It is often claimed that the SAT is an important indicator of the grades students will earn in the first year of college. The admission officer at a state university wants to analyze the relationship between the first-year GPA in college (College GPA) and the SAT score of the student (SAT), the unweighted high school GPA (HS GPA), and the student’s race (White equals 1 if the student is white, 0 otherwise). A portion of the data is shown in the accompanying table 

a. Estimate and interpret a regression model for college GPA using SAT, HS GPA, White, and the interactions of SAT with HS GPA and SAT with White as predictor variables. 

b. Predict the first-year college GPA of a white student with a high school GPA of 3.2 and SAT scores of 1200, 1300, and 1400. Make a corresponding prediction for a nonwhite student

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College GPA 4.00 1.78 ⠀ 3.38 SAT 1560 1060 ⠀ 1460 HS GPA 4.00 2.18 E 4.00 White 1 0 ⠀ 0