Canonical Correlation and Its Relationship to Discriminant Analysis and Multiple Regression

Abstract Canonical correlation analysis is concerned with the determination of a linear combination of each of two sets of variables such that the correlation between the two functions is a maximum. Under certain conditions this analysis is equivalent to discriminant analysis and under other conditions it is equivalent to multiple regression. In this paper the relationships among these techniques are discussed, equations relating to prediction by canonical variates are derived, a generalized correlation coefficient is proposed, and an example of canonical correlation analysis is presented.