In the fixed effects model with interaction, assume that there are 4 levels of factor A, 3 levels of factor B, and 3 observations for each of the 12 combinations of levels of the two factors. Then, the number of degrees of freedom for the error sum of squares (SSE) is
A) 36
B) 35
C) 24
D) 10
E) 9

Question

Quizplus · Accepted Answer

The total number of observations is 4 x 3 x 3 = 36. Since we have fixed effects for both factors A and B, the degrees of freedom for the model is dfm = (4-1) x (3-1) = 6. The degrees of freedom for the interaction term is dfi = (4-1) x (3-1) = 6 as well. Therefore, the degrees of freedom for error is dfE = (4 x 3 x 3) - dfm - dfi = 24.

In the Fixed Effects Model with Interaction, Assume That There