Lesson 8: Categorical Predictors

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Introduction

In Lesson 6, 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? In that case, we say that the predictors "interact." In this lesson, we learn how to formulate multiple regression models that contain "interaction effects" as a way to account for predictors that do interact.

We also investigate a special kind of model—called a "piecewise linear regression model"—that uses an interaction term as a way of creating a model that contains two or more different linear pieces.

Learning objectives and outcomes

Upon completion of this lesson, you should be able to do the following:

  • 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 — one 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 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 interaction terms.
  • Know the impact of leaving a necessary interaction term out of the model.
  • Know how to formulate a piecewise linear regression model for two or more connected linear pieces.