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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{t}, @var{df}] =} t_test_regression (@var{y}, @var{x}, @var{rr}, @var{r}, @var{alt})
## Perform a t test for the null hypothesis
## @nospell{@code{@var{rr} * @var{b} = @var{r}}} in a classical normal
## regression model @code{@var{y} = @var{x} * @var{b} + @var{e}}. Under the
## null, the test statistic @var{t} follows a @var{t} distribution with
## @var{df} degrees of freedom.
##
## If @var{r} is omitted, a value of 0 is assumed.
##
## With the optional argument string @var{alt}, the alternative of
## interest can be selected. If @var{alt} is @qcode{"!="} or
## @qcode{"<>"}, the null is tested against the two-sided alternative
## @nospell{@code{@var{rr} * @var{b} != @var{r}}}. If @var{alt} is @qcode{">"},
## the one-sided alternative
## @nospell{@code{@var{rr} * @var{b} > @var{r}}} is used. Similarly for
## @var{"<"}, the one-sided alternative
## @nospell{@code{@var{rr} * @var{b} < @var{r}}} is used. The default is the
## two-sided case.
##
## The p-value of the test is returned in @var{pval}.
##
## If no output argument is given, the p-value of the test is displayed.
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Test one linear hypothesis in linear regression model
function [pval, t, df] = t_test_regression (y, x, rr, r, alt)
if (nargin == 3)
r = 0;
alt = "!=";
elseif (nargin == 4)
if (ischar (r))
alt = r;
r = 0;
else
alt = "!=";
endif
elseif (! (nargin == 5))
print_usage ();
endif
if (! isscalar (r))
error ("t_test_regression: R must be a scalar");
elseif (! ischar (alt))
error ("t_test_regression: ALT must be a string");
endif
[T, k] = size (x);
if (! (isvector (y) && (length (y) == T)))
error ("t_test_regression: Y must be a vector of length rows (X)");
endif
s = size (rr);
if (! ((max (s) == k) && (min (s) == 1)))
error ("t_test_regression: RR must be a vector of length columns (X)");
endif
rr = reshape (rr, 1, k);
y = reshape (y, T, 1);
[b, v] = ols (y, x);
df = T - k;
t = (rr * b - r) / sqrt (v * rr * inv (x' * x) * rr');
cdf = tcdf (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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