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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 15.6 percent, and SAT I was last at 13.3 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?

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Answer:

0.156

Step-by-step explanation:

Given that :

% of Explained variance by certain predictors of first year college grade :

SAT 11 scores = 17%

GPA = 15.6%

SAT 1 = 13.3%

Fitting a least squares line :

y = First year college GPA

x = high school GPA

THE r² value which is Coefficient of determination is the percentage of explained variance given by the regression line. The r² value of GPA will the as given above 15.6%

r² = 15.6% = 15.6/100 = 0.156

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