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?
SOLUTION
a. b. & c.
The regression results follow.
The regression equation is
Y = - 43.2 + 0.372 X1 + 0.352 X2 + 19.1 X3
Predictor Coef SE Coef T P VIF
Constant -43.15 31.67 -1.36 0.192
X1 0.3716 0.3397 1.09 0.290 1.473
X2 0.3515 0.2917 1.21 0.246 1.445
X3 19.12 11.04 1.73 0.103 1.481
S = 13.9119 R-Sq = 49.8% R-Sq(adj) = 40.4%
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