Help needed in least square curve fit equation

Hi all,

I am trying to solve a least square non linear regression with the following data points:

X  1  2  3  4  5  6  7  8  9  10 
Y 2950  2452  2333  2274  2244  2222  2207  2195  2184  2176

The equation which I want to fit is:

Y=a*exp[-X/b]+c

a, b and c are constants defined to fit the curve..

Also, as you notice, the Y value decreases with each X, but it will gradually converge and not decrease after a certain value of X. So, I want to extrapolate the curve such that, at very high value of X (X = infinity), function Y converges to its asymptotic value.. In other words, with a certain high number of 'X', the "a*exp[-X/b]" term will tend toward 0, where "c" represents the convergence, and that value of "c" is being taken as final result..

Any type of help is appreciated.. Thanks for your consideration

Answer 1

[Matt J]

Here's a poor man's approach using FMINSEARCH, assuming,you don't have the Optimization Toolbox. If you do have the toolbox, LSQCURVEFIT would be worth a try.

   %Initial guess

   p0(3)=1000;
   z=[ones(10,1) , -X(:)]\log(Y(:)-p0(3));

   p0(1)=exp(z(1));
   p0(2)=1./z(2);

   %Solve
   p=fminsearch(@(p) norm( p(1)*exp(-X/p(2))+p(3)  - Y),   p0,optimset('MaxFunEvals',100000));

   a=p(1), b=p(2), c=p(3)

[Matt J]

You could also try FEX: fminspleas, which would be well applicable to you, since only one of your parameters, b, is nonlinear.