reglin

Description

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)

See Also

• pinv — pseudoinverse
• leastsq — Solves non-linear least squares problems
• qr — QR decomposition