How can I do non-linear regression for three varietals?
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I have matrix with three variables (x,y,z) I would like to get best non linear regression for these variables using like this equation: Eq=a*x+b*y+c*z+d
How can I get the constants and correlation coefficient?
Thanks in advance,
Star Strider on 23 Jan 2017
The equation you posted is linear. Assuming it is a stand-in for a nonlinear equation, the usual way of fitting a function of several variables is to create a matrix of the incependent variables and passing that as one argument to the objective and fitting functions.
% % % MAPPING: x = xyz(:,1), y = xyz(:,2), z = xyz(:,3), a = b(1), b= B(2), c = b(3), d = b(4)
xyz = [x(:) y(:) z(:)];
Eq = @(b,xyz) b(1).*xyz(:,1) + b(2).*xyz(:,2) + b(3)*zyz(:,3) + b(4);
Then just use them as arguments to whatever fitting function you want (such as nlinfit or lsqcurvefit).
More Answers (1)
the cyclist on 23 Jan 2017
Edited: the cyclist on 23 Jan 2017
Maybe this will help?
% Here is an example of using nlinfit(). For simplicity, none of
% of the fitted parameters are actually nonlinear!
% Define the data to be fit
x = (0:0.25:10)'; % Explanatory variables
y = x.^2;
z = x.^3;
E = 5 + 3*x + 7*y + 11*z; % Response variable (if response were perfect)
E = E + 500*randn((size(x)));% Add some noise to response variable
% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,X) F(1) + F(2).*X(:,1) + F(3).*X(:,2) + F(4).*X(:,3);
F_fitted = nlinfit([x y z],E,f,[1 1 1 1]);
% Display fitted coefficients
disp(['F = ',num2str(F_fitted)])
% Plot the data and fit
plot(z,E,'*',z,f(F_fitted,[x y z]),'g');