Chapter 14, Problem 19CE

The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. He thought that high school GPA, the verbal score on the Scholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are:

1. a. Consider the following correlation matrix. Which variable has the strongest correlation with the dependent variable? Some of the correlations among the independent variables are strong. Does this appear to be a problem?

1. b. Consider the following output. Compute the coefficient of multiple determination.

1. c. Conduct a global test of hypothesis from the preceding output. Does it appear that any of the regression coefficients are not equal to zero?
2. d. Conduct a test of hypothesis on each independent variable. Would you consider eliminating the variables “SAT_Verbal” and “SAT_Math”? Let α = .05.
3. e. The analysis has been rerun without “SAT_Verbal” and “SAT_Math.” See the following output. Compute the coefficient of determination. How much has R² changed from the previous analysis?

1. f. Following is a histogram of the residuals. Does the normality assumption for the residuals seem reasonable?

1. g. Following is a plot of the residuals and the $\hat{y}$ values. Do you see any violation of the assumptions?