Question: 14.31 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.52, Y = 2.643 + 0.469(X). X Y

14.31 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.52, Yˆ = 2.643 + 0.469(X).

X Y 4.00 6.00 6.00 3.00 7.00 7.00 8.00 5.00 9.00 4.00 10.00 12.00 12.00 9.00 14.00 8.00 MX = 8.75 MY = 6.75 SDX = 3.031 SDY = 2.727 Using this information, compute the following estimates of prediction error:

a. Calculate the sum of squared errors for the mean, SStotal .

b. Now, using the regression equation provided, calculate the sum of squared errors for the regression equation, SSerror .

c. Using your work, calculate the proportionate reduction in error for these data.

d. Check that this calculation of r 2 equals the square of the correlation coefficient.

e. Compute the standard error of the estimate.

f. Compute the standardized regression coefficient.

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