In regression analysis, what does R² describe?

In regression analysis, what does R² describe?

• A. The p-value of the model.
• B. The standard deviation of the dependent variable.
• C. The proportion of variance in the dependent variable explained by the independent variables.
• D. The average residual value.

Answer: (C)

R² describes the portion of variance in the dependent variable that the independent variables explain. In regression, the total variation in Y can be split into the part accounted for by the model and the part left as residual noise. R² is 1 minus the ratio of the residual sum of squares to the total sum of squares, i.e., the fraction of Y’s variability that the predictors explain. Values range from 0 to 1, with higher values indicating a better fit. This is distinct from the p-value, which tests whether the model’s parameters are statistically significant, the standard deviation of the dependent variable, which measures overall dispersion of Y, or the average residual, which isn’t a measure of explained variance.

R² describes the portion of variance in the dependent variable that the independent variables explain. In regression, the total variation in Y can be split into the part accounted for by the model and the part left as residual noise. R² is 1 minus the ratio of the residual sum of squares to the total sum of squares, i.e., the fraction of Y’s variability that the predictors explain. Values range from 0 to 1, with higher values indicating a better fit. This is distinct from the p-value, which tests whether the model’s parameters are statistically significant, the standard deviation of the dependent variable, which measures overall dispersion of Y, or the average residual, which isn’t a measure of explained variance.