11.60. Software reports four types of sums of squares in multiple regression models. The Type I (sometimes called sequential) sum ofsquares represents the variability explained by a variable, controlling for variables previously entered into the model.

The Type III (sometimes called partial) sum of squares represents the variability explained by that variable, controlling for all other variables in the model.

(a) For any multiple regression model, explain why the Type I sum of squares for xj is the regression sum of squares for the bivariatc model with xi as the predictor, whereas the Type 1 sum ofsquares forX2 equalsthe amount by which SSE decreases when X2 is added to the model.