Question: 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 mathematics score and high-school GPA.

= -1.41 + .0235 + .00486

where

= high-school grade point average

= SAT mathematics score

y = final college grade point average

A portion of the Minitab computer output follows.

The regression equation is

Y = -1.41 + .0235 X1 + .00486 X2

Predictor Coef SE Coef T

Constant -1. 4053 0.4848 __ -2.899___

X1 0.023467 0.008666 __2.708___

X2 0.00486____ 0.001077 ___ 4.513__

S = 0.1298 R–sq = ___ 0.9373___ R–sq( adj ) = ___ 0.919386___

Analysis of Variance

SOURCE DF SS MS F

Regression __2___ 1.76209 0.881045____ __ 52.3053___

Residual Error ___7__ 0.11791 0.016844286 ____ _____

Total 9 1.88000

a. Compute the missing entries in this output.

b. Use the F test and α = .05 to see whether a significant relationship is present.

c. Use the t test and α= .05 to test : = 0 and : = 0

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