How to fit multivariable equation?

I have n x 3 input data (n amount of examples for three properties) and n x 1 output data from real world observations. n is the number of examples I have.

In other words,

Inputs:

inputs=[1 2 3;
4 5 7;
2 4 6;
2 1 1;
....];

Outputs:

outputs=[15; 26; 29; 8...];

From my experience on the subject, I expect there is a relationship similar to:

output=input(1)*coef1+input(2)*coef2+input(3)*coef3+coef4;

How can I use matlab to find coef1, coef2, coef3 and coef4? I checked curve fiting and optimization help pages but I could not be sure about the best way.

(I guess I can drop the term coef4 if it makes things much harder to code beacuse I expect coef4 to be small.)

For example, for the numbers I wrote above (inputs and outputs), relationship is;

input(1)+2*input(2)+3*input(3)+1

so coef1 is 1, coef2 is 2, coef3 is 3 and coef4 is 1.

In real life values, equation will not fit exactly like this due to noise of the data.

Thank you,

Answer 1

[Torsten]

coeffs = [inputs, ones(size(inputs,1),1)] \ outputs

[Caglar]

Hi, thank you for your answer. I am aware this particular case can be solved by linear algebra but I was wondering for more general solutions incase my expected equaion is not correct. Could you also help with that?

[Torsten]

It is the general solution to minimize ||[inputs,1]*coeffs - outputs|| in the least squares sense.