The Pearson correlation between X₁ and Y is r = 0.50.When a second variable,X₂,is added to the regression equation,we obtain R² = 0.60.Adding the second variable increases the variability that is predicted by the regression equation for the Y scores by 36% - 25% = 11%.

Question

Quizplus · Accepted Answer

The increase in variability explained by the regression equation is calculated by squaring the correlation coefficients (to get R^2, the coefficient of determination) and then comparing these values. The initial R^2 (from r = 0.50) is 0.25 (since 0.50^2 = 0.25), indicating that 25% of the variability in Y is explained by the first variable. The R^2 for the model with the second variable added (from R² = 0.60) is 0.36 (since 0.60^2 = 0.36), indicating that 36% of the variability in Y is explained by the model with both variables. The increase in explained variability is indeed 11% (36% - 25%), but the explanation provided is correct, making the statement true in its calculation but the initial answer was marked incorrectly based on the explanation given.

The Pearson Correlation Between X1 and Y Is R =

The Pearson Correlation Between X₁ and Y Is R =