(Solution) - The director of graduate studies at a college of business -(2025 Original AI-Free Solution)

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The director of graduate studies at a college of business wants to predict the success of students in an MBA program using two independent variables, undergraduate grade point average (GPA) and GMAT score. Data from a random sample of 30 students, organized and stored in show that 20 successfully completed the program (coded as 1) and 10 did not (coded as 0):
a. Develop 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 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 0.05 level of significance, is there evidence that a point average and GMAT score to predict the probability of success in the MBA program is a good-fitting model?
e. At the 0.05 level of significance, is there evidence that undergraduate grade point average and GMAT score each make a significant contribution to the logistic regression model?
f. Develop a logistic regression model that includes only undergraduate grade point average to predict the probability of success in the MBA program.
g. Develop a logistic regression model that includes only GMAT score to predict the probability of success in the MBA program.
h. Compare the models in (a), (f), and (g). Evaluate the differences among the models.