Lesson 8: Categorical Predictors

Overview of this Lesson

In Lesson 5, we utilized a multiple regression model that contained binary or indicator variables to code the information about the treatment group to which rabbits had been assigned. In this lesson, we investigate the use of such indicator variables for coding qualitative or categorical predictors in multiple linear regression more extensively. Although we primarily focus on categorical predictors with just two categories or levels, the methods and concepts extend readily to general categorical variables that, rather than defining just two groups, define c groups.

What happens if the effect of a categorical predictor on the response y depends on another (quantitative) predictor? It turns out that we need to include interaction(s) between indicator variable(s) and the quantitative predictor to handle such a situation.

Key Learning Goals for this Lesson:
  • Formulate a multiple regression model that contains one qualitative (categorical) predictor and one quantitative predictor.
  • Determine the different mean response functions for different levels of a qualitative (categorical) predictor variable.
  • Answer certain research questions based on a regression model with one qualitative (categorical) predictor and one quantitative predictor.
  • Understand and appreciate the two advantages of fitting one regression function rather than separate regression functions for each level of the qualitative (categorical) predictor
  • Properly code a qualitative variable so that it can be incorporated into a multiple regression model.
  • Be able to figure out the impact of using different coding schemes.
  • Interpret the regression coefficients of a linear regression model containing a qualitative (categorical) predictor variable.
  • Understand the distinction between additive effects and interaction effects.
  • Understand the impact of including an indicator variable-quantitative predictor interaction term in a regression model.
  • Know how to use a formulated model to determine how to test whether there is an interaction between a qualitative (categorical) predictor and a quantitative predictor.
  • Know how to answer various research questions for models with indicator variable-quantitative predictor interaction terms.
  • Know the impact of leaving a necessary indicator variable-quantitative predictor interaction term out of the model.