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

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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

1 Answer 1

up vote 2 down vote accepted

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 ? –  osager Nov 14 '11 at 23:15
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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 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: 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. –  joriki Nov 14 '11 at 23:21
    
Ok I found it. Thanks I'll dig into it. –  osager Nov 14 '11 at 23:22
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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... –  J. M. Nov 14 '11 at 23:41

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