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A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84.

a. Find the regression equation for predicting GPA from SAT scores.
b. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r².)
c. Does the regression equation account for a significant portion of the variance in GPA? Use ∝ = .05 to evaluate the F - ratio.

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