# Simple non linear fitting question(Least Squares Fitting--Exponential) [duplicate]

Possible Duplicate:
easy to implement method to fit a power function (regression)

I have the following simple function: $h = cV^n$

h and V being the variables and $c$ and $n$ are parameters that I want to optimize. I have a series of values for $h$ and $V$. What are the options for guessing the parameters ? I know if the funtion is linear I can use linear least square for a maximum likelihood guess. But in my case it's non linear.

-
Hi thanks for editing my writings. How did you input Latex like math formulas ? –  osager Nov 14 '11 at 23:16
You can use a) "edit" to edit the post and see the source code to look at what others have done; b) use dollar signs to enclose $\TeX$ code, and c) right-click on any formula you see on this site and select "Show Source" to see the $\TeX$ source for it. –  joriki Nov 14 '11 at 23:23
Thanks. The right-click method is really cool ! –  osager Nov 14 '11 at 23:28

## marked as duplicate by Ｊ. Ｍ., Jonas Teuwen, Henning Makholm, t.b., Asaf KaragilaNov 15 '11 at 15:44

There is also least squares fitting for exponential functions. For the formulas you need to use, see mathworld ($y$ is your $h$ and $e^x$ is your $V$). If you don't like to evaluate the formulas from hand you can use software packages like Mathematica which come with ready algorithms for those problems.
Since you were thinking of interpreting the least squares fit as a maximum likelihood estimate, note that where the mathworld article says "it is often better to minimize the function ...", the factors $y_i$ account for the transformed variances. This Wikipedia article counsels against this transformation because of the effect on the errors. If you just want to get a good fit, this is a good method; if you want to interpret the result statistically, you need to be careful. –  joriki Nov 14 '11 at 23:20
@osager: If you're using Mathematica, then FindFit[] is the function to use. If you'll be implementing it on your own, well, there's this... –  Ｊ. Ｍ. Nov 14 '11 at 23:41