Abstract
This chapter discusses the nature of multivariate data analysis. Stripped to their mathematical essentials, multivariate methods represent a blending of concepts from matrix algebra, geometry, the calculus, and statistics. In function and in structure, multivariate techniques form a unified set of procedures that can be organized around a relatively few prototypical problems. Multivariate analysis is concerned with both the discovery and testing of patterns in associative data. The chapter describes three prototypical problems, calling for various types of multivariate analysis, in terms of a miniature and common data bank. Multivariate methods emphasize two types of variables: (1) more or less continuous variables, that is, interval-scaled measurements, and (2) binary-valued variables, coded as zero or one. Multiple regression, aside from being the most popular multivariate technique in applied research, provides a vehicle for subsequent discussion of all basic matrix operations and, in particular, the topics of determinants, matrix inversion, and matrix rank.
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