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C++ API

: [beta, sigma, r] = ols (y, x)

Ordinary least squares estimation.

OLS applies to the multivariate model y = x*b + e with mean (e) = 0 and cov (vec (e)) = kron (s, I). where y is a t by p matrix, x is a t by k matrix, b is a k by p matrix, and e is a t by p matrix.

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 is calculated directly via inv (x'*x) * x' * y if the matrix x'*x is of full rank. Otherwise, beta = pinv (x) * y where pinv (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.

See also: gls, pinv.

Package: octave