Predictive Distribution of Regression Vector and Residual Sum of Squares for Normal Multiple Regression Model

This article proposes predictive inference for the multiple regression model with independent normal errors. The distributions of the sample regression vector (SRV) and the residual sum of squares (RSS) for the model are derived by using invariant differentials. Also, the predictive distributions of the future regression vector (FRV) and the future residual sum of squares (FRSS) for the future regression model are obtained. Conditional on the realized responses, the FRV is found to follow a multivariate Student t distribution, and that of the residual sum of squares follows a scaled beta distribution. The new results have been applied to the market return and accounting rate data to illustrate its application.