MATLAB: Fit model with 3 independent variables and many parameters to data

Question

is it possible to fit the parameters of a non linear model with more than 2 independent variable (let's say 3 or 4 for example) to data???

here attached is my code, where the coefficients are a b c d and the independent variables are x,q,w

function [beta]=fitgen(Xtest,Ytest,Wtest,Ztest,p,p_low,p_up)

mdl=@(a,b,c,d,w,q,x) zfit(a,b,c,d,w,q,x);

algo1='Trust-Region';

fit_opt = fitoptions('Method','NonlinearLeastSquares',… 'Lower',p_low,'Upper',p_up,… 'Robust','on',… 'Normalize','off',… 'Algorithm',algo1); fit_typ = fittype(mdl,'option',fit_opt);

[Yfitt,gof,output]=fit([Xtest,Ytest,Wtest],Ztest,fit_typ,'Start',p)

%%where the function zfit is (I used a linear model just for sake of simplicity, but the final purpose is to fit a non linear model):

function [z]=zfit(a,b,c,d,w,q,x)

[x,q,w]=meshgrid(x,q,w);

z=a*x+b*q+c*w+d;

end

thank you very much in advance

Answer 1

Yes, if you have the Statistics Toolbox you can use the nlinfit() function to do this. Here is a very simple example.

function [] = nlinfitExample()
% 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=(0:1:10)'; % Explanatory variable
y = 5 + 3*x + 7*x.^2; % Response variable (if response were perfect)
y = y + 2*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 + F(3).*x.^2;
F_fitted = nlinfit(x,y,f,[1 1 1]);
% Display fitted coefficients
disp(['F = ',num2str(F_fitted)])
% Plot the data and fit
figure
plot(x,y,'*',x,f(F_fitted,x),'g');
legend('data','fit')
end

In my case, I just have one explanatory variable vector, x, but that could have been a matrix with multiple variables in each column.

Hope that helps.