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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.

Thanks in advance.

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    Hi thanks for editing my writings. How did you input Latex like math formulas ?2011-11-14
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    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.2011-11-14
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    Thanks. The right-click method is really cool !2011-11-14

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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.

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    Thanks for the reply. I DO use Mathematica. Just don't know which part of the document I should consult. Besides, aside from the ready made tools, what is the underlying theory for this simple optimisation problem ? I'm self learning convex optimisation right now and this should be a convex optimisation problem. If I have to implement my self, is it a iterative algorithm like Newton's methode ?2011-11-14
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    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](http://en.wikipedia.org/wiki/Non-linear_least_squares#Transformation_to_a_linear_model) 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.2011-11-14
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    @osager: How do you mean "what part of the document"? The entire page Listing linked to is a prescription for linearizing your problem; once without adjusted weights and once with adjusted weights.2011-11-14
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    Ok I found it. Thanks I'll dig into it.2011-11-14
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    @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](http://math.stackexchange.com/questions/3625)...2011-11-14