Confidence Intervals for the Response Mean of a Simple Regression Model Following Pretests

Abstract

This article presents new confidence intervals for the response mean of a simple regression model following the pretests of regression coefficients. Our proposed methods, based on residual model and bootstrap percentile-t confidence intervals, showed that new confidence intervals for the response mean based on the residual model have minimum coverage probability of 1-α and their expected lengths are shorter than the existing confidence interval when each of the regression coefficients approach zero. The pretested bootstrap percentile-t is preferable when the error distribution is the skewed distribution.