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%.