Chapter B.4, Problem 92E

Graduation Rules. Refer to Exercise B.86, where we investigated the possible presence and effect of multicollinearity in the regression of graduation rate on the 25th percentile of SAT scores for entering students, the 75th percentile of SAT scores for entering students, and the percentage of freshmen in the top 10% of their high school class for 45 colleges. We now add three additional predictor variables, student-to-faculty ratio, percentage of applicants accepted, and percentage of alumni giving to the college. The data for the additional predictor variables are in the table on page B-121. Use the technology of your choice to obtain the solution for the following problems.

1. a. Find the correlation coefficients between the six predictor variables.
2. b. Obtain the scatterplot matrix for the six predictor variables.
3. c. Obtain the VIFs for the six predictor variables in the regression analysis that includes all six predictor variables.
4. d. Assess the severity of multicollinearity in the regression analysis involving all six predictor variables.
5. e. Eliminate the predictor variable having the largest VIF and obtain the VIFs for the remaining five predictor variables in the regression analysis using these five predictor variables.
6. f. Assess the severity of multicollinearity in the five- variable regression analysis in part (e).
7. g. Compare the VIFs in part (c) with those in part (e). What is the effect of removing the predictor variable with the largest VIF?