The trivariate normal distribution: partial and multiple correlations and regressions

Abstract

In this chapter, the joint analysis of three variates is introduced in the simplest possible manner (without recourse to matrix and vector algebra, which will be briefly reviewed in chapter 24). The new notions with which the reader will become acquainted here will recur in later chapters on the so-called multivariate analysis of any number of variates (chapters 25 and 29 to 34). When the joint probability distribution of three variates is considered, the three dimensions of classical Euclidean geometry are already all occupied by the variates (see figures 23.2.1 and 23.3.1, for instance). Consequently, there is no dimension left for the coordinate axis of the frequency (compare with figure 19.1.2) or of the probability density (figure 19.2.1). However, the limitations of three-dimensional geometry do not impede the statistical analysis.