Residual sum of squares is defined as:

• A. A measure of the variability that cannot be explained by the model fitted to the data.
• B. The squared sum of the predictor variables.
• C. The variance of the residuals.
• D. The total variance across observations.

Answer: (D)

Residual sum of squares measures how far the observed values are from what the model predicts, by summing the squares of those gaps across all observations. In formula terms, it is the sum over observations of (observed y minus predicted ŷ) squared. This captures the variability in the data that the model cannot explain; a smaller RSS means a better fit.

It is not the squared sum of the predictor variables—the predictors’ magnitudes don’t by themselves indicate model fit. It is not the variance of the residuals—the variance is RSS divided by its degrees of freedom (n minus the number of parameters estimated). It is not the total variance across observations—the total variance is the total sum of squares around the mean, which is a different quantity. The two are linked by R-squared: R^2 = 1 minus RSS divided by TSS.