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 and 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.

The Role of Binary Variables

Categorical variables provide labels for observations to denote membership in distinct groups, or categories. A binary variable is a special case of a categorical variable. To illustrate, a binary variable may tell us whether someone has health insurance. A categorical variable could tell us whether someone has

• Private group insurance (offered by employers and associations),

• Private individual health insurance (through insurance companies),

• Public insurance (e.g., Medicare or Medicaid) or

• No health insurance.

For categorical variables, there may or may not be an ordering of the groups. For health insurance, it is difficult to order these four categories and say which is larger. In contrast, for education, we might group individuals into “low,” “intermediate,” and “high” years of education.