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Date:         Wed, 5 Apr 2006 11:39:50 -0300
Reply-To:     Hector Maletta <hmaletta@fibertel.com.ar>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Hector Maletta <hmaletta@fibertel.com.ar>
Subject:      Re: R, R square, and adjusted R square
Comments: To: Sibusiso Moyo <smoyo@targetrx.com>
In-Reply-To:  <B2A95412067E5C4CBA09E2E92D81BF290506CAAF@TRX-V01.targetrx.com>
Content-Type: text/plain; charset="us-ascii"

I concur with Sibusiso's point. In fact, a model explaining only a small fraction of variable's variance may still be substantively important and (sample permitting) statistically significant (suppose you find a risk factor explaining only 5% of variability in certain important disease (R2=0.05); if the sample is large enough for this finding to be statistically significant (i.e. not likely to have been obtained by chance from a population where in fact R2=0), it could prove something and be the basis for some valid intervention. However, I have some minor remarks on Sibusiso's message. 1. He wrote: "High R square and theoretically 'correct' signs and magnitudes for estimated coefficients, have very little to do with statistical adequacy (i.e. whether or not your model is well specified)." Well, R2 measures the adequacy of a LINEAR model to the data. A non significant R2 means a linear model does not explain much, but a nonlinear model with the same variables may explain more. Thus R2 DOES have something to say on whether your model is well specified, though I agree the "something" may be not much. In addition, that the model is well specified is more a substantive than a statistical consideration. 2. He also wrote: "It is much more important to ensure that your residuals satisfy all the OLS assumptions, and when that is done you do not have to worry about normality of your residuals because everything will be ok." In fact, checking whether residuals satisfy OLS assumptions involves checking the normality of residuals (which is one of OLS requirements). Cheers. Hector

-----Mensaje original----- De: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] En nombre de Sibusiso Moyo Enviado el: Wednesday, April 05, 2006 9:43 AM Para: SPSSX-L@LISTSERV.UGA.EDU Asunto: Re: R, R square, and adjusted R square

Karl,

I am assuming you are concerned about normality and R square because you are using R square as a reference point, to determine how good your model is? If this is correct I'd like to add a word of caution. High R square and theoretically 'correct' signs and magnitudes for estimated coefficients, have very little to do with statistical adequacy (i.e. whether or not your model is well specified). One canot judge the adequacy of an estimated regression based on the reported R square and the significance of the coefficients, but on the properties of the residuals. It is much more important to ensure that your residuals satisfy all the OLS assumptions, and when that is done you do not have to worry about normality of your residuals because everything will be ok.

So in short worry more about the properties of your residuals and ensure that there is no temporal dependence and heterogeneity, etc. Sometimes near perfect models can have very "low" R squares!!

Sibusiso.

-----Original Message----- From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On Behalf Of Karl Koch Sent: Wednesday, April 05, 2006 5:02 AM To: SPSSX-L@LISTSERV.UGA.EDU Subject: R, R square, and adjusted R square

Hello,

I have a question about the above measures from regression analysis.

How much does each of the measures (R, R square, and adjusted R square) depend on the assumption of normality? Or, to put it in different terms, how much could they divert from the measure stated in the SPSS model table when the normality test failed? Are these measure then completely unreliable (random) or is there still a level of confidence?

Best Wishes, Karl

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