ABSTRACT
This chapter examines methods for choosing good reduced models and focuses on checking the assumptions of regression models by looking at diagnostic statistics. It draws on new importance in multiple regressions because multiple regressions involve several predictor variables, each of which is a candidate for transformation. Variable selection methods fall into two categories: best subset selection methods and stepwise regression methods. In general, the mean squared error for the smaller model is a weighted average of the mean square for the variables being added and the mean squared error of the larger model. An alternative to fitting all models is to evaluate the variables one at a time and look at a sequence of models. Backwards elimination begins with the full model and sequentially eliminates from the model the least important variable. Most often, the initial model contains only the intercept, but many computer programs have options for including other variables in the initial model.
