In
statistics,
canonical-correlation analysis (
CCA) is a way of making sense of
cross-covariance matrices. If we have two vectors
X = (
X1, ...,
Xn) and
Y = (
Y1, ...,
Ym) of
random variables, and there are
correlations among the variables, then canonical-correlation analysis will find linear combinations of the
Xi and
Yj which have maximum correlation with each other. T. R. Knapp notes "virtually all of the commonly encountered
parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables." The method was first introduced by
Harold Hotelling in 1936.