Slope modified confidence bands for a simple linear regression model

Considerable attention has been directed in the statistical literature towards the construction of confidence bands for a simple linear regression model. These confidence bands allow the experimenter to make inferences about the model over a particular region of interest. However, in practice an experimenter will usually first check the significance of the regression line before proceeding with any further inferences such as those provided by the confidence bands. From a theoretical point of view, this raises the question of what the conditional confidence level of the confidence bands might be, and from a practical point of view it is unsatisfactory if the confidence bands contain lines that are inconsistent with the directional decision on the slope. In this paper it is shown how confidence bands can be modified to alleviate these two problems.