How to do Nonlinear Regression coding in Matlab?

[rahul.6sept]

Hi,
I've written a code in Matlab for nonlinear regression. But it is not executing. I'm attaching the same here. I want to calculate the value for kmax and ks in the code.

% To determine the value of Kmax and Ks for the model of bacteria growth
% given by      mu=(kmax*c^2)/(ks+c^2)
% can be rewritten as
% log(mu)=log(kmax*c^2)-log(ks+c^2)
% log(mu)=log(kmax)+2log(c)-2log(ks)*log(c)
% y = a0+a1*x+a2*u

         
mu=[1.10 3.34 5.29 6.66 7.58 8.18 8.60 8.89]; 
C=[0.5; 1.0; 1.5; 2.0; 2.5; 3.0; 3.5; 4.0];
C=repmat(C,1,1);
N=length(C);
xData=C;
yData=reshape(mu,8,1);
%% Calculate Linear Regression and plot
x=2*log(xData);
u=log(xData);

X=[ones(N,1),x,u];
Y=log(yData);

phi=inv(X'*X)*X'*Y;

a0=exp(phi(1));
a1=phi(2);
a2=phi(3);
phi_guess=[1;1];
phi_lsq=lsqnonlin(@(phi) mylsqnonlin(phi,x,y),phi_guess);

The function file is here below:

function [y,ks,kmax] = mylsqnonlin(phi,x,y,u)
% Get parameters
a0=phi(1);
a1=phi(2);
%a2=phi(3);

%% Calculation of the values of kmax & ks
y = a0+a1*x+a2*u ;
ks=-0.5*exp(a2);
kmax=exp(a0);

end

I'm getting the value of phi as NaN. It should give value as 1x3 matrix.




Rahul