Model sum of squares measures what in a regression or ANOVA?

• A. The total variation in the data.
• B. The residual variation not explained by the model.
• C. The sum of squared differences between observed and predicted values.
• D. The portion of variation explained by the model; the difference between total SS and residual SS.

Answer: (D)

In regression and ANOVA, the total variation in the dependent variable is split into two parts: variation explained by the model and residual variation not explained by the model. The model sum of squares captures the portion of this total variation that the regression model explains. It is the difference between the total sum of squares and the residual (unexplained) sum of squares, so it represents how much of the data’s variability is accounted for by the model’s predictions.

So, it’s not the total variation by itself, nor the residual variation, nor the raw squared differences between observed and predicted values—that last one is the residual sum of squares. The model sum of squares measures the explained portion, i.e., SST minus SSE.