1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2005, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
21 #include <gsl/gsl_cdf.h>
22 #include <gsl/gsl_matrix.h>
24 #include <data/dataset.h>
26 #include "language/command.h"
27 #include "language/lexer/lexer.h"
28 #include "language/lexer/value-parser.h"
29 #include "language/lexer/variable-parser.h"
32 #include "data/casegrouper.h"
33 #include "data/casereader.h"
34 #include "data/dictionary.h"
36 #include "math/covariance.h"
37 #include "math/linreg.h"
38 #include "math/moments.h"
40 #include "libpspp/message.h"
41 #include "libpspp/taint.h"
43 #include "output/tab.h"
46 #define _(msgid) gettext (msgid)
47 #define N_(msgid) msgid
50 #include <gl/intprops.h>
52 #define REG_LARGE_DATA 1000
58 const struct variable **vars;
61 const struct variable **dep_vars;
77 static void run_regression (const struct regression *cmd, struct casereader *input);
82 Transformations for saving predicted values
87 int n_trns; /* Number of transformations. */
88 int trns_id; /* Which trns is this one? */
89 linreg *c; /* Linear model for this trns. */
93 Gets the predicted values.
96 regression_trns_pred_proc (void *t_, struct ccase **c,
97 casenumber case_idx UNUSED)
101 struct reg_trns *trns = t_;
103 union value *output = NULL;
104 const union value *tmp;
106 const struct variable **vars = NULL;
108 assert (trns != NULL);
110 assert (model != NULL);
111 assert (model->depvar != NULL);
112 assert (model->pred != NULL);
114 vars = linreg_get_vars (model);
115 n_vals = linreg_n_coeffs (model);
116 vals = xnmalloc (n_vals, sizeof (*vals));
117 *c = case_unshare (*c);
119 output = case_data_rw (*c, model->pred);
121 for (i = 0; i < n_vals; i++)
123 tmp = case_data (*c, vars[i]);
126 output->f = linreg_predict (model, vals, n_vals);
128 return TRNS_CONTINUE;
135 regression_trns_resid_proc (void *t_, struct ccase **c,
136 casenumber case_idx UNUSED)
140 struct reg_trns *trns = t_;
142 union value *output = NULL;
143 const union value *tmp;
146 const struct variable **vars = NULL;
148 assert (trns != NULL);
150 assert (model != NULL);
151 assert (model->depvar != NULL);
152 assert (model->resid != NULL);
154 vars = linreg_get_vars (model);
155 n_vals = linreg_n_coeffs (model);
157 vals = xnmalloc (n_vals, sizeof (*vals));
158 *c = case_unshare (*c);
159 output = case_data_rw (*c, model->resid);
160 assert (output != NULL);
162 for (i = 0; i < n_vals; i++)
164 tmp = case_data (*c, vars[i]);
167 tmp = case_data (*c, model->depvar);
169 output->f = linreg_residual (model, obs, vals, n_vals);
172 return TRNS_CONTINUE;
177 reg_get_name (const struct dictionary *dict, const char *prefix)
182 /* XXX handle too-long prefixes */
183 name = xmalloc (strlen (prefix) + INT_BUFSIZE_BOUND (i) + 1);
186 sprintf (name, "%s%d", prefix, i);
187 if (dict_lookup_var (dict, name) == NULL)
193 Free the transformation. Free its linear model if this
194 transformation is the last one.
197 regression_trns_free (void *t_)
199 struct reg_trns *t = t_;
201 if (t->trns_id == t->n_trns)
211 reg_save_var (struct dataset *ds, const char *prefix, trns_proc_func * f,
212 linreg * c, struct variable **v, int n_trns)
214 struct dictionary *dict = dataset_dict (ds);
215 static int trns_index = 1;
217 struct variable *new_var;
218 struct reg_trns *t = NULL;
220 t = xmalloc (sizeof (*t));
221 t->trns_id = trns_index;
225 name = reg_get_name (dict, prefix);
226 new_var = dict_create_var_assert (dict, name, 0);
230 add_transformation (ds, f, regression_trns_free, t);
235 subcommand_save (const struct regression *cmd)
240 if ( cmd->resid ) n_trns++;
241 if ( cmd->pred ) n_trns++;
243 n_trns *= cmd->n_dep_vars;
245 for (lc = cmd->models; lc < cmd->models + cmd->n_dep_vars; lc++)
249 if ((*lc)->depvar != NULL)
254 reg_save_var (cmd->ds, "RES", regression_trns_resid_proc, *lc,
255 &(*lc)->resid, n_trns);
259 reg_save_var (cmd->ds, "PRED", regression_trns_pred_proc, *lc,
260 &(*lc)->pred, n_trns);
268 cmd_regression (struct lexer *lexer, struct dataset *ds)
271 struct regression regression;
272 const struct dictionary *dict = dataset_dict (ds);
274 memset (®ression, 0, sizeof (struct regression));
276 regression.anova = true;
277 regression.coeff = true;
280 regression.pred = false;
281 regression.resid = false;
285 /* Accept an optional, completely pointless "/VARIABLES=" */
286 lex_match (lexer, T_SLASH);
287 if (lex_match_id (lexer, "VARIABLES"))
289 if (! lex_force_match (lexer, T_EQUALS) )
293 if (!parse_variables_const (lexer, dict,
294 ®ression.vars, ®ression.n_vars,
295 PV_NO_DUPLICATE | PV_NUMERIC))
299 while (lex_token (lexer) != T_ENDCMD)
301 lex_match (lexer, T_SLASH);
303 if (lex_match_id (lexer, "DEPENDENT"))
305 if (! lex_force_match (lexer, T_EQUALS) )
308 if (!parse_variables_const (lexer, dict,
309 ®ression.dep_vars, ®ression.n_dep_vars,
310 PV_NO_DUPLICATE | PV_NUMERIC))
313 else if (lex_match_id (lexer, "METHOD"))
315 lex_match (lexer, T_EQUALS);
317 if (!lex_force_match_id (lexer, "ENTER"))
322 else if (lex_match_id (lexer, "STATISTICS"))
324 lex_match (lexer, T_EQUALS);
326 while (lex_token (lexer) != T_ENDCMD
327 && lex_token (lexer) != T_SLASH)
329 if (lex_match (lexer, T_ALL))
332 else if (lex_match_id (lexer, "DEFAULTS"))
335 else if (lex_match_id (lexer, "R"))
338 else if (lex_match_id (lexer, "COEFF"))
341 else if (lex_match_id (lexer, "ANOVA"))
344 else if (lex_match_id (lexer, "BCOV"))
349 lex_error (lexer, NULL);
354 else if (lex_match_id (lexer, "SAVE"))
356 lex_match (lexer, T_EQUALS);
358 while (lex_token (lexer) != T_ENDCMD
359 && lex_token (lexer) != T_SLASH)
361 if (lex_match_id (lexer, "PRED"))
363 regression.pred = true;
365 else if (lex_match_id (lexer, "RESID"))
367 regression.resid = true;
371 lex_error (lexer, NULL);
378 lex_error (lexer, NULL);
383 if (!regression.vars)
385 dict_get_vars (dict, ®ression.vars, ®ression.n_vars, 0);
389 regression.models = xcalloc (regression.n_dep_vars, sizeof *regression.models);
391 if (regression.pred || regression.resid)
393 if (proc_make_temporary_transformations_permanent (ds))
394 msg (SW, _("REGRESSION with SAVE ignores TEMPORARY. "
395 "Temporary transformations will be made permanent."));
399 struct casegrouper *grouper;
400 struct casereader *group;
403 grouper = casegrouper_create_splits (proc_open (ds), dict);
404 while (casegrouper_get_next_group (grouper, &group))
405 run_regression (®ression, group);
406 ok = casegrouper_destroy (grouper);
407 ok = proc_commit (ds) && ok;
410 if (regression.pred || regression.resid )
412 subcommand_save (®ression);
416 for (k = 0; k < regression.n_dep_vars; k++)
417 linreg_unref (regression.models[k]);
418 free (regression.models);
419 free (regression.vars);
420 free (regression.dep_vars);
424 if (regression.models)
426 for (k = 0; k < regression.n_dep_vars; k++)
427 linreg_unref (regression.models[k]);
428 free (regression.models);
430 free (regression.vars);
431 free (regression.dep_vars);
437 get_n_all_vars (const struct regression *cmd)
439 size_t result = cmd->n_vars;
443 result += cmd->n_dep_vars;
444 for (i = 0; i < cmd->n_dep_vars; i++)
446 for (j = 0; j < cmd->n_vars; j++)
448 if (cmd->vars[j] == cmd->dep_vars[i])
458 fill_all_vars (const struct variable **vars, const struct regression *cmd)
464 for (i = 0; i < cmd->n_vars; i++)
466 vars[i] = cmd->vars[i];
468 for (i = 0; i < cmd->n_dep_vars; i++)
471 for (j = 0; j < cmd->n_vars; j++)
473 if (cmd->dep_vars[i] == cmd->vars[j])
481 vars[i + cmd->n_vars] = cmd->dep_vars[i];
487 Is variable k the dependent variable?
490 is_depvar (const struct regression *cmd, size_t k, const struct variable *v)
492 return v == cmd->vars[k];
496 /* Identify the explanatory variables in v_variables. Returns
497 the number of independent variables. */
499 identify_indep_vars (const struct regression *cmd,
500 const struct variable **indep_vars,
501 const struct variable *depvar)
503 int n_indep_vars = 0;
506 for (i = 0; i < cmd->n_vars; i++)
507 if (!is_depvar (cmd, i, depvar))
508 indep_vars[n_indep_vars++] = cmd->vars[i];
509 if ((n_indep_vars < 1) && is_depvar (cmd, 0, depvar))
512 There is only one independent variable, and it is the same
513 as the dependent variable. Print a warning and continue.
516 gettext ("The dependent variable is equal to the independent variable."
517 "The least squares line is therefore Y=X."
518 "Standard errors and related statistics may be meaningless."));
520 indep_vars[0] = cmd->vars[0];
527 fill_covariance (gsl_matrix *cov, struct covariance *all_cov,
528 const struct variable **vars,
529 size_t n_vars, const struct variable *dep_var,
530 const struct variable **all_vars, size_t n_all_vars,
535 size_t dep_subscript;
537 const gsl_matrix *ssizes;
538 const gsl_matrix *mean_matrix;
539 const gsl_matrix *ssize_matrix;
542 gsl_matrix *cm = covariance_calculate_unnormalized (all_cov);
547 rows = xnmalloc (cov->size1 - 1, sizeof (*rows));
549 for (i = 0; i < n_all_vars; i++)
551 for (j = 0; j < n_vars; j++)
553 if (vars[j] == all_vars[i])
558 if (all_vars[i] == dep_var)
563 mean_matrix = covariance_moments (all_cov, MOMENT_MEAN);
564 ssize_matrix = covariance_moments (all_cov, MOMENT_NONE);
565 for (i = 0; i < cov->size1 - 1; i++)
567 means[i] = gsl_matrix_get (mean_matrix, rows[i], 0)
568 / gsl_matrix_get (ssize_matrix, rows[i], 0);
569 for (j = 0; j < cov->size2 - 1; j++)
571 gsl_matrix_set (cov, i, j, gsl_matrix_get (cm, rows[i], rows[j]));
572 gsl_matrix_set (cov, j, i, gsl_matrix_get (cm, rows[j], rows[i]));
575 means[cov->size1 - 1] = gsl_matrix_get (mean_matrix, dep_subscript, 0)
576 / gsl_matrix_get (ssize_matrix, dep_subscript, 0);
577 ssizes = covariance_moments (all_cov, MOMENT_NONE);
578 result = gsl_matrix_get (ssizes, dep_subscript, rows[0]);
579 for (i = 0; i < cov->size1 - 1; i++)
581 gsl_matrix_set (cov, i, cov->size1 - 1,
582 gsl_matrix_get (cm, rows[i], dep_subscript));
583 gsl_matrix_set (cov, cov->size1 - 1, i,
584 gsl_matrix_get (cm, rows[i], dep_subscript));
585 if (result > gsl_matrix_get (ssizes, rows[i], dep_subscript))
587 result = gsl_matrix_get (ssizes, rows[i], dep_subscript);
590 gsl_matrix_set (cov, cov->size1 - 1, cov->size1 - 1,
591 gsl_matrix_get (cm, dep_subscript, dep_subscript));
593 gsl_matrix_free (cm);
599 STATISTICS subcommand output functions.
601 static void reg_stats_r (linreg *, void *, const struct variable *);
602 static void reg_stats_coeff (linreg *, void *, const struct variable *);
603 static void reg_stats_anova (linreg *, void *, const struct variable *);
604 static void reg_stats_bcov (linreg *, void *, const struct variable *);
606 static void statistics_keyword_output (void (*)(linreg *, void *, const struct variable *),
607 bool, linreg *, void *, const struct variable *);
612 subcommand_statistics (const struct regression *cmd , linreg * c, void *aux,
613 const struct variable *var)
615 statistics_keyword_output (reg_stats_r, cmd->r, c, aux, var);
616 statistics_keyword_output (reg_stats_anova, cmd->anova, c, aux, var);
617 statistics_keyword_output (reg_stats_coeff, cmd->coeff, c, aux, var);
618 statistics_keyword_output (reg_stats_bcov, cmd->bcov, c, aux, var);
623 run_regression (const struct regression *cmd, struct casereader *input)
630 struct covariance *cov;
631 const struct variable **vars;
632 const struct variable **all_vars;
633 struct casereader *reader;
636 linreg **models = cmd->models;
638 n_all_vars = get_n_all_vars (cmd);
639 all_vars = xnmalloc (n_all_vars, sizeof (*all_vars));
640 fill_all_vars (all_vars, cmd);
641 vars = xnmalloc (cmd->n_vars, sizeof (*vars));
642 means = xnmalloc (n_all_vars, sizeof (*means));
643 cov = covariance_1pass_create (n_all_vars, all_vars,
644 dict_get_weight (dataset_dict (cmd->ds)), MV_ANY);
646 reader = casereader_clone (input);
647 reader = casereader_create_filter_missing (reader, all_vars, n_all_vars,
651 for (; (c = casereader_read (reader)) != NULL; case_unref (c))
653 covariance_accumulate (cov, c);
656 for (k = 0; k < cmd->n_dep_vars; k++)
659 const struct variable *dep_var = cmd->dep_vars[k];
662 n_indep = identify_indep_vars (cmd, vars, dep_var);
664 this_cm = gsl_matrix_alloc (n_indep + 1, n_indep + 1);
665 n_data = fill_covariance (this_cm, cov, vars, n_indep,
666 dep_var, all_vars, n_all_vars, means);
667 models[k] = linreg_alloc (dep_var, (const struct variable **) vars,
669 models[k]->depvar = dep_var;
670 for (i = 0; i < n_indep; i++)
672 linreg_set_indep_variable_mean (models[k], i, means[i]);
674 linreg_set_depvar_mean (models[k], means[i]);
676 For large data sets, use QR decomposition.
678 if (n_data > sqrt (n_indep) && n_data > REG_LARGE_DATA)
680 models[k]->method = LINREG_QR;
686 Find the least-squares estimates and other statistics.
688 linreg_fit (this_cm, models[k]);
690 if (!taint_has_tainted_successor (casereader_get_taint (input)))
692 subcommand_statistics (cmd, models[k], this_cm, dep_var);
698 _("No valid data found. This command was skipped."));
699 linreg_unref (models[k]);
702 gsl_matrix_free (this_cm);
705 casereader_destroy (reader);
709 casereader_destroy (input);
710 covariance_destroy (cov);
718 reg_stats_r (linreg *c, void *aux UNUSED, const struct variable *var)
728 rsq = linreg_ssreg (c) / linreg_sst (c);
729 adjrsq = 1.0 - (1.0 - rsq) * (linreg_n_obs (c) - 1.0) / (linreg_n_obs (c) - linreg_n_coeffs (c));
730 std_error = sqrt (linreg_mse (c));
731 t = tab_create (n_cols, n_rows);
732 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
733 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
734 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
735 tab_vline (t, TAL_0, 1, 0, 0);
737 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("R"));
738 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("R Square"));
739 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Adjusted R Square"));
740 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error of the Estimate"));
741 tab_double (t, 1, 1, TAB_RIGHT, sqrt (rsq), NULL);
742 tab_double (t, 2, 1, TAB_RIGHT, rsq, NULL);
743 tab_double (t, 3, 1, TAB_RIGHT, adjrsq, NULL);
744 tab_double (t, 4, 1, TAB_RIGHT, std_error, NULL);
745 tab_title (t, _("Model Summary (%s)"), var_to_string (var));
750 Table showing estimated regression coefficients.
753 reg_stats_coeff (linreg * c, void *aux_, const struct variable *var)
765 const struct variable *v;
767 gsl_matrix *cov = aux_;
770 n_rows = linreg_n_coeffs (c) + 3;
772 t = tab_create (n_cols, n_rows);
773 tab_headers (t, 2, 0, 1, 0);
774 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
775 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
776 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
777 tab_vline (t, TAL_0, 1, 0, 0);
779 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("B"));
780 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
781 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Beta"));
782 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t"));
783 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
784 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(Constant)"));
785 tab_double (t, 2, 1, 0, linreg_intercept (c), NULL);
786 std_err = sqrt (gsl_matrix_get (linreg_cov (c), 0, 0));
787 tab_double (t, 3, 1, 0, std_err, NULL);
788 tab_double (t, 4, 1, 0, 0.0, NULL);
789 t_stat = linreg_intercept (c) / std_err;
790 tab_double (t, 5, 1, 0, t_stat, NULL);
791 pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), (double) (linreg_n_obs (c) - linreg_n_coeffs (c)));
792 tab_double (t, 6, 1, 0, pval, NULL);
793 for (j = 0; j < linreg_n_coeffs (c); j++)
796 ds_init_empty (&tstr);
799 v = linreg_indep_var (c, j);
800 label = var_to_string (v);
801 /* Do not overwrite the variable's name. */
802 ds_put_cstr (&tstr, label);
803 tab_text (t, 1, this_row, TAB_CENTER, ds_cstr (&tstr));
805 Regression coefficients.
807 tab_double (t, 2, this_row, 0, linreg_coeff (c, j), NULL);
809 Standard error of the coefficients.
811 std_err = sqrt (gsl_matrix_get (linreg_cov (c), j + 1, j + 1));
812 tab_double (t, 3, this_row, 0, std_err, NULL);
814 Standardized coefficient, i.e., regression coefficient
815 if all variables had unit variance.
817 beta = sqrt (gsl_matrix_get (cov, j, j));
818 beta *= linreg_coeff (c, j) /
819 sqrt (gsl_matrix_get (cov, cov->size1 - 1, cov->size2 - 1));
820 tab_double (t, 4, this_row, 0, beta, NULL);
823 Test statistic for H0: coefficient is 0.
825 t_stat = linreg_coeff (c, j) / std_err;
826 tab_double (t, 5, this_row, 0, t_stat, NULL);
828 P values for the test statistic above.
831 2 * gsl_cdf_tdist_Q (fabs (t_stat),
832 (double) (linreg_n_obs (c) - linreg_n_coeffs (c)));
833 tab_double (t, 6, this_row, 0, pval, NULL);
836 tab_title (t, _("Coefficients (%s)"), var_to_string (var));
841 Display the ANOVA table.
844 reg_stats_anova (linreg * c, void *aux UNUSED, const struct variable *var)
848 const double msm = linreg_ssreg (c) / linreg_dfmodel (c);
849 const double mse = linreg_mse (c);
850 const double F = msm / mse;
851 const double pval = gsl_cdf_fdist_Q (F, c->dfm, c->dfe);
856 t = tab_create (n_cols, n_rows);
857 tab_headers (t, 2, 0, 1, 0);
859 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
861 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
862 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
863 tab_vline (t, TAL_0, 1, 0, 0);
865 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
866 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
867 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
868 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
869 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
871 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("Regression"));
872 tab_text (t, 1, 2, TAB_LEFT | TAT_TITLE, _("Residual"));
873 tab_text (t, 1, 3, TAB_LEFT | TAT_TITLE, _("Total"));
875 /* Sums of Squares */
876 tab_double (t, 2, 1, 0, linreg_ssreg (c), NULL);
877 tab_double (t, 2, 3, 0, linreg_sst (c), NULL);
878 tab_double (t, 2, 2, 0, linreg_sse (c), NULL);
881 /* Degrees of freedom */
882 tab_text_format (t, 3, 1, TAB_RIGHT, "%g", c->dfm);
883 tab_text_format (t, 3, 2, TAB_RIGHT, "%g", c->dfe);
884 tab_text_format (t, 3, 3, TAB_RIGHT, "%g", c->dft);
887 tab_double (t, 4, 1, TAB_RIGHT, msm, NULL);
888 tab_double (t, 4, 2, TAB_RIGHT, mse, NULL);
890 tab_double (t, 5, 1, 0, F, NULL);
892 tab_double (t, 6, 1, 0, pval, NULL);
894 tab_title (t, _("ANOVA (%s)"), var_to_string (var));
900 reg_stats_bcov (linreg * c, void *aux UNUSED, const struct variable *var)
912 n_cols = c->n_indeps + 1 + 2;
913 n_rows = 2 * (c->n_indeps + 1);
914 t = tab_create (n_cols, n_rows);
915 tab_headers (t, 2, 0, 1, 0);
916 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
917 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
918 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
919 tab_vline (t, TAL_0, 1, 0, 0);
920 tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Model"));
921 tab_text (t, 1, 1, TAB_CENTER | TAT_TITLE, _("Covariances"));
922 for (i = 0; i < linreg_n_coeffs (c); i++)
924 const struct variable *v = linreg_indep_var (c, i);
925 label = var_to_string (v);
926 tab_text (t, 2, i, TAB_CENTER, label);
927 tab_text (t, i + 2, 0, TAB_CENTER, label);
928 for (k = 1; k < linreg_n_coeffs (c); k++)
930 col = (i <= k) ? k : i;
931 row = (i <= k) ? i : k;
932 tab_double (t, k + 2, i, TAB_CENTER,
933 gsl_matrix_get (c->cov, row, col), NULL);
936 tab_title (t, _("Coefficient Correlations (%s)"), var_to_string (var));
941 statistics_keyword_output (void (*function) (linreg *, void *, const struct variable *var),
942 bool keyword, linreg * c, void *aux, const struct variable *var)
946 (*function) (c, aux, var);