Canonical correlation analysis: A process of analysis for investigating the relationship between the two groups of variables, by ?nding the linear functions of one of the sets of variables which maximally correlate with the linear functions of the variables in the other set. In numerous respects the process can be seen as an extension of multiple regressions to situations including more than a single response variable. Alternatively it can be considered as the analogous to principal components analysis except that the correlation rather than a variance is maximized.

An easy example of where this type of technique or method might be of interest is when the results of tests for, say, reading speed (x1), arithmetical speed (y1), reading power (x2), and arithmetical power (y4), are available from the sample of school children, and the question of interest is whether the reading ability (measured by x1 and x2) or not is related to arithmetical ability (as measured by y1 and y2).