Canonical Correlation Analysis

Canonical Correlation studies the relationship between two sets of variables simultaneously — finding linear combinations of each set that are maximally correlated with each other.

Step 1 — Provide your two sets

  • Set X — first group of variables (e.g. predictors)
  • Set Y — second group of variables (e.g. outcomes)

Both sets share the same subjects. Supports Excel Import, Sample Data Generator, and Manual Entry.

Step 2 — Results

Canonical functions:

  • Number of functions = min(p, q)
  • Canonical correlations and eigenvalues
  • Wilks' Lambda sequential tests per function

Coefficients and loadings:

  • Standardised canonical coefficients for Set X and Set Y
  • Canonical loadings (structure correlations)

Redundancy analysis:

  • Proportion of variance in one set explained by the other set's variate

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Statistical methods used

Eigenvalue problem

M = R_xx^-1 * R_xy * R_yy^-1 * R_yx

Eigenvalues = squared canonical correlations.

Sequential Wilks' Lambda (Bartlett)

For function k: Lambda_k = product(1 - eigenvalue_i) for i >= k.

chi2 = -n_eff * ln(Lambda_k) with df = (p-k)*(q-k).

H0: canonical correlations k through s are all zero.

Redundancy index

Redundancy(X|Y, func k) = variance_extracted * canonical_correlation_k^2

Directional: redundancy of X given Y differs from Y given X.