IUBio

regression toward the mean

jim horsman jhorsman at jovanet.com
Sat Feb 2 13:02:19 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"?

no typo.


>
>
>     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.

regression to the mean happens not because r^^2<1, but because the linear
coefficient (the slope of the line ) is less than 1.
It is not obvious to me why this coefficient would be less than one.
Also,  a common prediction for height
expected child's height= .5* mom's height +.5*dad's height  (+ or- 3 inches
for sex)
can not be correct because it does not take into consideration regression to
the mean.
>






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