### Copyright (C) 1996 John W. Eaton
###
### This file is part of Octave.
###
### Octave is free software; you can redistribute it and/or modify it
### under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2, or (at your option)
### any later version.
###
### Octave is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with Octave; see the file COPYING.  If not, write to the Free
### Software Foundation, 59 Temple Place - Suite 330, Boston, MA
### 02111-1307, USA.

## usage: [BETA, SIGMA [, R]] = ols (Y, X)
##
## Ordinary Least Squares (OLS) estimation for the multivariate model
##
##     Y = X*B + E,  mean(E) = 0,  cov(vec(E)) = kron(S,I)
##
## with Y ... T x p     As usual, each row of Y and X is an observation
##      X ... T x k     and each column a variable.
##      B ... k x p
##      E ... T x p.
##
## BETA is the OLS estimator for B, i.e.
##
##   BETA = pinv(X)*Y,
##
## where pinv(X) denotes the pseudoinverse of X.
## SIGMA is the OLS estimator for the matrix S, i.e.
##
##   SIGMA = (Y - X*BETA)'*(Y - X*BETA) / (T - rank(X)).
##
## R = Y - X*BETA is the matrix of OLS residuals.

## Author: Teresa Twaroch <twaroch@ci.tuwien.ac.at>
## Created: May 1993
## Adapted-By: jwe

function [BETA, SIGMA, R] = ols (Y, X)

  if (nargin != 2)
    error("usage : [BETA, SIGMA [, R]] = ols (Y, X)");
  endif

  [nr, nc] = size (X);
  [ry, cy] = size (Y);
  if (nr != ry)
    error ("ols: incorrect matrix dimensions");
  endif

  Z = X' * X;
  r = rank (Z);

  if (r == nc)
    BETA = inv (Z) * X' * Y;
  else
    BETA = pinv (X) * Y;
  endif

  R = Y - X * BETA;
  SIGMA = R' * R / (nr - r);

endfunction