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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 programUndergraduate grade point averageGMAT scoreSuccess in MBA programUndergraduate grade point averageGMAT score0000000000111112.933.053.113.243.363.413.453.603.643.572.752.813.033.103.066175575996165945675425515735366886476526086801111111111111113.173.243.413.373.463.573.623.663.693.703.783.843.773.793.97639632639619665694641594678624654718692632784
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.)X1X2X3X4X53.92.72.83.13.53.92.7514936454643350.20.070.30.080.10.0707.067.1477.27.816.255.1112.1912.3311.3013.0112.6310.429ii.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.
yx1x2x3Attendance
(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
440
0
1
0
1
0
0
0
0
1
1
0
1
0
0
10
1
1
0
1
0
0
1
1
1
1
1
1
0
1
11
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0I have been asked to attempt this question using SPSS. If you cannot assist or dont 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
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