Booklet of Code and Output for STAD29/STA 1007 Midterm Exam

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Booklet of Code and Output for STAD29/STA 1007 Midterm Exam

List of Figures in this document by page: List of Figures 1 NBA attendance data........................ 2 2 Regression model for NBA attendances............... 3 3 Residual plots for NBA attendances................ 4 4 Ozone layer data........................... 5 5 Ozone layer data processing part 1................. 5 6 Ozone layer data processing part 2................. 6 7 Ozone layer scatterplot........................ 7 8 New Zealand bird data........................ 8 9 Analysis 1 of NZ bird data...................... 9 10 Analysis 2 of NZ bird data...................... 10 11 Analysis 3 of NZ bird data...................... 11 12 Space shuttle data (summary).................... 11 13 Space shuttle part 1......................... 11 14 Space shuttle part 2......................... 12 15 Space shuttle part 3......................... 12 16 Predictions 1............................. 12 17 Prediction 2.............................. 13 18 Primary biliary cirrhosis data.................... 14 19 Survival analysis part 1....................... 14 20 Survival analysis part 2....................... 15 21 Survival analysis part 3....................... 16 22 Survival analysis part 4....................... 17 1

nba=read.table("nba-attendance.txt",header=t) nba team wins market.share finals attendance 1 Atlanta 47 2.070 no 16478 2 Boston 62 2.105 yes 18624 3 Charlotte 35 0.981 no 14526 4 Chicago 41 3.052 no 21197 5 Cleveland 66 1.332 yes 20010 6 Dallas 50 2.175 yes 20042 7 Denver 54 1.332 no 17223 8 Detroit 39 1.684 yes 21877 9 GoldenState 29 2.164 no 18942 10 Houston 53 1.840 no 17482 11 Indiana 36 0.974 no 14182 12 LAClippers 19 4.940 no 16170 13 LALakers 65 4.940 yes 18997 14 Memphis 24 0.589 no 12745 15 Miami 43 1.352 yes 18229 16 Milwaukee 34 0.791 no 15389 17 Minnesota 24 1.512 no 14505 18 NewJersey 34 6.495 no 15147 19 NewOrleans 49 0.527 no 16968 20 NewYork 32 6.495 no 19287 21 OklahomaCity 23 0.600 no 18693 22 Orlando 59 1.281 yes 17043 23 Philadelphia 41 2.578 no 15802 24 Phoenix 46 1.622 no 18422 25 Portland 54 1.027 no 20524 26 Sacramento 17 1.223 no 12571 27 SanAntonio 54 0.715 yes 18269 28 Toronto 33 4.900 no 18773 29 Utah 48 0.803 no 19903 30 Washington 19 2.028 no 16612 Figure 1: NBA attendance data 2

nba.1=lm(attendance~wins+market.share+finals,data=nba) summary(nba.1) Call: lm(formula = attendance ~ wins + market.share + finals, data = nba) Residuals: Min 1Q Median 3Q Max -2888.4-1490.0-411.6 1315.2 3886.8 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 13836.50 1473.50 9.390 7.73e-10 *** wins 68.26 34.87 1.958 0.0611. market.share 269.36 232.72 1.157 0.2576 finalsyes 1037.88 1088.32 0.954 0.3490 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2113 on 26 degrees of freedom Multiple R-squared: 0.3049,Adjusted R-squared: 0.2247 F-statistic: 3.802 on 3 and 26 DF, p-value: 0.02199 Figure 2: Regression model for NBA attendances 3

par(mfrow=c(2,2)) plot(nba.1) Residuals vs Fitted Normal Q Q Residuals 2000 0 2000 4000 21 4 8 Standardized residuals 1 0 1 2 8 4 21 16000 18000 20000 2 1 0 1 2 Fitted values Theoretical Quantiles Standardized residuals 0.0 0.4 0.8 1.2 Scale Location 8 4 21 Standardized residuals 1 0 1 2 Residuals vs Leverage 8 26 Cook's distance 0.5 18 16000 18000 20000 Fitted values 0.00 0.05 0.10 0.15 0.20 0.25 Leverage par(mfrow=c(1,1)) Figure 3: Residual plots for NBA attendances 4

ozone=read.table("inhibit.txt",header=t) ozone inhibit.deep uvb.deep inhibit.surface uvb.surface 1 0.0 0.00 7.0 0.01 2 1.0 0.00 7.0 0.02 3 6.0 0.01 7.0 0.03 4 9.5 0.01 9.0 0.04 5 10.0 0.00 11.0 0.03 6 14.0 0.01 12.5 0.03 7 20.0 0.03 21.0 0.04 8 25.0 0.02 NA NA 9 39.0 0.03 NA NA 10 59.0 0.03 NA NA suppressmessages(library(dplyr)) Figure 4: Ozone layer data ozone %>% mutate(inhibit=inhibit.deep,uvb=uvb.deep) %>% select(c(inhibit,uvb)) -> deep ozone %>% mutate(inhibit=inhibit.surface,uvb=uvb.surface) %>% select(c(inhibit,uvb)) -> surface Figure 5: Ozone layer data processing part 1 5

v=bind_rows(deep=deep,surface=surface,.id="depth") v Source: local data frame [20 x 3] depth inhibit uvb (chr) (dbl) (dbl) 1 deep 0.0 0.00 2 deep 1.0 0.00 3 deep 6.0 0.01 4 deep 9.5 0.01 5 deep 10.0 0.00 6 deep 14.0 0.01 7 deep 20.0 0.03 8 deep 25.0 0.02 9 deep 39.0 0.03 10 deep 59.0 0.03 11 surface 7.0 0.01 12 surface 7.0 0.02 13 surface 7.0 0.03 14 surface 9.0 0.04 15 surface 11.0 0.03 16 surface 12.5 0.03 17 surface 21.0 0.04 18 surface NA NA 19 surface NA NA 20 surface NA NA Figure 6: Ozone layer data processing part 2 6

library(ggplot2) ggplot(v,aes(x=uvb,y=inhibit,colour=depth))+ geom_point()+geom_smooth(method="lm") Warning: Removed 3 rows containing non-finite values (stat smooth). Warning: Removed 3 rows containing missing values (geom point). 60 40 depth inhibit 20 deep surface 0 0.00 0.01 0.02 0.03 0.04 uvb Figure 7: Ozone layer scatterplot 7

nzbirds=read.table("nzbird.txt",header=t) str(nzbirds) 'data.frame': 67 obs. of 15 variables: $ Species: Factor w/ 67 levels "Aca_cann","Aca_flam",..: 29 28 23 14 13 18 19 12 10 11. $ Status : int 1 1 1 0 0 1 0 1 0 0... $ Length : int 1520 1250 870 720 820 770 50 570 580 480... $ Mass : num 9600 5000 3360 2517 3170... $ Range : num 1.21 0.56 0.07 1.1 3.45 2.96 0.01 9.01 7.9 4.33... $ Migr : int 1 1 1 3 3 2 1 2 3 3... $ Insect : int 12 0 0 12 0 0 0 6 6 0... $ Diet : int 2 1 1 2 1 1 1 2 2 1... $ Clutch : num 6 6 4 3.8 5.9 5.9 4 12.6 8.3 8.7... $ Broods : int 1 1 1 1 1 1 2 1 1 1... $ Wood : int 0 0 0 0 0 0 0 0 0 0... $ Upland : int 0 0 0 0 0 0 0 0 0 0... $ Water : int 1 1 1 1 1 1 0 1 1 1... $ Release: int 6 10 3 1 2 10 1 17 3 5... $ Indiv : int 29 85 8 10 7 60 2 1539 102 32... Figure 8: New Zealand bird data 8

nzbirds.1=glm(status~length+mass+range+migr+insect+diet+ Clutch+Broods+Wood+Upland+Water+Release+Indiv, data=nzbirds,family="binomial") summary(nzbirds.1) Call: glm(formula = Status ~ Length + Mass + Range + Migr + Insect + Diet + Clutch + Broods + Wood + Upland + Water + Release + Indiv, family = "binomial", data = nzbirds) Deviance Residuals: Min 1Q Median 3Q Max -1.56830-0.25666-0.04783 0.10892 2.72372 Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) -6.338010 5.716762-1.109 0.2676 Length -0.002815 0.005317-0.529 0.5965 Mass 0.002668 0.001674 1.594 0.1110 Range -0.131607 0.350234-0.376 0.7071 Migr -2.043545 1.115824-1.831 0.0670. Insect 0.147992 0.212364 0.697 0.4859 Diet 2.028505 1.883201 1.077 0.2814 Clutch 0.079380 0.268305 0.296 0.7673 Broods 0.021770 0.928327 0.023 0.9813 Wood 2.490210 1.641601 1.517 0.1293 Upland -4.713474 2.864827-1.645 0.0999. Water 0.234944 2.670193 0.088 0.9299 Release -0.012916 0.193211-0.067 0.9467 Indiv 0.015926 0.008324 1.913 0.0557. --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 90.343 on 66 degrees of freedom Residual deviance: 26.496 on 53 degrees of freedom AIC: 54.496 Number of Fisher Scoring iterations: 8 Figure 9: Analysis 1 of NZ bird data 9

nzbirds.2=update(nzbirds.1,.~.-length-range-insect-clutch -Broods-Water-Release) summary(nzbirds.2) Call: glm(formula = Status ~ Mass + Migr + Diet + Wood + Upland + Indiv, family = "binomial", data = nzbirds) Deviance Residuals: Min 1Q Median 3Q Max -1.62601-0.32089-0.07121 0.10296 2.73035 Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) -5.1367680 2.7210950-1.888 0.059058. Mass 0.0019131 0.0007512 2.547 0.010876 * Migr -1.9596476 0.9658570-2.029 0.042466 * Diet 1.8677300 0.9987152 1.870 0.061465. Wood 2.3002854 1.3579902 1.694 0.090286. Upland -5.1221630 2.4552556-2.086 0.036960 * Indiv 0.0157164 0.0046631 3.370 0.000751 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 90.343 on 66 degrees of freedom Residual deviance: 28.052 on 60 degrees of freedom AIC: 42.052 Number of Fisher Scoring iterations: 7 Figure 10: Analysis 2 of NZ bird data 10

anova(nzbirds.2,nzbirds.1,test="chisq") Analysis of Deviance Table Model 1: Status ~ Mass + Migr + Diet + Wood + Upland + Indiv Model 2: Status ~ Length + Mass + Range + Migr + Insect + Diet + Clutch + Broods + Wood + Upland + Water + Release + Indiv Resid. Df Resid. Dev Df Deviance Pr(>Chi) 1 60 28.052 2 53 26.496 7 1.5554 0.9803 Figure 11: Analysis 3 of NZ bird data space.shuttle=read.table("space-shuttle.txt",header=t) str(space.shuttle) 'data.frame': 23 obs. of 5 variables: $ flight : int 1 2 3 5 6 7 8 9 10 11... $ distress : Factor w/ 3 levels "0","1-2","3+": 1 2 1 1 2 1 1 1 2 3... $ temp : int 66 70 69 68 67 72 73 70 57 63... $ date : int 7772 7986 8116 8350 8494 8569 8642 8732 8799 8862... $ z.computed.: num 14.1 14.1 14.7 15.6 16.3... Figure 12: Space shuttle data (summary) library(mass) Attaching package: MASS The following object is masked from package:dplyr : select space.shuttle.1=polr(distress~temp+date,data=space.shuttle) space.shuttle.2=polr(distress~date,data=space.shuttle) space.shuttle.3=polr(distress~temp,data=space.shuttle) Figure 13: Space shuttle part 1 11

anova(space.shuttle.2,space.shuttle.1) Likelihood ratio tests of ordinal regression models Response: distress Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi) 1 date 20 43.71774 2 temp + date 19 37.59413 1 vs 2 1 6.123617 0.01333876 Figure 14: Space shuttle part 2 anova(space.shuttle.3,space.shuttle.1) Likelihood ratio tests of ordinal regression models Response: distress Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi) 1 temp 20 47.92046 2 temp + date 19 37.59413 1 vs 2 1 10.32633 0.001311456 Figure 15: Space shuttle part 3 temps=c(67,75) dates=c(8600,9300) new=expand.grid(temp=temps,date=dates) pp=predict(space.shuttle.1,new,type="p") cbind(new,pp) temp date 0 1-2 3+ 1 67 8600 0.44659249 0.3679833 0.1854242 2 75 8600 0.76360667 0.1825854 0.0538079 3 67 9300 0.07472014 0.2306452 0.6946346 4 75 9300 0.24428243 0.3933556 0.3623620 Figure 16: Predictions 1 12

new=data.frame(temp=31,date=9524) pp=predict(space.shuttle.1,new,type="p") cbind(new,pp) temp date pp 0 31 9524 7.526113e-05 1-2 31 9524 3.343053e-04 3+ 31 9524 9.995904e-01 Figure 17: Prediction 2 13

pbc1=read.table("pbc.txt",header=t) str(pbc1) 'data.frame': 312 obs. of 9 variables: $ id : int 1 2 3 4 5 6 7 8 9 10... $ days : int 400 4500 1012 1925 1504 2503 1832 2466 2400 51... $ status : int 2 0 2 2 1 2 0 2 2 2... $ drug : int 1 1 1 1 2 2 2 2 1 2... $ age : int 21464 20617 25594 19994 13918 24201 20284 19379 15526 25772... $ edema : num 1 0 0.5 0.5 0 0 0 0 0 1... $ bilirubi: num 14.5 1.1 1.4 1.8 3.4 0.8 1 0.3 3.2 12.6... $ albumin : num 2.6 4.14 3.48 2.54 3.53 3.98 4.09 4 3.08 2.74... $ prothom : num 12.2 10.6 12 10.3 10.9 11 9.7 11 11 11.5... Figure 18: Primary biliary cirrhosis data library(survival) attach(pbc1) y=surv(days,status==2) head(y,n=20) [1] 400 4500+ 1012 1925 1504+ 2503 1832+ 2466 2400 51 3762 [12] 304 3577+ 1217 3584 3672+ 769 131 4232+ 1356 Figure 19: Survival analysis part 1 14

y.1=coxph(y~drug+age+edema+bilirubi+albumin+prothom) summary(y.1) Call: coxph(formula = y ~ drug + age + edema + bilirubi + albumin + prothom) n= 312, number of events= 125 coef exp(coef) se(coef) z Pr(> z ) drug -1.217e-02 9.879e-01 1.847e-01-0.066 0.947446 age 9.036e-05 1.000e+00 2.569e-05 3.517 0.000436 *** edema 8.198e-01 2.270e+00 3.104e-01 2.641 0.008262 ** bilirubi 1.160e-01 1.123e+00 1.507e-02 7.699 1.38e-14 *** albumin -1.210e+00 2.981e-01 2.345e-01-5.162 2.45e-07 *** prothom 2.658e-01 1.304e+00 7.403e-02 3.590 0.000330 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower.95 upper.95 drug 0.9879 1.0122 0.6879 1.419 age 1.0001 0.9999 1.0000 1.000 edema 2.2701 0.4405 1.2355 4.171 bilirubi 1.1230 0.8904 1.0903 1.157 albumin 0.2981 3.3544 0.1883 0.472 prothom 1.3045 0.7666 1.1283 1.508 Concordance= 0.827 (se = 0.029 ) Rsquare= 0.408 (max possible= 0.983 ) Likelihood ratio test= 163.5 on 6 df, p=0 Wald test = 183.7 on 6 df, p=0 Score (logrank) test = 284.7 on 6 df, p=0 Figure 20: Survival analysis part 2 15

drugs=c(1,2) ages=c(15000,20000) edemas=1 bilirubis=3 albumins=3.5 prothoms=10.5 new=expand.grid(drug=drugs,age=ages,edema=edemas,bilirubi=bilirubis, albumin=albumins,prothom=prothoms) colours=c("red","blue","green","black") cbind(new,colours) drug age edema bilirubi albumin prothom colours 1 1 15000 1 3 3.5 10.5 red 2 2 15000 1 3 3.5 10.5 blue 3 1 20000 1 3 3.5 10.5 green 4 2 20000 1 3 3.5 10.5 black Figure 21: Survival analysis part 3 16

pp=survfit(y.1,new) plot(pp,col=colours) 0.0 0.2 0.4 0.6 0.8 1.0 0 1000 2000 3000 4000 Figure 22: Survival analysis part 4 17

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