# Fit model with 3 independent variables and many parameters to data

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Manuel on 11 Feb 2013
Commented: the cyclist on 11 Oct 2021
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

the cyclist on 11 Feb 2013
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.
##### 2 CommentsShowHide 1 older comment
Thi Na Le on 25 Mar 2020

Manuel on 11 Feb 2013
Thank you very much it works.
Does anyone knows how to apply boundary condition to the parameters during the fitting using the function nlinfit?
Thank you a lot
the cyclist on 11 Feb 2013
I suggest you ask this as a new question. Questions buried within other questions rarely get attention.

NgocDuy Nguyen on 7 Oct 2021
Hello everyone,
I have tried to fit a function f(x,y,z) to determine F1, F2, F3, ...., F9 coefficients.
My code is as follows:
function [] = nlinfitExample()
[x1,x2,x3] = meshgrid(362:1,362:1,362:1);
[ff]=meshgrid(362:1);
f=[ff(x1,x2,x3)];
[F_fitted] = meshgrid(9:1);
[F] = meshgrid(9:1);
x = x1;
y = x2;
z = x3;
% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x,y,z) F(1)*exp(-((x-20)^2+(y-20)^2)/12)+F(2)*exp(-((x-38)^2+(y-50)^2)/43)+F(3)*exp(-((x-350)^2+(y-82)^2)/13)+F(4)*exp(-((x-58)^2+(y-82)^2)/24)+F(5)*exp(-((x-70)^2+(y-110)^2)/244)+F(6)+(0.0000532793*x^2-5-F(7)*(y-x)/(y+x))*ln(z-F(8)*((-1)^x+(-1)^y))+F(9)*0.0000532793*x^2+0.0000177598*x^2*ln(x+y)-0.022930657*x;
%F_fitted = nlinfit(x,y,z,f,[F(1), F(2), F(3), F(4), F(5), F(6), F(7), F(8), F(9)]);
F_fitted = nlinfit(x,y,z,f, [1 1 1 1 1 1 1 1 1]);
% Display fitted coefficients
disp(['F = ',num2str(F_fitted)])
end
But it gives the error as follows:
Error:
Requires a vector second input argument.
Error in nlinfitExample (line 17)
F_fitted = nlinfit(x,y,z,f, [1 1 1 1 1 1 1 1 1]);
Thank you.
the cyclist on 11 Oct 2021
Please open this as a new question, not making it an "answer" on a 8-year-old question