The geometry of the general linear model

Abstract

Two complementary geometric interpretations of data are used to discuss topics from elementary statistics including random variables, vectors of random variables, expectation, mean, variance, and the normal, F-, and t- probability distributions. The geometry of the general linear model and the associated hypothesis testing is developed, followed by a geometrically oriented discussion of the analysis of variance, simple regression, and multiple regression using examples. Geometry affords a rich discussion of orthogonality, multicollinearity, and suppressor variables, as well as multiple, partial, and semi-partial correlation. The last chapter describes the mathematical application of homogeneous coordinates and perspective projections in the computer program used to generate the representations of data vectors for several figures in this text.