```Date: Wed, 21 Jan 2004 17:22:38 -0600 Reply-To: Paul R Swank Sender: "SPSSX(r) Discussion" From: Paul R Swank Subject: Re: QUERY: Data assumptions for Linear Regression Comments: To: mgranaas@usd.edu In-Reply-To: Content-Type: text/plain; charset="us-ascii" Ah, okay, I agree with that. 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 2:56 PM To: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: QUERY: Data assumptions for Linear Regression 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 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 > 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 > > > ```

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