Regression

Question 1

The director of graduate studies at a well-known college of business
would like to predict the success of students in an MBA program. Two
explanatory variables, undergraduate grade point average and GMAT score,
were available for a random sample of 30 students, 20 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:

Success in MBA program Undergraduate

grade point average GMAT score Success in MBA program Undergraduate

grade point average GMAT score

0

0

0

0

0

0

0

0

0

0

1

1

1

1

1 2.93

3.05

3.11

3.24

3.36

3.41

3.45

3.60

3.64

3.57

2.75

2.81

3.03

3.10

3.06 617

557

599

616

594

567

542

551

573

536

688

647

652

608

680 1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 3.17

3.24

3.41

3.37

3.46

3.57

3.62

3.66

3.69

3.70

3.78

3.84

3.77

3.79

3.97 639

632

639

619

665

694

641

594

678

624

654

718

692

632

784



a. Fit a logistic regression model to predict the probability of
successful completion of the MBA program based on undergraduate grade
point average and GMAT score.

b. Explain the meaning of the regression coefficients for the model fit
in (a).





c. Predict the probability of successful completion of the program for a
student with an undergraduate grade point average of 3.25 and a GMAT
score of 600.

d. At the .05 level of significance, is there evidence that a logistic
regression model that uses undergraduate grade point average and GMAT
score to predict probability of success in the MBA program is a
good-fitting model?

e. At the .05 level of significance, is there evidence that
undergraduate grade point average and GMAT score each makes a
significant contribution to the logistic regression model?

Question 2

i. For the following set of data determine whether it is appropriate to
perform Factor analysis (check all necessary statistical tests, and
residuals.)

  X1 X2 X3 X4 X5

  3.9

2.7

2.8

3.1

3.5

3.9

2.7 51

49

36

45

46

43

35 0.2

0.07

0.3

0.08

0.1

0.07

0 7.06

7.14

7

7.2

7.81

6.25

5.11 12.19

12.33

11.30

13.01

12.63

10.42

9

ii. How many factors are required to represent the data?

iii. Rotate the factors using the varimax rotation and interpret these
factors.



Question 3

The manager of an amusement park would like to be able to predict daily
attendance, in order to develop more accurate plans about how much food
to order and how many ride operators to hire. After some consideration,
he decides that the following three factors are critical:

Day of the week (weekday or weekend)

Predicted weather (rain or no rain)

Whether or not special events are planned

He then took a random sample of 16 days, the data for which are shown
below.

y x1 x2 x3

Attendance

(000s) Weekend dummy

(0 = weekday)

(1 = weekend) Predicted weather dummy

(0 = rain)

(1 = no rain) Special events dummy

(0 = no special event)

(1 = special event)

25

37

40

22

45

21

29

34

39

44

48

37

49

28

39

44 0

0

1

0

1

0

0

0

0

1

1

0

1

0

0

1 0

1

1

0

1

0

0

1

1

1

1

1

1

0

1

1 1

0

0

0

1

0

0

0

1

0

1

0

1

0

0

0

I have been asked to attempt this question using SPSS. If you cannot
assist or don’t have access to SPSS I can work around using any other
methodology that you have and then compare the solutions to mine.

For this question you should provide the Variables Entered/Removed,
ANOVA, Model Summary and Coefficients tables.

a. Determine the fitted regression model?

b. Can we conclude at the one per cent significance level that weather
is a factor in determining attendance?

c. Do these results provide sufficient evidence that weekend attendance
is, on average, larger than weekday attendance? (Use) a = 0.05