Chapter B.5, Problem 104E

Graduation Rates. Refer to Exercise B.92 on page B-120, where we considered the regression analysis of graduation rate on the 25th percentile of SAT scores for entering students, the 75th percentile of SAT scores for entering students, the percentage of freshmen in the top 10% of their high school class, the student-to-faculty ratio, the percentage of applicants accepted, and the percentage of alumni giving to the college. Use the technology of your choice to do the following.

a. Use the forward selection method to obtain a regression equation for the data. (Take t_enter = 2.00, α_enter = 0.05.)

b. Use the backward elimination method to obtain a regression equation for the data. (Take t_remove = 2.00, α_remove = 0.05.)

c. Use stepwise regression to obtain a regression equation for these data. (Take t_enter = t_remove 2.00, α_enter = α_remove = 0.05.)

d. Are the regression equations obtained in parts (a), (b), and (c) the same?

e. For the regression equation selected by stepwise regression in part (c), obtain plots of residuals versus fitted values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.