IGEM:IMPERIAL/2006/Least Square Curve Fit

This is a brief tutorial on how to do the least square curve fit on Matlab to extract values.

Adopted from previous tutorials by Marcio von Muhlen, Maxim Shusteff, Nate Tedford, and other BE Students at MIT.

In order to generate a fit, you need to tell Matlab the form of the equation you believe the data should follow. Matlab has no way of knowing or telling you if your function is incorrect, so it's up to you to account for this. We first create a Matlab function file. For example, an equation of the form:

<amsmath>

f(x) = \frac{C_1 \times x}{1 + C_2 \times x}

</amsmath>

The function file might look like:

 function yhat = myfun(beta, x)
 c1 = beta(1);
 c2 = beta(2);
 yhat = (c1*x ./ (1 + c2.*x);

Since this is a function, it must be named myfun.m. The coefficients to be fitted are here contained in the input variable beta. Make sure to have this function in your working directory.

Create a matrix fitData which contains the information you want. You could use:

 >>fitData = dlmread('fitdata.txt', '\t', 1, 0);

Assign the X column to the variable X and the f(X) column to the variable Y, then plot the data.

 >>X = fitData(:,1);
 >>Y = fitData(:,2);
 >>semilogx(X, Y, 'bd')

We need to provide Matlab with initial guesses for our coefficient values. At this point it's a good idea to plot our function to see if the data makes sense with regards to it. We can start by guessing 1 for both coefficients; in a real experiment, your prior knowledge of what you are measuring would determine these guesses.

 >>hold on
 >>semilogx(X, (X ./(1 + 1.*X))

Now let's have Matlab figure out the best fit (least squares sense) of the data to this function, then plot the data together.

 >>Cfs = lsqcurvefit(@myfun, [1 1], X, Y)
 >>hold off
 >>semilogx(X, Y, 'bd', X, (Cfs(1)*X ./ (1 + Cfs(2)*X)), 'k-')

Here we plotted two sets of dta in the same command. See the help file for semilogx to understand how this works. Notice that although our guess wasn't very good, Matlab had no trouble finding good coefficients. This won't always be the case with more complicated data functions.

Additional resources: MIT's Matlab Answer Page

Another Matlab tutorial, with additional material on looping and solving ODE's in Matlab.