Date: Wed, 5 Apr 2006 11:39:50 0300
ReplyTo: Hector Maletta <hmaletta@fibertel.com.ar>
Sender: "SPSSX(r) Discussion" <SPSSXL@LISTSERV.UGA.EDU>
From: Hector Maletta <hmaletta@fibertel.com.ar>
Subject: Re: R, R square, and adjusted R square
InReplyTo: <B2A95412067E5C4CBA09E2E92D81BF290506CAAF@TRXV01.targetrx.com>
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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:SPSSXL@LISTSERV.UGA.EDU] En nombre de
Sibusiso Moyo
Enviado el: Wednesday, April 05, 2006 9:43 AM
Para: SPSSXL@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:SPSSXL@LISTSERV.UGA.EDU]On Behalf Of
Karl Koch
Sent: Wednesday, April 05, 2006 5:02 AM
To: SPSSXL@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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