Multivariate Regression Parameter Optimization

I am trying to find the values that will optimize parameters in an equation. Two measured values are related by an equation to equal a known value.

The equation is: y=a*(x^b)*(z^c)

x & z = measured values (vectors of length n)

a,b & c = the unknown free parameters (single values)

I also have known values Y that y should approximately equal. Therefore, I want to find the set of parameters a,b&c that minimizes the difference between Y and y (given all measured values).

What is the best way to do this in MATLAB?

Thanks!

-Andrew

Answer 1

[Teja Muppirala]

NLINFIT is good.

NonLinearModel.fit is also good.

But since your problem involves fitting a surface with only two independent variables, it can be done very simply using the Curve Fitting Toolbox functions.

You can do it interactively using CFTOOL and then generate the MATLAB code automatically (recommended), or if you want to write the code out by hand yourself, you can do something along these lines:

x = rand(100,1);
z = rand(100,1);

atrue = 2.5;
btrue = 1.7;
ctrue = 1.2;
Y = atrue*(x.^btrue).*(z.^ctrue) + 0.05*randn(size(x)) ;

scatter3(x,z,Y);

hold all;
F = fittype('a*x^b*z^c','Independent',{'x' 'z'});
M = fit([x z],Y,F) % Or specify an initial guess: M = fit([x z],Y,F,'Start',[0 0 0])
plot(M)

[Andrew]

I ended up using this approach - thanks so much! Worked perfectly.

Answer 2

[the cyclist]

I think that the function nlinfit() from the Statistics Toolbox will do what you want.

[Andrew]

This worked too, but I ended up implementing Teja's approach. Thank you for your fast response!