[R] Predicting correlated responses using canonical correlations in multivariate least squares

Michael Friendly friendly at yorku.ca
Sat Feb 27 20:04:23 CET 2016

On 2/27/2016 1:34 PM, Michael Friendly wrote:
> You might also find that an HE plot (library (heplots))
> is illuminating.

Follow-up:  Try the following with your example

hs.mod <- lm(cbind(y1, y2) ~ x1 + x2, data=hs.r)
heplot(hs.mod, fill=TRUE)

uv.mod <- lm(cbind(u1, u2) ~ v1 + v2, data = uv)
heplot(uv.mod, fill=TRUE, asp=1)

In the first plot, x1, x2 are highly correlated, but neither is 
individually significant in predicting y1, y2 by Roy's test.

The second plot is the transformation to canonical space,
where (u1, u2), (v1, v2) are uncorrelated and v1 is a highly
significant predictor of u1.


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