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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_num}, @var{df_den}] =} f_test_regression (@var{y}, @var{X}, @var{R}, @var{r}) |
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19 ## Perform an F test for the null hypothesis R * b = r in a classical |
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20 ## normal regression model y = X * b + e. |
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21 ## |
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22 ## Under the null, the test statistic @var{f} follows an F distribution |
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23 ## with @var{df_num} and @var{df_den} degrees of freedom. |
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24 ## |
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25 ## The p-value (1 minus the CDF of this distribution at @var{f}) is |
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26 ## returned in @var{pval}. |
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27 ## |
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28 ## If not given explicitly, @var{r} = 0. |
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29 ## |
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30 ## If no output argument is given, the p-value is displayed. |
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31 ## @end deftypefn |
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32 |
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33 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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34 ## Description: Test linear hypotheses in linear regression model |
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35 |
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36 function [pval, f, df_num, df_den] = f_test_regression (y, X, R, r) |
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37 |
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38 if (nargin < 3 || nargin > 4) |
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39 usage (["[pval, f, df_num, df_den] ", ... |
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40 "= f_test_regression (y, X, R [, r])"]); |
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41 endif |
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42 |
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43 [T, k] = size (X); |
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44 if !( is_vector (y) && (length (y) == T) ) |
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45 error (["f_test_regression: ", ... |
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46 "y must be a vector of length rows (X)."]); |
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47 endif |
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48 y = reshape (y, T, 1); |
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49 |
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50 [q, c_R ] = size (R); |
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51 if (c_R != k) |
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52 error (["f_test_regression: ", ... |
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53 "R must have as many columns as X."]); |
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54 endif |
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55 |
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56 if (nargin == 4) |
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57 s_r = size (r); |
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58 if ((min (s_r) != 1) || (max (s_r) != q)) |
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59 error (["f_test_regression: ", ... |
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60 "r must be a vector of length rows (R)."]); |
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61 endif |
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62 r = reshape (r, q, 1); |
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63 else |
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64 r = zeros (q, 1); |
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65 endif |
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66 |
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67 df_num = q; |
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68 df_den = T - k; |
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69 |
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70 [b, v] = ols (y, X); |
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71 diff = R * b - r; |
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72 f = diff' * inv (R * inv (X' * X) * R') * diff / ( q * v ); |
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73 pval = 1 - f_cdf (f, df_num, df_den); |
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74 |
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75 if (nargout == 0) |
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76 printf (" pval: %g\n", pval); |
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77 endif |
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78 |
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79 endfunction |
