ABSTRACT
This chapter looks at how the principal components reproduce the observed covariance or correlation matrix from which they were extracted. Principal components analysis (PCA) provides a way of reducing the complexity of multivariate data by reducing their dimensionality. A possible application for PCA arises in the field of economics, where complex data are often summarized by some kind of index number, for example, indices of prices, wage rates, cost of living, and so on. The principal components are most commonly used as a means of constructing an informative graphical representation of the data or as inputs to some other analysis. In the behavioral sciences, particularly psychology, the principal components are often considered an end in themselves, and researchers may then try to interpret them in a similar fashion to the factors in an exploratory factor analysis. The account of principal components given has them extracted from the covariance matrix of the data.
