2. The Associate Dean of an MBA programme wants to investigate whether a method can be developed that will accuratelyr predict how well an applicant witl perform in the MBA programme. This could potentially help signicantly with programme admission decisions. The Associate Dean has data on the following variables available for a random sample of BB students who completed the programme last year. For each student she has: MBA_GPA: Final result for MBA caiculated on a grade point average scale between D and 12. UnderGPA: Final result for the students undergraduate degree converted to the same grade point average scale as used for the MBA. GMAT: The total GMAT score {between 200 and 3013) Work: The number of years of work experience the student had on joining the MBA programme. BBA: A dummy variable indicating whether the student did an undergraduate business-related degree {1 J or something eise {including humanities, science, other degrees or no degree} {0}. Three regression models (A, B. and C.) built from the data are presented in Exhibits 1 to 3. a. Calculate the missing values for each of the regression models {1.5 marks each] b. By examining Exhibits 1 to 3. compare the overall tit of Models A, B, or C, and state which of these you would consider as the most appropriate [1D marks} c. For model C {Exhibit 3}, describe and interpret what the output means. {5 marks} d. Use model C to make a prediction of MBA Grade Point Average for a student with a BBc in Physics who achieved 50!} on GMAT and had 5 years of work experience on entering the programme. {3 marks} Discuss how you assess whether multicollinearity is likely to be present in a regression model and whether you believe there are reasons to believe that it is present in Model C? (3 marks) Regression Statistics Multiple R 0.6365 R Square 0.4052 Adjusted R Square 0.3984 Standard Error 0.8201 Observations 89 ANOVA dr SS MS F Significance F Regression 1 39.86 39.86 0.0000 Residual 87 58.51 0.67 Total 88 98.37 Coefficients |Standard Error 1 Stat P-value Lower 95% Upper 95% Intercept 1.7991 0.8304 2.1667 0.0330 0.1487 3.4496 GMAT 0.0111 0.0014 7.6983 0.0000 0.0082 0.0139 Exhibit 1: Model A Regression Statistics Multiple R 0.6808 R Square 0.4635 Adjusted R Square 0.4446 Standard Error 0.7879 Observations 89 ANOVA SS MS F Significance F Regression 3 45.60 15.20 24.48 0.0000 Residual 85 52.77 0.62 Total 88 98.37 Coefficients Standard Error t Sta P-value Lower 95% Upper 95% Intercept 0.4661 1.5056 0.3096 0.7576 -2.5275 3.4597 UnderGPA 0.0628 0.1199 0.5239 0.6017 -0.1756 0.3013 GMAT 0.0113 0.0014 8.1588 0.0000 0.0085 0.0140 Work 0.0926 0.0309 2.9958 0.0036 Exhibit 2: Model BRegression Statistics Multiple R 0.7341 R Square 0.5389 Adjusted R Sque 0.5226 Standard Error 0.7305 Observations 89 ANOVA SS MS F Significance F Regression 3 53.01 17.67 33.11 0.0000 Residual 85 45.36 0.53 Total 88 98.37 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.0629 0.8307 -0.0757 0.9398 -1.7145 1.5887 GMAT 0.0129 0.0014 0.0000 0.0102 0.0156 Work 0. 1047 0.0288 3.6293 0.0005 0.0473 0. 1620 BBA 0.7891 0.2094 3.7690 0.0003 0.3728 1.2054 Exhibit 3: Model C