Linear regression
[a,b,sig]=reglin(x,y)
solve the regression problem y=a*x+ b in the least square sense. sig is the standard deviation of the residual. x and y are two matrices of size x(p,n) and y(q,n), where n is the number of samples.
The estimator a is a matrix of size (q,p) and b is a vector of size (q,1)
// simulation of data for a(3,5) and b(3,1)
x=`rand`_(5,100);
aa=`testmatrix`_('magi',5);aa=aa(1:3,:);
bb=[9;10;11]
y=aa*x +bb*`ones`_(1,100)+ 0.1*`rand`_(3,100);
// identification
[a,b,sig]=reglin(x,y);
`max`_(`abs`_(aa-a))
`max`_(`abs`_(bb-b))
// an other example : fitting a polynomial
f=1:100; x=[f.*f; f];
y= [ 2,3]*x+ 10*`ones`_(f) + 0.1*`rand`_(f);
[a,b]=reglin(x,y)