The article "Examined Life: What Stanley H. Kaplan Taught Us About the SAT" (The New Yorker [December 17, 2001]: 86-92) included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 16 percent of the variance in first-year college grades. GPA was second at 15.4 percent, and SAT I was last at 13.3 percent."
a. If the data from this study were used to fit a least-squares line with y = first-year college GPA and x = high school GPA, what would be the value of r2 ?
b. The article stated that SAT II was the best predictor of first-year college grades. Do you think that predictions based on a least-squares line with y = first-year college GPA and x = SAT II score would be very accurate? Explain why or why not.