- gsl_matrix *sw;
- /*
- Subtract the means to improve the condition of the design
- matrix. This requires copying dm->m and Y. We do not divide by the
- standard deviations of the independent variables here since doing
- so would cause a miscalculation of the residual sums of
- squares. Dividing by the standard deviation is done GSL's linear
- regression functions, so if the design matrix has a poor
- condition, use QR decomposition.
-
- The design matrix here does not include a column for the intercept
- (i.e., a column of 1's). If using PSPP_LINREG_QR, we need that column,
- so design is allocated here when sweeping, or below if using QR.
- */
- design = gsl_matrix_alloc (dm->m->size1, dm->m->size2);
- for (i = 0; i < dm->m->size2; i++)
- {
- v = design_matrix_col_to_var (dm, i);
- m = pspp_linreg_get_indep_variable_mean (cache, v);
- for (j = 0; j < dm->m->size1; j++)
- {
- tmp = (gsl_matrix_get (dm->m, j, i) - m);
- gsl_matrix_set (design, j, i, tmp);
- }
- }
- sw = gsl_matrix_calloc (cache->n_indeps + 1, cache->n_indeps + 1);
- xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
-
- for (i = 0; i < xtx.matrix.size1; i++)
- {
- tmp = gsl_vector_get (cache->ssx, i);
- gsl_matrix_set (&(xtx.matrix), i, i, tmp);
- xi = gsl_matrix_column (design, i);
- for (j = (i + 1); j < xtx.matrix.size2; j++)
- {
- xj = gsl_matrix_column (design, j);
- gsl_blas_ddot (&(xi.vector), &(xj.vector), &tmp);
- gsl_matrix_set (&(xtx.matrix), i, j, tmp);
- }
- }
-
- gsl_matrix_set (sw, cache->n_indeps, cache->n_indeps, cache->sst);
- xty = gsl_matrix_column (sw, cache->n_indeps);
- /*
- This loop starts at 1, with i=0 outside the loop, so we can get
- the model sum of squares due to the first independent variable.
- */
- xi = gsl_matrix_column (design, 0);
- gsl_blas_ddot (&(xi.vector), Y, &tmp);
- gsl_vector_set (&(xty.vector), 0, tmp);
- tmp *= tmp / gsl_vector_get (cache->ssx, 0);
- gsl_vector_set (cache->ss_indeps, 0, tmp);
- for (i = 1; i < cache->n_indeps; i++)
- {
- xi = gsl_matrix_column (design, i);
- gsl_blas_ddot (&(xi.vector), Y, &tmp);
- gsl_vector_set (&(xty.vector), i, tmp);
- }
-
- /*
- Sweep on the matrix sw, which contains XtX, XtY and YtY.
- */
- reg_sweep (sw);
- cache->sse = gsl_matrix_get (sw, cache->n_indeps, cache->n_indeps);
- cache->mse = cache->sse / cache->dfe;
- /*
- Get the intercept.
- */
- m = cache->depvar_mean;
- for (i = 0; i < cache->n_indeps; i++)
- {
- tmp = gsl_matrix_get (sw, i, cache->n_indeps);
- cache->coeff[i]->estimate = tmp;
- m -= tmp * pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i));
- }
- /*
- Get the covariance matrix of the parameter estimates.
- Only the upper triangle is necessary.
- */
-
- /*
- The loops below do not compute the entries related
- to the estimated intercept.
- */
- for (i = 0; i < cache->n_indeps; i++)
- for (j = i; j < cache->n_indeps; j++)
- {
- tmp = -1.0 * cache->mse * gsl_matrix_get (sw, i, j);
- gsl_matrix_set (cache->cov, i + 1, j + 1, tmp);
- }
- /*
- Get the covariances related to the intercept.
- */
- xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
- xmxtx = gsl_matrix_submatrix (cache->cov, 0, 1, 1, cache->n_indeps);
- xm = gsl_matrix_calloc (1, cache->n_indeps);
- for (i = 0; i < xm->size2; i++)
- {
- gsl_matrix_set (xm, 0, i,
- pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i)));
- }
- rc = gsl_blas_dsymm (CblasRight, CblasUpper, cache->mse,
- &xtx.matrix, xm, 0.0, &xmxtx.matrix);
- gsl_matrix_free (xm);
- if (rc == GSL_SUCCESS)