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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, t, df] = t_test_regression (y, X, R [, r] [, alt])
##
## Performs an t test for the null hypothesis R * b = r in a classical
## normal regression model y = X * b + e.
## Under the null, the test statistic t follows a t distribution with
## df degrees of freedom.
##
## r is taken as 0 if not given explicitly.
##
## With the optional argument string alt, the alternative of interest
## can be selected.
## If alt is "!=" or "<>", the null is tested against the two-sided
## alternative R * b != r.
## If alt is ">", the one-sided alternative R * b > r is used,
## similarly for "<".
## The default is the two-sided case.
##
## pval is the p-value of the test.
##
## If no output argument is given, the p-value of the test is displayed.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Test one linear hypothesis in linear regression model
function [pval, t, df] = t_test_regression (y, X, R, r, alt)
if (nargin == 3)
r = 0;
alt = "!=";
elseif (nargin == 4)
if (isstr (r))
alt = r;
r = 0;
else
alt = "!=";
endif
elseif !(nargin == 5)
usage (["[pval, t, df] ", ...
"= t_test_regression (y, X, R [, r] [, alt]"]);
endif
if (! is_scalar (r))
error ("t_test_regression: r must be a scalar");
elseif (! isstr (alt))
error ("t_test_regression: alt must be a string");
endif
[T, k] = size (X);
if !(is_vector (y) && (length (y) == T))
error (["t_test_regression: ", ...
"y must be a vector of length rows (X)"]);
endif
s = size (R);
if !((max (s) == k) && (min (s) == 1))
error (["t_test_regression: ", ...
"R must be a vector of length columns (X)"]);
endif
R = reshape (R, 1, k);
y = reshape (y, T, 1);
[b, v] = ols (y, X);
df = T - k;
t = (R * b - r) / sqrt (v * R * inv (X' * X) * R');
cdf = t_cdf (t, df);
if (strcmp (alt, "!=") || strcmp (alt, "<>"))
pval = 2 * min (cdf, 1 - cdf);
elseif strcmp (alt, ">")
pval = 1 - cdf;
elseif strcmp (alt, "<")
pval = cdf;
else
error ("t_test_regression: the value %s for alt is not possible", alt);
endif
if (nargout == 0)
printf ("pval: %g\n", pval);
endif
endfunction
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