0
$\begingroup$

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.

  • 0
    @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.2012-08-13

2 Answers 2

1

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.

1

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.

  • 0
    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.2012-08-13