ABSTRACT
The approach that a canonical correlation analysis takes to answering this question is to search for a linear combination of X1 and X2
U a X a X1 1 2 2= +
and a linear combination of Y1 and Y2
V b Y b Y1 1 2 2= +
where these are chosen to make the correlation between U and V as large as possible. This is somewhat similar to the idea behind a principal components analysis, except that here a correlation is maximized instead of a variance.
