Date:         Fri, 28 Apr 2006 21:20:01 -0400
Reply-To:     Richard Ristow <wrristow@mindspring.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Richard Ristow <wrristow@mindspring.com>
Subject:      Re: correlation between covariates and DV
In-Reply-To:  <6250203B042D8349A920AA610383093601287B1B@UTHEVS3.mail.utho
              uston.edu>
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At 06:50 PM 4/26/2006, Swank, Paul R wrote:

>I would say, if the mean square error is smaller with the covariate in
>the model then leave it in.

Am I missing something? I believe the mean square error will be smaller
if you add ANY variable to a linear model, whether the variable
actually had anything to do with the DV or not. The simple way to see
this is, the fitting minimizes the mean square error. When you add a
variable, the old model is still available: it could be fit with a 0
coefficient on the new variable. So, mean-square error can't INCREASE.
It will decrease unless, let's see, I think, unless the new variable is
uncorrelated with the residuals from the model without the new
variable.

That's why t-tests and F-tests: to test whether the reduction in mean
square error is larger than expected by chance.