## 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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