What does R squared represent in regression?

• A. The proportion of variance in the dependent variable explained by the model.
• B. The variance of the residuals.
• C. The standard error of the estimate.
• D. The F-statistic.

Answer: (B)

R squared measures how much of the variability in the outcome is explained by the regression model. It tells you the proportion of the total variance in the dependent variable that the model accounts for. It’s computed as 1 minus the ratio of the residual sum of squares to the total sum of squares: R^2 = 1 − (SS_res / SS_tot). When the model does a good job predicting, SS_res is small and R^2 is close to 1, meaning most of the variation in the outcome is explained by the predictors. It’s not the variance of the residuals—that quantity is the residual (or error) variance, often summarized by the mean squared error, and its square root is the standard error of the estimate. The F-statistic is a separate measure that tests whether the model as a whole explains more variance than expected by chance.