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mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find  r^2.) Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.

mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find  r^2.) Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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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.

  1. Find the regression equation for predicting GPA from SAT scores.
  2. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find  r^2.)
  3. Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.
8. A professor obtains SAT scores and freshman grade point averages (GPAS) for a 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 a = .05 to evaluate the F-ratio.
Transcribed Image Text:8. A professor obtains SAT scores and freshman grade point averages (GPAS) for a 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 a = .05 to evaluate the F-ratio.
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