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In article <1992Oct11.153538.12821@zip.eecs.umich.edu> ayman@eecs.umich.edu (Ayman I. Kayssi) writes:
>I'm trying to fit data to a rational function. What is the transformation
>that I need to make to have a linear model?
>y = (a0 + a1*x + a2*x^2 + ... + am*x^m)/(1 + b1*x + b2*x^2 + ... + bn*x^n)
>means that:
>y + b1*y*x + b2*y*x^2 + ... + bn*y*x^n = a0 + a1*x + ... + am*x^m
>or:
>y = a0 + a1*x + ... + am*x^m + b1*(-y)*x + b2*(-y)*x^2 + ... + bn*(-y)*x^n

>I tried this and I'm not getting the right answers...is this the right 
>way to do it?

If you are trying a regression on your transformed equation, the estimates
will not even be consistent because of dependent variables on the right side.
There are ways that this can be handled (an INDICATION of how to do it is
to use higher powers of x to identify the situation, and to estimate it
as a single equation in a complete system), but this is very definitely
not optimal.  There is NO way to transform a non-linear model to a linear
model preserving the assumptions.  Figure out your assumptions, and then
use the appropriate statistical procedures.

A word of warning is appropriate.  Fitting a polynomial or a rational
function is very ill-conditioned, no matter how it is done.  You may
need not only the services of a good mathematical statistician, but
also an excellent numerical analyst.  You may very well need the numerical
analyst even if there are no random errors; crude programs are likely to
break down.

-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
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