Laurence wrote:
>
> Hi,
>
> Residuals coming from regression.
>
> I look for a method explaining ho how to make a chi-square on residuals
> (Without ploting anything) to prove or not the normality of the
> distribution.
>
> Programs or algorithms are welcome.
I do not suggest that you do this (especially handing it over to an
algorithm). The question that you need to answer is usually:
"Is the distribution of the residuals close enough to normal that it is
reasonable to minimize the sum of squared errors [essentially, to fit to
the conditional mean], and to assume no hidden important variables?"
(Note that under some circumstances "close enough" may be quite far
from normal. The important questions are "is the mean a good measure of
location?", "is least-squares robust enough?" and "is least-squares
powerful enough? For instance, if the residual distribution is
approximately symmetric and not much longer-tailed than the normal
distribution, any reasonable measure of location will coincide with the
mean, robustness will not be a problem, and least-squares will probably
be nearly as powerful as anything else that does not rely on very
specific (and nonrobust) models.)
The question which a test of normality will answer is:
"Is there evidence for any deviation whatsoever from normality?"
These are not the same question. In particular, with a large enough data
set, the test will usually reject the hypothesis of normality even when
the true distribution is very close to normal. Moreover, no simple test
of normality that I'm familiar with distinguishes between deviations
from normality that will make least-squares inadvisable and those that
do not.
I would suggest using boxplots of the residuals, with special attention
paid to points flagged as outliers.
-Robert Dawson
.
.
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