FindFit power law problem
- To: mathgroup at smc.vnet.net
- Subject: [mg117005] FindFit power law problem
- From: Greg Childers <jgchilders at mailaps.org>
- Date: Mon, 7 Mar 2011 05:48:40 -0500 (EST)
- Reply-to: gchilders at fullerton.edu
Hi,
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?
Greg