-- Fixture: small deterministic gaussian data with hand-written residuals
-- around y = 2 + 1.5*x1 - 0.5*x2. Kept literally in sync with
-- scripts/parity_reference.R (a perfect fit would make std errors and
-- p-values numerically unstable, so the residuals are deliberate).
CREATE TEMP TABLE t_gaussian (
    y  double precision,
    x1 double precision,
    x2 double precision
);
INSERT INTO t_gaussian VALUES
    (-0.3, 0, 5), (1.9, 1, 3), (1.3, 2, 8), (5.7, 3, 1),
    (3.5, 4, 9), (7.6, 5, 4), (7.3, 6, 7), (11.7, 7, 2),
    (10.9, 8, 6), (15.6, 9, 0), (11.7, 10, 10), (17.1, 11, 3);
-- Full output relation. Floating-point columns are rounded so the expected
-- output is platform-stable; row order is not guaranteed by design (order
-- independence), hence the explicit ORDER BY.
SELECT term,
       round(estimate::numeric, 4)      AS estimate,
       round(std_error::numeric, 4)     AS std_error,
       round(statistic::numeric, 4)     AS statistic,
       round(p_value::numeric, 4)       AS p_value,
       round(conf_low_95::numeric, 4)   AS conf_low_95,
       round(conf_high_95::numeric, 4)  AS conf_high_95,
       family, link, formula,
       n_obs, n_used, n_dropped,
       round(aic::numeric, 4)           AS aic,
       round(deviance::numeric, 4)      AS deviance,
       round(null_deviance::numeric, 4) AS null_deviance
FROM fbsql.fit_glm(
    relation => $$ SELECT y, x1, x2 FROM t_gaussian $$,
    formula  => 'y ~ x1 + x2',
    family   => 'gaussian')
ORDER BY term;
    term     | estimate | std_error | statistic | p_value | conf_low_95 | conf_high_95 |  family  |   link   |   formula   | n_obs | n_used | n_dropped |  aic   | deviance | null_deviance 
-------------+----------+-----------+-----------+---------+-------------+--------------+----------+----------+-------------+-------+--------+-----------+--------+----------+---------------
 (Intercept) |   2.1078 |    0.1535 |   13.7297 |  0.0000 |      1.8069 |       2.4087 | gaussian | identity | y ~ x1 + x2 |    12 |     12 |         0 | 1.6176 |   0.4128 |      353.2067
 x1          |   1.4892 |    0.0179 |   83.1145 |  0.0000 |      1.4541 |       1.5243 | gaussian | identity | y ~ x1 + x2 |    12 |     12 |         0 | 1.6176 |   0.4128 |      353.2067
 x2          |  -0.5101 |    0.0201 |  -25.3794 |  0.0000 |     -0.5494 |      -0.4707 | gaussian | identity | y ~ x1 + x2 |    12 |     12 |         0 | 1.6176 |   0.4128 |      353.2067
(3 rows)

-- family defaults to gaussian.
SELECT term, round(estimate::numeric, 4) AS estimate
FROM fbsql.fit_glm(
    relation => $$ SELECT y, x1 FROM t_gaussian $$,
    formula  => 'y ~ x1')
ORDER BY term;
    term     | estimate 
-------------+----------
 (Intercept) |  -0.4359
 x1          |   1.5035
(2 rows)