Partialed products are interactions; partialed powers are curve components.

The fact that simple (zero-order) correlations of products (XZ) and powers (X, X*) with other variables (Y) are not invariant over linear transformations of their constituents (X, Z) has led to confusion and anxiety about their use as independent variables in the representation of interactions and curve components in general multiple regression/correlation analysis. This article demonstrates that when their constituents are linearly partialed out, products and powers are invariant with regard to both their correlations and tests of significance; further, their raw score regression coefficients are simply rescaled. Partialed products and powers are not subject to constraints of orthogonality, level of scaling, or whether data arise from experiments or observational studies.