Applied Regression Modeling, 3rd Edition

Chapter 5Regression Model Building II

This chapter covers additional model building topics that should be addressed in any regression analysis. In Section 5.1, we consider the role that individual data points can play in a multiple linear regression model, particularly overly influential points. As with any mathematical model that attempts to approximate a potentially complex reality, there are a number of pitfalls that can cause problems with a multiple linear regression analysis. We outline a few of the major pitfalls in Section 5.2 and suggest some remedies. Adding transformations, interactions, and qualitative predictors to our toolbox (as discussed in Chapter 4) creates a very flexible methodology for using multiple linear regression modeling; Section 5.3 provides some guidelines and strategies for employing these methods successfully in real‐life applications. In Section 5.4, we discuss computer‐automated model selection methods, which are used to aid predictor selection for large datasets. Finally, in Section 5.5, we propose some graphical methods for understanding and presenting the results of a multiple linear regression model.

After reading this chapter, you should be able to

• Recognize a potential outlier with a highly unusual response value relative to its predicted value from a multiple linear regression model.
• Determine whether an outlier is the result of a data input mistake, an important predictor being omitted from the model, one or more regression assumptions ...