Graduation Rates. Regarding the relationship between college graduation rate and the predictor variables of student-to-faculty ratio, the percentage of freshmen in the top 10% of their high school class, and the percentage of applicants accepted.
a. Explain what it would mean for the assumptions for multiple linear regression inferences to be satisfied with student-to-faculty ratio, percentage of freshmen in the top 10% of their high school class, and percentage of applicants accepted as predictor variables for graduation rate.
b. Use the computer output to obtain the coefficient of determination, R2. Interpret your result.
c. How useful do the variables student-to-faculty ratio, percentage of freshmen in the top 10% of their high school class, and percentage of applicants accepted appear to be for predicting graduation rates at colleges and universities?
d. Determine and interpret the standard error of the estimate, se.
e. At the 5% significance level, do the data provide sufficient evidence to conclude that, taken together, student-to-faculty ratio, percentage of freshmen in the top 10% of their high school class, and percentage of applicants accepted are useful for predicting graduation rate?