Chapter Preview. This chapter extends the discussion of multiple linear regression by introducing statistical inference for handling several coefficients simultaneously. To motivate this extension, this chapter considers coefficients associated with categorical variables. These variables allow us to group observations into distinct categories. This chapter shows how to incorporate categorical variables into regression functions using binary variables, thus widening the scope of potential applications. Statistical inference for several coefficients allows analysts to make decisions about categorical variables, as well as other important applications. Categorical explanatory variables also provide the basis for an ANOVA model, a special type of regression model that permits easier analysis and interpretation.