The article “Examined Life: What Stanley 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 leastsquares line with y = first-year college GPA and x = high school GPA, what would be the value of r 2?
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.