IUBio

regression toward the mean

Zen Faulkes zfaulkes at panam.edu
Sat Feb 2 10:12:09 EST 2002


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




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