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

Kjetil Brinchmann Halvorsen kjetil at acelerate.com
Fri Oct 15 16:12:07 CEST 2004

```John Fox wrote:

>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).
>
I'm not sure if this are BLUE residuals, but the following function
transform to a
smaller set of independent, homoscedastic residuals and the calls
shapiro.test:
I've proposed to make this a method for shapiro.test for "lm" objects,
but it is
not accepted.

shapiro.test.lm
function (obj)
{
eff <- effects(obj)
rank <- obj\$rank
df.r <- obj\$df.residual
if (df.r < 3)
stop("To few degrees of freedom for residual for the test.")
data.name <- deparse(substitute(obj))
x <- eff[-(1:rank)]
res <- shapiro.test(x)
res\$data.name <- data.name
res\$method <- paste(res\$method, " for residuals of linear model")
res
}

Kjetil

> 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
>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
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>https://stat.ethz.ch/mailman/listinfo/r-help
>>http://www.R-project.org/posting-guide.html
>>
>>
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>
>
>
>

--

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
--  Mahdi Elmandjra

```