How to linear regress data on a log-log plot?

I have 5 data points plotted on a log-log scale, and I want to find a linear regression equation for it. The original (un-logged) equation I'm trying to find is in the form m=k*P^n. Plotting the data on a log-log scale makes it linear so I just need the slope and y-intercept to get the original equation (where k is the y-int and n is the slope). I forgot how to do this.

Answer 1

[Star Strider]

It is relatively easy with core MATLAB functions to do a nonlinear regression. See http://www.mathworks.com/matlabcentral/answers/171718-how-can-write-this-in-matlab#comment_262537 for a nonlinear regression of a function quite similar to yours.

The problem with log transformations, especially with only 5 data pairs, is that the additive, normally-distributed errors (that the least squares technique assumes) become log-normally distributed, giving potentially inaccurate parameter estimates.

Since ‘k’ is the y-intercept and ‘n’ is the slope, your objective function (replacing the ‘P’ function in my previous answer) and where k=b(1) and n=b(2) is:

m = @(b,P) b(1).*P.^b(2);

and the cost function becomes:

SSECF = @(b) sum((y - m(b,P)).^2);

If you absolutely must do a log-log regression, use polyfit:

B = polyfit(log(P), log(m), 1);

[Joey]

Thanks! Polyfit is exactly what I needed.

[Star Strider]

My pleasure!

I would still prefer you go with the nonlinear parameter estimation. It will give accurate parameter estimates.