Hello,
jim horsman wrote:
> can anyone give a genetic explanation (or reference) as to why this happens?
> is it just an application of the central limit theorem?
"Genetic?" Or is that perhaps a typo for "Generic"?
Anyway, I'll try. I'm not sure if it's an example of the central
limit theorem, because (as I understand it), the central limit theorem
applies to normal distributions, and I think "regression to the mean"
can occur in non-normally distributed data.
My understanding is that regression towards the mean occurs in cases
where the correlation between variables is not exact (in stats terms, r
< 1). E.g., height of parents and height of offspring (yes, this one is
an example of normally distributed data, I know). If parents are very
tall or very short, you wouldn't predict that their kids will be just as
tall / short. Because the correlation is not exact, you'd predict the
kids would be closer to the average height.
When the correlation between two variables drops to zero, when
you're given one variable, your best guess for the other is just to
predict its mean. For instance, the correlation between rolls of two
dice (this one isn't normally distributed!). If you roll a 6 on one,
your best guess for the other is the mean (3.5).
So extraordinary events tend to be followed by more ordinary ones.
--
Zen Faulkes
Department of Biology
University of Texas - Pan American
http://w3.panam.edu/~zfaulkes