The Moore-Penrose Inverse for the Classificatory Models

Abstract

Many procedures for deriving the Moore-Penrose inverse X^＋ have been developed, but the explicit forms of Moore-Penerose inverses for design matrices in analysis of variance models are not known heretofore. The purpose of this paper is to find explicit forms of X^＋ for the one-way and the two-way analysis of variance models. Consequently, the Moore-Penerose inverse X^＋ and the shortest solutions of them can be easily obtained to the level of pocket calculator by way of our results.