albinali wrote:

> Hi all,
> I've got a question about distributions, it might require a philosophical
> answer, what makes particular distributions of interest (e.g. the normal,
> chi-square, etc.) How did statisticians discover these distributions and why
> did they think that they are of importance?

I believe the Normal was 'discovered' by plotting a lot of astronomical data
measurements.  Presumably all were developed theoretically at some point.

Historians?  Real information?

> Second question: I cannot grasp the practical implications or meaning of
> normality in a data set, when is it ok to assume normality and why not
> assume something else, for example, in linear regression when it is assumed
> that the errors are normal... what does that really mean graphically, does
> it mean that plotting the errors in the sample we have will show as a normal
> curve???

this could be a very easy question, or a very hard one.  :)  Short form: It is
acceptable to assume a distribution is Normal when you have enough data to show
that it is, or when you anticipate that it will be Normal on theoretical
grounds.  But you have to be willing to check on this.  How much data is
'enough'?  Ah, there's the rub!  If you are very picky, that would be a very
lot.  If you are being sloppy or hasty, less will do.

In the case of residuals on linear regression:  In most intro books there is a
figure showing a series of Normal curves, centered on the best fit line and
running vertically to indicate the variation observable in the y (response)
measure.  If the residual variation is independent of x, then all these Normal
curves are alike in size.  If they are Normal, they all have the same shape.

> Third question: When we assume that the variance is constant, say the error
> term in linear regression, does that mean that the error term for each data
> point is equally dispersed around the fitted curve?

Yes, if I read you correctly.

> I know some question might not be phrased properly but any help or
> corrections with these questions will be highly appreciated.
> Fahd
>
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