Honest Confidence Intervals for the Error Variance in Stepwise Regression

An honest confidence interval for the error variance in a stepwise regression is a one-sided interval that adjusts for the effects of variable selection. The endpoint of this interval may be many times larger than the usual endpoint. Such adjustments are most important when selecting variables from a large number of available predictors, particularly in situations with more available predictors than observations. An illustration using a regression model of stock market returns illustrates the calculations.