DataScienceInPractice

Chapter 5: Logistic Regression and Prediction

In the example below we can see



#----------------------------------------------------------------------------
# regresión logística / Logistic Regression
#----------------------------------------------------------------------------

admitidos <- read.table("data/admitidos.csv", header = T, sep = "\t")
admitidos$rank <- factor(admitidos$rank)

modelo.logistico <- glm(admit ~ ., data = admitidos, family = binomial)
summary(modelo.logistico)

?predict

?predict.lm

predict(modelo.logistico)

# Use this with the type="response"
predict(modelo.logistico, type="response")

Output:


setwd("~/git/Bitbucket/u-tad/Mod11/clase_estadistica")
> admitidos <- read.table("data/admitidos.csv", header = T, sep = "\t")
> admitidos$rank <- factor(admitidos$rank)
> modelo.logistico <- glm(admit ~ ., data = admitidos, family = binomial)
> summary(modelo.logistico)

Call:
glm(formula = admit ~ ., family = binomial, data = admitidos)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.6268  -0.8662  -0.6388   1.1490   2.0790  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -3.989979   1.139951  -3.500 0.000465 ***
gre          0.002264   0.001094   2.070 0.038465 *  
gpa          0.804038   0.331819   2.423 0.015388 *  
rank2       -0.675443   0.316490  -2.134 0.032829 *  
rank3       -1.340204   0.345306  -3.881 0.000104 ***
rank4       -1.551464   0.417832  -3.713 0.000205 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 499.98  on 399  degrees of freedom
Residual deviance: 458.52  on 394  degrees of freedom
AIC: 470.52

Number of Fisher Scoring iterations: 4

> ?predict
> ?predict.lm
> predict(modelo.logistico)
            1             2             3             4             5             6             7             8             9 
-1.5671256381 -0.8848441651  1.0377117527 -1.5273304649 -2.0081113220 -0.5323457560 -0.3258687362 -1.2832160350 -1.3817057732 
           10            11            12            13            14            15            16            17            18 
 0.0715032422 -0.5137519242 -0.4046308187  0.9471347213 -0.6038882992  0.8112691741 -1.4773694429 -0.6635653213 -2.4566535806 
           19            20            21            22            23            24            25            26            27 
 0.1612594374  0.2961939140 -1.6491710655 -0.2522446785 -1.9154013896 -1.4367534334 -0.2509326137  0.7643389860  0.3165404670 
           28            29            30            31            32            33            34            35            36 
-1.3568409071 -0.3101689794 -0.1671941274 -1.2793908894 -0.9156936022 -1.2377998505 -0.3024921637 -0.6501078856 -1.3073371615 
           37            38            39            40            41            42            43            44            45 
-0.0634900822 -1.8209726881 -1.0165715790 -1.9978609489 -1.4515726918 -0.6826503817 -0.7740482494 -1.5366058086 -0.7164535561 
           46            47            48            49            50            51            52            53            54 
-1.5146175831 -0.5700851248 -2.0212383358 -2.5510822821 -1.7308868852 -0.7773655464 -2.0284578751 -1.1561611274 -0.4964096805 
           55            56            57            58            59            60            61            62            63 
-1.1501765563 -0.4383577109 -1.4972247673 -2.1058307962 -0.8249146320 -1.9154013896 -0.7046386072 -1.6039596464 -0.9301326808 
           64            65            66            67            68            69            70            71            72 
-0.6948288905 -0.8006658367 -0.4202717277 -0.9551517401  0.0672888267  0.2902864395  0.8206216144 -0.6648002895 -2.5143253705 
           73            74            75            76            77            78            79            80            81 
-1.7288310808 -0.1359048482 -1.1371266392 -0.4836462266 -1.3605383840 -0.3024921637 -0.2585919950  0.6301151112 -1.6246358070 
           82            83            84            85            86            87            88            89            90 
-0.7930827376 -1.3542673497 -2.3412116831 -1.3034349193 -1.0918886956 -0.6373618660 -0.5087158581  0.2323621386  0.0452492147 
           91            92            93            94            95            96            97            98            99 
-0.0008601372  0.5671041721  0.2818650698 -0.9962250259 -0.4050118129 -0.4934559433 -1.2619980736 -0.7080835730 -0.7646958090 
          100           101           102           103           104           105           106           107           108 
-1.7630483872 -2.0275599423 -1.1464019829 -2.0035159124 -0.9394851211  0.0050473372 -0.6017553982  0.4574926524 -1.0618600947 
          109           110           111           112           113           114           115           116           117 
-2.0685826559 -0.8045680789 -1.5251975639 -1.8486158770 -2.1028770589 -0.0423226929 -0.6122922345 -0.7181291807 -0.8951451104 
          118           119           120           121           122           123           124           125           126 
-0.0893042676  0.7965004879 -2.2124885786 -0.4808201582 -1.4317173674 -1.8611745655 -1.8019381999 -0.5801307325 -1.6010059091 
          127           128           129           130           131           132           133           134           135 
 0.2149693228 -0.8586672342 -0.8777522946 -1.9670886084 -0.7126789826 -0.9729247356 -0.6183273778 -1.7215344449 -1.0254327907 
          136           137           138           139           140           141           142           143           144 
-1.3275560458 -1.5959192709 -0.5289347424 -0.5277503463  0.2471308248 -0.0563219295 -1.1261325265 -0.9695908187 -1.2830883663 
          145           146           147           148           149           150           151           152           153 
-1.4943481267 -1.7118523970 -0.8447699564 -1.8831627910 -0.5633054276  0.3470602966  0.8286619899 -1.0420047703 -0.0482815540 
          154           155           156           157           158           159           160           161           162 
-1.2348461133 -0.9593404455 -1.9285284033 -1.3711689368 -0.0246002695 -0.3648099354 -0.6736615012 -0.7901290003 -0.4020580757 
          163           164           165           166           167           168           169           170           171 
-0.2179502755 -1.2928980829 -0.6987311327  0.8112691741 -1.9400137447 -0.6685748630 -0.9818198996 -1.0609115897 -1.6022408774 
          172           173           174           175           176           177           178           179           180 
-1.8480475518 -0.9923227837 -0.0960325783 -1.5709773082 -0.5518714728 -1.3813422134 -1.3291977182 -1.2487939633 -2.2307022306 
          181           182           183           184           185           186           187           188           189 
-0.8869770661 -1.2895641660  0.1358262462 -0.3551278875 -2.1659650947  0.0406538051 -1.1595289966 -1.0364269034 -0.9289482847 
          190           191           192           193           194           195           196           197           198 
-0.8396833181 -0.8523191033 -0.6723494364 -0.8577693014 -1.7944661496 -0.5167562336 -0.5108487591 -1.3672666946 -2.0386311516 
          199           200           201           202           203           204           205           206           207 
-1.0528712142 -1.1968542335 -0.8572780727 -0.7791348876  0.8112691741 -1.4385567269  0.4963824651 -0.5085881893  0.5319889329 
          208           209           210           211           212           213           214           215           216 
 0.3779097337 -1.5666344095 -0.5379236228 -1.1802822539 -0.9238616465 -1.3161983732 -1.1633035701 -0.4443928541 -1.4959127025 
          217           218           219           220           221           222           223           224           225 
-0.8883654131 -0.0216465323 -0.5523113148 -0.5108487591 -1.4701499036 -0.5822636336 -0.4748612971 -0.7286320649 -0.5221724794 
          226           227           228           229           230           231           232           233           234 
-0.8856650013 -0.3830235874 -1.8904594269 -0.8206488299 -0.2852270167 -1.5827922571 -1.3342843565 -1.0872932860 -2.2323439030 
          235           236           237           238           239           240           241           242           243 
 0.6598141046 -0.8091634886 -0.3648099354 -0.3623474268 -2.1096824662 -0.9711553945 -1.4499310194  0.2509053982 -1.4104223093 
          244           245           246           247           248           249           250           251           252 
-0.6724771052 -0.3229149990 -0.3748555432 -0.4401270521 -1.1202756242 -0.8636767758 -0.8818904278 -1.3855574433 -1.5565382296 
          253           254           255           256           257           258           259           260           261 
-0.2717703954 -1.4643195258 -1.0355554950 -1.1874246966 -0.8345966799 -0.7502906827 -0.6657487945 -0.1528064354 -0.6250556884 
          262           263           264           265           266           267           268           269           270 
-1.1363563751 -1.5878017988 -0.7502906827 -1.0169351388 -1.7842157765 -1.6682826503 -1.0448308387 -0.3436425462 -1.9386245832 
          271           272           273           274           275           276           277           278           279 
-0.0402411785 -1.4299480262 -0.1747946608  0.1739466092 -0.9793234387 -0.9107346327 -1.2573255674  0.2018423091 -1.5895205678 
          280           281           282           283           284           285           286           287           288 
-0.6462230777 -0.0029930383 -1.8857869206 -1.2729921864 -1.8714249387 -0.9433873633 -1.5214229904  0.4105624643 -1.0719827990 
          289           290           291           292           293           294           295           296           297 
-1.1971838411 -2.7732590587 -0.4875484688 -0.6186569854 -0.1506735344  1.0135906263 -0.8527589453 -1.5395595458 -0.1811419773 
          298           299           300           301           302           303           304           305           306 
-1.1553908634 -0.6285006543 -0.9660687562 -0.5628655855 -0.9411267935 -1.2269334066  0.0744569794 -2.5565830524 -1.4461058738 
          307           308           309           310           311           312           313           314           315 
-0.2183901176 -0.5298832473 -0.9259945475 -1.9378037470 -0.8459543524 -0.2200831766 -0.8044404101 -1.4292042866 -1.5366829052 
          316           317           318           319           320           321           322           323           324 
-1.7026276255 -1.4834045862 -0.8565343331 -1.4715390651 -0.1299459872 -1.7638692234 -0.7453317132 -1.9890768338 -1.5515021635 
          325           326           327           328           329           330           331           332           333 
-1.9817801979  0.6855769035 -0.4642481786 -0.5992928895 -0.6665696307 -2.0533998378 -0.4383577109 -0.9491671690 -0.6589690973 
          334           335           336           337           338           339           340           341           342 
-1.3042557555 -1.3618504488  0.3969442219 -1.6199633008 -1.6530227355 -0.1942689911 -1.0456516749 -1.8121885730 -1.9314050439 
          343           344           345           346           347           348           349           350           351 
-1.2332815375 -0.8917001445 -1.4591557909 -1.7617363224 -0.6132407395 -0.2967123580 -1.0580855212 -0.9699709984  0.3169803090 
          352           353           354           355           356           357           358           359           360 
-1.1683902083 -1.5082188801 -0.2501117775 -0.4033701405 -0.0096699624 -0.4511211648  0.3017717808 -1.0952059927 -0.5318884796 
          361           362           363           364           365           366           367           368           369 
 0.4036725326  0.0389018982 -0.6009345620 -0.8578969701 -0.0203344675 -2.0080342254 -1.9327171088 -1.0075826985  0.5395380798 
          370           371           372           373           374           375           376           377           378 
 0.2738246943 -0.4114105160 -0.7671922699 -0.5043986695  0.1235714552 -0.3580816248 -1.4672732630 -0.3428217100  0.3622688248 
          379           380           381           382           383           384           385           386           387 
-1.3723533329 -1.2717306937 -0.1455868961 -0.6365410298 -0.6204602788  0.7206921427 -1.4719192448 -0.6107268443  0.1138380207 
          388           389           390           391           392           393           394           395           396 
-0.6504888797 -0.6673904669 -0.3940177002 -0.4015668470 -0.0512352912 -1.2538806015 -0.2463372041 -1.0804373065 -0.0453278167 
          397           398           399           400 
-1.6178303997 -1.5091673850 -0.1455868961 -0.8438214514 
> predict(modelo.logistico, type="response")
         1          2          3          4          5          6          7          8          9         10         11 
0.17262654 0.29217496 0.73840825 0.17838461 0.11835391 0.36996994 0.41924616 0.21700328 0.20073518 0.51786820 0.37431440 
        12         13         14         15         16         17         18         19         20         21         22 
0.40020025 0.72053858 0.35345462 0.69237989 0.18582508 0.33993917 0.07895335 0.54022772 0.57351182 0.16122101 0.43727108 
        23         24         25         26         27         28         29         30         31         32         33 
0.12837525 0.19204860 0.43759396 0.68229503 0.57848091 0.20475422 0.42307349 0.45829857 0.21765393 0.28583616 0.22481919 
        34         35         36         37         38         39         40         41         42         43         44 
0.42494837 0.34296523 0.21293277 0.48413281 0.13931720 0.26569575 0.11942769 0.18975965 0.33567002 0.31560404 0.17702923 
        45         46         47         48         49         50         51         52         53         54         55 
0.32817441 0.18025548 0.36121718 0.11699101 0.07235381 0.15047417 0.31488795 0.11624726 0.23936553 0.37838478 0.24045684 
        56         57         58         59         60         61         62         63         64         65         66 
0.39213236 0.18283980 0.10853139 0.30472142 0.12837525 0.33078459 0.16742893 0.28289780 0.33295972 0.30988311 0.39645173 
        67         68         69         70         71         72         73         74         75         76         77 
0.27784995 0.51681586 0.57206626 0.69436828 0.33966212 0.07486000 0.15073716 0.46607599 0.24284830 0.38139149 0.20415281 
        78         79         80         81         82         83         84         85         86         87         88 
0.42494837 0.43570986 0.65251556 0.16456653 0.31150713 0.20517359 0.08776685 0.21358749 0.25126279 0.34584314 0.37549461 
        89         90         91         92         93         94         95         96         97         98         99 
0.55783057 0.51131037 0.49978497 0.63809471 0.57000341 0.26968427 0.40010880 0.37907977 0.22063013 0.33002244 0.31762762 
       100        101        102        103        104        105        106        107        108        109        110 
0.14640896 0.11633954 0.24114689 0.11883427 0.28100436 0.50126183 0.35394219 0.61241920 0.25695415 0.11218813 0.30904921 
       111        112        113        114        115        116        117        118        119        120        121 
0.17869743 0.13603549 0.10881750 0.48942091 0.35153649 0.32780508 0.29004920 0.47768876 0.68922540 0.09863460 0.38205848 
       122        123        124        125        126        127        128        129        130        131        132 
0.19283124 0.13456621 0.14161529 0.35890251 0.16784107 0.55353632 0.29761787 0.29364378 0.12270194 0.32900715 0.27429792 
       133        134        135        136        137        138        139        140        141        142        143 
0.35016196 0.15167362 0.26397051 0.20956391 0.16855273 0.37076538 0.37104174 0.56147017 0.48592324 0.24487554 0.27496207 
       144        145        146        147        148        149        150        151        152        153        154 
0.21702497 0.18326999 0.15292361 0.30053113 0.13202601 0.36278299 0.58590453 0.69607194 0.26076336 0.48793196 0.22533437 
       155        156        157        158        159        160        161        162        163        164        165 
0.27701027 0.12691355 0.20243105 0.49385024 0.40979572 0.33767745 0.31214097 0.40081797 0.44572710 0.21536268 0.33209361 
       166        167        168        169        170        171        172        173        174        175        176 
0.69237989 0.12564635 0.33881603 0.27253083 0.25713529 0.16766865 0.13610230 0.27045353 0.47601029 0.17207711 0.36543032 
       177        178        179        180        181        182        183        184        185        186        187 
0.20079352 0.20929210 0.22290898 0.09702710 0.29173405 0.21592659 0.53390445 0.41213948 0.10284874 0.51016205 0.23875288 
       188        189        190        191        192        193        194        195        196        197        198 
0.26184001 0.28313813 0.30160149 0.29894660 0.33797096 0.29780561 0.14252603 0.37361105 0.37499458 0.20306181 0.11520619 
       199        200        201        202        203        204        205        206        207        208        209 
0.25867413 0.23203530 0.29790835 0.31450637 0.69237989 0.19176895 0.62160882 0.37552455 0.62994688 0.59336886 0.17269671 
       210        211        212        213        214        215        216        217        218        219        220 
0.36867073 0.23500145 0.28417171 0.21145148 0.23806753 0.39069474 0.18303592 0.29144726 0.49458858 0.36532833 0.37499458 
       221        222        223        224        225        226        227        228        229        230        231 
0.18691983 0.35841190 0.38346629 0.32549498 0.37234438 0.29200523 0.40539785 0.13119209 0.30562595 0.42917277 0.17040039 
       232        233        234        235        236        237        238        239        240        241        242 
0.20845157 0.25212831 0.09688336 0.65921863 0.30806878 0.40979572 0.41039144 0.10815929 0.27465027 0.19001218 0.56239934 
       243        244        245        246        247        248        249        250        251        252        253 
0.19616746 0.33794240 0.41996550 0.40736827 0.39171070 0.24596016 0.29657173 0.29278619 0.20011793 0.17414395 0.43247252 
       254        255        256        257        258        259        260        261        262        263        264 
0.18780755 0.26200847 0.23371984 0.30267400 0.32075797 0.33944941 0.46187255 0.34863249 0.24298996 0.16969339 0.32075797 
       265        266        267        268        269        270        271        272        273        274        275 
0.26562483 0.14378335 0.15865328 0.26021896 0.41492493 0.12579904 0.48994106 0.19310678 0.45641226 0.54337733 0.27302605 
       276        277        278        279        280        281        282        283        284        285        286 
0.28684953 0.22143462 0.55028996 0.16945136 0.34384116 0.49925174 0.13172559 0.21874547 0.13337693 0.28021662 0.17925207 
       287        288        289        290        291        292        293        294        295        296        297 
0.60122274 0.25502619 0.23197657 0.05878643 0.38047126 0.35008696 0.46240272 0.73372225 0.29885443 0.17659931 0.45483793 
       298        299        300        301        302        303        304        305        306        307        308 
0.23950580 0.34785059 0.27566478 0.36288468 0.28067279 0.22671860 0.51860565 0.07198547 0.19060160 0.44561844 0.37054412 
       309        310        311        312        313        314        315        316        317        318        319 
0.28373804 0.12588934 0.30028221 0.44520022 0.30907647 0.19322270 0.17701800 0.15412239 0.18491373 0.29806393 0.18670880 
       320        321        322        323        324        325        326        327        328        329        330 
0.46755914 0.14630641 0.32183935 0.12035456 0.17486941 0.12112920 0.66498227 0.38597852 0.35450549 0.33926538 0.11370930 
       331        332        333        334        335        336        337        338        339        340        341 
0.39213236 0.27905234 0.34097123 0.21344965 0.20393972 0.59795326 0.16520993 0.16070084 0.45158492 0.26006097 0.14037382 
       342        343        344        345        346        347        348        349        350        351        352 
0.12659514 0.22560760 0.29075910 0.18859648 0.14657301 0.35132030 0.42636137 0.25767548 0.27488628 0.57858815 0.23714608 
       353        354        355        356        357        358        359        360        361        362        363 
0.18120291 0.43779599 0.40050290 0.49758253 0.38909423 0.57487559 0.25063922 0.37007654 0.59956970 0.50972425 0.35412991 
       364        365        366        367        368        369        370        371        372        373        374 
0.29777892 0.49491656 0.11836196 0.12645014 0.26745319 0.63170496 0.56803162 0.39857395 0.31708679 0.37650752 0.53085361 
       375        376        377        378        379        380        381        382        383        384        385 
0.41142403 0.18735742 0.41512421 0.58958954 0.20223990 0.21896113 0.46366743 0.34602886 0.34967678 0.67275941 0.18665107 
       386        387        388        389        390        391        392        393        394        395        396 
0.35189341 0.52842881 0.34287938 0.33908140 0.40275050 0.40093595 0.48719398 0.22202911 0.43872524 0.25342327 0.48866999 
       397        398        399        400 
0.16550430 0.18106222 0.46366743 0.30073055

So, we can see that the student number 400 has 30% of probability to be admitted in this program and student number 399 has 46%.