An article 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 17 percent of the variance in first-year college grades. GPA was second at 15.3 percent, and SAT I was last at 13.6 percent." 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 the value of r2 have been? r2 =_______

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1.
An article 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 17 percent of the variance in first-year college grades. GPA was second at 15.3 percent, and SAT I was last at 13.6 percent."
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 the value of r2 have been? r2 =_______
 
2.
A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since the plastic was molded (x, in hours). Summary quantities include n = 15, SSResid = 1,237.628, and SSTo = 24,619.737. Calculate and interpret the coefficient of determination. (Round the coefficient of determination to four decimal places when written as a decimal and 2 decimal places when written as a percent.)
The coefficient of determination equals _______ and tells us that ______ % of the variation in hardness is attributable to the approximate linear
relationship between time elapsed and hardness.

 

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