Error in using * in Non-linear regression

Hello,

I would like to fit an equation in the form y=k*(x1^a)*(x2^b)*(x3^c), where I know the data of x1,x2,x3 and y.

I have to determine the coefficients k, a, b, and c.

I am using the following code:

% Fit a nonlinear regression model.

modelfun = @(b,x) b(1)*[x(:,1).^b(2)] * [x(:,2).^b(3)] * [x(:,3).^b(4)];

beta0 = [0.2 0.33 0.33 0.166];

mdl = fitnlm(X,y,modelfun,beta0)

The above code is giving an error saying:

Error in y_vs_x (line 29)

mdl = fitnlm(X,y,modelfun,beta0)

Caused by:

Error using *

Inner matrix dimensions must agree.

If I replace the second and third asterisk (*) by plus (+) then the code looks as below and is working:

modelfun = @(b,x) b(1)*[x(:,1).^b(2)] + [x(:,2).^b(3)] + [x(:,3).^b(4)];

Can anyone help me where I am going wrong?

Thanks in advacne!

vidyadhar

Answer 1

[Torsten]

Elementwise multiplication is required:

modelfun = @(b,x) b(1)*(x(:,1).^b(2)).*(x(:,2).^b(3)).*(x(:,3).^b(4));

Answer 2

[Walter Roberson]

Take the log of both sides.

log(y) = log(cons) + a * log(x1) + b * log(x2) + c * log(x3)

This is a linear system, so you can construct

v = [log(x1(:)), log(x2(:)), log(x3(:)), ones(length(x1),1)] \ log(y(:))

and then a = v(1), b = v(2), c = v(3), d = exp(v(4))