11.80 Many colleges and universities develop regression models for predicting the grade-point average

(GPA), y, of incoming freshmen. This predicted GPA can then be used to help make admission decisions. Although most models use many independent variables to predict GPA, we will illustrate by choosing two variables:

verbal score on college entrance examination (percentile)

mathematics score on college entrance examination (percentile)

x2 =

x1 =

b2 R2 R2 a = 0.05 Maintenance Time (hours) Brand Experience

(months)

2.0 1 2 1.8 1 4 0.8 0 12 1.1 1 12 1.0 0 8 1.5 0 2 1.7 1 6 1.2 0 5 1.4 1 9 1.2 0 7 x2 =

x1 = b 1 if brand A 0 if brand I The data in table above are obtained for a random sample of 40 freshmen at one college.
a Fit the first-order model (no quadratic and no interaction terms)
Interpret the value of , and test whether these data indicate that the terms in the model are useful for predicting freshman GPA. Use .
b Sketch the relationship between predicted GPA and verbal score x1 for the following mathematics scores: .