Interpretation of linear regression models that include transformations or interaction terms

In linear regression analyses, we must often transform the dependent variable to meet the statistical assumptions of normality, variance stability, or linearity. Transformations, however, can complicate the interpretation of results because they change the scale on which the dependent variable is measured. In this setting, the inclusion of product terms or the transformation of some independent (or predictor) variables may further complicate interpretation. In this article, we present some interpretations of linear models that include transformations or product terms. We illustrate these interpretations using regression analyses designed to study determinants of serum testosterone levels. These examples show how one can present results using simple measures, such as medians, and interpret regression parameters.