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## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## This program 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.
##
## This program 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 this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: [pval, f, df_num, df_den] = f_test_regression (y, X, R [, r])
##
## Performs an F test for the null hypothesis R * b = r in a classical
## normal regression model y = X * b + e.
##
## Under the null, the test statistic f follows an F distribution with
## df_num and df_den degrees of freedom; pval is the p-value (1 minus
## the CDF of this distribution at f) of the test.
##
## If not given explicitly, r = 0.
##
## If no output argument is given, the p-value is displayed.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Test linear hypotheses in linear regression model
function [pval, f, df_num, df_den] = f_test_regression (y, X, R, r)
if (nargin < 3 || nargin > 4)
usage (["[pval, f, df_num, df_den] ", ...
"= f_test_regression (y, X, R [, r])"]);
endif
[T, k] = size (X);
if !( is_vector (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 (R);
if (c_R != k)
error (["f_test_regression: ", ...
"R 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 (R)."]);
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 = R * b - r;
f = diff' * inv (R * inv (X' * X) * R') * diff / ( q * v );
pval = 1 - f_cdf (f, df_num, df_den);
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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