Variance Explained in Regression: The Correlation Coefficient | Test Prep

Correlation Coefficient Calculation

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In a regression, the independent variable explains 79% of the variance in the dependent variable, leaving 21% unexplained. The slope coefficient is 0.67 and the intercept equals -10.2 The correlation coefficient between the two variables is

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A. B. C. D.

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In a univariate regression, the correlation coefficient between the dependent and the independent variables equals the square root of R-square. However, you should also be careful about the sign, which is not given by the R-square. Rather, you have to look at the sign of the slope coefficient. In this case, the slope coefficient is positive, implying that the dependent and the independent variables are positively correlated. The R-square equals 79% so the correlation coefficient equals +sqrt(0.79) = 0.89.

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