Many colleges and universities develop regression models for predicting the GPA of incoming freshmen.

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

xl = Verbal score on college entrance examination

(percentile)

x2 = Mathematics score on college entrance examination (percentile)

The data in the table on page 632 are obtained for a random sample of 40 freshmen at one college. The SPSS printout corresponding to the model y = PI, + Plxl + P2x2 + E is shown below the data.

a. Interpret the least squares estimates P, and P, in the context of this application.

b. Interpret the standard deviation and the adjusted coefficient of determination of the regression model in the context of this application.

c. Is this model useful for predicting GPA? Conduct a statistical test to justify your answer.

d. Sketch the relationship between predicted GPA, y, and verbal score, xl, for the following mathematics scores: x2 = 60,75, and 90.

e. The residuals from the first-order model are plotted against xl and x, and shown on p. 633. Analyze the two plots, and determine whether visual evidence exists that curvature (a quadratic term) for either x, or x, should be added to the model.