Chapter Preview. This chapter describes tools and techniques to help you select variables to enter into a linear regression model, beginning with an iterative model selection process. In applications with many potential explanatory variables, automatic variable selection procedures will help you quickly evaluate many models. Nonetheless, automatic procedures have serious limitations, including the inability to account properly for nonlinearities such as the impact of unusual points; this chapter expands on the discussion in Chapter 2 of unusual points. It also describes collinearity, a common feature of regression data where explanatory variables are linearly related to one another. Other topics that affect variable selection, including heteroscedasticity and out-of-sample validation, are also introduced.

An Iterative Approach to Data Analysis and Modeling

In our introduction of basic linear regression in Chapter 2, we examined the data graphically, hypothesized a model structure, and compared the data to a candidate model to formulate an improved model. Box (1980) describes this as an iterative process, which is shown in Figure 5.1.

This iterative process provides a useful recipe for structuring the task of specifying a model to represent a set of data. The first step, the model formulation stage, is accomplished by examining the data graphically and using prior knowledge of relationships, such as from economic theory or standard industry practice. The second step in the iteration is based on the assumptions of the specified model.