# CHAPTER 10

# VARIABLE SELECTION AND MODEL BUILDING

## 10.1 INTRODUCTION

### 10.1.1 Model-Building Problem

In the preceding chapters we have assumed that the regressor variables included in the model are known to be important. Our focus was on techniques to ensure that the functional form of the model was correct and that the underlying assumptions were not violated. In some applications theoretical considerations or prior experience can be helpful in selecting the regressors to be used in the model.

In previous chapters, we have employed the classical approach to regression model selection, which assumes that we have a very good idea of the basic form of the model and that we know all (or nearly all) of the regressors that should be used. Our basic strategy is as follows:

- Fit the full model (the model with all of the regressors under consideration).
- Perform a thorough analysis of this model, including a full residual analysis. Often, we should perform a thorough analysis to investigate possible collinearity.
- Determine if transformations of the response or of some of the regressors are necessary.
- Use the
*t* tests on the individual regressors to edit the model.
- Perform a thorough analysis of the edited model, especially a residual analysis, to determine the model's adequacy.

In most practical problems, especially those involving historical data, the analyst has a rather large pool of possible **candidate regressors**, of which only a few are likely to be important. Finding an appropriate subset ...