Predictive Inference on Equicorrelated Linear Regression Models

Abstract

Beyond the customary analysis through the estimation and hypothesis testing about the parameters of the multiple regression models, often a natural interest is to predict the responses for a given set of values of the predictors. The main objective of this article is to obtain the prediction distribution for a set of future responses from a multiple linear regression model which follow equicorrelation structure. It derives the marginal likelihood estimate for the equicorrelation parameter, ρ, and then uses the invariant differentials to compute the joint distribution of the unobserved but realized future errors. The prediction distribution is derived by using the structural relation of the model. The main finding of this paper is that the prediction distribution turned out to be a Student-t which depends only on the estimated ρ and is invariant to the degrees of freedom of the original Student-t distribution.