Developing a model for college GPA. 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: x1 = Verbal score on college entrance examination (percentile) x2 = Mathematics score on college entrance examination (percentile) The file contains data on these variables for a random sample of 40 freshmen at one college. (Selected observations are shown in the table.) Use the data to develop a useful prediction equation for college freshman GPA 1y2. Be sure to conduct a residual analysis for the model. Verbal, x1 Mathematics, x2 GPA, y 81 87 3.49 68 99 2.89 57 86 2.73 100 49 1.54 54 83 2.56 f f f 74 67 2.83 87 93 3.84 90 65 3.01 81 76 3.33 84 69 3.06