Sums of Squares - Multiple Regression and ANOVA

There is a close relationship between the multiple regression method and analysis of variance. In fact, both are special cases of the general linear model. For a detailed discussion of the general linear model, refer to the General Linear Model (GLM) Introductory Overview, as well as the Multiple Regression Overviews. In short, practically all experimental designs can be analyzed via multiple regression.

  Factor B
Factor A B1 B2
A1 3,4 4,5
A2 6,6 3,2

Let us consider a simple 2 x 2 between-groups design. Suppose that the entries in the table above are the data (for the dependent variable or DV) collected in the experiment. You could set up a datafile in the following manner:

DV A B AxB
3 1 1 1
4 1 1 1
4 1 -1 -1
5 1 -1 -1
6 -1 1 -1
6 -1 1 -1
3 -1 -1 1
2 -1 -1 1

Columns A and B contain the codes that identify the levels of factors A and B; the column denoted as AxB contains the product of the two columns A and B. You can analyze these data via multiple regression; specify variable DV as the dependent variable, and variables A through AxB as the independent variables. The significance tests for the regression coefficients will be identical to those computed via ANOVA for the main effects (A and B) and the interaction (AxB).