Ordinary least squares estimation for the multivariate model where
Each row of y and x is an observation and each column a variable.
The return values beta, sigma, and r are defined as follows.
- beta
- The OLS estimator for b, beta
= pinv (
x) *
y, wherepinv (
x)
denotes the pseudoinverse of x.- sigma
- The OLS estimator for the matrix s,
sigma = (y-x*beta)' * (y-x*beta) / (t-rank(x))- r
- The matrix of OLS residuals, r
=
y-
x*
beta.