Quantitative Methods: An Introduction for Business Management

15

Introduction to Multivariate Analysis

Multivariate analysis is the more-or-less natural extension of elementary inferential statistics to the case of multidimensional data. The first difficulty we encounter is the representation of data. How can we visualize data in multiple dimensions, on the basis of our limited ability to plot bidimensional and tridimensional diagrams? In Section 15.1 we show that this is just one of the many issues that we may have to face. The richness of problems and applications of multivariate analysis has given rise to a correspondingly rich array of methods. In the next two chapters we will outline a few of them, but in Section 15.2 we offer a more general classification. Finally, the mathematics involved in multivariate analysis is certainly not easier than that involved in univariate inferential statistics. Also probability theory in the multidimensional case is more challenging than what we have seen in the first part of the book, and the limited tools of correlation analysis should be expanded. However, for the limited purposes of the following treatment, we just need a few additional concepts; in Section 15.3 we illustrate the important role of linear algebra and matrix theory in multivariate methods.

15.1 ISSUES IN MULTIVARIATE ANALYSIS

In the next sections we briefly outline the main complication factors that arise when dealing with multidimensional data. Some of them are to be expected, but some are a bit surprising. Getting aware of these ...