Re: Correlation Depending on 3rd Variable?

(previous post cancelled since it's only 1 minute old;
I should say : "I propose" instead of "it is"...)

Am 05.12.2005 20:23 schrieb Eric M. Van:

>> "Eric M. Van" <emvan@xxxxxxxxxxxxxxxx> wrote in
>> news:Xns9723910B33E4Eemvanpostharvardedu@xxxxxxxxxxxxxx:
>>
>>
>
>>>>In the top quartile, A and B have a robust positive correlation.
>>>>
>>>>In the next, they have a mild positive correlation.
>>>>
>
>>
>>
>> Just to clarify, I'm looking first at the slope here, rather than the
>> strength of the correlation (although the latter, in my experience, tends
>> to follow along).

I propose a continuous generalization to take a three-factor
formula for correlation instead of the usual two; instead
of using
N
sum( xi*yi )
i=1
as basis for the correlation-coefficient, you have to use

N
sum( xi*yi*zi )
i=1

possibly instead if zi to take zi²

But I stopped this path, when I came across the difficulties
to determine theoretical limits/expected values or even
distributions for such coefficients.
Conceptually it could mean, for instance, how the correlation
between status and income changes linearly with the age,
or things like that.

I've also tried to get information about such mathematics, but
with not much success whenever tried.

I remember vaguely a book "3-mode-factoranalysis", where
I think they developed sort of 3-d-matrix-multiplication
(but maybe I was misinterpreting when I first came across
that booklet)
Just currently there is a discussion in sci.math about
x * x * x - Determinants, where this subject is also
touched. May something of this may be helpful...


Gottfried Helms
.

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