I am no statistician, so let me make sure I am understanding what you are
saying. Your point is that you may have an identical regression equation
despite the fact that the correlation may vary depending on the amount of
variation in X. If this is your point, I agree and recognize this--r is a
measure of the fit about the regression line.
Nonetheless, regression and correlation are the same in the bivariate case
with the exception of scale. In a bivariate regression, the standardized
Beta coefficient is equal to the Pearson r. As with any standardization, it
removes the scale of the variation and the result is that the slope
describes the relationship or B = r.
Brett
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]
Sent: Friday, May 19, 2000 11:43 AM
To: [EMAIL PROTECTED]
Subject: Re: Correlation
Magill, Brett <[EMAIL PROTECTED]> wrote:
>Mike,
>In the bivariate case, regression and correlation are identical.
This is false. Correlation is the measure of the
proportion of the variance of one variable explained by a
linear function of the other in a joint distribution, while
linear regression is the linear relation itself. One can
have non-linear versions as well.
If in fact E(Y|X) = aX + b, this will also be the case no
matter how selection is made on X, whereas the correlation
can vary greatly.
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