The director of graduate studies at a well-know college of business would like t
ID: 3232427 • Letter: T
Question
The director of graduate studies at a well-know college of business would like to predict the success of students in an MBA program. Two independent variables, undergraduate grade point average and GMAT score, were available for a random sample of 30 students, 0 of whom had successfully completed the program (coded as 1)and 10 of whom had not successfully completed the program in the required amount of time (coded as 0). The results are as follows: a. Use Logistic Regression Calculator and run a logistics regression to predict the probability of successful completion of MBA program based on undergraduate grade point average and GMA score. b. Explain the meaning of odds ratios in the model. c. At the 5% level of significance, is there evidence that undergraduate grade point average and GMAT score each make a significant contribution to the logistic regression model? d. Predict the probability of successful completion of the program for a student with an undergraduate grade average of 3.50 and GMAT scores of 550 and 600.Explanation / Answer
The answeres are provided through the R software.
> tt <- read.csv("clipboard",sep=" ")
> names(ttt
+ )
Error: object 'ttt' not found
> names(tt)
[1] "Success" "GPA" "GMAT"
> tt$Success <- as.factor(tt$Success)
> sucess_logistic <- glm(Success~.,tt)
Success GPA GMAT
1 0 2.93 617
2 0 3.05 557
3 0 3.11 599
4 0 3.24 616
5 0 3.36 594
6 0 3.41 567
7 0 3.45 542
8 0 3.80 551
9 0 3.64 573
10 0 3.57 536
11 1 2.75 688
12 1 2.81 647
13 1 3.03 652
14 1 3.10 608
15 1 3.06 680
16 1 3.17 639
17 1 3.24 632
18 1 3.41 639
19 1 3.37 619
20 1 3.46 665
21 1 3.57 694
22 1 3.62 641
23 1 3.66 594
24 1 3.69 678
25 1 3.70 624
26 1 3.76 654
27 1 3.84 718
28 1 3.77 692
29 1 3.79 632
30 1 3.97 784
Error in glm(Success ~ ., tt) : 'family' not recognized
> sucess_logistic <- glm(Success~.,tt,family=binomial)
Warning message:
glm.fit: fitted probabilities numerically 0 or 1 occurred
> summary(success_logistic)
Error in summary(success_logistic) : object 'success_logistic' not found
> summary(sucess_logistic)
Call:
glm(formula = Success ~ ., family = binomial, data = tt)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.63577 -0.01582 0.00306 0.06972 1.78349
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -122.68157 59.12531 -2.075 0.0380 *
GPA 8.06029 5.03471 1.601 0.1094
GMAT 0.15844 0.07561 2.096 0.0361 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 38.1909 on 29 degrees of freedom
Residual deviance: 8.1361 on 27 degrees of freedom
AIC: 14.136
Number of Fisher Scoring iterations: 9
> predict(sucess_logisttic)
Error in predict(sucess_logisttic) : object 'sucess_logisttic' not found
> predict(sucess_logistic)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-1.3067415 -9.8459766 -2.7078308 1.0335060 -1.4849651 -5.3598620 -8.9984795 -4.7514090 -2.5553493 -8.9818921 8.4917292 2.4792589 5.0447276 -1.3624633 9.7228886
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
4.1134326 3.5685646 6.0479013 2.5566667 10.5703857 16.0518108 8.0574437 0.9331208 14.4839866 6.0087669 11.2456188 22.0306758 17.3469857 8.0017220 33.5356294
The 5% level significange test shows that though GMAT is sigificient while GPA is not.