Homework 3
Stenroos
October 16, 2017
Loan Data
This is the Loan data set where our model will try to predict if a person will have good or bad credit. 1=Good Credit
library(car)## Warning: package 'car' was built under R version 3.4.2Loan <- read.csv("~/Business Analytics/LoanData.csv")
Loan$Status=recode(Loan$Status,"'Current'=1; else=0")
Loan$Status=as.numeric(levels(Loan$Status)[Loan$Status])Next I will split the data into a training set and test set.
n = length(Loan$Status)
n1 = floor(n*(.7))
n1## [1] 3927n2 = n-n1
train = sample(1:n,n1)Then I will find the model of the data.
XLoan <- model.matrix(Status~., data = Loan)[,-1]
XLoan[1:3,]## Credit.GradeAA Credit.GradeB Credit.GradeC Credit.GradeD Credit.GradeE
## 1 0 0 1 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## Credit.GradeHR Credit.GradeNC Amount Age Borrower.Rate
## 1 0 0 5000 4 0.150
## 2 1 0 1900 6 0.265
## 3 1 0 1000 3 0.150
## Debt.To.Income.Ratio
## 1 0.04
## 2 0.02
## 3 0.02xtrain <- XLoan[train,]
xnew <- XLoan[-train,]
ytrain <- Loan$Status[train]
ynew <- Loan$Status[-train]
m1=glm(Status~.,family=binomial,data=data.frame(Status=ytrain,xtrain))## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredsummary(m1)##
## Call:
## glm(formula = Status ~ ., family = binomial, data = data.frame(Status = ytrain,
## xtrain))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.3562 0.1366 0.2411 0.4043 2.1476
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.708e+00 4.913e-01 15.690 <2e-16 ***
## Credit.GradeAA 7.844e-01 6.095e-01 1.287 0.1981
## Credit.GradeB -2.225e-01 4.139e-01 -0.537 0.5910
## Credit.GradeC 3.356e-01 4.164e-01 0.806 0.4202
## Credit.GradeD 3.292e-01 4.202e-01 0.784 0.4333
## Credit.GradeE -4.205e-02 4.350e-01 -0.097 0.9230
## Credit.GradeHR -5.768e-01 4.455e-01 -1.295 0.1954
## Credit.GradeNC -1.180e+00 5.772e-01 -2.044 0.0410 *
## Amount -4.251e-05 1.806e-05 -2.354 0.0186 *
## Age -3.760e-01 2.688e-02 -13.990 <2e-16 ***
## Borrower.Rate -1.347e+01 1.615e+00 -8.342 <2e-16 ***
## Debt.To.Income.Ratio 1.573e-01 3.180e-01 0.495 0.6208
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2164.2 on 3926 degrees of freedom
## Residual deviance: 1699.8 on 3915 degrees of freedom
## AIC: 1723.8
##
## Number of Fisher Scoring iterations: 16Then I will predict for the test set.
ptest <- predict(m1,newdata=data.frame(xnew),type="response")
data.frame(ynew,ptest)[1:10,]## ynew ptest
## 1 1 0.9867793
## 2 1 0.7734458
## 3 1 0.9809819
## 6 1 0.9015963
## 9 1 0.9989262
## 17 0 0.7074237
## 21 1 0.9957397
## 23 1 0.8585450
## 24 1 0.9858988
## 26 1 0.9956696gg1=floor(ptest+0.5)
ttt=table(ynew,gg1)
ttt## gg1
## ynew 0 1
## 0 15 101
## 1 12 1556error=(ttt[1,2]+ttt[2,1])/n2
error ## [1] 0.06710214Our error is very low so this model is a good predictor.
bb=cbind(ptest,ynew)
bb1=bb[order(ptest,decreasing=TRUE),]
bb1## ptest ynew
## 5592 1.00000000 1
## 5593 1.00000000 1
## 5595 1.00000000 1
## 5606 1.00000000 1
## 5609 1.00000000 1
## 5610 1.00000000 1
## 5587 0.99980407 1
## 96 0.99922422 1
## 436 0.99920556 1
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## 88 0.99914624 1
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## 3136 0.22947139 1
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## 3269 0.20920691 1
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## 832 0.17207737 0
## 4967 0.15009901 0
## 4969 0.06234154 1
## 1725 0.03893029 0xbar=mean(ynew)
xbar## [1] 0.9311164axis=dim(n2)
ax=dim(n2)
ay=dim(n2)
axis[1]=1
ax[1]=xbar
ay[1]=bb1[1,2]
for (i in 2:n2) {
axis[i]=i
ax[i]=xbar*i
ay[i]=ay[i-1]+bb1[i,2]
}
aaa=cbind(bb1[,1],bb1[,2],ay,ax)
aaa[1:100,]## ay ax
## 5592 1.0000000 1 1 0.9311164
## 5593 1.0000000 1 2 1.8622328
## 5595 1.0000000 1 3 2.7933492
## 5606 1.0000000 1 4 3.7244656
## 5609 1.0000000 1 5 4.6555819
## 5610 1.0000000 1 6 5.5866983
## 5587 0.9998041 1 7 6.5178147
## 96 0.9992242 1 8 7.4489311
## 436 0.9992056 1 9 8.3800475
## 1053 0.9991750 1 10 9.3111639
## 88 0.9991462 1 11 10.2422803
## 448 0.9990920 1 12 11.1733967
## 474 0.9990831 1 13 12.1045131
## 1784 0.9990808 1 14 13.0356295
## 264 0.9990749 1 15 13.9667458
## 1961 0.9990625 1 16 14.8978622
## 4005 0.9990578 1 17 15.8289786
## 865 0.9990463 1 18 16.7600950
## 2372 0.9990273 1 19 17.6912114
## 1779 0.9990214 1 20 18.6223278
## 4006 0.9990032 1 21 19.5534442
## 864 0.9989925 1 22 20.4845606
## 2382 0.9989816 1 23 21.4156770
## 853 0.9989477 1 24 22.3467933
## 9 0.9989262 1 25 23.2779097
## 5541 0.9988556 1 26 24.2090261
## 369 0.9988433 1 27 25.1401425
## 3186 0.9988319 1 28 26.0712589
## 2963 0.9986276 1 29 27.0023753
## 451 0.9986243 1 30 27.9334917
## 256 0.9985823 1 31 28.8646081
## 2966 0.9984462 1 32 29.7957245
## 681 0.9983443 1 33 30.7268409
## 4789 0.9983320 1 34 31.6579572
## 5294 0.9981312 1 35 32.5890736
## 153 0.9981255 1 36 33.5201900
## 1606 0.9980727 1 37 34.4513064
## 305 0.9980709 1 38 35.3824228
## 3361 0.9980554 1 39 36.3135392
## 2147 0.9979662 1 40 37.2446556
## 850 0.9979640 1 41 38.1757720
## 254 0.9979579 1 42 39.1068884
## 127 0.9979409 1 43 40.0380048
## 5260 0.9979398 1 44 40.9691211
## 2752 0.9979396 1 45 41.9002375
## 1423 0.9979020 1 46 42.8313539
## 185 0.9978733 1 47 43.7624703
## 112 0.9978724 1 48 44.6935867
## 69 0.9978567 1 49 45.6247031
## 4725 0.9978446 1 50 46.5558195
## 2373 0.9978026 1 51 47.4869359
## 1075 0.9977055 1 52 48.4180523
## 2592 0.9976718 1 53 49.3491686
## 3371 0.9975280 1 54 50.2802850
## 3375 0.9974528 1 55 51.2114014
## 5034 0.9973377 1 56 52.1425178
## 3019 0.9973061 1 57 53.0736342
## 277 0.9972838 1 58 54.0047506
## 4734 0.9972496 1 59 54.9358670
## 620 0.9971861 0 59 55.8669834
## 1599 0.9971531 1 60 56.7980998
## 390 0.9971503 1 61 57.7292162
## 851 0.9971142 1 62 58.6603325
## 4786 0.9971010 1 63 59.5914489
## 1062 0.9969869 1 64 60.5225653
## 1814 0.9969467 1 65 61.4536817
## 454 0.9969444 1 66 62.3847981
## 594 0.9969082 1 67 63.3159145
## 3382 0.9969009 1 68 64.2470309
## 3180 0.9968967 1 69 65.1781473
## 4146 0.9967968 1 70 66.1092637
## 54 0.9967949 1 71 67.0403800
## 114 0.9967821 1 72 67.9714964
## 1229 0.9967291 1 73 68.9026128
## 3310 0.9966870 1 74 69.8337292
## 1247 0.9966659 1 75 70.7648456
## 1231 0.9966103 1 76 71.6959620
## 382 0.9965452 1 77 72.6270784
## 861 0.9965450 1 78 73.5581948
## 2779 0.9965229 1 79 74.4893112
## 2231 0.9963832 1 80 75.4204276
## 3308 0.9963763 1 81 76.3515439
## 1442 0.9963586 1 82 77.2826603
## 2957 0.9963539 1 83 78.2137767
## 3046 0.9963302 1 84 79.1448931
## 3369 0.9963280 1 85 80.0760095
## 4029 0.9963145 1 86 81.0071259
## 1251 0.9962981 1 87 81.9382423
## 1037 0.9962574 1 88 82.8693587
## 2606 0.9962458 1 89 83.8004751
## 4323 0.9961135 1 90 84.7315914
## 722 0.9960974 1 91 85.6627078
## 1809 0.9960762 1 92 86.5938242
## 4792 0.9960738 1 93 87.5249406
## 1627 0.9960314 1 94 88.4560570
## 4096 0.9959908 1 95 89.3871734
## 793 0.9959625 1 96 90.3182898
## 4011 0.9959153 1 97 91.2494062
## 5155 0.9959096 1 98 92.1805226
## 4892 0.9958807 1 99 93.1116390Finally we calculated the lift and the following plot shows it.
plot(axis,ay,xlab="number of cases",ylab="number of successes",main="Lift: CUM successes sorted by pred val/success prob")
points(axis,ax,type="l")
Titanic Data
The following model will try to predict if a passenger will survive the sinking of the Titanic. Survival is coded as a 1.
library(car)
T <- read.csv("~/Business Analytics/Titanic.csv")
T = T[-9:-11]
T$Gender=recode(T$Gender, "'male'=1; else=0")
T$Gender=as.numeric(levels(T$Gender)[T$Gender])Next I will split the data into a training set and test set.
n = length(T$Survived)
n1 = floor(n*(.7))
n1## [1] 730n2 = n-n1
train = sample(1:n,n1)Then I will find the model of the data.
XT <- model.matrix(Survived~., data = T)[,-1]
XT[1:3,]## Class Gender Age NumbSibOrSpsAbd NumbParOrChildAbd Fare
## 1 1 0 29.0000 0 0 211.3375
## 2 1 1 0.9167 1 2 151.5500
## 3 1 0 2.0000 1 2 151.5500
## EmbarkedAtQ EmbarkedAtS
## 1 0 1
## 2 0 1
## 3 0 1xtrain <- XT[train,]
xnew <- XT[-train,]
ytrain <- T$Survived[train]
ynew <- T$Survived[-train]
m2=glm(Survived~.,family=binomial,data=data.frame(Survived=ytrain,xtrain))
summary(m2)##
## Call:
## glm(formula = Survived ~ ., family = binomial, data = data.frame(Survived = ytrain,
## xtrain))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1989 -0.6982 -0.4138 0.6316 2.5035
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.3039565 0.6185117 8.575 < 2e-16 ***
## Class -0.9260208 0.1607787 -5.760 8.43e-09 ***
## Gender -2.6607217 0.2160287 -12.317 < 2e-16 ***
## Age -0.0415196 0.0080586 -5.152 2.57e-07 ***
## NumbSibOrSpsAbd -0.3100787 0.1279962 -2.423 0.01541 *
## NumbParOrChildAbd -0.0178921 0.1270975 -0.141 0.88805
## Fare 0.0007795 0.0024092 0.324 0.74627
## EmbarkedAtQ -1.7564827 0.5112079 -3.436 0.00059 ***
## EmbarkedAtS -0.7914461 0.2576162 -3.072 0.00212 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 992.18 on 729 degrees of freedom
## Residual deviance: 669.09 on 721 degrees of freedom
## AIC: 687.09
##
## Number of Fisher Scoring iterations: 5Then I will predict for the test set.
ptest <- predict(m2,newdata=data.frame(xnew),type="response")
data.frame(ynew,ptest)[1:10,]## ynew ptest
## 2 1 0.65925645
## 3 0 0.96358662
## 4 0 0.36643433
## 6 1 0.25990236
## 12 1 0.97062705
## 15 1 0.08530062
## 17 1 0.92251469
## 22 1 0.65950531
## 25 0 0.66807512
## 27 1 0.96610432gg1=floor(ptest+0.5)
ttt=table(ynew,gg1)
ttt## gg1
## ynew 0 1
## 0 163 30
## 1 39 81error=(ttt[1,2]+ttt[2,1])/n2
error## [1] 0.2204473Our error is high enough to say this model is not a good predictor with getting errors over 20% of the time.
bb=cbind(ptest,ynew)
bb1=bb[order(ptest,decreasing=TRUE),]
bb1## ptest ynew
## 12 0.97062705 1
## 109 0.96974311 1
## 27 0.96610432 1
## 264 0.96524735 1
## 3 0.96358662 0
## 106 0.95994898 1
## 66 0.95668486 1
## 115 0.95646261 1
## 212 0.95388471 1
## 172 0.95210234 1
## 95 0.95154976 1
## 97 0.94823682 0
## 122 0.94380030 1
## 191 0.94171302 1
## 167 0.94132912 1
## 435 0.94021963 1
## 35 0.93785263 1
## 17 0.92251469 1
## 32 0.92197013 1
## 386 0.91827851 1
## 63 0.91746042 1
## 815 0.91312340 1
## 80 0.91169280 1
## 215 0.90752415 1
## 28 0.90370048 1
## 451 0.89264260 1
## 74 0.89200115 1
## 310 0.88414610 1
## 597 0.87993076 1
## 414 0.87683789 1
## 876 0.87087665 1
## 359 0.87068752 1
## 300 0.86838370 1
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## 217 0.86670145 1
## 113 0.86583435 1
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## 500 0.85775192 1
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## 339 0.85261033 1
## 71 0.85191776 1
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## 33 0.76835568 1
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## 841 0.66874600 0
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## 995 0.12366343 1
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## 558 0.11924128 0
## 1035 0.11501072 0
## 805 0.11494660 0
## 574 0.11494197 1
## 770 0.11487689 1
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## 909 0.10840954 0
## 832 0.10688618 0
## 326 0.10444825 0
## 696 0.10298806 1
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## 795 0.09909504 0
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## 564 0.09644694 0
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## 813 0.09192968 0
## 733 0.09089368 0
## 395 0.08867624 0
## 996 0.08853423 0
## 15 0.08530062 1
## 692 0.08320954 0
## 425 0.08250046 0
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## 838 0.08158685 0
## 628 0.08054772 0
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## 937 0.07600810 0
## 690 0.07418753 0
## 584 0.07232032 0
## 599 0.07225041 0
## 388 0.07134018 1
## 968 0.07037766 0
## 821 0.06791368 0
## 741 0.06770698 0
## 1010 0.06708846 0
## 707 0.06517130 0
## 782 0.06512323 0
## 898 0.06407761 0
## 1012 0.06121902 0
## 819 0.06026419 0
## 311 0.05792163 0
## 721 0.05790958 0
## 1017 0.05362218 0
## 573 0.05113986 0
## 736 0.05101538 0
## 746 0.05056503 0
## 799 0.04923164 0
## 588 0.04916637 0
## 750 0.04889596 0
## 952 0.04760789 0
## 752 0.04576030 0
## 1029 0.04575009 0
## 755 0.04408799 0
## 427 0.03481474 0
## 674 0.03323736 0
## 893 0.03064662 0
## 728 0.02746983 0
## 715 0.01011026 0xbar=mean(ynew)
xbar## [1] 0.3833866##calculating the lift
axis=dim(n2)
ax=dim(n2)
ay=dim(n2)
axis[1]=1
ax[1]=xbar
ay[1]=bb1[1,2]
for (i in 2:n2) {
axis[i]=i
ax[i]=xbar*i
ay[i]=ay[i-1]+bb1[i,2]
}
aaa=cbind(bb1[,1],bb1[,2],ay,ax)
aaa[1:100,]## ay ax
## 12 0.9706270 1 1 0.3833866
## 109 0.9697431 1 2 0.7667732
## 27 0.9661043 1 3 1.1501597
## 264 0.9652473 1 4 1.5335463
## 3 0.9635866 0 4 1.9169329
## 106 0.9599490 1 5 2.3003195
## 66 0.9566849 1 6 2.6837061
## 115 0.9564626 1 7 3.0670927
## 212 0.9538847 1 8 3.4504792
## 172 0.9521023 1 9 3.8338658
## 95 0.9515498 1 10 4.2172524
## 97 0.9482368 0 10 4.6006390
## 122 0.9438003 1 11 4.9840256
## 191 0.9417130 1 12 5.3674121
## 167 0.9413291 1 13 5.7507987
## 435 0.9402196 1 14 6.1341853
## 35 0.9378526 1 15 6.5175719
## 17 0.9225147 1 16 6.9009585
## 32 0.9219701 1 17 7.2843450
## 386 0.9182785 1 18 7.6677316
## 63 0.9174604 1 19 8.0511182
## 815 0.9131234 1 20 8.4345048
## 80 0.9116928 1 21 8.8178914
## 215 0.9075242 1 22 9.2012780
## 28 0.9037005 1 23 9.5846645
## 451 0.8926426 1 24 9.9680511
## 74 0.8920012 1 25 10.3514377
## 310 0.8841461 1 26 10.7348243
## 597 0.8799308 1 27 11.1182109
## 414 0.8768379 1 28 11.5015974
## 876 0.8708766 1 29 11.8849840
## 359 0.8706875 1 30 12.2683706
## 300 0.8683837 1 31 12.6517572
## 304 0.8678098 1 32 13.0351438
## 217 0.8667015 1 33 13.4185304
## 113 0.8658343 1 34 13.8019169
## 594 0.8619203 0 34 14.1853035
## 500 0.8577519 1 35 14.5686901
## 551 0.8562118 1 36 14.9520767
## 609 0.8546959 0 36 15.3354633
## 339 0.8526103 1 37 15.7188498
## 71 0.8519178 1 38 16.1022364
## 255 0.8457103 1 39 16.4856230
## 309 0.8421260 1 40 16.8690096
## 301 0.8255751 1 41 17.2523962
## 822 0.8248783 1 42 17.6357827
## 345 0.8187726 1 43 18.0191693
## 519 0.8187321 1 44 18.4025559
## 604 0.8161923 1 45 18.7859425
## 165 0.8148461 1 46 19.1693291
## 321 0.8087136 1 47 19.5527157
## 699 0.8018191 1 48 19.9361022
## 524 0.8005494 1 49 20.3194888
## 798 0.7979670 1 50 20.7028754
## 949 0.7923574 0 50 21.0862620
## 429 0.7812997 0 50 21.4696486
## 436 0.7785071 1 51 21.8530351
## 962 0.7778908 1 52 22.2364217
## 522 0.7765600 0 52 22.6198083
## 143 0.7720077 1 53 23.0031949
## 332 0.7699642 1 54 23.3865815
## 33 0.7683557 1 55 23.7699681
## 1024 0.7612048 0 55 24.1533546
## 367 0.7489195 0 55 24.5367412
## 416 0.7401977 1 56 24.9201278
## 182 0.7332913 1 57 25.3035144
## 539 0.7243397 1 58 25.6869010
## 357 0.7203436 1 59 26.0702875
## 318 0.7164215 1 60 26.4536741
## 105 0.7147740 1 61 26.8370607
## 958 0.7044334 1 62 27.2204473
## 945 0.7009770 0 62 27.6038339
## 895 0.6957367 1 63 27.9872204
## 86 0.6873408 1 64 28.3706070
## 773 0.6869019 0 64 28.7539936
## 118 0.6862150 0 64 29.1373802
## 275 0.6737670 0 64 29.5207668
## 974 0.6697683 0 64 29.9041534
## 841 0.6687460 0 64 30.2875399
## 25 0.6680751 0 64 30.6709265
## 161 0.6600252 1 65 31.0543131
## 22 0.6595053 1 66 31.4376997
## 2 0.6592565 1 67 31.8210863
## 135 0.6583608 1 68 32.2044728
## 924 0.6524650 0 68 32.5878594
## 441 0.6517715 1 69 32.9712460
## 75 0.6506645 1 70 33.3546326
## 871 0.6468568 1 71 33.7380192
## 806 0.6460306 0 71 34.1214058
## 498 0.6439785 1 72 34.5047923
## 517 0.6439785 1 73 34.8881789
## 477 0.6426455 1 74 35.2715655
## 930 0.6406196 0 74 35.6549521
## 807 0.6364795 0 74 36.0383387
## 40 0.6357132 1 75 36.4217252
## 883 0.6310112 0 75 36.8051118
## 492 0.6226979 1 76 37.1884984
## 637 0.6214278 0 76 37.5718850
## 911 0.6155238 0 76 37.9552716
## 761 0.6083197 1 77 38.3386581Finally we calculated the lift and the following plot shows it.
plot(axis,ay,xlab="number of cases",ylab="number of successes",main="Lift: CUM successes sorted by pred val/success prob")
points(axis,ax,type="l")