Recovering sums of squares between full and reduced linear models

Abstract

Many statistical computing packages include, as part of their standard output, hypothesis tests for a particular reduced model of interest. In this article, we identify the hypotheses being tested in the full model using sums of squares generated in the reduced model. Also, given a sum of squares generated in the full model, we identify the hypothesis, if any, being tested in the reduced model of interest.

Keywords:

• Statistical Computing Packages
• regression
• ANOVA
• hypothesis
• subspace
• orthogonal projection