The scores for two within-term examinations, X1 and X2; the current grade point average (GPA), X3; and the final exam score, Y, for 20 students in a business statistics class are listed in Table P-18.

a. Fit a multiple regression model to predict the final exam score from the scores on the within-term exams and GPA. Is the regression significant? Explain.
b. Predict the final exam score for a student with within-term exam scores of 86 and 77 and a GPA of 3.4.
c. Compute the VIFs and examine the t statistics for checking the significance of the individual predictor variables. Is multicollinearity a problem? Explain.
d. Compute the mean leverage. Are any of the observations high leverage points?
e. Compute the standardized residuals. Identify any observation with a large standardized residual. Does the fitted model under- or overpredict the response for these observations?

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TABLE P-18 x,x,x,Y|х, х,х, 87 85 27 91 93 60 3.2 54 100 84 33 90 92 69 3.1 63 91 82 3.5 83 100 86 36 96 85 60 3.7 93 80 87 3.5 89 56 64 28 43100 96 3.8 97 81 48 3.1 75 69 S1 2.8 50 77 67 3.1 63 80 75 3.6 74 86 73 3.0 7874 70 3.1 58 79 90 3.8 98 79 66 2.9 87 96 69 3.7 99 95 83 3.3 57