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Is there any software that will fit a set of 2D points using a logarithmic curve?

I found this, which looks like the formulas I need, but I don't think I have a fancy enough calculator to solve that for me.

WolframAlpha has a LeastSquares[] function, but it looks like it only does linear regressions.

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Is this an example of what you're trying to do:… ? – Derek Allums Aug 12 '12 at 21:58
Any spreadsheet that does linear fits would allow you to take the log of your data before fitting. – Ross Millikan Aug 12 '12 at 22:18
@unit3000-21: That looks exactly like what I was looking for. Didn't know the syntax. Is there a reference somewhere? Anyway, if you made that an answer, I'd accept it. – mpen Aug 13 '12 at 0:15
up vote 1 down vote accepted

Here's an example of what you're trying to do in Wolfram Alpha. I think you can do the same thing in Mathematica using similar, or identical notation.

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I wouldn't be surprised if Wolfram Alpha is actually doing what Ross suggested: transform the $x$ data by $t_j = \log(x_j)$. Then $y = a \log(b x)$ becomes $y = a t + c$ where $t = \log(x)$ and $c = a \log(b)$. Thus this becomes a linear least-squares problem.

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That's a pretty clever way of solving it. – mpen Aug 13 '12 at 1:58
But not necessarily the best method, as the transformation with logarithms will also distort the errors inherent in the data. Most software (yes, even Excel!) allows for nonlinear least-squares fitting; look at their documentation for details. – Timmy Turner Aug 13 '12 at 2:07
What I would suggest is to use the log transformation to get initial values for the parameters and then use a nonlinear fitter with those as the initial values. My experience with nonlinear fitting is that having good initial parameter values is essential. – marty cohen Aug 13 '12 at 2:42
@marty, that is in fact the proper approach for these things. Use the linearization to obtain good initial values for your NLLS method. – J. M. Aug 13 '12 at 4:04
For a standard least-squares in the $y$ direction with the $x$ values considered as exact (which is what is happening here), transforming the $x$ values doesn't cause any "distortion". It really is a linear problem. If you were doing "total least-squares" where errors in both $x$ and $y$ are allowed, you would be right, the problem for a logarithmic fit would be nonlinear. – Robert Israel Aug 13 '12 at 6:25

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