R help - Jun 2009 - how to verify gauss-markov hypothesis for linear model validity?

Hello list: 

(This is probably a stupid question).  Is there a "quick and easy" way
to confirm the gauss-markov conditions of a linear multiple regression model? 
That the mean of the residuals is 0 can easily be tested for. The normality of
the residuals as well (shapiro-wilk?).  But what about homoscedasticity? And
independence of residuals with respect to the model variables?

Thanks in advance


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On Tue, 16 Jun 2009, jose romero wrote:
> Hello list:
>
> (This is probably a stupid question).?Is there a "quick and easy"
way to
> confirm the gauss-markov conditions of a linear multiple regression 
> model?
Well, those 'conditions' are  _assumptions_, and as often happens they 
can be hard to verify.?
> That the mean of the residuals is 0 can easily be tested for.
Wrong. In general, it cannot. The residuals at issue here are not the 
deviations of the data from the fitted values, which are set to have mean 
zero. Rather they are the unobserved differences between what is observed 
and what would have been predicted given the true values of the regression 
coefficients.
> The 
> normality of the residuals as well (shapiro-wilk?).?But what about 
> homoscedasticity?
Well, if you have a good candidate for departures from homoscedasticity, 
you are in business. But you have to 'know something' about your setup 
to be this lucky. Or, if you have replicate observations for some values 
of the regressors - as in designed experiments with replication - it is 
possible. If neither if these applies, it will usually be difficult.

> And independence of residuals with respect to the 
> model variables?
This can be tough. If there is a variable that is omitted and that is 
related to (e.g. correlated with) your regressors, then the assumption 
fails. But you cannot test for this in most circumstances.

Also, certain kinds of measurement error will cause the assumption 
to fail.

HTH,

Chuck
>
> Thanks in advance
>
>
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>
>
Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

I don't think that your questions are stupid, but they probably are the
wrong one(s).

There are 2 questions (or sets of questions) when thinking about your data for
doing statistical inference.

The first question is "does this assumption hold exactly?" e.g.
"are the residuals exactly normal?".

The second question is "is the assumption close enough to holding that I
will get reasonable results when I do my inference?" e.g. "Is the data
normal enough?" or "Is it close enough to normal?".

The first set of questions is easier to answer (the answer is "No"),
but generally the answer is uninteresting and sometimes misleading.

The second set of questions is more important/useful to answer, but requires
more thought/work by the researcher.

Hope this helps,  

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of jose romero
> Sent: Tuesday, June 16, 2009 7:27 PM
> To: r-help at r-project.org
> Subject: [R] how to verify gauss-markov hypothesis for linear model
> validity?
> 
> Hello list:
> 
> (This is probably a stupid question).? Is there a "quick and
easy" way
> to confirm the gauss-markov conditions of a linear multiple regression
> model?? That the mean of the residuals is 0 can easily be tested for.
> The normality of the residuals as well (shapiro-wilk?).? But what about
> homoscedasticity? And independence of residuals with respect to the
> model variables?
> 
> Thanks in advance
> 
> 
> 	[[alternative HTML version deleted]]