# How can I do non-linear regression for three varietals?

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Riyadh Muttaleb on 23 Jan 2017
Commented: Star Strider on 25 Jan 2017
Hi All,
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?
Riyadh Muttaleb on 23 Jan 2017
Thank you for your notes, let's say how can I regress three variables?, I have tried to apply the function you have mentioned but I couldn't to apply them for three variables

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.
Example:
% % % 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).
Star Strider on 25 Jan 2017
My pleasure.
You have described a linear model. I would do something like this:
Prms = [ones(size(SPM(:))), S(:), A(:)]\SPM(:);
a = Prms(1)
b = Prms(2)
c = Prms(3)
The core MATLAB linsolve function and the Statistics and Machine Learning Toolbox regress and glmfit functions (and several others) are also options.
That will work if your matrix is not sparse. If it is sparse, use the lsqr function.
See the documentation for the various functions to understand how to use them.

### 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
figure
plot(z,E,'*',z,f(F_fitted,[x y z]),'g');
legend('data','fit','Location','NorthWest')
Riyadh Muttaleb on 25 Jan 2017
Thank you for you cooperation,
I am a little confused with some numbers that you used,
this is my example:
SPM(dependent variable)=a+b*S+c*A (S and A are independent variable) I have values of SPM, S, and A and I would like to have the values of the constants a,b ,c with correlation coefficient R^2.
Thank you,