Canonical correlation calculator
Find linear combinations of two X variables and two Y variables that have the strongest possible correlation.
First pair of canonical variates
Points show the U₁ and V₁ linear-combination scores for each observation.
Canonical roots
| Function | Correlation ρ | ρ² |
|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||
How do I use this page?
- Paste four series in matching observation order.
- Read ρ₁ and ρ₂ and their squared values.
- Inspect the weights and first-pair plot while considering multicollinearity.
What this page does not do: This version accepts exactly two variables in each set. It does not calculate Wilks' significance test and rejects singular correlation matrices.
Further reading
Theory — what is canonical correlation?
Canonical correlation analysis compares entire sets of variables rather than single pairs. The calculator builds a linear function U from variables X1 and X2 and a function V from variables Y1 and Y2 so that the correlation between U and V is as large as possible. A second pair of functions captures the remaining linear dimension of the relationship, independent of the first. Unlike ordinary Pearson correlation, which compares just two variables, canonical correlation compares two linear combinations of entire variable sets at once.
Frequently asked questions
How is canonical correlation different from Pearson correlation?
Does a high ρ₁ mean every component is strongly related?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.