CCA & Correlation: Get variance fraction...

Determine from the selected CCA and Correlation objects the fraction of the variance explained by the selected canonical variate range.

## Settings

X or Y
  determines whether you select the dependent (y) or the independent (x) set.
Canonical variate range
  determines the canonical variates (or canonical variables).

## Remarks

1. In general the variance fractions for a particular canonical variate in the dependent and in the independent set are not the same.

2. In general, the variance fractions for all canonical variates do not sum to 1. (The technical reason is that for canonical correlation analysis in general the eigenvectors are not orthogonal, i.e. they overlap and therefore, necessarily, also the variance fractions overlap.)

## Algorithm

The formulas can be found on page 170 of Cooley & Lohnes (1971).

For example, the fraction of the variance explained by the ith canonical variable in the dependent set is:

fractionVariance = ((yi′ Ryy′ Ryy yi) / (yi′ Ryy yi)) / ny,

where yi is the eigenvector for dependent canonical variable i and Ryy is the correlation matrix for the ny variables in the dependent set.

### Links to this page

- CCA & Correlation: Get redundancy (sl)...