[R] heteroscedasticity problem

[robert.ptacnik at niva.no]

Dear Listers,

I have a regression problem (x->y) with biological data, where x influences
y in two ways, (1) y increases with x and (2) the variation around the mean
(residuals) decreases with increasing x, i.e. y becomes more 'predictable'
as x increases.
The relationship is saturating, y~a + bx + cx^2, gives a very good fit.

I know basically how to test for heteroscedasticity. My question is if
there is an elegant regression method, which captures both, the mean and
the (non-constant) variation around the mean. Such a method would ideally
yield an estimate of the mean and its variation, both as a function of x.

The pattern corresponds very well to some established ecological theory
(each x is the species richness of a community of primary producers, y is
the productivity of each community; productivity and its predictability
both increase with increasing species richness).

Apologies for the probably clumsy decription of my problem - I am
ecologist, not statistician (but a big fan of R).

Cheers,
Robert


Robert Ptacnik
Norwegian Institute for Water Research (NIVA)
Gaustadalléen 21
NO-0349 Oslo
 FON +47 982 277 81
FAX +47 221 852 00