fitting a hyperbole

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.

--
Stephen Sefick
Research Scientist
Southeastern Natural Sciences Academy

Let's not spend our time and resources thinking about things that are
so little or so large that all they really do for us is puff us up and
make us feel like gods. We are mammals, and have not exhausted the
annoying little problems of being mammals.

       -K. Mullis

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.
    

--
Stephen Sefick
Research Scientist
Southeastern Natural Sciences Academy

Let's not spend our time and resources thinking about things that are
so little or so large that all they really do for us is puff us up and
make us feel like gods. We are mammals, and have not exhausted the
annoying little problems of being mammals.

       -K. Mullis

    

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.)