Date: Jan 30, 2013 11:02 AM
Author: JK
Subject: fit power curve with best exponent to data

Hi,

I'm attempting to fit the following equation to a set of data characterizing something's autocorrelation function:

y=e^(a*x)^n

to determine 'best fit' a and n. An example of the data:

(x):
4.47481932596166
4.47660093553848
4.47838272239611
4.48016468632304
4.48194682710806
4.48372914454029
4.48551163840916
4.48729430850440
4.48907715461608
4.49086017653456
4.49264337405052
4.49442674695494
4.49621029503915
4.49799401809473
4.49977791591363
4.50156198828807
4.50334623501058
4.50513065587403
4.50691525067157
4.50870001919666
4.51048496124308
4.51227007660490
4.51405536507651
4.51584082645259
4.51762646052814
4.51941226709846
4.52119824595914
4.52298439690610
4.52477071973553
4.52655721424396
4.52834388022818
4.53013071748531
4.53191772581277
4.53370490500827
4.53549225486981
4.53727977519571
4.53906746578457
4.54085532643532
4.54264335694714
4.54443155711955
4.54621992675233
4.54800846564559
4.54979717359972
4.55158605041539
4.55337509589359
4.55516430983560
4.55695369204296
4.55874324231756
4.56053296046153
4.56232284627732


(y):
4.47481932596166
4.47660093553848
4.47838272239611
4.48016468632304
4.48194682710806
4.48372914454029
4.48551163840916
4.48729430850440
4.48907715461608
4.49086017653456
4.49264337405052
4.49442674695494
4.49621029503915
4.49799401809473
4.49977791591363
4.50156198828807
4.50334623501058
4.50513065587403
4.50691525067157
4.50870001919666
4.51048496124308
4.51227007660490
4.51405536507651
4.51584082645259
4.51762646052814
4.51941226709846
4.52119824595914
4.52298439690610
4.52477071973553
4.52655721424396
4.52834388022818
4.53013071748531
4.53191772581277
4.53370490500827
4.53549225486981
4.53727977519571
4.53906746578457
4.54085532643532
4.54264335694714
4.54443155711955
4.54621992675233
4.54800846564559
4.54979717359972
4.55158605041539
4.55337509589359
4.55516430983560
4.55695369204296
4.55874324231756
4.56053296046153
4.56232284627732

As far as I can tell, I can't use the curve fitting tool as it won't determine the best fit for exponent n, only a. I have an idea that involves iterating progressively closer solutions to the equation with varying a and n, but haven't yet worked out how to implement it.

Any ideas?

Cheers, JK