Question: The Scholastic Aptitude Test (or SAT) is a standardized college entrance test that is used by colleges and universities as a means for making admission decisions. The critical reading and mathematics components of the SAT are reported on a scale from 200 to 800. Several universities believe these scores are strong predictors of an incoming student's potential success, and they use these scores as important inputs when making admission decisions on potential freshman. The file Ruggles College contains freshman year GPA and the critical reading and mathematics SAT scores for a random sample of two hundred students who recently completed their freshman year at Ruggles College.
a. Develop an estimated multiple regression equation that includes critical reading and mathematics SAT scores as independent variables. How much variation in freshman GPA does this model explain? Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters b0, b1, and b2 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
b. Using the multiple linear regression model you developed in part a, what is the predicted freshman GPA of Bobby Engle, a student who has been admitted to Ruggles College with a 660 SAT score on critical reading and at a 630 SAT score on mathematics?
c. The Ruggles College Director of Admissions believes that the relationship between a student's scores on the critical reading component of the SAT and the student's freshman GPA varies with the student's score on the mathematics component of the SAT. Develop an estimated multiple regression equation that includes critical reading and mathematics SAT scores and their interaction as independent variables. How muchvariation in freshman GPA does this model explain? Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters b0, b1, b2, and b3 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Do these results support the conjecture made by the Ruggles College Director of Admissions?
d. Do you prefer the estimated regression model developed in part a or part c? Explain.
e. Can you think of any other factors that could be included in the model as independent variables?