fitting a hyperbole
On 21/09/2008, at 10:38 AM, Peter Dalgaard wrote:
stephen sefick wrote:
I am not sure if I am exaggerating or not read title as hyperbola On Sat, Sep 20, 2008 at 2:20 PM, stephen sefick <ssefick at gmail.com> wrote:
I have got a data set that is Gross Primary Productivity ~ Total Suspended Solids it is a hyperbola just like: plot(1/c(1:1000)) how do I model this relationship so that I can get all of the neat things that lm gives residuals etc. etc. so that I can see if my eyeball model stands up. Thanks for any help, pointers, or good things to read.
Well, it depends on the exact model you want to fit and the error characteristics. There's a straightforward linear model in the transformed x: lm(y ~ I(1/x)) but there are also transformed models like lm(1/y ~ x) or lm(log(y) ~ log(x)) but of course, y, 1/y, and log(y) can't all be homoscedastic normal variates. Going beyond the linearized models, you can use nls(), as in nls(y~ a/(x-b), start=c(a=1,b=0)) (which is linear for 1/y, but assumes that y rather than 1/y has constant variance.)
Nicely expressed. Succinct, clear, to the point, comprehensive. I
wish I'd said that!
(And that's not hyperbole. :-) )
So much more helpful than some postings I've seen recently to the
effect of ``Go away
and read a book on this topic.''
cheers,
Rolf
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