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

John Fox jfox at mcmaster.ca
Fri Oct 15 14:43:18 CEST 2004

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 Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4

> -----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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