[R] Testing for normality of residuals in a regression model

[Berton Gunter]

Quite right, John!

I have 2 additional questions:

1) Why test for normality of residuals? Suppose you reject -- then what?
(residual plots may give information on skewness, multi-modality, data
"anomalies" that can affect the data analysis).

2) Why test for normality? Is it EVER useful? Suppose you reject -- then
what?

(I am tempted to add a 3rd question -- why test at all? -- but that is
perhaps too iconoclastic and certainly off topic. Let the hounds remain
leashed for now.)

Cheers,

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box
 
 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of John Fox
> Sent: Friday, October 15, 2004 5:43 AM
> To: 'Federico Gherardini'; R-help at stat.math.ethz.ch
> Subject: RE: [R] Testing for normality of residuals in a 
> regression model
> 
> Dear Federico,
> 
> A problem with applying a standard test of normality to LS 
> residuals is that
> the residuals are correlated and heterskedastic even if the standard
> assumptions of the model hold. In a large sample, this is 
> unlikely to be
> problematic (unless there's an unusual data configuration), 
> but in a small
> sample the effect could be nontrivial.
> 
> One approach is to use BLUS residuals, which transform the LS 
> residuals to a
> smaller set of uncorrelated, homoskedastic residuals (assuming the
> correctness of the model). A search of R resources didn't 
> turn up anything
> for BLUS, but they shouldn't be hard to compute. This is a 
> standard topic
> covered in many econometrics texts.
> 
> You might consider the alternative of generating a 
> bootstrapped confidence
> envelope for the QQ plot; the qq.plot() function in the car 
> package will do
> this for a linear model.
> 
> I hope this helps,
>  John
> 
> --------------------------------
> John Fox
> Department of Sociology
> McMaster University
> Hamilton, Ontario
> Canada L8S 4M4
> 905-525-9140x23604
> http://socserv.mcmaster.ca/jfox 
> -------------------------------- 
> 
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch 
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
> > Federico Gherardini
> > Sent: Friday, October 15, 2004 7:44 AM
> > To: R-help at stat.math.ethz.ch
> > Subject: [R] Testing for normality of residuals in a 
> regression model
> > 
> > Hi all,
> > 
> > Is it possible to have a test value for assessing the 
> > normality of residuals from a linear regression model, 
> > instead of simply relying on qqplots?
> > I've tried to use fitdistr to try and fit the residuals with 
> > a normal distribution, but fitdsitr only returns the 
> > parameters of the distribution and the standard errors, not 
> > the p-value. Am I missing something?
> > 
> > Cheers,
> > 
> > Federico
> > 
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