nonlinear regression

After spending five hours reading how to use matlab for nonlinear regression I am so confused. I'm sure there must be some simple way to use a Non linear regression.

I have a function

y = m*x+d*g+d*(g^(1/k)+b^2+(b-x)^2)^k

where Im trying to find parameters m,d,g,k,b with 0<k<1

I have (x,y) data such as

(0.01, 0.00000020369272)

(0.02, 0.00000040738543)

(0.03, 0.00000061107815)

etc...

Is there some simple way to use Matlab to find the parameters?

Answer 1

[Matt Tearle]

If you have Statistics Toolbox, you can use nlinfit, although there's no guarantee that k will be in the interval (0,1). Make a function handle to your function:

f = @(c,x) c(1)*x+c(2)*c(3)+c(2)*(c(3)^(1/c(4))+c(5)^2+(c(5)-x).^2).^c(4);

f is a function of the parameters ( c ) and x. Make an initial guess of the parameters:

c = rand(5,1);

Then call nlinfit with the data you have:

cfit = nlinfit(xdata,ydata,f,c)

If you don't have Stats TB, you can brute-force it in MATLAB by making an error function to minimize. Define f as above. Then define

g = @(c) norm(f(c,xdata)-ydata);

Now use fminsearch to find the coefficients, starting with an initial guess (as before)

cfit = fminsearch(g,c)

If you have Optimization Toolbox, you can use fmincon to constrain k.

[john birt]

thanks, that helps, the second solution provided what I needed. Again Thank you so much.

[Matt Tearle]

Great. Thanks for the feedback

[Ho Nam Ernest Yim]

Can I know are there any other methods I can use also to compare the performances among methods. I used nlinfit and lsqcurvefit, I looked up and found fitnlm and lsqnonlin are same as the about methods. And I have looked into different methods such as ridge , robust , polyfit but none of them fit the case that lsqcurvefit is considering : as in lsqcurvefit(fun,x0,xdata,ydata) *nonlinear case Please help me =( , I have been looking at it for a while

[Mohamad Mossad]

Can I ask how to initialize the parameters in a better way, so that it doesn't change with every run because random numbers don't really solve the problem?