Date:         Wed, 21 Jan 2004 14:55:56 -0600
Reply-To:     mgranaas@usd.edu
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         mgranaas@usd.edu
Subject:      Re: QUERY: Data assumptions for Linear Regression
Content-type: text/plain; charset=us-ascii

The overall distribution of the outcome variable can
be quite skewed, or otherwise not normal.  I was
speaking of the conditional distributions of the
outcome variable for different levels of the
predictor(s).  Which is what you get when you look
at the residuals only.

 If you look at outcome scores for only x=c, then
both the residuals and the data points will have the
same distribution.

I think we are saying the same thing in somewhat
different ways.

Michael
****************************************************
Michael Granaas                 mgranaas@usd.edu
Assoc. Prof.                    Phone: 605 677 5295
Dept. of Psychology             FAX:  605 677 3195
University of South Dakota
414 E. Clark St.
Vermillion, SD 57069
*****************************************************

----- Original Message -----
From: Paul R Swank <Paul.R.Swank@uth.tmc.edu>
Date: Wednesday, January 21, 2004 2:18 pm
Subject: Re: QUERY: Data assumptions for Linear
Regression

> That is not actually the case. I have often seen
skewed
> distributions of
> outcomes have normally distributed (or at least
symmetrical and
> unimodal)residuals given skewed predictors. I
would expect that
> the opposite is true
> as well. The correct assumption is that the
residuals are normally and
> independently distributed with homogeneous
variances across the
> levels of
> the predictor(s).
>
> Paul R. Swank, Ph.D.
> Professor, Developmental Pediatrics
> Medical School
> UT Health Science Center at Houston
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion
[mailto:SPSSX-L@LISTSERV.UGA.EDU] On
> Behalf Of
> mgranaas@usd.edu
> Sent: Wednesday, January 21, 2004 9:06 AM
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: Re: QUERY: Data assumptions for Linear
Regression
>
>
> If the residuals are normally distributed so is that
> data.  Likewise if the data are normally distributed
> so are the residual.
>
> The regression model represents data as consisting
> of a systmatic part (the predicted value) and error.
> It is only the error that can be normally distributed.
>
> The outcome variable needs to be normally
> distributed within levels of the predictor
> variables.  We also need to assume that the outcome
> variable has the same error distribution at all
> levels of the predictors.
>
> There is no normality requirement for the predictors.
>
> MG
> ****************************************************
> Michael Granaas                 mgranaas@usd.edu
> Assoc. Prof.                    Phone: 605 677 5295
> Dept. of Psychology             FAX:  605 677 3195
> University of South Dakota
> 414 E. Clark St.
> Vermillion, SD 57069
> *****************************************************
>
> ----- Original Message -----
> From: Robert Fall <robert_fall@hotmail.com>
> Date: Wednesday, January 21, 2004 6:46 am
> Subject: QUERY: Data assumptions for Linear Regression
>
> > Hello all,
> >
> > Does anyone know know if all the predictor and
> outcome variables
> > shouldbe normally distributed for the assumptions
> to be met to
> > carry out a
> > Multiple Linear Regression - or is it just the
> residuals that need
> > to be
> > normally distributed?
> >
> > Thanks in advance,
> > Robert
> >
>