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Power Law, Exponential and Logarithmic Fit



26 Nov 2010 (Updated )

Finds and plots the linear fit to some data points when plotted on a log scale.

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  logfit(X,Y,graphType), where X is a vector and Y is a vector or a
              matrix will plot the data with the axis scaling determined
              by graphType as follows: graphType-> xscale, yscale
                 loglog-> log, log
                   logx -> log, linear
                   logy -> linear, log
                 linear -> linear, linear
              A line is then fit to the scaled data in a least squares
              See the 'notes' section below for help choosing a method.
  logfit(X,Y), will search through all the possible axis scalings and
              finish with the one that incurs the least error (with error
              measured as least squares on the linear-linear data.)

A power law relationship
[slope, intercept] = logfit(x,y,'loglog');
           yApprox = (10^intercept)*x.^(slope);

An exponential relationship
[slope, intercept] = logfit(x,y,'logy');
           yApprox = (10^intercept)*(10^slope).^x;

A logarithmic relationship
[slope, intercept] = logfit(x,y,'logx');
           yApprox = (intercept)+(slope)*log10(x);

A linear relationship
[slope, intercept] = logfit(x,y,'linear');
           yApprox = (intercept)+(slope)*x;

MATLAB release MATLAB 7.11 (R2010b)
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Comments and Ratings (9)
08 Feb 2015 Alberto Rodríguez Fernández

Thank you for your function!!

13 Nov 2013 Budi

Budi (view profile)

very usefull,,

by the way, how to make non linear curve fit using custom equation when plot on log scale?


23 Sep 2013 Saskia

Saskia (view profile)

11 Jul 2013 Franziska

Thanks a lot! Very helpful

23 May 2013 Shea

Shea (view profile)

Just what the Dr. ordered. Thank You.

11 Feb 2013 a

a (view profile)


30 Jan 2012 Shatrughan

Saviour !!!!!!!!!!

06 Jan 2012 none

none (view profile)


I use:

% y = a x^b
function [a b] = my_powerLawFit(y, x)


30 Jan 2011 Manas Hardas

Extremely cool!

09 Aug 2013

Updated to include Mean Squared Error

17 Dec 2013

fixed 'skipbegin' feature functionality

09 Jan 2014

Updated to use R2 as 'best fit' criterion rather than MSE

22 Aug 2014

Added new color option which lets you set the 'color' of both lines and markers with one parameter. Added robustness to NaN values.

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