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Science Forum Index » Space - Consult Forum » possible to get squared multiple correlation form...
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| Jinsong.Zhao at (no spam) gmail.com... |
 Posted: Sat Jul 19, 2008 5:38 pm |
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Guest
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Hi,
I just have a 4x4 correlation matrix. There are four vaiables, e.g.,
x1, x2, x3, x4.
Now, I hope to get squared multiple correlation (i.e., R^2) between x1
and x2, x3, x4.
Is it possible?
Any suggestions will be really appeciated.
Thanks,
Jinsong |
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| Ray Koopman... |
| Posted: Wed Jul 30, 2008 7:50 am |
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Guest
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On Jul 19, 8:38 pm, "Jinsong.Z... at (no spam) gmail.com" <Jinsong.Z... at (no spam) gmail.com>
wrote:
Quote: Hi,
I just have a 4x4 correlation matrix. There are four vaiables, e.g.,
x1, x2, x3, x4.
Now, I hope to get squared multiple correlation (i.e., R^2) between x1
and x2, x3, x4.
Is it possible?
Any suggestions will be really appeciated.
Thanks,
Jinsong
The squared multiple correlation of variable i with the k-1 other
variables in a k x k correlation matrix R is given by 1 - 1/a_ii,
where A = R^1. |
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| Ray Koopman... |
| Posted: Wed Jul 30, 2008 7:52 am |
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Guest
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On Jul 30, 10:50 am, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
Quote: On Jul 19, 8:38 pm, "Jinsong.Z... at (no spam) gmail.com" <Jinsong.Z... at (no spam) gmail.com
wrote:
Hi,
I just have a 4x4 correlation matrix. There are four vaiables, e.g.,
x1, x2, x3, x4.
Now, I hope to get squared multiple correlation (i.e., R^2) between x1
and x2, x3, x4.
Is it possible?
Any suggestions will be really appeciated.
Thanks,
Jinsong
The squared multiple correlation of variable i with the k-1 other
variables in a k x k correlation matrix R is given by 1 - 1/a_ii,
where A = R^1.
That should be A = R^-1. |
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| Ray Koopman... |
| Posted: Fri Aug 01, 2008 7:11 am |
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Guest
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On Fri, 1 Aug 2008 04:20:41 -0700 (PDT) cprice at (no spam) gmail.com wrote:
Quote: On Jul 30, 10:52 am, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
On Jul 30, 10:50 am, Ray Koopman <koop... at (no spam) sfu.ca> wrote:
On Jul 19, 8:38 pm, "Jinsong.Z... at (no spam) gmail.com" <Jinsong.Z... at (no spam) gmail.com
wrote:
Hi,
I just have a 4x4 correlation matrix. There are four vaiables, e.g.,
x1, x2, x3, x4.
Now, I hope to get squared multiple correlation (i.e., R^2) between
x1 and x2, x3, x4.
Is it possible?
Any suggestions will be really appeciated.
Thanks,
Jinsong
The squared multiple correlation of variable i with the k-1 other
variables in a k x k correlation matrix R is given by 1 - 1/a_ii,
where A = R^1.
That should be A = R^-1.
Hello,
Just wanted to say this is a pretty neat result I haven't heard of
before ... I'm interested to see some derivation of it, any book/paper
reference you could give?
Thanks,
-CP
This is a very old result, that I'm sure was known to Pearson but
that surprisingly many people today seem to be unaware of. The proof
follows from the formula for the inverse of a partitioned matrix.
See Special Case 1 at
<http://www.cs.nthu.edu.tw/~jang/book/addenda/matinv/matinv/>
The interpretation requires you to recognize that if A is the
covariance matrix of the predictors, b is the vector of their
covariances with a d.v., and c is the variance of the d.v.,
then k is the variance of the residuals from the regression. |
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