.6441   
Gorczanski                         0.3030     0.8520   0.7221   
GorStolowych                       0.7454**   0.3627   0.0399   
Kampinoski                        -0.2365     0.2481   0.3404   
Karkonoski                        -0.8876***  0.3024   0.0033   
Magurski                           0.2634     0.4690   0.5745   
Narwianski                         0.3721     0.6921   0.5908   
Ojcowski                           0.7709*    0.3955   0.0513   
Pieninski                         -1.3184*    0.7485   0.0782   
Poleski                           -0.1398     0.3903   0.7203   
Roztoczanski                      -0.1037     0.3437   0.7628   
Slowinski                         -0.7529**   0.3643   0.0387   
Swietokrzyski                      0.3487     0.3538   0.3243   
UjscieWarty                       -0.8697**   0.3932   0.0270   
Wielkopolski                       0.8712***  0.3232   0.0070   
Wigierski                         -0.0095     0.4398   0.9828   
Wolinski                           0.9989**   0.3913   0.0107   
Household income (10k PLN)         0.2589**   0.1025   0.0116   
Male                               0.1271*    0.0721   0.0779   
Higher education                   0.0210     0.0804   0.7939   
City                               0.1711**   0.0781   0.0285   
Winter                             0.8024***  0.0840   0.0000   
Hiking                             2.0642***  0.0794   0.0000   
Skiing                             1.3831***  0.2672   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2812     0.0952            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.7733     0.5005   0.1223   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2739.3576
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1777
AIC/n:                             0.9467
BIC/n:                             0.9831
n (observations):               5855
r (respondents):                5855
k (parameters):                   32
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.2499
median                           0.0000          2.2582
std                              0.7834          0.9431
min                              0.0000          0.0340
max                             20.0000          4.5242
quantile 0.025                   0.0000          0.6513
quantile 0.975                   2.0000          3.9440
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:34
Estimation took 0.97595 seconds (0 hours 0 minutes 0.97595 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.62 0.39 -0.096 0.012 0.057 -0.023 -0.029 0.2 0.12 -0.028 -0.12 0.051 0.044 0.22 -0.35 0.034 0.03 -0.025 0.0039 -0.027 0.048 0.027 0.091 0.061 0.0096 0.0037 0.019 0.18 0.44 0.29 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3916.7324884160             NaN     4178.0755797400     0.0009   2026-09-08 10:27:34
     1      4    0.0354476711    0.1292275026     3248.4996161103  668.2328723056     1114.0015941982     0.0081   2026-09-08 10:27:34
     2      5    0.0073740883    0.0216946027     3200.5417413529   47.9578747574      474.9578359016     0.0024   2026-09-08 10:27:34
     3      6    0.0056843736    0.0162459581     3186.4530283643   14.0887129886      388.6421289054     0.0023   2026-09-08 10:27:34
     4      7    0.0064508206    0.0152215294     3175.7201593894   10.7328689749      410.9702434595     0.0023   2026-09-08 10:27:34
     5      8    0.0286356361    0.0642797066     3144.1681679730   31.5519914164      416.2949463741     0.0024   2026-09-08 10:27:34
     6      9    0.0168658186    0.0346048320     3131.4963097369   12.6718582361      330.2149265841     0.0024   2026-09-08 10:27:34
     7     10    0.0131938763    0.0227153525     3125.2026588041    6.2936509328      348.1530186840     0.0026   2026-09-08 10:27:34
     8     11    0.0092637802    0.0123707120     3122.2572951522    2.9453636519      359.7919346263     0.0021   2026-09-08 10:27:34
     9     12    0.0285076697    0.0350763827     3114.1750165918    8.0822785604      377.1732804020     0.0027   2026-09-08 10:27:34
    10     13    0.0678778960    0.0811143505     3096.3002875135   17.8747290784      488.9207281452     0.0027   2026-09-08 10:27:34
    11     14    0.1663925945    0.1967833410     3055.2080507436   41.0922367698      712.6227703212     0.0028   2026-09-08 10:27:34
    12     15    0.3328256481    0.3921084590     2979.9322413865   75.2758093571      851.0049342750     0.0021   2026-09-08 10:27:34
    13     16    0.4852890199    0.5713432336     2887.8329100412   92.0993313453      749.6648019894     0.0020   2026-09-08 10:27:34
    14     17    0.3371889452    0.3979541824     2839.3389854301   48.4939246111      482.7900295225     0.0020   2026-09-08 10:27:34
    15     18    0.0405277485    0.0515053087     2825.9361466350   13.4028387951      255.7559247506     0.0023   2026-09-08 10:27:34
    16     19    0.0713906266    0.0857251358     2820.1207566102    5.8153900248      140.7401617218     0.0020   2026-09-08 10:27:34
    17     20    0.0600438249    0.0714178370     2818.2650059188    1.8557506915      168.3951387360     0.0024   2026-09-08 10:27:34
    18     21    0.0466649842    0.0562716464     2816.1561102680    2.1088956507      167.3576431139     0.0026   2026-09-08 10:27:34
    19     22    0.0477920257    0.0621965248     2811.5086488581    4.6474614099      146.6913829470     0.0025   2026-09-08 10:27:34
    20     23    0.0132811496    0.0392180525     2804.7747463367    6.7339025215       93.0740493573     0.0022   2026-09-08 10:27:34
    21     24    0.0908653295    0.1113271216     2799.1672728304    5.6074735063       41.8978533615     0.0020   2026-09-08 10:27:34
    22     25    0.0903747779    0.1064234360     2797.4330665127    1.7342063177       24.2935393811     0.0019   2026-09-08 10:27:34
    23     26    0.0281441408    0.0332518942     2797.2646013672    0.1684651454       23.1149031183     0.0023   2026-09-08 10:27:34
    24     27    0.0044171208    0.0054423409     2797.2379416384    0.0266597289       23.3116733388     0.0019   2026-09-08 10:27:34
    25     28    0.0055217611    0.0071513550     2797.1776194787    0.0603221597       23.7922955753     0.0021   2026-09-08 10:27:34
    26     29    0.0077506014    0.0108714896     2797.0340976444    0.1435218343       24.5244006853     0.0021   2026-09-08 10:27:34
    27     30    0.0126097119    0.0208063908     2796.6583480613    0.3757495831       25.6197445118     0.0021   2026-09-08 10:27:34
    28     31    0.0192557233    0.0422598191     2795.7442473826    0.9141006788       35.0220077986     0.0020   2026-09-08 10:27:34
    29     32    0.0408606867    0.0888171930     2793.6884515826    2.0557957999       53.8267050580     0.0021   2026-09-08 10:27:34
    30     33    0.0775132593    0.1621817629     2789.9839592897    3.7044922929       68.6593259186     0.0024   2026-09-08 10:27:34
    31     34    0.0955594270    0.1998674659     2785.7517361964    4.2322230933       59.4744947726     0.0025   2026-09-08 10:27:34
    32     35    0.0453185695    0.1054629601     2783.5946094673    2.1571267291       27.1678987797     0.0020   2026-09-08 10:27:35
    33     36    0.0233508586    0.0325307961     2783.1924196921    0.4021897752       18.3875958564     0.0019   2026-09-08 10:27:35
    34     37    0.0083160612    0.0185114188     2783.1566580539    0.0357616382       16.8010132261     0.0019   2026-09-08 10:27:35
    35     38    0.0029717755    0.0068025577     2783.1401676290    0.0164904249       15.9182315969     0.0019   2026-09-08 10:27:35
    36     39    0.0073341256    0.0183078018     2783.0681871303    0.0719804988       16.6783802117     0.0020   2026-09-08 10:27:35
    37     40    0.0091373235    0.0227300817     2782.9116146494    0.1565724809       17.8471996692     0.0025   2026-09-08 10:27:35
    38     41    0.0143938120    0.0365904019     2782.4781423748    0.4334722746       19.7283439905     0.0022   2026-09-08 10:27:35
    39     42    0.0199991714    0.0589440650     2781.4205580058    1.0575843690       26.6590079035     0.0021   2026-09-08 10:27:35
    40     43    0.0559911405    0.1279064352     2778.9209513961    2.4996066097       38.2866285581     0.0019   2026-09-08 10:27:35
    41     44    0.1654152699    0.2895019152     2774.0169573598    4.9039940363       52.8779734836     0.0020   2026-09-08 10:27:35
    42     45    0.3027746561    0.4909527809     2767.3997797900    6.6171775698       58.0014581844     0.0019   2026-09-08 10:27:35
    43     46    0.2714748622    0.4358358606     2762.9162096999    4.4835700900       42.0870210274     0.0019   2026-09-08 10:27:35
    44     47    0.0721561714    0.1409758398     2761.7516578425    1.1645518574       24.7880164532     0.0023   2026-09-08 10:27:35
    45     48    0.0145395587    0.0354090073     2761.6498130962    0.1018447463       20.4001674654     0.0020   2026-09-08 10:27:35
    46     49    0.0069709743    0.0126669042     2761.6259864436    0.0238266526       20.6474923636     0.0018   2026-09-08 10:27:35
    47     50    0.0166347028    0.0299723958     2761.5378226494    0.0881637942       20.8578683911     0.0019   2026-09-08 10:27:35
    48     51    0.0183965038    0.0341790795     2761.3524038998    0.1854187496       20.9393312845     0.0019   2026-09-08 10:27:35
    49     52    0.0210991612    0.0417226228     2760.8831214975    0.4692824023       20.5306576949     0.0020   2026-09-08 10:27:35
    50     53    0.0190443149    0.0398526363     2759.9544883372    0.9286331603       18.5140516154     0.0020   2026-09-08 10:27:35
    51     54    0.0548437976    0.1063057889     2758.5876119240    1.3668764131       13.4682210384     0.0020   2026-09-08 10:27:35
    52     55    0.1010661179    0.1761101822     2757.5427975889    1.0448143351        9.0856494730     0.0019   2026-09-08 10:27:35
    53     56    0.0656157187    0.1134925721     2757.2278475737    0.3149500152        8.7159007885     0.0020   2026-09-08 10:27:35
    54     57    0.0130686953    0.0247403555     2757.1907138469    0.0371337268        8.9215027493     0.0022   2026-09-08 10:27:35
    55     58    0.0013464513    0.0030150379     2757.1852434150    0.0054704319        8.9236806611     0.0022   2026-09-08 10:27:35
    56     59    0.0015238102    0.0037764563     2757.1748964656    0.0103469495        8.9007990059     0.0021   2026-09-08 10:27:35
    57     60    0.0022521747    0.0059503368     2757.1475609743    0.0273354913        8.8775218241     0.0022   2026-09-08 10:27:35
    58     61    0.0031467302    0.0094005714     2757.0779910945    0.0695698797       10.6474349625     0.0021   2026-09-08 10:27:35
    59     62    0.0071369874    0.0180979553     2756.9040085160    0.1739825785       13.1557535756     0.0021   2026-09-08 10:27:35
    60     63    0.0219347802    0.0418239482     2756.5033191394    0.4006893766       16.0357410469     0.0027   2026-09-08 10:27:35
    61     64    0.0511933564    0.0913232931     2755.7379842464    0.7653348930       17.4333506362     0.0019   2026-09-08 10:27:35
    62     65    0.0793574232    0.1414694570     2754.7723660378    0.9656182086       14.0367980442     0.0020   2026-09-08 10:27:35
    63     66    0.0601526842    0.1119184256     2754.1775487357    0.5948173020        9.9790305583     0.0018   2026-09-08 10:27:35
    64     67    0.0147502666    0.0321080953     2754.0279911236    0.1495576121        8.5972899474     0.0019   2026-09-08 10:27:35
    65     68    0.0053515774    0.0110261330     2754.0116441503    0.0163469734        8.3846553533     0.0024   2026-09-08 10:27:35
    66     69    0.0029357287    0.0051547620     2754.0068361462    0.0048080041        8.3797071716     0.0021   2026-09-08 10:27:35
    67     70    0.0062374242    0.0110069891     2753.9909937084    0.0158424378        8.4579324997     0.0019   2026-09-08 10:27:35
    68     71    0.0076559295    0.0139493844     2753.9551091498    0.0358845587        8.6101901147     0.0020   2026-09-08 10:27:35
    69     72    0.0096703995    0.0197649543     2753.8586664239    0.0964427258        8.8313344739     0.0019   2026-09-08 10:27:35
    70     73    0.0101516389    0.0249824834     2753.6275545098    0.2311119141        8.9502990393     0.0019   2026-09-08 10:27:35
    71     74    0.0181156686    0.0504396343     2753.1154240974    0.5121304124        8.4751739396     0.0020   2026-09-08 10:27:35
    72     75    0.0584810253    0.1247203500     2752.2398005945    0.8756235029        6.7654761128     0.0022   2026-09-08 10:27:35
    73     76    0.1069384820    0.1975073673     2751.3355887733    0.9042118212        6.9937114918     0.0019   2026-09-08 10:27:35
    74     77    0.0821122250    0.1422824189     2750.9290295342    0.4065592391        9.1760319683     0.0019   2026-09-08 10:27:35
    75     78    0.0194686086    0.0346070340     2750.8630280027    0.0660015315       10.6275005703     0.0019   2026-09-08 10:27:35
    76     79    0.0025883345    0.0073254403     2750.8573960898    0.0056319129       10.7469368743     0.0019   2026-09-08 10:27:35
    77     80    0.0017346821    0.0043625016     2750.8541572150    0.0032388748       10.7363640210     0.0020   2026-09-08 10:27:35
    78     81    0.0041413949    0.0100135068     2750.8423938235    0.0117633915       10.6607225113     0.0020   2026-09-08 10:27:35
    79     82    0.0051658186    0.0126653097     2750.8158905596    0.0265032640       10.4738038021     0.0024   2026-09-08 10:27:35
    80     83    0.0066098438    0.0178278786     2750.7459291902    0.0699613694        9.9639700224     0.0020   2026-09-08 10:27:35
    81     84    0.0109755210    0.0223479959     2750.5853647576    0.1605644326        8.7644686866     0.0019   2026-09-08 10:27:35
    82     85    0.0217877725    0.0438787195     2750.2640068559    0.3213579018        6.2801799129     0.0019   2026-09-08 10:27:35
    83     86    0.0377741514    0.0936785936     2749.8220577245    0.4419491313        6.2060298435     0.0019   2026-09-08 10:27:35
    84     87    0.0443344016    0.1107255093     2749.5117327038    0.3103250207        4.0036240564     0.0019   2026-09-08 10:27:35
    85     88    0.0219112375    0.0512553944     2749.4305721134    0.0811605904        3.5188008045     0.0018   2026-09-08 10:27:35
    86     89    0.0038362960    0.0084412590     2749.4235432039    0.0070289096        3.6391081525     0.0021   2026-09-08 10:27:35
    87     90    0.0010690329    0.0019401533     2749.4230178209    0.0005253830        3.5937584545     0.0022   2026-09-08 10:27:35
    88     91    0.0011083585    0.0021238369     2749.4221742130    0.0008436079        3.5329452179     0.0022   2026-09-08 10:27:35
    89     92    0.0019134594    0.0036940575     2749.4197504726    0.0024237404        3.4032963531     0.0021   2026-09-08 10:27:35
    90     93    0.0027215210    0.0053590540     2749.4137520536    0.0059984190        3.1540084867     0.0021   2026-09-08 10:27:35
    91     94    0.0037006368    0.0079799718     2749.3985332512    0.0152188025        2.6325442661     0.0022   2026-09-08 10:27:35
    92     95    0.0061106420    0.0119476275     2749.3633309841    0.0352022671        2.9136544276     0.0020   2026-09-08 10:27:35
    93     96    0.0108321537    0.0213512347     2749.2943876402    0.0689433439        3.4446663024     0.0029   2026-09-08 10:27:35
    94     97    0.0184626128    0.0372491553     2749.2022782157    0.0921094244        3.6599010839     0.0020   2026-09-08 10:27:35
    95     98    0.0187723319    0.0400175312     2749.1390924961    0.0631857196        4.0298032813     0.0019   2026-09-08 10:27:35
    96     99    0.0097564722    0.0192699136     2749.1217474472    0.0173450489        3.8434718089     0.0019   2026-09-08 10:27:35
    97    100    0.0021040561    0.0042667975     2749.1199608809    0.0017865663        3.4784058808     0.0019   2026-09-08 10:27:35
    98    101    0.0006757756    0.0012339982     2749.1195487761    0.0004121047        3.3566375570     0.0020   2026-09-08 10:27:35
    99    102    0.0014428067    0.0025496057     2749.1182134395    0.0013353366        3.0957576432     0.0020   2026-09-08 10:27:35
   100    103    0.0020807678    0.0033138288     2749.1151383928    0.0030750468        2.7213833691     0.0019   2026-09-08 10:27:35
   101    104    0.0036317784    0.0050375364     2749.1067274630    0.0084109298        2.2456543455     0.0019   2026-09-08 10:27:35
   102    105    0.0059256331    0.0078409055     2749.0854210727    0.0213063903        2.1470734316     0.0020   2026-09-08 10:27:35
   103    106    0.0098544398    0.0177376020     2749.0313000739    0.0541209988        2.2526575634     0.0019   2026-09-08 10:27:35
   104    107    0.0208425251    0.0477795509     2748.9029192343    0.1283808396        3.2255554039     0.0020   2026-09-08 10:27:35
   105    108    0.0566177908    0.1160181671     2748.6379782194    0.2649410149        6.4356928434     0.0019   2026-09-08 10:27:35
   106    109    0.1061229540    0.2076331771     2748.2414060429    0.3965721765        8.5665070792     0.0018   2026-09-08 10:27:35
   107    110    0.1095413774    0.2086937062     2747.9160786510    0.3253273920        7.2234694309     0.0022   2026-09-08 10:27:35
   108    111    0.0392321478    0.0747363811     2747.8069193371    0.1091593138        4.9286018061     0.0019   2026-09-08 10:27:35
   109    112    0.0085933183    0.0166557294     2747.7940238063    0.0128955309        4.9969301365     0.0020   2026-09-08 10:27:35
   110    113    0.0047292087    0.0095593494     2747.7929735670    0.0010502393        4.9597660650     0.0020   2026-09-08 10:27:35
   111    114    0.0034105162    0.0068380867     2747.7919324503    0.0010411167        4.9273550926     0.0020   2026-09-08 10:27:35
   112    115    0.0067546985    0.0136721972     2747.7885061918    0.0034262585        4.8488310786     0.0019   2026-09-08 10:27:35
   113    116    0.0088258700    0.0182772542     2747.7804350309    0.0080711609        4.7079325678     0.0020   2026-09-08 10:27:35
   114    117    0.0114155990    0.0250241738     2747.7595356256    0.0208994053        4.4138820071     0.0022   2026-09-08 10:27:35
   115    118    0.0087743898    0.0248307775     2747.7115200189    0.0480156067        3.8421756866     0.0020   2026-09-08 10:27:35
   116    119    0.0120423342    0.0241724449     2747.6170188741    0.0945011448        2.8467329558     0.0020   2026-09-08 10:27:35
   117    120    0.0450092814    0.0819800528     2747.4903092641    0.1267096100        1.9781394250     0.0019   2026-09-08 10:27:35
   118    121    0.0655981159    0.1220046238     2747.4037750731    0.0865341910        2.2474953756     0.0020   2026-09-08 10:27:35
   119    122    0.0341419398    0.0666715135     2747.3814654960    0.0223095771        2.1820830189     0.0021   2026-09-08 10:27:35
   120    123    0.0040654829    0.0099999329     2747.3795939311    0.0018715648        1.8972152667     0.0027   2026-09-08 10:27:35
   121    124    0.0006001759    0.0012562791     2747.3794335206    0.0001604106        1.8240555683     0.0028   2026-09-08 10:27:35
   122    125    0.0008869873    0.0017362198     2747.3791450188    0.0002885017        1.7360405250     0.0025   2026-09-08 10:27:35
   123    126    0.0014292648    0.0028614378     2747.3783595537    0.0007854652        1.5812885304     0.0020   2026-09-08 10:27:35
   124    127    0.0019399195    0.0041467536     2747.3763739704    0.0019855833        1.6263065159     0.0021   2026-09-08 10:27:35
   125    128    0.0030594678    0.0057593803     2747.3713547912    0.0050191791        1.7080986656     0.0021   2026-09-08 10:27:35
   126    129    0.0048089936    0.0075584386     2747.3595918954    0.0117628959        1.6736140364     0.0020   2026-09-08 10:27:35
   127    130    0.0063415390    0.0131816778     2747.3359908916    0.0236010038        1.2654898318     0.0025   2026-09-08 10:27:35
   128    131    0.0140459018    0.0272505612     2747.3026173838    0.0333735078        1.5459621504     0.0020   2026-09-08 10:27:35
   129    132    0.0193840046    0.0342574208     2747.2776390368    0.0249783469        1.4691657208     0.0019   2026-09-08 10:27:35
   130    133    0.0100428849    0.0182090360     2747.2702773018    0.0073617350        1.6414750858     0.0020   2026-09-08 10:27:35
   131    134    0.0020508066    0.0034281711     2747.2695192107    0.0007580911        1.6627767396     0.0018   2026-09-08 10:27:35
   132    135    0.0003706876    0.0008340971     2747.2694146569    0.0001045539        1.6330604735     0.0021   2026-09-08 10:27:35
   133    136    0.0004916537    0.0012336933     2747.2691849393    0.0002297175        1.5835412381     0.0024   2026-09-08 10:27:35
   134    137    0.0007981811    0.0018296644     2747.2685986885    0.0005862508        1.5029389320     0.0024   2026-09-08 10:27:35
   135    138    0.0013238015    0.0026739556     2747.2670593900    0.0015392985        1.3689003953     0.0027   2026-09-08 10:27:35
   136    139    0.0021695462    0.0038300197     2747.2630896199    0.0039697701        1.1483245666     0.0020   2026-09-08 10:27:35
   137    140    0.0035320692    0.0067828533     2747.2530064752    0.0100831447        1.0474493302     0.0019   2026-09-08 10:27:35
   138    141    0.0070096230    0.0170946021     2747.2286620421    0.0243444331        1.3049212145     0.0019   2026-09-08 10:27:35
   139    142    0.0211711759    0.0438238556     2747.1765663390    0.0520957031        2.0080832839     0.0019   2026-09-08 10:27:35
   140    143    0.0440631176    0.0870074602     2747.0920144744    0.0845518647        2.2193688159     0.0021   2026-09-08 10:27:35
   141    144    0.0532547546    0.1035200031     2747.0120892514    0.0799252230        2.7571563199     0.0022   2026-09-08 10:27:35
   142    145    0.0253962789    0.0502095542     2746.9798092787    0.0322799727        2.9252371771     0.0021   2026-09-08 10:27:35
   143    146    0.0041263912    0.0073968928     2746.9753245131    0.0044847657        2.7714757474     0.0022   2026-09-08 10:27:35
   144    147    0.0025492299    0.0051616048     2746.9750575981    0.0002669149        2.7039688659     0.0021   2026-09-08 10:27:35
   145    148    0.0009717763    0.0019105146     2746.9749520520    0.0001055461        2.6784296526     0.0019   2026-09-08 10:27:35
   146    149    0.0026514086    0.0051967876     2746.9744954476    0.0004566045        2.5922044605     0.0020   2026-09-08 10:27:35
   147    150    0.0032457666    0.0063605564     2746.9735207513    0.0009746963        2.4437796284     0.0025   2026-09-08 10:27:35
   148    151    0.0045769170    0.0090192337     2746.9709691723    0.0025515790        2.1108779594     0.0024   2026-09-08 10:27:35
   149    152    0.0039619617    0.0082931332     2746.9655469745    0.0054221978        1.4765010657     0.0020   2026-09-08 10:27:35
   150    153    0.0051302303    0.0067685746     2746.9562511087    0.0092958659        0.4613637418     0.0021   2026-09-08 10:27:35
   151    154    0.0110121877    0.0230505424     2746.9468005576    0.0094505511        0.4894899016     0.0021   2026-09-08 10:27:35
   152    155    0.0133586998    0.0265294142     2746.9425362538    0.0042643037        0.7234325416     0.0021   2026-09-08 10:27:35
   153    156    0.0052048142    0.0101985556     2746.9418699094    0.0006663444        0.5423699068     0.0026   2026-09-08 10:27:35
   154    157    0.0004538114    0.0009907855     2746.9418273222    0.0000425873        0.4536767424     0.0023   2026-09-08 10:27:35
   155    158    0.0001367450    0.0001583912     2746.9418126947    0.0000146275        0.4262792579     0.0027   2026-09-08 10:27:35
   156    159    0.0003777884    0.0004372211     2746.9417502310    0.0000624637        0.4170321527     0.0021   2026-09-08 10:27:35
   157    160    0.0005123510    0.0005698119     2746.9416132655    0.0001369655        0.4186088718     0.0021   2026-09-08 10:27:35
   158    161    0.0009007620    0.0009993929     2746.9412312495    0.0003820160        0.4197305936     0.0019   2026-09-08 10:27:35
   159    162    0.0014194249    0.0018327766     2746.9402753688    0.0009558808        0.4217412712     0.0029   2026-09-08 10:27:35
   160    163    0.0022558028    0.0042276947     2746.9378680188    0.0024073500        0.6655148208     0.0021   2026-09-08 10:27:35
   161    164    0.0041715874    0.0101597084     2746.9323272266    0.0055407922        1.3033128096     0.0020   2026-09-08 10:27:35
   162    165    0.0091317655    0.0215913537     2746.9216363465    0.0106908801        1.9775081878     0.0021   2026-09-08 10:27:35
   163    166    0.0136609028    0.0322928774     2746.9076952702    0.0139410763        2.1513412923     0.0020   2026-09-08 10:27:35
   164    167    0.0101579311    0.0243980808     2746.8985697458    0.0091255243        1.5075129245     0.0020   2026-09-08 10:27:35
   165    168    0.0034975861    0.0052249090     2746.8962975895    0.0022721564        1.6584101184     0.0020   2026-09-08 10:27:35
   166    169    0.0011322857    0.0028228990     2746.8960807853    0.0002168042        1.6280722252     0.0022   2026-09-08 10:27:35
   167    170    0.0004682061    0.0011161416     2746.8960289035    0.0000518818        1.6078129242     0.0021   2026-09-08 10:27:35
   168    171    0.0009511030    0.0022839767     2746.8958616046    0.0001672988        1.5596800380     0.0020   2026-09-08 10:27:35
   169    172    0.0012071867    0.0029254309     2746.8954784964    0.0003831082        1.4833148089     0.0020   2026-09-08 10:27:35
   170    173    0.0016415875    0.0040326522     2746.8944561168    0.0010223796        1.3358355473     0.0019   2026-09-08 10:27:35
   171    174    0.0017672888    0.0040651941     2746.8920168266    0.0024392902        1.0699360998     0.0019   2026-09-08 10:27:35
   172    175    0.0030398688    0.0050017930     2746.8866867439    0.0053300827        0.6109129666     0.0021   2026-09-08 10:27:35
   173    176    0.0074983307    0.0172271053     2746.8778020960    0.0088846479        0.7774936827     0.0024   2026-09-08 10:27:35
   174    177    0.0141436355    0.0317738711     2746.8689486298    0.0088534662        0.7105097298     0.0021   2026-09-08 10:27:35
   175    178    0.0108975453    0.0248234473     2746.8651145961    0.0038340337        0.4446767311     0.0020   2026-09-08 10:27:35
   176    179    0.0024907229    0.0060507233     2746.8645424691    0.0005721270        0.4259758143     0.0019   2026-09-08 10:27:35
   177    180    0.0003724015    0.0007293483     2746.8645108735    0.0000315956        0.4332476642     0.0019   2026-09-08 10:27:35
   178    181    0.0001434332    0.0003318789     2746.8645032430    0.0000076305        0.4341324580     0.0020   2026-09-08 10:27:35
   179    182    0.0004154816    0.0009666366     2746.8644694712    0.0000337718        0.4363156209     0.0025   2026-09-08 10:27:35
   180    183    0.0005169952    0.0012287097     2746.8643963228    0.0000731484        0.4388276325     0.0020   2026-09-08 10:27:35
   181    184    0.0008035516    0.0020022542     2746.8641903729    0.0002059500        0.4422439632     0.0020   2026-09-08 10:27:35
   182    185    0.0010171840    0.0028055302     2746.8636713549    0.0005190180        0.4451385222     0.0020   2026-09-08 10:27:35
   183    186    0.0018494687    0.0040885744     2746.8623317028    0.0013396521        0.4435421720     0.0019   2026-09-08 10:27:35
   184    187    0.0035650217    0.0073043462     2746.8590593292    0.0032723735        0.5913332360     0.0020   2026-09-08 10:27:35
   185    188    0.0098517508    0.0177880034     2746.8517818643    0.0072774649        0.9370856760     0.0019   2026-09-08 10:27:35
   186    189    0.0223909379    0.0394244545     2746.8389896160    0.0127922484        1.1651578909     0.0021   2026-09-08 10:27:35
   187    190    0.0312092900    0.0569999352     2746.8250014506    0.0139881654        0.9446037748     0.0020   2026-09-08 10:27:35
   188    191    0.0190720344    0.0384704112     2746.8180546368    0.0069468138        0.3805910240     0.0019   2026-09-08 10:27:35
   189    192    0.0030293379    0.0079732904     2746.8168465344    0.0012081024        0.1996396842     0.0020   2026-09-08 10:27:35
   190    193    0.0017294033    0.0030909820     2746.8167816050    0.0000649295        0.1990557053     0.0019   2026-09-08 10:27:35
   191    194    0.0003867540    0.0006922537     2746.8167788136    0.0000027914        0.1989410118     0.0020   2026-09-08 10:27:35
   192    195    0.0003438337    0.0006223391     2746.8167749381    0.0000038755        0.1988582736     0.0020   2026-09-08 10:27:35
   193    196    0.0006567185    0.0011999476     2746.8167628509    0.0000120872        0.1985753302     0.0023   2026-09-08 10:27:35
   194    197    0.0009571907    0.0017779796     2746.8167331997    0.0000296512        0.1978948687     0.0020   2026-09-08 10:27:35
   195    198    0.0014918326    0.0028557798     2746.8166538505    0.0000793492        0.1962897459     0.0020   2026-09-08 10:27:35
   196    199    0.0021232400    0.0043202256     2746.8164496809    0.0002041696        0.1927616002     0.0020   2026-09-08 10:27:35
   197    200    0.0028860102    0.0063782134     2746.8159241142    0.0005255667        0.2095175553     0.0019   2026-09-08 10:27:35
   198    201    0.0039843396    0.0089527367     2746.8146212083    0.0013029059        0.2437811502     0.0020   2026-09-08 10:27:35
   199    202    0.0060373756    0.0133403921     2746.8116402689    0.0029809394        0.2837427092     0.0019   2026-09-08 10:27:35
   200    203    0.0120460866    0.0258616293     2746.8060359994    0.0056042695        0.3044559671     0.0022   2026-09-08 10:27:35
   201    204    0.0280382037    0.0460063408     2746.7990692503    0.0069667491        0.2599743788     0.0020   2026-09-08 10:27:35
   202    205    0.0288486829    0.0454366598     2746.7948605248    0.0042087255        0.2068533731     0.0021   2026-09-08 10:27:35
   203    206    0.0101079838    0.0181623738     2746.7939275442    0.0009329806        0.2106015528     0.0019   2026-09-08 10:27:35
   204    207    0.0015477735    0.0034041009     2746.7938622756    0.0000652686        0.2018057242     0.0019   2026-09-08 10:27:35
   205    208    0.0004633361    0.0008267029     2746.7938596887    0.0000025870        0.1994955852     0.0019   2026-09-08 10:27:35
   206    209    0.0002780998    0.0004738277     2746.7938575630    0.0000021257        0.1981349244     0.0019   2026-09-08 10:27:35
   207    210    0.0006769580    0.0011555910     2746.7938492929    0.0000082701        0.1946289603     0.0023   2026-09-08 10:27:35
   208    211    0.0009171921    0.0015800239     2746.7938304082    0.0000188847        0.1894412318     0.0019   2026-09-08 10:27:35
   209    212    0.0014716645    0.0025797978     2746.7937786377    0.0000517704        0.1799262625     0.0020   2026-09-08 10:27:35
   210    213    0.0020497801    0.0037300141     2746.7936483768    0.0001302609        0.1634459201     0.0019   2026-09-08 10:27:35
   211    214    0.0025238072    0.0050719163     2746.7933216989    0.0003266779        0.1338353278     0.0020   2026-09-08 10:27:35
   212    215    0.0023702184    0.0057145493     2746.7925725113    0.0007491875        0.1048248643     0.0019   2026-09-08 10:27:35
   213    216    0.0033693724    0.0074794763     2746.7911428517    0.0014296597        0.1080992692     0.0021   2026-09-08 10:27:35
   214    217    0.0105958330    0.0174574274     2746.7893185912    0.0018242604        0.1152957095     0.0022   2026-09-08 10:27:35
   215    218    0.0141869502    0.0225673191     2746.7881681300    0.0011504613        0.1160510130     0.0020   2026-09-08 10:27:35
   216    219    0.0067185283    0.0112807059     2746.7878989989    0.0002691311        0.1130333170     0.0023   2026-09-08 10:27:35
   217    220    0.0007308379    0.0017222020     2746.7878790907    0.0000199081        0.1115190997     0.0019   2026-09-08 10:27:35
   218    221    0.0001577765    0.0002971150     2746.7878782960    0.0000007947        0.1112159605     0.0019   2026-09-08 10:27:35
   219    222    0.0001000996    0.0001718553     2746.7878777006    0.0000005953        0.1110503631     0.0019   2026-09-08 10:27:35
   220    223    0.0002565799    0.0004386903     2746.7878752973    0.0000024033        0.1106156279     0.0019   2026-09-08 10:27:35
   221    224    0.0003476215    0.0005952259     2746.7878698545    0.0000054428        0.1099928256     0.0024   2026-09-08 10:27:35
   222    225    0.0005725068    0.0009858538     2746.7878547813    0.0000150731        0.1088510704     0.0020   2026-09-08 10:27:35
   223    226    0.0008368376    0.0014673630     2746.7878163408    0.0000384406        0.1068371187     0.0019   2026-09-08 10:27:35
   224    227    0.0011770206    0.0021958442     2746.7877160527    0.0001002881        0.1029908801     0.0020   2026-09-08 10:27:35
   225    228    0.0013777817    0.0032671800     2746.7874622763    0.0002537764        0.0954387686     0.0020   2026-09-08 10:27:35
   226    229    0.0027224402    0.0057551477     2746.7868478390    0.0006144372        0.0804065425     0.0021   2026-09-08 10:27:35
   227    230    0.0064755772    0.0127551341     2746.7855308032    0.0013170359        0.1012170663     0.0020   2026-09-08 10:27:35
   228    231    0.0141826564    0.0257536571     2746.7833840097    0.0021467934        0.1250117972     0.0021   2026-09-08 10:27:35
   229    232    0.0181430025    0.0328930942     2746.7813435319    0.0020404778        0.1030844962     0.0019   2026-09-08 10:27:35
   230    233    0.0101887593    0.0187515010     2746.7805161594    0.0008273724        0.0744691085     0.0019   2026-09-08 10:27:35
   231    234    0.0018493919    0.0039175031     2746.7804033481    0.0001128114        0.0694856303     0.0019   2026-09-08 10:27:35
   232    235    0.0007662453    0.0014710712     2746.7803986450    0.0000047031        0.0684574772     0.0018   2026-09-08 10:27:35
   233    236    0.0001420420    0.0002560228     2746.7803984225    0.0000002225        0.0683944065     0.0021   2026-09-08 10:27:35
   234    237    0.0001902522    0.0003440975     2746.7803979559    0.0000004666        0.0683172524     0.0019   2026-09-08 10:27:35
   235    238    0.0003093997    0.0005623625     2746.7803967128    0.0000012431        0.0681543991     0.0022   2026-09-08 10:27:35
   236    239    0.0004841430    0.0008874491     2746.7803934870    0.0000032258        0.0678100586     0.0023   2026-09-08 10:27:35
   237    240    0.0007506252    0.0013971217     2746.7803850523    0.0000084347        0.0670730354     0.0019   2026-09-08 10:27:35
   238    241    0.0011139565    0.0021364467     2746.7803632263    0.0000218260        0.0654762095     0.0020   2026-09-08 10:27:35
   239    242    0.0015169538    0.0031128017     2746.7803076187    0.0000556076        0.0619480873     0.0019   2026-09-08 10:27:35
   240    243    0.0016331509    0.0041055010     2746.7801720684    0.0001355503        0.0541961888     0.0022   2026-09-08 10:27:35
   241    244    0.0022246292    0.0048391983     2746.7798755563    0.0002965122        0.0405674142     0.0019   2026-09-08 10:27:35
   242    245    0.0035734970    0.0082063451     2746.7793709829    0.0005045734        0.0425261708     0.0020   2026-09-08 10:27:35
   243    246    0.0090751843    0.0154249534     2746.7788521516    0.0005188312        0.0381939841     0.0024   2026-09-08 10:27:35
   244    247    0.0084124071    0.0142171049     2746.7786166989    0.0002354527        0.0310475193     0.0019   2026-09-08 10:27:35
   245    248    0.0025024386    0.0048379211     2746.7785800313    0.0000366676        0.0287129254     0.0020   2026-09-08 10:27:35
   246    249    0.0002896850    0.0006208005     2746.7785782866    0.0000017447        0.0287132220     0.0019   2026-09-08 10:27:35
   247    250    0.0000716891    0.0001292353     2746.7785782184    0.0000000682        0.0286078449     0.0018   2026-09-08 10:27:35
   248    251    0.0000716327    0.0001264991     2746.7785781192    0.0000000992        0.0285050944     0.0018   2026-09-08 10:27:35
   249    252    0.0001364401    0.0002419852     2746.7785778139    0.0000003053        0.0283140919     0.0021   2026-09-08 10:27:35
   250    253    0.0002023160    0.0003624481     2746.7785770615    0.0000007524        0.0280289591     0.0019   2026-09-08 10:27:35
   251    254    0.0003212173    0.0005860033     2746.7785750521    0.0000020094        0.0275512466     0.0019   2026-09-08 10:27:35
   252    255    0.0004753586    0.0008983728     2746.7785698808    0.0000051714        0.0273253621     0.0018   2026-09-08 10:27:35
   253    256    0.0006589412    0.0013454054     2746.7785565896    0.0000132911        0.0277875376     0.0020   2026-09-08 10:27:35
   254    257    0.0007433371    0.0018794904     2746.7785237456    0.0000328441        0.0281970147     0.0023   2026-09-08 10:27:35
   255    258    0.0010523778    0.0024710606     2746.7784492149    0.0000745307        0.0280056231     0.0021   2026-09-08 10:27:35
   256    259    0.0014896721    0.0039079574     2746.7783116812    0.0001375337        0.0260097262     0.0020   2026-09-08 10:27:35
   257    260    0.0040984990    0.0070687153     2746.7781468047    0.0001648765        0.0255545149     0.0021   2026-09-08 10:27:35
   258    261    0.0046604638    0.0075012437     2746.7780526029    0.0000942018        0.0266508100     0.0024   2026-09-08 10:27:35
   259    262    0.0018313291    0.0032631867     2746.7780331297    0.0000194732        0.0233127228     0.0019   2026-09-08 10:27:35
   260    263    0.0002370258    0.0005583091     2746.7780318724    0.0000012573        0.0214396251     0.0021   2026-09-08 10:27:35
   261    264    0.0000535002    0.0001063174     2746.7780318247    0.0000000477        0.0211436494     0.0020   2026-09-08 10:27:35
   262    265    0.0000355155    0.0000653601     2746.7780317827    0.0000000421        0.0209802839     0.0020   2026-09-08 10:27:35
   263    266    0.0000846229    0.0001559012     2746.7780316228    0.0000001598        0.0205850372     0.0020   2026-09-08 10:27:35
   264    267    0.0001160690    0.0002160539     2746.7780312545    0.0000003683        0.0200155483     0.0026   2026-09-08 10:27:35
   265    268    0.0001875594    0.0003560051     2746.7780302434    0.0000010111        0.0190163147     0.0028   2026-09-08 10:27:35
   266    269    0.0002687583    0.0005309367     2746.7780276668    0.0000025767        0.0173682332     0.0029   2026-09-08 10:27:35
   267    270    0.0003580765    0.0007778103     2746.7780210118    0.0000066550        0.0173919715     0.0030   2026-09-08 10:27:35
   268    271    0.0003866997    0.0010521781     2746.7780045508    0.0000164610        0.0183675921     0.0029   2026-09-08 10:27:35
   269    272    0.0005927901    0.0014569925     2746.7779669474    0.0000376033        0.0195430146     0.0029   2026-09-08 10:27:35
   270    273    0.0011745768    0.0028474952     2746.7778966058    0.0000703416        0.0202629686     0.0030   2026-09-08 10:27:35
   271    274    0.0030088059    0.0053549451     2746.7778099681    0.0000866377        0.0192617098     0.0027   2026-09-08 10:27:35
   272    275    0.0032268317    0.0054447907     2746.7777583714    0.0000515967        0.0167251349     0.0028   2026-09-08 10:27:35
   273    276    0.0011928775    0.0021828887     2746.7777471481    0.0000112233        0.0150959916     0.0027   2026-09-08 10:27:35
   274    277    0.0001476924    0.0003606856     2746.7777463894    0.0000007588        0.0148011119     0.0030   2026-09-08 10:27:35
   275    278    0.0000461470    0.0000889610     2746.7777463676    0.0000000217        0.0148077765     0.0029   2026-09-08 10:27:35
   276    279    0.0000170157    0.0000307523     2746.7777463579    0.0000000097        0.0148149833     0.0025   2026-09-08 10:27:35
   277    280    0.0000562610    0.0001016251     2746.7777463077    0.0000000502        0.0148395583     0.0030   2026-09-08 10:27:35
   278    281    0.0000716583    0.0001300560     2746.7777462010    0.0000001067        0.0148693773     0.0025   2026-09-08 10:27:35
   279    282    0.0001227802    0.0002248930     2746.7777458971    0.0000003039        0.0149153171     0.0023   2026-09-08 10:27:35
   280    283    0.0001812727    0.0003384243     2746.7777451288    0.0000007683        0.0149692567     0.0020   2026-09-08 10:27:35
   281    284    0.0002670045    0.0005208289     2746.7777431099    0.0000020189        0.0150101000     0.0020   2026-09-08 10:27:35
   282    285    0.0003464574    0.0007628140     2746.7777379650    0.0000051449        0.0149528163     0.0020   2026-09-08 10:27:35
   283    286    0.0004566737    0.0011237221     2746.7777252278    0.0000127372        0.0145536990     0.0025   2026-09-08 10:27:35
   284    287    0.0007649116    0.0019338130     2746.7776964469    0.0000287809        0.0132421874     0.0020   2026-09-08 10:27:35
   285    288    0.0024715913    0.0039755740     2746.7776436820    0.0000527648        0.0101792797     0.0019   2026-09-08 10:27:35
   286    289    0.0043526815    0.0064574327     2746.7775812954    0.0000623866        0.0078904300     0.0022   2026-09-08 10:27:35
   287    290    0.0035614087    0.0055359730     2746.7775463962    0.0000348992        0.0049309679     0.0022   2026-09-08 10:27:35
   288    291    0.0010144813    0.0018593282     2746.7775393803    0.0000070160        0.0043315455     0.0021   2026-09-08 10:27:35
   289    292    0.0001663095    0.0004157834     2746.7775389492    0.0000004310        0.0044225925     0.0023   2026-09-08 10:27:35
   290    293    0.0000637224    0.0000956824     2746.7775389412    0.0000000080        0.0044245644     0.0023   2026-09-08 10:27:35
   291    294    0.0000072816    0.0000108985     2746.7775389406    0.0000000006        0.0044234208     0.0022   2026-09-08 10:27:35
   292    295    0.0000288164    0.0000433370     2746.7775389368    0.0000000039        0.0044180696     0.0022   2026-09-08 10:27:35
   293    296    0.0000350926    0.0000531095     2746.7775389290    0.0000000078        0.0044108724     0.0021   2026-09-08 10:27:35
   294    297    0.0000624726    0.0000955146     2746.7775389062    0.0000000227        0.0043965066     0.0023   2026-09-08 10:27:35
   295    298    0.0000939280    0.0001462598     2746.7775388492    0.0000000570        0.0043709662     0.0024   2026-09-08 10:27:35
   296    299    0.0001458175    0.0002349070     2746.7775386988    0.0000001505        0.0043205756     0.0024   2026-09-08 10:27:35
   297    300    0.0002095021    0.0003617713     2746.7775383143    0.0000003845        0.0042187906     0.0023   2026-09-08 10:27:35
   298    301    0.0002662651    0.0005419891     2746.7775373526    0.0000009617        0.0040058971     0.0022   2026-09-08 10:27:35

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.585606e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.6989***  0.3824   0.0000   
TC/100 EUR                        -1.2794     0.8459   0.1304   
Babiogorski                        0.6391     0.6285   0.3092   
Bialowieski                       -0.1922     0.5619   0.7323   
Biebrzanski                        0.2221     0.6974   0.7501   
Bieszczadzki                       0.3345     0.4149   0.4201   
BoryTucholskie                     0.1101     0.3772   0.7703   
Drawienski                        -0.3242     0.5387   0.5473   
Gorczanski                         0.4187     0.8517   0.6230   
GorStolowych                       0.9497**   0.3717   0.0106   
Kampinoski                        -0.3634     0.2495   0.1452   
Karkonoski                        -0.8765***  0.3122   0.0050   
Magurski                           0.2706     0.4677   0.5629   
Narwianski                         0.0600     0.6824   0.9299   
Ojcowski                           0.6288     0.4039   0.1195   
Pieninski                         -1.5173**   0.7390   0.0401   
Poleski                            0.0614     0.4019   0.8785   
Roztoczanski                      -0.0703     0.3540   0.8426   
Slowinski                         -0.6070*    0.3584   0.0904   
Swietokrzyski                      0.2629     0.3645   0.4707   
UjscieWarty                       -0.8053**   0.3928   0.0403   
Wielkopolski                       0.7196**   0.3261   0.0273   
Wigierski                          0.1137     0.4435   0.7977   
Wolinski                           1.0709***  0.3931   0.0064   
Household income (10k PLN)         0.2890***  0.1022   0.0047   
Male                               0.1223*    0.0720   0.0893   
Higher education                   0.0113     0.0803   0.8885   
City                               0.1650**   0.0780   0.0344   
Winter                             0.8245***  0.0840   0.0000   
Hiking                             2.0880***  0.0792   0.0000   
Skiing                             1.4072***  0.2676   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2866     0.0950            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.7816     0.5168   0.1304   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2746.7775
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1755
AIC/n:                             0.9492
BIC/n:                             0.9857
n (observations):               5855
r (respondents):                5855
k (parameters):                   32
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1226
median                           0.0000          2.1322
std                              0.7834          0.9278
min                              0.0000          0.0266
max                             20.0000          5.0512
quantile 0.025                   0.0000          0.5807
quantile 0.975                   2.0000          3.9862
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:36
Estimation took 0.88429 seconds (0 hours 0 minutes 0.88429 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.53 -0.62 0.39 -0.1 0.012 0.053 -0.023 -0.032 0.19 0.12 -0.023 -0.12 0.053 0.049 0.23 -0.35 0.033 0.029 -0.029 0.0041 -0.028 0.051 0.025 0.09 0.063 0.0091 0.0041 0.02 0.18 0.44 0.29 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3916.5118304074             NaN     4168.3172962980     0.0001   2026-09-08 10:27:36
     1      4    0.0356222160    0.1298503509     3245.4854604930  671.0263699143     1107.2884454448     0.0071   2026-09-08 10:27:36
     2      5    0.0073883921    0.0216976183     3197.8197508336   47.6657096594      472.8507182316     0.0021   2026-09-08 10:27:36
     3      6    0.0057500118    0.0164229626     3183.5900752589   14.2296755747      389.8510535609     0.0021   2026-09-08 10:27:36
     4      7    0.0065637284    0.0154483848     3172.7054167724   10.8846584865      412.3487947766     0.0022   2026-09-08 10:27:36
     5      8    0.0289314885    0.0647794065     3140.8900857189   31.8153310535      417.1041940514     0.0020   2026-09-08 10:27:36
     6      9    0.0171081484    0.0350258309     3128.0328918015   12.8571939174      330.9320023777     0.0022   2026-09-08 10:27:36
     7     10    0.0133974606    0.0230365318     3121.6367805189    6.3961112826      349.1660922086     0.0023   2026-09-08 10:27:36
     8     11    0.0093991233    0.0125449879     3118.6503108641    2.9864696548      360.8944854227     0.0022   2026-09-08 10:27:36
     9     12    0.0287784207    0.0353811263     3110.4944917254    8.1558191387      378.3223149809     0.0021   2026-09-08 10:27:36
    10     13    0.0685512608    0.0818391536     3092.4419902727   18.0525014527      488.1341413091     0.0023   2026-09-08 10:27:36
    11     14    0.1679726218    0.1984424928     3050.9480623366   41.4939279361      711.4467186064     0.0021   2026-09-08 10:27:36
    12     15    0.3362487877    0.3957112359     2974.8595684283   76.0884939083      849.9489649307     0.0023   2026-09-08 10:27:36
    13     16    0.4914601238    0.5779775549     2881.5075714776   93.3519969508      747.8994169918     0.0024   2026-09-08 10:27:36
    14     17    0.3439538267    0.4055051218     2832.1360542512   49.3715172263      481.1491743177     0.0023   2026-09-08 10:27:36
    15     18    0.0421072248    0.0533267741     2818.6113427380   13.5247115132      255.2746798484     0.0022   2026-09-08 10:27:36
    16     19    0.0721871213    0.0865605499     2812.7938705868    5.8174721512      134.8099762235     0.0021   2026-09-08 10:27:36
    17     20    0.0613705394    0.0728731938     2810.9938945844    1.7999760024      162.5126791751     0.0021   2026-09-08 10:27:36
    18     21    0.0452172706    0.0543818852     2809.0794834252    1.9144111592      160.4985709948     0.0020   2026-09-08 10:27:36
    19     22    0.0485770525    0.0625230674     2804.7637041032    4.3157793220      139.8582844205     0.0028   2026-09-08 10:27:36
    20     23    0.0129384324    0.0375484238     2798.4547826668    6.3089214364       88.8828313986     0.0021   2026-09-08 10:27:36
    21     24    0.0857617671    0.1055841844     2793.0349831044    5.4197995624       38.9342050712     0.0019   2026-09-08 10:27:36
    22     25    0.0903107507    0.1062796442     2791.2846518508    1.7503312536       23.8001574026     0.0020   2026-09-08 10:27:36
    23     26    0.0294780500    0.0347695053     2791.1071732066    0.1774786441       21.3079087588     0.0020   2026-09-08 10:27:36
    24     27    0.0044954628    0.0055240817     2791.0819754583    0.0251977484       20.7638586815     0.0020   2026-09-08 10:27:36
    25     28    0.0050647108    0.0065386772     2791.0301942100    0.0517812482       21.2706105607     0.0020   2026-09-08 10:27:36
    26     29    0.0072866928    0.0101441338     2790.9038693534    0.1263248566       22.0614947678     0.0020   2026-09-08 10:27:36
    27     30    0.0117293505    0.0190888938     2790.5762706542    0.3275986992       23.2474308350     0.0020   2026-09-08 10:27:36
    28     31    0.0180164390    0.0387624502     2789.7745940120    0.8016766422       34.4378841183     0.0020   2026-09-08 10:27:36
    29     32    0.0347709802    0.0814119497     2787.9661011369    1.8084928751       51.8185518411     0.0025   2026-09-08 10:27:36
    30     33    0.0666423903    0.1500006622     2784.6716571226    3.2944440142       66.5728032362     0.0020   2026-09-08 10:27:36
    31     34    0.0838287020    0.1885986934     2780.8313811284    3.8402759942       58.4009050471     0.0020   2026-09-08 10:27:36
    32     35    0.0417349735    0.1038090194     2778.8146932106    2.0166879178       27.0588966818     0.0024   2026-09-08 10:27:36
    33     36    0.0225030696    0.0305206588     2778.4295901439    0.3851030667       16.4984298295     0.0021   2026-09-08 10:27:36
    34     37    0.0074811890    0.0179252844     2778.3957518062    0.0338383377       15.1125172274     0.0019   2026-09-08 10:27:36
    35     38    0.0024824982    0.0060972533     2778.3821166909    0.0136351153       14.3709934838     0.0026   2026-09-08 10:27:36
    36     39    0.0068920109    0.0167587123     2778.3216150844    0.0605016066       14.5088028469     0.0024   2026-09-08 10:27:36
    37     40    0.0086656535    0.0207815201     2778.1906687992    0.1309462852       15.5168235680     0.0019   2026-09-08 10:27:36
    38     41    0.0136572116    0.0338157205     2777.8264522638    0.3642165354       17.1669021179     0.0019   2026-09-08 10:27:36
    39     42    0.0180245278    0.0547184352     2776.9334883702    0.8929638936       23.3321095731     0.0020   2026-09-08 10:27:36
    40     43    0.0471621887    0.1182991777     2774.7907684701    2.1427199001       33.6854364042     0.0019   2026-09-08 10:27:36
    41     44    0.1425319422    0.2712044573     2770.4342801384    4.3564883317       47.0581707131     0.0028   2026-09-08 10:27:36
    42     45    0.2778362043    0.4845534706     2764.0968263764    6.3374537620       53.4848521358     0.0021   2026-09-08 10:27:36
    43     46    0.2787275283    0.4755514757     2759.2442798166    4.8525465598       40.2998348306     0.0020   2026-09-08 10:27:36
    44     47    0.0902226557    0.1741277501     2757.7770318034    1.4672480132       22.9997423802     0.0019   2026-09-08 10:27:36
    45     48    0.0161400568    0.0418440189     2757.6399537430    0.1370780605       16.8098297769     0.0024   2026-09-08 10:27:36
    46     49    0.0071451191    0.0134535478     2757.6258452871    0.0141084559       16.1672378049     0.0021   2026-09-08 10:27:36
    47     50    0.0113927571    0.0211937249     2757.5923484696    0.0334968174       15.5969184857     0.0024   2026-09-08 10:27:36
    48     51    0.0153081201    0.0288681757     2757.5132024537    0.0791460160       15.5603567670     0.0023   2026-09-08 10:27:36
    49     52    0.0196636913    0.0388946502     2757.3144864487    0.1987160050       15.2780181070     0.0025   2026-09-08 10:27:36
    50     53    0.0197915624    0.0390905186     2756.8779227453    0.4365637034       14.1504840540     0.0022   2026-09-08 10:27:36
    51     54    0.0226546390    0.0475688185     2756.1048964544    0.7730262909       11.1371209801     0.0028   2026-09-08 10:27:36
    52     55    0.0636365207    0.1206176045     2755.2560620558    0.8488343986        8.8881740288     0.0027   2026-09-08 10:27:36
    53     56    0.0753892882    0.1362195277     2754.8361442588    0.4199177970        8.1371057691     0.0028   2026-09-08 10:27:36
    54     57    0.0302036438    0.0555072780     2754.7591960777    0.0769481811        8.0993154959     0.0026   2026-09-08 10:27:36
    55     58    0.0041009347    0.0082242632     2754.7501299764    0.0090661012        8.2237343808     0.0020   2026-09-08 10:27:36
    56     59    0.0015176604    0.0031474636     2754.7434724726    0.0066575038        8.2658043253     0.0023   2026-09-08 10:27:36
    57     60    0.0030699972    0.0064394556     2754.7212137217    0.0222587509        8.3120824856     0.0020   2026-09-08 10:27:36
    58     61    0.0045527755    0.0097167862     2754.6694447292    0.0517689926        8.2825200908     0.0024   2026-09-08 10:27:36
    59     62    0.0099570609    0.0190981767     2754.5342412794    0.1352034498        9.8703714432     0.0022   2026-09-08 10:27:36
    60     63    0.0227949790    0.0396043089     2754.2218103272    0.3124309522       12.6909975825     0.0020   2026-09-08 10:27:36
    61     64    0.0464780296    0.0815300038     2753.5955759200    0.6262344072       14.9508528528     0.0025   2026-09-08 10:27:36
    62     65    0.0676197278    0.1267961698     2752.7324705812    0.8631053388       13.7027334406     0.0029   2026-09-08 10:27:36
    63     66    0.0496769357    0.1076675536     2752.1249721464    0.6074984348        9.1111832597     0.0023   2026-09-08 10:27:36
    64     67    0.0189655653    0.0351653669     2751.9523027352    0.1726694112        7.6433472915     0.0023   2026-09-08 10:27:36
    65     68    0.0074462280    0.0136636007     2751.9314546557    0.0208480794        7.2706067692     0.0020   2026-09-08 10:27:36
    66     69    0.0032699726    0.0056675191     2751.9271075398    0.0043471160        7.2331682991     0.0019   2026-09-08 10:27:36
    67     70    0.0054806172    0.0096250203     2751.9158316789    0.0112758608        7.1966498149     0.0019   2026-09-08 10:27:36
    68     71    0.0073232700    0.0131412156     2751.8888319585    0.0269997204        7.1463043630     0.0025   2026-09-08 10:27:36
    69     72    0.0096881926    0.0186404550     2751.8176486101    0.0711833484        7.0149740796     0.0024   2026-09-08 10:27:36
    70     73    0.0085198008    0.0234729610     2751.6439854333    0.1736631768        6.9241371235     0.0020   2026-09-08 10:27:36
    71     74    0.0142168147    0.0398330086     2751.2515481171    0.3924373162        7.0088640156     0.0019   2026-09-08 10:27:36
    72     75    0.0403675006    0.0989366252     2750.5437531890    0.7077949281        6.5552124117     0.0019   2026-09-08 10:27:36
    73     76    0.0890174643    0.1743553408     2749.7372086416    0.8065445474        7.3332493969     0.0019   2026-09-08 10:27:36
    74     77    0.0822529550    0.1472677687     2749.3174730292    0.4197356125        7.9266295393     0.0022   2026-09-08 10:27:36
    75     78    0.0258686895    0.0450113898     2749.2369235925    0.0805494367        9.4814287262     0.0028   2026-09-08 10:27:36
    76     79    0.0028442916    0.0076652824     2749.2298611962    0.0070623964        9.6675191900     0.0026   2026-09-08 10:27:36
    77     80    0.0013772998    0.0037997413     2749.2269903513    0.0028708448        9.6670721479     0.0028   2026-09-08 10:27:36
    78     81    0.0031927829    0.0090369514     2749.2163802841    0.0106100672        9.6179476159     0.0025   2026-09-08 10:27:36
    79     82    0.0038143118    0.0112634672     2749.1927464668    0.0236338173        9.4808776633     0.0025   2026-09-08 10:27:36
    80     83    0.0052553991    0.0159766059     2749.1295846194    0.0631618473        9.0808826223     0.0026   2026-09-08 10:27:36
    81     84    0.0091713328    0.0204041224     2748.9826534162    0.1469312032        8.0962658747     0.0025   2026-09-08 10:27:36
    82     85    0.0192203968    0.0417859924     2748.6773508091    0.3053026071        5.9391681446     0.0025   2026-09-08 10:27:36
    83     86    0.0395409791    0.0931082335     2748.2239388833    0.4534119258        6.2984529298     0.0025   2026-09-08 10:27:36
    84     87    0.0516657739    0.1199562155     2747.8598052945    0.3641335889        4.5245907661     0.0026   2026-09-08 10:27:36
    85     88    0.0250142723    0.0625762538     2747.7459397612    0.1138655333        3.0894394592     0.0024   2026-09-08 10:27:36
    86     89    0.0037466694    0.0108241131     2747.7342720763    0.0116676849        3.4129357793     0.0020   2026-09-08 10:27:36
    87     90    0.0013467683    0.0027121851     2747.7335907863    0.0006812899        3.3879550363     0.0027   2026-09-08 10:27:36
    88     91    0.0008314334    0.0017863180     2747.7329753849    0.0006154015        3.3597797885     0.0025   2026-09-08 10:27:36
    89     92    0.0018771644    0.0039932517     2747.7307445689    0.0022308160        3.2761897044     0.0026   2026-09-08 10:27:36
    90     93    0.0025565419    0.0053345348     2747.7256274073    0.0051171616        3.1138763776     0.0030   2026-09-08 10:27:36
    91     94    0.0038855009    0.0081190850     2747.7121796087    0.0134477985        2.7325312546     0.0025   2026-09-08 10:27:36
    92     95    0.0048015684    0.0114024794     2747.6811214693    0.0310581395        2.6661431368     0.0031   2026-09-08 10:27:36
    93     96    0.0092401521    0.0192852480     2747.6184335200    0.0626879492        3.1619876006     0.0027   2026-09-08 10:27:36
    94     97    0.0169160296    0.0351892728     2747.5302761079    0.0881574122        3.4553181458     0.0025   2026-09-08 10:27:36
    95     98    0.0195901044    0.0420484540     2747.4649606245    0.0653154834        3.6268588821     0.0028   2026-09-08 10:27:36
    96     99    0.0092699020    0.0226855463     2747.4455141208    0.0194465037        3.7383154315     0.0026   2026-09-08 10:27:36
    97    100    0.0024648737    0.0051896674     2747.4433003109    0.0022138099        3.4250232397     0.0025   2026-09-08 10:27:36
    98    101    0.0006682439    0.0013130804     2747.4428837126    0.0004165983        3.3051455220     0.0031   2026-09-08 10:27:36
    99    102    0.0011947040    0.0022643568     2747.4417700236    0.0011136890        3.0891388792     0.0029   2026-09-08 10:27:36
   100    103    0.0018153460    0.0031131130     2747.4390808863    0.0026891373        2.7620499376     0.0025   2026-09-08 10:27:36
   101    104    0.0031033437    0.0046382935     2747.4318717942    0.0072090921        2.3014254042     0.0027   2026-09-08 10:27:36
   102    105    0.0050981174    0.0071368944     2747.4134937489    0.0183780453        2.1126763039     0.0026   2026-09-08 10:27:36
   103    106    0.0084245324    0.0155355254     2747.3670730356    0.0464207134        1.9408517859     0.0025   2026-09-08 10:27:36
   104    107    0.0177611920    0.0413388220     2747.2576367326    0.1094363030        2.3258776735     0.0018   2026-09-08 10:27:36
   105    108    0.0476562954    0.0992658421     2747.0358682112    0.2217685214        4.9739333055     0.0019   2026-09-08 10:27:36
   106    109    0.0866498396    0.1728947045     2746.7167855916    0.3190826196        6.5218006882     0.0021   2026-09-08 10:27:36
   107    110    0.0839964495    0.1640032149     2746.4734998401    0.2432857514        5.5806070451     0.0020   2026-09-08 10:27:36
   108    111    0.0267316725    0.0535724656     2746.3989396967    0.0745601435        5.1186062491     0.0021   2026-09-08 10:27:36
   109    112    0.0063014823    0.0134933881     2746.3905156580    0.0084240387        5.1981940333     0.0020   2026-09-08 10:27:36
   110    113    0.0034221231    0.0070669673     2746.3895043385    0.0010113195        5.1642140138     0.0025   2026-09-08 10:27:36
   111    114    0.0040254662    0.0082731194     2746.3877707819    0.0017335566        5.1142538275     0.0024   2026-09-08 10:27:36
   112    115    0.0063585747    0.0132136536     2746.3830688614    0.0047019205        5.0186679047     0.0025   2026-09-08 10:27:36
   113    116    0.0085920624    0.0183595668     2746.3712138556    0.0118550058        4.8451419049     0.0026   2026-09-08 10:27:36
   114    117    0.0097405985    0.0226891305     2746.3414423040    0.0297715516        4.5172978821     0.0022   2026-09-08 10:27:36
   115    118    0.0087610182    0.0202541271     2746.2728738274    0.0685684765        3.9232568687     0.0020   2026-09-08 10:27:36
   116    119    0.0182427977    0.0405512673     2746.1410115730    0.1318622545        2.9931353922     0.0019   2026-09-08 10:27:36
   117    120    0.0588143359    0.1134135713     2745.9708084670    0.1702031060        3.7755797054     0.0020   2026-09-08 10:27:36
   118    121    0.0717796632    0.1391852023     2745.8620831197    0.1087253473        4.2931701067     0.0020   2026-09-08 10:27:36
   119    122    0.0312614076    0.0629467603     2745.8361477893    0.0259353304        3.4350651759     0.0019   2026-09-08 10:27:36
   120    123    0.0024881377    0.0068735645     2745.8340636174    0.0020841719        2.9697152659     0.0020   2026-09-08 10:27:36
   121    124    0.0008117146    0.0017408683     2745.8337901058    0.0002735115        2.8774096461     0.0019   2026-09-08 10:27:36
   122    125    0.0016113777    0.0033887046     2745.8330446697    0.0007454361        2.7120158137     0.0020   2026-09-08 10:27:36
   123    126    0.0021548710    0.0047018326     2745.8312778392    0.0017668305        2.4529523776     0.0020   2026-09-08 10:27:36
   124    127    0.0028179814    0.0067861289     2745.8266515846    0.0046262546        2.4245957859     0.0020   2026-09-08 10:27:36
   125    128    0.0041662197    0.0080332073     2745.8156607478    0.0109908368        2.4166715699     0.0021   2026-09-08 10:27:36
   126    129    0.0062829814    0.0093619728     2745.7922541855    0.0234065623        2.1244396556     0.0021   2026-09-08 10:27:36
   127    130    0.0119808672    0.0219443297     2745.7551146025    0.0371395830        1.4490361534     0.0019   2026-09-08 10:27:36
   128    131    0.0218209147    0.0384742516     2745.7212031300    0.0339114725        2.0472189675     0.0023   2026-09-08 10:27:36
   129    132    0.0155160399    0.0289355717     2745.7081708636    0.0130322664        1.5293301646     0.0025   2026-09-08 10:27:36
   130    133    0.0030116396    0.0071928649     2745.7064570248    0.0017138388        1.0476990582     0.0026   2026-09-08 10:27:36
   131    134    0.0005837701    0.0009331574     2745.7063251132    0.0001319116        1.0420105157     0.0025   2026-09-08 10:27:36
   132    135    0.0003055109    0.0006246484     2745.7062152293    0.0001098839        1.0381596241     0.0023   2026-09-08 10:27:36
   133    136    0.0006897074    0.0013667203     2745.7058235572    0.0003916721        1.0293255731     0.0023   2026-09-08 10:27:36
   134    137    0.0010115884    0.0018122418     2745.7049112164    0.0009123408        1.0165729208     0.0022   2026-09-08 10:27:36
   135    138    0.0017573292    0.0028147378     2745.7024498161    0.0024614003        0.9950622626     0.0023   2026-09-08 10:27:36
   136    139    0.0028373955    0.0046779892     2745.6963399142    0.0061099018        0.9619304733     0.0020   2026-09-08 10:27:36
   137    140    0.0044663890    0.0106155556     2745.6816791540    0.0146607602        1.4131879212     0.0026   2026-09-08 10:27:36
   138    141    0.0117469147    0.0253767957     2745.6513512512    0.0303279028        2.6682059412     0.0024   2026-09-08 10:27:36
   139    142    0.0248352989    0.0473918485     2745.6052402875    0.0461109636        3.6824941560     0.0020   2026-09-08 10:27:36
   140    143    0.0285181563    0.0511725933     2745.5664114473    0.0388288403        3.4785923995     0.0024   2026-09-08 10:27:36
   141    144    0.0123357959    0.0217472059     2745.5529212634    0.0134901839        3.2458938631     0.0021   2026-09-08 10:27:36
   142    145    0.0025763666    0.0043292984     2745.5511966624    0.0017246010        3.2296334773     0.0019   2026-09-08 10:27:36
   143    146    0.0010460244    0.0022721674     2745.5509283927    0.0002682697        3.1731107508     0.0025   2026-09-08 10:27:36
   144    147    0.0014149136    0.0029837716     2745.5504057816    0.0005226111        3.0882073455     0.0025   2026-09-08 10:27:36
   145    148    0.0020445251    0.0044122433     2745.5490399126    0.0013658690        2.9398669865     0.0020   2026-09-08 10:27:37
   146    149    0.0024819150    0.0057951745     2745.5455385943    0.0035013184        2.6824059602     0.0021   2026-09-08 10:27:37
   147    150    0.0029684462    0.0063255314     2745.5367502467    0.0087883476        2.2304638413     0.0019   2026-09-08 10:27:37
   148    151    0.0047547318    0.0088981228     2745.5161930116    0.0205572351        1.4656647352     0.0020   2026-09-08 10:27:37
   149    152    0.0154089245    0.0300642511     2745.4753989720    0.0407940396        1.4620129721     0.0021   2026-09-08 10:27:37
   150    153    0.0356952189    0.0672950451     2745.4189807049    0.0564182671        2.0255392481     0.0027   2026-09-08 10:27:37
   151    154    0.0400775715    0.0760417587     2745.3784966788    0.0404840261        1.4131644396     0.0028   2026-09-08 10:27:37
   152    155    0.0162649033    0.0321933798     2745.3672925803    0.0112040985        0.4853710346     0.0026   2026-09-08 10:27:37
   153    156    0.0018016949    0.0030389981     2745.3662980044    0.0009945758        0.4884388498     0.0022   2026-09-08 10:27:37
   154    157    0.0009266115    0.0017413615     2745.3662603345    0.0000376700        0.4865531801     0.0021   2026-09-08 10:27:37
   155    158    0.0003478540    0.0006415533     2745.3662444639    0.0000158705        0.4843046779     0.0024   2026-09-08 10:27:37
   156    159    0.0010999771    0.0020001958     2745.3661670759    0.0000773881        0.4762270810     0.0028   2026-09-08 10:27:37
   157    160    0.0014404667    0.0025601365     2745.3660011706    0.0001659053        0.4651312006     0.0020   2026-09-08 10:27:37
   158    161    0.0025115152    0.0043189064     2745.3655337133    0.0004674573        0.4451116366     0.0020   2026-09-08 10:27:37
   159    162    0.0038223584    0.0062817394     2745.3643677119    0.0011660014        0.4131959059     0.0020   2026-09-08 10:27:37
   160    163    0.0057813840    0.0091436521     2745.3614236168    0.0029440951        0.4009166774     0.0020   2026-09-08 10:27:37
   161    164    0.0074737222    0.0130352867     2745.3546324717    0.0067911451        0.5914847074     0.0021   2026-09-08 10:27:37
   162    165    0.0090809768    0.0224354103     2745.3414452213    0.0131872503        1.0228014273     0.0025   2026-09-08 10:27:37
   163    166    0.0168488151    0.0400314310     2745.3240445260    0.0174006953        1.6002679900     0.0020   2026-09-08 10:27:37
   164    167    0.0204028839    0.0439481325     2745.3124560187    0.0115885073        1.8163994200     0.0020   2026-09-08 10:27:37
   165    168    0.0106361353    0.0208887195     2745.3095290591    0.0029269596        1.6787094970     0.0021   2026-09-08 10:27:37
   166    169    0.0026210538    0.0043002854     2745.3092637892    0.0002652699        1.5746707879     0.0020   2026-09-08 10:27:37
   167    170    0.0004395827    0.0010816564     2745.3092197361    0.0000440531        1.5476378330     0.0023   2026-09-08 10:27:37
   168    171    0.0007957370    0.0019415319     2745.3090981854    0.0001215508        1.4964212487     0.0024   2026-09-08 10:27:37
   169    172    0.0010619758    0.0026459801     2745.3088100120    0.0002881733        1.4134060274     0.0026   2026-09-08 10:27:37
   170    173    0.0014288247    0.0037634161     2745.3080526465    0.0007573656        1.2569678137     0.0027   2026-09-08 10:27:37
   171    174    0.0018652001    0.0042613640     2745.3062389268    0.0018137197        0.9764753881     0.0024   2026-09-08 10:27:37
   172    175    0.0031426334    0.0044166007     2745.3023006258    0.0039383010        0.5009107953     0.0022   2026-09-08 10:27:37
   173    176    0.0052772772    0.0120816144     2745.2957890886    0.0065115372        0.3522506622     0.0021   2026-09-08 10:27:37
   174    177    0.0104543110    0.0233871180     2745.2894082547    0.0063808339        0.5350299774     0.0026   2026-09-08 10:27:37
   175    178    0.0084058238    0.0191631745     2745.2867084211    0.0026998336        0.4639154543     0.0023   2026-09-08 10:27:37
   176    179    0.0020448362    0.0051963867     2745.2863142357    0.0003941854        0.4268601292     0.0022   2026-09-08 10:27:37
   177    180    0.0003676967    0.0005432178     2745.2862907976    0.0000234382        0.4254175809     0.0021   2026-09-08 10:27:37
   178    181    0.0001078716    0.0002503275     2745.2862826357    0.0000081619        0.4250250946     0.0023   2026-09-08 10:27:37
   179    182    0.0003040515    0.0007185753     2745.2862465844    0.0000360513        0.4240264747     0.0023   2026-09-08 10:27:37
   180    183    0.0003689708    0.0009082664     2745.2861679235    0.0000786608        0.4226239694     0.0024   2026-09-08 10:27:37
   181    184    0.0006365706    0.0014523581     2745.2859471636    0.0002207599        0.4312003120     0.0025   2026-09-08 10:27:37
   182    185    0.0009935623    0.0020533895     2745.2853903294    0.0005568342        0.4433629373     0.0022   2026-09-08 10:27:37
   183    186    0.0015809070    0.0034351679     2745.2839546251    0.0014357042        0.4571532696     0.0022   2026-09-08 10:27:37
   184    187    0.0038510519    0.0078564752     2745.2804528082    0.0035018170        0.7299657758     0.0020   2026-09-08 10:27:37
   185    188    0.0108898883    0.0200971175     2745.2726969018    0.0077559064        1.1620353912     0.0020   2026-09-08 10:27:37
   186    189    0.0228870641    0.0422513010     2745.2591849621    0.0135119398        1.4399970888     0.0025   2026-09-08 10:27:37
   187    190    0.0298257762    0.0566563673     2745.2446568395    0.0145281226        1.1532923366     0.0025   2026-09-08 10:27:37
   188    191    0.0164740608    0.0339330218     2745.2376241539    0.0070326856        0.4542732007     0.0021   2026-09-08 10:27:37
   189    192    0.0025674477    0.0054208622     2745.2364389549    0.0011851990        0.1905729302     0.0019   2026-09-08 10:27:37
   190    193    0.0017996445    0.0033121785     2745.2363769418    0.0000620131        0.1923035621     0.0022   2026-09-08 10:27:37
   191    194    0.0003628879    0.0006789927     2745.2363739150    0.0000030268        0.1920628238     0.0020   2026-09-08 10:27:37
   192    195    0.0003848040    0.0007266992     2745.2363688639    0.0000050511        0.1918011811     0.0023   2026-09-08 10:27:37
   193    196    0.0006758711    0.0012889647     2745.2363542799    0.0000145841        0.1912317802     0.0021   2026-09-08 10:27:37
   194    197    0.0010097795    0.0019593515     2745.2363175547    0.0000367251        0.1901185935     0.0020   2026-09-08 10:27:37
   195    198    0.0015441161    0.0030941150     2745.2362204691    0.0000970856        0.1878508770     0.0021   2026-09-08 10:27:37
   196    199    0.0021680155    0.0046437623     2745.2359707265    0.0002497426        0.1922568228     0.0020   2026-09-08 10:27:37
   197    200    0.0030010201    0.0066653199     2745.2353358599    0.0006348666        0.2167813541     0.0020   2026-09-08 10:27:37
   198    201    0.0037741684    0.0089087811     2745.2338045969    0.0015312630        0.2495280990     0.0021   2026-09-08 10:27:37
   199    202    0.0050305058    0.0130980087     2745.2305336900    0.0032709069        0.2805911107     0.0020   2026-09-08 10:27:37
   200    203    0.0139762039    0.0262118169     2745.2252519851    0.0052817050        0.2780719513     0.0021   2026-09-08 10:27:37
   201    204    0.0244351747    0.0402159607     2745.2203123566    0.0049396285        0.2243586704     0.0020   2026-09-08 10:27:37
   202    205    0.0172074135    0.0291879112     2745.2183558679    0.0019564887        0.2324337309     0.0020   2026-09-08 10:27:37
   203    206    0.0035054417    0.0077996998     2745.2180948102    0.0002610577        0.2138356029     0.0020   2026-09-08 10:27:37
   204    207    0.0004968675    0.0013791895     2745.2180826977    0.0000121125        0.2066891801     0.0019   2026-09-08 10:27:37
   205    208    0.0001987010    0.0003590063     2745.2180805229    0.0000021748        0.2053986330     0.0020   2026-09-08 10:27:37
   206    209    0.0005943824    0.0010640814     2745.2180706402    0.0000098827        0.2016406799     0.0021   2026-09-08 10:27:37
   207    210    0.0007513958    0.0013579251     2745.2180494359    0.0000212043        0.1965778443     0.0020   2026-09-08 10:27:37
   208    211    0.0012325244    0.0022731329     2745.2179895294    0.0000599064        0.1872748479     0.0021   2026-09-08 10:27:37
   209    212    0.0016843921    0.0032494011     2745.2178390155    0.0001505139        0.1718411551     0.0021   2026-09-08 10:27:37
   210    213    0.0021931255    0.0045076655     2745.2174518713    0.0003871443        0.1503662413     0.0019   2026-09-08 10:27:37
   211    214    0.0021724796    0.0055501168     2745.2165161154    0.0009357559        0.1345750956     0.0020   2026-09-08 10:27:37
   212    215    0.0035203624    0.0085846793     2745.2144865121    0.0020296033        0.1164829941     0.0019   2026-09-08 10:27:37
   213    216    0.0112390228    0.0206816074     2745.2111111053    0.0033754068        0.0935707742     0.0019   2026-09-08 10:27:37
   214    217    0.0204054866    0.0340039515     2745.2077771729    0.0033339324        0.1012149044     0.0023   2026-09-08 10:27:37
   215    218    0.0152522135    0.0254280927     2745.2063505041    0.0014266688        0.1095762070     0.0021   2026-09-08 10:27:37
   216    219    0.0032276860    0.0064010099     2745.2061432442    0.0002072599        0.1113624746     0.0020   2026-09-08 10:27:37
   217    220    0.0004135737    0.0011172322     2745.2061339724    0.0000092718        0.1108464155     0.0022   2026-09-08 10:27:37
   218    221    0.0001588152    0.0002716390     2745.2061335254    0.0000004470        0.1106439341     0.0021   2026-09-08 10:27:37
   219    222    0.0002071833    0.0003517672     2745.2061326457    0.0000008798        0.1103804647     0.0021   2026-09-08 10:27:37
   220    223    0.0003467367    0.0005895332     2745.2061302496    0.0000023961        0.1099540084     0.0021   2026-09-08 10:27:37
   221    224    0.0005410055    0.0009233755     2745.2061240779    0.0000061717        0.1092825600     0.0025   2026-09-08 10:27:37
   222    225    0.0008507590    0.0014637887     2745.2061078582    0.0000162197        0.1081344053     0.0023   2026-09-08 10:27:37
   223    226    0.0012899069    0.0022607436     2745.2060657244    0.0000421338        0.1060547932     0.0023   2026-09-08 10:27:37
   224    227    0.0018536972    0.0034098684     2745.2059569053    0.0001088192        0.1020359204     0.0023   2026-09-08 10:27:37
   225    228    0.0023274652    0.0049824813     2745.2056826079    0.0002742974        0.0939335600     0.0021   2026-09-08 10:27:37
   226    229    0.0035647511    0.0074977385     2745.2050304272    0.0006521807        0.0775743198     0.0026   2026-09-08 10:27:37
   227    230    0.0074589836    0.0136527559     2745.2036878581    0.0013425690        0.0752493856     0.0019   2026-09-08 10:27:37
   228    231    0.0131759183    0.0256635413     2745.2016824551    0.0020054030        0.0788598007     0.0020   2026-09-08 10:27:37
   229    232    0.0172336519    0.0313437419     2745.2000456673    0.0016367878        0.0909906588     0.0020   2026-09-08 10:27:37
   230    233    0.0102395471    0.0173538175     2745.1995082855    0.0005373818        0.0844220752     0.0020   2026-09-08 10:27:37
   231    234    0.0016796555    0.0039682457     2745.1994508782    0.0000574073        0.0760495591     0.0019   2026-09-08 10:27:37
   232    235    0.0005116559    0.0009845992     2745.1994488742    0.0000020039        0.0752004176     0.0020   2026-09-08 10:27:37
   233    236    0.0001004388    0.0001894374     2745.1994486135    0.0000002607        0.0751212493     0.0019   2026-09-08 10:27:37
   234    237    0.0003170071    0.0005967621     2745.1994473484    0.0000012652        0.0748792229     0.0023   2026-09-08 10:27:37
   235    238    0.0004002307    0.0007581379     2745.1994446745    0.0000026739        0.0745204246     0.0020   2026-09-08 10:27:37
   236    239    0.0006822246    0.0013073553     2745.1994370611    0.0000076133        0.0737533471     0.0019   2026-09-08 10:27:37
   237    240    0.0009891921    0.0019390635     2745.1994179324    0.0000191287        0.0722540671     0.0019   2026-09-08 10:27:37
   238    241    0.0013972121    0.0028777280     2745.1993683668    0.0000495656        0.0690903699     0.0020   2026-09-08 10:27:37
   239    242    0.0016039688    0.0038025303     2745.1992466329    0.0001217339        0.0624596191     0.0020   2026-09-08 10:27:37
   240    243    0.0018758017    0.0043344337     2745.1989718135    0.0002748194        0.0490840808     0.0020   2026-09-08 10:27:37
   241    244    0.0026532026    0.0066535558     2745.1984724182    0.0004993953        0.0393102626     0.0025   2026-09-08 10:27:37
   242    245    0.0079403276    0.0142475418     2745.1978905329    0.0005818853        0.0394514705     0.0031   2026-09-08 10:27:37
   243    246    0.0089439643    0.0157083037     2745.1975725782    0.0003179547        0.0374340940     0.0028   2026-09-08 10:27:37
   244    247    0.0034401122    0.0065449904     2745.1975104949    0.0000620833        0.0294361561     0.0026   2026-09-08 10:27:37
   245    248    0.0003785097    0.0008682922     2745.1975067616    0.0000037333        0.0261364904     0.0025   2026-09-08 10:27:37
   246    249    0.0000919368    0.0001776897     2745.1975066497    0.0000001119        0.0261216306     0.0022   2026-09-08 10:27:37
   247    250    0.0000473857    0.0000873429     2745.1975065756    0.0000000741        0.0261356179     0.0026   2026-09-08 10:27:37
   248    251    0.0001322100    0.0002445294     2745.1975062492    0.0000003265        0.0261798727     0.0027   2026-09-08 10:27:37
   249    252    0.0001747953    0.0003267489     2745.1975055268    0.0000007223        0.0262367850     0.0023   2026-09-08 10:27:37
   250    253    0.0002909855    0.0005543745     2745.1975035091    0.0000020178        0.0263233732     0.0027   2026-09-08 10:27:37
   251    254    0.0004233883    0.0008370931     2745.1974983955    0.0000051135        0.0264274236     0.0025   2026-09-08 10:27:37
   252    255    0.0005928043    0.0012701153     2745.1974851314    0.0000132642        0.0265125839     0.0025   2026-09-08 10:27:37
   253    256    0.0006753397    0.0017988764     2745.1974521956    0.0000329358        0.0264328869     0.0024   2026-09-08 10:27:37
   254    257    0.0009409772    0.0024490648     2745.1973760292    0.0000761664        0.0257943584     0.0021   2026-09-08 10:27:37
   255    258    0.0013288992    0.0039067232     2745.1972296159    0.0001464133        0.0238708500     0.0023   2026-09-08 10:27:37
   256    259    0.0038430634    0.0070999970     2745.1970392438    0.0001903721        0.0234076047     0.0020   2026-09-08 10:27:37
   257    260    0.0048393396    0.0080712810     2745.1969157396    0.0001235042        0.0196592509     0.0021   2026-09-08 10:27:37
   258    261    0.0021874947    0.0039288905     2745.1968857766    0.0000299630        0.0164696298     0.0021   2026-09-08 10:27:37
   259    262    0.0002902605    0.0007576729     2745.1968834924    0.0000022843        0.0166194122     0.0020   2026-09-08 10:27:37
   260    263    0.0000668374    0.0001466547     2745.1968834241    0.0000000683        0.0167059501     0.0020   2026-09-08 10:27:37
   261    264    0.0000231175    0.0000433571     2745.1968834001    0.0000000240        0.0167343365     0.0020   2026-09-08 10:27:37
   262    265    0.0000815885    0.0001529646     2745.1968832685    0.0000001316        0.0168375106     0.0020   2026-09-08 10:27:37
   263    266    0.0001013037    0.0001922299     2745.1968829931    0.0000002754        0.0169692837     0.0022   2026-09-08 10:27:37
   264    267    0.0001719072    0.0003335038     2745.1968822045    0.0000007886        0.0172010899     0.0020   2026-09-08 10:27:37
   265    268    0.0002449522    0.0004965153     2745.1968802215    0.0000019830        0.0175522918     0.0021   2026-09-08 10:27:37
   266    269    0.0003367096    0.0007517783     2745.1968750470    0.0000051746        0.0180944131     0.0021   2026-09-08 10:27:37
   267    270    0.0003623281    0.0010621593     2745.1968621301    0.0000129168        0.0188572267     0.0021   2026-09-08 10:27:37
   268    271    0.0005407293    0.0014939355     2745.1968317499    0.0000303802        0.0197459435     0.0021   2026-09-08 10:27:37
   269    272    0.0009949855    0.0025953573     2745.1967710892    0.0000606607        0.0202119710     0.0021   2026-09-08 10:27:37
   270    273    0.0027288156    0.0049532919     2745.1966858797    0.0000852095        0.0191250716     0.0021   2026-09-08 10:27:37
   271    274    0.0035845548    0.0059291101     2745.1966232152    0.0000626645        0.0164095861     0.0022   2026-09-08 10:27:37
   272    275    0.0017622877    0.0030868209     2745.1966053242    0.0000178910        0.0144411741     0.0023   2026-09-08 10:27:37
   273    276    0.0002186282    0.0006284444     2745.1966036932    0.0000016310        0.0140282287     0.0022   2026-09-08 10:27:37
   274    277    0.0000660230    0.0001408413     2745.1966036444    0.0000000488        0.0140395151     0.0019   2026-09-08 10:27:37
   275    278    0.0000155613    0.0000271981     2745.1966036373    0.0000000071        0.0140494502     0.0022   2026-09-08 10:27:37
   276    279    0.0000563510    0.0000981459     2745.1966035980    0.0000000394        0.0140869386     0.0024   2026-09-08 10:27:37
   277    280    0.0000697771    0.0001220905     2745.1966035166    0.0000000814        0.0141326079     0.0024   2026-09-08 10:27:37
   278    281    0.0001216093    0.0002147012     2745.1966032819    0.0000002347        0.0142088930     0.0022   2026-09-08 10:27:37
   279    282    0.0001798494    0.0003232759     2745.1966026910    0.0000005910        0.0143128080     0.0022   2026-09-08 10:27:37
   280    283    0.0002689453    0.0005026199     2745.1966011330    0.0000015579        0.0144437027     0.0022   2026-09-08 10:27:37
   281    284    0.0003596864    0.0007426451     2745.1965971499    0.0000039831        0.0145497669     0.0021   2026-09-08 10:27:37
   282    285    0.0004238469    0.0010855346     2745.1965871876    0.0000099623        0.0144519199     0.0025   2026-09-08 10:27:37
   283    286    0.0006578877    0.0017479138     2745.1965641154    0.0000230722        0.0136575777     0.0025   2026-09-08 10:27:37
   284    287    0.0020964742    0.0034828431     2745.1965193463    0.0000447691        0.0112415920     0.0022   2026-09-08 10:27:37
   285    288    0.0041946735    0.0061417448     2745.1964601641    0.0000591822        0.0070748994     0.0023   2026-09-08 10:27:37
   286    289    0.0041162928    0.0062066893     2745.1964207079    0.0000394562        0.0060313652     0.0021   2026-09-08 10:27:37
   287    290    0.0015257487    0.0026024545     2745.1964108017    0.0000099062        0.0038657263     0.0020   2026-09-08 10:27:37

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.271845e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.4746***  0.3828   0.0000   
TC/100 EUR                        -1.2498     0.8455   0.1394   
Babiogorski                        0.5493     0.6297   0.3830   
Bialowieski                       -0.2620     0.5624   0.6413   
Biebrzanski                        0.2328     0.6984   0.7389   
Bieszczadzki                       0.2854     0.4172   0.4939   
BoryTucholskie                     0.1201     0.3775   0.7504   
Drawienski                        -0.3526     0.5400   0.5139   
Gorczanski                         0.3853     0.8501   0.6504   
GorStolowych                       0.9825***  0.3739   0.0086   
Kampinoski                        -0.3640     0.2512   0.1473   
Karkonoski                        -0.9133***  0.3137   0.0036   
Magurski                           0.2997     0.4681   0.5220   
Narwianski                         0.1114     0.6819   0.8702   
Ojcowski                           0.6554     0.4046   0.1053   
Pieninski                         -1.4745**   0.7400   0.0463   
Poleski                            0.0582     0.4022   0.8849   
Roztoczanski                      -0.0691     0.3549   0.8457   
Slowinski                         -0.6418*    0.3585   0.0734   
Swietokrzyski                      0.2767     0.3659   0.4495   
UjscieWarty                       -0.7882**   0.3955   0.0463   
Wielkopolski                       0.7355**   0.3280   0.0250   
Wigierski                          0.1077     0.4447   0.8087   
Wolinski                           1.0661***  0.3944   0.0069   
Household income (10k PLN)         0.2976***  0.1023   0.0036   
Male                               0.1202*    0.0720   0.0951   
Higher education                   0.0126     0.0803   0.8751   
City                               0.1676**   0.0780   0.0318   
Winter                             0.8238***  0.0839   0.0000   
Hiking                             2.0902***  0.0793   0.0000   
Skiing                             1.4063***  0.2672   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2830     0.0950            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.8001     0.5413   0.1394   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2745.1964
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1759
AIC/n:                             0.9487
BIC/n:                             0.9851
n (observations):               5855
r (respondents):                5855
k (parameters):                   32
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1162
median                           0.0000          2.1210
std                              0.7834          0.9249
min                              0.0000          0.0269
max                             20.0000          5.1370
quantile 0.025                   0.0000          0.5722
quantile 0.975                   2.0000          3.9713
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:37
Estimation took 0.87838 seconds (0 hours 0 minutes 0.87838 seconds).

====================================================
WN: all mountain parks as substitutes
====================================================
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.55 -0.48 0.57 0.064 0.0067 0.18 -0.14 0.048 -0.32 0.063 0.059 0.0099 0.0029 0.015 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3920.2557475321             NaN     3307.6021403753     0.0000   2026-09-08 10:27:38
     1      3    0.1941891806    0.4685715377     3767.5365554766  152.7191920555     1565.5833213315     0.0026   2026-09-08 10:27:38
     2      4    0.0616730872    0.1564806902     3262.4614734716  505.0750820050      792.1238087477     0.0015   2026-09-08 10:27:38
     3      6    0.0394160131    0.1039400771     3141.9425125854  120.5189608862      363.2916848437     0.0029   2026-09-08 10:27:38
     4      8    0.1499181566    0.1783676090     3072.3196782532   69.6228343322      297.6032253794     0.0032   2026-09-08 10:27:38
     5      9    0.5644485451    0.6693017681     2942.7045615763  129.6151166769      273.3833064018     0.0010   2026-09-08 10:27:38
     6     10    0.1229749784    0.1457330441     2931.1915667777   11.5129947985      232.7952653387     0.0010   2026-09-08 10:27:38
     7     11    0.1470445792    0.1735615778     2918.5976415540   12.5939252238      196.4464566406     0.0013   2026-09-08 10:27:38
     8     12    0.1898815216    0.2281578359     2899.5288732904   19.0687682636      168.8097113031     0.0011   2026-09-08 10:27:38
     9     13    0.2449414379    0.3108289932     2870.0503082106   29.4785650797      169.1907648884     0.0012   2026-09-08 10:27:38
    10     14    0.1744185221    0.2664258405     2841.7535310008   28.2967772098      116.2358541732     0.0014   2026-09-08 10:27:38
    11     15    0.0767240481    0.1324463127     2827.4267062039   14.3268247969       64.8100614300     0.0010   2026-09-08 10:27:38
    12     16    0.0830123753    0.1015219371     2824.2402385539    3.1864676500       50.6677396439     0.0013   2026-09-08 10:27:38
    13     17    0.0549079629    0.0649512143     2823.4249639062    0.8152746477       54.9305486271     0.0014   2026-09-08 10:27:38
    14     18    0.0356835941    0.0437960248     2822.7740092648    0.6509546414       59.3389851300     0.0010   2026-09-08 10:27:38
    15     19    0.0401162250    0.0513375878     2821.4655714370    1.3084378278       64.3470057173     0.0010   2026-09-08 10:27:38
    16     20    0.0490106469    0.0782968106     2818.3839876580    3.0815837790       68.7470816501     0.0010   2026-09-08 10:27:38
    17     21    0.0765341927    0.1193958196     2813.0731847314    5.3108029266       65.2598051554     0.0010   2026-09-08 10:27:38
    18     22    0.1249344312    0.1804612139     2807.1380594726    5.9351252587       52.2237865054     0.0010   2026-09-08 10:27:38
    19     23    0.0923915649    0.1603872066     2804.1931546586    2.9449048141       27.9719252206     0.0009   2026-09-08 10:27:38
    20     24    0.0469312442    0.0630547118     2803.6244981296    0.5686565289       25.4226040068     0.0009   2026-09-08 10:27:38
    21     25    0.0157771117    0.0203146314     2803.4208624834    0.2036356462       26.1368533256     0.0010   2026-09-08 10:27:38
    22     26    0.0234456743    0.0321453368     2802.9320678954    0.4887945880       26.5383739291     0.0010   2026-09-08 10:27:38
    23     27    0.0324828744    0.0534873042     2801.8228541133    1.1092137821       32.8220984377     0.0012   2026-09-08 10:27:38
    24     28    0.0673244465    0.1112612854     2799.2136712182    2.6091828952       51.4161792950     0.0013   2026-09-08 10:27:38
    25     29    0.1459755248    0.2165494681     2794.2523318924    4.9613393257       69.1217216574     0.0010   2026-09-08 10:27:38
    26     30    0.2248560527    0.3247861001     2787.6681855605    6.5841463319       70.8925099745     0.0009   2026-09-08 10:27:38
    27     31    0.1745347758    0.2643443942     2783.0944397256    4.5737458348       46.8062425890     0.0009   2026-09-08 10:27:38
    28     32    0.0572935886    0.0863647772     2781.6880316367    1.4064080890       38.1557782240     0.0009   2026-09-08 10:27:38
    29     33    0.0256156125    0.0447702897     2781.4157426277    0.2722890090       37.2970733645     0.0009   2026-09-08 10:27:38
    30     34    0.0184459889    0.0297599051     2781.1998598429    0.2158827848       35.9905871923     0.0009   2026-09-08 10:27:38
    31     35    0.0286255573    0.0530781158     2780.5273021533    0.6725576896       32.7632005601     0.0009   2026-09-08 10:27:38
    32     36    0.0401036532    0.0660358310     2779.0253426707    1.5019594827       26.9905059269     0.0009   2026-09-08 10:27:38
    33     37    0.0661383688    0.1290478202     2775.6573313967    3.3680112740       37.5496412462     0.0009   2026-09-08 10:27:38
    34     38    0.1709258497    0.2875346945     2770.2011908507    5.4561405460       46.1613898433     0.0009   2026-09-08 10:27:38
    35     39    0.2870606615    0.4167904769     2765.0161563026    5.1850345481       35.0959998013     0.0009   2026-09-08 10:27:38
    36     40    0.1909743648    0.2658676951     2762.9556898099    2.0604664927       13.6324661628     0.0012   2026-09-08 10:27:38
    37     41    0.0371574560    0.0614963985     2762.6807658425    0.2749239675       11.2583135249     0.0013   2026-09-08 10:27:38
    38     42    0.0069383664    0.0107714877     2762.6549385912    0.0258272513       10.8123957017     0.0010   2026-09-08 10:27:38
    39     43    0.0064414968    0.0104755955     2762.6202148960    0.0347236952       10.4946500337     0.0010   2026-09-08 10:27:38
    40     44    0.0120025216    0.0184412589     2762.5218780353    0.0983368607        9.9234348109     0.0011   2026-09-08 10:27:38
    41     45    0.0184902472    0.0283759576     2762.2927201092    0.2291579262        9.3509950768     0.0010   2026-09-08 10:27:38
    42     46    0.0290544139    0.0538725746     2761.7803151533    0.5124049558       10.5751899125     0.0009   2026-09-08 10:27:38
    43     47    0.0453901510    0.1024212601     2760.9056439718    0.8746711816       11.6670847096     0.0009   2026-09-08 10:27:38
    44     48    0.0649601446    0.1422303307     2759.9812063269    0.9244376448       12.8569099843     0.0010   2026-09-08 10:27:38
    45     49    0.0421529377    0.1007438247     2759.5357366755    0.4454696515        9.0001128409     0.0010   2026-09-08 10:27:38
    46     50    0.0175723595    0.0308610499     2759.4515003770    0.0842362985        7.4743892618     0.0009   2026-09-08 10:27:38
    47     51    0.0054074931    0.0092335845     2759.4380555010    0.0134448759        7.5348583965     0.0010   2026-09-08 10:27:38
    48     52    0.0044528427    0.0082981455     2759.4213845164    0.0166709846        7.3917780545     0.0009   2026-09-08 10:27:38
    49     53    0.0081004954    0.0135997202     2759.3751703053    0.0462142111        6.9028330070     0.0010   2026-09-08 10:27:38
    50     54    0.0121358253    0.0185507662     2759.2709499561    0.1042203492        5.7386773000     0.0010   2026-09-08 10:27:38
    51     55    0.0163332388    0.0328058733     2759.0565069678    0.2144429883        6.5653245545     0.0010   2026-09-08 10:27:38
    52     56    0.0284700571    0.0617519683     2758.7503871931    0.3061197747        6.4944137838     0.0009   2026-09-08 10:27:38
    53     57    0.0406259930    0.0755544220     2758.5141583214    0.2362288717        5.0688743842     0.0010   2026-09-08 10:27:38
    54     58    0.0224662894    0.0413630089     2758.4404212688    0.0737370526        4.0896718684     0.0009   2026-09-08 10:27:38
    55     59    0.0058494998    0.0095411698     2758.4300652051    0.0103560636        3.6631300162     0.0009   2026-09-08 10:27:38
    56     60    0.0021150611    0.0031830999     2758.4257694817    0.0042957235        3.4041446791     0.0010   2026-09-08 10:27:38
    57     61    0.0041693478    0.0062216253     2758.4124915838    0.0132778979        2.8994901209     0.0009   2026-09-08 10:27:38
    58     62    0.0059674309    0.0092752205     2758.3821403751    0.0303512087        3.0149876866     0.0009   2026-09-08 10:27:38
    59     63    0.0095634766    0.0196126486     2758.3050736432    0.0770667319        3.1704763748     0.0009   2026-09-08 10:27:38
    60     64    0.0213090608    0.0440110301     2758.1392237915    0.1658498517        5.0261584144     0.0009   2026-09-08 10:27:38
    61     65    0.0450821491    0.0874875444     2757.8543996609    0.2848241306        7.4477535900     0.0012   2026-09-08 10:27:38
    62     66    0.0576342167    0.1118035532     2757.5575252854    0.2968743755        7.4206145809     0.0014   2026-09-08 10:27:38
    63     67    0.0314506750    0.0658543513     2757.4145481645    0.1429771209        5.9855054239     0.0013   2026-09-08 10:27:38
    64     68    0.0094674619    0.0143322316     2757.3855201136    0.0290280509        6.8341006212     0.0013   2026-09-08 10:27:38
    65     69    0.0030962339    0.0069215562     2757.3767547405    0.0087653732        6.8760273094     0.0010   2026-09-08 10:27:38
    66     70    0.0045154099    0.0096758725     2757.3574463135    0.0193084269        6.8015641202     0.0009   2026-09-08 10:27:38
    67     71    0.0069300835    0.0118250682     2757.3108870559    0.0465592576        6.5270919204     0.0009   2026-09-08 10:27:38
    68     72    0.0104955571    0.0205789638     2757.1997261210    0.1111609349        5.7664292065     0.0009   2026-09-08 10:27:38
    69     73    0.0250983942    0.0569550874     2756.9760402835    0.2236858375        4.3571564933     0.0009   2026-09-08 10:27:38
    70     74    0.0597825406    0.1204761681     2756.6533650475    0.3226752360        5.7419145980     0.0009   2026-09-08 10:27:38
    71     75    0.0701617596    0.1369434122     2756.4064130916    0.2469519559        4.3619650629     0.0009   2026-09-08 10:27:38
    72     76    0.0304748552    0.0604589381     2756.3303457702    0.0760673215        2.6224411584     0.0009   2026-09-08 10:27:38
    73     77    0.0050539027    0.0082781528     2756.3213293958    0.0090163743        2.7340587066     0.0009   2026-09-08 10:27:38
    74     78    0.0018655997    0.0040839628     2756.3195555469    0.0017738489        2.7350902070     0.0009   2026-09-08 10:27:38
    75     79    0.0034043803    0.0068053115     2756.3151049632    0.0044505838        2.6971619400     0.0012   2026-09-08 10:27:38
    76     80    0.0047636848    0.0087457577     2756.3046976280    0.0104073352        2.5531452052     0.0013   2026-09-08 10:27:38
    77     81    0.0062331090    0.0112606230     2756.2798482601    0.0248493679        2.1989133292     0.0010   2026-09-08 10:27:38
    78     82    0.0080635195    0.0184484502     2756.2316052986    0.0482429615        2.0201876148     0.0009   2026-09-08 10:27:38
    79     83    0.0186613708    0.0390467074     2756.1663102400    0.0652950586        1.9647804899     0.0009   2026-09-08 10:27:38
    80     84    0.0231283695    0.0483996080     2756.1210603115    0.0452499285        2.1324143014     0.0009   2026-09-08 10:27:38
    81     85    0.0121298348    0.0257469406     2756.1081280294    0.0129322821        2.3292595415     0.0009   2026-09-08 10:27:38
    82     86    0.0027861767    0.0052119207     2756.1062834698    0.0018445596        2.3982656719     0.0009   2026-09-08 10:27:38
    83     87    0.0007379748    0.0017193278     2756.1053267728    0.0009566970        2.4207747305     0.0009   2026-09-08 10:27:38
    84     88    0.0017150354    0.0034678403     2756.1022153927    0.0031113801        2.4596755418     0.0009   2026-09-08 10:27:38
    85     89    0.0026624424    0.0052765508     2756.0950105260    0.0072048668        2.5012218265     0.0009   2026-09-08 10:27:38
    86     90    0.0048484231    0.0116178163     2756.0759870636    0.0190234624        2.5334164947     0.0009   2026-09-08 10:27:38
    87     91    0.0130132400    0.0278092710     2756.0311375901    0.0448494735        2.4888779482     0.0011   2026-09-08 10:27:38
    88     92    0.0304614991    0.0643821434     2755.9366115960    0.0945259940        2.3764220041     0.0014   2026-09-08 10:27:38
    89     93    0.0524377245    0.1132581011     2755.7913703571    0.1452412389        3.0843401137     0.0014   2026-09-08 10:27:38
    90     94    0.0537901204    0.1143060919     2755.6667867961    0.1245835611        3.3910348156     0.0013   2026-09-08 10:27:38
    91     95    0.0214726445    0.0423115354     2755.6219759698    0.0448108263        2.5676839248     0.0014   2026-09-08 10:27:38
    92     96    0.0049960291    0.0108581294     2755.6160856837    0.0058902861        2.8232466329     0.0014   2026-09-08 10:27:38
    93     97    0.0025866044    0.0055434724     2755.6152286134    0.0008570703        2.8270254758     0.0009   2026-09-08 10:27:38
    94     98    0.0033390136    0.0072641334     2755.6135462860    0.0016823273        2.7963977852     0.0009   2026-09-08 10:27:38
    95     99    0.0045238123    0.0101306594     2755.6093477348    0.0041985512        2.6927783192     0.0009   2026-09-08 10:27:38
    96    100    0.0047617402    0.0117169375     2755.5994718415    0.0098758933        2.4134181515     0.0009   2026-09-08 10:27:38
    97    101    0.0070840232    0.0112741079     2755.5796009334    0.0198709081        1.7885689090     0.0009   2026-09-08 10:27:38
    98    102    0.0115253063    0.0274880634     2755.5512072355    0.0283936979        0.7842866070     0.0014   2026-09-08 10:27:38
    99    103    0.0214578229    0.0463016691     2755.5295981160    0.0216091195        0.7523947383     0.0010   2026-09-08 10:27:38
   100    104    0.0143567615    0.0304821080     2755.5231731736    0.0064249423        0.5152668602     0.0010   2026-09-08 10:27:38
   101    105    0.0027174060    0.0063012463     2755.5225264104    0.0006467632        0.4918167470     0.0009   2026-09-08 10:27:38
   102    106    0.0004560068    0.0006925259     2755.5224663376    0.0000600729        0.4918549580     0.0009   2026-09-08 10:27:38
   103    107    0.0004429300    0.0007320004     2755.5223800405    0.0000862971        0.4908978597     0.0009   2026-09-08 10:27:38
   104    108    0.0007937748    0.0013232684     2755.5221284038    0.0002516367        0.4878957358     0.0009   2026-09-08 10:27:38
   105    109    0.0011404536    0.0019988488     2755.5215186245    0.0006097793        0.4809289693     0.0009   2026-09-08 10:27:38
   106    110    0.0016207209    0.0035191083     2755.5200170041    0.0015016204        0.4644301996     0.0009   2026-09-08 10:27:38
   107    111    0.0033724315    0.0068296528     2755.5168120090    0.0032049951        0.5375275500     0.0009   2026-09-08 10:27:38
   108    112    0.0066002824    0.0125952263     2755.5115173040    0.0052947050        1.1447710718     0.0009   2026-09-08 10:27:38
   109    113    0.0077334395    0.0157161668     2755.5063058213    0.0052114827        1.6240250861     0.0009   2026-09-08 10:27:38
   110    114    0.0040338094    0.0096999157     2755.5039453074    0.0023605139        1.6607886861     0.0010   2026-09-08 10:27:38
   111    115    0.0017114500    0.0028971068     2755.5033968641    0.0005484433        1.5195352373     0.0009   2026-09-08 10:27:38
   112    116    0.0006988785    0.0013054252     2755.5031008479    0.0002960162        1.4173309776     0.0012   2026-09-08 10:27:38
   113    117    0.0012424960    0.0020124062     2755.5023288854    0.0007719626        1.2343106172     0.0011   2026-09-08 10:27:38
   114    118    0.0019145781    0.0031004241     2755.5004562100    0.0018726754        0.9520799446     0.0009   2026-09-08 10:27:38
   115    119    0.0036108423    0.0079016266     2755.4955763322    0.0048798778        0.8062691345     0.0009   2026-09-08 10:27:38
   116    120    0.0114054214    0.0224374673     2755.4837611543    0.0118151779        1.0556064534     0.0009   2026-09-08 10:27:38
   117    121    0.0302677917    0.0577024462     2755.4577047124    0.0260564420        1.3307846184     0.0009   2026-09-08 10:27:38
   118    122    0.0620011352    0.1153374700     2755.4129186700    0.0447860423        2.0281137487     0.0010   2026-09-08 10:27:38
   119    123    0.0783642895    0.1439361863     2755.3658000706    0.0471185994        1.9009507387     0.0009   2026-09-08 10:27:38
   120    124    0.0410475584    0.0750030516     2755.3436213862    0.0221786845        0.8400915601     0.0009   2026-09-08 10:27:38
   121    125    0.0047766415    0.0076626052     2755.3399836990    0.0036376872        0.2982831182     0.0009   2026-09-08 10:27:38
   122    126    0.0048149052    0.0091345076     2755.3397961260    0.0001875730        0.2825142198     0.0009   2026-09-08 10:27:38
   123    127    0.0009484663    0.0017655117     2755.3397839675    0.0000121585        0.2809314467     0.0009   2026-09-08 10:27:38
   124    128    0.0013798206    0.0025876462     2755.3397560629    0.0000279047        0.2789936418     0.0010   2026-09-08 10:27:38
   125    129    0.0021231736    0.0040417437     2755.3396844067    0.0000716562        0.2759908025     0.0009   2026-09-08 10:27:38
   126    130    0.0032730444    0.0064057997     2755.3394961290    0.0001882777        0.2708832005     0.0009   2026-09-08 10:27:38
   127    131    0.0050146583    0.0098781809     2755.3390081191    0.0004880099        0.2619234541     0.0011   2026-09-08 10:27:38
   128    132    0.0086338709    0.0148866886     2755.3377541293    0.0012539899        0.2456484929     0.0010   2026-09-08 10:27:38
   129    133    0.0148140474    0.0218781689     2755.3346350266    0.0031191027        0.2643834700     0.0009   2026-09-08 10:27:38
   130    134    0.0241357956    0.0339265807     2755.3274603948    0.0071746317        0.3116573117     0.0009   2026-09-08 10:27:38
   131    135    0.0325563188    0.0623845899     2755.3137867511    0.0136736437        0.3375178959     0.0010   2026-09-08 10:27:38
   132    136    0.0598161134    0.1054136251     2755.2963200076    0.0174667436        0.2864659613     0.0009   2026-09-08 10:27:38
   133    137    0.0631499763    0.1043324076     2755.2853138420    0.0110061655        0.1666048488     0.0010   2026-09-08 10:27:38
   134    138    0.0241522004    0.0440002234     2755.2827577939    0.0025560481        0.0994526531     0.0010   2026-09-08 10:27:38
   135    139    0.0067796545    0.0094403333     2755.2825720838    0.0001857101        0.1096804632     0.0011   2026-09-08 10:27:38
   136    140    0.0010847140    0.0021055214     2755.2825672961    0.0000047877        0.1084928047     0.0015   2026-09-08 10:27:38
   137    141    0.0002527914    0.0004454369     2755.2825661843    0.0000011118        0.1079602845     0.0015   2026-09-08 10:27:38
   138    142    0.0009962324    0.0017779407     2755.2825593139    0.0000068704        0.1056400565     0.0013   2026-09-08 10:27:38
   139    143    0.0011796045    0.0021764023     2755.2825453408    0.0000139731        0.1026110044     0.0011   2026-09-08 10:27:38
   140    144    0.0020137470    0.0038382393     2755.2825050210    0.0000403198        0.0968500160     0.0009   2026-09-08 10:27:38
   141    145    0.0029164006    0.0057037448     2755.2824051961    0.0000998249        0.0938394836     0.0009   2026-09-08 10:27:38
   142    146    0.0044387106    0.0086364313     2755.2821516926    0.0002535035        0.1008833946     0.0010   2026-09-08 10:27:38
   143    147    0.0080947240    0.0120656093     2755.2815640899    0.0005876027        0.1060607207     0.0011   2026-09-08 10:27:38
   144    148    0.0130703198    0.0168391181     2755.2804062596    0.0011578303        0.0999585072     0.0013   2026-09-08 10:27:38
   145    149    0.0188138301    0.0262121849     2755.2788350599    0.0015711997        0.0697401664     0.0011   2026-09-08 10:27:38
   146    150    0.0244418062    0.0318763424     2755.2777401237    0.0010949362        0.0303477607     0.0009   2026-09-08 10:27:38
   147    151    0.0116633668    0.0186625594     2755.2774491850    0.0002909387        0.0100547930     0.0012   2026-09-08 10:27:38
   148    152    0.0027629285    0.0044808741     2755.2774248563    0.0000243287        0.0033858537     0.0013   2026-09-08 10:27:38
   149    153    0.0004769647    0.0006802352     2755.2774242756    0.0000005807        0.0031450374     0.0014   2026-09-08 10:27:38

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.505638e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3846***  0.2767   0.0000   
TC/100 EUR                        -1.6622**   0.7894   0.0352   
Babiogorski                        1.5039**   0.5917   0.0110   
Bieszczadzki                       0.0924     0.3128   0.7677   
Gorczanski                         0.1654     0.7252   0.8196   
GorStolowych                       1.4453***  0.3893   0.0002   
Karkonoski                        -1.1135***  0.3467   0.0013   
Magurski                           0.4378     0.4603   0.3416   
Pieninski                         -1.2556**   0.5881   0.0327   
Swietokrzyski                      0.1631     0.1407   0.2466   
Household income (10k PLN)         0.2762***  0.1014   0.0064   
Male                               0.1163     0.0718   0.1051   
Higher education                   0.0170     0.0800   0.8319   
City                               0.1415*    0.0755   0.0610   
Winter                             0.8201***  0.0834   0.0000   
Hiking                             2.0852***  0.0788   0.0000   
Skiing                             1.3992***  0.2657   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2903     0.0948            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.6016**   0.2857   0.0352   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2755.2774
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1729
AIC/n:                             0.9473
BIC/n:                             0.9678
n (observations):               5855
r (respondents):                5855
k (parameters):                   18
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.7225
median                           0.0000          1.7321
std                              0.7834          0.7394
min                              0.0000          0.0246
max                             20.0000          3.5357
quantile 0.025                   0.0000          0.4668
quantile 0.975                   2.0000          3.0518
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:38
Estimation took 0.2669 seconds (0 hours 0 minutes 0.2669 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.53 -0.45 0.57 0.034 -0.034 0.17 -0.13 0.077 -0.31 0.053 0.067 0.01 0.0027 0.014 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3919.7294698966             NaN     3766.6675439809     0.0001   2026-09-08 10:27:39
     1      4    0.0801967321    0.1911712107     3171.1801070588  748.5493628378      398.2985875915     0.0034   2026-09-08 10:27:39
     2      6    0.0818557366    0.1023182915     3140.1006120953   31.0794949635      419.5801405929     0.0028   2026-09-08 10:27:39
     3      7    0.0796407002    0.0967045233     3107.3650963979   32.7355156974      452.3735480900     0.0011   2026-09-08 10:27:39
     4      8    0.4114452852    0.5004156901     2994.3101998305  113.0548965675      474.1740829186     0.0010   2026-09-08 10:27:39
     5      9    0.1227986553    0.1496344014     2975.2036539682   19.1065458623      364.2176314708     0.0010   2026-09-08 10:27:39
     6     10    0.0880115555    0.1065462563     2965.0544378446   10.1492161236      255.6275127213     0.0011   2026-09-08 10:27:39
     7     11    0.0787438601    0.0951654999     2955.3527504810    9.7016873636      233.1734738552     0.0011   2026-09-08 10:27:39
     8     12    0.1518970723    0.1863448245     2934.2562052027   21.0965452783      330.9386256609     0.0011   2026-09-08 10:27:39
     9     13    0.2275290175    0.2885449396     2899.8191922873   34.4370129154      398.2171206389     0.0010   2026-09-08 10:27:39
    10     14    0.2546325927    0.3448463446     2859.1464977457   40.6726945416      329.8371832372     0.0011   2026-09-08 10:27:39
    11     15    0.1115277055    0.1937914291     2836.3422388998   22.8042588459      162.1047920242     0.0015   2026-09-08 10:27:39
    12     16    0.0418376750    0.0642188416     2830.6636851364    5.6785537633       80.1151172270     0.0012   2026-09-08 10:27:39
    13     17    0.0604637362    0.0730244390     2829.4033812565    1.2603038799       66.4883348717     0.0011   2026-09-08 10:27:39
    14     18    0.0301713792    0.0381308897     2828.9834816248    0.4198996318       72.2243787530     0.0010   2026-09-08 10:27:39
    15     19    0.0229779647    0.0293843866     2828.4303842077    0.5530974170       75.4561081527     0.0010   2026-09-08 10:27:39
    16     20    0.0405832468    0.0540074717     2826.7516919958    1.6786922119       80.0397018204     0.0010   2026-09-08 10:27:39
    17     21    0.0428710553    0.0745608687     2823.2695333486    3.4821586472       82.0712368754     0.0010   2026-09-08 10:27:39
    18     22    0.0848394248    0.1270678809     2816.8780686076    6.3914647410       79.6990012967     0.0010   2026-09-08 10:27:39
    19     23    0.1318758571    0.1875636449     2809.8523900439    7.0256785636       65.8628636334     0.0011   2026-09-08 10:27:39
    20     24    0.0958964316    0.1636162078     2806.3259854794    3.5264045646       31.4021531390     0.0010   2026-09-08 10:27:39
    21     25    0.0440213841    0.0608085469     2805.7034745897    0.6225108897       26.2666658855     0.0010   2026-09-08 10:27:39
    22     26    0.0110553539    0.0150288132     2805.5610606147    0.1424139750       26.4835089955     0.0010   2026-09-08 10:27:39
    23     27    0.0116384847    0.0175969715     2805.2967323366    0.2643282781       26.3200048254     0.0010   2026-09-08 10:27:39
    24     28    0.0163418435    0.0282650180     2804.6546083023    0.6421240343       28.7214065748     0.0011   2026-09-08 10:27:39
    25     29    0.0256008256    0.0564805231     2803.0639552234    1.5906530789       45.3821325711     0.0010   2026-09-08 10:27:39
    26     30    0.0767890526    0.1255289320     2799.4590021190    3.6049531044       67.3344585758     0.0010   2026-09-08 10:27:39
    27     31    0.1761489186    0.2568947251     2792.7054046893    6.7535974297       86.4981647187     0.0010   2026-09-08 10:27:39
    28     32    0.2679406810    0.3733715444     2784.2710704318    8.4343342575       82.3256519104     0.0010   2026-09-08 10:27:39
    29     33    0.1965009977    0.2735851541     2778.9819361231    5.2891343087       48.1336456712     0.0010   2026-09-08 10:27:39
    30     34    0.0361875363    0.0655884034     2777.6762604861    1.3056756370       36.8677835419     0.0010   2026-09-08 10:27:39
    31     35    0.0238633511    0.0383586784     2777.5160752588    0.1601852272       35.5366613288     0.0010   2026-09-08 10:27:39
    32     36    0.0139666583    0.0208329810     2777.4244130611    0.0916621978       34.6193789397     0.0010   2026-09-08 10:27:39
    33     37    0.0279911346    0.0436197505     2777.1109375343    0.3134755268       32.2215991420     0.0009   2026-09-08 10:27:39
    34     38    0.0284913509    0.0530742005     2776.4186037822    0.6923337521       28.0739627600     0.0009   2026-09-08 10:27:39
    35     39    0.0500618207    0.0759423094     2774.7223931579    1.6962106244       23.7290312691     0.0014   2026-09-08 10:27:39
    36     40    0.0738709673    0.1361127152     2771.4583737516    3.2640194062       33.4700320745     0.0013   2026-09-08 10:27:39
    37     41    0.1705251125    0.2701320909     2767.0617056202    4.3966681314       33.5646559474     0.0013   2026-09-08 10:27:39
    38     42    0.2158925617    0.3002499347     2764.1523826391    2.9093229811       19.4047842378     0.0013   2026-09-08 10:27:39
    39     43    0.0979182132    0.1363385690     2763.4288820281    0.7235006110       17.2035688985     0.0011   2026-09-08 10:27:39
    40     44    0.0150932498    0.0243105815     2763.3628585603    0.0660234678       17.5236637200     0.0010   2026-09-08 10:27:39
    41     45    0.0045621363    0.0063206829     2763.3442712690    0.0185872914       17.5546538909     0.0010   2026-09-08 10:27:39
    42     46    0.0108833020    0.0145068693     2763.2779933605    0.0662779085       17.5035819443     0.0010   2026-09-08 10:27:39
    43     47    0.0152825493    0.0190484768     2763.1337760153    0.1442173452       17.1820143086     0.0012   2026-09-08 10:27:39
    44     48    0.0262834436    0.0344303153     2762.7590957429    0.3746802724       16.0378004556     0.0010   2026-09-08 10:27:39
    45     49    0.0370825486    0.0676252158     2761.9532190501    0.8058766928       13.1828891698     0.0009   2026-09-08 10:27:39
    46     50    0.0780887745    0.1346572861     2760.5471891262    1.4060299239       14.5849786756     0.0010   2026-09-08 10:27:39
    47     51    0.1020743001    0.1827995053     2759.0646945555    1.4824945707       13.8989236998     0.0009   2026-09-08 10:27:39
    48     52    0.0567709469    0.1209981873     2758.3590013066    0.7056932489        7.7908904702     0.0009   2026-09-08 10:27:39
    49     53    0.0236854648    0.0318333578     2758.2413062310    0.1176950756        4.8801427653     0.0012   2026-09-08 10:27:39
    50     54    0.0058757221    0.0105532664     2758.2331607295    0.0081455016        4.9393997582     0.0010   2026-09-08 10:27:39
    51     55    0.0023652451    0.0039337921     2758.2301518401    0.0030088893        4.9584603233     0.0009   2026-09-08 10:27:39
    52     56    0.0062971962    0.0102122947     2758.2178703502    0.0122814900        5.0012364756     0.0009   2026-09-08 10:27:39
    53     57    0.0083372884    0.0130778182     2758.1912362957    0.0266340545        5.0401328612     0.0010   2026-09-08 10:27:39
    54     58    0.0135107125    0.0213848126     2758.1204003068    0.0708359889        5.0553352540     0.0009   2026-09-08 10:27:39
    55     59    0.0173202856    0.0340989411     2757.9619532939    0.1584470129        5.6543432604     0.0012   2026-09-08 10:27:39
    56     60    0.0342964789    0.0637866887     2757.6582585333    0.3036947607        6.1165031232     0.0009   2026-09-08 10:27:39
    57     61    0.0643485862    0.1020634079     2757.2754729157    0.3827856175        7.3536282348     0.0010   2026-09-08 10:27:39
    58     62    0.0585197123    0.0954609552     2757.0356942198    0.2397786960        8.2098611304     0.0013   2026-09-08 10:27:39
    59     63    0.0212758958    0.0394960870     2756.9765322917    0.0591619281        8.3088108476     0.0013   2026-09-08 10:27:39
    60     64    0.0059735188    0.0101300300     2756.9676372231    0.0088950686        7.9579966964     0.0009   2026-09-08 10:27:39
    61     65    0.0027147190    0.0058686723     2756.9606451731    0.0069920500        7.6795915712     0.0011   2026-09-08 10:27:39
    62     66    0.0049250153    0.0108158230     2756.9385827762    0.0220623969        7.0489814196     0.0013   2026-09-08 10:27:39
    63     67    0.0072637189    0.0140233273     2756.8871989778    0.0513837984        5.9972798757     0.0010   2026-09-08 10:27:39
    64     68    0.0116584037    0.0246480283     2756.7581462399    0.1290527378        4.3491320835     0.0009   2026-09-08 10:27:39
    65     69    0.0326412079    0.0567740060     2756.4825656694    0.2755805705        4.3068342004     0.0009   2026-09-08 10:27:39
    66     70    0.0767999706    0.1224819898     2756.0226815171    0.4598841523        6.0030081307     0.0013   2026-09-08 10:27:39
    67     71    0.1022251850    0.1645922145     2755.5715341120    0.4511474051        6.6007518067     0.0012   2026-09-08 10:27:39
    68     72    0.0570639858    0.1001923739     2755.3761096102    0.1954245019        6.1400346024     0.0014   2026-09-08 10:27:39
    69     73    0.0097936279    0.0204070022     2755.3455226492    0.0305869610        4.8063521680     0.0013   2026-09-08 10:27:39
    70     74    0.0042069040    0.0073081835     2755.3421914312    0.0033312180        4.3393800009     0.0011   2026-09-08 10:27:39
    71     75    0.0036755356    0.0060134882     2755.3386218718    0.0035695594        3.9815573062     0.0012   2026-09-08 10:27:39
    72     76    0.0067386016    0.0109378831     2755.3276113470    0.0110105247        3.2442816627     0.0009   2026-09-08 10:27:39
    73     77    0.0080974166    0.0134679165     2755.3021248062    0.0254865409        3.1670172009     0.0010   2026-09-08 10:27:39
    74     78    0.0101081836    0.0165533428     2755.2418133189    0.0603114873        2.9741379860     0.0012   2026-09-08 10:27:39
    75     79    0.0129624200    0.0283262385     2755.1281223293    0.1136909896        2.5774066063     0.0010   2026-09-08 10:27:39
    76     80    0.0282695682    0.0615598612     2754.9822556473    0.1458666820        3.8030868438     0.0010   2026-09-08 10:27:39
    77     81    0.0379578580    0.0713931556     2754.8904920701    0.0917635772        3.1924810856     0.0009   2026-09-08 10:27:39
    78     82    0.0195126947    0.0325503289     2754.8684739894    0.0220180807        3.5151109609     0.0010   2026-09-08 10:27:39
    79     83    0.0030004581    0.0051509183     2754.8661717364    0.0023022530        3.4610944311     0.0013   2026-09-08 10:27:39
    80     84    0.0009378757    0.0015690473     2754.8652788868    0.0008928496        3.3888868641     0.0014   2026-09-08 10:27:39
    81     85    0.0020799069    0.0034611390     2754.8621348100    0.0031440767        3.1824655862     0.0014   2026-09-08 10:27:39
    82     86    0.0028044670    0.0044420919     2754.8552066679    0.0069281421        2.8294191730     0.0009   2026-09-08 10:27:39
    83     87    0.0042584572    0.0076057756     2754.8378231348    0.0173835331        2.2873438648     0.0009   2026-09-08 10:27:39
    84     88    0.0072547047    0.0149856224     2754.8027239060    0.0350992288        2.2266561684     0.0012   2026-09-08 10:27:39
    85     89    0.0117483016    0.0286888743     2754.7496437725    0.0530801336        2.3382977538     0.0010   2026-09-08 10:27:39
    86     90    0.0149695756    0.0336510709     2754.7060877766    0.0435559958        2.0575526946     0.0009   2026-09-08 10:27:39
    87     91    0.0075401910    0.0175342474     2754.6912970667    0.0147907099        2.0444835185     0.0013   2026-09-08 10:27:39
    88     92    0.0024982894    0.0039533780     2754.6893226957    0.0019743710        2.0560668931     0.0009   2026-09-08 10:27:39
    89     93    0.0007399795    0.0013629370     2754.6888649130    0.0004577827        2.0612835113     0.0011   2026-09-08 10:27:39
    90     94    0.0012398653    0.0022254589     2754.6877113259    0.0011535871        2.0684172702     0.0014   2026-09-08 10:27:39
    91     95    0.0018872198    0.0030797161     2754.6848951624    0.0028161634        2.0745118445     0.0009   2026-09-08 10:27:39
    92     96    0.0031294281    0.0049051924     2754.6774360647    0.0074590977        2.0719237887     0.0010   2026-09-08 10:27:39
    93     97    0.0049094492    0.0099716655     2754.6586774984    0.0187585663        2.0354803970     0.0010   2026-09-08 10:27:39
    94     98    0.0120331242    0.0260614823     2754.6132004344    0.0454770640        2.2040029900     0.0011   2026-09-08 10:27:39
    95     99    0.0282911068    0.0645164471     2754.5160107880    0.0971896464        3.4304915486     0.0013   2026-09-08 10:27:39
    96    100    0.0558084818    0.1237348529     2754.3581254416    0.1578853464        4.3771040707     0.0013   2026-09-08 10:27:39
    97    101    0.0644759845    0.1417012256     2754.2091148907    0.1490105509        3.4276632346     0.0012   2026-09-08 10:27:39
    98    102    0.0292376827    0.0637122057     2754.1496935357    0.0594213550        1.4088367387     0.0014   2026-09-08 10:27:39
    99    103    0.0056935473    0.0102649001     2754.1416912995    0.0080022362        1.2123025580     0.0012   2026-09-08 10:27:39
   100    104    0.0032634237    0.0072564956     2754.1412814397    0.0004098598        1.2077050611     0.0011   2026-09-08 10:27:39
   101    105    0.0008584333    0.0019119552     2754.1411865771    0.0000948626        1.1985284007     0.0011   2026-09-08 10:27:39
   102    106    0.0024566742    0.0053930574     2754.1407660034    0.0004205737        1.1557349683     0.0010   2026-09-08 10:27:39
   103    107    0.0029979856    0.0064199814     2754.1399019904    0.0008640130        1.0663608141     0.0010   2026-09-08 10:27:39
   104    108    0.0042754238    0.0088194880     2754.1377366526    0.0021653378        0.8370137712     0.0010   2026-09-08 10:27:39
   105    109    0.0035056695    0.0071857102     2754.1336771348    0.0040595178        0.5115877902     0.0010   2026-09-08 10:27:39
   106    110    0.0043559238    0.0089692736     2754.1282703876    0.0054067472        0.4474139258     0.0010   2026-09-08 10:27:39
   107    111    0.0080470055    0.0189172489     2754.1247041232    0.0035662643        0.6759229185     0.0010   2026-09-08 10:27:39
   108    112    0.0058294842    0.0134322999     2754.1237784518    0.0009256714        0.7031124863     0.0010   2026-09-08 10:27:39
   109    113    0.0015490162    0.0032755883     2754.1236673139    0.0001111380        0.6376379153     0.0010   2026-09-08 10:27:39
   110    114    0.0004162404    0.0008505082     2754.1236169300    0.0000503839        0.6019260698     0.0010   2026-09-08 10:27:39
   111    115    0.0008226656    0.0017142189     2754.1234465205    0.0001704095        0.5212422244     0.0011   2026-09-08 10:27:39
   112    116    0.0011335643    0.0024897384     2754.1230519660    0.0003945545        0.4776830592     0.0011   2026-09-08 10:27:39
   113    117    0.0018846218    0.0045354362     2754.1219806223    0.0010713437        0.4925953428     0.0010   2026-09-08 10:27:39
   114    118    0.0035101035    0.0082768629     2754.1192963260    0.0026842963        0.5109737112     0.0009   2026-09-08 10:27:39
   115    119    0.0074709224    0.0166500553     2754.1126852232    0.0066111028        0.6363093278     0.0013   2026-09-08 10:27:39
   116    120    0.0157681901    0.0334217691     2754.0981418219    0.0145434014        1.3413917462     0.0011   2026-09-08 10:27:39
   117    121    0.0293207272    0.0579060056     2754.0729127880    0.0252290339        1.9983714663     0.0011   2026-09-08 10:27:39
   118    122    0.0340529737    0.0657472046     2754.0460842122    0.0268285758        2.4978285440     0.0010   2026-09-08 10:27:39
   119    123    0.0156476788    0.0336990003     2754.0330048689    0.0130793432        3.1246975904     0.0009   2026-09-08 10:27:39
   120    124    0.0049041325    0.0111639217     2754.0304842852    0.0025205837        3.1396194263     0.0009   2026-09-08 10:27:39
   121    125    0.0026430304    0.0058112617     2754.0300651915    0.0004190937        3.0646274245     0.0010   2026-09-08 10:27:39
   122    126    0.0025467097    0.0053856734     2754.0295035754    0.0005616160        2.9754711837     0.0009   2026-09-08 10:27:39
   123    127    0.0039480488    0.0084838880     2754.0279121947    0.0015913807        2.7948093953     0.0009   2026-09-08 10:27:39
   124    128    0.0043570251    0.0097903108     2754.0240578348    0.0038543599        2.4787222354     0.0010   2026-09-08 10:27:39
   125    129    0.0047813393    0.0092524902     2754.0147232441    0.0093345907        1.9016584733     0.0010   2026-09-08 10:27:39
   126    130    0.0092658737    0.0224281088     2753.9955120458    0.0192111982        1.0364534758     0.0011   2026-09-08 10:27:39
   127    131    0.0314127140    0.0647088857     2753.9664808291    0.0290312167        1.3518988158     0.0010   2026-09-08 10:27:39
   128    132    0.0453891914    0.0914947448     2753.9427567831    0.0237240460        0.9542399525     0.0010   2026-09-08 10:27:39
   129    133    0.0255192044    0.0516968835     2753.9349372343    0.0078195488        0.3871183793     0.0010   2026-09-08 10:27:39
   130    134    0.0033682120    0.0076838954     2753.9340528861    0.0008843482        0.3021945644     0.0010   2026-09-08 10:27:39
   131    135    0.0008928768    0.0019662060     2753.9340188931    0.0000339930        0.3001319785     0.0010   2026-09-08 10:27:39
   132    136    0.0003036513    0.0006097662     2753.9340113106    0.0000075825        0.3003215933     0.0009   2026-09-08 10:27:39
   133    137    0.0010912414    0.0021273189     2753.9339708375    0.0000404731        0.3016279414     0.0012   2026-09-08 10:27:39
   134    138    0.0014253625    0.0026480487     2753.9338864368    0.0000844007        0.3035708148     0.0013   2026-09-08 10:27:39
   135    139    0.0026310224    0.0045576500     2753.9336447415    0.0002416953        0.3069318297     0.0010   2026-09-08 10:27:39
   136    140    0.0042972668    0.0067382033     2753.9330390046    0.0006057368        0.3112814323     0.0011   2026-09-08 10:27:39
   137    141    0.0074465498    0.0104493329     2753.9314697056    0.0015692991        0.4471667739     0.0011   2026-09-08 10:27:39
   138    142    0.0125108292    0.0170251276     2753.9276260931    0.0038436124        0.7281248248     0.0010   2026-09-08 10:27:39
   139    143    0.0196413087    0.0331770398     2753.9189977585    0.0086283347        1.0703499295     0.0014   2026-09-08 10:27:39
   140    144    0.0307684087    0.0665299057     2753.9035260470    0.0154717115        1.2847462095     0.0010   2026-09-08 10:27:39
   141    145    0.0509785834    0.0971462001     2753.8860204246    0.0175056224        1.0319884081     0.0009   2026-09-08 10:27:39
   142    146    0.0382040428    0.0717595448     2753.8769185284    0.0091018962        0.4225261856     0.0009   2026-09-08 10:27:39
   143    147    0.0122093807    0.0208987466     2753.8752110543    0.0017074742        0.1415135453     0.0009   2026-09-08 10:27:39
   144    148    0.0035910465    0.0064042366     2753.8751111088    0.0000999455        0.1356252011     0.0010   2026-09-08 10:27:39
   145    149    0.0006649305    0.0013085922     2753.8751083104    0.0000027984        0.1339403219     0.0010   2026-09-08 10:27:39
   146    150    0.0003105524    0.0006036373     2753.8751063639    0.0000019465        0.1330452614     0.0009   2026-09-08 10:27:39
   147    151    0.0008393849    0.0016483539     2753.8750979374    0.0000084265        0.1339183032     0.0009   2026-09-08 10:27:39
   148    152    0.0011032289    0.0022123476     2753.8750792085    0.0000187289        0.1350560040     0.0010   2026-09-08 10:27:39
   149    153    0.0018006479    0.0037474995     2753.8750270145    0.0000521939        0.1367808847     0.0013   2026-09-08 10:27:39
   150    154    0.0029053062    0.0056760012     2753.8748947786    0.0001322359        0.1389713346     0.0013   2026-09-08 10:27:39
   151    155    0.0049948450    0.0086829885     2753.8745527430    0.0003420356        0.1412336877     0.0009   2026-09-08 10:27:39
   152    156    0.0083910860    0.0126825999     2753.8737089311    0.0008438119        0.1415257257     0.0009   2026-09-08 10:27:39
   153    157    0.0132521514    0.0188883408     2753.8717891745    0.0019197566        0.1340619874     0.0010   2026-09-08 10:27:39
   154    158    0.0193479587    0.0322343359     2753.8682340310    0.0035551435        0.1080660632     0.0009   2026-09-08 10:27:39
   155    159    0.0376001053    0.0523157194     2753.8639380285    0.0042960025        0.0752050264     0.0009   2026-09-08 10:27:39
   156    160    0.0337612012    0.0504100287     2753.8614539379    0.0024840906        0.0375260315     0.0009   2026-09-08 10:27:39
   157    161    0.0107012871    0.0210856067     2753.8609337090    0.0005202289        0.0234112076     0.0009   2026-09-08 10:27:39
   158    162    0.0030655693    0.0043631453     2753.8609002559    0.0000334531        0.0189759960     0.0009   2026-09-08 10:27:39
   159    163    0.0005834856    0.0008345467     2753.8608996272    0.0000006287        0.0183789095     0.0009   2026-09-08 10:27:39
   160    164    0.0000607670    0.0000864499     2753.8608996004    0.0000000268        0.0183528010     0.0010   2026-09-08 10:27:39
   161    165    0.0001648311    0.0002368114     2753.8608994870    0.0000001134        0.0182935336     0.0012   2026-09-08 10:27:39
   162    166    0.0002164829    0.0003143607     2753.8608992400    0.0000002470        0.0182179566     0.0014   2026-09-08 10:27:39
   163    167    0.0003700361    0.0005468794     2753.8608985452    0.0000006948        0.0180747216     0.0014   2026-09-08 10:27:39
   164    168    0.0005855250    0.0008482662     2753.8608967881    0.0000017570        0.0178049982     0.0013   2026-09-08 10:27:39
   165    169    0.0009833532    0.0013511859     2753.8608922214    0.0000045668        0.0172375890     0.0009   2026-09-08 10:27:39
   166    170    0.0016016126    0.0020522526     2753.8608808567    0.0000113647        0.0160201504     0.0008   2026-09-08 10:27:39
   167    171    0.0024510614    0.0029336106     2753.8608544017    0.0000264550        0.0159647521     0.0008   2026-09-08 10:27:39
   168    172    0.0030082994    0.0038036259     2753.8608027902    0.0000516115        0.0150775494     0.0008   2026-09-08 10:27:39
   169    173    0.0028118315    0.0050338612     2753.8607336629    0.0000691272        0.0104490113     0.0008   2026-09-08 10:27:39
   170    174    0.0048277976    0.0061321662     2753.8606866319    0.0000470310        0.0037764318     0.0008   2026-09-08 10:27:39
   171    175    0.0028524883    0.0039258404     2753.8606745030    0.0000121290        0.0013929514     0.0009   2026-09-08 10:27:39

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','3.697119e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.2708***  0.2500   0.0000   
TC/100 EUR                        -1.5656**   0.7778   0.0441   
Babiogorski                        1.5404***  0.5429   0.0045   
Bieszczadzki                      -0.1068     0.2868   0.7096   
Gorczanski                         0.0441     0.7083   0.9503   
GorStolowych                       1.3331***  0.3527   0.0002   
Karkonoski                        -1.0645***  0.3141   0.0007   
Magurski                           0.6774     0.4370   0.1211   
Pieninski                         -1.2262**   0.5855   0.0363   
Swietokrzyski                      0.1133     0.1261   0.3687   
Household income (10k PLN)         0.3389***  0.1126   0.0026   
Male                               0.1164     0.0718   0.1051   
Higher education                   0.0185     0.0801   0.8175   
City                               0.1369*    0.0755   0.0696   
Winter                             0.8161***  0.0835   0.0000   
Hiking                             2.0857***  0.0789   0.0000   
Skiing                             1.3801***  0.2672   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2938     0.0945            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.6387**   0.3173   0.0441   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2753.8607
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1733
AIC/n:                             0.9468
BIC/n:                             0.9674
n (observations):               5855
r (respondents):                5855
k (parameters):                   18
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.9364
median                           0.0000          1.9333
std                              0.7834          0.8370
min                              0.0000          0.0250
max                             20.0000          4.9654
quantile 0.025                   0.0000          0.5313
quantile 0.975                   2.0000          3.5345
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:39
Estimation took 0.30281 seconds (0 hours 0 minutes 0.30281 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.52 -0.39 0.53 -0.0058 -0.071 0.14 -0.12 0.11 -0.27 0.043 0.1 0.011 0.0027 0.013 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3919.0957608383             NaN     4685.0127770805     0.0001   2026-09-08 10:27:40
     1      4    0.0668669547    0.1568806386     3194.6127462720  724.4830145663      400.7944448347     0.0033   2026-09-08 10:27:40
     2      5    0.0053061848    0.0084978912     3189.9417414125    4.6710048594      381.2692710731     0.0015   2026-09-08 10:27:40
     3      6    0.0236425395    0.0316794155     3179.1295071839   10.8122342287      328.8645796693     0.0013   2026-09-08 10:27:40
     4      7    0.0326151315    0.0410480095     3167.1312437430   11.9982634409      418.6610252728     0.0009   2026-09-08 10:27:40
     5      8    0.1255064244    0.1565450960     3127.7743874293   39.3568563136      665.1041199696     0.0009   2026-09-08 10:27:40
     6      9    0.1707126559    0.2124697845     3081.4674216643   46.3069657650      781.8422865563     0.0009   2026-09-08 10:27:40
     7     10    0.1800922202    0.2241387374     3038.3119068229   43.1555148414      677.6803512713     0.0009   2026-09-08 10:27:40
     8     11    0.1019905635    0.1270924121     3017.4415553035   20.8703515194      455.9342349060     0.0010   2026-09-08 10:27:40
     9     12    0.0503543250    0.0631775478     3007.8862093342    9.5553459693      286.1834025531     0.0010   2026-09-08 10:27:40
    10     13    0.0511576100    0.0654039897     2997.2604371333   10.6257722009      356.6978434740     0.0012   2026-09-08 10:27:40
    11     14    0.1036381637    0.1346799596     2975.2169357210   22.0435014124      540.7440256429     0.0010   2026-09-08 10:27:40
    12     15    0.1962471483    0.2578423892     2935.3276268577   39.8893088632      669.0266150079     0.0009   2026-09-08 10:27:40
    13     16    0.2878474853    0.3824594013     2883.5854311200   51.7421957377      585.5438240250     0.0012   2026-09-08 10:27:40
    14     17    0.2051696237    0.2782156120     2853.4335915934   30.1518395267      293.9021155037     0.0011   2026-09-08 10:27:40
    15     18    0.0251078690    0.0402454740     2845.8518651701    7.5817264233      140.3856978086     0.0010   2026-09-08 10:27:40
    16     19    0.0356752047    0.0475267992     2843.9626251790    1.8892399911       88.3105112192     0.0011   2026-09-08 10:27:40
    17     20    0.0246271882    0.0324832183     2843.5346299481    0.4279952309       96.4242105216     0.0011   2026-09-08 10:27:40
    18     21    0.0201179752    0.0256609073     2843.0591198982    0.4755100499       99.7215859247     0.0010   2026-09-08 10:27:40
    19     22    0.0389711382    0.0487572118     2841.6255998763    1.4335200219      103.8389631275     0.0010   2026-09-08 10:27:40
    20     23    0.0508785659    0.0681265947     2838.4554170292    3.1701828472      105.7694227013     0.0010   2026-09-08 10:27:40
    21     24    0.0661650545    0.1096494309     2831.7473976833    6.7080193459      103.0301203531     0.0009   2026-09-08 10:27:40
    22     25    0.1407666907    0.1787810658     2821.9162266719    9.8311710114      100.2165728785     0.0010   2026-09-08 10:27:40
    23     26    0.1608210605    0.2232812791     2813.9668964517    7.9493302201       53.5634838522     0.0011   2026-09-08 10:27:40
    24     27    0.0873686181    0.1364575079     2811.5553092238    2.4115872279       38.2662416779     0.0013   2026-09-08 10:27:40
    25     28    0.0300215999    0.0377874028     2811.2184891437    0.3368200801       35.9979191073     0.0011   2026-09-08 10:27:40
    26     29    0.0126939901    0.0159674511     2811.0176044115    0.2008847322       34.3892557290     0.0010   2026-09-08 10:27:40
    27     30    0.0223083169    0.0296076358     2810.4243837790    0.5932206325       33.3612544092     0.0010   2026-09-08 10:27:40
    28     31    0.0298288421    0.0458076700     2809.0717651062    1.3526186728       36.1231299153     0.0010   2026-09-08 10:27:40
    29     32    0.0491943644    0.0936167317     2805.7085224810    3.3632426251       53.9696358893     0.0010   2026-09-08 10:27:40
    30     33    0.1286114360    0.1932321361     2798.6439658798    7.0645566013       74.0014198710     0.0010   2026-09-08 10:27:40
    31     34    0.2545606059    0.3484533534     2787.1316587146   11.5123071652       83.8436568982     0.0011   2026-09-08 10:27:40
    32     35    0.2971635351    0.3948197796     2776.1824688594   10.9491898552       65.3589715122     0.0012   2026-09-08 10:27:40
    33     36    0.1326879464    0.1932303201     2771.4132282085    4.7692406508       29.9388943009     0.0010   2026-09-08 10:27:40
    34     37    0.0383297141    0.0619436574     2770.6216501087    0.7915780999       19.7108972564     0.0012   2026-09-08 10:27:40
    35     38    0.0219468637    0.0300356234     2770.5659539132    0.0556961955       18.9337180049     0.0011   2026-09-08 10:27:40
    36     39    0.0096569748    0.0127891102     2770.5380271867    0.0279267266       18.6765445489     0.0011   2026-09-08 10:27:40
    37     40    0.0231224629    0.0312582337     2770.4331205869    0.1049065998       18.0054715628     0.0010   2026-09-08 10:27:40
    38     41    0.0271817790    0.0389881508     2770.2145102609    0.2186103260       17.0238177225     0.0013   2026-09-08 10:27:40
    39     42    0.0361122634    0.0606815704     2769.6495607151    0.5649495457       15.2721123839     0.0010   2026-09-08 10:27:40
    40     43    0.0497492647    0.0826335995     2768.4454441794    1.2041165357       20.5957415775     0.0011   2026-09-08 10:27:40
    41     44    0.0603096707    0.1261364785     2766.3498196006    2.0956245788       22.9409854504     0.0010   2026-09-08 10:27:40
    42     45    0.1091842078    0.1840518659     2764.1711801837    2.1786394169       17.9221894603     0.0011   2026-09-08 10:27:40
    43     46    0.1172550110    0.1556179248     2763.1981806112    0.9729995724       17.5411364501     0.0010   2026-09-08 10:27:40
    44     47    0.0380561446    0.0532964110     2763.0596710329    0.1385095783       15.7454985945     0.0010   2026-09-08 10:27:40
    45     48    0.0055933427    0.0099331640     2763.0438123662    0.0158586667       14.9064694020     0.0010   2026-09-08 10:27:40
    46     49    0.0048153595    0.0092195521     2763.0202027814    0.0236095847       14.3272186577     0.0014   2026-09-08 10:27:40
    47     50    0.0089618363    0.0157512980     2762.9532435230    0.0669592584       14.7820254772     0.0011   2026-09-08 10:27:40
    48     51    0.0148006858    0.0236514264     2762.7898243102    0.1634192128       15.2582464191     0.0013   2026-09-08 10:27:40
    49     52    0.0255035389    0.0407396958     2762.3876672187    0.4021570916       15.4270601663     0.0011   2026-09-08 10:27:40
    50     53    0.0394277777    0.0784537296     2761.5199094367    0.8677577820       14.2923119274     0.0010   2026-09-08 10:27:40
    51     54    0.0833666668    0.1472760367     2760.0562579242    1.4636515125       11.3482031953     0.0012   2026-09-08 10:27:40
    52     55    0.1305899413    0.1901311069     2758.5812074269    1.4750504973       14.3377634250     0.0012   2026-09-08 10:27:40
    53     56    0.0865627609    0.1181138056     2757.9151458233    0.6660616036       10.2987300990     0.0014   2026-09-08 10:27:40
    54     57    0.0215722458    0.0350887306     2757.8001907240    0.1149550993        6.6031044984     0.0010   2026-09-08 10:27:40
    55     58    0.0054943385    0.0122415152     2757.7912660110    0.0089247129        6.6639218777     0.0014   2026-09-08 10:27:40
    56     59    0.0028391600    0.0050898399     2757.7863605343    0.0049054767        6.6836029805     0.0012   2026-09-08 10:27:40
    57     60    0.0076964628    0.0133088693     2757.7653264725    0.0210340618        6.7214852381     0.0011   2026-09-08 10:27:40
    58     61    0.0095939305    0.0161160150     2757.7200124944    0.0453139781        6.7352482578     0.0011   2026-09-08 10:27:40
    59     62    0.0136916143    0.0237114411     2757.6017705237    0.1182419708        6.6614062831     0.0014   2026-09-08 10:27:40
    60     63    0.0159375991    0.0341989660     2757.3497700566    0.2520004671        6.3364400707     0.0013   2026-09-08 10:27:40
    61     64    0.0400531838    0.0680769281     2756.9173781975    0.4323918592        6.0448018034     0.0012   2026-09-08 10:27:40
    62     65    0.0676408714    0.1089691596     2756.4763550750    0.4410231225        6.0428298024     0.0012   2026-09-08 10:27:40
    63     66    0.0503204569    0.0889836593     2756.2718869082    0.2044681668        5.5947076902     0.0010   2026-09-08 10:27:40
    64     67    0.0166670258    0.0287502759     2756.2363980582    0.0354888500        5.7695961728     0.0009   2026-09-08 10:27:40
    65     68    0.0026538965    0.0053166903     2756.2323928700    0.0040051882        5.6182762799     0.0012   2026-09-08 10:27:40
    66     69    0.0015499267    0.0036075016     2756.2287717544    0.0036211156        5.4802650065     0.0010   2026-09-08 10:27:40
    67     70    0.0028524402    0.0069473467     2756.2171974659    0.0115742885        5.1670569208     0.0014   2026-09-08 10:27:40
    68     71    0.0041132507    0.0093825581     2756.1896784355    0.0275190304        5.2448457382     0.0016   2026-09-08 10:27:40
    69     72    0.0071160687    0.0153099311     2756.1177627589    0.0719156766        5.3436673457     0.0014   2026-09-08 10:27:40
    70     73    0.0132312228    0.0310678148     2755.9476493008    0.1701134581        5.3118437839     0.0013   2026-09-08 10:27:40
    71     74    0.0434131289    0.0740479865     2755.5893972364    0.3582520644        4.9055233839     0.0013   2026-09-08 10:27:40
    72     75    0.0922917656    0.1424590599     2755.0340712384    0.5553259980        7.9792069614     0.0013   2026-09-08 10:27:40
    73     76    0.1085206028    0.1629659864     2754.5508304451    0.4832407933        8.4451019350     0.0012   2026-09-08 10:27:40
    74     77    0.0485235141    0.0761303834     2754.3805461397    0.1702843054        7.2824884668     0.0013   2026-09-08 10:27:40
    75     78    0.0068626421    0.0140256290     2754.3583587138    0.0221874259        7.7314632044     0.0013   2026-09-08 10:27:40
    76     79    0.0040737669    0.0070730037     2754.3549728850    0.0033858288        7.7034302178     0.0010   2026-09-08 10:27:40
    77     80    0.0049993992    0.0083423223     2754.3493321615    0.0056407236        7.6164674565     0.0010   2026-09-08 10:27:40
    78     81    0.0075782207    0.0128122127     2754.3343184697    0.0150136918        7.4026582262     0.0009   2026-09-08 10:27:40
    79     82    0.0090278902    0.0163648190     2754.2976551783    0.0366632914        6.9275106671     0.0009   2026-09-08 10:27:40
    80     83    0.0094742649    0.0182221502     2754.2128177816    0.0848373967        5.8962768880     0.0009   2026-09-08 10:27:40
    81     84    0.0142556075    0.0311510682     2754.0517609010    0.1610568806        3.9994475597     0.0009   2026-09-08 10:27:40
    82     85    0.0394267381    0.0726830274     2753.8466110627    0.2051498383        3.9189443546     0.0010   2026-09-08 10:27:40
    83     86    0.0507660703    0.0849381535     2753.7202987509    0.1263123119        3.6803297659     0.0012   2026-09-08 10:27:40
    84     87    0.0223294877    0.0367821042     2753.6921832171    0.0281155338        2.3796912300     0.0010   2026-09-08 10:27:40
    85     88    0.0024760609    0.0051156687     2753.6899497256    0.0022334915        1.8583649623     0.0010   2026-09-08 10:27:40
    86     89    0.0005593230    0.0011342631     2753.6896193440    0.0003303815        1.7654402801     0.0009   2026-09-08 10:27:40
    87     90    0.0010471074    0.0023013578     2753.6886171831    0.0010021610        1.5797585631     0.0009   2026-09-08 10:27:40
    88     91    0.0013604127    0.0031080711     2753.6863232770    0.0022939061        1.4355006992     0.0013   2026-09-08 10:27:40
    89     92    0.0024644531    0.0046966257     2753.6804698036    0.0058534734        1.5096115688     0.0013   2026-09-08 10:27:40
    90     93    0.0038988623    0.0067467783     2753.6677687962    0.0127010074        1.4969654047     0.0016   2026-09-08 10:27:40
    91     94    0.0049255112    0.0115583516     2753.6456183812    0.0221504149        1.3634455079     0.0014   2026-09-08 10:27:40
    92     95    0.0067393017    0.0177782992     2753.6221005268    0.0235178545        1.6970374238     0.0011   2026-09-08 10:27:40
    93     96    0.0071004455    0.0152456847     2753.6106550215    0.0114455053        1.5584241781     0.0013   2026-09-08 10:27:40
    94     97    0.0025999684    0.0055576167     2753.6085640538    0.0020909677        1.6066449916     0.0010   2026-09-08 10:27:40
    95     98    0.0006863919    0.0011529091     2753.6083010573    0.0002629965        1.6123216723     0.0010   2026-09-08 10:27:40
    96     99    0.0004816883    0.0008108985     2753.6080244806    0.0002765766        1.6140599155     0.0012   2026-09-08 10:27:40
    97    100    0.0009504681    0.0015267885     2753.6071560429    0.0008684377        1.6154965583     0.0014   2026-09-08 10:27:40
    98    101    0.0014338142    0.0022388505     2753.6050510970    0.0021049459        1.6138154889     0.0013   2026-09-08 10:27:40
    99    102    0.0024017163    0.0042841848     2753.5994472234    0.0056038736        1.6011404695     0.0010   2026-09-08 10:27:40
   100    103    0.0045504281    0.0099519567     2753.5853638562    0.0140833672        1.5561733610     0.0009   2026-09-08 10:27:40
   101    104    0.0122162744    0.0256106753     2753.5511068718    0.0342569844        2.1250536733     0.0010   2026-09-08 10:27:40
   102    105    0.0284652421    0.0604269988     2753.4774421408    0.0736647310        3.4909523983     0.0010   2026-09-08 10:27:40
   103    106    0.0513820757    0.1119272541     2753.3560323172    0.1214098236        4.2987029185     0.0010   2026-09-08 10:27:40
   104    107    0.0557901725    0.1254857248     2753.2380857923    0.1179465249        3.3516716424     0.0010   2026-09-08 10:27:40
   105    108    0.0246909387    0.0548612789     2753.1887341719    0.0493516203        1.3964708859     0.0009   2026-09-08 10:27:40
   106    109    0.0047612265    0.0099105205     2753.1817027165    0.0070314554        1.0501719222     0.0010   2026-09-08 10:27:40
   107    110    0.0034577453    0.0074172815     2753.1813280760    0.0003746405        1.1084768838     0.0010   2026-09-08 10:27:40
   108    111    0.0008364409    0.0018432254     2753.1812547681    0.0000733080        1.1094113141     0.0010   2026-09-08 10:27:40
   109    112    0.0021768044    0.0047960355     2753.1809554226    0.0002993454        1.1030370560     0.0013   2026-09-08 10:27:40
   110    113    0.0027604137    0.0060570871     2753.1803127538    0.0006426689        1.0784488768     0.0015   2026-09-08 10:27:40
   111    114    0.0042272797    0.0092485517     2753.1786028606    0.0017098931        0.9949586149     0.0015   2026-09-08 10:27:40
   112    115    0.0047062645    0.0104915594     2753.1748208444    0.0037820162        0.7802276224     0.0013   2026-09-08 10:27:40
   113    116    0.0038721241    0.0083279297     2753.1677318682    0.0070889763        0.5165038451     0.0011   2026-09-08 10:27:40
   114    117    0.0082622220    0.0171507956     2753.1592018451    0.0085300231        0.6374397566     0.0010   2026-09-08 10:27:40
   115    118    0.0124235444    0.0272997503     2753.1542420055    0.0049598396        0.7290863205     0.0010   2026-09-08 10:27:40
   116    119    0.0068440947    0.0151741765     2753.1531635753    0.0010784302        0.7390908822     0.0010   2026-09-08 10:27:40
   117    120    0.0012794958    0.0028197949     2753.1530525739    0.0001110014        0.6888192143     0.0012   2026-09-08 10:27:40
   118    121    0.0003010603    0.0007177596     2753.1529974041    0.0000551697        0.6613254085     0.0011   2026-09-08 10:27:40
   119    122    0.0006633126    0.0015592877     2753.1527965309    0.0002008732        0.6129914901     0.0014   2026-09-08 10:27:40
   120    123    0.0010089196    0.0022267722     2753.1523365608    0.0004599701        0.6126036462     0.0011   2026-09-08 10:27:40
   121    124    0.0019648370    0.0040970852     2753.1510744582    0.0012621026        0.6268402743     0.0011   2026-09-08 10:27:40
   122    125    0.0037189595    0.0076676073     2753.1478787031    0.0031957551        0.6453752584     0.0011   2026-09-08 10:27:40
   123    126    0.0084775801    0.0164119271     2753.1397424199    0.0081362833        0.6645974594     0.0009   2026-09-08 10:27:40
   124    127    0.0188354520    0.0365960553     2753.1203456145    0.0193968054        0.8703588478     0.0009   2026-09-08 10:27:40
   125    128    0.0380872750    0.0768062971     2753.0797926203    0.0405529942        1.5079591921     0.0009   2026-09-08 10:27:40
   126    129    0.0587293218    0.1252557524     2753.0173698165    0.0624228038        1.7740088099     0.0009   2026-09-08 10:27:40
   127    130    0.0528925247    0.1170770957     2752.9637209694    0.0536488471        1.3639703378     0.0009   2026-09-08 10:27:40
   128    131    0.0180774746    0.0370067502     2752.9447248490    0.0189961204        1.0329519779     0.0009   2026-09-08 10:27:40
   129    132    0.0084431113    0.0162744700     2752.9424468645    0.0022779845        0.8443349371     0.0013   2026-09-08 10:27:40
   130    133    0.0031509764    0.0064652245     2752.9423427585    0.0001041060        0.8130839928     0.0010   2026-09-08 10:27:40
   131    134    0.0007848267    0.0016769627     2752.9423115324    0.0000312262        0.8059704665     0.0013   2026-09-08 10:27:40
   132    135    0.0023967437    0.0051693548     2752.9421588942    0.0001526382        0.7766615504     0.0010   2026-09-08 10:27:40
   133    136    0.0028277319    0.0061824489     2752.9418449004    0.0003139938        0.7227632825     0.0009   2026-09-08 10:27:40
   134    137    0.0039950966    0.0089843354     2752.9410256342    0.0008192661        0.5910857286     0.0009   2026-09-08 10:27:40
   135    138    0.0040949421    0.0081545075     2752.9393617145    0.0016639197        0.5086792000     0.0010   2026-09-08 10:27:40
   136    139    0.0027396679    0.0047622874     2752.9367384726    0.0026232419        0.4796908532     0.0010   2026-09-08 10:27:40
   137    140    0.0090993212    0.0183932509     2752.9344497204    0.0022887521        0.4509354525     0.0009   2026-09-08 10:27:40
   138    141    0.0092522489    0.0193010608     2752.9336071832    0.0008425373        0.5004370273     0.0010   2026-09-08 10:27:40
   139    142    0.0030170994    0.0065788588     2752.9334925979    0.0001145853        0.4441341279     0.0009   2026-09-08 10:27:40
   140    143    0.0004353138    0.0008970432     2752.9334739773    0.0000186206        0.4457141145     0.0010   2026-09-08 10:27:40
   141    144    0.0004341432    0.0008920007     2752.9334387651    0.0000352122        0.4483009734     0.0009   2026-09-08 10:27:40
   142    145    0.0006535510    0.0014505427     2752.9333456580    0.0000931071        0.4523754040     0.0010   2026-09-08 10:27:40
   143    146    0.0010772770    0.0024503062     2752.9331044101    0.0002412479        0.4582697811     0.0010   2026-09-08 10:27:40
   144    147    0.0020936720    0.0043871941     2752.9324764949    0.0006279152        0.4660281921     0.0011   2026-09-08 10:27:40
   145    148    0.0044416149    0.0083168480     2752.9308703064    0.0016061885        0.4737194479     0.0010   2026-09-08 10:27:40
   146    149    0.0096925097    0.0166988609     2752.9268985241    0.0039717824        0.5411433433     0.0014   2026-09-08 10:27:40
   147    150    0.0202242999    0.0335154538     2752.9179147188    0.0089838053        1.0269923550     0.0019   2026-09-08 10:27:40
   148    151    0.0356310011    0.0588210468     2752.9014332294    0.0164814894        1.4330474710     0.0017   2026-09-08 10:27:40
   149    152    0.0412577341    0.0703473117     2752.8819232720    0.0195099573        1.3049111972     0.0015   2026-09-08 10:27:40
   150    153    0.0215177243    0.0382354838     2752.8710029605    0.0109203115        0.6074898172     0.0018   2026-09-08 10:27:40
   151    154    0.0054716934    0.0121875645     2752.8688046661    0.0021982945        0.1893893992     0.0016   2026-09-08 10:27:40
   152    155    0.0043413069    0.0072005587     2752.8686678035    0.0001368625        0.1885181917     0.0016   2026-09-08 10:27:40
   153    156    0.0007378016    0.0012384285     2752.8686632961    0.0000045074        0.1890592196     0.0015   2026-09-08 10:27:40
   154    157    0.0003405439    0.0005832958     2752.8686599326    0.0000033635        0.1893122153     0.0015   2026-09-08 10:27:40
   155    158    0.0008660124    0.0015073124     2752.8686460415    0.0000138911        0.1899726184     0.0013   2026-09-08 10:27:40
   156    159    0.0011394073    0.0020401888     2752.8686147815    0.0000312600        0.1908185795     0.0012   2026-09-08 10:27:40
   157    160    0.0018112528    0.0034128803     2752.8685281251    0.0000866564        0.1920857801     0.0010   2026-09-08 10:27:40
   158    161    0.0028302020    0.0051262506     2752.8683081689    0.0002199562        0.1936055591     0.0011   2026-09-08 10:27:40
   159    162    0.0046503545    0.0077400355     2752.8677397733    0.0005683956        0.1948357611     0.0011   2026-09-08 10:27:40
   160    163    0.0073068986    0.0113270235     2752.8663378362    0.0014019372        0.1936378484     0.0011   2026-09-08 10:27:40
   161    164    0.0103744773    0.0180864995     2752.8631527442    0.0031850920        0.1843420568     0.0014   2026-09-08 10:27:40
   162    165    0.0207873653    0.0342718355     2752.8572716493    0.0058810949        0.2082756249     0.0014   2026-09-08 10:27:40
   163    166    0.0414283376    0.0559219686     2752.8502063861    0.0070652632        0.1851508236     0.0014   2026-09-08 10:27:40
   164    167    0.0376928020    0.0506842579     2752.8461585594    0.0040478267        0.0949095550     0.0011   2026-09-08 10:27:40
   165    168    0.0108036020    0.0190316476     2752.8453214498    0.0008371096        0.0803055143     0.0011   2026-09-08 10:27:40
   166    169    0.0023457906    0.0040758552     2752.8452682345    0.0000532153        0.0716826564     0.0011   2026-09-08 10:27:40
   167    170    0.0006215019    0.0008796993     2752.8452670206    0.0000012139        0.0702043076     0.0012   2026-09-08 10:27:40
   168    171    0.0001423642    0.0001903736     2752.8452667075    0.0000003131        0.0702845523     0.0011   2026-09-08 10:27:40
   169    172    0.0005873519    0.0007791398     2752.8452647205    0.0000019870        0.0711046087     0.0010   2026-09-08 10:27:40
   170    173    0.0007274563    0.0009540830     2752.8452606841    0.0000040365        0.0720675179     0.0011   2026-09-08 10:27:40
   171    174    0.0013150576    0.0016966990     2752.8452489744    0.0000117096        0.0736935804     0.0011   2026-09-08 10:27:40
   172    175    0.0020322819    0.0025603772     2752.8452196810    0.0000292934        0.0759583312     0.0010   2026-09-08 10:27:40
   173    176    0.0032779949    0.0040119869     2752.8451431814    0.0000764997        0.0790071336     0.0011   2026-09-08 10:27:40
   174    177    0.0049627161    0.0059769557     2752.8449528984    0.0001902829        0.0821141488     0.0011   2026-09-08 10:27:40
   175    178    0.0067360867    0.0088346343     2752.8445084120    0.0004444864        0.0825066930     0.0011   2026-09-08 10:27:40
   176    179    0.0070793846    0.0139077045     2752.8436357387    0.0008726733        0.0731873090     0.0010   2026-09-08 10:27:40
   177    180    0.0168237823    0.0225361905     2752.8424509401    0.0011847986        0.0468127780     0.0012   2026-09-08 10:27:40
   178    181    0.0199951548    0.0250946835     2752.8416265898    0.0008243504        0.0230040603     0.0011   2026-09-08 10:27:40
   179    182    0.0093373131    0.0132858300     2752.8414077770    0.0002188128        0.0075855269     0.0010   2026-09-08 10:27:40
   180    183    0.0025557757    0.0031863233     2752.8413895306    0.0000182464        0.0007768346     0.0010   2026-09-08 10:27:40

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','1.657773e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.2747***  0.2019   0.0000   
TC/100 EUR                        -1.4700**   0.7337   0.0451   
Babiogorski                        1.4742***  0.4580   0.0013   
Bieszczadzki                      -0.2426     0.2285   0.2883   
Gorczanski                         0.0996     0.6502   0.8782   
GorStolowych                       1.1045***  0.2931   0.0002   
Karkonoski                        -0.8899***  0.2605   0.0006   
Magurski                           0.8077**   0.3745   0.0310   
Pieninski                         -1.1988**   0.5703   0.0355   
Swietokrzyski                      0.0908     0.1016   0.3718   
Household income (10k PLN)         0.4800***  0.1448   0.0009   
Male                               0.1180     0.0720   0.1013   
Higher education                   0.0231     0.0802   0.7736   
City                               0.1309*    0.0754   0.0826   
Winter                             0.8096***  0.0838   0.0000   
Hiking                             2.0869***  0.0790   0.0000   
Skiing                             1.3593***  0.2694   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3023     0.0938            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.6803**   0.3396   0.0451   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2752.8414
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1736
AIC/n:                             0.9465
BIC/n:                             0.9670
n (observations):               5855
r (respondents):                5855
k (parameters):                   18
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.3643
median                           0.0000          2.3002
std                              0.7834          1.0883
min                              0.0000          0.0258
max                             20.0000          8.1215
quantile 0.025                   0.0000          0.6384
quantile 0.975                   2.0000          4.6816
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:40
Estimation took 0.33474 seconds (0 hours 0 minutes 0.33474 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.51 -0.43 0.55 0.0055 -0.031 0.13 -0.11 0.11 -0.3 0.044 0.058 0.01 0.0021 0.013 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3919.3228561544             NaN     4468.2607050564     0.0000   2026-09-08 10:27:41
     1      4    0.0728175558    0.1714884898     3148.4058535985  770.9170025559      410.2494322033     0.0038   2026-09-08 10:27:41
     2      5    0.0063136856    0.0088274634     3143.7885394478    4.6173141507      394.0144009397     0.0016   2026-09-08 10:27:41
     3      6    0.0452802483    0.0574206316     3124.5751883162   19.2133511317      355.0529068111     0.0013   2026-09-08 10:27:41
     4      7    0.0550316229    0.0673490300     3105.5359398966   19.0392484195      504.2487904362     0.0011   2026-09-08 10:27:41
     5      8    0.1809714596    0.2203118896     3053.2280272852   52.3079126115      667.3751090001     0.0012   2026-09-08 10:27:41
     6      9    0.1739999472    0.2114410752     3010.2298118178   42.9982154674      675.4319809061     0.0013   2026-09-08 10:27:41
     7     10    0.1337418360    0.1623553517     2981.5055909090   28.7242209088      484.8316351317     0.0014   2026-09-08 10:27:41
     8     11    0.0617778554    0.0748737012     2970.2920129169   11.2135779921      310.8674971055     0.0013   2026-09-08 10:27:41
     9     12    0.0444808554    0.0541993915     2962.0581200829    8.2338928340      263.6696945176     0.0015   2026-09-08 10:27:41
    10     13    0.0813335420    0.1003381416     2946.4186209740   15.6394991090      397.5602067953     0.0013   2026-09-08 10:27:41
    11     14    0.1601016698    0.1998296138     2916.3433758024   30.0752451716      538.2940973699     0.0012   2026-09-08 10:27:41
    12     15    0.2617829450    0.3309537862     2871.1050436494   45.2383321529      543.5470238004     0.0011   2026-09-08 10:27:41
    13     16    0.2458923982    0.3181029500     2835.0403905245   36.0646531250      326.6453299231     0.0012   2026-09-08 10:27:41
    14     17    0.0662551650    0.0947630414     2823.4761126179   11.5642779066      160.8888367174     0.0011   2026-09-08 10:27:41
    15     18    0.0312532450    0.0391496667     2820.7859171305    2.6901954875       62.1131160226     0.0010   2026-09-08 10:27:41
    16     19    0.0345898852    0.0435899123     2820.1663647774    0.6195523531       68.1526893225     0.0010   2026-09-08 10:27:41
    17     20    0.0162003831    0.0203654606     2819.8380630858    0.3283016916       70.8344063923     0.0010   2026-09-08 10:27:41
    18     21    0.0340067354    0.0431446038     2818.7458755580    1.0921875278       74.1200486382     0.0010   2026-09-08 10:27:41
    19     22    0.0383334320    0.0547943453     2816.5063177783    2.2395577797       75.1262008329     0.0011   2026-09-08 10:27:41
    20     23    0.0409684770    0.0843228430     2811.8963936273    4.6099241510       76.8417046484     0.0011   2026-09-08 10:27:41
    21     24    0.0766171172    0.1288060004     2805.8599702003    6.0364234269       69.5078351357     0.0012   2026-09-08 10:27:41
    22     25    0.0831487705    0.1509990734     2801.7470405994    4.1129296009       34.3356832838     0.0012   2026-09-08 10:27:41
    23     26    0.0607652638    0.0811912100     2800.7728892231    0.9741513763       24.2971773873     0.0011   2026-09-08 10:27:41
    24     27    0.0157827928    0.0196582001     2800.6579074443    0.1149817788       23.5894770255     0.0012   2026-09-08 10:27:41
    25     28    0.0061918195    0.0086290559     2800.5844359108    0.0734715334       23.6745589221     0.0011   2026-09-08 10:27:41
    26     29    0.0110517367    0.0166843610     2800.3597984882    0.2246374227       23.9857323936     0.0011   2026-09-08 10:27:41
    27     30    0.0154533590    0.0267237068     2799.8392311428    0.5205673454       26.8921576472     0.0011   2026-09-08 10:27:41
    28     31    0.0258954206    0.0573473337     2798.5006743216    1.3385568212       37.7633376326     0.0011   2026-09-08 10:27:41
    29     32    0.0743981022    0.1265047334     2795.4711798909    3.0294944307       51.7880655984     0.0012   2026-09-08 10:27:41
    30     33    0.1703641546    0.2592948713     2789.6426753045    5.8285045864       63.8648508244     0.0012   2026-09-08 10:27:41
    31     34    0.2638261328    0.3811935333     2782.0592162385    7.5834590660       60.5472150377     0.0014   2026-09-08 10:27:41
    32     35    0.2037869347    0.2888460792     2777.0157153722    5.0435008663       43.1213298951     0.0014   2026-09-08 10:27:41
    33     36    0.0359685097    0.0676358029     2775.6942917671    1.3214236051       42.9706965819     0.0014   2026-09-08 10:27:41
    34     37    0.0241364672    0.0417075889     2775.5306128133    0.1636789538       40.5572312912     0.0013   2026-09-08 10:27:41
    35     38    0.0130322798    0.0204117107     2775.4569184216    0.0736943917       39.4550758819     0.0011   2026-09-08 10:27:41
    36     39    0.0262250026    0.0424227103     2775.2075014797    0.2494169419       36.8337436089     0.0012   2026-09-08 10:27:41
    37     40    0.0278494083    0.0512229671     2774.6514946301    0.5560068496       32.6084729079     0.0011   2026-09-08 10:27:41
    38     41    0.0481957507    0.0691012308     2773.2374508378    1.4140437923       24.3796669280     0.0011   2026-09-08 10:27:41
    39     42    0.0737503445    0.1121041885     2770.2580235977    2.9794272401       31.8799167409     0.0011   2026-09-08 10:27:41
    40     43    0.1587082318    0.2612656736     2765.3809026340    4.8771209637       36.0720581050     0.0011   2026-09-08 10:27:41
    41     44    0.2711260494    0.3933235027     2760.8695491466    4.5113534874       25.9332067379     0.0011   2026-09-08 10:27:41
    42     45    0.1815151636    0.2599879975     2759.1331500011    1.7363991455       14.3985236513     0.0012   2026-09-08 10:27:41
    43     46    0.0330183458    0.0587379949     2758.9193662439    0.2137837572       13.5959943421     0.0010   2026-09-08 10:27:41
    44     47    0.0065886392    0.0093006104     2758.9051863173    0.0141799266       13.7060313881     0.0010   2026-09-08 10:27:41
    45     48    0.0040624526    0.0065313468     2758.8923882798    0.0127980375       13.8228718705     0.0011   2026-09-08 10:27:41
    46     49    0.0087647938    0.0134342698     2758.8501196068    0.0422686731       14.0025082453     0.0011   2026-09-08 10:27:41
    47     50    0.0128694302    0.0179437313     2758.7545259728    0.0955936339       13.9972883253     0.0011   2026-09-08 10:27:41
    48     51    0.0207216826    0.0279455758     2758.5210876630    0.2334383098       13.2913089845     0.0011   2026-09-08 10:27:41
    49     52    0.0274848270    0.0465568041     2758.0603199824    0.4607676807       10.8368033719     0.0011   2026-09-08 10:27:41
    50     53    0.0421556410    0.0813253125     2757.4041978853    0.6561220970       10.6353909631     0.0013   2026-09-08 10:27:41
    51     54    0.0397268946    0.0932051586     2756.9151224963    0.4890753890        8.5403608859     0.0014   2026-09-08 10:27:41
    52     55    0.0241353172    0.0499351752     2756.7704890234    0.1446334729        4.6920056079     0.0010   2026-09-08 10:27:41
    53     56    0.0087608873    0.0119176295     2756.7555123811    0.0149766423        4.7431886126     0.0010   2026-09-08 10:27:41
    54     57    0.0017328287    0.0028961878     2756.7533002213    0.0022121599        4.7681353231     0.0010   2026-09-08 10:27:41
    55     58    0.0026435367    0.0044183818     2756.7481600035    0.0051402178        4.8045029632     0.0010   2026-09-08 10:27:41
    56     59    0.0038690934    0.0065282059     2756.7354143476    0.0127456559        4.8517001577     0.0010   2026-09-08 10:27:41
    57     60    0.0058002159    0.0103697569     2756.7024034180    0.0330109297        4.9038077154     0.0010   2026-09-08 10:27:41
    58     61    0.0090013660    0.0179906671     2756.6220859346    0.0803174833        4.9206744302     0.0010   2026-09-08 10:27:41
    59     62    0.0191982979    0.0371992725     2756.4442064447    0.1778794899        5.9205249799     0.0010   2026-09-08 10:27:41
    60     63    0.0458562532    0.0736535485     2756.1345149756    0.3096914691        6.6635876324     0.0010   2026-09-08 10:27:41
    61     64    0.0656850435    0.1007598550     2755.8005801815    0.3339347941        7.6740389810     0.0010   2026-09-08 10:27:41
    62     65    0.0419517515    0.0676339873     2755.6356834156    0.1648967659        9.1667128387     0.0010   2026-09-08 10:27:41
    63     66    0.0108276675    0.0182345658     2755.6042382752    0.0314451405        8.6416620014     0.0010   2026-09-08 10:27:41
    64     67    0.0030031784    0.0065291862     2755.5996733561    0.0045649190        8.2062644372     0.0010   2026-09-08 10:27:41
    65     68    0.0027973000    0.0053825785     2755.5947097813    0.0049635749        7.8292172678     0.0010   2026-09-08 10:27:41
    66     69    0.0049979233    0.0093183458     2755.5798097167    0.0149000646        7.0762681977     0.0010   2026-09-08 10:27:41
    67     70    0.0078798192    0.0117583975     2755.5438924707    0.0359172460        5.8774859813     0.0010   2026-09-08 10:27:41
    68     71    0.0133679863    0.0171340578     2755.4526418248    0.0912506459        4.0964739958     0.0011   2026-09-08 10:27:41
    69     72    0.0202890185    0.0385945253     2755.2465890232    0.2060528015        4.2168666318     0.0010   2026-09-08 10:27:41
    70     73    0.0606966708    0.0974970369     2754.8617789242    0.3848100991        4.5636497169     0.0009   2026-09-08 10:27:41
    71     74    0.1077633026    0.1647169306     2754.3973750484    0.4644038758        5.7734813909     0.0009   2026-09-08 10:27:41
    72     75    0.0889572257    0.1361193913     2754.1298704220    0.2675046264        4.3258674642     0.0009   2026-09-08 10:27:41
    73     76    0.0209895500    0.0374456608     2754.0737922872    0.0560781348        3.4193178901     0.0010   2026-09-08 10:27:41
    74     77    0.0046325881    0.0082853553     2754.0699297495    0.0038625377        3.4085415820     0.0010   2026-09-08 10:27:41
    75     78    0.0018555248    0.0029205945     2754.0693918906    0.0005378589        3.3825478353     0.0009   2026-09-08 10:27:41
    76     79    0.0039688427    0.0060827256     2754.0677026016    0.0016892890        3.2967731622     0.0010   2026-09-08 10:27:41
    77     80    0.0053428424    0.0079468856     2754.0639468080    0.0037557936        3.1064671749     0.0009   2026-09-08 10:27:41
    78     81    0.0078129028    0.0111975397     2754.0545295464    0.0094172616        2.6270757140     0.0011   2026-09-08 10:27:41
    79     82    0.0078790199    0.0115408744     2754.0353427512    0.0191867952        1.6294986843     0.0013   2026-09-08 10:27:41
    80     83    0.0085240658    0.0137103367     2754.0058562286    0.0294865226        1.2431571976     0.0013   2026-09-08 10:27:41
    81     84    0.0115851599    0.0269464440     2753.9809296081    0.0249266205        1.3877425146     0.0009   2026-09-08 10:27:41
    82     85    0.0137095813    0.0237155644     2753.9722127711    0.0087168371        1.6919650683     0.0009   2026-09-08 10:27:41
    83     86    0.0048954059    0.0073044431     2753.9710912839    0.0011214871        1.5479469685     0.0010   2026-09-08 10:27:41
    84     87    0.0007283220    0.0011082068     2753.9708940339    0.0001972500        1.5601333238     0.0009   2026-09-08 10:27:41
    85     88    0.0007991830    0.0013772824     2753.9704683688    0.0004256652        1.5738210482     0.0010   2026-09-08 10:27:41
    86     89    0.0012535224    0.0021407611     2753.9693869401    0.0010814286        1.5925933717     0.0010   2026-09-08 10:27:41
    87     90    0.0020852023    0.0036361226     2753.9665847320    0.0028022082        1.6168774878     0.0013   2026-09-08 10:27:41
    88     91    0.0033741975    0.0067559799     2753.9595852577    0.0069994742        1.6393296149     0.0009   2026-09-08 10:27:41
    89     92    0.0070986806    0.0139402454     2753.9431994810    0.0163857767        1.6328104146     0.0010   2026-09-08 10:27:41
    90     93    0.0141022925    0.0279448749     2753.9107089194    0.0324905616        2.2429125378     0.0009   2026-09-08 10:27:41
    91     94    0.0202147983    0.0431381338     2753.8654596664    0.0452492529        2.9783188768     0.0009   2026-09-08 10:27:41
    92     95    0.0209051881    0.0373722150     2753.8321489965    0.0333106700        3.2984892264     0.0009   2026-09-08 10:27:41
    93     96    0.0088165171    0.0127536060     2753.8224891134    0.0096598831        3.7221086381     0.0009   2026-09-08 10:27:41
    94     97    0.0022934621    0.0047182350     2753.8212867748    0.0012023386        3.6632619394     0.0009   2026-09-08 10:27:41
    95     98    0.0011556119    0.0022873768     2753.8208034632    0.0004833116        3.6003978567     0.0009   2026-09-08 10:27:41
    96     99    0.0021787822    0.0044061087     2753.8192685743    0.0015348889        3.4519507781     0.0009   2026-09-08 10:27:41
    97    100    0.0024495328    0.0052706290     2753.8157193181    0.0035492562        3.2159076171     0.0010   2026-09-08 10:27:41
    98    101    0.0037148276    0.0065194877     2753.8063860620    0.0093332561        2.7742381923     0.0011   2026-09-08 10:27:41
    99    102    0.0064304079    0.0104940037     2753.7845724252    0.0218136368        2.0121963249     0.0011   2026-09-08 10:27:41
   100    103    0.0139252292    0.0318419467     2753.7394149440    0.0451574812        2.2809962942     0.0009   2026-09-08 10:27:41
   101    104    0.0340790231    0.0712203800     2753.6718546887    0.0675602553        2.6947342285     0.0012   2026-09-08 10:27:41
   102    105    0.0442087919    0.0879399470     2753.6156066017    0.0562480870        1.8241376394     0.0012   2026-09-08 10:27:41
   103    106    0.0222148522    0.0430965011     2753.5968826213    0.0187239805        0.9363216598     0.0013   2026-09-08 10:27:41
   104    107    0.0028963262    0.0048379800     2753.5948617889    0.0020208324        0.8403917348     0.0010   2026-09-08 10:27:41
   105    108    0.0012545715    0.0028108957     2753.5947535857    0.0001082032        0.8169980645     0.0010   2026-09-08 10:27:41
   106    109    0.0005518525    0.0011795671     2753.5947026849    0.0000509008        0.8071278197     0.0010   2026-09-08 10:27:41
   107    110    0.0015129477    0.0032413963     2753.5944815268    0.0002211580        0.7707742228     0.0009   2026-09-08 10:27:41
   108    111    0.0018718026    0.0040674626     2753.5940066310    0.0004748958        0.7020359372     0.0009   2026-09-08 10:27:41
   109    112    0.0026805490    0.0060664666     2753.5927584423    0.0012481887        0.5355081233     0.0013   2026-09-08 10:27:41
   110    113    0.0030895051    0.0067034252     2753.5900675840    0.0026908583        0.5034527531     0.0011   2026-09-08 10:27:41
   111    114    0.0037805673    0.0069068010     2753.5853080834    0.0047595006        0.4559792884     0.0009   2026-09-08 10:27:41
   112    115    0.0070900592    0.0143740309     2753.5801572979    0.0051507855        1.0534155388     0.0013   2026-09-08 10:27:41
   113    116    0.0084638031    0.0173106744     2753.5775773748    0.0025799231        1.3049271051     0.0013   2026-09-08 10:27:41
   114    117    0.0036625948    0.0077882166     2753.5770832182    0.0004941566        1.2311259915     0.0014   2026-09-08 10:27:41
   115    118    0.0006549471    0.0014901554     2753.5770013183    0.0000818999        1.1668291011     0.0013   2026-09-08 10:27:41
   116    119    0.0004907714    0.0011190839     2753.5768913802    0.0001099382        1.1016889790     0.0014   2026-09-08 10:27:41
   117    120    0.0008186580    0.0019572309     2753.5765766125    0.0003147677        0.9827538755     0.0014   2026-09-08 10:27:41
   118    121    0.0014202364    0.0031599215     2753.5757890187    0.0007875938        0.7968223235     0.0013   2026-09-08 10:27:41
   119    122    0.0028493274    0.0058878379     2753.5737199242    0.0020690944        0.5134242169     0.0013   2026-09-08 10:27:41
   120    123    0.0058108919    0.0120213990     2753.5685000954    0.0052198288        0.5161300812     0.0010   2026-09-08 10:27:41
   121    124    0.0129721911    0.0267330695     2753.5558534765    0.0126466189        0.7236891093     0.0010   2026-09-08 10:27:41
   122    125    0.0266278145    0.0571796624     2753.5287618720    0.0270916045        1.6360640935     0.0009   2026-09-08 10:27:41
   123    126    0.0457216554    0.0988304526     2753.4845527914    0.0442090806        2.2643939623     0.0009   2026-09-08 10:27:41
   124    127    0.0479526246    0.1038363527     2753.4423250852    0.0422277063        1.8267866756     0.0010   2026-09-08 10:27:41
   125    128    0.0172699627    0.0419684386     2753.4249491849    0.0173759003        1.9133857085     0.0009   2026-09-08 10:27:41
   126    129    0.0064152976    0.0131723967     2753.4224655327    0.0024836523        1.8457022342     0.0009   2026-09-08 10:27:41
   127    130    0.0030902895    0.0067072389     2753.4222820080    0.0001835246        1.8019421309     0.0009   2026-09-08 10:27:41
   128    131    0.0015250419    0.0032801019     2753.4221635030    0.0001185050        1.7767854304     0.0009   2026-09-08 10:27:41
   129    132    0.0035721690    0.0076135259     2753.4217128741    0.0004506290        1.7053751712     0.0010   2026-09-08 10:27:41
   130    133    0.0044852334    0.0094177035     2753.4207151058    0.0009977683        1.5845475782     0.0010   2026-09-08 10:27:41
   131    134    0.0059624393    0.0122014360     2753.4181709651    0.0025441407        1.3342720729     0.0010   2026-09-08 10:27:41
   132    135    0.0047152937    0.0091055240     2753.4128506156    0.0053203495        0.8881540728     0.0010   2026-09-08 10:27:41
   133    136    0.0067369299    0.0148080829     2753.4041850941    0.0086655214        0.5455025132     0.0010   2026-09-08 10:27:41
   134    137    0.0180209050    0.0408038110     2753.3961076401    0.0080774541        0.3757342079     0.0010   2026-09-08 10:27:41
   135    138    0.0170755274    0.0381716998     2753.3928914424    0.0032161977        0.2732761967     0.0013   2026-09-08 10:27:41
   136    139    0.0055153584    0.0116451257     2753.3924593236    0.0004321188        0.2876989571     0.0013   2026-09-08 10:27:41
   137    140    0.0004843609    0.0006709338     2753.3924372313    0.0000220923        0.2929550226     0.0013   2026-09-08 10:27:41
   138    141    0.0001129013    0.0002415790     2753.3924312251    0.0000060063        0.2942608869     0.0013   2026-09-08 10:27:41
   139    142    0.0003322920    0.0007624512     2753.3924034564    0.0000277687        0.2981528531     0.0013   2026-09-08 10:27:41
   140    143    0.0004354001    0.0009727669     2753.3923436898    0.0000597666        0.3031578533     0.0009   2026-09-08 10:27:41
   141    144    0.0007606125    0.0016325605     2753.3921748408    0.0001688490        0.3115317433     0.0009   2026-09-08 10:27:41
   142    145    0.0013293577    0.0025016867     2753.3917492004    0.0004256404        0.3234528450     0.0011   2026-09-08 10:27:41
   143    146    0.0026773554    0.0045718542     2753.3906463603    0.0011028401        0.3539516095     0.0009   2026-09-08 10:27:41
   144    147    0.0054158394    0.0101522598     2753.3879294063    0.0027169540        0.6175878644     0.0010   2026-09-08 10:27:41
   145    148    0.0123822087    0.0243781970     2753.3817570987    0.0061723076        0.9516341304     0.0009   2026-09-08 10:27:41
   146    149    0.0280355145    0.0505992092     2753.3703753676    0.0113817310        1.1988346097     0.0009   2026-09-08 10:27:41
   147    150    0.0410486529    0.0713607738     2753.3567335832    0.0136417845        1.0293149588     0.0009   2026-09-08 10:27:41
   148    151    0.0278995444    0.0480760072     2753.3489541810    0.0077794022        0.4573763321     0.0009   2026-09-08 10:27:41
   149    152    0.0040507854    0.0092158272     2753.3473580093    0.0015961717        0.1269490105     0.0009   2026-09-08 10:27:41
   150    153    0.0027324277    0.0053992456     2753.3472565530    0.0001014563        0.1308141254     0.0010   2026-09-08 10:27:41
   151    154    0.0006902867    0.0012214355     2753.3472534565    0.0000030965        0.1314388478     0.0010   2026-09-08 10:27:41
   152    155    0.0002739930    0.0004853249     2753.3472516158    0.0000018407        0.1317057644     0.0009   2026-09-08 10:27:41
   153    156    0.0007827037    0.0014048715     2753.3472431722    0.0000084436        0.1324734739     0.0009   2026-09-08 10:27:41
   154    157    0.0010041386    0.0018492203     2753.3472246957    0.0000184765        0.1334279761     0.0010   2026-09-08 10:27:41
   155    158    0.0016294105    0.0031407829     2753.3471728597    0.0000518360        0.1349128080     0.0014   2026-09-08 10:27:41
   156    159    0.0022635141    0.0047106815     2753.3470418471    0.0001310127        0.1368278234     0.0010   2026-09-08 10:27:41
   157    160    0.0037680799    0.0071351601     2753.3467026422    0.0003392049        0.1389023604     0.0009   2026-09-08 10:27:41
   158    161    0.0060239178    0.0103015729     2753.3458660767    0.0008365655        0.1395465577     0.0010   2026-09-08 10:27:41
   159    162    0.0088234187    0.0155909593     2753.3439624369    0.0019036398        0.1341615569     0.0010   2026-09-08 10:27:41
   160    163    0.0161469350    0.0282313282     2753.3404373192    0.0035251177        0.1404502266     0.0009   2026-09-08 10:27:41
   161    164    0.0338760079    0.0469437034     2753.3361787878    0.0042585314        0.1198791434     0.0009   2026-09-08 10:27:41
   162    165    0.0320216612    0.0444949513     2753.3337193176    0.0024594702        0.0578555430     0.0009   2026-09-08 10:27:41
   163    166    0.0098209594    0.0177119987     2753.3332052085    0.0005141091        0.0446444919     0.0009   2026-09-08 10:27:41
   164    167    0.0020419398    0.0035882540     2753.3331721436    0.0000330649        0.0393466897     0.0009   2026-09-08 10:27:41
   165    168    0.0005105075    0.0007445537     2753.3331714469    0.0000006967        0.0397466599     0.0009   2026-09-08 10:27:41
   166    169    0.0000905417    0.0001231671     2753.3331713355    0.0000001113        0.0397180706     0.0009   2026-09-08 10:27:41
   167    170    0.0003988144    0.0005380430     2753.3331705866    0.0000007489        0.0395721827     0.0013   2026-09-08 10:27:41
   168    171    0.0004878243    0.0006498000     2753.3331690882    0.0000014984        0.0393886494     0.0014   2026-09-08 10:27:41
   169    172    0.0008929878    0.0011676269     2753.3331647134    0.0000043748        0.0390232650     0.0012   2026-09-08 10:27:41
   170    173    0.0013880299    0.0017655799     2753.3331538055    0.0000109080        0.0402925399     0.0011   2026-09-08 10:27:41
   171    174    0.0022681895    0.0027833090     2753.3331253588    0.0000284467        0.0420739498     0.0014   2026-09-08 10:27:41
   172    175    0.0034893720    0.0041451597     2753.3330550497    0.0000703091        0.0438309147     0.0010   2026-09-08 10:27:41
   173    176    0.0048390111    0.0059737134     2753.3328932197    0.0001618300        0.0438585020     0.0009   2026-09-08 10:27:41
   174    177    0.0048362377    0.0087038909     2753.3325862985    0.0003069213        0.0380754543     0.0009   2026-09-08 10:27:41
   175    178    0.0095622599    0.0131992464     2753.3321974538    0.0003888447        0.0229939387     0.0009   2026-09-08 10:27:41
   176    179    0.0112007903    0.0142276469     2753.3319553788    0.0002420750        0.0095693260     0.0010   2026-09-08 10:27:41
   177    180    0.0052851474    0.0073144831     2753.3318996705    0.0000557084        0.0028536817     0.0009   2026-09-08 10:27:41

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','6.385131e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.0511***  0.2676   0.0000   
TC/100 EUR                        -1.4523*    0.7474   0.0520   
Babiogorski                        1.4777***  0.4901   0.0026   
Bieszczadzki                      -0.2939     0.2585   0.2555   
Gorczanski                        -0.0025     0.6774   0.9970   
GorStolowych                       1.1198***  0.3059   0.0003   
Karkonoski                        -0.9250***  0.2718   0.0007   
Magurski                           0.7856*    0.4083   0.0544   
Pieninski                         -1.0711*    0.5850   0.0671   
Swietokrzyski                      0.0923     0.1117   0.4084   
Household income (10k PLN)         0.2626***  0.1016   0.0097   
Male                               0.1185*    0.0718   0.0987   
Higher education                   0.0128     0.0800   0.8733   
City                               0.1313*    0.0753   0.0813   
Winter                             0.8120***  0.0835   0.0000   
Hiking                             2.0770***  0.0788   0.0000   
Skiing                             1.3749***  0.2659   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2893     0.0949            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.6886*    0.3543   0.0520   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2753.3319
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1735
AIC/n:                             0.9467
BIC/n:                             0.9672
n (observations):               5855
r (respondents):                5855
k (parameters):                   18
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.2499
median                           0.0000          2.2582
std                              0.7834          0.9431
min                              0.0000          0.0340
max                             20.0000          4.5242
quantile 0.025                   0.0000          0.6513
quantile 0.975                   2.0000          3.9440
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:42
Estimation took 0.311 seconds (0 hours 0 minutes 0.311 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.55 -0.48 0.55 0.049 0.04 0.14 -0.1 0.058 -0.32 0.054 0.059 0.01 0.0027 0.014 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3919.5978766421             NaN     4175.0575742055     0.0001   2026-09-08 10:27:42
     1      4    0.0746433899    0.1765509105     3169.6605343699  749.9373422722      401.9191915087     0.0036   2026-09-08 10:27:42
     2      5    0.0068383228    0.0090713812     3165.1320842625    4.5284501073      387.5414413326     0.0013   2026-09-08 10:27:42
     3      6    0.0661484099    0.0821337127     3138.7182214036   26.4138628589      385.0314144615     0.0011   2026-09-08 10:27:42
     4      7    0.0744147059    0.0902588530     3114.3364593763   24.3817620273      525.9530710801     0.0012   2026-09-08 10:27:42
     5      8    0.2272024875    0.2749181566     3052.4739233287   61.8625360477      676.6366565185     0.0012   2026-09-08 10:27:42
     6      9    0.1872001816    0.2266837919     3009.3122975168   43.1616258119      620.2127181964     0.0009   2026-09-08 10:27:42
     7     10    0.1289945119    0.1565988561     2984.2298360630   25.0824614538      420.6136927476     0.0012   2026-09-08 10:27:42
     8     11    0.0588644568    0.0718873111     2974.3855517592    9.8442843038      269.3450624217     0.0011   2026-09-08 10:27:42
     9     12    0.0522887151    0.0649671534     2965.0011988314    9.3843529278      280.1890597169     0.0010   2026-09-08 10:27:42
    10     13    0.0991955054    0.1258599451     2946.3094192264   18.6917796050      415.9560222046     0.0011   2026-09-08 10:27:42
    11     14    0.1821718715    0.2354561173     2912.6495411394   33.6598780870      522.3034316304     0.0015   2026-09-08 10:27:42
    12     15    0.2592777664    0.3422036919     2868.9385427812   43.7109983581      462.7804359040     0.0013   2026-09-08 10:27:42
    13     16    0.1804488926    0.2483912903     2842.5485321812   26.3900106000      238.2388249846     0.0013   2026-09-08 10:27:42
    14     17    0.0155022945    0.0362470597     2835.8621351182    6.6863970630      116.5636381992     0.0015   2026-09-08 10:27:42
    15     18    0.0373127265    0.0476782128     2834.2968118390    1.5653232793       70.1746787526     0.0014   2026-09-08 10:27:42
    16     19    0.0242608871    0.0314971424     2833.8987483935    0.3980634454       78.0811716717     0.0014   2026-09-08 10:27:42
    17     20    0.0196854196    0.0251963267     2833.4337294519    0.4650189417       81.6316110479     0.0014   2026-09-08 10:27:42
    18     21    0.0364978293    0.0474049436     2832.0444514093    1.3892780426       86.1259608604     0.0011   2026-09-08 10:27:42
    19     22    0.0424314051    0.0656046341     2829.0991663920    2.9452850173       88.0145194794     0.0013   2026-09-08 10:27:42
    20     23    0.0675918042    0.1062729818     2823.4396336807    5.6595327113       86.2792609192     0.0010   2026-09-08 10:27:42
    21     24    0.1157337722    0.1615102687     2816.6068352584    6.8327984223       72.7337968649     0.0010   2026-09-08 10:27:42
    22     25    0.0969084071    0.1619422307     2812.6194946812    3.9873405772       36.1473957084     0.0013   2026-09-08 10:27:42
    23     26    0.0533386245    0.0723853315     2811.8097081276    0.8097865536       27.8593471405     0.0013   2026-09-08 10:27:42
    24     27    0.0139888354    0.0177553701     2811.6691119623    0.1405961653       26.8350109548     0.0010   2026-09-08 10:27:42
    25     28    0.0112588430    0.0152680549     2811.4797512743    0.1893606880       26.3815642896     0.0010   2026-09-08 10:27:42
    26     29    0.0176890019    0.0259539666     2810.9776191318    0.5021321425       25.7837849100     0.0013   2026-09-08 10:27:42
    27     30    0.0263161417    0.0470123005     2809.7496762193    1.2279429126       38.5702694543     0.0011   2026-09-08 10:27:42
    28     31    0.0609671699    0.1025515347     2806.7767350972    2.9729411221       56.9708549867     0.0011   2026-09-08 10:27:42
    29     32    0.1551967809    0.2228199165     2800.5011598026    6.2755752946       77.6264522176     0.0010   2026-09-08 10:27:42
    30     33    0.2965100718    0.3993845336     2790.3735029861   10.1276568165       87.0874628500     0.0010   2026-09-08 10:27:42
    31     34    0.3359271442    0.4419477460     2780.7436412010    9.6298617851       66.8362080185     0.0010   2026-09-08 10:27:42
    32     35    0.1397028633    0.1963159382     2776.6698659671    4.0737752339       43.6238282159     0.0010   2026-09-08 10:27:42
    33     36    0.0316301736    0.0594426258     2776.0086118678    0.6612540993       42.0736499582     0.0010   2026-09-08 10:27:42
    34     37    0.0237095763    0.0328860327     2775.9137382168    0.0948736510       40.7755863301     0.0011   2026-09-08 10:27:42
    35     38    0.0233175916    0.0322180934     2775.7786350913    0.1351031255       39.4068583860     0.0010   2026-09-08 10:27:42
    36     39    0.0363493073    0.0524611355     2775.4040575019    0.3745775894       36.5544795397     0.0011   2026-09-08 10:27:42
    37     40    0.0399759546    0.0671290140     2774.5220445778    0.8820129241       31.2079627335     0.0012   2026-09-08 10:27:42
    38     41    0.0592296399    0.0847259824     2772.5066952934    2.0153492843       26.6282051540     0.0010   2026-09-08 10:27:42
    39     42    0.0788283781    0.1477760072     2768.8887464439    3.6179488496       30.5151596016     0.0010   2026-09-08 10:27:42
    40     43    0.1992876148    0.2836726054     2764.7672912844    4.1214551594       26.0016297267     0.0009   2026-09-08 10:27:42
    41     44    0.2096496168    0.2743108184     2762.6553227257    2.1119685588       13.7004298492     0.0009   2026-09-08 10:27:42
    42     45    0.0732372809    0.1001841794     2762.2883622485    0.3669604772       12.0955744467     0.0009   2026-09-08 10:27:42
    43     46    0.0096688451    0.0138971000     2762.2655759195    0.0227863290       11.6919072800     0.0009   2026-09-08 10:27:42
    44     47    0.0028249854    0.0037864017     2762.2578305409    0.0077453785       11.6405895455     0.0010   2026-09-08 10:27:42
    45     48    0.0078387401    0.0102529706     2762.2253861452    0.0324443957       11.4727298446     0.0010   2026-09-08 10:27:42
    46     49    0.0105190115    0.0132781883     2762.1572284164    0.0681577288       11.0788732413     0.0009   2026-09-08 10:27:42
    47     50    0.0176870674    0.0238659540     2761.9810050635    0.1762233529        9.9382923819     0.0009   2026-09-08 10:27:42
    48     51    0.0249522820    0.0426131541     2761.6188797635    0.3621253000        7.3582865131     0.0009   2026-09-08 10:27:42
    49     52    0.0427320339    0.0753608790     2761.0387424214    0.5801373421       10.6357923132     0.0014   2026-09-08 10:27:42
    50     53    0.0446501520    0.0889673544     2760.5154871706    0.5232552509        9.5540472250     0.0014   2026-09-08 10:27:42
    51     54    0.0214829520    0.0516802541     2760.3138886246    0.2015985460        5.6887510511     0.0014   2026-09-08 10:27:42
    52     55    0.0118230026    0.0149443386     2760.2858591802    0.0280294444        5.9575085858     0.0009   2026-09-08 10:27:42
    53     56    0.0027055111    0.0045129660     2760.2819753946    0.0038837856        5.8599521762     0.0009   2026-09-08 10:27:42
    54     57    0.0030736791    0.0049691992     2760.2755697709    0.0064056238        5.7048328262     0.0009   2026-09-08 10:27:42
    55     58    0.0050916630    0.0080331819     2760.2580001633    0.0175696076        5.7432764950     0.0009   2026-09-08 10:27:42
    56     59    0.0073135051    0.0118176812     2760.2141481222    0.0438520411        5.8077186061     0.0009   2026-09-08 10:27:42
    57     60    0.0102432780    0.0202459428     2760.1051186253    0.1090294968        5.8239099851     0.0010   2026-09-08 10:27:42
    58     61    0.0235253355    0.0429221997     2759.8612238442    0.2438947811        5.6390151461     0.0009   2026-09-08 10:27:42
    59     62    0.0609474484    0.0910239938     2759.4204455425    0.4407783017        7.3844391775     0.0009   2026-09-08 10:27:42
    60     63    0.0947458125    0.1348107365     2758.9150756661    0.5053698764        8.8007261302     0.0010   2026-09-08 10:27:42
    61     64    0.0680017800    0.0993131657     2758.6428094840    0.2722661821       10.5877777014     0.0010   2026-09-08 10:27:42
    62     65    0.0163868425    0.0272190253     2758.5856965172    0.0571129668        9.8455367845     0.0010   2026-09-08 10:27:42
    63     66    0.0042099596    0.0088222410     2758.5781692739    0.0075272433        9.2326056977     0.0009   2026-09-08 10:27:42
    64     67    0.0034876497    0.0060484308     2758.5720944292    0.0060748447        8.8156048202     0.0009   2026-09-08 10:27:42
    65     68    0.0062669046    0.0114738287     2758.5524806076    0.0196138217        7.9092078173     0.0010   2026-09-08 10:27:42
    66     69    0.0090235435    0.0139289056     2758.5067460623    0.0457345453        6.5033031428     0.0009   2026-09-08 10:27:42
    67     70    0.0156078040    0.0196133933     2758.3902936633    0.1164523990        5.6424680118     0.0009   2026-09-08 10:27:42
    68     71    0.0234833911    0.0423301694     2758.1345881117    0.2557055516        5.6463265297     0.0009   2026-09-08 10:27:42
    69     72    0.0680440919    0.1057624050     2757.6808233713    0.4537647404        4.8783253969     0.0009   2026-09-08 10:27:42
    70     73    0.1152236431    0.1684571187     2757.1870038191    0.4938195522        6.3255266682     0.0012   2026-09-08 10:27:42
    71     74    0.0852106424    0.1242160266     2756.9441937414    0.2428100777        4.4056447847     0.0013   2026-09-08 10:27:42
    72     75    0.0163699491    0.0292429113     2756.9022478030    0.0419459385        2.8443992865     0.0009   2026-09-08 10:27:42
    73     76    0.0037068235    0.0069754111     2756.8996819760    0.0025658269        2.8030216485     0.0011   2026-09-08 10:27:42
    74     77    0.0016088111    0.0024740001     2756.8990818354    0.0006001406        2.7806374548     0.0011   2026-09-08 10:27:42
    75     78    0.0045075673    0.0067139944     2756.8965811498    0.0025006856        2.6839471654     0.0009   2026-09-08 10:27:42
    76     79    0.0056661409    0.0081423698     2756.8913635398    0.0052176100        2.4777553759     0.0009   2026-09-08 10:27:42
    77     80    0.0083247716    0.0115839772     2756.8781688047    0.0131947352        1.9441241863     0.0009   2026-09-08 10:27:42
    78     81    0.0076843367    0.0122976337     2756.8525468104    0.0256219942        1.5155602966     0.0009   2026-09-08 10:27:42
    79     82    0.0085834248    0.0183229359     2756.8160381741    0.0365086363        1.4864044697     0.0009   2026-09-08 10:27:42
    80     83    0.0129395990    0.0293301204     2756.7890878893    0.0269502848        2.0003439182     0.0009   2026-09-08 10:27:42
    81     84    0.0124306302    0.0207753265     2756.7811314876    0.0079564017        2.1564953002     0.0009   2026-09-08 10:27:42
    82     85    0.0037438605    0.0053515413     2756.7801704869    0.0009610007        1.9710544040     0.0009   2026-09-08 10:27:42
    83     86    0.0007572220    0.0011627657     2756.7798645589    0.0003059280        1.8764967807     0.0009   2026-09-08 10:27:42
    84     87    0.0012798886    0.0021820179     2756.7789076419    0.0009569170        1.6862912952     0.0009   2026-09-08 10:27:42
    85     88    0.0016395533    0.0031127059     2756.7766935138    0.0022141281        1.7114246755     0.0012   2026-09-08 10:27:42
    86     89    0.0029114313    0.0056011663     2756.7708377175    0.0058557964        1.7433161876     0.0010   2026-09-08 10:27:42
    87     90    0.0049328282    0.0106130929     2756.7569709672    0.0138667503        1.7657254040     0.0009   2026-09-08 10:27:42
    88     91    0.0107665184    0.0217446532     2756.7273521039    0.0296188633        1.7337628170     0.0009   2026-09-08 10:27:42
    89     92    0.0179845519    0.0377931799     2756.6801788849    0.0471732190        2.6689854760     0.0010   2026-09-08 10:27:42
    90     93    0.0189060226    0.0416985001     2756.6365557708    0.0436231141        2.9461052852     0.0013   2026-09-08 10:27:42
    91     94    0.0129224678    0.0206073681     2756.6191712259    0.0173845450        2.6843326582     0.0010   2026-09-08 10:27:42
    92     95    0.0032136139    0.0059975660     2756.6164699092    0.0027013167        2.7569549634     0.0009   2026-09-08 10:27:42
    93     96    0.0012575468    0.0025690583     2756.6158733137    0.0005965954        2.7237918691     0.0009   2026-09-08 10:27:42
    94     97    0.0017633209    0.0036329797     2756.6145557099    0.0013176039        2.6564837322     0.0013   2026-09-08 10:27:42
    95     98    0.0022579155    0.0048598302     2756.6112598334    0.0032958765        2.5331546417     0.0009   2026-09-08 10:27:42
    96     99    0.0032437405    0.0061233631     2756.6027567424    0.0085030909        2.2945503074     0.0010   2026-09-08 10:27:42
    97    100    0.0047723636    0.0093302733     2756.5820152462    0.0207414963        1.8358951588     0.0009   2026-09-08 10:27:42
    98    101    0.0116387708    0.0266475162     2756.5360213676    0.0459938786        2.1241184001     0.0011   2026-09-08 10:27:42
    99    102    0.0308386623    0.0664368332     2756.4555965804    0.0804247872        3.1214687381     0.0013   2026-09-08 10:27:42
   100    103    0.0472293917    0.1021985617     2756.3679624958    0.0876340846        2.7861447628     0.0013   2026-09-08 10:27:42
   101    104    0.0354133156    0.0730747844     2756.3241789942    0.0437835016        1.6043332158     0.0012   2026-09-08 10:27:42
   102    105    0.0070848411    0.0147232901     2756.3164525699    0.0077264244        1.2958141511     0.0009   2026-09-08 10:27:42
   103    106    0.0021188340    0.0047867904     2756.3159369278    0.0005156421        1.1553441500     0.0009   2026-09-08 10:27:42
   104    107    0.0008505218    0.0018475851     2756.3158230774    0.0001138503        1.1197346306     0.0009   2026-09-08 10:27:42
   105    108    0.0019788246    0.0043462026     2756.3154108674    0.0004122100        1.0308943267     0.0009   2026-09-08 10:27:42
   106    109    0.0024675551    0.0055603761     2756.3145060172    0.0009048502        1.0317374308     0.0008   2026-09-08 10:27:42
   107    110    0.0034949397    0.0080520780     2756.3121588101    0.0023472072        1.0032111458     0.0009   2026-09-08 10:27:42
   108    111    0.0038187970    0.0085102354     2756.3071158760    0.0050429341        0.8751317921     0.0008   2026-09-08 10:27:42
   109    112    0.0043932196    0.0088024882     2756.2983676376    0.0087482384        0.6645106338     0.0008   2026-09-08 10:27:42
   110    113    0.0095167243    0.0201625152     2756.2892624882    0.0091051493        0.7643463359     0.0011   2026-09-08 10:27:42
   111    114    0.0111022138    0.0229689762     2756.2849883374    0.0042741509        0.9671385884     0.0012   2026-09-08 10:27:42
   112    115    0.0043176357    0.0094636335     2756.2842459521    0.0007423852        0.8917945287     0.0009   2026-09-08 10:27:42
   113    116    0.0006142585    0.0013939510     2756.2841615410    0.0000844112        0.8387665089     0.0009   2026-09-08 10:27:42
   114    117    0.0003539192    0.0007162788     2756.2840801658    0.0000813751        0.7988859244     0.0009   2026-09-08 10:27:42
   115    118    0.0006990545    0.0014178205     2756.2838160244    0.0002641414        0.7123886155     0.0010   2026-09-08 10:27:42
   116    119    0.0009744790    0.0021437330     2756.2831870926    0.0006289318        0.6835874753     0.0009   2026-09-08 10:27:42
   117    120    0.0016501728    0.0039620385     2756.2815295204    0.0016575723        0.6764225137     0.0009   2026-09-08 10:27:42
   118    121    0.0034733410    0.0077676481     2756.2775270910    0.0040024294        0.6600458197     0.0009   2026-09-08 10:27:42
   119    122    0.0076281475    0.0162249216     2756.2686627387    0.0088643523        0.8299170339     0.0009   2026-09-08 10:27:42
   120    123    0.0147233258    0.0294243698     2756.2533579872    0.0153047515        1.7569212573     0.0009   2026-09-08 10:27:42
   121    124    0.0183038745    0.0354798412     2756.2370798574    0.0162781298        2.3698300241     0.0009   2026-09-08 10:27:42
   122    125    0.0095217225    0.0199066200     2756.2290851653    0.0079946921        2.2186814521     0.0010   2026-09-08 10:27:42
   123    126    0.0027215851    0.0056033117     2756.2274942105    0.0015909548        1.8604968736     0.0011   2026-09-08 10:27:42
   124    127    0.0012454447    0.0027646083     2756.2271827119    0.0003114986        1.7161455189     0.0010   2026-09-08 10:27:42
   125    128    0.0013560258    0.0029805942     2756.2266843009    0.0004984110        1.6735993592     0.0010   2026-09-08 10:27:42
   126    129    0.0018476180    0.0043040102     2756.2253272295    0.0013570714        1.6258426107     0.0009   2026-09-08 10:27:42
   127    130    0.0026478939    0.0048793530     2756.2218951633    0.0034320661        1.5414694611     0.0009   2026-09-08 10:27:42
   128    131    0.0042295206    0.0065404837     2756.2131262063    0.0087689570        1.4296820506     0.0009   2026-09-08 10:27:42
   129    132    0.0110764500    0.0222613905     2756.1920968298    0.0210293765        1.5531309031     0.0010   2026-09-08 10:27:42
   130    133    0.0356913100    0.0678808459     2756.1475080620    0.0445887678        2.0856269553     0.0010   2026-09-08 10:27:42
   131    134    0.0752247859    0.1427335878     2756.0768586685    0.0706493935        2.9121469557     0.0009   2026-09-08 10:27:42
   132    135    0.0895292424    0.1711299702     2756.0130643147    0.0637943538        2.2653971312     0.0009   2026-09-08 10:27:42
   133    136    0.0411886152    0.0808311758     2755.9891471581    0.0239171566        0.8030797278     0.0009   2026-09-08 10:27:42
   134    137    0.0044098093    0.0065199518     2755.9861477695    0.0029993886        0.4907046314     0.0009   2026-09-08 10:27:42
   135    138    0.0036361390    0.0069171923     2755.9860255083    0.0001222612        0.4813380745     0.0008   2026-09-08 10:27:42
   136    139    0.0006960881    0.0013371139     2755.9860150089    0.0000104994        0.4810163611     0.0008   2026-09-08 10:27:42
   137    140    0.0015117855    0.0029319253     2755.9859793320    0.0000356769        0.4806081181     0.0014   2026-09-08 10:27:42
   138    141    0.0020499651    0.0040392646     2755.9858979935    0.0000813385        0.4798492177     0.0014   2026-09-08 10:27:42
   139    142    0.0033286884    0.0067431322     2755.9856738300    0.0002241635        0.4778535840     0.0014   2026-09-08 10:27:42
   140    143    0.0048405061    0.0102017417     2755.9851032957    0.0005705343        0.4730134080     0.0014   2026-09-08 10:27:42
   141    144    0.0077303185    0.0153734389     2755.9836280844    0.0014752113        0.4610597850     0.0014   2026-09-08 10:27:42
   142    145    0.0135846503    0.0216744655     2755.9799753402    0.0036527442        0.4324607366     0.0014   2026-09-08 10:27:42
   143    146    0.0228897657    0.0298010942     2755.9716063600    0.0083689802        0.3759066731     0.0014   2026-09-08 10:27:42
   144    147    0.0321461464    0.0496007848     2755.9558545631    0.0157517969        0.4735992917     0.0013   2026-09-08 10:27:42
   145    148    0.0527670883    0.0886453176     2755.9362234101    0.0196311530        0.4170269923     0.0014   2026-09-08 10:27:42
   146    149    0.0577714710    0.0941834917     2755.9243270642    0.0118963459        0.2365279739     0.0009   2026-09-08 10:27:42
   147    150    0.0219822702    0.0418927791     2755.9216951924    0.0026318717        0.1816808277     0.0009   2026-09-08 10:27:42
   148    151    0.0058432318    0.0077083303     2755.9215147189    0.0001804735        0.1886590338     0.0009   2026-09-08 10:27:42
   149    152    0.0008182525    0.0015278939     2755.9215095086    0.0000052104        0.1865892815     0.0009   2026-09-08 10:27:42
   150    153    0.0002931859    0.0005040845     2755.9215073152    0.0000021933        0.1856545648     0.0009   2026-09-08 10:27:42
   151    154    0.0009777318    0.0016854961     2755.9214958562    0.0000114590        0.1823923921     0.0009   2026-09-08 10:27:42
   152    155    0.0012308944    0.0021476015     2755.9214715864    0.0000242698        0.1780955223     0.0009   2026-09-08 10:27:42
   153    156    0.0020812065    0.0037131192     2755.9214025374    0.0000690490        0.1703028073     0.0009   2026-09-08 10:27:42
   154    157    0.0029790827    0.0055660313     2755.9212289878    0.0001735496        0.1706765416     0.0009   2026-09-08 10:27:42
   155    158    0.0040975671    0.0085210718     2755.9207792676    0.0004497202        0.1768389595     0.0009   2026-09-08 10:27:42
   156    159    0.0074096652    0.0124561779     2755.9196742657    0.0011050019        0.1822155630     0.0009   2026-09-08 10:27:42
   157    160    0.0131866754    0.0189548060     2755.9171774282    0.0024968375        0.1795138061     0.0009   2026-09-08 10:27:42
   158    161    0.0195679015    0.0331934294     2755.9126309607    0.0045464676        0.1933283923     0.0009   2026-09-08 10:27:42
   159    162    0.0371004885    0.0527591488     2755.9073119010    0.0053190597        0.1532658001     0.0009   2026-09-08 10:27:42
   160    163    0.0319662764    0.0481150316     2755.9043869487    0.0029249523        0.0612299104     0.0011   2026-09-08 10:27:42
   161    164    0.0107159133    0.0188043109     2755.9038123585    0.0005745902        0.0432793549     0.0009   2026-09-08 10:27:42
   162    165    0.0027147014    0.0039001673     2755.9037779219    0.0000344365        0.0403815865     0.0009   2026-09-08 10:27:42
   163    166    0.0005085877    0.0007445755     2755.9037772615    0.0000006604        0.0396262365     0.0011   2026-09-08 10:27:42
   164    167    0.0000758919    0.0001081142     2755.9037771737    0.0000000879        0.0395230155     0.0009   2026-09-08 10:27:42
   165    168    0.0003386644    0.0004861478     2755.9037765659    0.0000006078        0.0390679578     0.0009   2026-09-08 10:27:42
   166    169    0.0004013245    0.0005839966     2755.9037753575    0.0000012084        0.0385179719     0.0009   2026-09-08 10:27:42
   167    170    0.0007079127    0.0010540722     2755.9037718227    0.0000035349        0.0374799250     0.0009   2026-09-08 10:27:42
   168    171    0.0010371942    0.0015948881     2755.9037630363    0.0000087864        0.0357570068     0.0009   2026-09-08 10:27:42
   169    172    0.0017600237    0.0025155282     2755.9037402398    0.0000227965        0.0326190284     0.0009   2026-09-08 10:27:42
   170    173    0.0028450439    0.0037210842     2755.9036846946    0.0000555452        0.0324320489     0.0008   2026-09-08 10:27:42
   171    174    0.0042004320    0.0052278572     2755.9035612095    0.0001234851        0.0344009440     0.0009   2026-09-08 10:27:42
   172    175    0.0045341452    0.0072284995     2755.9033447622    0.0002164473        0.0309528335     0.0009   2026-09-08 10:27:42
   173    176    0.0070082849    0.0102428849     2755.9031091301    0.0002356321        0.0185715196     0.0008   2026-09-08 10:27:42
   174    177    0.0077033725    0.0098270235     2755.9029928945    0.0001162356        0.0071368316     0.0009   2026-09-08 10:27:42
   175    178    0.0028242653    0.0043044511     2755.9029728681    0.0000200264        0.0016741893     0.0010   2026-09-08 10:27:42

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','4.009019e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3765***  0.2340   0.0000   
TC/100 EUR                        -1.6900**   0.7562   0.0254   
Babiogorski                        1.4897***  0.5059   0.0032   
Bieszczadzki                       0.0094     0.2468   0.9696   
Gorczanski                         0.3523     0.6762   0.6024   
GorStolowych                       1.1058***  0.3184   0.0005   
Karkonoski                        -0.8530***  0.2809   0.0024   
Magurski                           0.4639     0.4005   0.2467   
Pieninski                         -1.2158**   0.5772   0.0352   
Swietokrzyski                      0.1496     0.1141   0.1897   
Household income (10k PLN)         0.2759***  0.1014   0.0065   
Male                               0.1187*    0.0717   0.0982   
Higher education                   0.0140     0.0800   0.8612   
City                               0.1412*    0.0753   0.0608   
Winter                             0.8250***  0.0835   0.0000   
Hiking                             2.0838***  0.0788   0.0000   
Skiing                             1.4019***  0.2656   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2898     0.0948            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.5917**   0.2648   0.0254   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2755.9030
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1727
AIC/n:                             0.9475
BIC/n:                             0.9681
n (observations):               5855
r (respondents):                5855
k (parameters):                   18
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1226
median                           0.0000          2.1322
std                              0.7834          0.9278
min                              0.0000          0.0266
max                             20.0000          5.0512
quantile 0.025                   0.0000          0.5807
quantile 0.975                   2.0000          3.9862
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:42
Estimation took 0.28314 seconds (0 hours 0 minutes 0.28314 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.54 -0.45 0.54 0.034 0.0078 0.14 -0.11 0.073 -0.3 0.052 0.06 0.01 0.0028 0.014 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3919.6302003826             NaN     4165.2013524611     0.0001   2026-09-08 10:27:43
     1      4    0.0750780628    0.1775841455     3167.0058829492  752.6243174334      403.3857079107     0.0031   2026-09-08 10:27:43
     2      5    0.0069243518    0.0091519812     3162.4256280933    4.5802548559      389.1117889967     0.0014   2026-09-08 10:27:43
     3      6    0.0692110204    0.0858622075     3134.7670921375   27.6585359558      391.8938376186     0.0016   2026-09-08 10:27:43
     4      7    0.0766463979    0.0929657917     3109.6461814402   25.1209106973      529.7853795620     0.0012   2026-09-08 10:27:43
     5      8    0.2306378641    0.2791056483     3046.9653910317   62.6807904085      674.1618470214     0.0014   2026-09-08 10:27:43
     6      9    0.1840754837    0.2229174704     3004.7045553880   42.2608356437      608.4793517854     0.0010   2026-09-08 10:27:43
     7     10    0.1245026233    0.1511205992     2980.7019890066   24.0025663814      409.5955586476     0.0014   2026-09-08 10:27:43
     8     11    0.0572410434    0.0698462087     2971.1571499805    9.5448390261      262.5960866181     0.0014   2026-09-08 10:27:43
     9     12    0.0539495260    0.0669036330     2961.4986915141    9.6584584664      284.2573850757     0.0014   2026-09-08 10:27:43
    10     13    0.1035529147    0.1310149101     2942.1166622330   19.3820292811      420.1072040132     0.0011   2026-09-08 10:27:43
    11     14    0.1890276862    0.2435661602     2907.4969912738   34.6196709592      521.5645439531     0.0012   2026-09-08 10:27:43
    12     15    0.2632831352    0.3466362271     2863.6089800107   43.8880112631      452.6364108407     0.0014   2026-09-08 10:27:43
    13     16    0.1747021904    0.2406331635     2838.1657952289   25.4431847818      231.2016213720     0.0014   2026-09-08 10:27:43
    14     17    0.0121369037    0.0314961881     2831.8491794657    6.3166157632      111.9093243934     0.0013   2026-09-08 10:27:43
    15     18    0.0387004564    0.0492574489     2830.3604648116    1.4887146541       69.3400270447     0.0013   2026-09-08 10:27:43
    16     19    0.0237638827    0.0307378678     2829.9768981499    0.3835666617       76.5689902087     0.0011   2026-09-08 10:27:43
    17     20    0.0205149987    0.0262054587     2829.4931358647    0.4837622852       80.0347342912     0.0011   2026-09-08 10:27:43
    18     21    0.0367037412    0.0477673319     2828.0883655408    1.4047703238       84.1724413596     0.0011   2026-09-08 10:27:43
    19     22    0.0423646967    0.0664969852     2825.1004022073    2.9879633335       85.5243293916     0.0013   2026-09-08 10:27:43
    20     23    0.0677633890    0.1068037418     2819.4662040715    5.6341981358       83.3826330426     0.0011   2026-09-08 10:27:43
    21     24    0.1129842293    0.1608370472     2812.8438519792    6.6223520923       68.4119758075     0.0012   2026-09-08 10:27:43
    22     25    0.0905569387    0.1567089432     2809.1591543480    3.6846976311       34.2360365639     0.0010   2026-09-08 10:27:43
    23     26    0.0504057981    0.0674226408     2808.4489499774    0.7102043707       26.9927925896     0.0010   2026-09-08 10:27:43
    24     27    0.0128775568    0.0164181934     2808.3211393686    0.1278106087       26.1820887771     0.0010   2026-09-08 10:27:43
    25     28    0.0111393019    0.0152467237     2808.1344620903    0.1866772783       25.8349500668     0.0014   2026-09-08 10:27:43
    26     29    0.0171762327    0.0255070496     2807.6480902996    0.4863717907       25.3529348043     0.0012   2026-09-08 10:27:43
    27     30    0.0257713769    0.0468250145     2806.4499443669    1.1981459327       37.3643653063     0.0011   2026-09-08 10:27:43
    28     31    0.0602042420    0.1020390746     2803.5668650644    2.8830793025       54.7583276614     0.0011   2026-09-08 10:27:43
    29     32    0.1525518326    0.2210141750     2797.5188139622    6.0480511022       74.0529737901     0.0011   2026-09-08 10:27:43
    30     33    0.2873027618    0.3905599376     2787.9177147658    9.6010991964       82.1495946523     0.0010   2026-09-08 10:27:43
    31     34    0.3164508803    0.4202352671     2779.0463611246    8.8713536412       62.1039994738     0.0011   2026-09-08 10:27:43
    32     35    0.1232928861    0.1770384921     2775.4526222760    3.5937388487       43.2446841379     0.0013   2026-09-08 10:27:43
    33     36    0.0287192863    0.0569306779     2774.8928047045    0.5598175714       41.3829012884     0.0010   2026-09-08 10:27:43
    34     37    0.0213082980    0.0299338108     2774.8036370094    0.0891676952       40.1330061384     0.0011   2026-09-08 10:27:43
    35     38    0.0240272318    0.0337622422     2774.6542273529    0.1494096565       38.6035145056     0.0013   2026-09-08 10:27:43
    36     39    0.0349672589    0.0517146085     2774.2596910581    0.3945362947       35.5896888694     0.0012   2026-09-08 10:27:43
    37     40    0.0376879899    0.0668978843     2773.3145453691    0.9451456890       29.8820828762     0.0011   2026-09-08 10:27:43
    38     41    0.0604592438    0.0853776743     2771.1905057169    2.1240396522       26.5373040758     0.0011   2026-09-08 10:27:43
    39     42    0.0780874995    0.1599675624     2767.4452172321    3.7452884848       31.4188685273     0.0011   2026-09-08 10:27:43
    40     43    0.2088406378    0.2957860617     2763.3577180087    4.0874992234       26.0543828142     0.0012   2026-09-08 10:27:43
    41     44    0.2017675758    0.2663111365     2761.3875359925    1.9701820162       13.5481616319     0.0011   2026-09-08 10:27:43
    42     45    0.0636751427    0.0893886937     2761.0684860364    0.3190499561       12.1422484819     0.0011   2026-09-08 10:27:43
    43     46    0.0087395144    0.0120625214     2761.0488599530    0.0196260834       11.8166504210     0.0011   2026-09-08 10:27:43
    44     47    0.0028955776    0.0039649730     2761.0406432060    0.0082167470       11.7633834621     0.0010   2026-09-08 10:27:43
    45     48    0.0079059458    0.0105537819     2761.0066302258    0.0340129802       11.5824828001     0.0010   2026-09-08 10:27:43
    46     49    0.0106798268    0.0137487667     2760.9346781756    0.0719520502       11.1595038724     0.0011   2026-09-08 10:27:43
    47     50    0.0178270043    0.0246238541     2760.7497415938    0.1849365818        9.9585011081     0.0011   2026-09-08 10:27:43
    48     51    0.0262729835    0.0441850264     2760.3714825841    0.3782590097        7.2802284485     0.0011   2026-09-08 10:27:43
    49     52    0.0437447877    0.0779760769     2759.7734496327    0.5980329515       10.6726114499     0.0012   2026-09-08 10:27:43
    50     53    0.0457815489    0.0908385361     2759.2460257729    0.5274238597        9.3383094099     0.0012   2026-09-08 10:27:43
    51     54    0.0214553934    0.0515096487     2759.0490994300    0.1969263429        6.0938221976     0.0011   2026-09-08 10:27:43
    52     55    0.0113273007    0.0146155529     2759.0224617982    0.0266376319        6.2946532613     0.0014   2026-09-08 10:27:43
    53     56    0.0026945405    0.0044274109     2759.0185366952    0.0039251030        6.1811899452     0.0012   2026-09-08 10:27:43
    54     57    0.0032977691    0.0052854398     2759.0114675678    0.0070691274        5.9956250935     0.0012   2026-09-08 10:27:43
    55     58    0.0052753881    0.0082719584     2758.9926234532    0.0188441147        5.7315876984     0.0011   2026-09-08 10:27:43
    56     59    0.0075893222    0.0122931686     2758.9451936826    0.0474297706        5.8035723715     0.0011   2026-09-08 10:27:43
    57     60    0.0102414998    0.0211212025     2758.8284024872    0.1167911954        5.8266864874     0.0011   2026-09-08 10:27:43
    58     61    0.0250469635    0.0451312798     2758.5702481377    0.2581543495        6.1363816159     0.0011   2026-09-08 10:27:43
    59     62    0.0629875974    0.0940843429     2758.1178733238    0.4523748138        7.0730373811     0.0011   2026-09-08 10:27:43
    60     63    0.0931811265    0.1332738226     2757.6278420728    0.4900312511        8.9232868662     0.0011   2026-09-08 10:27:43
    61     64    0.0615415131    0.0911579422     2757.3849613835    0.2428806892       10.2267668383     0.0011   2026-09-08 10:27:43
    62     65    0.0145344185    0.0232966537     2757.3381472595    0.0468141241        9.3425263392     0.0011   2026-09-08 10:27:43
    63     66    0.0039683917    0.0080046711     2757.3315709335    0.0065763259        8.7673810170     0.0011   2026-09-08 10:27:43
    64     67    0.0036207415    0.0063836761     2757.3248618131    0.0067091205        8.3093229835     0.0010   2026-09-08 10:27:43
    65     68    0.0060316890    0.0113411457     2757.3042678734    0.0205939397        7.3735210959     0.0010   2026-09-08 10:27:43
    66     69    0.0094406659    0.0140532250     2757.2552794832    0.0489883901        5.8989074720     0.0010   2026-09-08 10:27:43
    67     70    0.0160111042    0.0203010771     2757.1318460306    0.1234334527        5.6704214903     0.0010   2026-09-08 10:27:43
    68     71    0.0236991953    0.0458116010     2756.8614269596    0.2704190710        5.6438516978     0.0011   2026-09-08 10:27:43
    69     72    0.0726665473    0.1120437084     2756.3881287344    0.4732982252        4.8235646775     0.0010   2026-09-08 10:27:43
    70     73    0.1181009543    0.1725611736     2755.8850220634    0.5031066710        6.5963414410     0.0011   2026-09-08 10:27:43
    71     74    0.0829811551    0.1214374192     2755.6460793285    0.2389427349        4.3783750622     0.0010   2026-09-08 10:27:43
    72     75    0.0142022356    0.0268512858     2755.6063703730    0.0397089554        3.2783229592     0.0010   2026-09-08 10:27:43
    73     76    0.0036972064    0.0070366962     2755.6039435329    0.0024268401        3.2137287682     0.0010   2026-09-08 10:27:43
    74     77    0.0016986756    0.0026159255     2755.6032493462    0.0006941867        3.1830320647     0.0012   2026-09-08 10:27:43
    75     78    0.0048377033    0.0072286046     2755.6002769344    0.0029724118        3.0547369511     0.0011   2026-09-08 10:27:43
    76     79    0.0059756943    0.0086338403     2755.5941181697    0.0061587646        2.7937758364     0.0014   2026-09-08 10:27:43
    77     80    0.0084781552    0.0119637580     2755.5787215874    0.0153965823        2.1423968428     0.0010   2026-09-08 10:27:43
    78     81    0.0069350817    0.0123813865     2755.5497014767    0.0290201107        1.6253018038     0.0009   2026-09-08 10:27:43
    79     82    0.0093082925    0.0202285715     2755.5107254428    0.0389760339        1.5606394642     0.0009   2026-09-08 10:27:43
    80     83    0.0142902901    0.0304839964     2755.4846111498    0.0261142930        2.0364235589     0.0009   2026-09-08 10:27:43
    81     84    0.0117963010    0.0192127519     2755.4777736428    0.0068375070        2.0760892371     0.0010   2026-09-08 10:27:43
    82     85    0.0030339273    0.0043617537     2755.4769916926    0.0007819503        1.8783621641     0.0009   2026-09-08 10:27:43
    83     86    0.0006855758    0.0010981690     2755.4766733069    0.0003183857        1.7788773139     0.0009   2026-09-08 10:27:43
    84     87    0.0012633704    0.0022699798     2755.4755851771    0.0010881298        1.7492699254     0.0010   2026-09-08 10:27:43
    85     88    0.0017977178    0.0032323771     2755.4731025838    0.0024825933        1.7737502954     0.0009   2026-09-08 10:27:43
    86     89    0.0031632821    0.0059869763     2755.4665080135    0.0065945703        1.8041223642     0.0012   2026-09-08 10:27:43
    87     90    0.0054507618    0.0115929801     2755.4509893615    0.0155186520        1.8224381184     0.0012   2026-09-08 10:27:43
    88     91    0.0114859845    0.0238927350     2755.4181314790    0.0328578825        1.7813424880     0.0011   2026-09-08 10:27:43
    89     92    0.0187286109    0.0407238198     2755.3668882810    0.0512431980        2.8358282006     0.0011   2026-09-08 10:27:43
    90     93    0.0194034544    0.0429720587     2755.3212222186    0.0456660624        2.8557777519     0.0009   2026-09-08 10:27:43
    91     94    0.0122196634    0.0196072759     2755.3039754013    0.0172468173        2.6184946723     0.0009   2026-09-08 10:27:43
    92     95    0.0032115652    0.0059364593     2755.3014191880    0.0025562133        2.6450822851     0.0010   2026-09-08 10:27:43
    93     96    0.0012465216    0.0025996911     2755.3008204452    0.0005987429        2.6061204003     0.0014   2026-09-08 10:27:43
    94     97    0.0018610962    0.0039289843     2755.2993934094    0.0014270357        2.5279472399     0.0011   2026-09-08 10:27:43
    95     98    0.0023612328    0.0051460302     2755.2958890835    0.0035043260        2.3897952486     0.0010   2026-09-08 10:27:43
    96     99    0.0031785436    0.0065017107     2755.2868011031    0.0090879804        2.1238641352     0.0009   2026-09-08 10:27:43
    97    100    0.0045952714    0.0097342396     2755.2648162840    0.0219848191        1.6723290970     0.0011   2026-09-08 10:27:43
    98    101    0.0113201005    0.0277519535     2755.2166593281    0.0481569559        2.2458639895     0.0013   2026-09-08 10:27:43
    99    102    0.0292925260    0.0681105862     2755.1349078891    0.0817514390        3.0798223201     0.0010   2026-09-08 10:27:43
   100    103    0.0455182510    0.1008746988     2755.0504186354    0.0844892537        2.5669266578     0.0010   2026-09-08 10:27:43
   101    104    0.0320657435    0.0676040540     2755.0114083078    0.0390103276        1.6762004164     0.0010   2026-09-08 10:27:43
   102    105    0.0056251903    0.0122909105     2755.0051504801    0.0062578277        1.3464277096     0.0009   2026-09-08 10:27:43
   103    106    0.0018134997    0.0043615548     2755.0047479941    0.0004024859        1.2187787693     0.0009   2026-09-08 10:27:43
   104    107    0.0007348467    0.0017270558     2755.0046347678    0.0001132264        1.1835490854     0.0009   2026-09-08 10:27:43
   105    108    0.0018980674    0.0043802955     2755.0041891230    0.0004456447        1.0874654372     0.0009   2026-09-08 10:27:43
   106    109    0.0024334249    0.0054670968     2755.0032297577    0.0009593653        1.0113450509     0.0010   2026-09-08 10:27:43
   107    110    0.0035948463    0.0077879693     2755.0007592289    0.0024705288        0.9953067405     0.0009   2026-09-08 10:27:43
   108    111    0.0035879915    0.0077924754     2754.9956357962    0.0051234327        0.8755325875     0.0012   2026-09-08 10:27:43
   109    112    0.0043305192    0.0090859355     2754.9873583635    0.0082774328        0.5772853544     0.0011   2026-09-08 10:27:43
   110    113    0.0089386875    0.0199143758     2754.9798064456    0.0075519179        0.7190351891     0.0010   2026-09-08 10:27:43
   111    114    0.0085396682    0.0190981728     2754.9768562547    0.0029501909        0.8395505754     0.0012   2026-09-08 10:27:43
   112    115    0.0028461404    0.0064747952     2754.9764342693    0.0004219853        0.7594734074     0.0009   2026-09-08 10:27:43
   113    116    0.0004045965    0.0008545265     2754.9763801332    0.0000541362        0.7189867069     0.0009   2026-09-08 10:27:43
   114    117    0.0003767516    0.0006964962     2754.9763002708    0.0000798623        0.6758005077     0.0009   2026-09-08 10:27:43
   115    118    0.0006447408    0.0012119798     2754.9760722639    0.0002280069        0.5941303726     0.0009   2026-09-08 10:27:43
   116    119    0.0009298183    0.0019277162     2754.9755046597    0.0005676042        0.5604168356     0.0009   2026-09-08 10:27:43
   117    120    0.0015098923    0.0035156040     2754.9740462279    0.0014584318        0.5522085118     0.0009   2026-09-08 10:27:43
   118    121    0.0029607086    0.0070033295     2754.9705594106    0.0034868173        0.5343346088     0.0009   2026-09-08 10:27:43
   119    122    0.0063992596    0.0144111055     2754.9631692386    0.0073901721        0.8706238962     0.0009   2026-09-08 10:27:43
   120    123    0.0109787893    0.0246050779     2754.9514932537    0.0116759849        1.6353933706     0.0009   2026-09-08 10:27:43
   121    124    0.0117411598    0.0259449093     2754.9409005534    0.0105927003        1.9857935059     0.0009   2026-09-08 10:27:43
   122    125    0.0052773707    0.0119320200     2754.9366979314    0.0042026221        1.7390766683     0.0010   2026-09-08 10:27:43
   123    126    0.0016309606    0.0036564075     2754.9359966087    0.0007013226        1.4734504261     0.0009   2026-09-08 10:27:43
   124    127    0.0007393046    0.0017479692     2754.9357970031    0.0001996056        1.3738073120     0.0010   2026-09-08 10:27:43
   125    128    0.0011378883    0.0027320493     2754.9352971215    0.0004998816        1.2973519417     0.0010   2026-09-08 10:27:43
   126    129    0.0015686601    0.0033698447     2754.9340811085    0.0012160130        1.2521107679     0.0009   2026-09-08 10:27:43
   127    130    0.0025898172    0.0039598637     2754.9308719169    0.0032091915        1.2227627667     0.0009   2026-09-08 10:27:43
   128    131    0.0040118890    0.0071541184     2754.9228809584    0.0079909585        1.3015345528     0.0009   2026-09-08 10:27:43
   129    132    0.0111616206    0.0248142237     2754.9039845580    0.0188964004        1.3574190524     0.0009   2026-09-08 10:27:43
   130    133    0.0324075384    0.0682850666     2754.8659469892    0.0380375688        2.0801084609     0.0009   2026-09-08 10:27:43
   131    134    0.0612378656    0.1274562370     2754.8115596836    0.0543873056        2.5286230322     0.0009   2026-09-08 10:27:43
   132    135    0.0610305261    0.1268160779     2754.7704817601    0.0410779235        1.6573346869     0.0009   2026-09-08 10:27:43
   133    136    0.0203240083    0.0431892006     2754.7583587007    0.0121230594        0.4817563650     0.0009   2026-09-08 10:27:43
   134    137    0.0028793146    0.0070018877     2754.7571934537    0.0011652471        0.4534165948     0.0010   2026-09-08 10:27:43
   135    138    0.0019829141    0.0041425010     2754.7571518659    0.0000415878        0.4472742830     0.0012   2026-09-08 10:27:43
   136    139    0.0004803611    0.0010014651     2754.7571416990    0.0000101669        0.4464720829     0.0010   2026-09-08 10:27:43
   137    140    0.0016260422    0.0034123596     2754.7570876626    0.0000540364        0.4438498430     0.0010   2026-09-08 10:27:43
   138    141    0.0020017685    0.0042602494     2754.7569747112    0.0001129513        0.4402238860     0.0010   2026-09-08 10:27:43
   139    142    0.0034827057    0.0073254833     2754.7566519277    0.0003227835        0.4328992963     0.0009   2026-09-08 10:27:43
   140    143    0.0057082962    0.0107357104     2754.7558443707    0.0008075571        0.4194761127     0.0010   2026-09-08 10:27:43
   141    144    0.0098985322    0.0158631394     2754.7537643585    0.0020800121        0.3929042095     0.0009   2026-09-08 10:27:43
   142    145    0.0164977014    0.0220414550     2754.7487439888    0.0050203698        0.3411606730     0.0009   2026-09-08 10:27:43
   143    146    0.0250415210    0.0340661603     2754.7378765974    0.0108673914        0.3875467692     0.0009   2026-09-08 10:27:43
   144    147    0.0347025928    0.0655800941     2754.7199007131    0.0179758842        0.4388807239     0.0010   2026-09-08 10:27:43
   145    148    0.0577280420    0.0986236397     2754.7023300198    0.0175706934        0.3142734315     0.0012   2026-09-08 10:27:43
   146    149    0.0400291321    0.0730623526     2754.6949398233    0.0073901964        0.1907924851     0.0009   2026-09-08 10:27:43
   147    150    0.0119914852    0.0208850569     2754.6938925046    0.0010473188        0.1670798107     0.0011   2026-09-08 10:27:43
   148    151    0.0026942915    0.0039926040     2754.6938470515    0.0000454531        0.1642998614     0.0015   2026-09-08 10:27:43
   149    152    0.0004356340    0.0007631823     2754.6938449557    0.0000020959        0.1628013108     0.0010   2026-09-08 10:27:43
   150    153    0.0005455441    0.0009546388     2754.6938409379    0.0000040178        0.1607905947     0.0010   2026-09-08 10:27:43
   151    154    0.0009128556    0.0016148086     2754.6938298966    0.0000110413        0.1573100481     0.0009   2026-09-08 10:27:43
   152    155    0.0013967506    0.0025204981     2754.6938015743    0.0000283223        0.1548282771     0.0009   2026-09-08 10:27:43
   153    156    0.0021380011    0.0040020316     2754.6937271684    0.0000744058        0.1585965464     0.0009   2026-09-08 10:27:43
   154    157    0.0031051385    0.0061753273     2754.6935348410    0.0001923274        0.1639833980     0.0009   2026-09-08 10:27:43
   155    158    0.0053532272    0.0093031161     2754.6930437289    0.0004911122        0.1708702220     0.0009   2026-09-08 10:27:43
   156    159    0.0091051037    0.0135971963     2754.6918420512    0.0012016777        0.1770343027     0.0009   2026-09-08 10:27:43
   157    160    0.0142956133    0.0207148812     2754.6891873696    0.0026546816        0.1745178595     0.0009   2026-09-08 10:27:43
   158    161    0.0220412614    0.0363021854     2754.6845715835    0.0046157860        0.1743396659     0.0009   2026-09-08 10:27:43
   159    162    0.0379809642    0.0548885047     2754.6796310687    0.0049405148        0.1258089604     0.0009   2026-09-08 10:27:43
   160    163    0.0300175184    0.0453937762     2754.6772533699    0.0023776988        0.0475558600     0.0010   2026-09-08 10:27:43
   161    164    0.0080086858    0.0158122943     2754.6768567789    0.0003965910        0.0419460707     0.0010   2026-09-08 10:27:43
   162    165    0.0021363836    0.0031826072     2754.6768368401    0.0000199389        0.0386210425     0.0010   2026-09-08 10:27:43
   163    166    0.0003812799    0.0005585381     2754.6768364763    0.0000003638        0.0380442183     0.0010   2026-09-08 10:27:43
   164    167    0.0000827898    0.0001203680     2754.6768363754    0.0000001009        0.0379323467     0.0009   2026-09-08 10:27:43
   165    168    0.0003529146    0.0005173875     2754.6768357035    0.0000006719        0.0374615590     0.0009   2026-09-08 10:27:43
   166    169    0.0004233366    0.0006304356     2754.6768343490    0.0000013545        0.0368840315     0.0009   2026-09-08 10:27:43
   167    170    0.0007745436    0.0011294573     2754.6768304114    0.0000039376        0.0358036233     0.0009   2026-09-08 10:27:43
   168    171    0.0012257406    0.0017107238     2754.6768206023    0.0000098091        0.0340167623     0.0009   2026-09-08 10:27:43
   169    172    0.0020473614    0.0026905477     2754.6767951747    0.0000254276        0.0327682235     0.0009   2026-09-08 10:27:43
   170    173    0.0032363693    0.0039729777     2754.6767331988    0.0000619758        0.0355030296     0.0009   2026-09-08 10:27:43
   171    174    0.0046050065    0.0055875270     2754.6765954408    0.0001377581        0.0367561849     0.0009   2026-09-08 10:27:43
   172    175    0.0045991670    0.0078286206     2754.6763539872    0.0002414536        0.0321478338     0.0009   2026-09-08 10:27:43
   173    176    0.0080426481    0.0112037901     2754.6760911844    0.0002628028        0.0185998571     0.0010   2026-09-08 10:27:43
   174    177    0.0084261756    0.0106708522     2754.6759615639    0.0001296205        0.0061848927     0.0010   2026-09-08 10:27:43
   175    178    0.0032458345    0.0046157867     2754.6759392351    0.0000223288        0.0016544750     0.0010   2026-09-08 10:27:43

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','3.971184e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.2889***  0.2338   0.0000   
TC/100 EUR                        -1.5783**   0.7546   0.0365   
Babiogorski                        1.4521***  0.5066   0.0042   
Bieszczadzki                      -0.0899     0.2467   0.7155   
Gorczanski                         0.1928     0.6759   0.7754   
GorStolowych                       1.1542***  0.3196   0.0003   
Karkonoski                        -0.9087***  0.2820   0.0013   
Magurski                           0.5716     0.4007   0.1537   
Pieninski                         -1.1469**   0.5782   0.0473   
Swietokrzyski                      0.1359     0.1145   0.2352   
Household income (10k PLN)         0.2798***  0.1015   0.0058   
Male                               0.1172     0.0718   0.1025   
Higher education                   0.0137     0.0800   0.8645   
City                               0.1407*    0.0753   0.0617   
Winter                             0.8243***  0.0835   0.0000   
Hiking                             2.0858***  0.0789   0.0000   
Skiing                             1.3978***  0.2656   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.2900     0.0947            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    0.6336**   0.3029   0.0365   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2754.6759
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1731
AIC/n:                             0.9471
BIC/n:                             0.9676
n (observations):               5855
r (respondents):                5855
k (parameters):                   18
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1162
median                           0.0000          2.1210
std                              0.7834          0.9249
min                              0.0000          0.0269
max                             20.0000          5.1370
quantile 0.025                   0.0000          0.5722
quantile 0.975                   2.0000          3.9713
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:43
Estimation took 0.30058 seconds (0 hours 0 minutes 0.30058 seconds).

====================================================
FS: correlation filtered substitutes
====================================================
Substitutes kept: Bieszczadzki, Karkonoski, Swietokrzyski
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.66 -0.099 -0.03 0.062 0.083 0.062 0.009 0.0046 0.005 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.9399761754             NaN     3302.3317538369     0.0000   2026-09-08 10:27:44
     1      3    0.2355597357    0.4000758102     3247.0258927876  681.9140833878      665.2197097473     0.0029   2026-09-08 10:27:44
     2      4    0.0362371828    0.0745477822     3173.2180007389   73.8078920487      449.9713517207     0.0010   2026-09-08 10:27:44
     3      5    0.0466729295    0.0720914090     3144.5772824183   28.6407183206      344.2803404146     0.0010   2026-09-08 10:27:44
     4      6    0.0454734077    0.0539038835     3124.7969300838   19.7803523345      308.0986149130     0.0010   2026-09-08 10:27:44
     5      7    0.4655426242    0.5524498182     2983.3872358978  141.4096941860      501.4533753534     0.0010   2026-09-08 10:27:44
     6      8    0.2676096599    0.3230272986     2924.8352789555   58.5519569424      432.5808930811     0.0010   2026-09-08 10:27:44
     7      9    0.2117556503    0.2609524655     2891.8374194074   32.9978595480      250.2231070830     0.0009   2026-09-08 10:27:44
     8     10    0.0855819143    0.1076083323     2883.6820890563    8.1553303511      144.3672412433     0.0008   2026-09-08 10:27:44
     9     11    0.0575525206    0.0749564220     2878.2043006281    5.4777884282      155.6723795391     0.0008   2026-09-08 10:27:44
    10     12    0.0893935965    0.1255742648     2868.0924629116   10.1118377165      228.2405870162     0.0009   2026-09-08 10:27:44
    11     13    0.1245941762    0.1977529543     2851.8723704721   16.2200924395      260.2445120781     0.0008   2026-09-08 10:27:44
    12     14    0.1169772046    0.2240672069     2834.9767450104   16.8956254616      193.5061053242     0.0008   2026-09-08 10:27:44
    13     15    0.0588602460    0.1126102278     2827.4169478578    7.5597971526       99.7078734427     0.0009   2026-09-08 10:27:44
    14     16    0.0308963512    0.0418944682     2825.7079948839    1.7089529739       47.9703266480     0.0008   2026-09-08 10:27:44
    15     17    0.0260735447    0.0362852028     2825.1874451446    0.5205497393       49.9252170337     0.0009   2026-09-08 10:27:44
    16     18    0.0172218709    0.0257650938     2824.7210018001    0.4664433445       56.7426513323     0.0008   2026-09-08 10:27:44
    17     19    0.0323656788    0.0524600311     2823.3405750358    1.3804267643       67.5934259305     0.0009   2026-09-08 10:27:44
    18     20    0.0505940629    0.0905649027     2820.4306243621    2.9099506737       78.1891916357     0.0010   2026-09-08 10:27:44
    19     21    0.1347821658    0.1799469154     2814.8828238903    5.5478004718       89.9757879491     0.0012   2026-09-08 10:27:44
    20     22    0.2126382914    0.2606771561     2808.3018331939    6.5809906964       84.8115089443     0.0012   2026-09-08 10:27:44
    21     23    0.1638141119    0.2101685908     2804.5210338034    3.7807993905       39.7077561768     0.0010   2026-09-08 10:27:44
    22     24    0.0458244013    0.0737240661     2803.6999560225    0.8210777809       24.7177479132     0.0008   2026-09-08 10:27:44
    23     25    0.0137525216    0.0210830929     2803.4683372952    0.2316187274       26.5451468022     0.0008   2026-09-08 10:27:44
    24     26    0.0156017268    0.0273866614     2803.0275126242    0.4408246709       27.9199347357     0.0008   2026-09-08 10:27:44
    25     27    0.0214720224    0.0479713741     2802.0114056786    1.0161069456       36.6787210509     0.0008   2026-09-08 10:27:44
    26     28    0.0670894932    0.1030977053     2799.7780297060    2.2333759726       62.3704771848     0.0008   2026-09-08 10:27:44
    27     29    0.1504087432    0.2035077768     2795.9403778352    3.8376518708       82.5146069287     0.0008   2026-09-08 10:27:44
    28     30    0.2091389631    0.2739227667     2791.7993898433    4.1409879920       74.0771479151     0.0008   2026-09-08 10:27:44
    29     31    0.1276523370    0.1759274335     2789.6625115664    2.1368782769       38.0149987033     0.0010   2026-09-08 10:27:44
    30     32    0.0302766370    0.0441122917     2789.1730478080    0.4894637583       20.3681224959     0.0011   2026-09-08 10:27:44
    31     33    0.0136405043    0.0224565914     2789.0315342650    0.1415135431       20.4656996231     0.0010   2026-09-08 10:27:44
    32     34    0.0173636843    0.0298004392     2788.7486845627    0.2828497023       23.6637043991     0.0011   2026-09-08 10:27:44
    33     35    0.0228637399    0.0430989442     2788.0563647383    0.6923198244       30.1643391776     0.0008   2026-09-08 10:27:44
    34     36    0.0392267572    0.0799813200     2786.5038757394    1.5524889989       37.7804589562     0.0008   2026-09-08 10:27:44
    35     37    0.0930452098    0.1805849790     2783.7130670475    2.7908086919       44.1868706480     0.0008   2026-09-08 10:27:44
    36     38    0.1915500201    0.2914630140     2780.5667190877    3.1463479598       38.6523278616     0.0008   2026-09-08 10:27:44
    37     39    0.1673755092    0.2296542727     2778.9272836137    1.6394354740       18.7844352252     0.0008   2026-09-08 10:27:44
    38     40    0.0497156385    0.0693898721     2778.5960999351    0.3311836786       10.8986573824     0.0009   2026-09-08 10:27:44
    39     41    0.0076627579    0.0144619178     2778.5395671284    0.0565328066       10.8657342266     0.0008   2026-09-08 10:27:44
    40     42    0.0080820032    0.0139573481     2778.4597146659    0.0798524625       11.9110319416     0.0010   2026-09-08 10:27:44
    41     43    0.0151615149    0.0240348197     2778.2466878201    0.2130268458       13.3858869386     0.0008   2026-09-08 10:27:44
    42     44    0.0237138069    0.0433881594     2777.7773580776    0.4693297425       15.9204566391     0.0008   2026-09-08 10:27:44
    43     45    0.0444088670    0.0919503869     2776.8809896161    0.8963684615       20.8350800453     0.0008   2026-09-08 10:27:44
    44     46    0.0809680822    0.1483182064     2775.7632429057    1.1177467105       18.9809193879     0.0010   2026-09-08 10:27:44
    45     47    0.0725708866    0.1311922646     2775.0611718379    0.7020710678        9.3884167356     0.0009   2026-09-08 10:27:44
    46     48    0.0224925917    0.0473330387     2774.8828152431    0.1783565948        7.8245190673     0.0008   2026-09-08 10:27:44
    47     49    0.0078797275    0.0121476640     2774.8538619299    0.0289533133        8.2532199682     0.0008   2026-09-08 10:27:44
    48     50    0.0049879669    0.0083045184     2774.8298531680    0.0240087619        8.4130687944     0.0009   2026-09-08 10:27:44
    49     51    0.0098105848    0.0149323075     2774.7595734020    0.0702797660        8.5441580301     0.0008   2026-09-08 10:27:44
    50     52    0.0138836521    0.0215199532     2774.6104570478    0.1491163541        8.3412416192     0.0011   2026-09-08 10:27:44
    51     53    0.0193917338    0.0437135425     2774.3190194442    0.2914376037        8.3773333759     0.0011   2026-09-08 10:27:44
    52     54    0.0387494374    0.0757080158     2773.9556913806    0.3633280635        8.0050430628     0.0011   2026-09-08 10:27:44
    53     55    0.0384774024    0.0749858777     2773.7276501430    0.2280412377        5.0821093216     0.0011   2026-09-08 10:27:44
    54     56    0.0130289354    0.0304672111     2773.6736444567    0.0540056863        3.2908421356     0.0008   2026-09-08 10:27:44
    55     57    0.0043626799    0.0061763703     2773.6674172794    0.0062271773        2.9350022709     0.0008   2026-09-08 10:27:44
    56     58    0.0018080066    0.0028188482     2773.6642074571    0.0032098222        2.8596497306     0.0009   2026-09-08 10:27:44
    57     59    0.0040176596    0.0058710996     2773.6539118727    0.0102955844        2.6037909249     0.0010   2026-09-08 10:27:44
    58     60    0.0056310829    0.0079208274     2773.6332388440    0.0206730288        2.4147723371     0.0010   2026-09-08 10:27:44
    59     61    0.0075522094    0.0139653439     2773.5934688015    0.0397700424        1.8423355888     0.0012   2026-09-08 10:27:44
    60     62    0.0106427006    0.0211479979     2773.5472475023    0.0462212993        2.2038942656     0.0010   2026-09-08 10:27:44
    61     63    0.0109972919    0.0198275146     2773.5207734628    0.0264740394        1.8305179206     0.0010   2026-09-08 10:27:44
    62     64    0.0038547453    0.0082924885     2773.5151063069    0.0056671559        1.3949660111     0.0011   2026-09-08 10:27:44
    63     65    0.0014530292    0.0019587194     2773.5143891263    0.0007171806        1.3960102125     0.0011   2026-09-08 10:27:44
    64     66    0.0008236116    0.0010917357     2773.5138326036    0.0005565228        1.3942388135     0.0012   2026-09-08 10:27:44
    65     67    0.0017652524    0.0022800613     2773.5120521980    0.0017804055        1.3822361596     0.0012   2026-09-08 10:27:44
    66     68    0.0025451807    0.0036226238     2773.5082171652    0.0038350328        1.3463782020     0.0011   2026-09-08 10:27:44
    67     69    0.0047530101    0.0073105651     2773.5000297691    0.0081873961        1.2527217386     0.0011   2026-09-08 10:27:44
    68     70    0.0088429218    0.0123262862     2773.4880202467    0.0120095224        1.2967483111     0.0011   2026-09-08 10:27:44
    69     71    0.0092597214    0.0133446200     2773.4780955408    0.0099247060        1.1472024718     0.0008   2026-09-08 10:27:44
    70     72    0.0034455490    0.0065837004     2773.4746769424    0.0034185984        0.8687744280     0.0008   2026-09-08 10:27:44
    71     73    0.0014614867    0.0018621391     2773.4741096382    0.0005673042        0.8771719749     0.0008   2026-09-08 10:27:44
    72     74    0.0005936728    0.0008553856     2773.4738469391    0.0002626992        0.8853587157     0.0008   2026-09-08 10:27:44
    73     75    0.0011031617    0.0015863801     2773.4730746814    0.0007722577        0.8973482840     0.0008   2026-09-08 10:27:44
    74     76    0.0015445528    0.0023900213     2773.4713113886    0.0017632928        0.9012393595     0.0008   2026-09-08 10:27:44
    75     77    0.0032725172    0.0052333720     2773.4670301400    0.0042812487        0.8721340315     0.0008   2026-09-08 10:27:44
    76     78    0.0096461991    0.0116965607     2773.4586268310    0.0084033090        1.1159672447     0.0008   2026-09-08 10:27:44
    77     79    0.0182668123    0.0204619769     2773.4468436557    0.0117831753        1.2518785049     0.0008   2026-09-08 10:27:44
    78     80    0.0178381999    0.0197150433     2773.4382392491    0.0086044067        1.0243392618     0.0008   2026-09-08 10:27:44
    79     81    0.0059097044    0.0074123579     2773.4356874375    0.0025518115        1.0784309603     0.0008   2026-09-08 10:27:44
    80     82    0.0010433905    0.0017569762     2773.4353483283    0.0003391093        1.0106725873     0.0012   2026-09-08 10:27:44
    81     83    0.0006942715    0.0009376737     2773.4352142477    0.0001340805        0.9675688395     0.0012   2026-09-08 10:27:44
    82     84    0.0012941061    0.0017973704     2773.4348059888    0.0004082589        0.8623864665     0.0011   2026-09-08 10:27:44
    83     85    0.0014394861    0.0021099157     2773.4339433097    0.0008626791        0.6871260310     0.0009   2026-09-08 10:27:44
    84     86    0.0025583617    0.0031597695     2773.4321177107    0.0018255989        0.4458547135     0.0010   2026-09-08 10:27:44
    85     87    0.0033517551    0.0060317416     2773.4295308580    0.0025868528        0.3901554765     0.0008   2026-09-08 10:27:44
    86     88    0.0062416518    0.0083071487     2773.4275336723    0.0019971856        0.2433393369     0.0008   2026-09-08 10:27:44
    87     89    0.0040372932    0.0049720513     2773.4269359325    0.0005977398        0.0926878830     0.0008   2026-09-08 10:27:44
    88     90    0.0007338098    0.0010972299     2773.4268769293    0.0000590032        0.0323748387     0.0008   2026-09-08 10:27:44
    89     91    0.0001326205    0.0001855261     2773.4268751430    0.0000017863        0.0328923913     0.0008   2026-09-08 10:27:44
    90     92    0.0000221462    0.0000338257     2773.4268749809    0.0000001622        0.0324867614     0.0008   2026-09-08 10:27:44
    91     93    0.0000643300    0.0000971010     2773.4268742827    0.0000006981        0.0301963940     0.0010   2026-09-08 10:27:44
    92     94    0.0000652765    0.0001036998     2773.4268730533    0.0000012294        0.0254313933     0.0011   2026-09-08 10:27:44
    93     95    0.0000685959    0.0001181712     2773.4268708026    0.0000022507        0.0153406451     0.0011   2026-09-08 10:27:44
    94     96    0.0000741955    0.0001247338     2773.4268686451    0.0000021575        0.0092027403     0.0011   2026-09-08 10:27:44
    95     97    0.0000894778    0.0001502460     2773.4268676905    0.0000009546        0.0035370553     0.0010   2026-09-08 10:27:44
    96     98    0.0000486266    0.0000730738     2773.4268675518    0.0000001387        0.0007677118     0.0008   2026-09-08 10:27:44

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','2.324053e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.9619***  0.2090   0.0000   
TC/100 EUR                        -0.6736***  0.1281   0.0000   
Bieszczadzki                      -0.0080     0.1226   0.9482   
Karkonoski                         0.3690***  0.0879   0.0000   
Swietokrzyski                      0.3076***  0.1116   0.0058   
Household income (10k PLN)         0.2648***  0.1020   0.0094   
Male                               0.1176     0.0722   0.1032   
Higher education                   0.0261     0.0802   0.7450   
City                               0.0932     0.0743   0.2097   
Winter                             0.8431***  0.0841   0.0000   
Hiking                             2.0907***  0.0789   0.0000   
Skiing                             1.4075***  0.2668   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3460     0.0923            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.4845***  0.2823   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2773.4269
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1675
AIC/n:                             0.9518
BIC/n:                             0.9666
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.7225
median                           0.0000          1.7321
std                              0.7834          0.7394
min                              0.0000          0.0246
max                             20.0000          3.5357
quantile 0.025                   0.0000          0.4668
quantile 0.975                   2.0000          3.0518
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:44
Estimation took 0.1621 seconds (0 hours 0 minutes 0.1621 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.64 -0.079 -0.037 0.048 0.075 0.073 0.009 0.005 0.0048 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3929.0681461864             NaN     3760.2532893380     0.0001   2026-09-08 10:27:45
     1      3    0.2261444729    0.3760924930     3282.7565983405  646.3115478460      862.4475162800     0.0028   2026-09-08 10:27:45
     2      4    0.0408042901    0.0781276134     3186.2432192379   96.5133791026      459.8755659585     0.0013   2026-09-08 10:27:45
     3      5    0.0360748509    0.0648156748     3158.8272090485   27.4160101894      349.5889536658     0.0014   2026-09-08 10:27:45
     4      7    0.2755245971    0.3294943252     3050.0627616597  108.7644473889      443.6716959435     0.0024   2026-09-08 10:27:45
     5      8    0.4595854259    0.5558831158     2935.3201543168  114.7426073428      395.2099792779     0.0011   2026-09-08 10:27:45
     6      9    0.1825867419    0.2233649369     2911.7458862446   23.5742680722      265.3799975587     0.0012   2026-09-08 10:27:45
     7     10    0.1067213617    0.1301787802     2903.4013461730    8.3445400716      178.0214148571     0.0012   2026-09-08 10:27:45
     8     11    0.0894904417    0.1101708286     2896.0005363563    7.4008098167      186.0678207694     0.0012   2026-09-08 10:27:45
     9     12    0.1451489010    0.1866441178     2881.4307377942   14.5697985621      256.6272695367     0.0013   2026-09-08 10:27:45
    10     13    0.1701991212    0.2442178917     2860.3888948923   21.0418429020      268.0207107976     0.0013   2026-09-08 10:27:45
    11     14    0.1222209657    0.2214963341     2841.0598433836   19.3290515087      176.6272981124     0.0013   2026-09-08 10:27:45
    12     15    0.0591901106    0.1035908518     2833.5120637450    7.5477796386       80.0745189195     0.0014   2026-09-08 10:27:45
    13     16    0.0602447531    0.0732185158     2831.8659870667    1.6460766783       48.9232995349     0.0011   2026-09-08 10:27:45
    14     17    0.0384642957    0.0486358588     2831.3105107434    0.5554763233       58.0783006091     0.0010   2026-09-08 10:27:45
    15     18    0.0234904144    0.0313007986     2830.7688198510    0.5416908924       62.7177365540     0.0012   2026-09-08 10:27:45
    16     19    0.0416863444    0.0612052864     2829.1085542428    1.6602656083       70.2997261631     0.0010   2026-09-08 10:27:45
    17     20    0.0531258708    0.0975188736     2825.5914175823    3.5171366605       77.0835466830     0.0009   2026-09-08 10:27:45
    18     21    0.1455712084    0.1888448733     2818.7552582962    6.8361592861       83.6946037907     0.0010   2026-09-08 10:27:45
    19     22    0.2332899330    0.2825574557     2810.4225857852    8.3326725110       81.5811260811     0.0010   2026-09-08 10:27:45
    20     23    0.1844924516    0.2431686986     2805.5217093253    4.9008764599       41.7199942583     0.0018   2026-09-08 10:27:45
    21     24    0.0594234599    0.0909399719     2804.4881334545    1.0335758709       29.1964058198     0.0012   2026-09-08 10:27:45
    22     25    0.0169245935    0.0236435542     2804.2531346496    0.2349988049       30.3856227160     0.0013   2026-09-08 10:27:45
    23     26    0.0162071530    0.0252309283     2803.8788926122    0.3742420374       30.8685679359     0.0012   2026-09-08 10:27:45
    24     27    0.0232423966    0.0426606210     2802.9793052975    0.8995873147       32.0953790039     0.0012   2026-09-08 10:27:45
    25     28    0.0468123115    0.0848274135     2800.9583319428    2.0209733548       55.1988736025     0.0014   2026-09-08 10:27:45
    26     29    0.1208826910    0.1731016551     2797.1631997688    3.7951321740       77.0154416688     0.0013   2026-09-08 10:27:45
    27     30    0.2000119593    0.2641491281     2792.4115603831    4.7516393857       77.1960196979     0.0011   2026-09-08 10:27:45
    28     31    0.1622003560    0.2146279184     2789.3911933258    3.0203670573       46.1287097921     0.0012   2026-09-08 10:27:45
    29     32    0.0379603843    0.0668808542     2788.5910828408    0.8001104851       18.4843019231     0.0014   2026-09-08 10:27:45
    30     33    0.0151777848    0.0274949243     2788.4539644146    0.1371184261       18.4464530337     0.0014   2026-09-08 10:27:45
    31     34    0.0127310026    0.0202469134     2788.3282049104    0.1257595043       19.5924682392     0.0012   2026-09-08 10:27:45
    32     35    0.0199304320    0.0375557601     2787.9381557162    0.3900491942       24.4100577926     0.0013   2026-09-08 10:27:45
    33     36    0.0258818372    0.0519028547     2787.0780473680    0.8601083481       30.2128615887     0.0010   2026-09-08 10:27:45
    34     37    0.0446365929    0.1044739349     2785.2146887239    1.8633586442       35.6734538002     0.0012   2026-09-08 10:27:45
    35     38    0.1143967374    0.2064964593     2782.3835325256    2.8311561982       37.0747697845     0.0009   2026-09-08 10:27:45
    36     39    0.1785359963    0.2612755832     2779.9530923848    2.4304401408       25.3224707527     0.0013   2026-09-08 10:27:45
    37     40    0.1080353232    0.1453672890     2779.0937292538    0.8593631310       12.1177779530     0.0010   2026-09-08 10:27:45
    38     41    0.0192325349    0.0335572234     2778.9676913685    0.1260378853       11.5802402500     0.0015   2026-09-08 10:27:45
    39     42    0.0056220728    0.0100296546     2778.9260891659    0.0416022026       11.4377663169     0.0012   2026-09-08 10:27:45
    40     43    0.0117811707    0.0189473822     2778.8032104446    0.1228787213       11.0699694115     0.0012   2026-09-08 10:27:45
    41     44    0.0177966272    0.0276055633     2778.5330546551    0.2701557895       12.1605674450     0.0012   2026-09-08 10:27:45
    42     45    0.0291359070    0.0572944679     2777.9050361489    0.6280185062       16.5821939769     0.0012   2026-09-08 10:27:45
    43     46    0.0509791961    0.1156191110     2776.8062733706    1.0987627783       20.2700072098     0.0012   2026-09-08 10:27:45
    44     47    0.0771101352    0.1706816232     2775.5642132900    1.2420600805       16.3471502147     0.0012   2026-09-08 10:27:45
    45     48    0.0601351668    0.1260318899     2774.9112573039    0.6529559861        8.1126853067     0.0009   2026-09-08 10:27:45
    46     49    0.0179349156    0.0365585705     2774.7793698608    0.1318874431        6.6702977435     0.0011   2026-09-08 10:27:45
    47     50    0.0062050178    0.0110522796     2774.7631128925    0.0162569683        7.0120120661     0.0012   2026-09-08 10:27:45
    48     51    0.0036372074    0.0074763113     2774.7497323839    0.0133805085        7.1548947026     0.0010   2026-09-08 10:27:45
    49     52    0.0075129137    0.0140265836     2774.7084069626    0.0413254214        7.2817073511     0.0010   2026-09-08 10:27:45
    50     53    0.0105255913    0.0175463404     2774.6216366651    0.0867702975        7.0775396005     0.0012   2026-09-08 10:27:45
    51     54    0.0140573604    0.0286758042     2774.4505685208    0.1710681442        5.9631460959     0.0012   2026-09-08 10:27:45
    52     55    0.0243710448    0.0497827900     2774.2363082506    0.2142602702        4.9627246689     0.0012   2026-09-08 10:27:45
    53     56    0.0288364499    0.0556665593     2774.1001383567    0.1361698939        3.7029340324     0.0010   2026-09-08 10:27:45
    54     57    0.0122816360    0.0268041386     2774.0673353249    0.0328030318        2.8107130306     0.0011   2026-09-08 10:27:45
    55     58    0.0033749747    0.0056176896     2774.0635157358    0.0038195890        2.7649465080     0.0012   2026-09-08 10:27:45
    56     59    0.0013473942    0.0020892578     2774.0615727079    0.0019430279        2.7521974317     0.0013   2026-09-08 10:27:45
    57     60    0.0029880033    0.0044244845     2774.0551395828    0.0064331251        2.7214036975     0.0012   2026-09-08 10:27:45
    58     61    0.0042847692    0.0064448941     2774.0414119101    0.0137276728        2.6664128996     0.0012   2026-09-08 10:27:45
    59     62    0.0075590518    0.0124772355     2774.0109192115    0.0304926986        2.5565311640     0.0012   2026-09-08 10:27:45
    60     63    0.0150580629    0.0216709490     2773.9633549600    0.0475642515        2.6139000338     0.0012   2026-09-08 10:27:45
    61     64    0.0177315117    0.0264108235     2773.9193324994    0.0440224606        2.9273185041     0.0012   2026-09-08 10:27:45
    62     65    0.0082888628    0.0156494349     2773.9017957913    0.0175367082        2.2377211037     0.0012   2026-09-08 10:27:45
    63     66    0.0030992290    0.0046307185     2773.8986894153    0.0031063760        2.2613534950     0.0012   2026-09-08 10:27:45
    64     67    0.0012018819    0.0017351377     2773.8975831255    0.0011062898        2.2722128027     0.0012   2026-09-08 10:27:45
    65     68    0.0020887095    0.0028724180     2773.8947028955    0.0028802299        2.2807009573     0.0012   2026-09-08 10:27:45
    66     69    0.0032184123    0.0042862672     2773.8879909916    0.0067119039        2.2651765736     0.0013   2026-09-08 10:27:45
    67     70    0.0053962302    0.0088600141     2773.8717213198    0.0162696719        2.1700492399     0.0009   2026-09-08 10:27:45
    68     71    0.0164192774    0.0197075347     2773.8391632558    0.0325580640        1.9565183486     0.0010   2026-09-08 10:27:45
    69     72    0.0321129359    0.0354691156     2773.7920154284    0.0471478274        2.8241562888     0.0009   2026-09-08 10:27:45
    70     73    0.0330206144    0.0362160484     2773.7556455049    0.0363699234        2.4130860234     0.0012   2026-09-08 10:27:45
    71     74    0.0119319476    0.0149181146     2773.7440503149    0.0115951900        1.7538508760     0.0012   2026-09-08 10:27:45
    72     75    0.0025710389    0.0034143304     2773.7423412654    0.0017090495        1.7852223597     0.0012   2026-09-08 10:27:45
    73     76    0.0012068129    0.0017876876     2773.7416131369    0.0007281285        1.7601676249     0.0009   2026-09-08 10:27:45
    74     77    0.0020285514    0.0033391338     2773.7394003240    0.0022128129        1.6833786292     0.0011   2026-09-08 10:27:45
    75     78    0.0026185004    0.0041015933     2773.7345269866    0.0048733374        1.5356098392     0.0009   2026-09-08 10:27:45
    76     79    0.0037193937    0.0073308956     2773.7233560962    0.0111708904        1.2309511873     0.0011   2026-09-08 10:27:45
    77     80    0.0117298223    0.0160784055     2773.7043878355    0.0189682608        1.3471819872     0.0013   2026-09-08 10:27:45
    78     81    0.0220210950    0.0259163138     2773.6842315731    0.0201562624        1.2964703408     0.0013   2026-09-08 10:27:45
    79     82    0.0174517831    0.0199315168     2773.6747367035    0.0094948696        0.7683500733     0.0012   2026-09-08 10:27:45
    80     83    0.0040708634    0.0055501389     2773.6731356425    0.0016010610        0.7396602068     0.0012   2026-09-08 10:27:45
    81     84    0.0005527501    0.0011461771     2773.6730199651    0.0001156774        0.6963334418     0.0009   2026-09-08 10:27:45
    82     85    0.0003329238    0.0004846438     2773.6729756282    0.0000443369        0.6754814882     0.0008   2026-09-08 10:27:45
    83     86    0.0008447216    0.0012192986     2773.6728042565    0.0001713717        0.6080390677     0.0009   2026-09-08 10:27:45
    84     87    0.0009163201    0.0014551615     2773.6724674580    0.0003367986        0.4952536942     0.0012   2026-09-08 10:27:45
    85     88    0.0017103577    0.0020431000     2773.6717719940    0.0006954640        0.3093002371     0.0012   2026-09-08 10:27:45
    86     89    0.0020556969    0.0027354812     2773.6708868660    0.0008851279        0.2137065846     0.0012   2026-09-08 10:27:45
    87     90    0.0017898101    0.0033115020     2773.6703009075    0.0005859585        0.0961022725     0.0012   2026-09-08 10:27:45
    88     91    0.0013721100    0.0019724645     2773.6701591138    0.0001417938        0.0414811363     0.0012   2026-09-08 10:27:45
    89     92    0.0003168726    0.0004871943     2773.6701480957    0.0000110181        0.0063525137     0.0012   2026-09-08 10:27:45
    90     93    0.0000543437    0.0000631546     2773.6701478560    0.0000002397        0.0039777208     0.0012   2026-09-08 10:27:45
    91     94    0.0000031279    0.0000065460     2773.6701478534    0.0000000026        0.0039466154     0.0009   2026-09-08 10:27:45
    92     95    0.0000014969    0.0000029422     2773.6701478516    0.0000000018        0.0038962908     0.0009   2026-09-08 10:27:45
    93     96    0.0000040366    0.0000082287     2773.6701478438    0.0000000078        0.0036082933     0.0011   2026-09-08 10:27:45

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.593327e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.8732***  0.1915   0.0000   
TC/100 EUR                        -0.5680***  0.1150   0.0000   
Bieszczadzki                      -0.0413     0.1074   0.7006   
Karkonoski                         0.2895***  0.0779   0.0002   
Swietokrzyski                      0.2665***  0.0999   0.0076   
Household income (10k PLN)         0.2950***  0.1103   0.0075   
Male                               0.1150     0.0723   0.1117   
Higher education                   0.0289     0.0803   0.7192   
City                               0.0881     0.0743   0.2358   
Winter                             0.8442***  0.0842   0.0000   
Hiking                             2.0918***  0.0789   0.0000   
Skiing                             1.4035***  0.2679   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3542     0.0918            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.7606***  0.3564   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2773.6701
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1674
AIC/n:                             0.9519
BIC/n:                             0.9667
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.9364
median                           0.0000          1.9333
std                              0.7834          0.8370
min                              0.0000          0.0250
max                             20.0000          4.9654
quantile 0.025                   0.0000          0.5313
quantile 0.975                   2.0000          3.5345
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:45
Estimation took 0.20355 seconds (0 hours 0 minutes 0.20355 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.63 -0.054 -0.04 0.032 0.061 0.1 0.009 0.0056 0.0046 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3929.3122187632             NaN     4676.1661434420     0.0001   2026-09-08 10:27:46
     1      3    0.2116041319    0.3423696198     3385.0555583942  544.2566603690     1450.0256173417     0.0024   2026-09-08 10:27:46
     2      4    0.0492799494    0.0858477075     3222.4095518427  162.6460065515      597.9218763885     0.0010   2026-09-08 10:27:46
     3      5    0.0342011152    0.0663222796     3189.8597617932   32.5497900495      336.4424833439     0.0011   2026-09-08 10:27:46
     4      6    0.0107072591    0.0174101811     3180.6417654177    9.2179963755      354.5466376023     0.0009   2026-09-08 10:27:46
     5      7    0.0904440097    0.1168130415     3137.5490699020   43.0926955157      375.4060458624     0.0012   2026-09-08 10:27:46
     6      8    0.2224846120    0.2759376658     3064.9107889256   72.6382809764      581.5979468088     0.0013   2026-09-08 10:27:46
     7      9    0.3406438363    0.4159352263     2990.7624271041   74.1483618215      623.9836778049     0.0014   2026-09-08 10:27:46
     8     10    0.2357055887    0.2842085255     2958.3510870903   32.4113400138      442.9437803837     0.0012   2026-09-08 10:27:46
     9     11    0.1021425601    0.1220638526     2945.0592945940   13.2917924964      241.6443835718     0.0013   2026-09-08 10:27:46
    10     12    0.0462382860    0.0618243987     2934.7498906579   10.3094039360      348.2775509269     0.0012   2026-09-08 10:27:46
    11     13    0.0290932869    0.0588313348     2922.8840869882   11.8658036697      465.2080047519     0.0013   2026-09-08 10:27:46
    12     14    0.0616938220    0.1035635074     2904.3007823165   18.5833046717      514.0627496351     0.0014   2026-09-08 10:27:46
    13     15    0.0984302415    0.1699063133     2878.8340281322   25.4667541843      428.0567324607     0.0012   2026-09-08 10:27:46
    14     16    0.1283269549    0.2048179966     2857.1382101309   21.6958180013      256.6175624187     0.0013   2026-09-08 10:27:46
    15     17    0.0989688802    0.1323171444     2850.4283844024    6.7098257285       91.4635103792     0.0013   2026-09-08 10:27:46
    16     18    0.0386739673    0.0495915358     2849.4437452905    0.9846391119       73.3162501601     0.0010   2026-09-08 10:27:46
    17     19    0.0235698318    0.0317124116     2848.7945222832    0.6492230074       65.9388461841     0.0012   2026-09-08 10:27:46
    18     20    0.0412137391    0.0616092583     2847.1532685688    1.6412537143       86.2694537486     0.0011   2026-09-08 10:27:46
    19     21    0.0669427614    0.1041452801     2843.6451467819    3.5081217869      114.7350219318     0.0010   2026-09-08 10:27:46
    20     22    0.1466065684    0.1920342302     2836.2042051263    7.4409416556      153.5033548922     0.0010   2026-09-08 10:27:46
    21     23    0.2453712358    0.2911149757     2824.5499142694   11.6542908569      167.7906925842     0.0010   2026-09-08 10:27:46
    22     24    0.2561524053    0.2976742156     2813.5964851726   10.9534290968      117.2693280744     0.0012   2026-09-08 10:27:46
    23     25    0.0904942134    0.1459257084     2809.0092806115    4.5872045611       45.3748161870     0.0013   2026-09-08 10:27:46
    24     26    0.0557373703    0.0798529565     2807.9382802795    1.0710003320       40.3758946402     0.0013   2026-09-08 10:27:46
    25     27    0.0342277795    0.0469570582     2807.6351435569    0.3031367226       37.8388346039     0.0013   2026-09-08 10:27:46
    26     28    0.0269097434    0.0380218928     2807.2487541873    0.3863893696       36.0225668767     0.0012   2026-09-08 10:27:46
    27     29    0.0394278188    0.0679623608     2806.0709877039    1.1777664834       35.1120760617     0.0009   2026-09-08 10:27:46
    28     30    0.0433876113    0.0881308467     2803.5200818896    2.5509058143       32.2205182733     0.0009   2026-09-08 10:27:46
    29     31    0.0838545329    0.1537914234     2798.3760328964    5.1440489931       31.9896291501     0.0008   2026-09-08 10:27:46
    30     32    0.2066248845    0.2745628661     2791.7014282089    6.6746046875       26.4694812165     0.0009   2026-09-08 10:27:46
    31     33    0.2576157209    0.2989454940     2787.3730073501    4.3284208588       20.7786753030     0.0009   2026-09-08 10:27:46
    32     34    0.1105781602    0.1339096808     2786.4043409286    0.9686664216       17.3368263204     0.0010   2026-09-08 10:27:46
    33     35    0.0133636979    0.0248041714     2786.3168345534    0.0875063752       15.1893833690     0.0010   2026-09-08 10:27:46
    34     36    0.0048359727    0.0091284176     2786.2679930291    0.0488415243       14.1149930930     0.0010   2026-09-08 10:27:46
    35     37    0.0118543736    0.0214021640     2786.0897354123    0.1782576168       12.6243013838     0.0009   2026-09-08 10:27:46
    36     38    0.0164985578    0.0316719152     2785.7116270734    0.3781083390       14.1786254910     0.0010   2026-09-08 10:27:46
    37     39    0.0330375622    0.0639170119     2784.8268510822    0.8847759911       16.4726125959     0.0010   2026-09-08 10:27:46
    38     40    0.0569817482    0.1150432987     2783.3095607363    1.5172903459       19.2018830287     0.0009   2026-09-08 10:27:46
    39     41    0.0654607941    0.1535290085     2781.6323663762    1.6771943601       17.0169453996     0.0010   2026-09-08 10:27:46
    40     42    0.0526720240    0.1031127128     2780.7723909771    0.8599753991       15.4744141631     0.0011   2026-09-08 10:27:46
    41     43    0.0190239665    0.0336333446     2780.5919983983    0.1803925788       14.0681695257     0.0009   2026-09-08 10:27:46
    42     44    0.0066131328    0.0126451936     2780.5608267470    0.0311716513       14.3595555709     0.0009   2026-09-08 10:27:46
    43     45    0.0063600405    0.0117788304     2780.5176592846    0.0431674624       14.5558097187     0.0010   2026-09-08 10:27:46
    44     46    0.0120627549    0.0196189880     2780.3938172416    0.1238420430       14.7428161352     0.0010   2026-09-08 10:27:46
    45     47    0.0189960368    0.0288993998     2780.1018375524    0.2919796893       14.5837466065     0.0010   2026-09-08 10:27:46
    46     48    0.0368360932    0.0592906058     2779.4322207672    0.6696167851       13.2512995769     0.0010   2026-09-08 10:27:46
    47     49    0.0874490107    0.1289197730     2778.2290050800    1.2032156872       15.1125225188     0.0009   2026-09-08 10:27:46
    48     50    0.1288858809    0.1997741523     2776.8511799846    1.3778250954       13.8936927588     0.0009   2026-09-08 10:27:46
    49     51    0.0840364967    0.1507398929     2776.1256722022    0.7255077824        7.9146922463     0.0009   2026-09-08 10:27:46
    50     52    0.0226727959    0.0419874259     2775.9862889387    0.1393832635        4.8365034530     0.0009   2026-09-08 10:27:46
    51     53    0.0067188591    0.0108401104     2775.9768636456    0.0094252932        4.9326722050     0.0010   2026-09-08 10:27:46
    52     54    0.0024595094    0.0035144602     2775.9746385526    0.0022250929        4.9584669104     0.0010   2026-09-08 10:27:46
    53     55    0.0065097111    0.0089915115     2775.9658414118    0.0087971408        5.0145340637     0.0009   2026-09-08 10:27:46
    54     56    0.0084999687    0.0112739852     2775.9472322320    0.0186091798        5.0615523529     0.0009   2026-09-08 10:27:46
    55     57    0.0132435470    0.0180956816     2775.8998043762    0.0474278558        5.0660235386     0.0009   2026-09-08 10:27:46
    56     58    0.0163296077    0.0282039394     2775.8050009251    0.0948034511        4.9047167625     0.0009   2026-09-08 10:27:46
    57     59    0.0408636335    0.0483188263     2775.6624586636    0.1425422615        4.4205919777     0.0009   2026-09-08 10:27:46
    58     60    0.0509385939    0.0589978661     2775.5466815681    0.1157770955        4.2026816891     0.0008   2026-09-08 10:27:46
    59     61    0.0257222676    0.0366629211     2775.5060113134    0.0406702547        3.9197589906     0.0009   2026-09-08 10:27:46
    60     62    0.0081011286    0.0108900399     2775.4990539464    0.0069573670        3.9073862971     0.0009   2026-09-08 10:27:46
    61     63    0.0026566317    0.0038943029     2775.4958990760    0.0031548704        3.8054490317     0.0010   2026-09-08 10:27:46
    62     64    0.0042834302    0.0067298400     2775.4868488001    0.0090502759        3.5511128082     0.0009   2026-09-08 10:27:46
    63     65    0.0051641492    0.0092009624     2775.4660328536    0.0208159465        3.2699909560     0.0008   2026-09-08 10:27:46
    64     66    0.0107093568    0.0168444583     2775.4149649038    0.0510679498        3.0792469842     0.0008   2026-09-08 10:27:46
    65     67    0.0316715686    0.0356744044     2775.3120548412    0.1029100626        2.7465128095     0.0008   2026-09-08 10:27:46
    66     68    0.0617495263    0.0663649997     2775.1605753105    0.1514795307        4.2251192513     0.0008   2026-09-08 10:27:46
    67     69    0.0635847085    0.0722069885     2775.0411545911    0.1194207194        3.9569667271     0.0011   2026-09-08 10:27:46
    68     70    0.0230705601    0.0337498825     2775.0023068031    0.0388477880        2.7202864044     0.0009   2026-09-08 10:27:46
    69     71    0.0038481151    0.0073709245     2774.9973456446    0.0049611585        2.4691289986     0.0008   2026-09-08 10:27:46
    70     72    0.0022848986    0.0028141439     2774.9959936236    0.0013520210        2.4443293330     0.0008   2026-09-08 10:27:46
    71     73    0.0042173870    0.0052365473     2774.9920735703    0.0039200532        2.3545797439     0.0008   2026-09-08 10:27:46
    72     74    0.0042740134    0.0063007254     2774.9834986001    0.0085749702        2.1653205197     0.0008   2026-09-08 10:27:46
    73     75    0.0046147868    0.0084857740     2774.9639959799    0.0195026202        1.9334370553     0.0008   2026-09-08 10:27:46
    74     76    0.0079777956    0.0152655346     2774.9314886971    0.0325072827        1.3732135779     0.0011   2026-09-08 10:27:46
    75     77    0.0218897563    0.0267880625     2774.8979743764    0.0335143207        1.4164537333     0.0009   2026-09-08 10:27:46
    76     78    0.0206052277    0.0230000200     2774.8828967431    0.0150776333        0.9019222490     0.0009   2026-09-08 10:27:46
    77     79    0.0061217178    0.0072985656     2774.8805430169    0.0023537262        0.5577522925     0.0009   2026-09-08 10:27:46
    78     80    0.0005866914    0.0011052362     2774.8803906875    0.0001523294        0.5402580196     0.0009   2026-09-08 10:27:46
    79     81    0.0001678953    0.0003933191     2774.8803331201    0.0000575674        0.5259188733     0.0009   2026-09-08 10:27:46
    80     82    0.0004460804    0.0010485790     2774.8800965681    0.0002365520        0.4753874184     0.0008   2026-09-08 10:27:46
    81     83    0.0006391830    0.0012932004     2774.8796294974    0.0004670706        0.4505442690     0.0008   2026-09-08 10:27:46
    82     84    0.0010668235    0.0020342638     2774.8786250499    0.0010044476        0.4061191874     0.0008   2026-09-08 10:27:46
    83     85    0.0012509935    0.0029104850     2774.8772510118    0.0013740381        0.3014656599     0.0009   2026-09-08 10:27:46
    84     86    0.0017729604    0.0034240926     2774.8762206053    0.0010304064        0.1774022190     0.0008   2026-09-08 10:27:46
    85     87    0.0010429879    0.0020823310     2774.8759263125    0.0002942929        0.0900334449     0.0008   2026-09-08 10:27:46
    86     88    0.0002622889    0.0005798709     2774.8758988513    0.0000274612        0.0565866160     0.0008   2026-09-08 10:27:46
    87     89    0.0000468512    0.0000967717     2774.8758978334    0.0000010179        0.0485526480     0.0008   2026-09-08 10:27:46
    88     90    0.0000143129    0.0000273605     2774.8758974734    0.0000003599        0.0462603875     0.0010   2026-09-08 10:27:46
    89     91    0.0000524819    0.0000879425     2774.8758957163    0.0000017572        0.0431850052     0.0012   2026-09-08 10:27:46
    90     92    0.0000753326    0.0001090866     2774.8758923987    0.0000033175        0.0447623352     0.0012   2026-09-08 10:27:46
    91     93    0.0001291124    0.0001808302     2774.8758852719    0.0000071268        0.0415112453     0.0012   2026-09-08 10:27:46
    92     94    0.0001310299    0.0002408086     2774.8758759436    0.0000093283        0.0284686028     0.0010   2026-09-08 10:27:46
    93     95    0.0001466739    0.0002496015     2774.8758693475    0.0000065961        0.0120742414     0.0009   2026-09-08 10:27:46
    94     96    0.0000678329    0.0001414162     2774.8758676177    0.0000017297        0.0047928408     0.0009   2026-09-08 10:27:46
    95     97    0.0000276232    0.0000416776     2774.8758674721    0.0000001457        0.0017072869     0.0008   2026-09-08 10:27:46

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','3.650259e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.8164***  0.1576   0.0000   
TC/100 EUR                        -0.4311***  0.0904   0.0000   
Bieszczadzki                      -0.0581     0.0816   0.4765   
Karkonoski                         0.1991***  0.0583   0.0006   
Swietokrzyski                      0.2037**   0.0812   0.0121   
Household income (10k PLN)         0.3923***  0.1355   0.0038   
Male                               0.1118     0.0724   0.1227   
Higher education                   0.0345     0.0805   0.6680   
City                               0.0820     0.0744   0.2707   
Winter                             0.8425***  0.0845   0.0000   
Hiking                             2.0945***  0.0790   0.0000   
Skiing                             1.3994***  0.2694   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3670     0.0911            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.3195***  0.4862   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2774.8759
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1670
AIC/n:                             0.9523
BIC/n:                             0.9671
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.3643
median                           0.0000          2.3002
std                              0.7834          1.0883
min                              0.0000          0.0258
max                             20.0000          8.1215
quantile 0.025                   0.0000          0.6384
quantile 0.975                   2.0000          4.6816
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:46
Estimation took 0.18604 seconds (0 hours 0 minutes 0.18604 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.63 -0.064 -0.036 0.039 0.064 0.062 0.009 0.0048 0.0052 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3929.2089831952             NaN     4460.2477592396     0.0001   2026-09-08 10:27:46
     1      3    0.2197951378    0.3577910977     3307.4707118059  621.7382713893     1197.8102522659     0.0025   2026-09-08 10:27:46
     2      4    0.0455999987    0.0827226869     3172.2863278745  135.1843839314      511.2276705908     0.0012   2026-09-08 10:27:46
     3      5    0.0328924094    0.0645040250     3141.9805965018   30.3057313727      353.8367144665     0.0012   2026-09-08 10:27:46
     4      7    0.1548484897    0.2003856614     3074.0844773738   67.8961191280      396.1007988700     0.0025   2026-09-08 10:27:46
     5      8    0.2489252372    0.2998516281     2987.2892943546   86.7951830192      410.2490052120     0.0011   2026-09-08 10:27:46
     6      9    0.4081504647    0.4857912342     2917.9296686859   69.3596256687      173.5473106916     0.0009   2026-09-08 10:27:46
     7     10    0.0712439673    0.0825889618     2912.3095793138    5.6200893721      237.7090136136     0.0013   2026-09-08 10:27:46
     8     11    0.1402609761    0.1626508913     2899.3566703358   12.9529089780      323.4382411947     0.0010   2026-09-08 10:27:46
     9     12    0.1813995091    0.2185911289     2879.0080278635   20.3486424723      366.0255755261     0.0010   2026-09-08 10:27:46
    10     13    0.1957785734    0.2643057131     2852.1779747988   26.8300530647      315.4347358835     0.0013   2026-09-08 10:27:47
    11     14    0.1149233137    0.1729772117     2833.3654409609   18.8125338379      168.4930975100     0.0011   2026-09-08 10:27:47
    12     15    0.0600535424    0.0873701547     2826.6681124724    6.6973284885       72.2758432979     0.0009   2026-09-08 10:27:47
    13     16    0.0424281648    0.0492708258     2825.7131247092    0.9549877632       49.7842872512     0.0012   2026-09-08 10:27:47
    14     17    0.0219046974    0.0260253600     2825.3205086602    0.3926160489       52.0699374271     0.0012   2026-09-08 10:27:47
    15     18    0.0365247849    0.0458676128     2824.3575921179    0.9629165423       67.3609076794     0.0010   2026-09-08 10:27:47
    16     19    0.0425432882    0.0641121073     2822.3745890598    1.9830030581       79.0040967604     0.0011   2026-09-08 10:27:47
    17     20    0.0634155311    0.1086301786     2818.1862919042    4.1882971556       79.0652069656     0.0015   2026-09-08 10:27:47
    18     21    0.1182501610    0.1702354019     2812.1074561239    6.0788357804       65.6247015326     0.0013   2026-09-08 10:27:47
    19     22    0.1242882424    0.1996663535     2807.1942333980    4.9132227259       29.6020057527     0.0011   2026-09-08 10:27:47
    20     23    0.0872269221    0.1172865291     2805.6769084811    1.5173249169       24.1389331750     0.0012   2026-09-08 10:27:47
    21     24    0.0291157496    0.0349572038     2805.4468865959    0.2300218851       22.9424004285     0.0013   2026-09-08 10:27:47
    22     25    0.0115795485    0.0153860366     2805.3173067949    0.1295798010       23.5851035666     0.0013   2026-09-08 10:27:47
    23     26    0.0201458376    0.0287165084     2804.9493058471    0.3680009477       24.2933056259     0.0014   2026-09-08 10:27:47
    24     27    0.0277921413    0.0465676534     2804.1248998652    0.8244059819       24.6759157338     0.0010   2026-09-08 10:27:47
    25     28    0.0567658833    0.0964462300     2802.2045169791    1.9203828861       24.1646323322     0.0009   2026-09-08 10:27:47
    26     29    0.1354878455    0.1847153124     2798.7095325254    3.4949844537       24.9744388002     0.0012   2026-09-08 10:27:47
    27     30    0.2120898532    0.2659687554     2794.4412633154    4.2682692100       28.8641888299     0.0011   2026-09-08 10:27:47
    28     31    0.1560977220    0.1970717629     2791.9018474475    2.5394158678       25.1414074698     0.0014   2026-09-08 10:27:47
    29     32    0.0405553604    0.0605403086     2791.2614567866    0.6403906610       24.3102213364     0.0012   2026-09-08 10:27:47
    30     33    0.0162499652    0.0288858931     2791.1357584942    0.1256982923       22.7086737222     0.0010   2026-09-08 10:27:47
    31     34    0.0139877237    0.0227549204     2791.0015273821    0.1342311121       21.4761543084     0.0010   2026-09-08 10:27:47
    32     35    0.0194193439    0.0388100694     2790.6024851561    0.3990422260       27.3707247914     0.0010   2026-09-08 10:27:47
    33     36    0.0298715250    0.0518671193     2789.6926561852    0.9098289709       37.7943563360     0.0010   2026-09-08 10:27:47
    34     37    0.0486899808    0.1056226851     2787.6055058581    2.0871503272       52.3320450764     0.0010   2026-09-08 10:27:47
    35     38    0.1583270771    0.2376581288     2783.9304725089    3.6750333492       62.8042293997     0.0010   2026-09-08 10:27:47
    36     39    0.2825364386    0.3710480649     2779.8419120460    4.0885604629       53.1519603168     0.0012   2026-09-08 10:27:47
    37     40    0.2178251256    0.2740497919     2777.7834729028    2.0584391432       26.2322858225     0.0013   2026-09-08 10:27:47
    38     41    0.0525835571    0.0748885105     2777.4153851106    0.3680877922       15.5948581446     0.0010   2026-09-08 10:27:47
    39     42    0.0082436916    0.0140825829     2777.3736974645    0.0416876461       13.4790958858     0.0010   2026-09-08 10:27:47
    40     43    0.0067019996    0.0116100759     2777.3254493481    0.0482481164       17.3140385986     0.0009   2026-09-08 10:27:47
    41     44    0.0131784330    0.0208780782     2777.1826842239    0.1427651242       24.2340298873     0.0010   2026-09-08 10:27:47
    42     45    0.0195964867    0.0311068863     2776.8632668928    0.3194173311       33.0033387577     0.0009   2026-09-08 10:27:47
    43     46    0.0277924198    0.0625009701     2776.1789671858    0.6842997070       41.8117309873     0.0009   2026-09-08 10:27:47
    44     47    0.0575040429    0.1187328202     2775.1300067753    1.0489604105       42.0394671329     0.0009   2026-09-08 10:27:47
    45     48    0.0763302020    0.1487585841     2774.2035014769    0.9265052984       26.5555936283     0.0008   2026-09-08 10:27:47
    46     49    0.0406556770    0.0851715434     2773.8606994989    0.3428019780        8.1501843065     0.0009   2026-09-08 10:27:47
    47     50    0.0127582591    0.0201634013     2773.8141141551    0.0465853438        3.8659109743     0.0009   2026-09-08 10:27:47
    48     51    0.0027367074    0.0066723123     2773.8087682151    0.0053459400        3.9761385292     0.0009   2026-09-08 10:27:47
    49     52    0.0026200060    0.0057716026     2773.8023507374    0.0064174777        4.0567140167     0.0010   2026-09-08 10:27:47
    50     53    0.0045204995    0.0100831684     2773.7838195565    0.0185311809        4.6751502840     0.0010   2026-09-08 10:27:47
    51     54    0.0059510683    0.0128758758     2773.7438629206    0.0399566359        5.6926722038     0.0009   2026-09-08 10:27:47
    52     55    0.0084046551    0.0183045425     2773.6665166270    0.0773462936        6.0796054645     0.0009   2026-09-08 10:27:47
    53     56    0.0146140878    0.0293858686     2773.5703163888    0.0962002382        4.8138268228     0.0010   2026-09-08 10:27:47
    54     57    0.0179300267    0.0339856770     2773.5105163423    0.0598000465        3.1331592947     0.0010   2026-09-08 10:27:47
    55     58    0.0081516427    0.0176798657     2773.4964216055    0.0140947368        2.5671344641     0.0010   2026-09-08 10:27:47
    56     59    0.0016645169    0.0039713345     2773.4948165090    0.0016050965        2.5346777391     0.0010   2026-09-08 10:27:47
    57     60    0.0006645511    0.0013984998     2773.4939971771    0.0008193319        2.5246617626     0.0010   2026-09-08 10:27:47
    58     61    0.0015054787    0.0029889327     2773.4912117645    0.0027854126        2.5001800624     0.0009   2026-09-08 10:27:47
    59     62    0.0022603730    0.0044253431     2773.4850151408    0.0061966237        2.4564148580     0.0010   2026-09-08 10:27:47
    60     63    0.0062244384    0.0088650442     2773.4697092321    0.0153059087        2.3920604616     0.0011   2026-09-08 10:27:47
    61     64    0.0141978530    0.0174809157     2773.4394271001    0.0302821320        3.3198267620     0.0011   2026-09-08 10:27:47
    62     65    0.0237057326    0.0290178355     2773.3956316089    0.0437954911        3.5450600781     0.0010   2026-09-08 10:27:47
    63     66    0.0209869993    0.0281971665     2773.3618850329    0.0337465760        2.6724286812     0.0009   2026-09-08 10:27:47
    64     67    0.0055773036    0.0120083686     2773.3509245877    0.0109604452        2.0408811898     0.0010   2026-09-08 10:27:47
    65     68    0.0018810762    0.0035417045     2773.3490302316    0.0018943561        2.1213389926     0.0009   2026-09-08 10:27:47
    66     69    0.0012710275    0.0020204249     2773.3478573364    0.0011728952        2.1056570779     0.0010   2026-09-08 10:27:47
    67     70    0.0019964597    0.0035794212     2773.3443348127    0.0035225237        2.0284032918     0.0010   2026-09-08 10:27:47
    68     71    0.0030089381    0.0047045376     2773.3363445221    0.0079902906        1.9817587716     0.0010   2026-09-08 10:27:47
    69     72    0.0056294797    0.0098016186     2773.3175048541    0.0188396680        2.7928201334     0.0009   2026-09-08 10:27:47
    70     73    0.0195312228    0.0230555242     2773.2828283158    0.0346765383        3.3559065431     0.0010   2026-09-08 10:27:47
    71     74    0.0364303860    0.0395151845     2773.2402237581    0.0426045577        2.8405299768     0.0010   2026-09-08 10:27:47
    72     75    0.0315085993    0.0338360607     2773.2152357452    0.0249880129        1.2785594427     0.0010   2026-09-08 10:27:47
    73     76    0.0082435966    0.0103228700     2773.2096858250    0.0055499203        1.1495781331     0.0011   2026-09-08 10:27:47
    74     77    0.0012177785    0.0022870766     2773.2091523814    0.0005334436        1.1550405120     0.0012   2026-09-08 10:27:47
    75     78    0.0008226703    0.0010830064     2773.2089426033    0.0002097780        1.1693354813     0.0011   2026-09-08 10:27:47
    76     79    0.0018080350    0.0024836423     2773.2081767872    0.0007658161        1.1847245706     0.0010   2026-09-08 10:27:47
    77     80    0.0016851801    0.0029069719     2773.2065814805    0.0015953067        1.1653553801     0.0009   2026-09-08 10:27:47
    78     81    0.0021232544    0.0041193967     2773.2029776503    0.0036038302        1.0410229678     0.0009   2026-09-08 10:27:47
    79     82    0.0036445816    0.0069628921     2773.1973325432    0.0056451072        0.7296435336     0.0010   2026-09-08 10:27:47
    80     83    0.0086989085    0.0110239890     2773.1920573335    0.0052752097        0.4498698912     0.0010   2026-09-08 10:27:47
    81     84    0.0072821585    0.0085430370     2773.1900032204    0.0020541131        0.2043524244     0.0010   2026-09-08 10:27:47
    82     85    0.0019008428    0.0025497982     2773.1897316261    0.0002715943        0.1517991492     0.0009   2026-09-08 10:27:47
    83     86    0.0002027515    0.0003912137     2773.1897198560    0.0000117701        0.1281902619     0.0009   2026-09-08 10:27:47
    84     87    0.0000550723    0.0000855147     2773.1897183882    0.0000014678        0.1236393934     0.0009   2026-09-08 10:27:47
    85     88    0.0001491646    0.0002239887     2773.1897126619    0.0000057263        0.1101864906     0.0011   2026-09-08 10:27:47
    86     89    0.0001804771    0.0002801428     2773.1897012221    0.0000114398        0.0895485460     0.0013   2026-09-08 10:27:47
    87     90    0.0003096589    0.0004138410     2773.1896757114    0.0000255107        0.0745793620     0.0014   2026-09-08 10:27:47
    88     91    0.0003659613    0.0004870183     2773.1896381786    0.0000375328        0.0602382900     0.0012   2026-09-08 10:27:47
    89     92    0.0003199893    0.0005790297     2773.1896063954    0.0000317832        0.0286739117     0.0009   2026-09-08 10:27:47
    90     93    0.0002838530    0.0004658500     2773.1895957050    0.0000106904        0.0139575480     0.0009   2026-09-08 10:27:47
    91     94    0.0001128095    0.0001695747     2773.1895945087    0.0000011963        0.0111484358     0.0008   2026-09-08 10:27:47
    92     95    0.0000202889    0.0000260199     2773.1895944640    0.0000000447        0.0103298314     0.0009   2026-09-08 10:27:47
    93     96    0.0000026824    0.0000040746     2773.1895944568    0.0000000072        0.0101387003     0.0011   2026-09-08 10:27:47
    94     97    0.0000072750    0.0000126960     2773.1895944227    0.0000000341        0.0093064842     0.0011   2026-09-08 10:27:47
    95     98    0.0000090821    0.0000152050     2773.1895943598    0.0000000629        0.0078595456     0.0009   2026-09-08 10:27:47
    96     99    0.0000190443    0.0000238610     2773.1895942291    0.0000001307        0.0054121285     0.0012   2026-09-08 10:27:47
    97    100    0.0000239112    0.0000298251     2773.1895940704    0.0000001587        0.0041688831     0.0011   2026-09-08 10:27:47

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.344657e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.6989***  0.2120   0.0000   
TC/100 EUR                        -0.4406***  0.1010   0.0000   
Bieszczadzki                      -0.0955     0.0918   0.2982   
Karkonoski                         0.2063***  0.0679   0.0024   
Swietokrzyski                      0.2255***  0.0873   0.0098   
Household income (10k PLN)         0.2616**   0.1022   0.0105   
Male                               0.1158     0.0722   0.1088   
Higher education                   0.0246     0.0803   0.7590   
City                               0.0910     0.0744   0.2210   
Winter                             0.8413***  0.0842   0.0000   
Hiking                             2.0856***  0.0789   0.0000   
Skiing                             1.3969***  0.2672   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3517     0.0921            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.2696***  0.5203   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2773.1896
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1675
AIC/n:                             0.9517
BIC/n:                             0.9666
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.2499
median                           0.0000          2.2582
std                              0.7834          0.9431
min                              0.0000          0.0340
max                             20.0000          4.5242
quantile 0.025                   0.0000          0.6513
quantile 0.975                   2.0000          3.9440
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:47
Estimation took 0.19919 seconds (0 hours 0 minutes 0.19919 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.66 -0.084 -0.025 0.052 0.072 0.063 0.009 0.0051 0.0055 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.9287468675             NaN     4167.9340449010     0.0000   2026-09-08 10:27:47
     1      3    0.2208334704    0.3622538054     3309.4781309195  619.4506159480     1077.5197488517     0.0019   2026-09-08 10:27:47
     2      4    0.0443489522    0.0812628552     3189.2597737512  120.2183571683      470.2423127254     0.0009   2026-09-08 10:27:47
     3      5    0.0318731508    0.0637490903     3160.7357484859   28.5240252653      349.9931360454     0.0009   2026-09-08 10:27:47
     4      7    0.1848852151    0.2271873106     3070.8057133751   89.9300351108      330.3321698456     0.0037   2026-09-08 10:27:47
     5      8    0.5199235916    0.6223572938     2940.4020063844  130.4037069907      133.8190249387     0.0012   2026-09-08 10:27:47
     6      9    0.1831910839    0.2166683727     2925.9724677683   14.4295386161      213.9009910899     0.0013   2026-09-08 10:27:47
     7     10    0.1006039438    0.1180313370     2919.3640104241    6.6084573442      229.4607605903     0.0014   2026-09-08 10:27:47
     8     11    0.1643525086    0.1946184498     2906.1791378576   13.1848725665      219.8232550892     0.0010   2026-09-08 10:27:47
     9     12    0.2059741025    0.2556684336     2885.2500554966   20.9290823610      170.7746081054     0.0011   2026-09-08 10:27:47
    10     13    0.1814905923    0.2647337269     2860.1986843431   25.0513711535       85.8078094798     0.0014   2026-09-08 10:27:47
    11     14    0.1090524982    0.1604763536     2844.3190790957   15.8796052474       67.7349601142     0.0010   2026-09-08 10:27:47
    12     15    0.0796710061    0.1114009010     2839.7974754226    4.5216036731       58.0066506500     0.0011   2026-09-08 10:27:47
    13     16    0.0612977931    0.0717446209     2838.8822883099    0.9151871127       56.1534088329     0.0012   2026-09-08 10:27:47
    14     17    0.0351856582    0.0427606177     2838.3635299374    0.5187583726       57.4332669339     0.0010   2026-09-08 10:27:47
    15     18    0.0362669355    0.0460438553     2837.4338827676    0.9296471698       60.6973205330     0.0009   2026-09-08 10:27:47
    16     19    0.0493084923    0.0732708932     2835.0959122240    2.3379705436       66.8261888964     0.0010   2026-09-08 10:27:47
    17     20    0.0765914984    0.1177330660     2830.3007747906    4.7951374334       72.9205464491     0.0012   2026-09-08 10:27:47
    18     21    0.1667966338    0.2073817759     2822.5143154948    7.7864592958       80.1899385957     0.0013   2026-09-08 10:27:47
    19     22    0.2018836304    0.2614896127     2815.3377518700    7.1765636249       69.6334002396     0.0010   2026-09-08 10:27:47
    20     23    0.1026175292    0.1648073393     2812.6489019504    2.6888499195       41.6336008951     0.0010   2026-09-08 10:27:47
    21     24    0.0359158669    0.0468785347     2812.2017386397    0.4471633107       29.0327681497     0.0012   2026-09-08 10:27:47
    22     25    0.0137285211    0.0187399744     2811.9591701779    0.2425684618       30.6871510336     0.0013   2026-09-08 10:27:47
    23     26    0.0215410083    0.0332077190     2811.3122280982    0.6469420797       32.9516323764     0.0013   2026-09-08 10:27:47
    24     27    0.0296751527    0.0578895714     2809.8771580528    1.4350700453       61.4686349698     0.0011   2026-09-08 10:27:47
    25     28    0.0897007983    0.1293065226     2806.6072740051    3.2698840477      101.9064552257     0.0010   2026-09-08 10:27:47
    26     29    0.1961848703    0.2523775845     2800.8826043300    5.7246696751      133.7914653973     0.0009   2026-09-08 10:27:47
    27     30    0.2788681366    0.3447253911     2794.3726074099    6.5099969201      120.9396001481     0.0010   2026-09-08 10:27:47
    28     31    0.1761750965    0.2236186096     2790.7965169581    3.5760904518       60.3143662028     0.0010   2026-09-08 10:27:47
    29     32    0.0377931244    0.0561874471     2789.9504297919    0.8460871662       26.9179875341     0.0010   2026-09-08 10:27:47
    30     33    0.0260428058    0.0357604129     2789.7920944651    0.1583353268       26.7558608243     0.0010   2026-09-08 10:27:47
    31     34    0.0225610361    0.0303005153     2789.6050196805    0.1870747846       28.7457507165     0.0010   2026-09-08 10:27:47
    32     35    0.0341648066    0.0513067902     2789.0521843466    0.5528353338       37.6064990814     0.0010   2026-09-08 10:27:47
    33     36    0.0360841024    0.0648463514     2787.8224711462    1.2297132005       48.5742006522     0.0009   2026-09-08 10:27:47
    34     37    0.0559865718    0.1171074073     2785.2511717428    2.5712994034       58.4133429024     0.0011   2026-09-08 10:27:47
    35     38    0.1491211742    0.2367689094     2781.5786285169    3.6725432259       54.6819933067     0.0009   2026-09-08 10:27:47
    36     39    0.2271522381    0.2950403967     2778.7878959315    2.7907325854       32.4537425553     0.0011   2026-09-08 10:27:47
    37     40    0.1270993675    0.1553545778     2777.9636809586    0.8242149729       12.8013005899     0.0012   2026-09-08 10:27:47
    38     41    0.0204040690    0.0319398517     2777.8738886657    0.0897922929        9.2553175915     0.0009   2026-09-08 10:27:47
    39     42    0.0045337050    0.0071777066     2777.8522696538    0.0216190119       10.5184905913     0.0009   2026-09-08 10:27:47
    40     43    0.0097363888    0.0146912939     2777.7842677057    0.0680019481       12.7343791562     0.0008   2026-09-08 10:27:47
    41     44    0.0138069299    0.0204060102     2777.6378025556    0.1464651501       15.2921273180     0.0009   2026-09-08 10:27:47
    42     45    0.0216958482    0.0385468590     2777.2924531133    0.3453494423       18.0392469389     0.0010   2026-09-08 10:27:47
    43     46    0.0336748170    0.0715813677     2776.6844646632    0.6079884501       18.3597990583     0.0009   2026-09-08 10:27:47
    44     47    0.0543617325    0.1053624144     2775.9836831163    0.7007815470       13.5620379848     0.0012   2026-09-08 10:27:47
    45     48    0.0436681169    0.0824420082     2775.6077708395    0.3759122768        5.7176082180     0.0011   2026-09-08 10:27:47
    46     49    0.0155907848    0.0282687110     2775.5305945486    0.0771762909        4.2028132990     0.0011   2026-09-08 10:27:47
    47     50    0.0048578582    0.0079717839     2775.5217390053    0.0088555433        4.2733725590     0.0012   2026-09-08 10:27:47
    48     51    0.0022494947    0.0044608826     2775.5158068923    0.0059321129        4.3181292698     0.0010   2026-09-08 10:27:47
    49     52    0.0048201448    0.0090167768     2775.4964636320    0.0193432603        4.4025745568     0.0009   2026-09-08 10:27:47
    50     53    0.0068052556    0.0117900769     2775.4551305684    0.0413330636        4.4838407619     0.0010   2026-09-08 10:27:47
    51     54    0.0096238209    0.0198379819     2775.3663274916    0.0888030768        4.5080712715     0.0013   2026-09-08 10:27:47
    52     55    0.0219849716    0.0343848154     2775.2358462684    0.1304812232        4.4819381232     0.0009   2026-09-08 10:27:47
    53     56    0.0296005530    0.0437385433     2775.1277186099    0.1081276585        3.9692206607     0.0008   2026-09-08 10:27:47
    54     57    0.0157388231    0.0266751545     2775.0909165412    0.0368020687        3.6903069800     0.0011   2026-09-08 10:27:47
    55     58    0.0039257882    0.0072952982     2775.0853724439    0.0055440974        3.6183587677     0.0010   2026-09-08 10:27:47
    56     59    0.0013913473    0.0022832828     2775.0833509420    0.0020215019        3.6038824980     0.0010   2026-09-08 10:27:47
    57     60    0.0025864685    0.0040936363     2775.0776084572    0.0057424848        3.5740356576     0.0009   2026-09-08 10:27:47
    58     61    0.0038929220    0.0061562832     2775.0643377390    0.0132707181        3.5118294783     0.0009   2026-09-08 10:27:47
    59     62    0.0086033068    0.0126077608     2775.0311076508    0.0332300882        3.3619165351     0.0009   2026-09-08 10:27:47
    60     63    0.0233489888    0.0274118518     2774.9608021810    0.0703054698        3.0458174269     0.0008   2026-09-08 10:27:47
    61     64    0.0467237351    0.0521577400     2774.8453513172    0.1154508638        4.6540629915     0.0009   2026-09-08 10:27:47
    62     65    0.0546322723    0.0621312024     2774.7346201330    0.1107311842        5.0508730413     0.0009   2026-09-08 10:27:47
    63     66    0.0252835165    0.0330694577     2774.6874015213    0.0472186117        3.8306116160     0.0008   2026-09-08 10:27:47
    64     67    0.0050395756    0.0076509048     2774.6789442824    0.0084572389        3.5005281328     0.0009   2026-09-08 10:27:47
    65     68    0.0026648075    0.0036454694     2774.6764214452    0.0025228372        3.5081299108     0.0009   2026-09-08 10:27:47
    66     69    0.0037732640    0.0054822118     2774.6704553852    0.0059660600        3.4405699929     0.0009   2026-09-08 10:27:47
    67     70    0.0044366795    0.0067333854     2774.6565990874    0.0138562978        3.2278366633     0.0009   2026-09-08 10:27:47
    68     71    0.0069827592    0.0105416936     2774.6249247579    0.0316743296        2.6698105128     0.0009   2026-09-08 10:27:47
    69     72    0.0199373585    0.0248404443     2774.5684640507    0.0564607072        1.7014738910     0.0009   2026-09-08 10:27:47
    70     73    0.0411034721    0.0447703413     2774.5040774108    0.0643866400        2.0686118238     0.0009   2026-09-08 10:27:47
    71     74    0.0362829083    0.0389285714     2774.4703495954    0.0337278154        1.2810283149     0.0009   2026-09-08 10:27:48
    72     75    0.0099344580    0.0120877899     2774.4639269662    0.0064226292        1.0502021361     0.0008   2026-09-08 10:27:48
    73     76    0.0013403152    0.0020456621     2774.4634579596    0.0004690067        1.0522944853     0.0008   2026-09-08 10:27:48
    74     77    0.0005752255    0.0007548173     2774.4633379761    0.0001199835        1.0422189686     0.0009   2026-09-08 10:27:48
    75     78    0.0014108436    0.0019021823     2774.4628738759    0.0004641002        0.9958715026     0.0008   2026-09-08 10:27:48
    76     79    0.0014147040    0.0022692468     2774.4619414810    0.0009323949        0.8945020408     0.0009   2026-09-08 10:27:48
    77     80    0.0019740012    0.0032926960     2774.4598834793    0.0020580017        0.6767465048     0.0008   2026-09-08 10:27:48
    78     81    0.0032386587    0.0047390883     2774.4568954429    0.0029880364        0.4753825153     0.0009   2026-09-08 10:27:48
    79     82    0.0046126744    0.0065029875     2774.4544263065    0.0024691365        0.3067984695     0.0010   2026-09-08 10:27:48
    80     83    0.0038302758    0.0046363414     2774.4536142464    0.0008120601        0.1617305429     0.0009   2026-09-08 10:27:48
    81     84    0.0009894414    0.0013676341     2774.4535245823    0.0000896641        0.1214358745     0.0008   2026-09-08 10:27:48
    82     85    0.0001441874    0.0002095266     2774.4535200620    0.0000045203        0.1055615243     0.0008   2026-09-08 10:27:48
    83     86    0.0000637176    0.0000833692     2774.4535176485    0.0000024135        0.1081004419     0.0008   2026-09-08 10:27:48
    84     87    0.0001821928    0.0002233500     2774.4535077808    0.0000098676        0.1125247562     0.0008   2026-09-08 10:27:48
    85     88    0.0002476357    0.0002913292     2774.4534882962    0.0000194847        0.1124266736     0.0008   2026-09-08 10:27:48
    86     89    0.0003618887    0.0004727032     2774.4534472991    0.0000409970        0.0986749170     0.0008   2026-09-08 10:27:48
    87     90    0.0003718721    0.0006311452     2774.4533932832    0.0000540159        0.0623235583     0.0009   2026-09-08 10:27:48
    88     91    0.0004832171    0.0006478120     2774.4533553045    0.0000379787        0.0346387520     0.0011   2026-09-08 10:27:48
    89     92    0.0002261231    0.0003684872     2774.4533453189    0.0000099856        0.0149313487     0.0012   2026-09-08 10:27:48
    90     93    0.0000924430    0.0001093299     2774.4533444696    0.0000008493        0.0133353196     0.0011   2026-09-08 10:27:48
    91     94    0.0000117331    0.0000183608     2774.4533444385    0.0000000311        0.0129649316     0.0012   2026-09-08 10:27:48
    92     95    0.0000033630    0.0000061140     2774.4533444241    0.0000000144        0.0127526973     0.0011   2026-09-08 10:27:48
    93     96    0.0000097161    0.0000179501     2774.4533443593    0.0000000648        0.0117598316     0.0012   2026-09-08 10:27:48
    94     97    0.0000118547    0.0000215568     2774.4533442406    0.0000001187        0.0098578696     0.0011   2026-09-08 10:27:48
    95     98    0.0000252797    0.0000322040     2774.4533440132    0.0000002274        0.0059794312     0.0012   2026-09-08 10:27:48
    96     99    0.0000304004    0.0000387026     2774.4533437716    0.0000002416        0.0033927019     0.0011   2026-09-08 10:27:48

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','8.138056e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.8943***  0.1847   0.0000   
TC/100 EUR                        -0.5356***  0.1000   0.0000   
Bieszczadzki                      -0.0312     0.0921   0.7350   
Karkonoski                         0.2751***  0.0638   0.0000   
Swietokrzyski                      0.2608***  0.0902   0.0038   
Household income (10k PLN)         0.2647***  0.1021   0.0095   
Male                               0.1180     0.0722   0.1021   
Higher education                   0.0261     0.0802   0.7446   
City                               0.0935     0.0743   0.2080   
Winter                             0.8490***  0.0842   0.0000   
Hiking                             2.0904***  0.0789   0.0000   
Skiing                             1.4155***  0.2670   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3490     0.0921            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.8671***  0.3484   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2774.4533
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1672
AIC/n:                             0.9522
BIC/n:                             0.9670
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1226
median                           0.0000          2.1322
std                              0.7834          0.9278
min                              0.0000          0.0266
max                             20.0000          5.0512
quantile 0.025                   0.0000          0.5807
quantile 0.975                   2.0000          3.9862
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:48
Estimation took 0.19474 seconds (0 hours 0 minutes 0.19474 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.65 -0.079 -0.03 0.048 0.071 0.063 0.0088 0.0052 0.0055 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.8694724387             NaN     4158.2888012415     0.0001   2026-09-08 10:27:48
     1      3    0.2215259960    0.3634500632     3305.3290552676  623.5404171710     1063.8055580762     0.0026   2026-09-08 10:27:48
     2      4    0.0440989814    0.0810731973     3186.3639477108  118.9651075568      471.3939069199     0.0011   2026-09-08 10:27:48
     3      5    0.0320067202    0.0640624684     3157.7142342856   28.6497134252      351.2170170569     0.0012   2026-09-08 10:27:48
     4      7    0.1890481733    0.2316559063     3065.2996196409   92.4146146447      325.2442516400     0.0022   2026-09-08 10:27:48
     5      8    0.5358321970    0.6411299637     2934.2619124559  131.0377071850      170.3112178502     0.0011   2026-09-08 10:27:48
     6      9    0.1661383052    0.1965900380     2921.7129038958   12.5490085600      224.8070201328     0.0011   2026-09-08 10:27:48
     7     10    0.1085828810    0.1275891703     2914.5834326744    7.1294712214      225.3683577902     0.0011   2026-09-08 10:27:48
     8     11    0.1586820498    0.1882030523     2901.8189591935   12.7644734809      195.3891709486     0.0011   2026-09-08 10:27:48
     9     12    0.2032591362    0.2527201299     2881.0718937684   20.7470654251      154.0705816265     0.0013   2026-09-08 10:27:48
    10     13    0.1803174128    0.2631213729     2856.1742073781   24.8976863904      125.0758146530     0.0011   2026-09-08 10:27:48
    11     14    0.1100515393    0.1636967725     2840.1599120653   16.0142953128       79.8142494659     0.0009   2026-09-08 10:27:48
    12     15    0.0777988749    0.1098987221     2835.6437532439    4.5161588214       52.4897235347     0.0010   2026-09-08 10:27:48
    13     16    0.0629053396    0.0738675063     2834.6881653762    0.9555878678       54.9767341276     0.0010   2026-09-08 10:27:48
    14     17    0.0344097510    0.0422197682     2834.1881697499    0.4999956262       57.9685777990     0.0010   2026-09-08 10:27:48
    15     18    0.0323483696    0.0417823504     2833.3455084247    0.8426613252       62.3124600874     0.0009   2026-09-08 10:27:48
    16     19    0.0454726963    0.0695234981     2831.1321010670    2.2134073577       69.7949152427     0.0011   2026-09-08 10:27:48
    17     20    0.0721760141    0.1123181347     2826.6137449810    4.5183560860       76.6342213784     0.0010   2026-09-08 10:27:48
    18     21    0.1597435094    0.2009709751     2819.1869302273    7.4268147538       89.6991321373     0.0010   2026-09-08 10:27:48
    19     22    0.1950250238    0.2529238037     2812.3102991014    6.8766311259       73.5241006518     0.0012   2026-09-08 10:27:48
    20     23    0.1003437912    0.1589680006     2809.7080669906    2.6022321108       38.7026507075     0.0014   2026-09-08 10:27:48
    21     24    0.0337707984    0.0449094300     2809.2750827382    0.4329842524       28.2345997776     0.0014   2026-09-08 10:27:48
    22     25    0.0123393345    0.0175888515     2809.0498567018    0.2252260364       29.7179309532     0.0011   2026-09-08 10:27:48
    23     26    0.0189717069    0.0309112651     2808.4565164681    0.5933402337       31.5647271161     0.0010   2026-09-08 10:27:48
    24     27    0.0264631029    0.0539191484     2807.1374310326    1.3190854355       58.1594251204     0.0010   2026-09-08 10:27:48
    25     28    0.0826462777    0.1210280277     2804.1277032113    3.0097278212       95.6942192517     0.0010   2026-09-08 10:27:48
    26     29    0.1837604582    0.2380668567     2798.8450861175    5.2826170938      125.0706403636     0.0010   2026-09-08 10:27:48
    27     30    0.2641927156    0.3278094221     2792.8147937725    6.0302923450      112.5434104378     0.0010   2026-09-08 10:27:48
    28     31    0.1694677846    0.2150494859     2789.5042381172    3.3105556553       55.9608001923     0.0010   2026-09-08 10:27:48
    29     32    0.0330719994    0.0530853447     2788.7359779228    0.7682601944       25.9158688259     0.0010   2026-09-08 10:27:48
    30     33    0.0225967216    0.0320246291     2788.5897143497    0.1462635731       25.6265022019     0.0010   2026-09-08 10:27:48
    31     34    0.0206707390    0.0287014828     2788.4067341553    0.1829801945       27.3800582842     0.0010   2026-09-08 10:27:48
    32     35    0.0298065000    0.0475019352     2787.8784835910    0.5282505642       35.1955796854     0.0010   2026-09-08 10:27:48
    33     36    0.0349831997    0.0621189312     2786.6932698561    1.1852137350       44.8191833457     0.0011   2026-09-08 10:27:48
    34     37    0.0539812423    0.1171913032     2784.2202309869    2.4730388692       53.2111740127     0.0010   2026-09-08 10:27:48
    35     38    0.1503386362    0.2361196999     2780.6701968135    3.5500341733       51.8462116259     0.0009   2026-09-08 10:27:48
    36     39    0.2212927172    0.2893028047     2777.9532590312    2.7169377823       31.5234967316     0.0010   2026-09-08 10:27:48
    37     40    0.1209459676    0.1497521071     2777.1396447513    0.8136142799       11.9758233203     0.0009   2026-09-08 10:27:48
    38     41    0.0180881233    0.0304790609     2777.0492073788    0.0904373724        9.3809060383     0.0010   2026-09-08 10:27:48
    39     42    0.0045330130    0.0072966776     2777.0269742083    0.0222331706       10.3929706057     0.0010   2026-09-08 10:27:48
    40     43    0.0097418678    0.0149669846     2776.9569902989    0.0699839093       12.1022009387     0.0009   2026-09-08 10:27:48
    41     44    0.0138593552    0.0206296544     2776.8060653842    0.1509249148       14.0040163520     0.0010   2026-09-08 10:27:48
    42     45    0.0218777941    0.0389199530     2776.4498003061    0.3562650781       15.8844050221     0.0011   2026-09-08 10:27:48
    43     46    0.0347182820    0.0732952690     2775.8205580012    0.6292423049       16.0361697585     0.0010   2026-09-08 10:27:48
    44     47    0.0554488324    0.1097136843     2775.0911096401    0.7294483611       13.2085846383     0.0010   2026-09-08 10:27:48
    45     48    0.0455611385    0.0870804231     2774.6964868861    0.3946227540        6.0057554319     0.0010   2026-09-08 10:27:48
    46     49    0.0157203385    0.0297728384     2774.6146411381    0.0818457480        4.2219279872     0.0010   2026-09-08 10:27:48
    47     50    0.0049868868    0.0081754840     2774.6051806866    0.0094604515        4.2950593092     0.0009   2026-09-08 10:27:48
    48     51    0.0023138363    0.0045890253     2774.5988712238    0.0063094628        4.3413877644     0.0010   2026-09-08 10:27:48
    49     52    0.0049521538    0.0092640110     2774.5783275400    0.0205436838        4.4289582029     0.0010   2026-09-08 10:27:48
    50     53    0.0069748164    0.0120927586     2774.5344852275    0.0438423125        4.5138038960     0.0010   2026-09-08 10:27:48
    51     54    0.0098056815    0.0204001803     2774.4405700859    0.0939151416        4.5410568033     0.0010   2026-09-08 10:27:48
    52     55    0.0225411416    0.0354576369     2774.3034494084    0.1371206775        4.3723273682     0.0010   2026-09-08 10:27:48
    53     56    0.0301254240    0.0448535370     2774.1910376779    0.1124117305        3.9968153297     0.0010   2026-09-08 10:27:48
    54     57    0.0158227446    0.0270198955     2774.1533399968    0.0376976811        3.7158082227     0.0010   2026-09-08 10:27:48
    55     58    0.0039326521    0.0072735139     2774.1477518327    0.0055881641        3.6437940947     0.0010   2026-09-08 10:27:48
    56     59    0.0013817403    0.0022778071     2774.1457079811    0.0020438516        3.6291371026     0.0009   2026-09-08 10:27:48
    57     60    0.0025963818    0.0041359882     2774.1398376031    0.0058703780        3.5984902842     0.0009   2026-09-08 10:27:48
    58     61    0.0038990645    0.0062157494     2774.1263110803    0.0135265228        3.5350802695     0.0009   2026-09-08 10:27:48
    59     62    0.0086733613    0.0127469711     2774.0924685408    0.0338425395        3.3830148224     0.0009   2026-09-08 10:27:48
    60     63    0.0234522368    0.0276098801     2774.0212048720    0.0712636688        3.0648212025     0.0009   2026-09-08 10:27:48
    61     64    0.0465846886    0.0521198203     2773.9052310017    0.1159738703        4.7541691767     0.0010   2026-09-08 10:27:48
    62     65    0.0536812706    0.0611986379     2773.7957551072    0.1094758944        5.0980563602     0.0009   2026-09-08 10:27:48
    63     66    0.0242028281    0.0319178519     2773.7500181850    0.0457369223        3.8461563371     0.0010   2026-09-08 10:27:48
    64     67    0.0048914179    0.0074478091     2773.7418699522    0.0081482328        3.5531982575     0.0010   2026-09-08 10:27:48
    65     68    0.0025786753    0.0035914177     2773.7392615238    0.0026084284        3.5618309369     0.0010   2026-09-08 10:27:48
    66     69    0.0037115384    0.0055655858     2773.7328336493    0.0064278745        3.4941345080     0.0010   2026-09-08 10:27:48
    67     70    0.0045702890    0.0067798968     2773.7180590940    0.0147745553        3.2789290433     0.0010   2026-09-08 10:27:48
    68     71    0.0071939328    0.0111295433     2773.6843231132    0.0337359808        2.7099178051     0.0009   2026-09-08 10:27:48
    69     72    0.0215876270    0.0263998790     2773.6249185055    0.0594046077        1.6849893968     0.0010   2026-09-08 10:27:48
    70     73    0.0426072038    0.0463041485     2773.5585218605    0.0663966450        2.1321052430     0.0009   2026-09-08 10:27:48
    71     74    0.0359745556    0.0387047051     2773.5248129757    0.0337088848        1.2805567067     0.0009   2026-09-08 10:27:48
    72     75    0.0091412278    0.0114017493     2773.5186238017    0.0061891740        1.0879667515     0.0009   2026-09-08 10:27:48
    73     76    0.0012819507    0.0020385126     2773.5181890153    0.0004347864        1.0911884569     0.0010   2026-09-08 10:27:48
    74     77    0.0005816950    0.0007473692     2773.5180767799    0.0001122354        1.0815687178     0.0010   2026-09-08 10:27:48
    75     78    0.0014487646    0.0019158728     2773.5176341702    0.0004426098        1.0345664243     0.0011   2026-09-08 10:27:48
    76     79    0.0014461158    0.0022591875     2773.5167530751    0.0008810950        0.9299477259     0.0011   2026-09-08 10:27:48
    77     80    0.0020534592    0.0032207598     2773.5148264659    0.0019266092        0.6790666548     0.0013   2026-09-08 10:27:48
    78     81    0.0033306220    0.0045416028     2773.5120985060    0.0027279600        0.4126599685     0.0010   2026-09-08 10:27:48
    79     82    0.0045132860    0.0061891506     2773.5099336174    0.0021648886        0.2789576328     0.0009   2026-09-08 10:27:48
    80     83    0.0036202250    0.0043212578     2773.5092591295    0.0006744880        0.1418557094     0.0011   2026-09-08 10:27:48
    81     84    0.0008950168    0.0012306141     2773.5091888997    0.0000702298        0.1108502733     0.0008   2026-09-08 10:27:48
    82     85    0.0001329332    0.0001804600     2773.5091852221    0.0000036776        0.1156833232     0.0008   2026-09-08 10:27:48
    83     86    0.0000687868    0.0000853087     2773.5091827683    0.0000024539        0.1177042285     0.0009   2026-09-08 10:27:48
    84     87    0.0001787663    0.0002117333     2773.5091734220    0.0000093463        0.1201891519     0.0011   2026-09-08 10:27:48
    85     88    0.0002406748    0.0002838321     2773.5091545658    0.0000188562        0.1174369245     0.0012   2026-09-08 10:27:48
    86     89    0.0003311099    0.0004617247     2773.5091152318    0.0000393340        0.0997150046     0.0012   2026-09-08 10:27:48
    87     90    0.0004112377    0.0006261711     2773.5090631420    0.0000520898        0.0598723053     0.0011   2026-09-08 10:27:48
    88     91    0.0004877579    0.0006387033     2773.5090264879    0.0000366541        0.0365888268     0.0009   2026-09-08 10:27:48
    89     92    0.0002232872    0.0003578893     2773.5090168071    0.0000096808        0.0154200841     0.0009   2026-09-08 10:27:48
    90     93    0.0000907196    0.0001060701     2773.5090159802    0.0000008269        0.0140684089     0.0008   2026-09-08 10:27:48
    91     94    0.0000104968    0.0000183309     2773.5090159480    0.0000000322        0.0137181207     0.0008   2026-09-08 10:27:48
    92     95    0.0000041725    0.0000068478     2773.5090159310    0.0000000171        0.0134867861     0.0008   2026-09-08 10:27:48
    93     96    0.0000112581    0.0000189911     2773.5090158583    0.0000000726        0.0124543960     0.0009   2026-09-08 10:27:48
    94     97    0.0000125057    0.0000230894     2773.5090157234    0.0000001349        0.0104419453     0.0008   2026-09-08 10:27:48
    95     98    0.0000266811    0.0000342006     2773.5090154664    0.0000002570        0.0063538174     0.0009   2026-09-08 10:27:48
    96     99    0.0000323654    0.0000413419     2773.5090151928    0.0000002736        0.0032423469     0.0012   2026-09-08 10:27:48

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','7.795436e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.8225***  0.1848   0.0000   
TC/100 EUR                        -0.5096***  0.1004   0.0000   
Bieszczadzki                      -0.0580     0.0925   0.5304   
Karkonoski                         0.2527***  0.0642   0.0001   
Swietokrzyski                      0.2530***  0.0907   0.0053   
Household income (10k PLN)         0.2685***  0.1022   0.0086   
Male                               0.1165     0.0722   0.1066   
Higher education                   0.0253     0.0803   0.7522   
City                               0.0935     0.0743   0.2079   
Winter                             0.8491***  0.0842   0.0000   
Hiking                             2.0907***  0.0789   0.0000   
Skiing                             1.4140***  0.2670   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3491     0.0920            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.9625***  0.3865   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2773.5090
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1674
AIC/n:                             0.9518
BIC/n:                             0.9667
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1162
median                           0.0000          2.1210
std                              0.7834          0.9249
min                              0.0000          0.0269
max                             20.0000          5.1370
quantile 0.025                   0.0000          0.5722
quantile 0.975                   2.0000          3.9713
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:49
Estimation took 0.19603 seconds (0 hours 0 minutes 0.19603 seconds).

====================================================
PCA: principal components of substitutes
====================================================
TC_fuel_mat: 3 principal components, 98.33% of the variance
TC_33_wage_mat: 3 principal components, 98.32% of the variance
TC_100_wage_mat: 3 principal components, 98.34% of the variance
TC_MNL_mat: 3 principal components, 98.35% of the variance
TC_iMXL_mat: 3 principal components, 98.31% of the variance
TC_iMXL_d_mat: 3 principal components, 98.31% of the variance
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.54 -0.085 0.0077 0.028 0.099 0.062 0.0092 0.0048 0.006 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3927.9516065181             NaN     2683.3579935134     0.0000   2026-09-08 10:27:49
     1      3    0.4036839625    0.5099159849     3185.0415760204  742.9100304977      396.1512923985     0.0020   2026-09-08 10:27:49
     2      5    0.5550107204    0.6768280410     2984.5202305671  200.5213454533      504.7285907558     0.0020   2026-09-08 10:27:49
     3      6    0.3471500864    0.4446740874     2887.5406975847   96.9795329824      407.8711297431     0.0008   2026-09-08 10:27:49
     4      7    0.3888190820    0.5170535475     2816.2024777768   71.3382198079      143.0214674291     0.0008   2026-09-08 10:27:49
     5      8    0.1699139042    0.2254477368     2803.3973812751   12.8050965016      122.5330842028     0.0010   2026-09-08 10:27:49
     6      9    0.1028302837    0.1366824629     2797.9509018137    5.4464794614      104.2159922933     0.0009   2026-09-08 10:27:49
     7     10    0.0883550425    0.1261767402     2792.3241013240    5.6268004897       72.9831355692     0.0009   2026-09-08 10:27:49
     8     11    0.0758634851    0.1169717233     2786.4033946765    5.9207066475       48.2134275842     0.0010   2026-09-08 10:27:49
     9     12    0.0650971267    0.0807329396     2783.2688116090    3.1345830675       25.7237380736     0.0010   2026-09-08 10:27:49
    10     13    0.0427959572    0.0612144260     2782.2987982140    0.9700133949       23.5322414049     0.0008   2026-09-08 10:27:49
    11     14    0.0303277266    0.0393431504     2781.8555373444    0.4432608696       22.1624354437     0.0008   2026-09-08 10:27:49
    12     15    0.0254148632    0.0357898576     2781.3017728363    0.5537645081       26.8517399805     0.0008   2026-09-08 10:27:49
    13     16    0.0272548057    0.0560673720     2780.2194976910    1.0822751453       37.5323586658     0.0008   2026-09-08 10:27:49
    14     17    0.0380155095    0.0861069117     2778.7042915613    1.5152061297       40.9422313921     0.0008   2026-09-08 10:27:49
    15     18    0.0405847325    0.0984329958     2777.4247530800    1.2795384813       38.6424480618     0.0008   2026-09-08 10:27:49
    16     19    0.0292532116    0.0561198321     2776.9255929583    0.4991601216       19.1183741647     0.0008   2026-09-08 10:27:49
    17     20    0.0108876229    0.0148278745     2776.8100109644    0.1155819939       11.6368487844     0.0008   2026-09-08 10:27:49
    18     21    0.0032628891    0.0062521435     2776.7440883118    0.0659226526       11.6138868293     0.0008   2026-09-08 10:27:49
    19     22    0.0090432524    0.0130736552     2776.6215315534    0.1225567584       17.1731890130     0.0009   2026-09-08 10:27:49
    20     23    0.0227385322    0.0290163880     2776.3891545377    0.2323770157       32.1032891133     0.0008   2026-09-08 10:27:49
    21     24    0.0545362988    0.0656880491     2775.9169376589    0.4722168789       48.3501964999     0.0009   2026-09-08 10:27:49
    22     25    0.1011782293    0.1180318172     2775.1516125307    0.7653251282       55.5975989421     0.0009   2026-09-08 10:27:49
    23     26    0.1212002672    0.1388132562     2774.3498871702    0.8017253605       39.8127002361     0.0010   2026-09-08 10:27:49
    24     27    0.0622885924    0.0720883245     2773.9396540800    0.4102330902       11.7211423926     0.0008   2026-09-08 10:27:49
    25     28    0.0102046730    0.0168460228     2773.8185825356    0.1210715444        9.4149139814     0.0008   2026-09-08 10:27:49
    26     29    0.0061148358    0.0124293217     2773.7407515040    0.0778310316       10.6774046505     0.0007   2026-09-08 10:27:49
    27     30    0.0109467283    0.0238379762     2773.5554867791    0.1852647249       19.6754128932     0.0008   2026-09-08 10:27:49
    28     31    0.0416037227    0.0540196893     2773.1623778561    0.3931089230       29.6373044163     0.0009   2026-09-08 10:27:49
    29     32    0.1153608514    0.1251908723     2772.4323637741    0.7300140820       36.6106431286     0.0010   2026-09-08 10:27:49
    30     33    0.1857524314    0.1914761999     2771.5763416522    0.8560221219       31.3188446703     0.0008   2026-09-08 10:27:49
    31     34    0.1417920119    0.1457460933     2771.0716839181    0.5046577341       14.3803458442     0.0007   2026-09-08 10:27:49
    32     35    0.0287465434    0.0385319720     2770.9447812196    0.1269026985        5.2570772597     0.0008   2026-09-08 10:27:49
    33     36    0.0086902339    0.0133371394     2770.9231532561    0.0216279635        4.2486320979     0.0014   2026-09-08 10:27:49
    34     37    0.0081006401    0.0109389373     2770.9024531492    0.0207001069        4.7255603911     0.0011   2026-09-08 10:27:49
    35     38    0.0090542457    0.0162748670     2770.8516270373    0.0508261119        5.0731962498     0.0009   2026-09-08 10:27:49
    36     39    0.0098602198    0.0191807207     2770.7735064868    0.0781205505        4.8472083611     0.0009   2026-09-08 10:27:49
    37     40    0.0224620666    0.0323145373     2770.6957759124    0.0777305743        3.3675758495     0.0009   2026-09-08 10:27:49
    38     41    0.0256821081    0.0305756227     2770.6631121522    0.0326637602        1.9721746859     0.0008   2026-09-08 10:27:49
    39     42    0.0097875781    0.0118170057     2770.6576286120    0.0054835402        1.3368585934     0.0008   2026-09-08 10:27:49
    40     43    0.0016248787    0.0024938049     2770.6564808135    0.0011477984        1.0767916957     0.0008   2026-09-08 10:27:49
    41     44    0.0016564913    0.0030425225     2770.6542833990    0.0021974146        1.1491696574     0.0011   2026-09-08 10:27:49
    42     45    0.0026443451    0.0045681070     2770.6497587734    0.0045246256        1.2349378684     0.0013   2026-09-08 10:27:49
    43     46    0.0034025433    0.0070170733     2770.6424608392    0.0072979342        1.2999003921     0.0011   2026-09-08 10:27:49
    44     47    0.0051593081    0.0084599941     2770.6356615779    0.0067992612        0.9920175472     0.0011   2026-09-08 10:27:49
    45     48    0.0039374560    0.0060490297     2770.6327806485    0.0028809294        0.6977953949     0.0011   2026-09-08 10:27:49
    46     49    0.0012399269    0.0023336028     2770.6321782399    0.0006024086        0.8413611748     0.0012   2026-09-08 10:27:49
    47     50    0.0005608976    0.0009823842     2770.6318822544    0.0002959855        0.8936391163     0.0012   2026-09-08 10:27:49
    48     51    0.0009836922    0.0018246742     2770.6310831601    0.0007990943        0.9748232190     0.0012   2026-09-08 10:27:49
    49     52    0.0020934104    0.0034833577     2770.6292101029    0.0018730572        1.0800834979     0.0011   2026-09-08 10:27:49
    50     53    0.0064983507    0.0084855125     2770.6245829886    0.0046271143        1.2104785522     0.0011   2026-09-08 10:27:49
    51     54    0.0159004429    0.0191565337     2770.6148630507    0.0097199379        1.4247000443     0.0011   2026-09-08 10:27:49
    52     55    0.0296809118    0.0348835270     2770.5990756190    0.0157874316        1.6758517851     0.0011   2026-09-08 10:27:49
    53     56    0.0332381463    0.0390397818     2770.5836994430    0.0153761760        2.2974855705     0.0011   2026-09-08 10:27:49
    54     57    0.0160502336    0.0197425803     2770.5761434560    0.0075559870        2.3406148527     0.0012   2026-09-08 10:27:49
    55     58    0.0022750484    0.0044139452     2770.5733931178    0.0027503382        2.1275015476     0.0011   2026-09-08 10:27:49
    56     59    0.0014619108    0.0030612512     2770.5706144058    0.0027787120        1.8644161833     0.0012   2026-09-08 10:27:49
    57     60    0.0037970681    0.0067828234     2770.5638999086    0.0067144972        1.4835735158     0.0011   2026-09-08 10:27:49
    58     61    0.0159765687    0.0204665015     2770.5496292601    0.0142706485        1.9979238656     0.0011   2026-09-08 10:27:49
    59     62    0.0414616415    0.0502729290     2770.5243777236    0.0252515365        2.2338828010     0.0011   2026-09-08 10:27:49
    60     63    0.0622599603    0.0744481179     2770.4970055931    0.0273721306        1.6974505586     0.0012   2026-09-08 10:27:49
    61     64    0.0429526576    0.0513991962     2770.4829719688    0.0140336243        1.6959195203     0.0011   2026-09-08 10:27:49
    62     65    0.0076153549    0.0101555495     2770.4798761279    0.0030958409        1.2875199905     0.0011   2026-09-08 10:27:49
    63     66    0.0016205179    0.0027068951     2770.4790112111    0.0008649169        1.1801072163     0.0012   2026-09-08 10:27:49
    64     67    0.0022663053    0.0035465213     2770.4774834056    0.0015278055        1.1932098509     0.0011   2026-09-08 10:27:49
    65     68    0.0029599259    0.0039017260     2770.4741153487    0.0033680569        1.1287242552     0.0013   2026-09-08 10:27:49
    66     69    0.0055273459    0.0092196808     2770.4681666839    0.0059486648        0.8779215818     0.0010   2026-09-08 10:27:49
    67     70    0.0150744107    0.0200189989     2770.4615753726    0.0065913113        0.5980883297     0.0009   2026-09-08 10:27:49
    68     71    0.0152465105    0.0194114856     2770.4582466739    0.0033286986        0.3791861870     0.0008   2026-09-08 10:27:49
    69     72    0.0051110647    0.0065951965     2770.4576577838    0.0005888901        0.0930679911     0.0008   2026-09-08 10:27:49
    70     73    0.0004979304    0.0006527044     2770.4576256836    0.0000321003        0.0666631301     0.0008   2026-09-08 10:27:50
    71     74    0.0001483751    0.0002081359     2770.4576242833    0.0000014002        0.0649851551     0.0008   2026-09-08 10:27:50
    72     75    0.0001387488    0.0001901472     2770.4576224690    0.0000018144        0.0609183484     0.0008   2026-09-08 10:27:50
    73     76    0.0001973908    0.0002783176     2770.4576181320    0.0000043369        0.0482148464     0.0008   2026-09-08 10:27:50
    74     77    0.0001382378    0.0002016693     2770.4576122162    0.0000059158        0.0264802663     0.0008   2026-09-08 10:27:50
    75     78    0.0001445727    0.0002520203     2770.4576074633    0.0000047529        0.0097246237     0.0008   2026-09-08 10:27:50
    76     79    0.0001995263    0.0002838590     2770.4576060228    0.0000014405        0.0031974618     0.0008   2026-09-08 10:27:50
    77     80    0.0000778072    0.0001062033     2770.4576058782    0.0000001446        0.0008626554     0.0008   2026-09-08 10:27:50

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','3.213638e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -1.6110***  0.5381   0.0028   
TC/100 EUR                        -0.9007***  0.3073   0.0034   
PC1                                0.1958     0.1258   0.1197   
PC2                                0.2165***  0.0579   0.0002   
PC3                                0.3424***  0.1271   0.0070   
Household income (10k PLN)         0.2666***  0.1019   0.0089   
Male                               0.1183     0.0721   0.1008   
Higher education                   0.0262     0.0801   0.7440   
City                               0.0987     0.0744   0.1843   
Winter                             0.8395***  0.0840   0.0000   
Hiking                             2.0894***  0.0788   0.0000   
Skiing                             1.4084***  0.2662   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3356     0.0928            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.1102***  0.3787   0.0034   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2770.4576
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1684
AIC/n:                             0.9508
BIC/n:                             0.9656
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.7225
median                           0.0000          1.7321
std                              0.7834          0.7394
min                              0.0000          0.0246
max                             20.0000          3.5357
quantile 0.025                   0.0000          0.4668
quantile 0.975                   2.0000          3.0518
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:50
Estimation took 0.1434 seconds (0 hours 0 minutes 0.1434 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.6 -0.046 -0.0053 0.021 0.09 0.068 0.0092 0.0053 0.0059 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.2732862422             NaN     3011.3062999463     0.0001   2026-09-08 10:27:50
     1      3    0.3902227641    0.4741067390     3192.8541301965  735.4191560457      389.9648456068     0.0022   2026-09-08 10:27:50
     2      5    0.4048866602    0.5431499849     3044.0325133403  148.8216168562      591.6668331254     0.0025   2026-09-08 10:27:50
     3      6    0.1643994718    0.2157304226     2963.8055541977   80.2269591427      401.9748789980     0.0008   2026-09-08 10:27:50
     4      7    0.5584347023    0.7107184624     2834.8519856348  128.9535685629      185.1817964269     0.0011   2026-09-08 10:27:50
     5      8    0.2070144100    0.2612585273     2815.2193802413   19.6326053935      182.2208718489     0.0009   2026-09-08 10:27:50
     6      9    0.1566405802    0.1972022693     2804.9914834626   10.2278967786      159.9897520543     0.0009   2026-09-08 10:27:50
     7     10    0.1221299539    0.1597031299     2796.2705944318    8.7208890308      119.8328594753     0.0012   2026-09-08 10:27:50
     8     11    0.0867720065    0.1408174554     2787.4202869386    8.8503074932       60.7873524464     0.0012   2026-09-08 10:27:50
     9     12    0.0757940002    0.0827117847     2782.9832467784    4.4370401603       33.6809691882     0.0010   2026-09-08 10:27:50
    10     13    0.0481456916    0.0676103994     2781.8437107568    1.1395360216       17.8364922078     0.0012   2026-09-08 10:27:50
    11     14    0.0305588088    0.0389036036     2781.5259964870    0.3177142697       15.1568556343     0.0013   2026-09-08 10:27:50
    12     15    0.0192139666    0.0258605738     2781.2527309411    0.2732655459       17.6838212558     0.0010   2026-09-08 10:27:50
    13     16    0.0246219912    0.0415370308     2780.6404171276    0.6123138136       28.7933790549     0.0009   2026-09-08 10:27:50
    14     17    0.0332735632    0.0640318341     2779.6007066416    1.0397104860       36.5380566636     0.0012   2026-09-08 10:27:50
    15     18    0.0412889902    0.0881180445     2778.4031596705    1.1975469711       30.4979669190     0.0011   2026-09-08 10:27:50
    16     19    0.0303716182    0.0701207063     2777.7514334569    0.6517262136       12.0192006772     0.0009   2026-09-08 10:27:50
    17     20    0.0207550195    0.0289659779     2777.5906778856    0.1607555713       11.5791500164     0.0011   2026-09-08 10:27:50
    18     21    0.0063176703    0.0089370509     2777.5467806422    0.0438972433       11.6345331369     0.0013   2026-09-08 10:27:50
    19     22    0.0058276327    0.0101443655     2777.4758923190    0.0708883232       11.6620994168     0.0010   2026-09-08 10:27:50
    20     23    0.0165264719    0.0215683847     2777.3059295433    0.1699627757       17.0211542356     0.0013   2026-09-08 10:27:50
    21     24    0.0463379029    0.0521926754     2776.9209005625    0.3850289808       31.8547366932     0.0012   2026-09-08 10:27:50
    22     25    0.1079003365    0.1169771519     2776.1497348791    0.7711656834       48.2976918476     0.0012   2026-09-08 10:27:50
    23     26    0.1806481272    0.1938473561     2775.0337186651    1.1160162140       53.4387003929     0.0010   2026-09-08 10:27:50
    24     27    0.1671455186    0.1795906649     2774.1199343575    0.9137843076       34.1308582369     0.0011   2026-09-08 10:27:50
    25     28    0.0497107569    0.0571339585     2773.7672266557    0.3527077018       13.1927044397     0.0013   2026-09-08 10:27:50
    26     29    0.0102660020    0.0161123113     2773.6735886495    0.0936380062       11.4857328076     0.0012   2026-09-08 10:27:50
    27     30    0.0094662919    0.0148254782     2773.5822644005    0.0913242490       11.0845422245     0.0010   2026-09-08 10:27:50
    28     31    0.0164488655    0.0238432025     2773.3375081119    0.2447562886       21.6181695890     0.0012   2026-09-08 10:27:50
    29     32    0.0388650271    0.0539766555     2772.8750301273    0.4624779846       31.8704847539     0.0012   2026-09-08 10:27:50
    30     33    0.1153032727    0.1261114629     2772.2038297463    0.6712003810       33.4486068045     0.0011   2026-09-08 10:27:50
    31     34    0.1446665900    0.1501424984     2771.7151659369    0.4886638094       20.0495360510     0.0010   2026-09-08 10:27:50
    32     35    0.0695828309    0.0723460758     2771.5650364183    0.1501295186        5.0951876292     0.0008   2026-09-08 10:27:50
    33     36    0.0071235280    0.0109915492     2771.5440704471    0.0209659712        3.7728368758     0.0011   2026-09-08 10:27:50
    34     37    0.0028572442    0.0042972098     2771.5371555664    0.0069148806        3.9775979927     0.0011   2026-09-08 10:27:50
    35     38    0.0054920958    0.0081429657     2771.5188800312    0.0182755352        4.0171775999     0.0012   2026-09-08 10:27:50
    36     39    0.0068355433    0.0107609965     2771.4862479690    0.0326320622        5.9350768787     0.0009   2026-09-08 10:27:50
    37     40    0.0099060140    0.0179648212     2771.4387962092    0.0474517599        6.2631062060     0.0013   2026-09-08 10:27:50
    38     41    0.0129769544    0.0215186422     2771.4045795329    0.0342166763        3.7685118871     0.0013   2026-09-08 10:27:50
    39     42    0.0093521549    0.0131197374     2771.3941363165    0.0104432164        1.2160244422     0.0012   2026-09-08 10:27:50
    40     43    0.0023864126    0.0037034816     2771.3924091871    0.0017271294        1.1206171934     0.0009   2026-09-08 10:27:50
    41     44    0.0012072604    0.0017498701     2771.3912652353    0.0011439518        1.1744203362     0.0008   2026-09-08 10:27:50
    42     45    0.0022363227    0.0034702068     2771.3880567759    0.0032084594        1.4263535381     0.0008   2026-09-08 10:27:50
    43     46    0.0027730824    0.0058500025     2771.3817309889    0.0063257870        1.9192677684     0.0008   2026-09-08 10:27:50
    44     47    0.0055410806    0.0105313648     2771.3709855792    0.0107454097        2.3569462906     0.0008   2026-09-08 10:27:50
    45     48    0.0065364994    0.0125950464     2771.3605981704    0.0103874087        1.7643005477     0.0008   2026-09-08 10:27:50
    46     49    0.0034058239    0.0079392244     2771.3558407077    0.0047574627        1.3860810611     0.0009   2026-09-08 10:27:50
    47     50    0.0018156136    0.0026672130     2771.3547114883    0.0011292194        1.1644484559     0.0008   2026-09-08 10:27:50
    48     51    0.0009032441    0.0013111212     2771.3540781632    0.0006333252        1.0624952726     0.0008   2026-09-08 10:27:50
    49     52    0.0014752428    0.0023445328     2771.3524410147    0.0016371484        1.0120154795     0.0008   2026-09-08 10:27:50
    50     53    0.0029661496    0.0046064760     2771.3486509378    0.0037900769        1.6579183002     0.0008   2026-09-08 10:27:50
    51     54    0.0091092093    0.0113817874     2771.3398454341    0.0088055036        2.5081109101     0.0008   2026-09-08 10:27:50
    52     55    0.0205326264    0.0242972332     2771.3235378684    0.0163075658        3.1814975124     0.0010   2026-09-08 10:27:50
    53     56    0.0312636767    0.0367919567     2771.3028928229    0.0206450455        2.8884608895     0.0009   2026-09-08 10:27:50
    54     57    0.0243230345    0.0293747706     2771.2889798085    0.0139130144        2.9788882507     0.0011   2026-09-08 10:27:50
    55     58    0.0069939084    0.0099485676     2771.2836706824    0.0053091261        3.1862154631     0.0011   2026-09-08 10:27:50
    56     59    0.0020719420    0.0035086202     2771.2804677246    0.0032029577        3.1048157825     0.0010   2026-09-08 10:27:50
    57     60    0.0033908798    0.0059390891     2771.2737892060    0.0066785186        2.8801330404     0.0012   2026-09-08 10:27:50
    58     61    0.0132119844    0.0166418450     2771.2580268124    0.0157623936        2.4377577945     0.0009   2026-09-08 10:27:50
    59     62    0.0396861553    0.0464867449     2771.2227712794    0.0352555330        3.8443141158     0.0008   2026-09-08 10:27:50
    60     63    0.0870734872    0.1000210060     2771.1606603508    0.0621109286        4.8384755663     0.0008   2026-09-08 10:27:50
    61     64    0.1196098278    0.1365457218     2771.0920475050    0.0686128459        3.9723871084     0.0008   2026-09-08 10:27:50
    62     65    0.0721749280    0.0826548765     2771.0574164185    0.0346310864        1.6288392608     0.0008   2026-09-08 10:27:50
    63     66    0.0045161402    0.0086784533     2771.0511878305    0.0062285880        0.3415796758     0.0012   2026-09-08 10:27:50
    64     67    0.0071563765    0.0083625029     2771.0508191531    0.0003686775        0.3138632049     0.0013   2026-09-08 10:27:50
    65     68    0.0017768750    0.0020386277     2771.0507875922    0.0000315609        0.3032770880     0.0013   2026-09-08 10:27:50
    66     69    0.0025624743    0.0029530163     2771.0507167345    0.0000708577        0.2734251922     0.0012   2026-09-08 10:27:50
    67     70    0.0026823523    0.0031527370     2771.0505792416    0.0001374929        0.2067601440     0.0009   2026-09-08 10:27:50
    68     71    0.0010163459    0.0016053893     2771.0503721294    0.0002071122        0.1038461414     0.0009   2026-09-08 10:27:50
    69     72    0.0026729538    0.0031530634     2771.0502080778    0.0001640515        0.0563792479     0.0008   2026-09-08 10:27:50
    70     73    0.0036009154    0.0041067055     2771.0501551115    0.0000529663        0.0404524302     0.0008   2026-09-08 10:27:50
    71     74    0.0013201788    0.0015142905     2771.0501492868    0.0000058247        0.0304970457     0.0008   2026-09-08 10:27:50
    72     75    0.0001629492    0.0001935358     2771.0501487405    0.0000005463        0.0310987899     0.0008   2026-09-08 10:27:50
    73     76    0.0001086481    0.0001330431     2771.0501480336    0.0000007069        0.0309720154     0.0012   2026-09-08 10:27:50
    74     77    0.0001503387    0.0001913573     2771.0501462678    0.0000017658        0.0284904825     0.0012   2026-09-08 10:27:50
    75     78    0.0000960231    0.0001619855     2771.0501433851    0.0000028828        0.0212086642     0.0013   2026-09-08 10:27:50
    76     79    0.0001116538    0.0001802217     2771.0501402907    0.0000030944        0.0103065346     0.0012   2026-09-08 10:27:50
    77     80    0.0002097354    0.0002700740     2771.0501388616    0.0000014290        0.0066336444     0.0012   2026-09-08 10:27:50
    78     81    0.0001183550    0.0001447999     2771.0501386292    0.0000002324        0.0014987074     0.0012   2026-09-08 10:27:50

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','4.975282e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -1.7215***  0.5565   0.0020   
TC/100 EUR                        -0.7428***  0.2771   0.0073   
PC1                                0.1482     0.1134   0.1912   
PC2                                0.1726***  0.0502   0.0006   
PC3                                0.2930**   0.1138   0.0100   
Household income (10k PLN)         0.2697**   0.1082   0.0127   
Male                               0.1156     0.0722   0.1092   
Higher education                   0.0288     0.0802   0.7198   
City                               0.0927     0.0744   0.2129   
Winter                             0.8416***  0.0841   0.0000   
Hiking                             2.0910***  0.0789   0.0000   
Skiing                             1.4035***  0.2673   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3451     0.0922            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.3463***  0.5022   0.0073   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2771.0501
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1682
AIC/n:                             0.9510
BIC/n:                             0.9658
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.9364
median                           0.0000          1.9333
std                              0.7834          0.8370
min                              0.0000          0.0250
max                             20.0000          4.9654
quantile 0.025                   0.0000          0.5313
quantile 0.975                   2.0000          3.5345
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:51
Estimation took 0.1704 seconds (0 hours 0 minutes 0.1704 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.8 0.04 -0.034 0.012 0.08 0.087 0.0094 0.006 0.0054 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3929.3914642100             NaN     3667.1757335002     0.0001   2026-09-08 10:27:51
     1      3    0.3594406905    0.4139159965     3218.7252542784  710.6662099316      592.2845991989     0.0027   2026-09-08 10:27:51
     2      4    0.0502992098    0.0668604207     3175.2857723258   43.4394819526      389.6879052848     0.0014   2026-09-08 10:27:51
     3      5    0.1251690272    0.1906855296     3109.0882595542   66.1975127717      434.5224091599     0.0011   2026-09-08 10:27:51
     4      6    0.1106928785    0.1453414747     3063.0804947237   46.0077648304      552.7846112341     0.0011   2026-09-08 10:27:51
     5      7    0.4820268476    0.6167437632     2918.7581836553  144.3223110684      389.5140682133     0.0012   2026-09-08 10:27:51
     6      8    0.2517575567    0.3134842620     2874.9604942011   43.7976894542      345.1989793327     0.0013   2026-09-08 10:27:51
     7      9    0.2115688847    0.2582753748     2848.1164588694   26.8440353318      325.1780507113     0.0010   2026-09-08 10:27:51
     8     10    0.1978172848    0.2425062073     2824.3539909543   23.7624679151      257.4624798671     0.0013   2026-09-08 10:27:51
     9     11    0.1770762267    0.2309040559     2801.8714432985   22.4825476558      207.4328085210     0.0011   2026-09-08 10:27:51
    10     12    0.0949350092    0.1206854394     2790.3230796178   11.5483636808      132.4881907067     0.0010   2026-09-08 10:27:51
    11     13    0.0391694826    0.0597664426     2787.4026155873    2.9204640304       43.7216632228     0.0011   2026-09-08 10:27:51
    12     14    0.0351599015    0.0443659226     2786.7937073465    0.6089082408       30.7204072419     0.0011   2026-09-08 10:27:51
    13     15    0.0173536841    0.0231638488     2786.5190330290    0.2746743176       28.7129113667     0.0012   2026-09-08 10:27:51
    14     16    0.0176020195    0.0297966442     2786.0075416630    0.5114913659       34.6062774325     0.0011   2026-09-08 10:27:51
    15     17    0.0367938952    0.0524734538     2784.9178228501    1.0897188130       52.7616878226     0.0010   2026-09-08 10:27:51
    16     18    0.0629197650    0.0844222119     2783.2585303273    1.6592925228       57.5542844536     0.0010   2026-09-08 10:27:51
    17     19    0.0602192949    0.0940034317     2781.8312631227    1.4272672046       35.5296441127     0.0010   2026-09-08 10:27:51
    18     20    0.0368562080    0.0529270697     2781.3206787717    0.5105843510       11.8537810285     0.0010   2026-09-08 10:27:51
    19     21    0.0121516850    0.0162820173     2781.2407048746    0.0799738971       11.9316839318     0.0011   2026-09-08 10:27:51
    20     22    0.0037404214    0.0063535461     2781.2070324731    0.0336724015       11.9535043769     0.0009   2026-09-08 10:27:51
    21     23    0.0079128467    0.0139644642     2781.1075602297    0.0994722434       11.9539417742     0.0009   2026-09-08 10:27:51
    22     24    0.0181276245    0.0262985987     2780.8964072223    0.2111530075       19.5130110340     0.0010   2026-09-08 10:27:51
    23     25    0.0489646011    0.0604460022     2780.4331561551    0.4632510672       32.3122127332     0.0010   2026-09-08 10:27:51
    24     26    0.0922585571    0.1084781225     2779.7008438232    0.7323123319       40.3505334927     0.0010   2026-09-08 10:27:51
    25     27    0.1074839654    0.1262831838     2778.9791397174    0.7217041058       32.8169709496     0.0009   2026-09-08 10:27:51
    26     28    0.0524577013    0.0670545982     2778.6295845710    0.3495551463       14.5566910374     0.0010   2026-09-08 10:27:51
    27     29    0.0107545128    0.0173633343     2778.5240584709    0.1055261001       13.9524661265     0.0009   2026-09-08 10:27:51
    28     30    0.0062915959    0.0112362690     2778.4446535585    0.0794049124       14.7077311074     0.0010   2026-09-08 10:27:51
    29     31    0.0103849087    0.0197295616     2778.2474722051    0.1971813534       15.3335538268     0.0009   2026-09-08 10:27:51
    30     32    0.0356483898    0.0455811885     2777.8372686931    0.4102035119       26.9650751353     0.0009   2026-09-08 10:27:51
    31     33    0.1022995605    0.1125664696     2777.0796535956    0.7576150975       37.8000249696     0.0009   2026-09-08 10:27:51
    32     34    0.1662921386    0.1777502498     2776.1954484305    0.8842051651       34.3769444312     0.0009   2026-09-08 10:27:51
    33     35    0.1282443532    0.1382702723     2775.6801860958    0.5152623347       15.7658588041     0.0010   2026-09-08 10:27:51
    34     36    0.0300208805    0.0377733424     2775.5508131382    0.1293729575        7.1794562276     0.0011   2026-09-08 10:27:51
    35     37    0.0043299903    0.0083274485     2775.5241575212    0.0266556171        7.0145586573     0.0010   2026-09-08 10:27:51
    36     38    0.0047081310    0.0077461050     2775.4938354939    0.0303220273        6.9901583528     0.0010   2026-09-08 10:27:51
    37     39    0.0087515721    0.0128245042     2775.4190406626    0.0747948313       12.3703225816     0.0009   2026-09-08 10:27:51
    38     40    0.0130804929    0.0254242521     2775.2707784276    0.1482622350       22.1739999167     0.0010   2026-09-08 10:27:51
    39     41    0.0406966875    0.0552818272     2775.0266516532    0.2441267744       29.1188332578     0.0010   2026-09-08 10:27:51
    40     42    0.0637892814    0.0759327848     2774.7897929332    0.2368587200       24.0863123382     0.0010   2026-09-08 10:27:51
    41     43    0.0443176589    0.0497271144     2774.6814646731    0.1083282601       10.2991304921     0.0010   2026-09-08 10:27:51
    42     44    0.0090451682    0.0118473270     2774.6594157758    0.0220488973        3.8074970263     0.0010   2026-09-08 10:27:51
    43     45    0.0020664292    0.0037062957     2774.6538640716    0.0055517043        3.5967668035     0.0010   2026-09-08 10:27:51
    44     46    0.0028108469    0.0047533270     2774.6445890692    0.0092750024        4.1228217537     0.0010   2026-09-08 10:27:51
    45     47    0.0051428019    0.0075390546     2774.6232757150    0.0213133542        8.2648908756     0.0010   2026-09-08 10:27:51
    46     48    0.0087027535    0.0147062445     2774.5787503212    0.0445253938       13.0259174522     0.0010   2026-09-08 10:27:51
    47     49    0.0168981323    0.0290350169     2774.5063644229    0.0723858982       15.4206291877     0.0010   2026-09-08 10:27:51
    48     50    0.0246378698    0.0381064425     2774.4368533374    0.0695110855       11.1554924831     0.0010   2026-09-08 10:27:51
    49     51    0.0150665510    0.0232176022     2774.4077588934    0.0290944440        3.6080707989     0.0009   2026-09-08 10:27:51
    50     52    0.0031224205    0.0057143871     2774.4030213292    0.0047375642        1.6731478250     0.0010   2026-09-08 10:27:51
    51     53    0.0011216877    0.0018820327     2774.4022587881    0.0007625411        1.5914830518     0.0010   2026-09-08 10:27:51
    52     54    0.0012056105    0.0020188286     2774.4011271569    0.0011316312        1.5492491539     0.0009   2026-09-08 10:27:51
    53     55    0.0019501614    0.0034740928     2774.3981542935    0.0029728634        2.0440376232     0.0009   2026-09-08 10:27:51
    54     56    0.0037847632    0.0061676192     2774.3913944618    0.0067598316        3.1599587019     0.0009   2026-09-08 10:27:51
    55     57    0.0101635409    0.0128093055     2774.3774370567    0.0139574052        4.2842289253     0.0009   2026-09-08 10:27:51
    56     58    0.0187974471    0.0224636609     2774.3566050128    0.0208320439        4.4400311177     0.0010   2026-09-08 10:27:51
    57     59    0.0199182486    0.0247182290     2774.3385961190    0.0180088937        3.0723144392     0.0009   2026-09-08 10:27:51
    58     60    0.0086714156    0.0130053783     2774.3309380612    0.0076580578        3.1432410085     0.0010   2026-09-08 10:27:51
    59     61    0.0026400230    0.0041333685     2774.3282169016    0.0027211596        2.8906754932     0.0010   2026-09-08 10:27:51
    60     62    0.0021030941    0.0033667383     2774.3249176802    0.0032992214        2.5824492152     0.0009   2026-09-08 10:27:51
    61     63    0.0039052959    0.0070403470     2774.3162192019    0.0086984782        2.1892791896     0.0011   2026-09-08 10:27:51
    62     64    0.0143493924    0.0181348124     2774.2948888571    0.0213303448        3.7830549969     0.0009   2026-09-08 10:27:51
    63     65    0.0433713483    0.0498479609     2774.2428785734    0.0520102837        6.2647103986     0.0009   2026-09-08 10:27:51
    64     66    0.1065065135    0.1188472501     2774.1326059284    0.1102726450        8.9823695946     0.0009   2026-09-08 10:27:51
    65     67    0.1969179448    0.2173179392     2773.9551767219    0.1774292066        9.9622248625     0.0012   2026-09-08 10:27:51
    66     68    0.2123162497    0.2333699590     2773.7900749926    0.1651017293        6.8834327526     0.0012   2026-09-08 10:27:51
    67     69    0.0842162378    0.0937614288     2773.7233074360    0.0667675565        4.0314744355     0.0013   2026-09-08 10:27:51
    68     70    0.0108767949    0.0157380693     2773.7128043436    0.0105030924        3.6120843225     0.0011   2026-09-08 10:27:51
    69     71    0.0121850267    0.0137136527     2773.7106748918    0.0021294519        3.3971085331     0.0011   2026-09-08 10:27:51
    70     72    0.0152221228    0.0171426022     2773.7067288856    0.0039460062        3.0120930502     0.0009   2026-09-08 10:27:51
    71     73    0.0148740139    0.0172781684     2773.6984719785    0.0082569071        2.2550712679     0.0009   2026-09-08 10:27:51
    72     74    0.0065832628    0.0073217259     2773.6850167462    0.0134552323        1.3533742516     0.0009   2026-09-08 10:27:51
    73     75    0.0289030956    0.0325164952     2773.6723318055    0.0126849407        0.9986776560     0.0009   2026-09-08 10:27:51
    74     76    0.0357573112    0.0396216334     2773.6672300893    0.0051017161        0.3339610612     0.0009   2026-09-08 10:27:51
    75     77    0.0135408328    0.0150866003     2773.6665426749    0.0006874145        0.1009017642     0.0009   2026-09-08 10:27:51
    76     78    0.0011283020    0.0013561927     2773.6665136376    0.0000290373        0.1049823445     0.0009   2026-09-08 10:27:51
    77     79    0.0001126413    0.0001407001     2773.6665117089    0.0000019287        0.1031837588     0.0009   2026-09-08 10:27:51
    78     80    0.0002242452    0.0002744327     2773.6665067779    0.0000049310        0.0961581673     0.0009   2026-09-08 10:27:51
    79     81    0.0002524985    0.0003306333     2773.6664971687    0.0000096092        0.0793288765     0.0009   2026-09-08 10:27:51
    80     82    0.0002164662    0.0003277092     2773.6664812316    0.0000159371        0.0566616227     0.0009   2026-09-08 10:27:51
    81     83    0.0002390083    0.0003489131     2773.6664667030    0.0000145286        0.0408619184     0.0015   2026-09-08 10:27:51
    82     84    0.0003378850    0.0004218543     2773.6664609689    0.0000057342        0.0135059736     0.0011   2026-09-08 10:27:51
    83     85    0.0001599100    0.0001922726     2773.6664602221    0.0000007468        0.0021286922     0.0009   2026-09-08 10:27:51

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.803136e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.1703***  0.6251   0.0005   
TC/100 EUR                        -0.4266*    0.2526   0.0912   
PC1                                0.0560     0.1011   0.5798   
PC2                                0.1108***  0.0356   0.0018   
PC3                                0.2147**   0.1069   0.0447   
Household income (10k PLN)         0.3232**   0.1309   0.0135   
Male                               0.1128     0.0724   0.1193   
Higher education                   0.0335     0.0805   0.6776   
City                               0.0821     0.0746   0.2709   
Winter                             0.8413***  0.0844   0.0000   
Hiking                             2.0955***  0.0791   0.0000   
Skiing                             1.3959***  0.2691   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3646     0.0911            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.3441*    1.3877   0.0912   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2773.6665
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1674
AIC/n:                             0.9519
BIC/n:                             0.9667
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.3643
median                           0.0000          2.3002
std                              0.7834          1.0883
min                              0.0000          0.0258
max                             20.0000          8.1215
quantile 0.025                   0.0000          0.6384
quantile 0.975                   2.0000          4.6816
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:52
Estimation took 0.16746 seconds (0 hours 0 minutes 0.16746 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.56 -0.057 0.00091 0.019 0.076 0.062 0.0091 0.005 0.0061 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.3785666607             NaN     3513.3164523790     0.0001   2026-09-08 10:27:52
     1      3    0.3816251155    0.4447667598     3171.2712204885  757.1073461722      385.1234778944     0.0025   2026-09-08 10:27:52
     2      4    0.0383134829    0.0508600043     3146.4620019476   24.8092185409      369.1670570521     0.0013   2026-09-08 10:27:52
     3      5    0.4239386131    0.5352303073     3006.9522935307  139.5097084169      617.2444432992     0.0012   2026-09-08 10:27:52
     4      6    0.1793174993    0.2234547821     2944.2783533854   62.6739401453      508.3945910508     0.0011   2026-09-08 10:27:52
     5      7    0.5291178443    0.6586665996     2826.7821884405  117.4961649449      205.3697717363     0.0009   2026-09-08 10:27:52
     6      8    0.2050071614    0.2523294782     2808.9638137852   17.8183746553      194.3017074834     0.0013   2026-09-08 10:27:52
     7      9    0.1479496924    0.1825505929     2799.8669649027    9.0968488825      163.6225251678     0.0012   2026-09-08 10:27:52
     8     10    0.1042193584    0.1349599433     2792.5594518728    7.3075130300      115.5378155179     0.0013   2026-09-08 10:27:52
     9     11    0.0713054229    0.1042639361     2785.7653336534    6.7941182194       58.8520706509     0.0013   2026-09-08 10:27:52
    10     12    0.0530455253    0.0642428044     2782.8571436378    2.9081900156       25.9624265516     0.0010   2026-09-08 10:27:52
    11     13    0.0422258952    0.0543575030     2782.1787691097    0.6783745281       16.2109703512     0.0013   2026-09-08 10:27:52
    12     14    0.0225501102    0.0279851659     2781.9699110344    0.2088580753       14.2590629299     0.0013   2026-09-08 10:27:52
    13     15    0.0178345730    0.0236921753     2781.7181034293    0.2518076051       18.3961980470     0.0013   2026-09-08 10:27:52
    14     16    0.0250385553    0.0423055734     2781.1103338310    0.6077695983       29.1187417597     0.0010   2026-09-08 10:27:52
    15     17    0.0321287798    0.0667827406     2780.0698347221    1.0404991089       35.9395798393     0.0010   2026-09-08 10:27:52
    16     18    0.0436129738    0.0895248955     2778.8925347053    1.1773000168       28.5182801395     0.0009   2026-09-08 10:27:52
    17     19    0.0327479114    0.0675035756     2778.2954616321    0.5970730732       11.5291908342     0.0009   2026-09-08 10:27:52
    18     20    0.0217615391    0.0278691259     2778.1630913361    0.1323702960       11.6168455029     0.0009   2026-09-08 10:27:52
    19     21    0.0072248419    0.0095390198     2778.1247399170    0.0383514191       11.6642137935     0.0009   2026-09-08 10:27:52
    20     22    0.0090630957    0.0130824729     2778.0491584280    0.0755814891       11.6971167470     0.0009   2026-09-08 10:27:52
    21     23    0.0156473810    0.0248434627     2777.8689127526    0.1802456753       15.8341390235     0.0009   2026-09-08 10:27:52
    22     24    0.0452545369    0.0555333447     2777.4577934488    0.4111193038       24.3301834782     0.0013   2026-09-08 10:27:52
    23     25    0.1024544386    0.1159518791     2776.6748860372    0.7829074116       31.6630387136     0.0013   2026-09-08 10:27:52
    24     26    0.1585698299    0.1761907941     2775.6539013510    1.0209846862       29.9578638025     0.0011   2026-09-08 10:27:52
    25     27    0.1246040371    0.1417316392     2774.9432181813    0.7106831697       17.2002573204     0.0011   2026-09-08 10:27:52
    26     28    0.0272198032    0.0435737632     2774.6993228921    0.2438952892       11.8007540790     0.0008   2026-09-08 10:27:52
    27     29    0.0095788942    0.0167868811     2774.6285730061    0.0707498860        9.5160732881     0.0011   2026-09-08 10:27:52
    28     30    0.0085964495    0.0152967495     2774.5377604566    0.0908125495       10.4368831115     0.0012   2026-09-08 10:27:52
    29     31    0.0162124318    0.0245742081     2774.2965644298    0.2411960268       14.9690944557     0.0012   2026-09-08 10:27:52
    30     32    0.0428386073    0.0573368394     2773.7998992067    0.4966652230       25.5998372837     0.0010   2026-09-08 10:27:52
    31     33    0.1269576429    0.1394919364     2772.9727428720    0.8271563347       32.2492578426     0.0008   2026-09-08 10:27:52
    32     34    0.1827234372    0.1928284919     2772.2079478471    0.7647950249       24.7204938327     0.0012   2026-09-08 10:27:52
    33     35    0.1077859686    0.1144860926     2771.9003805699    0.3075672772        9.2182315077     0.0012   2026-09-08 10:27:52
    34     36    0.0151829211    0.0223098918     2771.8488740904    0.0515064796        4.4765480273     0.0012   2026-09-08 10:27:52
    35     37    0.0041468149    0.0066194304     2771.8400570252    0.0088170651        4.1690429553     0.0009   2026-09-08 10:27:52
    36     38    0.0053262401    0.0076688047     2771.8266021694    0.0134548559        3.8096088968     0.0012   2026-09-08 10:27:52
    37     39    0.0059276845    0.0111317389     2771.7952581984    0.0313439710        6.5830095695     0.0009   2026-09-08 10:27:52
    38     40    0.0082468229    0.0156107221     2771.7401559808    0.0551022176        9.1864362399     0.0013   2026-09-08 10:27:52
    39     41    0.0159062042    0.0256237716     2771.6758700815    0.0642858993        8.5379534608     0.0011   2026-09-08 10:27:52
    40     42    0.0189756014    0.0265725914     2771.6406215090    0.0352485725        4.2606437259     0.0012   2026-09-08 10:27:52
    41     43    0.0095073324    0.0121063689     2771.6329770901    0.0076444189        1.4118542222     0.0010   2026-09-08 10:27:52
    42     44    0.0017345219    0.0027275334     2771.6316894200    0.0012876701        1.6797817820     0.0009   2026-09-08 10:27:52
    43     45    0.0010569220    0.0020196270     2771.6302048407    0.0014845792        1.8791651580     0.0010   2026-09-08 10:27:52
    44     46    0.0019340362    0.0038693983     2771.6261628660    0.0040419747        2.2207665188     0.0009   2026-09-08 10:27:52
    45     47    0.0042666735    0.0071026817     2771.6175406326    0.0086222334        3.7011346406     0.0012   2026-09-08 10:27:52
    46     48    0.0094409429    0.0137738204     2771.6014576594    0.0160829732        5.1409644075     0.0010   2026-09-08 10:27:52
    47     49    0.0134410102    0.0193159655     2771.5821993626    0.0192582968        4.6904499263     0.0008   2026-09-08 10:27:52
    48     50    0.0096170345    0.0150238734     2771.5701525247    0.0120468379        2.3298239886     0.0009   2026-09-08 10:27:52
    49     51    0.0021825651    0.0055011719     2771.5662651064    0.0038874182        1.7992474150     0.0012   2026-09-08 10:27:52
    50     52    0.0013661006    0.0022960416     2771.5643058726    0.0019592338        1.5960444748     0.0012   2026-09-08 10:27:52
    51     53    0.0020820321    0.0033749087     2771.5601585693    0.0041473033        2.5745260100     0.0010   2026-09-08 10:27:52
    52     54    0.0051997758    0.0074060870     2771.5500990266    0.0100595427        4.7336058056     0.0009   2026-09-08 10:27:52
    53     55    0.0172470444    0.0202462916     2771.5258141162    0.0242849104        7.8344388695     0.0008   2026-09-08 10:27:52
    54     56    0.0441466894    0.0495866516     2771.4748258340    0.0509882822       11.2408532134     0.0008   2026-09-08 10:27:52
    55     57    0.0830844465    0.0924775962     2771.3939542359    0.0808715982       12.4418497131     0.0008   2026-09-08 10:27:52
    56     58    0.0913386839    0.1020512865     2771.3189736426    0.0749805933        8.5169136844     0.0009   2026-09-08 10:27:52
    57     59    0.0400939361    0.0463345089     2771.2861637416    0.0328099010        4.9545471482     0.0008   2026-09-08 10:27:52
    58     60    0.0042226805    0.0063764587     2771.2768194097    0.0093443319        5.1585079140     0.0008   2026-09-08 10:27:52
    59     61    0.0027990752    0.0050969695     2771.2689723220    0.0078470877        5.0654871370     0.0008   2026-09-08 10:27:52
    60     62    0.0044039410    0.0075397933     2771.2490891359    0.0198831861        4.8809414341     0.0008   2026-09-08 10:27:52
    61     63    0.0194030329    0.0245522877     2771.2077586778    0.0413304581        7.9355810938     0.0008   2026-09-08 10:27:52
    62     64    0.0613696297    0.0700574526     2771.1354900516    0.0722686262        9.9082717640     0.0008   2026-09-08 10:27:52
    63     65    0.0985527007    0.1101487145     2771.0605997724    0.0748902792        7.8868129680     0.0008   2026-09-08 10:27:52
    64     66    0.0703412775    0.0782680075     2771.0254233982    0.0351763742        3.0883263512     0.0008   2026-09-08 10:27:52
    65     67    0.0123747192    0.0147735141     2771.0196857602    0.0057376380        0.4277591118     0.0008   2026-09-08 10:27:52
    66     68    0.0033899608    0.0041485437     2771.0193814077    0.0003043525        0.2698308251     0.0008   2026-09-08 10:27:52
    67     69    0.0010842030    0.0012241262     2771.0193627758    0.0000186320        0.2643259407     0.0008   2026-09-08 10:27:52
    68     70    0.0013168414    0.0014920422     2771.0193283518    0.0000344239        0.2486383623     0.0008   2026-09-08 10:27:52
    69     71    0.0016789741    0.0019400622     2771.0192516498    0.0000767021        0.2057066150     0.0008   2026-09-08 10:27:52
    70     72    0.0010995007    0.0014707845     2771.0191241984    0.0001274513        0.1215690124     0.0009   2026-09-08 10:27:52
    71     73    0.0009412823    0.0013601904     2771.0189952036    0.0001289948        0.0784850475     0.0009   2026-09-08 10:27:52
    72     74    0.0023219447    0.0026260186     2771.0189383448    0.0000568588        0.0311751488     0.0009   2026-09-08 10:27:52
    73     75    0.0012421190    0.0013972158     2771.0189295900    0.0000087548        0.0235547823     0.0011   2026-09-08 10:27:52
    74     76    0.0001965486    0.0002292402     2771.0189290305    0.0000005595        0.0255777256     0.0010   2026-09-08 10:27:52
    75     77    0.0000323529    0.0000420418     2771.0189288325    0.0000001979        0.0260455807     0.0008   2026-09-08 10:27:52
    76     78    0.0000635284    0.0000896781     2771.0189281076    0.0000007249        0.0257212671     0.0008   2026-09-08 10:27:52
    77     79    0.0000486641    0.0000831782     2771.0189269514    0.0000011562        0.0222341843     0.0009   2026-09-08 10:27:52
    78     80    0.0000734518    0.0000999110     2771.0189253466    0.0000016048        0.0131611652     0.0008   2026-09-08 10:27:52
    79     81    0.0000817705    0.0001307784     2771.0189243577    0.0000009889        0.0074440735     0.0007   2026-09-08 10:27:52
    80     82    0.0000661306    0.0000899915     2771.0189241155    0.0000002422        0.0023472389     0.0008   2026-09-08 10:27:52

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','6.679077e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -1.8027***  0.5323   0.0007   
TC/100 EUR                        -0.6021***  0.2325   0.0096   
PC1                                0.0996     0.0952   0.2958   
PC2                                0.1377***  0.0436   0.0016   
PC3                                0.2511***  0.0951   0.0083   
Household income (10k PLN)         0.2648***  0.1020   0.0094   
Male                               0.1160     0.0722   0.1079   
Higher education                   0.0247     0.0802   0.7584   
City                               0.0951     0.0744   0.2017   
Winter                             0.8389***  0.0841   0.0000   
Hiking                             2.0847***  0.0789   0.0000   
Skiing                             1.3978***  0.2667   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3427     0.0925            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.6608***  0.6413   0.0096   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2771.0189
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1682
AIC/n:                             0.9510
BIC/n:                             0.9658
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.2499
median                           0.0000          2.2582
std                              0.7834          0.9431
min                              0.0000          0.0340
max                             20.0000          4.5242
quantile 0.025                   0.0000          0.6513
quantile 0.975                   2.0000          3.9440
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:53
Estimation took 0.14832 seconds (0 hours 0 minutes 0.14832 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.05 -0.00014 0.021 0.086 0.062 0.0093 0.0053 0.0063 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.2346978410             NaN     3303.3164992098     0.0001   2026-09-08 10:27:53
     1      3    0.3814839230    0.4513229185     3190.5517570207  737.6829408202      385.7909870755     0.0024   2026-09-08 10:27:53
     2      4    0.0406252640    0.0586512567     3160.1854630372   30.3662939835      375.6883136554     0.0012   2026-09-08 10:27:53
     3      5    0.3444265577    0.4544361136     3032.2036066424  127.9818563948      529.4717203531     0.0012   2026-09-08 10:27:53
     4      6    0.1803002714    0.2280215415     2968.9547976020   63.2488090404      504.5522410511     0.0012   2026-09-08 10:27:53
     5      7    0.5440418331    0.6830833175     2841.5819276836  127.3728699184      221.0632705838     0.0013   2026-09-08 10:27:53
     6      8    0.2101972232    0.2598919170     2820.5659376422   21.0159900414      218.6097753951     0.0009   2026-09-08 10:27:53
     7      9    0.1642614575    0.2032434794     2808.3009586818   12.2649789604      189.3302244709     0.0011   2026-09-08 10:27:53
     8     10    0.1279360010    0.1659863036     2797.6943279672   10.6066307145      135.7505049163     0.0012   2026-09-08 10:27:53
     9     11    0.0864279277    0.1312910765     2788.2005131231    9.4938148442       90.6939915690     0.0012   2026-09-08 10:27:53
    10     12    0.0651188983    0.0731965045     2784.2163377693    3.9841753538       43.1445226861     0.0010   2026-09-08 10:27:53
    11     13    0.0448652368    0.0585406697     2783.3293630548    0.8869747144       16.5508252173     0.0009   2026-09-08 10:27:53
    12     14    0.0246412824    0.0306701821     2783.0815033773    0.2478596775       15.2807471495     0.0011   2026-09-08 10:27:53
    13     15    0.0174944574    0.0234179158     2782.8201349051    0.2613684722       15.9504684996     0.0009   2026-09-08 10:27:53
    14     16    0.0251959880    0.0428600227     2782.1784501437    0.6416847614       25.7145358563     0.0009   2026-09-08 10:27:53
    15     17    0.0334030679    0.0675471588     2781.0860678439    1.0923822998       32.4108752661     0.0013   2026-09-08 10:27:53
    16     18    0.0447089514    0.0912953750     2779.8379010460    1.2481667979       26.5825464440     0.0011   2026-09-08 10:27:53
    17     19    0.0321080848    0.0685314689     2779.2042835384    0.6336175076       11.5577588391     0.0012   2026-09-08 10:27:53
    18     20    0.0218481487    0.0282863621     2779.0640311938    0.1402523446       11.6386359933     0.0011   2026-09-08 10:27:53
    19     21    0.0074219563    0.0098297547     2779.0246021069    0.0394290869       11.6881382759     0.0013   2026-09-08 10:27:53
    20     22    0.0092368198    0.0131937784     2778.9500516059    0.0745505010       11.7229395529     0.0012   2026-09-08 10:27:53
    21     23    0.0160909615    0.0251823941     2778.7724977878    0.1775538181       15.7712827719     0.0014   2026-09-08 10:27:53
    22     24    0.0458838817    0.0557096663     2778.3691925751    0.4033052127       24.9364230558     0.0014   2026-09-08 10:27:53
    23     25    0.1044360392    0.1168358891     2777.5899186773    0.7792738978       33.4335401122     0.0010   2026-09-08 10:27:53
    24     26    0.1658270648    0.1818769735     2776.5379677694    1.0519509079       32.9506570069     0.0011   2026-09-08 10:27:53
    25     27    0.1376084476    0.1538383086     2775.7634087691    0.7745590004       19.0059667233     0.0012   2026-09-08 10:27:53
    26     28    0.0343457054    0.0505239873     2775.4778602456    0.2855485234       12.0082889460     0.0008   2026-09-08 10:27:53
    27     29    0.0115553582    0.0186528150     2775.3968816441    0.0809786015        9.6934812369     0.0011   2026-09-08 10:27:53
    28     30    0.0081554017    0.0150370548     2775.3104495346    0.0864321095       10.2908256016     0.0010   2026-09-08 10:27:53
    29     31    0.0143623720    0.0238036120     2775.0768356205    0.2336139141       14.6532465539     0.0009   2026-09-08 10:27:53
    30     32    0.0390861479    0.0533374229     2774.6106643861    0.4661712344       26.0017826501     0.0012   2026-09-08 10:27:53
    31     33    0.1195879618    0.1314913330     2773.8428010342    0.7678633519       33.4420962242     0.0013   2026-09-08 10:27:53
    32     34    0.1716065794    0.1805634632     2773.1499208180    0.6928802162       25.9515423475     0.0012   2026-09-08 10:27:53
    33     35    0.1009080535    0.1062712915     2772.8774174786    0.2725033393        9.9554942326     0.0011   2026-09-08 10:27:53
    34     36    0.0142472413    0.0198554353     2772.8315606365    0.0458568421        4.4935732218     0.0012   2026-09-08 10:27:53
    35     37    0.0038586888    0.0060624179     2772.8225077421    0.0090528944        4.0775694022     0.0012   2026-09-08 10:27:53
    36     38    0.0053956808    0.0076568903     2772.8078000872    0.0147076549        4.3444760176     0.0009   2026-09-08 10:27:53
    37     39    0.0055283785    0.0107797241     2772.7754717495    0.0323283377        8.1386703886     0.0009   2026-09-08 10:27:53
    38     40    0.0094506725    0.0159554112     2772.7199641121    0.0555076374       11.2171945111     0.0012   2026-09-08 10:27:53
    39     41    0.0161259299    0.0255939463     2772.6587476086    0.0612165035       10.0443214167     0.0011   2026-09-08 10:27:53
    40     42    0.0182095422    0.0245996096     2772.6272296158    0.0315179928        4.7240763628     0.0012   2026-09-08 10:27:53
    41     43    0.0084467358    0.0102833547     2772.6207184486    0.0065111671        1.3275819438     0.0010   2026-09-08 10:27:53
    42     44    0.0015452743    0.0023491340     2772.6194772409    0.0012412078        1.6186444653     0.0010   2026-09-08 10:27:53
    43     45    0.0010898200    0.0020752005     2772.6177959591    0.0016812817        1.8611049961     0.0010   2026-09-08 10:27:53
    44     46    0.0021233542    0.0038042170     2772.6135691146    0.0042268445        2.6029034055     0.0009   2026-09-08 10:27:53
    45     47    0.0041624439    0.0071813606     2772.6047989201    0.0087701945        4.4056971416     0.0011   2026-09-08 10:27:53
    46     48    0.0085527208    0.0132274194     2772.5899606613    0.0148382589        5.5299528987     0.0010   2026-09-08 10:27:53
    47     49    0.0107030569    0.0165019801     2772.5746875666    0.0152730947        4.2921430507     0.0009   2026-09-08 10:27:53
    48     50    0.0061651800    0.0105971348     2772.5668879672    0.0077995994        2.0019440279     0.0012   2026-09-08 10:27:53
    49     51    0.0015762831    0.0034342272     2772.5645330845    0.0023548828        1.5953821921     0.0010   2026-09-08 10:27:53
    50     52    0.0012590513    0.0018760095     2772.5628403286    0.0016927558        1.4283326813     0.0009   2026-09-08 10:27:53
    51     53    0.0021789846    0.0035120811     2772.5585707128    0.0042696158        3.0072908725     0.0009   2026-09-08 10:27:53
    52     54    0.0064949823    0.0083342524     2772.5483931187    0.0101775941        5.3062859952     0.0010   2026-09-08 10:27:53
    53     55    0.0199338728    0.0229643726     2772.5237349868    0.0246581319        8.5695620977     0.0009   2026-09-08 10:27:53
    54     56    0.0483645204    0.0544114849     2772.4727959998    0.0509389870       11.9760235718     0.0012   2026-09-08 10:27:53
    55     57    0.0869459473    0.0975480143     2772.3939014197    0.0788945800       12.7992854549     0.0009   2026-09-08 10:27:53
    56     58    0.0897092773    0.1013488753     2772.3235943273    0.0703070925        8.3058886401     0.0008   2026-09-08 10:27:53
    57     59    0.0354311905    0.0416846572     2772.2939069075    0.0296874197        5.0601272114     0.0009   2026-09-08 10:27:53
    58     60    0.0039986366    0.0055929723     2772.2850773776    0.0088295300        5.0291448166     0.0008   2026-09-08 10:27:53
    59     61    0.0031651126    0.0053298455     2772.2766381209    0.0084392567        4.7937609113     0.0012   2026-09-08 10:27:53
    60     62    0.0044415705    0.0078880910     2772.2555048214    0.0211332994        5.3062372325     0.0012   2026-09-08 10:27:53
    61     63    0.0223143825    0.0281196961     2772.2126359549    0.0428688665        8.2689631365     0.0012   2026-09-08 10:27:53
    62     64    0.0659986497    0.0761219268     2772.1426776579    0.0699582970        9.6565981757     0.0009   2026-09-08 10:27:53
    63     65    0.0959682917    0.1083383570     2772.0784527132    0.0642249447        6.8865753873     0.0011   2026-09-08 10:27:53
    64     66    0.0586250573    0.0657228184     2772.0531047079    0.0253480053        2.2845530304     0.0010   2026-09-08 10:27:53
    65     67    0.0072311903    0.0091082706     2772.0497269749    0.0033777330        0.2300375425     0.0009   2026-09-08 10:27:53
    66     68    0.0029053473    0.0035053426     2772.0495820980    0.0001448769        0.1701301741     0.0009   2026-09-08 10:27:53
    67     69    0.0007242065    0.0008265002     2772.0495729840    0.0000091140        0.1623254453     0.0011   2026-09-08 10:27:53
    68     70    0.0010940944    0.0012550961     2772.0495517440    0.0000212400        0.1437189208     0.0012   2026-09-08 10:27:53
    69     71    0.0011984070    0.0014101426     2772.0495097119    0.0000420321        0.1065479927     0.0012   2026-09-08 10:27:53
    70     72    0.0006166855    0.0009309074     2772.0494428433    0.0000668686        0.0851268826     0.0010   2026-09-08 10:27:53
    71     73    0.0009763801    0.0012298876     2772.0493847286    0.0000581147        0.0509247933     0.0012   2026-09-08 10:27:53
    72     74    0.0016364588    0.0018579629     2772.0493634413    0.0000212873        0.0220170517     0.0010   2026-09-08 10:27:53
    73     75    0.0006938723    0.0007903905     2772.0493608215    0.0000026199        0.0173620625     0.0009   2026-09-08 10:27:53
    74     76    0.0000864403    0.0001037667     2772.0493606581    0.0000001634        0.0185419584     0.0013   2026-09-08 10:27:53
    75     77    0.0000223290    0.0000295038     2772.0493605636    0.0000000945        0.0187330932     0.0012   2026-09-08 10:27:53
    76     78    0.0000416259    0.0000591749     2772.0493602422    0.0000003213        0.0178920654     0.0013   2026-09-08 10:27:53
    77     79    0.0000326455    0.0000549889     2772.0493597378    0.0000005044        0.0145245306     0.0012   2026-09-08 10:27:53
    78     80    0.0000559598    0.0000655816     2772.0493590980    0.0000006398        0.0074841689     0.0012   2026-09-08 10:27:53
    79     81    0.0000538916    0.0000816743     2772.0493587488    0.0000003492        0.0033954052     0.0012   2026-09-08 10:27:53
    80     82    0.0000359358    0.0000498462     2772.0493586759    0.0000000729        0.0009267959     0.0012   2026-09-08 10:27:53

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','2.804804e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -1.8078***  0.5381   0.0008   
TC/100 EUR                        -0.6364**   0.2479   0.0103   
PC1                                0.1238     0.1000   0.2157   
PC2                                0.1504***  0.0420   0.0003   
PC3                                0.2827***  0.1040   0.0066   
Household income (10k PLN)         0.2637***  0.1019   0.0097   
Male                               0.1196*    0.0722   0.0976   
Higher education                   0.0260     0.0802   0.7458   
City                               0.0965     0.0744   0.1944   
Winter                             0.8463***  0.0841   0.0000   
Hiking                             2.0877***  0.0788   0.0000   
Skiing                             1.4106***  0.2665   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3427     0.0923            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.5713**   0.6121   0.0103   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2772.0494
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1679
AIC/n:                             0.9513
BIC/n:                             0.9662
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1226
median                           0.0000          2.1322
std                              0.7834          0.9278
min                              0.0000          0.0266
max                             20.0000          5.0512
quantile 0.025                   0.0000          0.5807
quantile 0.975                   2.0000          3.9862
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:54
Estimation took 0.16165 seconds (0 hours 0 minutes 0.16165 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.61 -0.04 -0.005 0.019 0.085 0.063 0.0092 0.0054 0.0063 0.18 0.44 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3928.2346668716             NaN     3296.0795252289     0.0000   2026-09-08 10:27:54
     1      3    0.3829391694    0.4534125389     3188.0681779550  740.1664889166      386.6728446027     0.0024   2026-09-08 10:27:54
     2      4    0.0410329245    0.0582846592     3158.1654739460   29.9027040090      375.4856985368     0.0013   2026-09-08 10:27:54
     3      5    0.3674646004    0.4811273965     3024.5716261377  133.5938478083      529.8307828909     0.0009   2026-09-08 10:27:54
     4      6    0.1816666044    0.2294887893     2960.9374928314   63.6341333063      490.5346741780     0.0012   2026-09-08 10:27:54
     5      7    0.5329397260    0.6689286216     2838.2992372173  122.6382556141      217.1848241050     0.0009   2026-09-08 10:27:54
     6      8    0.2059625170    0.2546702296     2818.3650675295   19.9341696878      213.0778762350     0.0013   2026-09-08 10:27:54
     7      9    0.1616436533    0.2002765963     2806.6051084093   11.7599591202      183.4154838663     0.0011   2026-09-08 10:27:54
     8     10    0.1249509837    0.1628355510     2796.4257149390   10.1793934703      130.2954671671     0.0009   2026-09-08 10:27:54
     9     11    0.0855602481    0.1271890745     2787.3915503478    9.0341645912       84.4874844502     0.0013   2026-09-08 10:27:54
    10     12    0.0628320949    0.0720935422     2783.6601151492    3.7314351987       38.7625614366     0.0013   2026-09-08 10:27:54
    11     13    0.0446328031    0.0579264507     2782.8269077622    0.8332073870       16.5042275011     0.0012   2026-09-08 10:27:54
    12     14    0.0243734960    0.0303807898     2782.5824663414    0.2444414207       15.1321738881     0.0012   2026-09-08 10:27:54
    13     15    0.0181608360    0.0243725615     2782.3087735377    0.2736928037       16.4149016880     0.0013   2026-09-08 10:27:54
    14     16    0.0257476269    0.0441983350     2781.6444947213    0.6642788164       26.3152328345     0.0012   2026-09-08 10:27:54
    15     17    0.0336955973    0.0691611314     2780.5275200346    1.1169746867       32.7462782062     0.0012   2026-09-08 10:27:54
    16     18    0.0446196859    0.0917440829     2779.2874262156    1.2400938190       26.1513770159     0.0010   2026-09-08 10:27:54
    17     19    0.0330800159    0.0675272740     2778.6794423878    0.6079838278       11.5697893175     0.0010   2026-09-08 10:27:54
    18     20    0.0214458394    0.0275902317     2778.5473972742    0.1320451136       11.6518757261     0.0011   2026-09-08 10:27:54
    19     21    0.0073008181    0.0096712548     2778.5077022914    0.0396949828       11.6997261298     0.0014   2026-09-08 10:27:54
    20     22    0.0096388578    0.0138409255     2778.4274471457    0.0802551457       11.7338923488     0.0013   2026-09-08 10:27:54
    21     23    0.0171279480    0.0261821081     2778.2400947151    0.1873524306       16.3423193267     0.0011   2026-09-08 10:27:54
    22     24    0.0485758785    0.0586335089     2777.8137850564    0.4263096587       25.5526428919     0.0010   2026-09-08 10:27:54
    23     25    0.1086955100    0.1217293818     2777.0025553346    0.8112297217       33.7176612824     0.0009   2026-09-08 10:27:54
    24     26    0.1685030390    0.1854614728     2775.9333562884    1.0691990462       32.4043223409     0.0009   2026-09-08 10:27:54
    25     27    0.1336207139    0.1501916028     2775.1747323629    0.7586239255       17.9515405446     0.0009   2026-09-08 10:27:54
    26     28    0.0298422168    0.0461408304     2774.9042455995    0.2704867634       11.6571528583     0.0009   2026-09-08 10:27:54
    27     29    0.0108025697    0.0182126040     2774.8255117250    0.0787338745        9.5324479774     0.0008   2026-09-08 10:27:54
    28     30    0.0083197567    0.0155853729     2774.7324589635    0.0930527615       10.5128049898     0.0009   2026-09-08 10:27:54
    29     31    0.0148036236    0.0245976063     2774.4851592058    0.2472997576       16.2464726860     0.0008   2026-09-08 10:27:54
    30     32    0.0425805931    0.0571816361     2773.9916358788    0.4935233270       27.7310629359     0.0008   2026-09-08 10:27:54
    31     33    0.1252390202    0.1378689045     2773.1999496431    0.7916862357       34.2458260560     0.0008   2026-09-08 10:27:54
    32     34    0.1725045151    0.1821295349     2772.5153419413    0.6846077019       25.2219104988     0.0008   2026-09-08 10:27:54
    33     35    0.0955802947    0.1012027306     2772.2609174683    0.2544244730        8.9653213159     0.0008   2026-09-08 10:27:54
    34     36    0.0118836314    0.0178277360     2772.2198514729    0.0410659954        4.4792506623     0.0008   2026-09-08 10:27:54
    35     37    0.0037284977    0.0058854569     2772.2109107255    0.0089407473        4.1004228744     0.0008   2026-09-08 10:27:54
    36     38    0.0056162288    0.0082257148     2772.1943142276    0.0165964979        4.6183966366     0.0008   2026-09-08 10:27:54
    37     39    0.0055381282    0.0112126654     2772.1592363486    0.0350778790        8.2727926297     0.0008   2026-09-08 10:27:54
    38     40    0.0103217440    0.0172422558     2772.0993210185    0.0599153301       11.0632823617     0.0008   2026-09-08 10:27:54
    39     41    0.0168483463    0.0269627415     2772.0364461484    0.0628748700        9.4800963111     0.0008   2026-09-08 10:27:54
    40     42    0.0179672970    0.0245647337     2772.0059766728    0.0304694756        4.2061448896     0.0009   2026-09-08 10:27:54
    41     43    0.0076998214    0.0096390211     2772.0000020104    0.0059746624        1.5180110754     0.0010   2026-09-08 10:27:54
    42     44    0.0014371178    0.0022940117     2771.9986799896    0.0013220208        1.7902721345     0.0009   2026-09-08 10:27:54
    43     45    0.0012048885    0.0024975454     2771.9964783563    0.0022016333        2.0698725743     0.0009   2026-09-08 10:27:54
    44     46    0.0022659357    0.0044543459     2771.9911836773    0.0052946791        2.8522058688     0.0009   2026-09-08 10:27:54
    45     47    0.0053628106    0.0086892909     2771.9800199495    0.0111637277        4.7693168602     0.0009   2026-09-08 10:27:54
    46     48    0.0106297067    0.0157106388     2771.9615726914    0.0184472582        5.8746981507     0.0009   2026-09-08 10:27:54
    47     49    0.0128503724    0.0191113465     2771.9430205836    0.0185521078        4.4297290379     0.0010   2026-09-08 10:27:54
    48     50    0.0069864860    0.0117749905     2771.9338053206    0.0092152629        2.1548665419     0.0012   2026-09-08 10:27:54
    49     51    0.0017388296    0.0038051641     2771.9309247620    0.0028805586        1.7065884194     0.0009   2026-09-08 10:27:54
    50     52    0.0014171134    0.0022691097     2771.9285985916    0.0023261704        1.6753147765     0.0008   2026-09-08 10:27:54
    51     53    0.0025155797    0.0044015488     2771.9226188871    0.0059797046        3.4838610784     0.0012   2026-09-08 10:27:54
    52     54    0.0084328116    0.0107123228     2771.9083689156    0.0142499715        6.1249938967     0.0011   2026-09-08 10:27:54
    53     55    0.0256305439    0.0294922996     2771.8741332021    0.0342357135        9.8265509485     0.0010   2026-09-08 10:27:54
    54     56    0.0610966309    0.0687314967     2771.8048039122    0.0693292899       13.5160435727     0.0010   2026-09-08 10:27:54
    55     57    0.1057555557    0.1185931718     2771.7019141297    0.1028897825       13.9433721081     0.0010   2026-09-08 10:27:54
    56     58    0.1014582922    0.1145256453     2771.6166834301    0.0852306996        8.4876263662     0.0009   2026-09-08 10:27:54
    57     59    0.0346778087    0.0411007312     2771.5837388087    0.0329446215        5.4522642329     0.0008   2026-09-08 10:27:54
    58     60    0.0040609374    0.0062925548     2771.5739955840    0.0097432246        5.4369332462     0.0009   2026-09-08 10:27:54
    59     61    0.0041484837    0.0064994466     2771.5635360552    0.0104595288        5.1966372520     0.0010   2026-09-08 10:27:54
    60     62    0.0048150913    0.0088444125     2771.5376056109    0.0259304443        5.7710445947     0.0010   2026-09-08 10:27:54
    61     63    0.0250519437    0.0315491801     2771.4865391959    0.0510664150        8.7088854459     0.0009   2026-09-08 10:27:54
    62     64    0.0710709218    0.0820079762     2771.4093046221    0.0772345738        9.5448473425     0.0010   2026-09-08 10:27:54
    63     65    0.0943179532    0.1066371960     2771.3468960233    0.0624085988        6.1112312181     0.0010   2026-09-08 10:27:54
    64     66    0.0497189948    0.0559706595     2771.3262339095    0.0206621137        1.7268439067     0.0009   2026-09-08 10:27:54
    65     67    0.0040695939    0.0059731222     2771.3239818038    0.0022521058        0.2045636002     0.0013   2026-09-08 10:27:54
    66     68    0.0023736818    0.0028340113     2771.3238973738    0.0000844300        0.1760342431     0.0011   2026-09-08 10:27:54
    67     69    0.0005815823    0.0006689769     2771.3238863221    0.0000110517        0.1681405228     0.0010   2026-09-08 10:27:54
    68     70    0.0014829808    0.0017229135     2771.3238425047    0.0000438174        0.1385321720     0.0010   2026-09-08 10:27:54
    69     71    0.0011609132    0.0014248020     2771.3237741065    0.0000683982        0.1084524608     0.0009   2026-09-08 10:27:54
    70     72    0.0004771765    0.0007982015     2771.3236767173    0.0000973891        0.0900695096     0.0009   2026-09-08 10:27:54
    71     73    0.0015507387    0.0018292851     2771.3236161025    0.0000606148        0.0413393624     0.0008   2026-09-08 10:27:54
    72     74    0.0014857690    0.0016932221     2771.3236008451    0.0000152574        0.0247970654     0.0008   2026-09-08 10:27:54
    73     75    0.0003988212    0.0004618304     2771.3235995917    0.0000012534        0.0202693536     0.0009   2026-09-08 10:27:54
    74     76    0.0000382250    0.0000493975     2771.3235994542    0.0000001375        0.0211955257     0.0008   2026-09-08 10:27:54
    75     77    0.0000365738    0.0000518409     2771.3235991878    0.0000002664        0.0216476356     0.0008   2026-09-08 10:27:54
    76     78    0.0000390157    0.0000635023     2771.3235986319    0.0000005559        0.0203468442     0.0008   2026-09-08 10:27:54
    77     79    0.0000430445    0.0000686563     2771.3235977356    0.0000008963        0.0150833561     0.0010   2026-09-08 10:27:54
    78     80    0.0000715017    0.0000880600     2771.3235968983    0.0000008372        0.0064554525     0.0010   2026-09-08 10:27:54
    79     81    0.0000563360    0.0000876130     2771.3235965642    0.0000003342        0.0028110164     0.0009   2026-09-08 10:27:54

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','8.525777e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -1.9096***  0.5380   0.0004   
TC/100 EUR                        -0.5913**   0.2485   0.0173   
PC1                                0.1000     0.1003   0.3185   
PC2                                0.1421***  0.0423   0.0008   
PC3                                0.2740***  0.1044   0.0087   
Household income (10k PLN)         0.2666***  0.1020   0.0090   
Male                               0.1184     0.0722   0.1009   
Higher education                   0.0254     0.0802   0.7518   
City                               0.0965     0.0744   0.1947   
Winter                             0.8464***  0.0841   0.0000   
Hiking                             2.0874***  0.0789   0.0000   
Skiing                             1.4104***  0.2664   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3431     0.0923            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    1.6912**   0.7106   0.0173   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2771.3236
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1681
AIC/n:                             0.9511
BIC/n:                             0.9659
n (observations):               5855
r (respondents):                5855
k (parameters):                   13
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1162
median                           0.0000          2.1210
std                              0.7834          0.9249
min                              0.0000          0.0269
max                             20.0000          5.1370
quantile 0.025                   0.0000          0.5722
quantile 0.975                   2.0000          3.9713
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:55
Estimation took 0.1468 seconds (0 hours 0 minutes 0.1468 seconds).

====================================================
MS: closest (minimum cost) substitute
====================================================
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.57 -0.06 -0.0042 0.058 0.01 0.0033 -0.004 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.6386321699             NaN     2682.5023623804     0.0000   2026-09-08 10:27:55
     1      3    0.3593550680    0.4852636541     3191.2098566733  743.4287754966      428.4516633095     0.0018   2026-09-08 10:27:55
     2      4    0.0520295868    0.0611407660     3161.8940080452   29.3158486282      388.6687052540     0.0008   2026-09-08 10:27:55
     3      5    0.5608520406    0.6542772652     2988.6678082822  173.2261997630      438.1376015453     0.0012   2026-09-08 10:27:55
     4      6    0.2313952984    0.2835307538     2932.8031407905   55.8646674917      335.2917811659     0.0010   2026-09-08 10:27:55
     5      7    0.3250598805    0.4187592046     2876.5153777606   56.2877630299      166.6317200308     0.0008   2026-09-08 10:27:55
     6      8    0.1152145751    0.1557201881     2867.3981836226    9.1171941380      107.0391717047     0.0008   2026-09-08 10:27:55
     7      9    0.0652935241    0.0936025298     2863.3100813826    4.0881022400       88.9062997176     0.0008   2026-09-08 10:27:55
     8     10    0.0804943561    0.1295892736     2856.9581555019    6.3519258807      135.5415659919     0.0007   2026-09-08 10:27:55
     9     11    0.1616567980    0.2281820849     2844.9273042484   12.0308512536      172.4484867721     0.0008   2026-09-08 10:27:55
    10     12    0.2361482223    0.3123596599     2828.8909484054   16.0363558430      159.7357124782     0.0010   2026-09-08 10:27:55
    11     13    0.1939206100    0.2611080608     2817.1930760140   11.6978723914       82.5570402643     0.0012   2026-09-08 10:27:55
    12     14    0.0616986861    0.1040373747     2813.3579271177    3.8351488962       44.1121545045     0.0011   2026-09-08 10:27:55
    13     15    0.0469984834    0.0675480321     2812.0759147745    1.2820123432       31.4440868062     0.0009   2026-09-08 10:27:55
    14     16    0.0352055519    0.0607035994     2810.9217291803    1.1541855942       42.6434898414     0.0008   2026-09-08 10:27:55
    15     17    0.0388213084    0.0803742293     2808.6195359267    2.3021932536       55.7627725195     0.0009   2026-09-08 10:27:55
    16     18    0.0724571775    0.1425948990     2803.8752529764    4.7442829504       67.1962985622     0.0009   2026-09-08 10:27:55
    17     19    0.1688137427    0.2373287882     2797.5643029719    6.3109500044       57.1025361430     0.0008   2026-09-08 10:27:55
    18     20    0.2135087126    0.2557882096     2793.1270434691    4.4372595028       26.0440382478     0.0007   2026-09-08 10:27:55
    19     21    0.1018600809    0.1289640048     2791.9292849864    1.1977584827       13.7966720462     0.0008   2026-09-08 10:27:55
    20     22    0.0172351288    0.0296941494     2791.7794025358    0.1498824506       12.6269654007     0.0008   2026-09-08 10:27:55
    21     23    0.0092798321    0.0166299279     2791.6583565736    0.1210459622       13.9088260288     0.0008   2026-09-08 10:27:55
    22     24    0.0184423429    0.0374390479     2791.2946032482    0.3637533254       15.5835325433     0.0009   2026-09-08 10:27:55
    23     25    0.0272131651    0.0617910591     2790.6321511011    0.6624521471       16.0179184006     0.0007   2026-09-08 10:27:55
    24     26    0.0564897371    0.1022878423     2789.6368773817    0.9952737195       16.1886088791     0.0007   2026-09-08 10:27:55
    25     27    0.0592672000    0.0992343181     2788.8779141350    0.7589632466       11.0187216227     0.0008   2026-09-08 10:27:55
    26     28    0.0232932779    0.0481876339     2788.6114023587    0.2665117763        9.0295812780     0.0008   2026-09-08 10:27:55
    27     29    0.0097269865    0.0174547855     2788.5554507486    0.0559516100        8.9326512353     0.0008   2026-09-08 10:27:55
    28     30    0.0049968073    0.0097635578     2788.5187568653    0.0366938834        8.8694983928     0.0008   2026-09-08 10:27:55
    29     31    0.0097793896    0.0191430679     2788.4115773648    0.1071795005        8.6606485559     0.0008   2026-09-08 10:27:55
    30     32    0.0221447163    0.0341165491     2788.1847232354    0.2268541293        8.1610913683     0.0008   2026-09-08 10:27:55
    31     33    0.0623569192    0.0750340909     2787.7375186379    0.4472045975       10.1129148804     0.0007   2026-09-08 10:27:55
    32     34    0.1049185674    0.1206691047     2787.1728811482    0.5646374897       11.7997440497     0.0007   2026-09-08 10:27:55
    33     35    0.0900556352    0.1077800040     2786.8019553013    0.3709258469        8.4908352492     0.0007   2026-09-08 10:27:55
    34     36    0.0269852487    0.0414112802     2786.6909237972    0.1110315041        7.7669255965     0.0007   2026-09-08 10:27:55
    35     37    0.0066771623    0.0119733712     2786.6554123530    0.0355114442        7.2575442670     0.0008   2026-09-08 10:27:55
    36     38    0.0072690054    0.0124952152     2786.6019258067    0.0534865463        6.5951291934     0.0008   2026-09-08 10:27:55
    37     39    0.0119199398    0.0234138609     2786.4764762610    0.1254495456        6.1647938559     0.0008   2026-09-08 10:27:55
    38     40    0.0391252483    0.0499022703     2786.2339013697    0.2425748913        6.4083230141     0.0009   2026-09-08 10:27:55
    39     41    0.0777707516    0.0888015519     2785.9002459961    0.3336553736        8.5786131887     0.0012   2026-09-08 10:27:55
    40     42    0.0776421188    0.0879564477     2785.6629957447    0.2372502514        6.8359906535     0.0012   2026-09-08 10:27:55
    41     43    0.0270647183    0.0358850578     2785.5920432560    0.0709524887        3.6980482103     0.0012   2026-09-08 10:27:55
    42     44    0.0052467988    0.0085269707     2785.5794431807    0.0126000753        3.5044702852     0.0014   2026-09-08 10:27:55
    43     45    0.0030805049    0.0053309606     2785.5703961552    0.0090470255        3.5449160385     0.0011   2026-09-08 10:27:55
    44     46    0.0061038137    0.0097924541     2785.5454254696    0.0249706857        3.3295165327     0.0016   2026-09-08 10:27:55
    45     47    0.0080189599    0.0148720358     2785.4996251045    0.0458003651        2.9962232879     0.0015   2026-09-08 10:27:55
    46     48    0.0170184944    0.0271606136     2785.4327290793    0.0668960252        3.3647252052     0.0011   2026-09-08 10:27:55
    47     49    0.0241330163    0.0317073986     2785.3829395154    0.0497895639        3.1798137035     0.0012   2026-09-08 10:27:55
    48     50    0.0137203261    0.0179652806     2785.3664826283    0.0164568870        1.9468120001     0.0012   2026-09-08 10:27:55
    49     51    0.0028819028    0.0051191929     2785.3627894866    0.0036931417        2.0150504179     0.0009   2026-09-08 10:27:55
    50     52    0.0021938415    0.0033446643     2785.3592242184    0.0035652682        2.0811116792     0.0009   2026-09-08 10:27:55
    51     53    0.0040133367    0.0065576482     2785.3496822230    0.0095419954        2.1333483089     0.0009   2026-09-08 10:27:55
    52     54    0.0077521098    0.0123538387     2785.3299458686    0.0197363544        2.0559472321     0.0008   2026-09-08 10:27:55
    53     55    0.0142787977    0.0235048208     2785.2955381785    0.0344076901        2.4675950870     0.0007   2026-09-08 10:27:55
    54     56    0.0189590425    0.0295649733     2785.2601974102    0.0353407683        2.4914000957     0.0007   2026-09-08 10:27:55
    55     57    0.0113169712    0.0182800282     2785.2436161029    0.0165813073        1.3679173246     0.0007   2026-09-08 10:27:55
    56     58    0.0034292652    0.0050788800     2785.2406922584    0.0029238445        1.0345990101     0.0007   2026-09-08 10:27:55
    57     59    0.0011449223    0.0019273111     2785.2402681236    0.0004241348        1.0309998359     0.0007   2026-09-08 10:27:55
    58     60    0.0009181169    0.0016577812     2785.2397635806    0.0005045430        0.9924382194     0.0008   2026-09-08 10:27:55
    59     61    0.0013493811    0.0024854892     2785.2385286543    0.0012349263        0.8530817405     0.0008   2026-09-08 10:27:55
    60     62    0.0022498828    0.0030470906     2785.2365499235    0.0019787308        0.5636190397     0.0008   2026-09-08 10:27:55
    61     63    0.0029793345    0.0047845906     2785.2345056406    0.0020442829        0.3748341053     0.0008   2026-09-08 10:27:55
    62     64    0.0028322421    0.0046051518     2785.2336110016    0.0008946390        0.1792752746     0.0008   2026-09-08 10:27:55
    63     65    0.0011442165    0.0018598100     2785.2334732921    0.0001377095        0.0311711039     0.0008   2026-09-08 10:27:55
    64     66    0.0001565691    0.0002867923     2785.2334670971    0.0000061950        0.0121718859     0.0007   2026-09-08 10:27:55
    65     67    0.0000263126    0.0000380055     2785.2334669840    0.0000001131        0.0105590218     0.0007   2026-09-08 10:27:55
    66     68    0.0000072983    0.0000116001     2785.2334669399    0.0000000441        0.0099208013     0.0007   2026-09-08 10:27:55
    67     69    0.0000229361    0.0000382832     2785.2334667354    0.0000002046        0.0087174506     0.0007   2026-09-08 10:27:55
    68     70    0.0000231496    0.0000359023     2785.2334664822    0.0000002532        0.0068706158     0.0008   2026-09-08 10:27:55
    69     71    0.0000260538    0.0000419980     2785.2334662271    0.0000002551        0.0032471863     0.0007   2026-09-08 10:27:55
    70     72    0.0000176215    0.0000334539     2785.2334661379    0.0000000892        0.0013752351     0.0007   2026-09-08 10:27:55

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.124777e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3275***  0.1240   0.0000   
TC/100 EUR                        -0.4033***  0.0937   0.0000   
closest substitute                -0.1072     0.1410   0.4472   
Household income (10k PLN)         0.2437**   0.1027   0.0176   
Male                               0.1176     0.0727   0.1060   
Higher education                   0.0131     0.0808   0.8713   
City                               0.0426     0.0741   0.5655   
Winter                             0.8526***  0.0849   0.0000   
Hiking                             2.1141***  0.0792   0.0000   
Skiing                             1.3669***  0.2697   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4045     0.0897            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.4792***  0.5759   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2785.2335
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1639
AIC/n:                             0.9552
BIC/n:                             0.9677
n (observations):               5855
r (respondents):                5855
k (parameters):                   11
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.7225
median                           0.0000          1.7321
std                              0.7834          0.7394
min                              0.0000          0.0246
max                             20.0000          3.5357
quantile 0.025                   0.0000          0.4668
quantile 0.975                   2.0000          3.0518
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:56
Estimation took 0.12375 seconds (0 hours 0 minutes 0.12375 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.056 -0.0037 0.082 0.01 0.0037 -0.004 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.0974031161             NaN     3010.4458113778     0.0001   2026-09-08 10:27:56
     1      3    0.3450712758    0.4519770360     3194.8550072193  739.2423958968      429.0389859978     0.0020   2026-09-08 10:27:56
     2      4    0.0439314482    0.0527524010     3169.2145229125   25.6404843068      388.5306503459     0.0010   2026-09-08 10:27:56
     3      5    0.3832351075    0.4469634084     3043.6828639282  125.5316589843      499.6221215240     0.0012   2026-09-08 10:27:56
     4      6    0.2387438971    0.2850474101     2980.5780108418   63.1048530863      475.4653940148     0.0010   2026-09-08 10:27:56
     5      7    0.4185755034    0.5192379553     2895.4412920347   85.1367188071      232.4930162806     0.0010   2026-09-08 10:27:56
     6      8    0.1653927694    0.2172452987     2877.0844983923   18.3567936424      150.0649366769     0.0009   2026-09-08 10:27:56
     7      9    0.0774530872    0.1088716956     2871.7271641376    5.3573342548      103.4370991635     0.0010   2026-09-08 10:27:56
     8     10    0.0514417802    0.0831500391     2867.3841771030    4.3429870345      119.5211811730     0.0010   2026-09-08 10:27:56
     9     11    0.1205683614    0.1669784611     2857.7258716739    9.6583054291      185.9384666939     0.0010   2026-09-08 10:27:56
    10     12    0.2081256451    0.2661210282     2842.2150432877   15.5108283862      221.6676772268     0.0011   2026-09-08 10:27:56
    11     13    0.2651626824    0.3310985120     2824.7216512914   17.4933919963      176.7188437432     0.0010   2026-09-08 10:27:56
    12     14    0.1442142831    0.1938955447     2815.9256885852    8.7959627062       68.3140408175     0.0009   2026-09-08 10:27:56
    13     15    0.0428982562    0.0620463709     2813.5373035022    2.3883850830       45.1767669883     0.0010   2026-09-08 10:27:56
    14     16    0.0326804943    0.0580587337     2812.4411264843    1.0961770178       37.1484388926     0.0010   2026-09-08 10:27:56
    15     17    0.0253738258    0.0550143386     2811.0942745050    1.3468519793       54.9375923122     0.0008   2026-09-08 10:27:56
    16     18    0.0515351545    0.0959801775     2807.7819866584    3.3122878466       79.1721576413     0.0007   2026-09-08 10:27:56
    17     19    0.0900769319    0.1693124083     2801.8505158014    5.9314708569       93.0420117109     0.0007   2026-09-08 10:27:56
    18     20    0.2061193950    0.2715867397     2794.7225196841    7.1279961174       71.7513290986     0.0007   2026-09-08 10:27:56
    19     21    0.2069680326    0.2393612257     2790.7159170803    4.0066026037       24.1110420529     0.0007   2026-09-08 10:27:56
    20     22    0.0755107164    0.0959408561     2789.9170370267    0.7988800536       10.9968023380     0.0007   2026-09-08 10:27:56
    21     23    0.0099967314    0.0188914477     2789.8289171381    0.0881198887        9.9631226800     0.0007   2026-09-08 10:27:56
    22     24    0.0080316803    0.0155381061     2789.7228662081    0.1060509300       10.6131543791     0.0009   2026-09-08 10:27:56
    23     25    0.0157935019    0.0317277013     2789.4319503244    0.2909158838       13.0879245994     0.0011   2026-09-08 10:27:56
    24     26    0.0253399384    0.0554134933     2788.8677859316    0.5641643928       16.7145267218     0.0007   2026-09-08 10:27:56
    25     27    0.0479570428    0.0932195552     2787.9968980612    0.8708878703       16.9467832670     0.0010   2026-09-08 10:27:56
    26     28    0.0491956832    0.0970985330     2787.2720084280    0.7248896332       11.6244313431     0.0011   2026-09-08 10:27:56
    27     29    0.0229925840    0.0505761600     2786.9934476889    0.2785607391        9.2441194875     0.0010   2026-09-08 10:27:56
    28     30    0.0093609450    0.0176669656     2786.9350785481    0.0583691409        9.1476492616     0.0011   2026-09-08 10:27:56
    29     31    0.0049360520    0.0090353737     2786.9021205288    0.0329580193        9.0913699609     0.0012   2026-09-08 10:27:56
    30     32    0.0095615703    0.0171820954     2786.8069819007    0.0951386281        8.9093201485     0.0008   2026-09-08 10:27:56
    31     33    0.0179330560    0.0297273768     2786.6020778692    0.2049040315        8.4698741181     0.0009   2026-09-08 10:27:56
    32     34    0.0546715196    0.0669296124     2786.1794387833    0.4226390859        9.2437765949     0.0009   2026-09-08 10:27:56
    33     35    0.1010401083    0.1164148189     2785.5974577617    0.5819810216       11.7616301947     0.0007   2026-09-08 10:27:56
    34     36    0.0993097255    0.1174904902     2785.1646990808    0.4327586809        9.0732633313     0.0008   2026-09-08 10:27:56
    35     37    0.0354134418    0.0505834585     2785.0254070441    0.1392920367        6.9986331387     0.0008   2026-09-08 10:27:56
    36     38    0.0073334398    0.0125364386     2784.9937724991    0.0316345450        6.5676796231     0.0008   2026-09-08 10:27:56
    37     39    0.0052776029    0.0087661787     2784.9639114330    0.0298610661        6.1870007387     0.0009   2026-09-08 10:27:56
    38     40    0.0095347204    0.0162381566     2784.8842532515    0.0796581815        5.5616241785     0.0008   2026-09-08 10:27:56
    39     41    0.0207069619    0.0314441197     2784.7214715591    0.1627816923        5.6508465351     0.0007   2026-09-08 10:27:56
    40     42    0.0567876548    0.0666236222     2784.4418017212    0.2796698379        7.6396493695     0.0008   2026-09-08 10:27:56
    41     43    0.0829184997    0.0913330259     2784.1615349459    0.2802667753        7.9863959813     0.0008   2026-09-08 10:27:56
    42     44    0.0533652022    0.0604034057     2784.0309773362    0.1305576097        5.2595469743     0.0007   2026-09-08 10:27:56
    43     45    0.0087683722    0.0159968487     2784.0029639841    0.0280133521        4.0735534643     0.0007   2026-09-08 10:27:56
    44     46    0.0036208323    0.0056193104     2783.9926492850    0.0103146991        4.1733575921     0.0007   2026-09-08 10:27:56
    45     47    0.0055767903    0.0083519911     2783.9700735082    0.0225757768        4.0823811821     0.0010   2026-09-08 10:27:56
    46     48    0.0083138881    0.0135126944     2783.9215061661    0.0485673422        3.6080808541     0.0008   2026-09-08 10:27:56
    47     49    0.0173184002    0.0277121039     2783.8309095771    0.0905965890        3.9044194241     0.0009   2026-09-08 10:27:56
    48     50    0.0339782342    0.0450303489     2783.7235748024    0.1073347747        4.6211031306     0.0009   2026-09-08 10:27:56
    49     51    0.0307877021    0.0396839958     2783.6613540823    0.0622207201        3.4936781851     0.0011   2026-09-08 10:27:56
    50     52    0.0092739596    0.0143473457     2783.6467497630    0.0146043194        1.9889242904     0.0014   2026-09-08 10:27:56
    51     53    0.0025282261    0.0035008704     2783.6436674875    0.0030822755        2.1234498476     0.0014   2026-09-08 10:27:56
    52     54    0.0025120719    0.0033161926     2783.6394667435    0.0042007439        2.1841311644     0.0013   2026-09-08 10:27:56
    53     55    0.0043758640    0.0059640564     2783.6288697964    0.0105969472        2.1845532510     0.0013   2026-09-08 10:27:56
    54     56    0.0059286247    0.0111386007     2783.6079295000    0.0209402964        1.9820360783     0.0012   2026-09-08 10:27:56
    55     57    0.0108932359    0.0201219827     2783.5767066468    0.0312228532        2.1101045820     0.0010   2026-09-08 10:27:56
    56     58    0.0126466849    0.0223449636     2783.5519168373    0.0247898095        1.7940921623     0.0009   2026-09-08 10:27:56
    57     59    0.0055933349    0.0112813804     2783.5438324273    0.0080844100        0.8167413773     0.0009   2026-09-08 10:27:56
    58     60    0.0021563838    0.0027804481     2783.5428394509    0.0009929765        0.8179845974     0.0009   2026-09-08 10:27:56
    59     61    0.0005447953    0.0009113679     2783.5426530912    0.0001863597        0.8122291414     0.0009   2026-09-08 10:27:56
    60     62    0.0007849208    0.0013420858     2783.5422498281    0.0004032631        0.7712841820     0.0009   2026-09-08 10:27:56
    61     63    0.0010306180    0.0017892126     2783.5414339116    0.0008159165        0.6518895041     0.0008   2026-09-08 10:27:56
    62     64    0.0019343215    0.0026256702     2783.5401081378    0.0013257738        0.4015033469     0.0008   2026-09-08 10:27:56
    63     65    0.0022994420    0.0035500318     2783.5389055469    0.0012025909        0.2703042840     0.0008   2026-09-08 10:27:56
    64     66    0.0013711512    0.0028322110     2783.5384410489    0.0004644980        0.1118245025     0.0008   2026-09-08 10:27:56
    65     67    0.0005045850    0.0009760641     2783.5383813241    0.0000597247        0.0160915884     0.0008   2026-09-08 10:27:56
    66     68    0.0000971262    0.0001615600     2783.5383790720    0.0000022521        0.0054158906     0.0009   2026-09-08 10:27:56
    67     69    0.0000143439    0.0000207108     2783.5383790419    0.0000000300        0.0049389599     0.0009   2026-09-08 10:27:56
    68     70    0.0000027630    0.0000043549     2783.5383790339    0.0000000080        0.0049783517     0.0009   2026-09-08 10:27:56
    69     71    0.0000109713    0.0000181061     2783.5383789873    0.0000000467        0.0046513721     0.0009   2026-09-08 10:27:56
    70     72    0.0000097596    0.0000167745     2783.5383789301    0.0000000571        0.0035636001     0.0009   2026-09-08 10:27:56
    71     73    0.0000140220    0.0000204448     2783.5383788680    0.0000000621        0.0015615108     0.0010   2026-09-08 10:27:56

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.185253e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3806***  0.1200   0.0000   
TC/100 EUR                        -0.3687***  0.0828   0.0000   
closest substitute                -0.0934     0.1242   0.4522   
Household income (10k PLN)         0.3838***  0.1046   0.0002   
Male                               0.1167     0.0728   0.1087   
Higher education                   0.0205     0.0808   0.7995   
City                               0.0451     0.0741   0.5429   
Winter                             0.8469***  0.0849   0.0000   
Hiking                             2.1106***  0.0792   0.0000   
Skiing                             1.3678***  0.2700   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4042     0.0896            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.7123***  0.6088   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2783.5384
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1644
AIC/n:                             0.9546
BIC/n:                             0.9671
n (observations):               5855
r (respondents):                5855
k (parameters):                   11
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.9364
median                           0.0000          1.9333
std                              0.7834          0.8370
min                              0.0000          0.0250
max                             20.0000          4.9654
quantile 0.025                   0.0000          0.5313
quantile 0.975                   2.0000          3.5345
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:57
Estimation took 0.15185 seconds (0 hours 0 minutes 0.15185 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.6 -0.047 -0.0034 0.12 0.01 0.0044 -0.0039 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3933.6163677496             NaN     3665.9906847480     0.0000   2026-09-08 10:27:57
     1      3    0.3167070119    0.3983849271     3212.2663093772  721.3500583723      432.9119600328     0.0018   2026-09-08 10:27:57
     2      4    0.0319823148    0.0438316180     3189.4703356302   22.7959737470      386.6734651484     0.0007   2026-09-08 10:27:57
     3      5    0.1463068200    0.1766106605     3135.5053116487   53.9650239815      422.5617660242     0.0008   2026-09-08 10:27:57
     4      6    0.1519209133    0.1786752827     3089.0009545083   46.5043571404      577.6054093897     0.0008   2026-09-08 10:27:57
     5      7    0.4828114014    0.5769323681     2970.5066683279  118.4942861805      582.6430749043     0.0007   2026-09-08 10:27:57
     6      8    0.3088158215    0.3828323923     2912.8378177962   57.6688505317      318.4887518093     0.0007   2026-09-08 10:27:57
     7      9    0.1814553813    0.2380241293     2889.8908948211   22.9469229751      184.4277002398     0.0007   2026-09-08 10:27:57
     8     10    0.0615123407    0.0913484057     2884.2222174042    5.6686774168      130.9971746845     0.0007   2026-09-08 10:27:57
     9     11    0.0440815492    0.0621384534     2879.9740416848    4.2481757194      136.0282312075     0.0007   2026-09-08 10:27:57
    10     12    0.0977828198    0.1191626225     2871.1177344340    8.8563072508      233.6244210332     0.0008   2026-09-08 10:27:57
    11     13    0.1847346015    0.2170024048     2855.5043747201   15.6133597139      310.7418616443     0.0007   2026-09-08 10:27:57
    12     14    0.2742580863    0.3230309854     2834.9589436609   20.5454310593      289.2858663795     0.0007   2026-09-08 10:27:57
    13     15    0.1982234974    0.2398624468     2822.4103835830   12.5485600779      140.1920429174     0.0007   2026-09-08 10:27:57
    14     16    0.0273375515    0.0394610816     2819.0179600251    3.3924235579       59.5508118970     0.0007   2026-09-08 10:27:57
    15     17    0.0311605019    0.0424109878     2817.8275565736    1.1904034515       41.9655157515     0.0007   2026-09-08 10:27:57
    16     18    0.0217769101    0.0360729814     2816.8273342411    1.0002223325       56.7119504619     0.0008   2026-09-08 10:27:57
    17     19    0.0414642348    0.0705796429     2814.1078696930    2.7194645481       94.1927104520     0.0007   2026-09-08 10:27:57
    18     20    0.0788908250    0.1290040364     2808.7030225524    5.4048471406      131.0259778946     0.0007   2026-09-08 10:27:57
    19     21    0.1573086110    0.2490300928     2800.0482808659    8.6547416865      138.1565271712     0.0007   2026-09-08 10:27:57
    20     22    0.2461200826    0.2957683703     2792.6075477713    7.4407330946       80.8713606122     0.0007   2026-09-08 10:27:57
    21     23    0.1538257663    0.1684443260     2789.9624686838    2.6450790875       18.1961606257     0.0008   2026-09-08 10:27:57
    22     24    0.0282988666    0.0424451726     2789.6813628326    0.2811058512        9.9488697577     0.0008   2026-09-08 10:27:57
    23     25    0.0053681791    0.0098215734     2789.6281786828    0.0531841498        9.9919738726     0.0008   2026-09-08 10:27:57
    24     26    0.0113601519    0.0205249635     2789.4704938811    0.1576848017       13.1384444094     0.0008   2026-09-08 10:27:57
    25     27    0.0169571572    0.0323067292     2789.1465076238    0.3239862573       17.3808464135     0.0008   2026-09-08 10:27:57
    26     28    0.0281658083    0.0628098381     2788.4783535738    0.6681540500       20.6442495858     0.0008   2026-09-08 10:27:57
    27     29    0.0468524837    0.0950567048     2787.5828222162    0.8955313576       18.3052574452     0.0007   2026-09-08 10:27:57
    28     30    0.0419814232    0.0895271451     2786.9277346855    0.6550875308       10.6008117462     0.0007   2026-09-08 10:27:57
    29     31    0.0192904995    0.0405923185     2786.7231204766    0.2046142088        9.4911990717     0.0007   2026-09-08 10:27:57
    30     32    0.0075437541    0.0138918773     2786.6886296458    0.0344908309        9.4286394347     0.0007   2026-09-08 10:27:57
    31     33    0.0039323743    0.0073693640     2786.6668388587    0.0217907870        9.3872195533     0.0007   2026-09-08 10:27:57
    32     34    0.0081907259    0.0150762147     2786.5973276362    0.0695112225        9.2414329144     0.0007   2026-09-08 10:27:57
    33     35    0.0130204172    0.0239377544     2786.4472886817    0.1500389546        8.8961779341     0.0008   2026-09-08 10:27:57
    34     36    0.0431824305    0.0526608271     2786.1186110335    0.3286776482        8.0689347648     0.0007   2026-09-08 10:27:57
    35     37    0.0884568464    0.0980700435     2785.6143953999    0.5042156336       10.5941653385     0.0008   2026-09-08 10:27:57
    36     38    0.1039135598    0.1169397394     2785.1636677281    0.4507276718        9.9815547153     0.0008   2026-09-08 10:27:57
    37     39    0.0489953844    0.0636125426     2784.9850082919    0.1786594362        6.4745794465     0.0008   2026-09-08 10:27:57
    38     40    0.0091919047    0.0165138503     2784.9465397774    0.0384685145        6.6296529527     0.0007   2026-09-08 10:27:57
    39     41    0.0044877404    0.0077411987     2784.9244837135    0.0220560639        6.8404472813     0.0009   2026-09-08 10:27:57
    40     42    0.0083633967    0.0135321455     2784.8648187389    0.0596649746        7.0401675825     0.0009   2026-09-08 10:27:57
    41     43    0.0126245445    0.0234305080     2784.7334761811    0.1313425579        7.1299658734     0.0008   2026-09-08 10:27:57
    42     44    0.0460275915    0.0557322447     2784.4539114914    0.2795646897        6.8742712997     0.0008   2026-09-08 10:27:57
    43     45    0.0993915628    0.1066198677     2784.0370346930    0.4168767984        9.0547597432     0.0007   2026-09-08 10:27:57
    44     46    0.1155992081    0.1210056849     2783.6884771247    0.3485575684        8.7492390645     0.0007   2026-09-08 10:27:57
    45     47    0.0505756580    0.0569545734     2783.5638454457    0.1246316790        5.7421003089     0.0007   2026-09-08 10:27:57
    46     48    0.0077567518    0.0121890646     2783.5418639807    0.0219814650        5.0400630306     0.0007   2026-09-08 10:27:57
    47     49    0.0034008084    0.0059442844     2783.5321075391    0.0097564416        4.9476858552     0.0007   2026-09-08 10:27:57
    48     50    0.0065491384    0.0103945631     2783.5051633897    0.0269441494        4.5533473084     0.0007   2026-09-08 10:27:57
    49     51    0.0089067938    0.0132738102     2783.4517972089    0.0533661808        3.6849992028     0.0007   2026-09-08 10:27:57
    50     52    0.0139563649    0.0257923212     2783.3580038235    0.0937933854        2.8932747056     0.0007   2026-09-08 10:27:57
    51     53    0.0316831701    0.0415872663     2783.2640361878    0.0939676358        2.9738370372     0.0010   2026-09-08 10:27:57
    52     54    0.0278298475    0.0343616597     2783.2216346201    0.0424015677        1.7342464236     0.0010   2026-09-08 10:27:57
    53     55    0.0073498868    0.0105137043     2783.2152233321    0.0064112880        0.7120245954     0.0008   2026-09-08 10:27:57
    54     56    0.0011684912    0.0017606390     2783.2148187789    0.0004045532        0.7336812847     0.0007   2026-09-08 10:27:57
    55     57    0.0003439960    0.0006416946     2783.2146607028    0.0001580761        0.7285723133     0.0007   2026-09-08 10:27:57
    56     58    0.0009712920    0.0017271812     2783.2140334403    0.0006272626        0.6936226993     0.0007   2026-09-08 10:27:57
    57     59    0.0012384024    0.0021912498     2783.2129109822    0.0011224581        0.6137741044     0.0007   2026-09-08 10:27:57
    58     60    0.0021311997    0.0035067398     2783.2109594703    0.0019515119        0.4458855381     0.0007   2026-09-08 10:27:57
    59     61    0.0021056501    0.0041466592     2783.2091921127    0.0017673576        0.3345182151     0.0007   2026-09-08 10:27:57
    60     62    0.0013894544    0.0031021630     2783.2084679312    0.0007241814        0.1889278895     0.0007   2026-09-08 10:27:57
    61     63    0.0005649862    0.0011445052     2783.2083601414    0.0001077899        0.2163668946     0.0007   2026-09-08 10:27:57
    62     64    0.0001665381    0.0002863545     2783.2083430207    0.0000171206        0.2128745197     0.0007   2026-09-08 10:27:57
    63     65    0.0001729314    0.0003047430     2783.2083154596    0.0000275611        0.2026993485     0.0007   2026-09-08 10:27:57
    64     66    0.0002584526    0.0004979789     2783.2082478478    0.0000676118        0.1979216093     0.0007   2026-09-08 10:27:57
    65     67    0.0003824315    0.0007800078     2783.2081154779    0.0001323699        0.1776633031     0.0007   2026-09-08 10:27:57
    66     68    0.0007931874    0.0012004713     2783.2079278670    0.0001876109        0.1169640235     0.0008   2026-09-08 10:27:57
    67     69    0.0010351850    0.0012815110     2783.2077902516    0.0001376154        0.0757479075     0.0007   2026-09-08 10:27:57
    68     70    0.0005092335    0.0007084429     2783.2077507688    0.0000394828        0.0209830891     0.0007   2026-09-08 10:27:57
    69     71    0.0001092185    0.0001993281     2783.2077471768    0.0000035920        0.0045406726     0.0007   2026-09-08 10:27:57
    70     72    0.0000195478    0.0000380581     2783.2077470817    0.0000000951        0.0024231137     0.0007   2026-09-08 10:27:57

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','6.607908e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.4870***  0.1144   0.0000   
TC/100 EUR                        -0.3005***  0.0659   0.0000   
closest substitute                -0.0705     0.0985   0.4743   
Household income (10k PLN)         0.5823***  0.1107   0.0000   
Male                               0.1152     0.0729   0.1138   
Higher education                   0.0301     0.0809   0.7103   
City                               0.0466     0.0742   0.5304   
Winter                             0.8380***  0.0850   0.0000   
Hiking                             2.1096***  0.0793   0.0000   
Skiing                             1.3697***  0.2708   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4101     0.0892            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    3.3280***  0.7302   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2783.2077
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1645
AIC/n:                             0.9545
BIC/n:                             0.9670
n (observations):               5855
r (respondents):                5855
k (parameters):                   11
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.3643
median                           0.0000          2.3002
std                              0.7834          1.0883
min                              0.0000          0.0258
max                             20.0000          8.1215
quantile 0.025                   0.0000          0.6384
quantile 0.975                   2.0000          4.6816
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:57
Estimation took 0.11345 seconds (0 hours 0 minutes 0.11345 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.57 -0.047 -0.0066 0.057 0.01 0.0035 -0.0041 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3933.9567045634             NaN     3511.9840964929     0.0000   2026-09-08 10:27:58
     1      3    0.3326779908    0.4217540587     3175.3525792571  758.6041253064      436.6347156611     0.0021   2026-09-08 10:27:58
     2      4    0.0362805842    0.0457842294     3152.3058712555   23.0467080015      393.7076573883     0.0010   2026-09-08 10:27:58
     3      5    0.2214312650    0.2591221605     3075.2737448113   77.0321264443      483.0143869264     0.0011   2026-09-08 10:27:58
     4      6    0.1918629366    0.2232862271     3020.7732443090   54.5005005023      567.5545004473     0.0010   2026-09-08 10:27:58
     5      7    0.4559180915    0.5425468929     2918.4318543558  102.3413899532      391.1628478044     0.0010   2026-09-08 10:27:58
     6      8    0.2232566227    0.2781104343     2884.0178348226   34.4140195332      202.9918233440     0.0009   2026-09-08 10:27:58
     7      9    0.1101014102    0.1458203307     2873.4857226149   10.5321122077      129.7527648221     0.0010   2026-09-08 10:27:58
     8     10    0.0411535761    0.0622169164     2869.7852918149    3.7004308000       93.5253612873     0.0008   2026-09-08 10:27:58
     9     11    0.0592753598    0.0893168864     2863.8682468947    5.9170449202      171.5993013810     0.0007   2026-09-08 10:27:58
    10     12    0.1231517438    0.1686988737     2852.5233310786   11.3449158161      248.8346047782     0.0007   2026-09-08 10:27:58
    11     13    0.2076643522    0.2768705938     2835.2752938476   17.2480372311      269.9955642627     0.0007   2026-09-08 10:27:58
    12     14    0.2114352139    0.2825568303     2820.4142874413   14.8610064063      176.5105848463     0.0009   2026-09-08 10:27:58
    13     15    0.0698447701    0.1033124748     2815.1424356002    5.2718518410       55.9346904364     0.0011   2026-09-08 10:27:58
    14     16    0.0204776633    0.0373844841     2813.7596193055    1.3828162947       37.7950596955     0.0010   2026-09-08 10:27:58
    15     17    0.0214057399    0.0390980073     2812.9700113249    0.7896079806       45.9867439156     0.0010   2026-09-08 10:27:58
    16     18    0.0229772151    0.0477442095     2811.6042146967    1.3657966282       62.2843819201     0.0007   2026-09-08 10:27:58
    17     19    0.0521840445    0.0936728549     2808.2238023114    3.3804123853       94.6161628602     0.0008   2026-09-08 10:27:58
    18     20    0.1051116740    0.1818302460     2802.0837349386    6.1400673728      116.8659578256     0.0008   2026-09-08 10:27:58
    19     21    0.2280507533    0.2881655743     2794.5194868561    7.5642480825       95.6853379589     0.0010   2026-09-08 10:27:58
    20     22    0.2135800025    0.2410638940     2790.1055194336    4.4139674225       34.8971537466     0.0008   2026-09-08 10:27:58
    21     23    0.0709939192    0.0889384507     2789.1876517319    0.9178677017       14.1858731546     0.0008   2026-09-08 10:27:58
    22     24    0.0089064051    0.0187133091     2789.0759921891    0.1116595428       15.0324752095     0.0007   2026-09-08 10:27:58
    23     25    0.0091022130    0.0158492246     2788.9415489790    0.1344432102       16.7723878605     0.0007   2026-09-08 10:27:58
    24     26    0.0186528499    0.0322429795     2788.5713612888    0.3701876902       19.9715590422     0.0008   2026-09-08 10:27:58
    25     27    0.0278775627    0.0585020456     2787.8266227054    0.7447385834       27.1540418723     0.0007   2026-09-08 10:27:58
    26     28    0.0554104198    0.1058534133     2786.5960319875    1.2305907179       29.7289204490     0.0012   2026-09-08 10:27:58
    27     29    0.0713315868    0.1232768710     2785.4504755789    1.1455564086       21.0865433874     0.0009   2026-09-08 10:27:58
    28     30    0.0380166551    0.0699707500     2784.9624117340    0.4880638449        9.1915396675     0.0007   2026-09-08 10:27:58
    29     31    0.0132485421    0.0222265080     2784.8726031923    0.0898085417        9.0415487999     0.0007   2026-09-08 10:27:58
    30     32    0.0046387933    0.0088784923     2784.8501899007    0.0224132916        9.0066381820     0.0007   2026-09-08 10:27:58
    31     33    0.0067725624    0.0129079306     2784.8008998233    0.0492900773        8.9223182471     0.0007   2026-09-08 10:27:58
    32     34    0.0104412563    0.0200742005     2784.6850883338    0.1158114895        8.6952673799     0.0006   2026-09-08 10:27:58
    33     35    0.0259383022    0.0383388020     2784.4326903312    0.2523980026        8.1404176256     0.0008   2026-09-08 10:27:58
    34     36    0.0610129975    0.0739066958     2784.0157315666    0.4169587646        9.9675352250     0.0008   2026-09-08 10:27:58
    35     37    0.0827446794    0.0995018574     2783.6023121076    0.4134194591        9.7475660611     0.0007   2026-09-08 10:27:58
    36     38    0.0491189966    0.0665453560     2783.4143719601    0.1879401474        6.2369209949     0.0010   2026-09-08 10:27:58
    37     39    0.0091511789    0.0205350167     2783.3711503577    0.0432216024        6.1519044502     0.0008   2026-09-08 10:27:58
    38     40    0.0045730503    0.0079114704     2783.3504649838    0.0206853738        5.7992040760     0.0007   2026-09-08 10:27:58
    39     41    0.0075617512    0.0126937757     2783.3003830237    0.0500819602        5.5548363225     0.0008   2026-09-08 10:27:58
    40     42    0.0128571073    0.0225043520     2783.1878034709    0.1125795527        5.5332910970     0.0007   2026-09-08 10:27:58
    41     43    0.0425483098    0.0510064839     2782.9458681662    0.2419353047        6.1343777499     0.0007   2026-09-08 10:27:58
    42     44    0.0891288355    0.0963615566     2782.5698855383    0.3759826280        9.2985625996     0.0010   2026-09-08 10:27:58
    43     45    0.1054132703    0.1125213673     2782.2327123992    0.3371731390        8.8143990403     0.0012   2026-09-08 10:27:58
    44     46    0.0485196610    0.0570862108     2782.0999612049    0.1327511943        5.5246804826     0.0009   2026-09-08 10:27:58
    45     47    0.0081447149    0.0133986322     2782.0742351660    0.0257260389        5.0530703469     0.0008   2026-09-08 10:27:58
    46     48    0.0036619211    0.0065361526     2782.0626392808    0.0115958852        5.0652844953     0.0007   2026-09-08 10:27:58
    47     49    0.0066642792    0.0109378461     2782.0320691702    0.0305701106        4.8340897390     0.0008   2026-09-08 10:27:58
    48     50    0.0093077256    0.0150573757     2781.9692481674    0.0628210029        4.1659208190     0.0008   2026-09-08 10:27:58
    49     51    0.0193124760    0.0310976802     2781.8531392966    0.1161088708        4.4355035933     0.0007   2026-09-08 10:27:58
    50     52    0.0430652649    0.0526013616     2781.7232715531    0.1298677435        4.5505851328     0.0007   2026-09-08 10:27:58
    51     53    0.0405815566    0.0469681241     2781.6540211199    0.0692504332        3.1510067208     0.0007   2026-09-08 10:27:58
    52     54    0.0123024437    0.0160707677     2781.6402111453    0.0138099747        1.6346745416     0.0011   2026-09-08 10:27:58
    53     55    0.0021473799    0.0031701903     2781.6381454881    0.0020656572        1.7343575154     0.0008   2026-09-08 10:27:58
    54     56    0.0017045479    0.0024868702     2781.6358297677    0.0023157204        1.8083326660     0.0007   2026-09-08 10:27:58
    55     57    0.0032271750    0.0045925545     2781.6294379633    0.0063918043        1.8701372956     0.0007   2026-09-08 10:27:58
    56     58    0.0043662918    0.0075052405     2781.6167773606    0.0126606027        1.7893164219     0.0007   2026-09-08 10:27:58
    57     59    0.0073286336    0.0135051101     2781.5964752077    0.0203021530        1.4763267889     0.0007   2026-09-08 10:27:58
    58     60    0.0098751680    0.0164865772     2781.5786694123    0.0178057953        1.3930317665     0.0007   2026-09-08 10:27:58
    59     61    0.0054687902    0.0101035028     2781.5720100149    0.0066593974        0.6748595061     0.0007   2026-09-08 10:27:58
    60     62    0.0019212850    0.0028429542     2781.5711275731    0.0008824418        0.5840815967     0.0007   2026-09-08 10:27:58
    61     63    0.0004447076    0.0007502289     2781.5710272251    0.0001003480        0.5871788481     0.0008   2026-09-08 10:27:58
    62     64    0.0003784022    0.0006815106     2781.5708969696    0.0001302555        0.5748678158     0.0007   2026-09-08 10:27:58
    63     65    0.0006444880    0.0011471655     2781.5705603039    0.0003366657        0.5208419520     0.0007   2026-09-08 10:27:58
    64     66    0.0009945418    0.0015875607     2781.5699553074    0.0006049965        0.3906550104     0.0007   2026-09-08 10:27:58
    65     67    0.0016829002    0.0023510936     2781.5691816052    0.0007737022        0.2043932913     0.0007   2026-09-08 10:27:58
    66     68    0.0013337556    0.0024260161     2781.5687137482    0.0004678569        0.1297961530     0.0007   2026-09-08 10:27:58
    67     69    0.0006043446    0.0012560045     2781.5686075337    0.0001062146        0.0324996955     0.0007   2026-09-08 10:27:58
    68     70    0.0001650423    0.0002946269     2781.5686001351    0.0000073985        0.0120180527     0.0008   2026-09-08 10:27:58
    69     71    0.0000318138    0.0000446273     2781.5685999722    0.0000001629        0.0099998532     0.0007   2026-09-08 10:27:58
    70     72    0.0000045602    0.0000065486     2781.5685999529    0.0000000192        0.0096684765     0.0007   2026-09-08 10:27:58
    71     73    0.0000169549    0.0000249918     2781.5685998490    0.0000001040        0.0078753277     0.0007   2026-09-08 10:27:58
    72     74    0.0000167683    0.0000259579     2781.5685997005    0.0000001485        0.0058458132     0.0007   2026-09-08 10:27:58
    73     75    0.0000252090    0.0000346115     2781.5685994957    0.0000002048        0.0036197775     0.0007   2026-09-08 10:27:58
    74     76    0.0000169139    0.0000310086     2781.5685993826    0.0000001132        0.0019003692     0.0007   2026-09-08 10:27:58

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.409558e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.2740***  0.1247   0.0000   
TC/100 EUR                        -0.3194***  0.0722   0.0000   
closest substitute                -0.1051     0.1081   0.3307   
Household income (10k PLN)         0.2329**   0.1027   0.0233   
Male                               0.1183     0.0727   0.1038   
Higher education                   0.0165     0.0807   0.8382   
City                               0.0496     0.0741   0.5035   
Winter                             0.8449***  0.0848   0.0000   
Hiking                             2.1033***  0.0792   0.0000   
Skiing                             1.3581***  0.2695   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3989     0.0898            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    3.1313***  0.7075   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2781.5686
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1650
AIC/n:                             0.9539
BIC/n:                             0.9664
n (observations):               5855
r (respondents):                5855
k (parameters):                   11
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.2499
median                           0.0000          2.2582
std                              0.7834          0.9431
min                              0.0000          0.0340
max                             20.0000          4.5242
quantile 0.025                   0.0000          0.6513
quantile 0.975                   2.0000          3.9440
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:58
Estimation took 0.13214 seconds (0 hours 0 minutes 0.13214 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.046 -0.0046 0.062 0.009 0.0038 -0.0032 0.18 0.45 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.8287728437             NaN     3301.9790241112     0.0000   2026-09-08 10:27:59
     1      3    0.3353865831    0.4302763726     3192.3055928858  742.5231799579      432.2121900136     0.0017   2026-09-08 10:27:59
     2      4    0.0387091005    0.0477766050     3168.7256072593   23.5799856265      390.2334653195     0.0007   2026-09-08 10:27:59
     3      5    0.2659307084    0.3097334697     3078.5730522116   90.1525550477      489.4606002592     0.0007   2026-09-08 10:27:59
     4      6    0.2132239168    0.2494141819     3019.5248555431   59.0481966685      545.8844204254     0.0007   2026-09-08 10:27:59
     5      7    0.4652738979    0.5592501786     2917.9357710764  101.5890844667      327.4584771188     0.0007   2026-09-08 10:27:59
     6      8    0.2138134465    0.2705662662     2887.6610630674   30.2747080090      191.1723907899     0.0009   2026-09-08 10:27:59
     7      9    0.1022970226    0.1385490789     2878.7976095279    8.8634535394      124.7286075754     0.0008   2026-09-08 10:27:59
     8     10    0.0430317263    0.0677219344     2874.8695012134    3.9281083145      104.3850326009     0.0011   2026-09-08 10:27:59
     9     11    0.0794997862    0.1132148188     2867.5374510383    7.3320501751      182.3340135496     0.0010   2026-09-08 10:27:59
    10     12    0.1520383215    0.1992169950     2854.4671199319   13.0703311064      247.4961422474     0.0010   2026-09-08 10:27:59
    11     13    0.2339796647    0.3000317900     2836.4085449038   18.0585750280      242.5019829325     0.0010   2026-09-08 10:27:59
    12     14    0.1912404197    0.2494775956     2823.8055001502   12.6030447536      131.9988202120     0.0010   2026-09-08 10:27:59
    13     15    0.0425340173    0.0667448112     2820.0140103425    3.7914898078       51.4978922452     0.0010   2026-09-08 10:27:59
    14     16    0.0246906488    0.0448358334     2818.8027850242    1.2112253183       36.5419725473     0.0007   2026-09-08 10:27:59
    15     17    0.0212082310    0.0414122794     2817.8370874998    0.9656975244       49.2738628278     0.0008   2026-09-08 10:27:59
    16     18    0.0326586092    0.0649853863     2815.6802143186    2.1568731812       75.6605586961     0.0010   2026-09-08 10:27:59
    17     19    0.0676341006    0.1230168313     2811.0525663653    4.6276479533      104.9068760057     0.0007   2026-09-08 10:27:59
    18     20    0.1524982836    0.2312515717     2803.6820054064    7.3705609589      110.7622554239     0.0007   2026-09-08 10:27:59
    19     21    0.2406309489    0.2884948679     2796.9831364275    6.6988689790       66.4809708917     0.0011   2026-09-08 10:27:59
    20     22    0.1536650867    0.1743479949     2794.4217380947    2.5613983328       20.2655287601     0.0012   2026-09-08 10:27:59
    21     23    0.0304136664    0.0464734183     2794.0937565884    0.3279815063       13.3577817175     0.0009   2026-09-08 10:27:59
    22     24    0.0062913369    0.0123905347     2794.0042930696    0.0894635188       14.8227494875     0.0011   2026-09-08 10:27:59
    23     25    0.0153495984    0.0273213441     2793.7290522727    0.2752407969       17.1051520062     0.0009   2026-09-08 10:27:59
    24     26    0.0227945661    0.0444901619     2793.1843154875    0.5447367852       21.6695332716     0.0009   2026-09-08 10:27:59
    25     27    0.0416257785    0.0873416807     2792.1344792105    1.0498362771       26.0980063204     0.0008   2026-09-08 10:27:59
    26     28    0.0673652726    0.1207374426     2790.9180898236    1.2163893868       22.2338787790     0.0009   2026-09-08 10:27:59
    27     29    0.0527892539    0.0927002047     2790.2074186797    0.7106711439       10.9817432219     0.0007   2026-09-08 10:27:59
    28     30    0.0149901465    0.0332542991     2790.0314022616    0.1760164181        9.3216104600     0.0009   2026-09-08 10:27:59
    29     31    0.0069331149    0.0125582241     2789.9985910774    0.0328111842        9.2680234979     0.0010   2026-09-08 10:27:59
    30     32    0.0052679791    0.0098636833     2789.9629585890    0.0356324884        9.2093410318     0.0012   2026-09-08 10:27:59
    31     33    0.0101648571    0.0188362463     2789.8586141540    0.1043444350        9.0146071621     0.0013   2026-09-08 10:27:59
    32     34    0.0199403897    0.0324316409     2789.6376131943    0.2210009597        8.5533328026     0.0010   2026-09-08 10:27:59
    33     35    0.0550939605    0.0680130868     2789.2169101040    0.4207030903        9.8276146267     0.0008   2026-09-08 10:27:59
    34     36    0.0892927839    0.1055626923     2788.7138377773    0.5030723267       11.0460839763     0.0007   2026-09-08 10:27:59
    35     37    0.0713584443    0.0898899520     2788.4114996615    0.3023381158        7.6792677986     0.0007   2026-09-08 10:27:59
    36     38    0.0186656128    0.0333404787     2788.3303898349    0.0811098266        6.4968497291     0.0007   2026-09-08 10:27:59
    37     39    0.0056722877    0.0098310605     2788.3057309649    0.0246588699        6.1767401778     0.0008   2026-09-08 10:27:59
    38     40    0.0064537242    0.0107302709     2788.2658280052    0.0399029597        5.7399574655     0.0010   2026-09-08 10:27:59
    39     41    0.0105486576    0.0191260054     2788.1684537516    0.0973742537        5.5333644609     0.0010   2026-09-08 10:27:59
    40     42    0.0315081979    0.0409710968     2787.9592531556    0.2092005960        5.5166306593     0.0009   2026-09-08 10:27:59
    41     43    0.0753055727    0.0837113335     2787.6046234674    0.3546296882        8.8391910514     0.0010   2026-09-08 10:27:59
    42     44    0.1034825269    0.1113244015     2787.2442773046    0.3603461628        9.1217392163     0.0012   2026-09-08 10:27:59
    43     45    0.0611637372    0.0693840284     2787.0759171006    0.1683602040        5.9594116418     0.0009   2026-09-08 10:27:59
    44     46    0.0094133394    0.0173924898     2787.0402898992    0.0356272014        4.8022483319     0.0009   2026-09-08 10:27:59
    45     47    0.0039142828    0.0067269051     2787.0283970446    0.0118928546        4.8647826675     0.0009   2026-09-08 10:27:59
    46     48    0.0058807143    0.0096791644     2787.0026675303    0.0257295143        4.7124828082     0.0007   2026-09-08 10:27:59
    47     49    0.0087711983    0.0140377529     2786.9464017223    0.0562658080        4.1248509411     0.0007   2026-09-08 10:27:59
    48     50    0.0159600488    0.0279571190     2786.8383647980    0.1080369242        4.4216425906     0.0007   2026-09-08 10:27:59
    49     51    0.0395655475    0.0501642074     2786.7026899809    0.1356748172        4.8507695040     0.0007   2026-09-08 10:27:59
    50     52    0.0428172669    0.0505560266     2786.6173401844    0.0853497965        3.7685308561     0.0007   2026-09-08 10:27:59
    51     53    0.0162051783    0.0206970522     2786.5963058661    0.0210343183        2.0454823254     0.0007   2026-09-08 10:27:59
    52     54    0.0028639866    0.0042915738     2786.5929712122    0.0033346539        1.8848742143     0.0007   2026-09-08 10:27:59
    53     55    0.0019210757    0.0027321874     2786.5899808111    0.0029904011        1.9628604437     0.0007   2026-09-08 10:27:59
    54     56    0.0037818820    0.0052977816     2786.5814272372    0.0085535739        2.0354404052     0.0009   2026-09-08 10:27:59
    55     57    0.0050929589    0.0088062844     2786.5645603501    0.0168668870        1.9623544572     0.0010   2026-09-08 10:27:59
    56     58    0.0087322012    0.0164826720     2786.5366350494    0.0279253007        1.7853622758     0.0010   2026-09-08 10:27:59
    57     59    0.0120413083    0.0206124332     2786.5110864050    0.0255486444        1.7449123229     0.0008   2026-09-08 10:27:59
    58     60    0.0069993990    0.0129069542     2786.5008945189    0.0101918862        0.8745766453     0.0007   2026-09-08 10:27:59
    59     61    0.0024445182    0.0035955548     2786.4994504139    0.0014441049        0.6880980261     0.0007   2026-09-08 10:27:59
    60     62    0.0005956395    0.0010017030     2786.4992910089    0.0001594050        0.6938446980     0.0007   2026-09-08 10:27:59
    61     63    0.0004500654    0.0008194738     2786.4991091020    0.0001819069        0.6805704906     0.0007   2026-09-08 10:27:59
    62     64    0.0007978625    0.0014195586     2786.4986223999    0.0004867021        0.6164387118     0.0007   2026-09-08 10:27:59
    63     65    0.0011899425    0.0018919108     2786.4977690575    0.0008533425        0.4618392303     0.0007   2026-09-08 10:27:59
    64     66    0.0020122522    0.0028198805     2786.4966915523    0.0010775051        0.2481322557     0.0008   2026-09-08 10:27:59
    65     67    0.0015585636    0.0029201548     2786.4960615844    0.0006299679        0.1539584717     0.0008   2026-09-08 10:27:59
    66     68    0.0007119185    0.0014970022     2786.4959235381    0.0001380464        0.0373956625     0.0008   2026-09-08 10:27:59
    67     69    0.0001878402    0.0003359934     2786.4959143298    0.0000092083        0.0121226152     0.0008   2026-09-08 10:27:59
    68     70    0.0000351101    0.0000489885     2786.4959141366    0.0000001931        0.0099688005     0.0008   2026-09-08 10:27:59
    69     71    0.0000048997    0.0000070906     2786.4959141148    0.0000000218        0.0096228805     0.0008   2026-09-08 10:27:59
    70     72    0.0000185634    0.0000273624     2786.4959139963    0.0000001186        0.0077213032     0.0009   2026-09-08 10:27:59
    71     73    0.0000173287    0.0000277336     2786.4959138321    0.0000001641        0.0061953459     0.0008   2026-09-08 10:27:59
    72     74    0.0000250636    0.0000359868     2786.4959136166    0.0000002156        0.0036418894     0.0007   2026-09-08 10:27:59
    73     75    0.0000177853    0.0000313793     2786.4959135069    0.0000001097        0.0018026856     0.0007   2026-09-08 10:27:59

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.457757e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3578***  0.1222   0.0000   
TC/100 EUR                        -0.3194***  0.0755   0.0000   
closest substitute                -0.0827     0.1133   0.4655   
Household income (10k PLN)         0.2569**   0.1029   0.0125   
Male                               0.1148     0.0727   0.1142   
Higher education                   0.0157     0.0807   0.8458   
City                               0.0529     0.0741   0.4753   
Winter                             0.8544***  0.0849   0.0000   
Hiking                             2.1201***  0.0791   0.0000   
Skiing                             1.3906***  0.2699   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4010     0.0898            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    3.1312***  0.7400   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2786.4959
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1635
AIC/n:                             0.9556
BIC/n:                             0.9681
n (observations):               5855
r (respondents):                5855
k (parameters):                   11
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1226
median                           0.0000          2.1322
std                              0.7834          0.9278
min                              0.0000          0.0266
max                             20.0000          5.0512
quantile 0.025                   0.0000          0.5807
quantile 0.975                   2.0000          3.9862
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:27:59
Estimation took 0.12872 seconds (0 hours 0 minutes 0.12872 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.049 -0.0036 0.062 0.0089 0.0041 -0.0031 0.18 0.45 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.3731800170             NaN     3294.8099301039     0.0001   2026-09-08 10:28:00
     1      3    0.3364701068    0.4318697056     3189.7741664913  744.5990135258      432.9854210387     0.0018   2026-09-08 10:28:00
     2      4    0.0390327242    0.0480359885     3166.0508565650   23.7233099262      391.1423788300     0.0008   2026-09-08 10:28:00
     3      5    0.2729127682    0.3176266379     3073.6604967714   92.3903597936      493.1177894877     0.0008   2026-09-08 10:28:00
     4      6    0.2151590686    0.2517489387     3014.1792915721   59.4812051993      544.0372259164     0.0008   2026-09-08 10:28:00
     5      7    0.4635029201    0.5575426223     2913.2640272362  100.9152643359      318.4869360303     0.0009   2026-09-08 10:28:00
     6      8    0.2106210821    0.2667398222     2883.8664452202   29.3975820160      187.3416110225     0.0010   2026-09-08 10:28:00
     7      9    0.1005731738    0.1361279123     2875.3435401280    8.5229050922      122.4574685114     0.0009   2026-09-08 10:28:00
     8     10    0.0433135728    0.0678230462     2871.4560256957    3.8875144323      104.7138264211     0.0010   2026-09-08 10:28:00
     9     11    0.0807968509    0.1157804144     2864.0440753019    7.4119503938      181.8850518617     0.0008   2026-09-08 10:28:00
    10     12    0.1533841284    0.2019619755     2850.9380443550   13.1060309470      244.9484471996     0.0008   2026-09-08 10:28:00
    11     13    0.2335409918    0.3005096781     2833.0539300269   17.8841143281      236.9056332966     0.0008   2026-09-08 10:28:00
    12     14    0.1856188613    0.2432162404     2820.8915456036   12.1623844233      126.1779160523     0.0007   2026-09-08 10:28:00
    13     15    0.0412523243    0.0641157017     2817.2846118484    3.6069337551       50.3252087950     0.0007   2026-09-08 10:28:00
    14     16    0.0251144748    0.0458990084     2816.1087683827    1.1758434658       36.0656454290     0.0007   2026-09-08 10:28:00
    15     17    0.0208052931    0.0415576620     2815.1451179503    0.9636504324       49.3254648371     0.0008   2026-09-08 10:28:00
    16     18    0.0333870548    0.0665363658     2812.9446451024    2.2004728478       75.4814491314     0.0009   2026-09-08 10:28:00
    17     19    0.0688257643    0.1251533976     2808.2837677182    4.6608773842      103.8237624026     0.0009   2026-09-08 10:28:00
    18     20    0.1563940375    0.2340325485     2800.9442674438    7.3395002745      108.0734735183     0.0010   2026-09-08 10:28:00
    19     21    0.2393922855    0.2858298150     2794.4435115431    6.5007559006       63.1593712651     0.0008   2026-09-08 10:28:00
    20     22    0.1478193210    0.1685523078     2792.0387866372    2.4047249059       19.4987625916     0.0007   2026-09-08 10:28:00
    21     23    0.0279583163    0.0439466155     2791.7397120581    0.2990745791       13.2514735147     0.0008   2026-09-08 10:28:00
    22     24    0.0062256483    0.0121477052     2791.6517312829    0.0879807752       14.6616673617     0.0008   2026-09-08 10:28:00
    23     25    0.0156371086    0.0277689354     2791.3718819339    0.2798493489       16.9244954190     0.0008   2026-09-08 10:28:00
    24     26    0.0229183243    0.0450441794     2790.8246685378    0.5472133961       21.4169171244     0.0009   2026-09-08 10:28:00
    25     27    0.0424728320    0.0882410018     2789.7806222821    1.0440462557       25.5684953348     0.0009   2026-09-08 10:28:00
    26     28    0.0668730217    0.1195323555     2788.6023311389    1.1782911432       21.4071731819     0.0009   2026-09-08 10:28:00
    27     29    0.0503732025    0.0889684489     2787.9369262667    0.6654048722       10.5464840820     0.0008   2026-09-08 10:28:00
    28     30    0.0143650060    0.0312954340     2787.7772869401    0.1596393267        9.2512021082     0.0013   2026-09-08 10:28:00
    29     31    0.0065659648    0.0119105647     2787.7461520742    0.0311348659        9.1993170800     0.0011   2026-09-08 10:28:00
    30     32    0.0055019982    0.0102384068     2787.7083502803    0.0378017939        9.1356408939     0.0012   2026-09-08 10:28:00
    31     33    0.0102431132    0.0190040265     2787.6012464363    0.1071038440        8.9326661036     0.0010   2026-09-08 10:28:00
    32     34    0.0212066669    0.0335837337     2787.3730249572    0.2282214791        8.4513504138     0.0010   2026-09-08 10:28:00
    33     35    0.0570339335    0.0700556589     2786.9463272213    0.4266977359        9.9880112870     0.0011   2026-09-08 10:28:00
    34     36    0.0901242668    0.1067166033     2786.4478000625    0.4985271588       10.9435959815     0.0009   2026-09-08 10:28:00
    35     37    0.0690941437    0.0875707188     2786.1591599742    0.2886400884        7.4105309687     0.0009   2026-09-08 10:28:00
    36     38    0.0168656478    0.0312234688     2786.0838790172    0.0752809569        6.4563930345     0.0008   2026-09-08 10:28:00
    37     39    0.0054770085    0.0094272838     2786.0599052021    0.0239738151        6.1272528282     0.0008   2026-09-08 10:28:00
    38     40    0.0065949490    0.0109617264     2786.0185052621    0.0413999400        5.7075233836     0.0008   2026-09-08 10:28:00
    39     41    0.0105935246    0.0194318891     2785.9190699274    0.0994353347        5.4975699828     0.0009   2026-09-08 10:28:00
    40     42    0.0326700208    0.0421139347     2785.7061442579    0.2129256695        5.5411550978     0.0009   2026-09-08 10:28:00
    41     43    0.0764595651    0.0848666831     2785.3532039842    0.3529402738        8.8852628164     0.0008   2026-09-08 10:28:00
    42     44    0.1018047695    0.1096472598     2785.0068874799    0.3463165043        8.9061748889     0.0007   2026-09-08 10:28:00
    43     45    0.0570351963    0.0651671722     2784.8527084079    0.1541790719        5.6961324513     0.0008   2026-09-08 10:28:00
    44     46    0.0089016651    0.0158705627     2784.8209513400    0.0317570679        4.7690235949     0.0008   2026-09-08 10:28:00
    45     47    0.0037610132    0.0064532704     2784.8093417409    0.0116095991        4.8225226491     0.0007   2026-09-08 10:28:00
    46     48    0.0060424966    0.0098414564     2784.7824530430    0.0268886979        4.6578859606     0.0007   2026-09-08 10:28:00
    47     49    0.0088294835    0.0142957012     2784.7249359735    0.0575170695        4.0462657136     0.0007   2026-09-08 10:28:00
    48     50    0.0173465559    0.0290647870     2784.6158475757    0.1090883979        4.3874449103     0.0008   2026-09-08 10:28:00
    49     51    0.0402060561    0.0505740243     2784.4840884742    0.1317591015        4.8237246860     0.0007   2026-09-08 10:28:00
    50     52    0.0408960356    0.0483956064     2784.4055402107    0.0785482635        3.6339745654     0.0007   2026-09-08 10:28:00
    51     53    0.0141912861    0.0185564453     2784.3872576164    0.0182825943        1.9852644325     0.0007   2026-09-08 10:28:00
    52     54    0.0026412755    0.0039077432     2784.3841721977    0.0030854187        1.8867332078     0.0007   2026-09-08 10:28:00
    53     55    0.0020520297    0.0028987751     2784.3808920287    0.0032801691        1.9670086130     0.0007   2026-09-08 10:28:00
    54     56    0.0038734882    0.0054318027     2784.3718915857    0.0090004429        2.0336381361     0.0010   2026-09-08 10:28:00
    55     57    0.0052398807    0.0092941589     2784.3540813391    0.0178102467        1.9439903477     0.0009   2026-09-08 10:28:00
    56     58    0.0091859368    0.0171473458     2784.3255270394    0.0285542997        1.8297614141     0.0009   2026-09-08 10:28:00
    57     59    0.0120741304    0.0207351510     2784.3004906041    0.0250364353        1.7137212810     0.0008   2026-09-08 10:28:00
    58     60    0.0065045070    0.0122432603     2784.2911189119    0.0093716923        0.8275159740     0.0007   2026-09-08 10:28:00
    59     61    0.0023080586    0.0032897776     2784.2898697051    0.0012492068        0.6896772690     0.0007   2026-09-08 10:28:00
    60     62    0.0005435952    0.0009362344     2784.2897217169    0.0001479882        0.6931896257     0.0007   2026-09-08 10:28:00
    61     63    0.0004806333    0.0008821164     2784.2895233766    0.0001983403        0.6774946708     0.0007   2026-09-08 10:28:00
    62     64    0.0007994333    0.0014341983     2784.2890244229    0.0004989537        0.6090784629     0.0008   2026-09-08 10:28:00
    63     65    0.0012578862    0.0019443538     2784.2881493909    0.0008750321        0.4458271251     0.0007   2026-09-08 10:28:00
    64     66    0.0020269533    0.0028492192     2784.2870951654    0.0010542255        0.2438477776     0.0007   2026-09-08 10:28:00
    65     67    0.0014779426    0.0028651399     2784.2865118108    0.0005833545        0.1432764909     0.0007   2026-09-08 10:28:00
    66     68    0.0006630173    0.0013943006     2784.2863933181    0.0001184927        0.0325838990     0.0007   2026-09-08 10:28:00
    67     69    0.0001656275    0.0002986101     2784.2863860195    0.0000072987        0.0122114540     0.0008   2026-09-08 10:28:00
    68     70    0.0000307968    0.0000424900     2784.2863858719    0.0000001475        0.0103861493     0.0007   2026-09-08 10:28:00
    69     71    0.0000050313    0.0000071726     2784.2863858478    0.0000000241        0.0100135244     0.0008   2026-09-08 10:28:00
    70     72    0.0000200818    0.0000293686     2784.2863857098    0.0000001380        0.0078547354     0.0007   2026-09-08 10:28:00
    71     73    0.0000189896    0.0000292477     2784.2863855257    0.0000001841        0.0062981951     0.0007   2026-09-08 10:28:00
    72     74    0.0000260741    0.0000376926     2784.2863852958    0.0000002300        0.0035434882     0.0007   2026-09-08 10:28:00
    73     75    0.0000178443    0.0000316032     2784.2863851886    0.0000001071        0.0017326728     0.0007   2026-09-08 10:28:00

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','5.257199e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3406***  0.1221   0.0000   
TC/100 EUR                        -0.3322***  0.0758   0.0000   
closest substitute                -0.0792     0.1137   0.4863   
Household income (10k PLN)         0.2598**   0.1029   0.0115   
Male                               0.1127     0.0727   0.1211   
Higher education                   0.0158     0.0808   0.8449   
City                               0.0538     0.0741   0.4674   
Winter                             0.8541***  0.0849   0.0000   
Hiking                             2.1200***  0.0791   0.0000   
Skiing                             1.3799***  0.2700   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3995     0.0898            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    3.0103***  0.6869   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2784.2864
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1642
AIC/n:                             0.9548
BIC/n:                             0.9674
n (observations):               5855
r (respondents):                5855
k (parameters):                   11
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1162
median                           0.0000          2.1210
std                              0.7834          0.9249
min                              0.0000          0.0269
max                             20.0000          5.1370
quantile 0.025                   0.0000          0.5722
quantile 0.975                   2.0000          3.9713
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:00
Estimation took 0.12985 seconds (0 hours 0 minutes 0.12985 seconds).

====================================================
NS: no substitutes
====================================================
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.57 -0.063 0.058 0.01 0.0033 -0.004 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.6017719337             NaN     2682.4376621216     0.0001   2026-09-08 10:28:01
     1      3    0.4001789233    0.5017858499     3195.5352297439  739.0665421899      421.5963988196     0.0021   2026-09-08 10:28:01
     2      5    0.5878345315    0.6917425880     2992.4378312215  203.0973985224      449.4634092010     0.0014   2026-09-08 10:28:01
     3      6    0.2985219907    0.3740971966     2914.5634488656   77.8743823558      280.3329650096     0.0006   2026-09-08 10:28:01
     4      7    0.2970459717    0.3906540035     2867.1556339240   47.4078149417      136.3053557831     0.0011   2026-09-08 10:28:01
     5      8    0.1160299081    0.1550811313     2859.9899831619    7.1656507621       89.5505198378     0.0009   2026-09-08 10:28:01
     6      9    0.0676558212    0.0937791422     2856.6317915637    3.3581915981       94.2303379222     0.0009   2026-09-08 10:28:01
     7     10    0.0911039772    0.1408417402     2850.7906954534    5.8410961104      130.2611737067     0.0009   2026-09-08 10:28:01
     8     11    0.1662957674    0.2351146421     2840.0147319496   10.7759635037      153.9328893436     0.0010   2026-09-08 10:28:01
     9     12    0.2464393748    0.3208390626     2825.3984008853   14.6163310643      136.0460312004     0.0008   2026-09-08 10:28:01
    10     13    0.2121922971    0.2833217831     2814.1485068118   11.2498940735       67.6892435179     0.0011   2026-09-08 10:28:01
    11     14    0.0932202862    0.1320246818     2810.2260657995    3.9224410123       38.6610623211     0.0010   2026-09-08 10:28:01
    12     15    0.0524843017    0.0716508857     2808.9827140865    1.2433517129       29.3370797657     0.0008   2026-09-08 10:28:01
    13     16    0.0425276332    0.0690460877     2807.7752568494    1.2074572371       39.0971232487     0.0007   2026-09-08 10:28:01
    14     17    0.0419546941    0.0830110064     2805.5683140179    2.2069428315       50.4153927567     0.0007   2026-09-08 10:28:01
    15     18    0.0691887244    0.1446259757     2801.0837316690    4.4845823490       56.5531757922     0.0007   2026-09-08 10:28:01
    16     19    0.1684499644    0.2319897023     2795.5686422006    5.5150894683       44.2980802440     0.0009   2026-09-08 10:28:01
    17     20    0.1989220939    0.2394721077     2792.0663337061    3.5023084945       19.8423613585     0.0010   2026-09-08 10:28:01
    18     21    0.0855428245    0.1115643346     2791.2370974321    0.8292362740       12.2110534177     0.0007   2026-09-08 10:28:01
    19     22    0.0146518566    0.0250125255     2791.1187199995    0.1183774326       11.7423804164     0.0007   2026-09-08 10:28:01
    20     23    0.0111762257    0.0199814317     2790.9798295808    0.1388904187       12.9543889120     0.0008   2026-09-08 10:28:01
    21     24    0.0190989364    0.0396956339     2790.6195593594    0.3602702214       14.0624443786     0.0007   2026-09-08 10:28:01
    22     25    0.0319333165    0.0651033476     2789.9892886535    0.6302707058       13.1872469849     0.0007   2026-09-08 10:28:01
    23     26    0.0546638338    0.0935560386     2789.1986375053    0.7906511482       11.0993479828     0.0011   2026-09-08 10:28:01
    24     27    0.0447509627    0.0751094855     2788.7249199862    0.4737175191        9.0671812672     0.0008   2026-09-08 10:28:01
    25     28    0.0150306920    0.0320608282     2788.5929665637    0.1319534225        8.8736253114     0.0007   2026-09-08 10:28:01
    26     29    0.0069671904    0.0123934982     2788.5581341597    0.0348324040        8.8090867611     0.0010   2026-09-08 10:28:01
    27     30    0.0061867142    0.0115410433     2788.5118270800    0.0463070797        8.7122902221     0.0009   2026-09-08 10:28:01
    28     31    0.0110009161    0.0221535699     2788.3890065236    0.1228205565        8.4156524926     0.0010   2026-09-08 10:28:01
    29     32    0.0369114648    0.0451142374     2788.1275413600    0.2614651636        7.7012806024     0.0011   2026-09-08 10:28:01
    30     33    0.0868498448    0.0929802807     2787.6643502965    0.4631910635       10.6104058223     0.0007   2026-09-08 10:28:01
    31     34    0.1209260861    0.1275995451     2787.1651884487    0.4991618478       10.5660828479     0.0008   2026-09-08 10:28:01
    32     35    0.0780967994    0.0880732568     2786.9008519917    0.2643364570        9.1325972770     0.0008   2026-09-08 10:28:01
    33     36    0.0157022255    0.0274828819     2786.8251300451    0.0757219466        8.3822617881     0.0008   2026-09-08 10:28:01
    34     37    0.0061810565    0.0113943924     2786.7833912427    0.0417388024        7.7884320406     0.0008   2026-09-08 10:28:01
    35     38    0.0095351928    0.0185220557     2786.6902229221    0.0931683206        6.7051463711     0.0007   2026-09-08 10:28:01
    36     39    0.0274863264    0.0376185717     2786.4966388067    0.1935841154        6.5493002158     0.0009   2026-09-08 10:28:01
    37     40    0.0715303249    0.0806408773     2786.1592542693    0.3373845374        8.3396089958     0.0009   2026-09-08 10:28:01
    38     41    0.1044622687    0.1125242068     2785.8088908109    0.3503634584        8.6451924302     0.0008   2026-09-08 10:28:01
    39     42    0.0664650097    0.0741799387     2785.6414630526    0.1674277584        5.4355107991     0.0010   2026-09-08 10:28:01
    40     43    0.0087365523    0.0180818514     2785.6090608306    0.0324022219        3.1597606774     0.0010   2026-09-08 10:28:01
    41     44    0.0038946656    0.0063041003     2785.6030121616    0.0060486690        3.2836770548     0.0007   2026-09-08 10:28:01
    42     45    0.0042802456    0.0064945318     2785.5945376233    0.0084745383        3.1819754583     0.0007   2026-09-08 10:28:01
    43     46    0.0053437201    0.0088742117     2785.5762751317    0.0182624915        2.6732318788     0.0007   2026-09-08 10:28:01
    44     47    0.0066034885    0.0114751475     2785.5505429398    0.0257321919        1.5834412967     0.0010   2026-09-08 10:28:01
    45     48    0.0105341482    0.0163978408     2785.5302427390    0.0203002008        1.2078723307     0.0007   2026-09-08 10:28:01
    46     49    0.0093338742    0.0120696013     2785.5240316271    0.0062111119        0.6093131316     0.0009   2026-09-08 10:28:01
    47     50    0.0025478204    0.0034804088     2785.5233832389    0.0006483882        0.3390675479     0.0008   2026-09-08 10:28:01
    48     51    0.0003401603    0.0004993208     2785.5233262765    0.0000569623        0.3528714829     0.0007   2026-09-08 10:28:01
    49     52    0.0003274999    0.0004451446     2785.5232510050    0.0000752715        0.3525717405     0.0010   2026-09-08 10:28:01
    50     53    0.0005507865    0.0007835478     2785.5230760465    0.0001749585        0.3168942758     0.0010   2026-09-08 10:28:01
    51     54    0.0007681639    0.0011183828     2785.5228242855    0.0002517610        0.2168242334     0.0007   2026-09-08 10:28:01
    52     55    0.0010982300    0.0013106419     2785.5226099494    0.0002143362        0.1076589936     0.0007   2026-09-08 10:28:01
    53     56    0.0005979223    0.0008288179     2785.5225385214    0.0000714280        0.0444140818     0.0006   2026-09-08 10:28:01
    54     57    0.0001842137    0.0002672423     2785.5225306383    0.0000078831        0.0062718644     0.0007   2026-09-08 10:28:01
    55     58    0.0000326951    0.0000515724     2785.5225303885    0.0000002498        0.0023305007     0.0009   2026-09-08 10:28:01

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','8.684758e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3128***  0.1223   0.0000   
TC/100 EUR                        -0.4640***  0.0493   0.0000   
Household income (10k PLN)         0.2439**   0.1026   0.0175   
Male                               0.1175     0.0727   0.1060   
Higher education                   0.0141     0.0807   0.8614   
City                               0.0425     0.0740   0.5658   
Winter                             0.8528***  0.0849   0.0000   
Hiking                             2.1131***  0.0791   0.0000   
Skiing                             1.3701***  0.2694   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4036     0.0897            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.1551***  0.2289   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2785.5225
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1638
AIC/n:                             0.9549
BIC/n:                             0.9663
n (observations):               5855
r (respondents):                5855
k (parameters):                   10
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.7225
median                           0.0000          1.7321
std                              0.7834          0.7394
min                              0.0000          0.0246
max                             20.0000          3.5357
quantile 0.025                   0.0000          0.4668
quantile 0.975                   2.0000          3.0518
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:01
Estimation took 0.10709 seconds (0 hours 0 minutes 0.10709 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.059 0.082 0.01 0.0038 -0.004 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.0617472777             NaN     3010.3797349618     0.0001   2026-09-08 10:28:02
     1      3    0.3884610159    0.4685125233     3196.4430669672  737.6186803105      419.0414756994     0.0019   2026-09-08 10:28:02
     2      5    0.5032141240    0.5899178933     3029.2640787890  167.1789881782      569.5372123121     0.0018   2026-09-08 10:28:02
     3      6    0.2647212216    0.3285615598     2946.7079222825   82.5561565065      385.7933821984     0.0009   2026-09-08 10:28:02
     4      7    0.3604569840    0.4641208994     2878.4540446098   68.2538776727      154.4396039876     0.0011   2026-09-08 10:28:02
     5      8    0.1402123020    0.1824589021     2869.0513299511    9.4027146588      107.0828012877     0.0009   2026-09-08 10:28:02
     6      9    0.0804045732    0.1079056924     2865.2821664852    3.7691634658       94.4660890969     0.0011   2026-09-08 10:28:02
     7     10    0.0887919737    0.1309339900     2859.9416121226    5.3405543626      130.7071629366     0.0009   2026-09-08 10:28:02
     8     11    0.1560203607    0.2279865767     2849.1731424855   10.7684696371      161.1723925069     0.0009   2026-09-08 10:28:02
     9     12    0.2489514007    0.3196193299     2833.2696315424   15.9035109431      155.6142686672     0.0010   2026-09-08 10:28:02
    10     13    0.2606489138    0.3229991607     2818.3606050042   14.9090265382       94.1758245210     0.0009   2026-09-08 10:28:02
    11     14    0.1188234316    0.1804796261     2811.9820057193    6.3785992848       47.9045942460     0.0010   2026-09-08 10:28:02
    12     15    0.0682224934    0.0881780946     2810.2827189076    1.6992868118       38.3263743734     0.0010   2026-09-08 10:28:02
    13     16    0.0475987781    0.0746793419     2809.1303070998    1.1524118077       35.7481398463     0.0010   2026-09-08 10:28:02
    14     17    0.0419688369    0.0767191090     2807.3204691961    1.8098379037       46.7836134289     0.0008   2026-09-08 10:28:02
    15     18    0.0633928751    0.1233479997     2803.2103599334    4.1101092626       56.6623236179     0.0008   2026-09-08 10:28:02
    16     19    0.1243256290    0.2053702708     2796.9506680602    6.2596918733       53.7817538900     0.0008   2026-09-08 10:28:02
    17     20    0.2259848141    0.2789156091     2791.3924467226    5.5582213376       31.1666518072     0.0007   2026-09-08 10:28:02
    18     21    0.1531400868    0.1875051331     2789.3735029634    2.0189437592       13.6276568669     0.0010   2026-09-08 10:28:02
    19     22    0.0344095708    0.0523350415     2789.1321848901    0.2413180734        9.7356716829     0.0010   2026-09-08 10:28:02
    20     23    0.0063515473    0.0116303275     2789.0725967590    0.0595881310        9.7661103160     0.0010   2026-09-08 10:28:02
    21     24    0.0132208724    0.0257160598     2788.8853451766    0.1872515824        9.8110388362     0.0009   2026-09-08 10:28:02
    22     25    0.0184775408    0.0391851439     2788.5385860699    0.3467591067        9.9376096380     0.0010   2026-09-08 10:28:02
    23     26    0.0394482841    0.0700386884     2787.9381059257    0.6004801443        9.7223233449     0.0010   2026-09-08 10:28:02
    24     27    0.0464844260    0.0817292082     2787.3711357382    0.5669701875        9.4796702046     0.0010   2026-09-08 10:28:02
    25     28    0.0287592359    0.0523246021     2787.1115082023    0.2596275358        9.2468293534     0.0010   2026-09-08 10:28:02
    26     29    0.0096223925    0.0191813337     2787.0498553002    0.0616529022        9.1445610063     0.0011   2026-09-08 10:28:02
    27     30    0.0048733585    0.0089054315     2787.0196466937    0.0302086064        9.0843209824     0.0010   2026-09-08 10:28:02
    28     31    0.0081214549    0.0152018802     2786.9436709671    0.0759757266        8.9128429282     0.0009   2026-09-08 10:28:02
    29     32    0.0198066328    0.0286398167     2786.7701351785    0.1735357886        8.4752337617     0.0010   2026-09-08 10:28:02
    30     33    0.0601172277    0.0666643497     2786.3911434227    0.3789917558        8.9654885726     0.0007   2026-09-08 10:28:02
    31     34    0.1226247313    0.1274125417     2785.7847709427    0.6063724800       12.4761986380     0.0008   2026-09-08 10:28:02
    32     35    0.1450398414    0.1511222863     2785.2145235250    0.5702474177       10.9056705684     0.0010   2026-09-08 10:28:02
    33     36    0.0699636254    0.0800323785     2784.9674804809    0.2470430441        9.8908328034     0.0010   2026-09-08 10:28:02
    34     37    0.0106069503    0.0192574455     2784.9086279689    0.0588525120        9.1015000212     0.0009   2026-09-08 10:28:02
    35     38    0.0054110265    0.0096401866     2784.8742224261    0.0344055427        8.5391846740     0.0008   2026-09-08 10:28:02
    36     39    0.0094350661    0.0167910549     2784.7860708286    0.0881515975        7.3718099095     0.0009   2026-09-08 10:28:02
    37     40    0.0184833850    0.0313114051     2784.6116298419    0.1744409867        6.5876201739     0.0010   2026-09-08 10:28:02
    38     41    0.0584521291    0.0691313648     2784.3208157905    0.2908140514        7.6477293301     0.0011   2026-09-08 10:28:02
    39     42    0.0873369296    0.0948362041     2784.0493806516    0.2714351389        7.5717998143     0.0008   2026-09-08 10:28:02
    40     43    0.0548406638    0.0600330535     2783.9365786158    0.1128020358        4.7201747299     0.0007   2026-09-08 10:28:02
    41     44    0.0082260897    0.0141014453     2783.9169527437    0.0196258721        3.0527883593     0.0009   2026-09-08 10:28:02
    42     45    0.0025070202    0.0043526814     2783.9119384476    0.0050142961        3.0740025272     0.0008   2026-09-08 10:28:02
    43     46    0.0036728847    0.0059612171     2783.9021945149    0.0097439327        2.9021240597     0.0007   2026-09-08 10:28:02
    44     47    0.0055857514    0.0082544321     2783.8827946362    0.0193998786        2.3688047366     0.0007   2026-09-08 10:28:02
    45     48    0.0063496793    0.0129404158     2783.8537856932    0.0290089430        1.8800394217     0.0006   2026-09-08 10:28:02
    46     49    0.0094371648    0.0169303019     2783.8305001099    0.0232855834        1.3704249280     0.0007   2026-09-08 10:28:02
    47     50    0.0071604476    0.0114358890     2783.8229556044    0.0075445054        0.7012588554     0.0008   2026-09-08 10:28:02
    48     51    0.0016849898    0.0031984306     2783.8221328661    0.0008227383        0.4049227048     0.0007   2026-09-08 10:28:02
    49     52    0.0003989429    0.0005539234     2783.8220620965    0.0000707696        0.4225427010     0.0007   2026-09-08 10:28:02
    50     53    0.0003475935    0.0004734326     2783.8219761023    0.0000859943        0.4237904331     0.0007   2026-09-08 10:28:02
    51     54    0.0006174341    0.0008686347     2783.8217614303    0.0002146719        0.3893125310     0.0007   2026-09-08 10:28:02
    52     55    0.0008031581    0.0012323400     2783.8214320915    0.0003293388        0.2836206208     0.0007   2026-09-08 10:28:02
    53     56    0.0013079434    0.0015481215     2783.8211095163    0.0003225752        0.1364417724     0.0009   2026-09-08 10:28:02
    54     57    0.0008516755    0.0011099458     2783.8209800216    0.0001294947        0.0662390145     0.0008   2026-09-08 10:28:02
    55     58    0.0002679826    0.0004103973     2783.8209621954    0.0000178263        0.0113624519     0.0011   2026-09-08 10:28:02
    56     59    0.0000577911    0.0000859504     2783.8209614874    0.0000007080        0.0014146176     0.0010   2026-09-08 10:28:02

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','4.697573e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3677***  0.1186   0.0000   
TC/100 EUR                        -0.4215***  0.0440   0.0000   
Household income (10k PLN)         0.3831***  0.1046   0.0002   
Male                               0.1165     0.0728   0.1092   
Higher education                   0.0213     0.0808   0.7917   
City                               0.0449     0.0741   0.5442   
Winter                             0.8474***  0.0849   0.0000   
Hiking                             2.1097***  0.0792   0.0000   
Skiing                             1.3715***  0.2696   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4035     0.0896            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.3727***  0.2477   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2783.8210
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1643
AIC/n:                             0.9543
BIC/n:                             0.9657
n (observations):               5855
r (respondents):                5855
k (parameters):                   10
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          1.9364
median                           0.0000          1.9333
std                              0.7834          0.8370
min                              0.0000          0.0250
max                             20.0000          4.9654
quantile 0.025                   0.0000          0.5313
quantile 0.975                   2.0000          3.5345
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:02
Estimation took 0.11571 seconds (0 hours 0 minutes 0.11571 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.6 -0.049 0.12 0.01 0.0044 -0.004 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3933.5785276857             NaN     3665.9106575700     0.0000   2026-09-08 10:28:03
     1      3    0.3604003306    0.4119821836     3207.1029375685  726.4755901172      415.1135508881     0.0017   2026-09-08 10:28:03
     2      4    0.0371892941    0.0444448643     3186.0490930802   21.0538444883      382.0212474719     0.0008   2026-09-08 10:28:03
     3      5    0.4090358279    0.4793167572     3053.6016666171  132.4474264631      619.1544806519     0.0007   2026-09-08 10:28:03
     4      6    0.2449239922    0.2939677451     2989.2583914783   64.3432751388      580.6530841130     0.0007   2026-09-08 10:28:03
     5      7    0.4219039654    0.5248820542     2904.2060255138   85.0523659646      242.4906836962     0.0009   2026-09-08 10:28:03
     6      8    0.1629198821    0.2141596062     2886.7755732602   17.4304522535      161.3064821318     0.0012   2026-09-08 10:28:03
     7      9    0.0753879942    0.1066231849     2881.6497192723    5.1258539880      116.4816270132     0.0010   2026-09-08 10:28:03
     8     10    0.0534616680    0.0851733347     2877.1705470877    4.4791721845      155.4220312693     0.0010   2026-09-08 10:28:03
     9     11    0.1273089331    0.1705496820     2867.0277602697   10.1427868180      239.6130641525     0.0007   2026-09-08 10:28:03
    10     12    0.2236786551    0.2736473542     2850.2634833323   16.7642769374      289.4807625265     0.0007   2026-09-08 10:28:03
    11     13    0.2976784033    0.3519134674     2830.2404390597   20.0230442725      241.2775185627     0.0006   2026-09-08 10:28:03
    12     14    0.1819879098    0.2262363502     2819.1672894962   11.0731495636      101.0050258191     0.0007   2026-09-08 10:28:03
    13     15    0.0492865149    0.0700412378     2816.1744329257    2.9928565704       54.3199656893     0.0007   2026-09-08 10:28:03
    14     16    0.0394250028    0.0640584498     2814.9695296315    1.2049032942       43.1147294493     0.0007   2026-09-08 10:28:03
    15     17    0.0324077335    0.0574463352     2813.6766663930    1.2928632384       66.6712504131     0.0008   2026-09-08 10:28:03
    16     18    0.0488575933    0.0916114656     2810.5568610336    3.1198053595       94.9248185267     0.0010   2026-09-08 10:28:03
    17     19    0.0909657423    0.1540759885     2804.4825267005    6.0743343331      116.3224762546     0.0011   2026-09-08 10:28:03
    18     20    0.1846639194    0.2659839191     2796.1695073431    8.3130193574      102.0853295898     0.0007   2026-09-08 10:28:03
    19     21    0.2437368993    0.2843775528     2790.4221655233    5.7473418198       46.7967107168     0.0007   2026-09-08 10:28:03
    20     22    0.1202221259    0.1432767036     2788.9402977091    1.4818678142       11.1893155204     0.0007   2026-09-08 10:28:03
    21     23    0.0173288239    0.0299196170     2788.8257282484    0.1145694607        9.8451602691     0.0009   2026-09-08 10:28:03
    22     24    0.0041736738    0.0083110108     2788.7850337441    0.0406945043        9.8683525002     0.0010   2026-09-08 10:28:03
    23     25    0.0123067445    0.0227623363     2788.6274229236    0.1576108205        9.9154964861     0.0007   2026-09-08 10:28:03
    24     26    0.0171005773    0.0338456553     2788.3394890436    0.2879338800        9.9449726974     0.0007   2026-09-08 10:28:03
    25     27    0.0367630349    0.0632659284     2787.8110828510    0.5284061926        9.9165076047     0.0007   2026-09-08 10:28:03
    26     28    0.0461159325    0.0778967523     2787.2746620943    0.5364207568        9.7793289794     0.0009   2026-09-08 10:28:03
    27     29    0.0291377102    0.0545929968     2787.0012200057    0.2734420886        9.6030442602     0.0011   2026-09-08 10:28:03
    28     30    0.0099275206    0.0199543006     2786.9371999434    0.0640200623        9.5094494339     0.0009   2026-09-08 10:28:03
    29     31    0.0046579661    0.0080081825     2786.9131969654    0.0240029780        9.4616896654     0.0007   2026-09-08 10:28:03
    30     32    0.0071617552    0.0121384787     2786.8581736470    0.0550233184        9.3410017211     0.0007   2026-09-08 10:28:03
    31     33    0.0123809952    0.0216598496     2786.7265798064    0.1315938405        9.0265790066     0.0007   2026-09-08 10:28:03
    32     34    0.0435616580    0.0506330772     2786.4168899686    0.3096898378        8.2263249680     0.0011   2026-09-08 10:28:03
    33     35    0.1072928590    0.1119637673     2785.8210182208    0.5958717479       12.1743736045     0.0007   2026-09-08 10:28:03
    34     36    0.1743440873    0.1784571321     2785.0439909463    0.7770272745       14.0069873349     0.0009   2026-09-08 10:28:03
    35     37    0.1389487849    0.1464267129     2784.5295917686    0.5143991777        9.9775185837     0.0008   2026-09-08 10:28:03
    36     38    0.0318508908    0.0452777040     2784.3817220469    0.1478697217        8.7463977801     0.0007   2026-09-08 10:28:03
    37     39    0.0072000506    0.0130887722     2784.3526171316    0.0291049153        8.2813866670     0.0007   2026-09-08 10:28:03
    38     40    0.0068925114    0.0105661964     2784.3230981245    0.0295190071        7.8531756468     0.0007   2026-09-08 10:28:03
    39     41    0.0095414017    0.0168785529     2784.2428307203    0.0802674042        6.9130379424     0.0008   2026-09-08 10:28:03
    40     42    0.0129437791    0.0266169988     2784.0887529049    0.1540778154        5.9736021828     0.0009   2026-09-08 10:28:03
    41     43    0.0479139388    0.0584453426     2783.8535682075    0.2351846974        6.2362572092     0.0012   2026-09-08 10:28:03
    42     44    0.0728793226    0.0783559279     2783.6645666552    0.1890015522        6.1200381770     0.0010   2026-09-08 10:28:03
    43     45    0.0435468261    0.0465365132     2783.6000701999    0.0644964554        3.9538501150     0.0010   2026-09-08 10:28:03
    44     46    0.0073703663    0.0106297399     2783.5898493508    0.0102208491        2.7753891729     0.0007   2026-09-08 10:28:03
    45     47    0.0021803996    0.0032293635     2783.5857842528    0.0040650979        2.9341671994     0.0006   2026-09-08 10:28:03
    46     48    0.0041583732    0.0056921863     2783.5751272102    0.0106570426        3.1182221936     0.0006   2026-09-08 10:28:03
    47     49    0.0060146715    0.0086336676     2783.5540135455    0.0211136647        3.1052641475     0.0007   2026-09-08 10:28:03
    48     50    0.0091523320    0.0156246974     2783.5178058433    0.0362077023        2.5336018945     0.0010   2026-09-08 10:28:03
    49     51    0.0149180056    0.0206044322     2783.4828571858    0.0349486574        1.8343465898     0.0010   2026-09-08 10:28:03
    50     52    0.0103853820    0.0145269319     2783.4679318819    0.0149253039        1.0455025405     0.0011   2026-09-08 10:28:03
    51     53    0.0027231201    0.0045081700     2783.4657703596    0.0021615223        0.4805492501     0.0010   2026-09-08 10:28:03
    52     54    0.0007352344    0.0010501853     2783.4656224584    0.0001479012        0.5116826950     0.0009   2026-09-08 10:28:03
    53     55    0.0002850245    0.0004539769     2783.4655456037    0.0000768546        0.5143596346     0.0011   2026-09-08 10:28:03
    54     56    0.0007012620    0.0010997213     2783.4652743857    0.0002712180        0.4895047541     0.0011   2026-09-08 10:28:03
    55     57    0.0007578089    0.0013423038     2783.4648334678    0.0004409179        0.4017816560     0.0008   2026-09-08 10:28:03
    56     58    0.0014102663    0.0019059653     2783.4642342448    0.0005992229        0.2157023911     0.0007   2026-09-08 10:28:03
    57     59    0.0013439021    0.0018577255     2783.4638717659    0.0003624790        0.1271226843     0.0010   2026-09-08 10:28:03
    58     60    0.0005760373    0.0010433560     2783.4637863715    0.0000853944        0.0350497689     0.0007   2026-09-08 10:28:03
    59     61    0.0001716449    0.0002704171     2783.4637804086    0.0000059629        0.0036667672     0.0007   2026-09-08 10:28:03

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.999609e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.4770***  0.1134   0.0000   
TC/100 EUR                        -0.3403***  0.0355   0.0000   
Household income (10k PLN)         0.5803***  0.1106   0.0000   
Male                               0.1148     0.0729   0.1150   
Higher education                   0.0306     0.0809   0.7053   
City                               0.0463     0.0742   0.5331   
Winter                             0.8390***  0.0850   0.0000   
Hiking                             2.1088***  0.0792   0.0000   
Skiing                             1.3737***  0.2705   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4097     0.0892            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.9386***  0.3065   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2783.4638
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1644
AIC/n:                             0.9542
BIC/n:                             0.9656
n (observations):               5855
r (respondents):                5855
k (parameters):                   10
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.3643
median                           0.0000          2.3002
std                              0.7834          1.0883
min                              0.0000          0.0258
max                             20.0000          8.1215
quantile 0.025                   0.0000          0.6384
quantile 0.975                   2.0000          4.6816
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:03
Estimation took 0.10344 seconds (0 hours 0 minutes 0.10344 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.57 -0.052 0.057 0.01 0.0035 -0.0041 0.18 0.44 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3933.8925955813             NaN     3511.8150941771     0.0000   2026-09-08 10:28:04
     1      3    0.3781536761    0.4367699257     3175.7033436042  758.1892519771      421.5847742562     0.0015   2026-09-08 10:28:04
     2      5    0.3981051708    0.4662282231     3054.1502970575  121.5530465467      724.6452199600     0.0014   2026-09-08 10:28:04
     3      6    0.1805746374    0.2237049127     2978.5003231944   75.6499738631      499.4991090648     0.0008   2026-09-08 10:28:04
     4      7    0.4380998084    0.5438384417     2882.4817115182   96.0186116762      158.2234778344     0.0009   2026-09-08 10:28:04
     5      8    0.1604817996    0.2003260618     2870.5689420489   11.9127694693      114.0979685377     0.0009   2026-09-08 10:28:04
     6      9    0.0923311178    0.1169631035     2866.4232429995    4.1456990494       93.2157164678     0.0011   2026-09-08 10:28:04
     7     10    0.0829194658    0.1116694665     2861.8830366884    4.5402063111      130.3715801183     0.0008   2026-09-08 10:28:04
     8     11    0.1315444626    0.2025797626     2852.0943204844    9.7887162040      167.7095171115     0.0008   2026-09-08 10:28:04
     9     12    0.1935065661    0.2800501561     2837.2840631803   14.8102573041      172.1368367327     0.0009   2026-09-08 10:28:04
    10     13    0.2262222355    0.2974789442     2821.9415525240   15.3425106562      118.5662630786     0.0010   2026-09-08 10:28:04
    11     14    0.1196534509    0.1866693080     2814.3434266792    7.5981258448       45.7319296329     0.0011   2026-09-08 10:28:04
    12     15    0.0736551604    0.0918777930     2812.4744861516    1.8689405276       38.1979803978     0.0010   2026-09-08 10:28:04
    13     16    0.0449487720    0.0636459382     2811.5853456868    0.8891404648       34.5220631684     0.0008   2026-09-08 10:28:04
    14     17    0.0412920035    0.0667730541     2810.2573130584    1.3280326284       42.3400893446     0.0007   2026-09-08 10:28:04
    15     18    0.0480395079    0.0988269847     2807.2613060440    2.9960070145       51.2009792453     0.0010   2026-09-08 10:28:04
    16     19    0.0891887177    0.1726980029     2801.4959336649    5.7653723791       60.0640232687     0.0007   2026-09-08 10:28:04
    17     20    0.2190931329    0.2809811419     2794.2361473400    7.2597863248       49.9535303820     0.0007   2026-09-08 10:28:04
    18     21    0.2301365781    0.2759391028     2789.6540741712    4.5820731689       22.0210770840     0.0010   2026-09-08 10:28:04
    19     22    0.0892772589    0.1219865366     2788.6201065037    1.0339676674       13.3991750932     0.0010   2026-09-08 10:28:04
    20     23    0.0147952857    0.0246750196     2788.5018302323    0.1182762715       14.4483098685     0.0008   2026-09-08 10:28:04
    21     24    0.0094007235    0.0166366989     2788.3825663415    0.1192638908       15.5155157350     0.0007   2026-09-08 10:28:04
    22     25    0.0175319033    0.0345488481     2788.0419301087    0.3406362328       16.7424830577     0.0010   2026-09-08 10:28:04
    23     26    0.0260989595    0.0576108005     2787.3954497441    0.6464803646       16.5227583691     0.0010   2026-09-08 10:28:04
    24     27    0.0564989280    0.0963176377     2786.3973009196    0.9981488245       14.2299151905     0.0009   2026-09-08 10:28:04
    25     28    0.0629553541    0.0994719939     2785.5880893106    0.8092116090       10.4371832256     0.0007   2026-09-08 10:28:04
    26     29    0.0267422914    0.0518119300     2785.2934992300    0.2945900806        9.1598568785     0.0007   2026-09-08 10:28:04
    27     30    0.0102667493    0.0182773607     2785.2406998248    0.0527994052        9.0669853139     0.0007   2026-09-08 10:28:04
    28     31    0.0039904817    0.0078179977     2785.2189075465    0.0217922783        9.0270063374     0.0006   2026-09-08 10:28:04
    29     32    0.0076713798    0.0148307978     2785.1555440757    0.0633634708        8.8935126687     0.0007   2026-09-08 10:28:04
    30     33    0.0130119441    0.0237897875     2785.0173578328    0.1381862429        8.5627352301     0.0007   2026-09-08 10:28:04
    31     34    0.0423700845    0.0511255532     2784.7184458900    0.2989119428        7.7632896128     0.0008   2026-09-08 10:28:04
    32     35    0.0856872619    0.0933868565     2784.2650231841    0.4534227058       10.5029145408     0.0007   2026-09-08 10:28:04
    33     36    0.0986561345    0.1088721012     2783.8667964738    0.3982267104        9.2107222959     0.0008   2026-09-08 10:28:04
    34     37    0.0461305121    0.0587816066     2783.7074722938    0.1593241800        8.2860514910     0.0007   2026-09-08 10:28:04
    35     38    0.0084915938    0.0167327079     2783.6654819830    0.0419903108        8.0185599859     0.0007   2026-09-08 10:28:04
    36     39    0.0056655191    0.0098253908     2783.6310346342    0.0344473488        7.6863002532     0.0007   2026-09-08 10:28:04
    37     40    0.0100011094    0.0181342557     2783.5412005998    0.0898340344        6.9614584720     0.0008   2026-09-08 10:28:04
    38     41    0.0275933745    0.0369826053     2783.3486638874    0.1925367124        6.3204672689     0.0008   2026-09-08 10:28:04
    39     42    0.0754016860    0.0831819967     2782.9828964838    0.3657674036        8.4597433402     0.0009   2026-09-08 10:28:04
    40     43    0.1223867432    0.1286654738     2782.5429156221    0.4399808617       10.0129306523     0.0007   2026-09-08 10:28:04
    41     44    0.0943809323    0.1011202939     2782.2820567866    0.2608588355        7.3188387645     0.0008   2026-09-08 10:28:04
    42     45    0.0188696195    0.0291033086     2782.2191748679    0.0628819187        4.1741469680     0.0007   2026-09-08 10:28:04
    43     46    0.0052336343    0.0089511849     2782.2090332783    0.0101415896        4.2693044682     0.0007   2026-09-08 10:28:04
    44     47    0.0047962429    0.0067208756     2782.1997785564    0.0092547219        4.1806742175     0.0007   2026-09-08 10:28:04
    45     48    0.0063913760    0.0109435215     2782.1748104808    0.0249680756        3.7257267100     0.0007   2026-09-08 10:28:04
    46     49    0.0079647745    0.0130420218     2782.1322311366    0.0425793442        2.6841907962     0.0007   2026-09-08 10:28:04
    47     50    0.0137737836    0.0229140986     2782.0795545183    0.0526766182        1.9285827040     0.0007   2026-09-08 10:28:04
    48     51    0.0211149222    0.0263553034     2782.0500478163    0.0295067020        1.4772678791     0.0007   2026-09-08 10:28:04
    49     52    0.0106211705    0.0128511846     2782.0439405327    0.0061072836        0.5775317617     0.0007   2026-09-08 10:28:04
    50     53    0.0013515542    0.0022690988     2782.0435144715    0.0004260612        0.4793626625     0.0007   2026-09-08 10:28:04
    51     54    0.0002679211    0.0004064405     2782.0434467533    0.0000677182        0.4908526108     0.0007   2026-09-08 10:28:04
    52     55    0.0005674465    0.0008513597     2782.0432452857    0.0002014676        0.4907293808     0.0007   2026-09-08 10:28:04
    53     56    0.0007075952    0.0011355587     2782.0428883248    0.0003569609        0.4390019093     0.0007   2026-09-08 10:28:04
    54     57    0.0011694341    0.0017168320     2782.0423454959    0.0005428289        0.2862196498     0.0007   2026-09-08 10:28:04
    55     58    0.0015148654    0.0018097567     2782.0419398486    0.0004056472        0.1358858389     0.0008   2026-09-08 10:28:04
    56     59    0.0007764263    0.0011240159     2782.0418154750    0.0001243736        0.0497595033     0.0007   2026-09-08 10:28:04
    57     60    0.0002224068    0.0003462143     2782.0418036627    0.0000118123        0.0089168027     0.0007   2026-09-08 10:28:04
    58     61    0.0000338906    0.0000619496     2782.0418033262    0.0000003366        0.0054817806     0.0009   2026-09-08 10:28:04
    59     62    0.0000055300    0.0000065892     2782.0418033171    0.0000000091        0.0051494926     0.0008   2026-09-08 10:28:04
    60     63    0.0000064133    0.0000075795     2782.0418033015    0.0000000156        0.0046388497     0.0008   2026-09-08 10:28:04
    61     64    0.0000096392    0.0000125332     2782.0418032651    0.0000000364        0.0042743540     0.0007   2026-09-08 10:28:04
    62     65    0.0000112350    0.0000166906     2782.0418032069    0.0000000582        0.0034977726     0.0007   2026-09-08 10:28:04

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.957178e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.2602***  0.1237   0.0000   
TC/100 EUR                        -0.3786***  0.0388   0.0000   
Household income (10k PLN)         0.2328**   0.1027   0.0234   
Male                               0.1181     0.0727   0.1044   
Higher education                   0.0177     0.0807   0.8266   
City                               0.0488     0.0741   0.5098   
Winter                             0.8456***  0.0848   0.0000   
Hiking                             2.1022***  0.0792   0.0000   
Skiing                             1.3627***  0.2691   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3983     0.0899            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.6410***  0.2706   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2782.0418
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1649
AIC/n:                             0.9537
BIC/n:                             0.9651
n (observations):               5855
r (respondents):                5855
k (parameters):                   10
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.2499
median                           0.0000          2.2582
std                              0.7834          0.9431
min                              0.0000          0.0340
max                             20.0000          4.5242
quantile 0.025                   0.0000          0.6513
quantile 0.975                   2.0000          3.9440
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:04
Estimation took 0.11666 seconds (0 hours 0 minutes 0.11666 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.049 0.062 0.0091 0.0038 -0.0032 0.18 0.45 0.28 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.7823922147             NaN     3301.8810446740     0.0001   2026-09-08 10:28:05
     1      3    0.3800376191    0.4460625860     3191.9268034317  742.8555887830      419.3313668104     0.0019   2026-09-08 10:28:05
     2      5    0.4471737399    0.5216766359     3056.5626384316  135.3641650002      694.0377671895     0.0018   2026-09-08 10:28:05
     3      6    0.1966417561    0.2450044481     2977.5874072243   78.9752312073      461.8621645160     0.0010   2026-09-08 10:28:05
     4      7    0.4231171138    0.5302922443     2888.4423507745   89.1450564498      160.4835847283     0.0009   2026-09-08 10:28:05
     5      8    0.1600409226    0.2019519456     2876.9363375233   11.5060132512      115.1146840760     0.0009   2026-09-08 10:28:05
     6      9    0.0930177574    0.1201696283     2872.6415357097    4.2948018136       98.2959877525     0.0008   2026-09-08 10:28:05
     7     10    0.0884993509    0.1234783350     2867.5350330306    5.1065026792      134.6569865118     0.0007   2026-09-08 10:28:05
     8     11    0.1365005099    0.2181126517     2856.8676161741   10.6674168564      167.8518937057     0.0007   2026-09-08 10:28:05
     9     12    0.2185564911    0.2976045036     2841.0746627236   15.7929534505      165.3781984507     0.0007   2026-09-08 10:28:05
    10     13    0.2377616264    0.3028693067     2825.6971168607   15.3775458630      104.9769826545     0.0010   2026-09-08 10:28:05
    11     14    0.1125346444    0.1770078908     2818.8275842514    6.8695326092       46.5958877105     0.0011   2026-09-08 10:28:05
    12     15    0.0725822973    0.0909525386     2817.0631768311    1.7644074203       39.6905821466     0.0011   2026-09-08 10:28:05
    13     16    0.0475437249    0.0704532751     2816.0179606585    1.0452161727       34.3816880198     0.0008   2026-09-08 10:28:05
    14     17    0.0420121377    0.0713254658     2814.4111015065    1.6068591520       42.8044347384     0.0007   2026-09-08 10:28:05
    15     18    0.0546741943    0.1144274505     2810.6353392307    3.7757622757       55.1315077452     0.0008   2026-09-08 10:28:05
    16     19    0.1109859255    0.1946925849     2804.1798541248    6.4554851060       58.7353642348     0.0010   2026-09-08 10:28:05
    17     20    0.2336818318    0.2931461864     2797.2221465147    6.9577076101       41.2438164115     0.0010   2026-09-08 10:28:05
    18     21    0.1968088290    0.2385951589     2793.8502622938    3.3718842209       19.2939538538     0.0009   2026-09-08 10:28:05
    19     22    0.0579760007    0.0835743423     2793.3002029662    0.5500593276       12.4417904330     0.0009   2026-09-08 10:28:05
    20     23    0.0096935863    0.0167412352     2793.2097837135    0.0904192527       13.6952873591     0.0007   2026-09-08 10:28:05
    21     24    0.0129009569    0.0236461155     2793.0213938409    0.1883898726       15.0312262607     0.0007   2026-09-08 10:28:05
    22     25    0.0193327584    0.0396497709     2792.6103195240    0.4110743169       15.9206898040     0.0007   2026-09-08 10:28:05
    23     26    0.0356433778    0.0712354218     2791.8354799321    0.7748395919       14.7134414983     0.0008   2026-09-08 10:28:05
    24     27    0.0604237696    0.1006721867     2790.8884573969    0.9470225352       11.4485874510     0.0008   2026-09-08 10:28:05
    25     28    0.0495665738    0.0819692455     2790.3113884776    0.5770689193        9.5266842601     0.0008   2026-09-08 10:28:05
    26     29    0.0153689597    0.0336651296     2790.1582396058    0.1531488718        9.3335616548     0.0008   2026-09-08 10:28:05
    27     30    0.0066455247    0.0123992848     2790.1270266441    0.0312129616        9.2783568175     0.0008   2026-09-08 10:28:05
    28     31    0.0049887108    0.0094496365     2790.0937686295    0.0332580146        9.2136325156     0.0007   2026-09-08 10:28:05
    29     32    0.0094717655    0.0185499329     2789.9966584504    0.0971101791        8.9977501234     0.0008   2026-09-08 10:28:05
    30     33    0.0245820765    0.0341006208     2789.7874496675    0.2092087829        8.4778090699     0.0008   2026-09-08 10:28:05
    31     34    0.0661384642    0.0736993165     2789.3768190055    0.4106306620        9.8762319410     0.0007   2026-09-08 10:28:05
    32     35    0.1094646382    0.1171165658     2788.8544678863    0.5223511192       11.3667610575     0.0008   2026-09-08 10:28:05
    33     36    0.0924970924    0.1033027148     2788.5076581620    0.3468097243        8.9860872574     0.0006   2026-09-08 10:28:05
    34     37    0.0269846518    0.0396691524     2788.4001581582    0.1075000038        8.7889169778     0.0007   2026-09-08 10:28:05
    35     38    0.0068499878    0.0120283334     2788.3638481883    0.0363099699        8.3880939519     0.0007   2026-09-08 10:28:05
    36     39    0.0074900444    0.0128092862     2788.3074346788    0.0564135095        7.8074628467     0.0008   2026-09-08 10:28:05
    37     40    0.0128270765    0.0243325096     2788.1716872163    0.1357474625        6.6910940005     0.0007   2026-09-08 10:28:05
    38     41    0.0454951746    0.0549274315     2787.8920640906    0.2796231257        6.7210135126     0.0007   2026-09-08 10:28:05
    39     42    0.1004712242    0.1081779620     2787.4566997690    0.4353643216        9.8797197509     0.0007   2026-09-08 10:28:05
    40     43    0.1192764095    0.1258196654     2787.0796500795    0.3770496895        8.9851699890     0.0007   2026-09-08 10:28:05
    41     44    0.0542724709    0.0619275503     2786.9383886588    0.1412614208        5.3057861965     0.0007   2026-09-08 10:28:05
    42     45    0.0079848819    0.0132368389     2786.9152368669    0.0231517918        4.0612054208     0.0008   2026-09-08 10:28:05
    43     46    0.0041236129    0.0059812138     2786.9082520096    0.0069848574        4.0402144879     0.0007   2026-09-08 10:28:05
    44     47    0.0062465142    0.0095194558     2786.8914754221    0.0167765875        3.7571735408     0.0007   2026-09-08 10:28:05
    45     48    0.0068599110    0.0110033015     2786.8600083203    0.0314671018        3.0037525268     0.0007   2026-09-08 10:28:05
    46     49    0.0086866985    0.0170721433     2786.8127800489    0.0472282714        1.8558943642     0.0007   2026-09-08 10:28:05
    47     50    0.0177938747    0.0246290840     2786.7764375453    0.0363425035        1.6779789883     0.0007   2026-09-08 10:28:05
    48     51    0.0142342384    0.0174884878     2786.7651253321    0.0113122133        0.8101414443     0.0007   2026-09-08 10:28:05
    49     52    0.0033715317    0.0045777545     2786.7639765284    0.0011488036        0.4580191200     0.0007   2026-09-08 10:28:05
    50     53    0.0004327863    0.0006443959     2786.7638853322    0.0000911962        0.4805338730     0.0007   2026-09-08 10:28:05
    51     54    0.0003663051    0.0005324088     2786.7637755886    0.0001097436        0.4864238275     0.0007   2026-09-08 10:28:05
    52     55    0.0006754539    0.0009911003     2786.7634914007    0.0002841879        0.4586087637     0.0007   2026-09-08 10:28:05
    53     56    0.0008001346    0.0014086519     2786.7630362252    0.0004551755        0.3529591288     0.0008   2026-09-08 10:28:05
    54     57    0.0014915149    0.0018491247     2786.7625493634    0.0004868618        0.1625740373     0.0007   2026-09-08 10:28:05
    55     58    0.0011376970    0.0014393300     2786.7623279023    0.0002214610        0.0867107916     0.0007   2026-09-08 10:28:05
    56     59    0.0003368876    0.0005822576     2786.7622924582    0.0000354442        0.0172177151     0.0007   2026-09-08 10:28:05
    57     60    0.0000858926    0.0001294147     2786.7622908024    0.0000016558        0.0049162345     0.0007   2026-09-08 10:28:05
    58     61    0.0000133250    0.0000174311     2786.7622907757    0.0000000267        0.0040645284     0.0008   2026-09-08 10:28:05
    59     62    0.0000024730    0.0000028916     2786.7622907705    0.0000000052        0.0038852852     0.0007   2026-09-08 10:28:05
    60     63    0.0000104994    0.0000130079     2786.7622907393    0.0000000313        0.0035668558     0.0007   2026-09-08 10:28:05
    61     64    0.0000082100    0.0000129797     2786.7622907018    0.0000000375        0.0029515675     0.0007   2026-09-08 10:28:05

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','8.936342e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3463***  0.1210   0.0000   
TC/100 EUR                        -0.3664***  0.0395   0.0000   
Household income (10k PLN)         0.2568**   0.1028   0.0125   
Male                               0.1147     0.0727   0.1143   
Higher education                   0.0169     0.0807   0.8346   
City                               0.0524     0.0741   0.4793   
Winter                             0.8549***  0.0849   0.0000   
Hiking                             2.1190***  0.0791   0.0000   
Skiing                             1.3946***  0.2695   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.4002     0.0898            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.7295***  0.2944   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2786.7623
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1635
AIC/n:                             0.9553
BIC/n:                             0.9667
n (observations):               5855
r (respondents):                5855
k (parameters):                   10
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1226
median                           0.0000          2.1322
std                              0.7834          0.9278
min                              0.0000          0.0266
max                             20.0000          5.0512
quantile 0.025                   0.0000          0.5807
quantile 0.975                   2.0000          3.9862
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:05
Estimation took 0.13254 seconds (0 hours 0 minutes 0.13254 seconds).
 
__________________________________________________________________________________________________________________
 
Estimating Negative Binomial (NB2) regression model ...
without truncation
without censoring.
Using linear regression estimates as starting values
Initial values: [-0.58 -0.051 0.062 0.0089 0.0041 -0.0031 0.18 0.45 0.27 0]

Opmization algorithm: <strong>quasi-newton
</strong>Gradient: <strong>user-supplied, analytical 
</strong>Hessian: <strong>off, </strong><strong>retained from optimization 
</strong>
 Iter.  Eval.         max|dB|            Step                f(x)         df prev          Opt. Cond.   Iter sec             Date/time
     0      1             NaN             NaN     3934.3353283414             NaN     3294.7369663439     0.0001   2026-09-08 10:28:06
     1      3    0.3812044178    0.4477198291     3189.5884775476  744.7468507938      420.2110006735     0.0021   2026-09-08 10:28:06
     2      5    0.4507364136    0.5257428140     3051.5465184638  138.0419590838      684.8882875511     0.0021   2026-09-08 10:28:06
     3      6    0.2028657419    0.2521253582     2972.1940548530   79.3524636108      458.5528415571     0.0009   2026-09-08 10:28:06
     4      7    0.4176633482    0.5240855621     2884.6282247543   87.5658300987      158.8849122326     0.0009   2026-09-08 10:28:06
     5      8    0.1593530261    0.2010322626     2873.2775390831   11.3506856712      113.7855727994     0.0009   2026-09-08 10:28:06
     6      9    0.0924347371    0.1192513112     2869.0517121265    4.2258269566       97.3281753428     0.0010   2026-09-08 10:28:06
     7     10    0.0883137655    0.1228722480     2864.0087846799    5.0429274466      133.1975862450     0.0011   2026-09-08 10:28:06
     8     11    0.1351828487    0.2166665390     2853.4904082826   10.5183763974      165.7618649945     0.0009   2026-09-08 10:28:06
     9     12    0.2163594084    0.2951864063     2837.9475867217   15.5428215609      162.9074620565     0.0010   2026-09-08 10:28:06
    10     13    0.2346863278    0.2996232974     2822.8675406656   15.0800460561      102.9400865807     0.0009   2026-09-08 10:28:06
    11     14    0.1120473098    0.1756200262     2816.1393993529    6.7281413127       46.1730818866     0.0010   2026-09-08 10:28:06
    12     15    0.0722207383    0.0904504180     2814.4088417516    1.7305576013       39.4531559495     0.0012   2026-09-08 10:28:06
    13     16    0.0471124584    0.0695014670     2813.3783162482    1.0305255034       34.2493826074     0.0010   2026-09-08 10:28:06
    14     17    0.0421587452    0.0711994358     2811.7725339305    1.6057823178       42.6433548765     0.0010   2026-09-08 10:28:06
    15     18    0.0550191618    0.1142989065     2808.0164898198    3.7560441106       54.6154182498     0.0011   2026-09-08 10:28:06
    16     19    0.1126401774    0.1953134267     2801.6116084745    6.4048813453       58.1978863255     0.0010   2026-09-08 10:28:06
    17     20    0.2332955408    0.2921043818     2794.7614189776    6.8501894970       40.7152236810     0.0010   2026-09-08 10:28:06
    18     21    0.1939939966    0.2354502410     2791.4706928239    3.2907261537       19.0269948637     0.0008   2026-09-08 10:28:06
    19     22    0.0562502428    0.0816560046     2790.9391096245    0.5315831994       12.2846271499     0.0008   2026-09-08 10:28:06
    20     23    0.0095084637    0.0163597923     2790.8507299445    0.0883796800       13.5101531434     0.0011   2026-09-08 10:28:06
    21     24    0.0128815170    0.0235787676     2790.6631944869    0.1875354576       14.8366831964     0.0010   2026-09-08 10:28:06
    22     25    0.0193089300    0.0393944635     2790.2569936609    0.4062008260       15.6974637531     0.0009   2026-09-08 10:28:06
    23     26    0.0356343372    0.0709283828     2789.4937132803    0.7632803806       14.4489861319     0.0010   2026-09-08 10:28:06
    24     27    0.0596944648    0.0995682479     2788.5713292944    0.9223839859       11.2534157268     0.0010   2026-09-08 10:28:06
    25     28    0.0481645749    0.0801437982     2788.0174082733    0.5539210210        9.4530019407     0.0008   2026-09-08 10:28:06
    26     29    0.0150795296    0.0325654500     2787.8722902084    0.1451180650        9.2608323639     0.0008   2026-09-08 10:28:06
    27     30    0.0064311392    0.0120030413     2787.8420558317    0.0302343766        9.2053339261     0.0007   2026-09-08 10:28:06
    28     31    0.0050650825    0.0095362990     2787.8081946725    0.0338611592        9.1377008440     0.0007   2026-09-08 10:28:06
    29     32    0.0094599770    0.0185668053     2787.7106248824    0.0975697901        8.9168206540     0.0007   2026-09-08 10:28:06
    30     33    0.0252824907    0.0345930780     2787.4999016503    0.2107232321        8.3859310046     0.0007   2026-09-08 10:28:06
    31     34    0.0671807613    0.0746075837     2787.0893135604    0.4105880899        9.9183800753     0.0007   2026-09-08 10:28:06
    32     35    0.1099127628    0.1175493836     2786.5720174053    0.5172961551       11.2578712062     0.0007   2026-09-08 10:28:06
    33     36    0.0911687285    0.1019304855     2786.2338931787    0.3381242266        8.9679061227     0.0010   2026-09-08 10:28:06
    34     37    0.0257977376    0.0383566003     2786.1303780327    0.1035151460        8.7461610055     0.0008   2026-09-08 10:28:06
    35     38    0.0067104858    0.0117319965     2786.0948223563    0.0355556764        8.3435100934     0.0008   2026-09-08 10:28:06
    36     39    0.0074942241    0.0128380984     2786.0380812466    0.0567411097        7.7503550488     0.0009   2026-09-08 10:28:06
    37     40    0.0129352000    0.0243783889     2785.9024387407    0.1356425059        6.6171681118     0.0007   2026-09-08 10:28:06
    38     41    0.0458816688    0.0552933964     2785.6237949356    0.2786438051        6.7941316067     0.0007   2026-09-08 10:28:06
    39     42    0.1004250834    0.1081097573     2785.1950285402    0.4287663954        9.8243665934     0.0007   2026-09-08 10:28:06
    40     43    0.1173983682    0.1238723761     2784.8304045124    0.3646240278        8.7990736432     0.0007   2026-09-08 10:28:06
    41     44    0.0519829516    0.0594978159     2784.6970891617    0.1333153507        5.1507323146     0.0007   2026-09-08 10:28:06
    42     45    0.0076574480    0.0126635346     2784.6755839586    0.0215052031        4.0240779903     0.0007   2026-09-08 10:28:06
    43     46    0.0039977810    0.0058122742     2784.6688129816    0.0067709770        4.0001226772     0.0007   2026-09-08 10:28:06
    44     47    0.0061533676    0.0094746848     2784.6520917091    0.0167212725        3.7087733648     0.0007   2026-09-08 10:28:06
    45     48    0.0067825330    0.0108646463     2784.6212020215    0.0308896876        2.9445097286     0.0007   2026-09-08 10:28:06
    46     49    0.0086550889    0.0170176679     2784.5755342639    0.0456677576        1.7971035645     0.0007   2026-09-08 10:28:06
    47     50    0.0174421551    0.0240526162     2784.5414988885    0.0340353754        1.6105006905     0.0007   2026-09-08 10:28:06
    48     51    0.0134266645    0.0165394543     2784.5313163772    0.0101825113        0.7623523454     0.0010   2026-09-08 10:28:06
    49     52    0.0030298214    0.0041779385     2784.5303246308    0.0009917464        0.4482566074     0.0009   2026-09-08 10:28:06
    50     53    0.0003981174    0.0005920815     2784.5302418875    0.0000827433        0.4683958398     0.0007   2026-09-08 10:28:06
    51     54    0.0003752186    0.0005445080     2784.5301310698    0.0001108177        0.4735463672     0.0007   2026-09-08 10:28:06
    52     55    0.0006598629    0.0009714540     2784.5298573401    0.0002737297        0.4439710364     0.0007   2026-09-08 10:28:06
    53     56    0.0008156942    0.0013983920     2784.5294189850    0.0004383551        0.3363832898     0.0007   2026-09-08 10:28:06
    54     57    0.0014598843    0.0017972425     2784.5289658122    0.0004531728        0.1521807655     0.0008   2026-09-08 10:28:06
    55     58    0.0010698639    0.0013661069     2784.5287671194    0.0001986928        0.0802639794     0.0007   2026-09-08 10:28:06
    56     59    0.0003169923    0.0005365561     2784.5287368874    0.0000302321        0.0152936771     0.0007   2026-09-08 10:28:06
    57     60    0.0000769968    0.0001172266     2784.5287355425    0.0000013449        0.0050195388     0.0007   2026-09-08 10:28:06
    58     61    0.0000119617    0.0000154085     2784.5287355204    0.0000000220        0.0042754107     0.0008   2026-09-08 10:28:06
    59     62    0.0000027276    0.0000032087     2784.5287355145    0.0000000059        0.0040722112     0.0007   2026-09-08 10:28:06
    60     63    0.0000106040    0.0000132466     2784.5287354813    0.0000000331        0.0037030348     0.0007   2026-09-08 10:28:06
    61     64    0.0000086758    0.0000135327     2784.5287354405    0.0000000408        0.0030750360     0.0007   2026-09-08 10:28:06

<a href = "matlab: helpview('optim','local_min_unconstrained','CSHelpWindow');">Local minimum found</a>.

Optimization completed because the <a href = "matlab: helpview('optim','grad_size','CSHelpWindow');">size of the gradient</a> is less than
the value of the <a href = "matlab: helpview('optim','optimality_tolerance_unc','CSHelpWindow');">optimality tolerance</a>.

<<a href = "matlab: createExitMsg({'optim:fminusub:Exit1basic'},{'optim:fminusub:Exit1detailed','9.330344e-07','1.000000e-06'},true,true);;">stopping criteria details</a>>

__________________________________________________________________________________________________________________

<strong>Negative Binomial </strong><strong>
</strong>                                                                 
var.                                coef.    st.err.  p-value   
Constant                          -2.3296***  0.1209   0.0000   
TC/100 EUR                        -0.3772***  0.0397   0.0000   
Household income (10k PLN)         0.2597**   0.1028   0.0116   
Male                               0.1126     0.0727   0.1212   
Higher education                   0.0170     0.0807   0.8335   
City                               0.0534     0.0741   0.4713   
Winter                             0.8546***  0.0849   0.0000   
Hiking                             2.1190***  0.0791   0.0000   
Skiing                             1.3835***  0.2697   0.0000   
 
                                                                 
                                  Overdispersion parameters      
var.                                coef.    st.err.            
ln alpha                           0.3989     0.0898            
 
                                                                 
                                  Consumer Surplus               
var.                                coef.    st.err.  p-value   
-1/(TC/100 EUR)                    2.6511***  0.2793   0.0000   
 
<strong>Model diagnostics: 
</strong>LL at convergence:             -2784.5287
LL at constant(s) only:        -3331.2932
McFadden's pseudo-R²:              0.1641
AIC/n:                             0.9546
BIC/n:                             0.9660
n (observations):               5855
r (respondents):                5855
k (parameters):                   10
 
Estimation method      maximum likelihood
Optimization method    quasi-newton
Gradient               user-supplied, analytical
Hessian                off, retained from optimization
                       
Descriptive statistics 
var                                   Y      TC/100 EUR
mean                             0.2362          2.1162
median                           0.0000          2.1210
std                              0.7834          0.9249
min                              0.0000          0.0269
max                             20.0000          5.1370
quantile 0.025                   0.0000          0.5722
quantile 0.975                   2.0000          3.9713
 
 
Estimation completed on Tuesday, 2026-09-08 at 10:28:06
Estimation took 0.11901 seconds (0 hours 0 minutes 0.11901 seconds).
Saved C:\Users\Katarzyna\Desktop\TPN_substitutes\coding\replication package (2)\replication package\CDM_results\CS_seasonal_by_specification.xlsx

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2 of 4: run_linked_models (mt)
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mt_TC_0  (1 of 6)
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