In this chapter, the authors’ begin by illustrating the use of models with both categorical and continuous predictors within the context of an experimental design, where the primary interest is in the effects of the categorical variables. They also illustrate the use of these models in a context where the researcher's interest is primarily in the effects of the continuous predictor when a categorical one is controlled. Most classic treatments of the analysis of covariance (ANCOVA) specify that an assumption, referred to as the homogeneity of regression assumption, is crucial to the use and interpretation of ANCOVA results. Models involving both categorical and continuous predictor variables have, however, a wide range of application outside of experimental research designs. For instance, in sociology or political science, one might be interested in the effects of both a categorical variable and a continuous one on some dependent variable, and might wish to estimate each of these effects when controlling for the other.