The standard parameterization of a regression model with a linear X qualitative interaction involving three groups on the latter variable is: (13)Y=B0+B1X1+B2D2+B3D3+B4(X1·D2)+B5(X1·D3)+E where D2 and D3 are dummy variables with unit values for persons in groups 2 and 3, respectively, and other symbols were defined above. In Equation 13, group 1 is the reference group, and D2 and D3 allow one to determine whether groups 2 and 3 differ from group 1 in mean level (or intercept) or in moderation with X1. A mean-centered version of Equation 13 is: (14)Y=B0*+B1*X1*+B2*D2+B3*D3+B4*(X1*·D2)+B5*(X1*·D3)+E where all symbols were defined above. Again, only the quantitative predictor was mean-centered, to retain interpretive advantages of regression coefficients for the dummy variables.
