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FindFit power law problem

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  • Subject: [mg117005] FindFit power law problem
  • From: Greg Childers <jgchilders at>
  • Date: Mon, 7 Mar 2011 05:48:40 -0500 (EST)
  • Reply-to: gchilders at


I'm having a problem with FindFit and a power law problem.  Here's the data:

data = {{1004, 0.003977}, {9970, 0.006494}, {100000, 0.012921}, 
{1001000, .059795}}

I'm wanting to fit it to a function of the form y = a x^b, and determine 
the best value of b.  When entered into Excel, it returns the exponent b 
= 0.383.  However, Mathematica gives

FindFit[data, a x^b, {a, b}, x]
{a->0.0000145749, b->0.601807}

A graph of these values overlaid on the original data simply didn't look 
right.  Another way to find the exponent b is to take the log of both 
sides and do a linear fit:

Fit[Log[10, data], {1, x}, x]
-3.64936 + 0.383174 x

And sure enough the exponent is 0.383 in agreement with Excel.  Why does 
FindFit give a different value?


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