Overview of Canonical Correlation Analysis

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Overview of Canonical Correlation Analysis

*Canonical correlation analysis*
is a technique for analyzing the relationship between two sets (or groups) of variables. Each set can contain multiple variables.

Given two sets of variables, canonical correlation analysis finds a linear combination from each set, called a *canonical variable*,
such that the correlation between the two canonical variables is maximized. This correlation between the two canonical variables
is the first canonical correlation. The first canonical correlation is at least as large as the multiple correlation between
any variable and the opposite set of variables. The coefficients of the linear combinations are canonical coefficients or
canonical weights. It is customary to normalize the canonical coefficients so that each canonical variable has a variance
of 1.

Canonical correlation analysis continues by finding a second set of canonical variables, uncorrelated with the first pair,
that produces the second-highest correlation coefficient. The process of constructing canonical variables continues until
the number of pairs of canonical variables equals the number of variables in the smaller group.

Each canonical variable is uncorrelated with all the other canonical variables of either set except for the one corresponding
canonical variable in the opposite set. However, the canonical variables do not represent jointly perpendicular directions
through the space of the original variables.

You can run the Canonical Correlation analysis by selecting → → from the main menu. The analysis is implemented by calling the CANCORR procedure in SAS/STAT software. See the CANCORR procedure
documentation in the
*SAS/STAT User's Guide* for additional details.

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