THE MOORE-PENROSE INVERSE MATRIX FOR THE BALANCED ANOVA MODELS

Abstract

Since the design matrix of the balanced linear model with no interactions has special form, the general solution of the normal equations can be easily found. From the relationships between the minimum norm least squares solution and the Moore-Penrose inverse we can obtain the explicit form of the Moore-Penrose inverse X⁺ of the design matrix of the model y=Xβ+ε for the balanced model with no interaction.