**Canonical correlation analysis** uses metric variables
divided into two sets - a dependent and an independent set (criterion
and predictor). This technique constructs a new, linear variate
from a set of variables so that the correlation between the two
variables is maximized. Canonical correlation analysis produces
canonical loadings (similar to factor loadings) that show the
correlation between each variable and each of the variates. From
this information, redundancies are calculated that represent the
amount of variance in the dependent variables that is explained
by the independent variate.

Canonical correlation can be performed either using the variance/covariance or the correlation matrix. The results are identical, except for the canonical loadings, which are standardized for variances in the case of the correlation matrix. You should understand why a covariance matrix of standardized data is the same as a correlation matrix.

Construct linear combinations for the Xs and Ys as:

*W* = v_{1}X_{1} + v_{2}X_{2}
+ v_{q}X_{q}

*Z* = u_{1}Y_{1} + u_{2}Y_{2}
+ u_{p}Y_{p}

Now adjust **u**s and **v**s such that r_{[wz]}
is at a maximum as discussed in this document.

last modified: 02/25/08