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

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?

Thanks in advance,

Riyadh

[abuzer]

If you need to fit data with a nonlinear model, transform the variables to make the relationship linear. Alternatively, try to fit a nonlinear function directly using either the Statistics and Machine Learning Toolbox™ nlinfit function, the Optimization Toolbox™ lsqcurvefit function, or by applying functions in the Curve Fitting Toolbox™.

[the cyclist]

I don't understand. Where is the nonlinearity?

[abuzer]

I assumed he wrote wrong equation. Because he asks nonlinear..

[Riyadh Muttaleb]

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

Answer 1

[Star Strider]

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).

[Riyadh Muttaleb]

Thank you for your answer,

I have used this equation but it doesn't work, beta = nlinfit(x,y,z,Eq); Thank you for your cooperation

[Star Strider]

What is your dependent variable (the variable you want to fit ‘x,y,z’ to?

Your call to nlinfit has to be:

B = nlinfit(xyz, a, Eq, B0);

or:

B = nlinfit(xyz, a(:), Eq, B0);

where ‘a’ is your dependent variable vector, and ‘B0’ is your vector of initial parameter estimates.

[Riyadh Muttaleb]

Thank you,

this exactly what I have:

SPM(dependent variable)=a+b*S+c*A (S and A are independent variable)

so the equatio will be B = nlinfit(SA, a(:), Eq, B0)?; What is B0? 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.

Thanks in advance

[Star Strider]

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.

Answer 2

[the cyclist]

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]

Thank you for your response, I would like to regress x,y,z, three variables

best

[the cyclist]

I edited my example, so that it now uses three explanatory variables: x,y,z.

(It is not important that I happened to used x itself to define y and z.)

[Riyadh Muttaleb]

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,