ABSTRACT
Fitting a model to a set of data does not ordinarily complete the analysis. One usually wants to establish which effects are likely to be real and which are accidents of sampling. Central to this endeavor are the hypothesis tests, which help one decide whether a particular effect stands out about the accidental fluctuation of the scores. Statistical techniques also are used to construct confidence intervals for parameters and scores, but those techniques are not discussed here. Most of the statistical testing procedures used in multivariate statistics can be formulated geometrically. This chapter describes this geometry. In its essentials, the statistical analysis of a multiple regression works by dividing subject space into two orthogonal subspaces, one of which contains the systematic effects of the regression and the other only the random effects of sampling error. Where the systematic subspace is multidimensional, it may be further divided into individual effects.
