A statistical manoeuvre which defines covariation for 2 groups of random variables—x and y—and seeks to identify linear combinations of the x's and the y's which have maximum correlation with each other.
The first canonical correlation analysis considered the relationship between athletes' likelihood of reporting concussion symptoms to the coach in a regular or big game with athletes' perceptions of the climate.
To test the hypotheses, we conducted a canonical correlation analysis (Tabachnick & Fidell, 2013), with the ICM skills specified as loading on the skills variates, and the ICM outcomes specified as loading on the outcomes variates.
In the canonical correlation analysis, the first two canonical variables explained approximately 89.73% of the total available variation in the data (73.74% for the first canonical variable, 15.99% for the second) (Table 2).
For the first canonical function, results yielded maximum canonical correlation coefficient (between the linear combinations of predictor and criterion variables) = .585 with squared canonical correlation = .342.
The orthogonal regularization canonical correlation analysis (ORCCA) algorithm  is that the original formula of CCA algorithm with orthogonal constraints is substituted for CCA conjugate orthogonalization [6, 7].