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## Copyright (C) 1995-2013 Kurt Hornik
##
## 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 3 of the License, 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, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_num}, @var{df_den}] =} f_test_regression (@var{y}, @var{x}, @var{rr}, @var{r})
## Perform an F test for the null hypothesis @nospell{rr * b = r} in a
## classical normal regression model y = X * b + e.
##
## Under the null, the test statistic @var{f} follows an F distribution
## with @var{df_num} and @var{df_den} degrees of freedom.
##
## The p-value (1 minus the CDF of this distribution at @var{f}) is
## returned in @var{pval}.
##
## If not given explicitly, @var{r} = 0.
##
## If no output argument is given, the p-value is displayed.
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Test linear hypotheses in linear regression model
function [pval, f, df_num, df_den] = f_test_regression (y, x, rr, r)
if (nargin < 3 || nargin > 4)
print_usage ();
endif
[T, k] = size (x);
if (! (isvector (y) && (length (y) == T)))
error ("f_test_regression: Y must be a vector of length rows (X)");
endif
y = reshape (y, T, 1);
[q, c_R ] = size (rr);
if (c_R != k)
error ("f_test_regression: RR must have as many columns as X");
endif
if (nargin == 4)
s_r = size (r);
if ((min (s_r) != 1) || (max (s_r) != q))
error ("f_test_regression: R must be a vector of length rows (RR)");
endif
r = reshape (r, q, 1);
else
r = zeros (q, 1);
endif
df_num = q;
df_den = T - k;
[b, v] = ols (y, x);
diff = rr * b - r;
f = diff' * inv (rr * inv (x' * x) * rr') * diff / (q * v);
pval = 1 - fcdf (f, df_num, df_den);
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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