Equation 1 can be fit using raw scores on X1 and X2, but regression coefficients and standard errors for X1 and X2 can be rather volatile if the product term is in the equation. To reduce these problems, many experts (e.g., Cohen et al., 2003), recommend centering X1 and X2 at their respective means, leading to:(2)Y=B0*+B1*X1*+B2*X2*+B3*(X1*·X2*)+E where X1*andX2* are sample-mean-centered versions of X1 and X2, respectively, asterisks on B0* through B3* indicate weights for mean-centered predictors, and other symbols were defined above. Sample-mean-centering often reduces correlations among predictors and leads to many interpretive advantages (see, e.g., Aiken & West, 1991; Cleary & Kessler 1982).
