Chapter 10 Multiple regression continued

This section deals with some more advanced topics in ANOVAs and regression. It serves as a continuation to the first chapter on regression, and in particular focuses on multiple regressions. This chapter will cover the following:

• ANCOVA
• Hierarchical regressions
• Model selection
• Identifying and handling outliers

This module won’t cover continuous interactions because they are often considered under the topic of moderation - for which there will be a separate module.

Recall that the basic multiple regression looks something like this:

\[ y = \beta_0 + \beta_1x_1 +\beta_2x_2 + \epsilon_i \] As a reminder, the coefficients in this formula correspond to the following:

• \(\beta_1\) is the coefficient for predictor \(x_1\); i.e. as \(x_1\) increases by 1 unit, \(\hat y\) (the predicted y value) increases by \(\beta_1\) units, assuming \(x_2\) does not change
• \(\beta_2\) is the coefficient for predictor \(x_2\), and describes how \(\hat y\) changes assuming \(x_1\) does not change
• \(\epsilon_i\) is the error term, which we assume is normally distributed

We can expand this formula out to include \(n\) predictors, as follows:

\[ y = \beta_0 + \beta_1x_1 +\beta_2x_2 + ... \beta_nx_n + \epsilon_i \]