Win-probabilities for regression models

This paper considers inferences concerning future observations for regression models. Specifically, the differences between future observations at two designated sets of input values are considered. Win-probabilities, which are the probabilities that one of the future observations will exceed the other, constitute a special case of this analysis. These win-probabilities, together with the more general inferences on the difference between the future observations, provide a useful and easily interpretable tool with which a practitioner can assess the information provided by the regression model, and can make decisions regarding which of the two designated sets of input values would be optimal. A multiple-linear-regression model is considered in detail, although the results can be applied to any regression model with normally distributed errors. Central and non-central tt-distributions are used for the analysis, and several examples of the methodologies are presented.