## Proc cancor

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Posts: 471

# Proc cancor

Hi All -

In canonical correlation, the ith eigenvalue of the matrix R (where R is the product of the inverse of the variance-covariance matrix of y, the covariance matrix of x and y, the inverse of the variance-covariance matrix of x, and the covariance matrix of y and x) is equal to the ith canonical correlation squared.

Why then does SAS output the eigenvalues derived by CanRsq / (1 - CanRsq) rather than having the eigenvalues be equal to CanRsq?

What is the significance behind eigen values? Also It would be juicy if someone of you tell me with simple example when 'proc concor' should be used over 'proc corr'? B ecause I'm not clear although I tried to difference between them.

Thanks!

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Posts: 471

Posts: 2,035

## Re: Proc cancor

```Why then does SAS output the eigenvalues derived by CanRsq / (1 - CanRsq) rather than having the eigenvalues be equal to CanRsq?

```

The documentation for PROC CANCORR is pretty clear on this point. It says: "Eigenvalues of INV(E)*H, which are equal to CanRsq/(1–CanRsq), where CanRsq is the corresponding squared canonical correlation."

But you can convert CanRsq/(1-CanRsq) into CanRsq if you want.

```Also It would be juicy if someone of you tell me with simple example when 'proc concor' should be used over 'proc corr'?

```

PROC CORR gives you all requested pairwise correlations (the correlation of, for example, X1 with X2)

PROC CANCORR is a multivariate procedure, it gives you correlations of linear combinations of variables in the VAR statement with linear combinations of variables in the WITH statement.

--
Paige Miller
Super Contributor
Posts: 471

## Re: Proc cancor

Do we need to concentrate on the values of CanRsq/(1–CanRsq) when there is no correlation and also no significant values?

If you can explain the eigen value calculation (INV(E)*H) it would be great.

Thanks again.

Posts: 2,035

## Re: Proc cancor

```Do we need to concentrate on the values of CanRsq/(1–CanRsq) when there is no correlation and also no significant values?

```

Probably not

```If you can explain the eigen value calculation (INV(E)*H) it would be great.

```

Explain how eigenvalues are calculated? No, I can't do that.

Or explain why they are calculated? They are calculated to determine the relative proportion of variability explained by each canonical component.

--
Paige Miller
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