Fit a square root function to data

I would like to fit a function of form y=K*x^.5+c, where Matlab finds the best fit values of K&c. What's the best way to do this? Thanks!

Answer 1

[Star Strider]

Your function is actually linear, so you can use any linear regression function such as the Statistics Toolbox regress function, since it supplies several statistics on the fit.

Otherwise, use the mldivide function or ‘\’ operator. Assuming x and y are row vectors in your original data:

x = linspace(0, 10, 15);                % Create Data
y = 3.*sqrt(x)+5 + 0.1*randn(size(x));  % Create Data

p = [sqrt(x)'  ones(size(y'))]\y';      % Estimate Parameters

The vector of estimated parameters correspond to p(1)=K and p(2)=c.

If x and y are column vectors, eliminate the transpose (') operators in the ‘p’ calcualation.

You can also use polyfit and its friends, remembering to use sqrt(x) instead of x in the argument list:

yp = polyfit(sqrt(x), y, 1);