Exponential Regression

[Stiganator]

I have a data set that can be fitted pretty well with a linear fit. However I would like to do an exponential fit to see if that would also cover the range I haven't yet sampled (it looks to be tapering towards the extremes so I'll have to widen the range)

If I take the natural log of the data and then fit a linear curve the exponential coefficients will be

linear fit of ln(X) vs Y is y=ax+b


exponential equivalent is y = e^a*e^x + e^b or y= e^ax+e^b

Is that right? I don't know why this is eluding me since it is pretty basic.

Any quick way to do this with Matlab? I know there is a polyfit function, but help didn't pop up anything on exponential fits.

 

[CycloWizard]

Simple to do in MATLAB.

%input the data as x= and y=
%after data is loaded,
logy=log(y);
params=[1,1];%initial parameter estimates
[params,SSR]=fminunc(@(params) FitExponentials(x,y,logy),params);

[SSR,yhat]=FitExponential(x,y,logy)

function [SSR,yhat]=FitExponential(x,y,logy)
yhat=params(1)*exp(params(2)*x);
logyhat=log(yhat);
SSR=sum((logy-logyhat).^2);
end

edit: added a re-run of the function so you get the fitted values (yhat).

 

[DrPizza]

Another software program that's very simple to use and fit all sorts of curves is graphical analysis. It's sold by Vernier. They have a free demo (which, IIRC, is the complete version that expires after one month.) Google search for it... my wife just beeped her horn or I would.