What does R-squared tell you?

What does R-squared tell you?

• A. Proportion of variance in y explained by the model.
• B. The standard error of the estimate.
• C. The correlation between x and y.
• D. The slope of the regression line.

Answer: (A)

R-squared tells you what portion of the variability in the outcome variable is accounted for by the regression model. It’s computed as 1 minus the proportion of variability that the model’s residuals fail to explain, relative to the total variability in the outcome. Values closer to 1 mean the model captures most of the variation in y, while values near 0 mean little of the variation is explained. It’s a measure of goodness of fit, not the precision of individual predictions or the slope. In simple linear regression, R-squared relates to the strength of the x–y relationship, since it equals the square of the correlation between x and y, but with multiple predictors it generalizes to the proportion of explained variance across all included variables.

R-squared tells you what portion of the variability in the outcome variable is accounted for by the regression model. It’s computed as 1 minus the proportion of variability that the model’s residuals fail to explain, relative to the total variability in the outcome. Values closer to 1 mean the model captures most of the variation in y, while values near 0 mean little of the variation is explained. It’s a measure of goodness of fit, not the precision of individual predictions or the slope. In simple linear regression, R-squared relates to the strength of the x–y relationship, since it equals the square of the correlation between x and y, but with multiple predictors it generalizes to the proportion of explained variance across all included variables.