Stepwise regression is an approach to selecting a subset of effects for a regression model. Use stepwise regression when there is little theory to guide the selection of terms for a model, and the modeler wants to use whatever seems to provide a good fit. The approach is somewhat controversial. The significance levels on the statistics for selected models violate the standard statistical assumptions because the model has been selected rather than tested within a fixed model. On the positive side, the approach has been helpful for 30 years in reducing the number of terms. The book Subset Selection in Regression, by A. J. Miller (1990), brings statistical sense to model selection statistics.
This chapter uses the term significance probability in a mechanical way to represent that the calculation would be valid in a fixed model, recognizing that the true significance probability could be nowhere near the reported one.
The Stepwise Fit also includes features for looking at all possible models (including heredity factors) and model averaging.