52. Analyzing College Grade Point Average. Recall that in exercise 49, the admissions officer for Clearwater College developed the following estimated regression equation relating final college GPA to the student’s SAT mathe matics score and high-school GPA.

yˆ 5 21.41 1 .0235x1 1 .00486x2 where x1 5 x2 5 y 5 high-school grade point average SAT mathematics score final college grade point average A portion of the associated computer output follows.

The regression equation is Y = −1.41 + .0235 XI + .00486 X2 Predictor Coef SE Coef T Constant −1.4053 .4848 _____ X1 .023467 .008666 _____ X2 _______ .001077 _____ S = .1298 R-Sq = _______ R-Sq (adj) = _______ Analysis of Variance SouRCE DF SS MS F Regression _____ 1.76209 _____ _____ Residual Error _____ _____ _____ Total 9 1.88000

a. Complete the missing entries in this output.

b. Use the F test and a .05 level of significance to see whether a significant relationship is present.

c. Use the t test and a = .05 to test H0: b1 = 0 and H0: b2 = 0.

d. Did the estimated regression equation provide a good fit to the data? Explain.