# nonlinear regression

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john birt on 20 Feb 2011
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?

Matt Tearle on 21 Feb 2011
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.
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?