src/ports/postgres/modules/glm/test/gaussian.sql_in - madlib - Git at Google

 DROP TABLE IF EXISTS abalone CASCADE;

 CREATE TABLE abalone (
     id integer,
     sex text,
     length double precision,
     diameter double precision,
     height double precision,
     whole double precision,
     shucked double precision,
     viscera double precision,
     shell double precision,
     rings integer
 );

 INSERT INTO abalone VALUES
 (3151, 'F', 0.655000000000000027, 0.505000000000000004, 0.165000000000000008, 1.36699999999999999, 0.583500000000000019, 0.351499999999999979, 0.396000000000000019, 10),
 (2026, 'F', 0.550000000000000044, 0.469999999999999973, 0.149999999999999994, 0.920499999999999985, 0.381000000000000005, 0.243499999999999994, 0.267500000000000016, 10),
 (3751, 'I', 0.434999999999999998, 0.375, 0.110000000000000001, 0.41549999999999998, 0.170000000000000012, 0.0759999999999999981, 0.14499999999999999, 8),
 (720, 'I', 0.149999999999999994, 0.100000000000000006, 0.0250000000000000014, 0.0149999999999999994, 0.00449999999999999966, 0.00400000000000000008, 0.0050000000000000001, 2),
 (1635, 'F', 0.574999999999999956, 0.469999999999999973, 0.154999999999999999, 1.1160000000000001, 0.509000000000000008, 0.237999999999999989, 0.340000000000000024, 10),
 (2648, 'I', 0.5, 0.390000000000000013, 0.125, 0.582999999999999963, 0.293999999999999984, 0.132000000000000006, 0.160500000000000004, 8),
 (1796, 'F', 0.57999999999999996, 0.429999999999999993, 0.170000000000000012, 1.47999999999999998, 0.65349999999999997, 0.32400000000000001, 0.41549999999999998, 10),
 (209, 'F', 0.525000000000000022, 0.41499999999999998, 0.170000000000000012, 0.832500000000000018, 0.275500000000000023, 0.168500000000000011, 0.309999999999999998, 13),
 (1451, 'I', 0.455000000000000016, 0.33500000000000002, 0.135000000000000009, 0.501000000000000001, 0.274000000000000021, 0.0995000000000000051, 0.106499999999999997, 7),
 (1108, 'I', 0.510000000000000009, 0.380000000000000004, 0.115000000000000005, 0.515499999999999958, 0.214999999999999997, 0.113500000000000004, 0.166000000000000009, 8),
 (3675, 'F', 0.594999999999999973, 0.450000000000000011, 0.165000000000000008, 1.08099999999999996, 0.489999999999999991, 0.252500000000000002, 0.279000000000000026, 12),
 (2108, 'F', 0.675000000000000044, 0.550000000000000044, 0.179999999999999993, 1.68849999999999989, 0.562000000000000055, 0.370499999999999996, 0.599999999999999978, 15),
 (3312, 'F', 0.479999999999999982, 0.380000000000000004, 0.135000000000000009, 0.507000000000000006, 0.191500000000000004, 0.13650000000000001, 0.154999999999999999, 12),
 (882, 'M', 0.655000000000000027, 0.520000000000000018, 0.165000000000000008, 1.40949999999999998, 0.585999999999999965, 0.290999999999999981, 0.405000000000000027, 9),
 (3402, 'M', 0.479999999999999982, 0.395000000000000018, 0.149999999999999994, 0.681499999999999995, 0.214499999999999996, 0.140500000000000014, 0.2495, 18),
 (829, 'I', 0.409999999999999976, 0.325000000000000011, 0.100000000000000006, 0.394000000000000017, 0.20799999999999999, 0.0655000000000000027, 0.105999999999999997, 6),
 (1305, 'M', 0.535000000000000031, 0.434999999999999998, 0.149999999999999994, 0.716999999999999971, 0.347499999999999976, 0.14449999999999999, 0.194000000000000006, 9),
 (3613, 'M', 0.599999999999999978, 0.46000000000000002, 0.179999999999999993, 1.1399999999999999, 0.422999999999999987, 0.257500000000000007, 0.364999999999999991, 10),
 (1068, 'I', 0.340000000000000024, 0.265000000000000013, 0.0800000000000000017, 0.201500000000000012, 0.0899999999999999967, 0.0475000000000000006, 0.0550000000000000003, 5),
 (2446, 'M', 0.5, 0.380000000000000004, 0.135000000000000009, 0.583500000000000019, 0.22950000000000001, 0.126500000000000001, 0.179999999999999993, 12),
 (1393, 'M', 0.635000000000000009, 0.474999999999999978, 0.170000000000000012, 1.19350000000000001, 0.520499999999999963, 0.269500000000000017, 0.366499999999999992, 10),
 (359, 'M', 0.744999999999999996, 0.584999999999999964, 0.214999999999999997, 2.49900000000000011, 0.92649999999999999, 0.471999999999999975, 0.699999999999999956, 17),
 (549, 'F', 0.564999999999999947, 0.450000000000000011, 0.160000000000000003, 0.79500000000000004, 0.360499999999999987, 0.155499999999999999, 0.23000000000000001, 12),
 (1154, 'F', 0.599999999999999978, 0.474999999999999978, 0.160000000000000003, 1.02649999999999997, 0.484999999999999987, 0.2495, 0.256500000000000006, 9),
 (1790, 'F', 0.54500000000000004, 0.385000000000000009, 0.149999999999999994, 1.11850000000000005, 0.542499999999999982, 0.244499999999999995, 0.284499999999999975, 9),
 (3703, 'F', 0.665000000000000036, 0.540000000000000036, 0.195000000000000007, 1.76400000000000001, 0.850500000000000034, 0.361499999999999988, 0.469999999999999973, 11),
 (1962, 'F', 0.655000000000000027, 0.515000000000000013, 0.179999999999999993, 1.41199999999999992, 0.619500000000000051, 0.248499999999999999, 0.496999999999999997, 11),
 (1665, 'I', 0.604999999999999982, 0.469999999999999973, 0.14499999999999999, 0.802499999999999991, 0.379000000000000004, 0.226500000000000007, 0.220000000000000001, 9),
 (635, 'M', 0.359999999999999987, 0.294999999999999984, 0.100000000000000006, 0.210499999999999993, 0.0660000000000000031, 0.0524999999999999981, 0.0749999999999999972, 9),
 (3901, 'M', 0.445000000000000007, 0.344999999999999973, 0.140000000000000013, 0.475999999999999979, 0.205499999999999988, 0.101500000000000007, 0.108499999999999999, 15),
 (2734, 'I', 0.41499999999999998, 0.33500000000000002, 0.100000000000000006, 0.357999999999999985, 0.169000000000000011, 0.067000000000000004, 0.104999999999999996, 7),
 (3856, 'M', 0.409999999999999976, 0.33500000000000002, 0.115000000000000005, 0.440500000000000003, 0.190000000000000002, 0.0850000000000000061, 0.135000000000000009, 8),
 (827, 'I', 0.395000000000000018, 0.28999999999999998, 0.0950000000000000011, 0.303999999999999992, 0.127000000000000002, 0.0840000000000000052, 0.076999999999999999, 6),
 (3381, 'I', 0.190000000000000002, 0.130000000000000004, 0.0449999999999999983, 0.0264999999999999993, 0.00899999999999999932, 0.0050000000000000001, 0.00899999999999999932, 5),
 (3972, 'I', 0.400000000000000022, 0.294999999999999984, 0.0950000000000000011, 0.252000000000000002, 0.110500000000000001, 0.0575000000000000025, 0.0660000000000000031, 6),
 (1155, 'M', 0.599999999999999978, 0.455000000000000016, 0.170000000000000012, 1.1915, 0.695999999999999952, 0.239499999999999991, 0.239999999999999991, 8),
 (3467, 'M', 0.640000000000000013, 0.5, 0.170000000000000012, 1.4544999999999999, 0.642000000000000015, 0.357499999999999984, 0.353999999999999981, 9),
 (2433, 'F', 0.609999999999999987, 0.484999999999999987, 0.165000000000000008, 1.08699999999999997, 0.425499999999999989, 0.232000000000000012, 0.380000000000000004, 11),
 (552, 'I', 0.614999999999999991, 0.489999999999999991, 0.154999999999999999, 0.988500000000000045, 0.41449999999999998, 0.195000000000000007, 0.344999999999999973, 13),
 (1425, 'F', 0.729999999999999982, 0.57999999999999996, 0.190000000000000002, 1.73750000000000004, 0.678499999999999992, 0.434499999999999997, 0.520000000000000018, 11),
 (2402, 'F', 0.584999999999999964, 0.41499999999999998, 0.154999999999999999, 0.69850000000000001, 0.299999999999999989, 0.145999999999999991, 0.195000000000000007, 12),
 (1748, 'F', 0.699999999999999956, 0.535000000000000031, 0.174999999999999989, 1.77299999999999991, 0.680499999999999994, 0.479999999999999982, 0.512000000000000011, 15),
 (3983, 'I', 0.57999999999999996, 0.434999999999999998, 0.149999999999999994, 0.891499999999999959, 0.362999999999999989, 0.192500000000000004, 0.251500000000000001, 6),
 (335, 'F', 0.739999999999999991, 0.599999999999999978, 0.195000000000000007, 1.97399999999999998, 0.597999999999999976, 0.408499999999999974, 0.709999999999999964, 16),
 (1587, 'I', 0.515000000000000013, 0.349999999999999978, 0.104999999999999996, 0.474499999999999977, 0.212999999999999995, 0.122999999999999998, 0.127500000000000002, 10),
 (2448, 'I', 0.275000000000000022, 0.204999999999999988, 0.0800000000000000017, 0.096000000000000002, 0.0359999999999999973, 0.0184999999999999991, 0.0299999999999999989, 6),
 (1362, 'F', 0.604999999999999982, 0.474999999999999978, 0.174999999999999989, 1.07600000000000007, 0.463000000000000023, 0.219500000000000001, 0.33500000000000002, 9),
 (2799, 'M', 0.640000000000000013, 0.484999999999999987, 0.149999999999999994, 1.09800000000000009, 0.519499999999999962, 0.222000000000000003, 0.317500000000000004, 10),
 (1413, 'F', 0.67000000000000004, 0.505000000000000004, 0.174999999999999989, 1.01449999999999996, 0.4375, 0.271000000000000019, 0.3745, 10),
 (1739, 'F', 0.67000000000000004, 0.540000000000000036, 0.195000000000000007, 1.61899999999999999, 0.739999999999999991, 0.330500000000000016, 0.465000000000000024, 11),
 (1152, 'M', 0.584999999999999964, 0.465000000000000024, 0.160000000000000003, 0.955500000000000016, 0.45950000000000002, 0.235999999999999988, 0.265000000000000013, 7),
 (2427, 'I', 0.564999999999999947, 0.434999999999999998, 0.154999999999999999, 0.782000000000000028, 0.271500000000000019, 0.16800000000000001, 0.284999999999999976, 14),
 (1777, 'M', 0.484999999999999987, 0.369999999999999996, 0.154999999999999999, 0.967999999999999972, 0.418999999999999984, 0.245499999999999996, 0.236499999999999988, 9),
 (3294, 'M', 0.574999999999999956, 0.455000000000000016, 0.184999999999999998, 1.15599999999999992, 0.552499999999999991, 0.242999999999999994, 0.294999999999999984, 13),
 (1403, 'M', 0.650000000000000022, 0.510000000000000009, 0.190000000000000002, 1.54200000000000004, 0.715500000000000025, 0.373499999999999999, 0.375, 9),
 (2256, 'M', 0.510000000000000009, 0.395000000000000018, 0.14499999999999999, 0.61850000000000005, 0.215999999999999998, 0.138500000000000012, 0.239999999999999991, 12),
 (3984, 'F', 0.584999999999999964, 0.450000000000000011, 0.125, 0.873999999999999999, 0.354499999999999982, 0.20749999999999999, 0.225000000000000006, 6),
 (1116, 'M', 0.525000000000000022, 0.405000000000000027, 0.119999999999999996, 0.755499999999999949, 0.3755, 0.155499999999999999, 0.201000000000000012, 9),
 (1366, 'M', 0.609999999999999987, 0.474999999999999978, 0.170000000000000012, 1.02649999999999997, 0.434999999999999998, 0.233500000000000013, 0.303499999999999992, 10),
 (3759, 'I', 0.525000000000000022, 0.400000000000000022, 0.140000000000000013, 0.605500000000000038, 0.260500000000000009, 0.107999999999999999, 0.209999999999999992, 9);


 DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
 SELECT glm(
     'abalone',
     'abalone_out',
     'rings',
     'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
     'family=gaussian, link=identity'
 );

 SELECT
     assert(relative_error(ARRAY[0.997553983448236, -2.00220770198294, -2.38237621266428, 88.6791075055313, 11.8100239757845, -25.3192976658248, -9.4550584312097, -3.72450665767602], coef) < 1e-4, 'wrong coef'),
     assert(relative_error(-119.506940681, log_likelihood) < 1e-4, 'wrong log_likelihood'),
     assert(relative_error(ARRAY[1.78323811632271, 12.5513613314091, 15.7314928158976, 20.2562380620116, 5.89920538789372, 6.76993998744087, 10.0832608221583, 9.93889730891343], std_err) < 1e-4, 'wrong std_err'),
     assert(relative_error(ARRAY[0.559405933687272, -0.159521158631017, -0.151439932658949, 4.37786657295658, 2.00196860411418, -3.73995895278178, -0.937698488412787, -0.374740430644735], t_stats) < 1e-4, 'wrong t_stats'),
     assert(relative_error(ARRAY[0.578286340104612, 0.873876297316166, 0.880214691535476, 5.80912431853212e-05, 0.0505170037034926, 0.000460004387928058, 0.352734399919449, 0.709377533942504], p_values) < 1e-4, 'wrong p_values'),
     assert(relative_error(3.62838797857, dispersion) < 1e-4, 'wrong dispersion')
 FROM abalone_out;

 ------------------------------------------------------------

 DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
 SELECT glm(
     'abalone',
     'abalone_out',
     'rings',
     'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
     'family=gaussian, link=inverse'
 );

 SELECT
     assert(relative_error(ARRAY[0.207505893301398, 0.121692677273364, -0.13743526302674, -0.973758981785658, -0.0881650764717561, 0.201488111012545, 0.0486202647973386, 0.0915246696608111], coef) < 1e-4, 'wrong coef'),
     assert(relative_error(-124.390370629, log_likelihood) < 1e-4, 'wrong log_likelihood'),
     assert(relative_error(ARRAY[0.0340567087639318, 0.144909354770801, 0.185838850959084, 0.209563197751552, 0.0473915910403184, 0.0658474252895474, 0.0929236924714683, 0.0973507352624716], std_err) < 1e-4, 'wrong std_err'),
     assert(relative_error(ARRAY[6.09295204477186, 0.839784825940617, -0.739539995633092, -4.64661253613861, -1.86035274478862, 3.05992390934881, 0.523227860454073, 0.94015386133497], t_stats) < 1e-4, 'wrong t_stats'),
     assert(relative_error(ARRAY[1.37277829098147e-07, 0.404873600352569, 0.462904806101211, 2.33957307776227e-05, 0.0684951360271206, 0.0034969162088071, 0.603038329735201, 0.351485606551847], p_values) < 1e-4, 'wrong p_values'),
     assert(relative_error(4.26991902085, dispersion) < 1e-4, 'wrong dispersion')
 FROM abalone_out;

 ------------------------------------------------------------

 DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
 SELECT glm(
     'abalone',
     'abalone_out',
     'rings',
     'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
     'family=gaussian, link=log'
 );

 SELECT
     assert(relative_error(ARRAY[1.24642691358571, -0.710823591814181, 0.631879078261415, 9.7633031368507, 1.00681604973084, -2.31553977293938, -0.62212281355569, -0.681150079395847], coef) < 1e-4, 'wrong coef'),
     assert(relative_error(-121.439926239, log_likelihood) < 1e-4, 'wrong log_likelihood'),
     assert(relative_error(ARRAY[0.274311389188441, 1.36956583660479, 1.73245430104351, 2.10363764593199, 0.511047771609972, 0.649645203994886, 0.94355127671166, 0.965386925520628], std_err) < 1e-4, 'wrong std_err'),
     assert(relative_error(ARRAY[4.54383945658728, -0.519013816507238, 0.364730589361472, 4.64115250824255, 1.97010163366731, -3.56431442686, -0.659341817356054, -0.705572099009428], t_stats) < 1e-4, 'wrong t_stats'),
     assert(relative_error(ARRAY[3.32026977680014e-05, 0.605953093865339, 0.716791689842453, 2.38365422133465e-05, 0.0541628180005122, 0.000792113263000157, 0.51258581879907, 0.48360324365538], p_values) < 1e-4, 'wrong p_values'),
     assert(relative_error(3.86987789994, dispersion) < 1e-4, 'wrong dispersion')
 FROM abalone_out;

 ------------------------------------------------------------
 -- Grouping support

 DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
 SELECT glm(
     'abalone',
     'abalone_out',
     'rings',
     'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
     'family=gaussian, link=identity',
     'sex'
 );

 SELECT
     assert(relative_error(ARRAY[0.209710168944741, 19.0036159909532, -21.5653997488975, 106.856474437712, 35.0095220501715, -41.750182394032, -63.884749494387, -37.377686641516], coef) < 1e-4, 'wrong coef'),
     assert(relative_error(-38.2338243376, log_likelihood) < 1e-4, 'wrong log_likelihood'),
     assert(relative_error(ARRAY[8.45728488507485, 40.2935117639766, 48.4372582378544, 42.1844318159701, 16.0440013310081, 20.8141398246576, 23.0878072228745, 34.994310628607], std_err) < 1e-4, 'wrong std_err'),
     assert(relative_error(ARRAY[0.0247963940903576, 0.471629678303267, -0.44522337831343, 2.53307843291273, 2.18209418759577, -2.0058567274816, -2.76703408330144, -1.06810752862669], t_stats) < 1e-4, 'wrong t_stats'),
     assert(relative_error(ARRAY[0.980624944052056, 0.645650692577156, 0.664083467030224, 0.0262703800464156, 0.0497070449993228, 0.0679529287394978, 0.0170553935436379, 0.306488464561412], p_values) < 1e-4, 'wrong p_values'),
     assert(relative_error(4.46527584187, dispersion) < 1e-4, 'wrong dispersion')
 FROM abalone_out where sex = 'M';

 ------------------------------------------------------------

 DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
 SELECT glm(
     'abalone',
     'abalone_out',
     'rings',
     'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
     'family=gaussian, link=inverse',
     'sex'
 );

 SELECT
     assert(relative_error(ARRAY[0.184074822293059, 0.0631806170942958, -0.00650837763786568, -1.20067479469727, -0.240597039447159, 0.294074324448698, 0.587970076573244, 0.200570270495788], coef) < 1e-4, 'wrong coef'),
     assert(relative_error(-35.3262201512, log_likelihood) < 1e-4, 'wrong log_likelihood'),
     assert(relative_error(ARRAY[0.0694466050297355, 0.264723907580007, 0.382477169907492, 0.34807791627604, 0.096508309661607, 0.153781362466539, 0.23420835627635, 0.232015594885046], std_err) < 1e-4, 'wrong std_err'),
     assert(relative_error(ARRAY[2.65059497457423, 0.238666079206317, -0.017016382022069, -3.44944260624992, -2.49301889433956, 1.9122884576646, 2.51045729503981, 0.864468918975739], t_stats) < 1e-4, 'wrong t_stats'),
     assert(relative_error(ARRAY[0.0211557834211453, 0.815391641340597, 0.986703199019439, 0.00480992607214596, 0.0282751471734034, 0.0800034483814998, 0.0273848180365069, 0.404279997259952], p_values) < 1e-3, 'wrong p_values'),
     assert(relative_error(3.33866317325, dispersion) < 1e-4, 'wrong dispersion')
 FROM abalone_out where sex = 'M';

 ------------------------------------------------------------

 DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
 SELECT glm(
     'abalone',
     'abalone_out',
     'rings',
     'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
     'family=gaussian, link=log',
     'sex'
 );

 SELECT
     assert(relative_error(ARRAY[1.39427729177307, 0.486930615615555, -0.855747900922272, 11.3639612621932, 2.85472895058833, -3.47679916783533, -5.96248073440894, -2.78828800807937], coef) < 1e-4, 'wrong coef'),
     assert(relative_error(-37.1607275903, log_likelihood) < 1e-4, 'wrong log_likelihood'),
     assert(relative_error(ARRAY[0.769986839024755, 3.3952158034843, 4.40195784717915, 3.93519362383163, 1.27601166566703, 1.802330542242, 2.27259663876784, 2.90100018116101], std_err) < 1e-4, 'wrong std_err'),
     assert(relative_error(ARRAY[1.81078067975684, 0.143416690955505, -0.194401657314972, 2.88777690464144, 2.23722794030729, -1.92905745441698, -2.62364232732548, -0.961147133387448], t_stats) < 1e-4, 'wrong t_stats'),
     assert(relative_error(ARRAY[0.0952657004232437, 0.88834126296204, 0.849113623796413, 0.0136322946375411, 0.0450212457473478, 0.0777087160148953, 0.0222349991922514, 0.355445860304514], p_values) < 1e-4, 'wrong p_values'),
     assert(relative_error(4.0109424558, dispersion) < 1e-4, 'wrong dispersion')
 FROM abalone_out where sex = 'M';
	DROP TABLE IF EXISTS abalone CASCADE;

	CREATE TABLE abalone (
	id integer,
	sex text,
	length double precision,
	diameter double precision,
	height double precision,
	whole double precision,
	shucked double precision,
	viscera double precision,
	shell double precision,
	rings integer
	);

	INSERT INTO abalone VALUES
	(3151, 'F', 0.655000000000000027, 0.505000000000000004, 0.165000000000000008, 1.36699999999999999, 0.583500000000000019, 0.351499999999999979, 0.396000000000000019, 10),
	(2026, 'F', 0.550000000000000044, 0.469999999999999973, 0.149999999999999994, 0.920499999999999985, 0.381000000000000005, 0.243499999999999994, 0.267500000000000016, 10),
	(3751, 'I', 0.434999999999999998, 0.375, 0.110000000000000001, 0.41549999999999998, 0.170000000000000012, 0.0759999999999999981, 0.14499999999999999, 8),
	(720, 'I', 0.149999999999999994, 0.100000000000000006, 0.0250000000000000014, 0.0149999999999999994, 0.00449999999999999966, 0.00400000000000000008, 0.0050000000000000001, 2),
	(1635, 'F', 0.574999999999999956, 0.469999999999999973, 0.154999999999999999, 1.1160000000000001, 0.509000000000000008, 0.237999999999999989, 0.340000000000000024, 10),
	(2648, 'I', 0.5, 0.390000000000000013, 0.125, 0.582999999999999963, 0.293999999999999984, 0.132000000000000006, 0.160500000000000004, 8),
	(1796, 'F', 0.57999999999999996, 0.429999999999999993, 0.170000000000000012, 1.47999999999999998, 0.65349999999999997, 0.32400000000000001, 0.41549999999999998, 10),
	(209, 'F', 0.525000000000000022, 0.41499999999999998, 0.170000000000000012, 0.832500000000000018, 0.275500000000000023, 0.168500000000000011, 0.309999999999999998, 13),
	(1451, 'I', 0.455000000000000016, 0.33500000000000002, 0.135000000000000009, 0.501000000000000001, 0.274000000000000021, 0.0995000000000000051, 0.106499999999999997, 7),
	(1108, 'I', 0.510000000000000009, 0.380000000000000004, 0.115000000000000005, 0.515499999999999958, 0.214999999999999997, 0.113500000000000004, 0.166000000000000009, 8),
	(3675, 'F', 0.594999999999999973, 0.450000000000000011, 0.165000000000000008, 1.08099999999999996, 0.489999999999999991, 0.252500000000000002, 0.279000000000000026, 12),
	(2108, 'F', 0.675000000000000044, 0.550000000000000044, 0.179999999999999993, 1.68849999999999989, 0.562000000000000055, 0.370499999999999996, 0.599999999999999978, 15),
	(3312, 'F', 0.479999999999999982, 0.380000000000000004, 0.135000000000000009, 0.507000000000000006, 0.191500000000000004, 0.13650000000000001, 0.154999999999999999, 12),
	(882, 'M', 0.655000000000000027, 0.520000000000000018, 0.165000000000000008, 1.40949999999999998, 0.585999999999999965, 0.290999999999999981, 0.405000000000000027, 9),
	(3402, 'M', 0.479999999999999982, 0.395000000000000018, 0.149999999999999994, 0.681499999999999995, 0.214499999999999996, 0.140500000000000014, 0.2495, 18),
	(829, 'I', 0.409999999999999976, 0.325000000000000011, 0.100000000000000006, 0.394000000000000017, 0.20799999999999999, 0.0655000000000000027, 0.105999999999999997, 6),
	(1305, 'M', 0.535000000000000031, 0.434999999999999998, 0.149999999999999994, 0.716999999999999971, 0.347499999999999976, 0.14449999999999999, 0.194000000000000006, 9),
	(3613, 'M', 0.599999999999999978, 0.46000000000000002, 0.179999999999999993, 1.1399999999999999, 0.422999999999999987, 0.257500000000000007, 0.364999999999999991, 10),
	(1068, 'I', 0.340000000000000024, 0.265000000000000013, 0.0800000000000000017, 0.201500000000000012, 0.0899999999999999967, 0.0475000000000000006, 0.0550000000000000003, 5),
	(2446, 'M', 0.5, 0.380000000000000004, 0.135000000000000009, 0.583500000000000019, 0.22950000000000001, 0.126500000000000001, 0.179999999999999993, 12),
	(1393, 'M', 0.635000000000000009, 0.474999999999999978, 0.170000000000000012, 1.19350000000000001, 0.520499999999999963, 0.269500000000000017, 0.366499999999999992, 10),
	(359, 'M', 0.744999999999999996, 0.584999999999999964, 0.214999999999999997, 2.49900000000000011, 0.92649999999999999, 0.471999999999999975, 0.699999999999999956, 17),
	(549, 'F', 0.564999999999999947, 0.450000000000000011, 0.160000000000000003, 0.79500000000000004, 0.360499999999999987, 0.155499999999999999, 0.23000000000000001, 12),
	(1154, 'F', 0.599999999999999978, 0.474999999999999978, 0.160000000000000003, 1.02649999999999997, 0.484999999999999987, 0.2495, 0.256500000000000006, 9),
	(1790, 'F', 0.54500000000000004, 0.385000000000000009, 0.149999999999999994, 1.11850000000000005, 0.542499999999999982, 0.244499999999999995, 0.284499999999999975, 9),
	(3703, 'F', 0.665000000000000036, 0.540000000000000036, 0.195000000000000007, 1.76400000000000001, 0.850500000000000034, 0.361499999999999988, 0.469999999999999973, 11),
	(1962, 'F', 0.655000000000000027, 0.515000000000000013, 0.179999999999999993, 1.41199999999999992, 0.619500000000000051, 0.248499999999999999, 0.496999999999999997, 11),
	(1665, 'I', 0.604999999999999982, 0.469999999999999973, 0.14499999999999999, 0.802499999999999991, 0.379000000000000004, 0.226500000000000007, 0.220000000000000001, 9),
	(635, 'M', 0.359999999999999987, 0.294999999999999984, 0.100000000000000006, 0.210499999999999993, 0.0660000000000000031, 0.0524999999999999981, 0.0749999999999999972, 9),
	(3901, 'M', 0.445000000000000007, 0.344999999999999973, 0.140000000000000013, 0.475999999999999979, 0.205499999999999988, 0.101500000000000007, 0.108499999999999999, 15),
	(2734, 'I', 0.41499999999999998, 0.33500000000000002, 0.100000000000000006, 0.357999999999999985, 0.169000000000000011, 0.067000000000000004, 0.104999999999999996, 7),
	(3856, 'M', 0.409999999999999976, 0.33500000000000002, 0.115000000000000005, 0.440500000000000003, 0.190000000000000002, 0.0850000000000000061, 0.135000000000000009, 8),
	(827, 'I', 0.395000000000000018, 0.28999999999999998, 0.0950000000000000011, 0.303999999999999992, 0.127000000000000002, 0.0840000000000000052, 0.076999999999999999, 6),
	(3381, 'I', 0.190000000000000002, 0.130000000000000004, 0.0449999999999999983, 0.0264999999999999993, 0.00899999999999999932, 0.0050000000000000001, 0.00899999999999999932, 5),
	(3972, 'I', 0.400000000000000022, 0.294999999999999984, 0.0950000000000000011, 0.252000000000000002, 0.110500000000000001, 0.0575000000000000025, 0.0660000000000000031, 6),
	(1155, 'M', 0.599999999999999978, 0.455000000000000016, 0.170000000000000012, 1.1915, 0.695999999999999952, 0.239499999999999991, 0.239999999999999991, 8),
	(3467, 'M', 0.640000000000000013, 0.5, 0.170000000000000012, 1.4544999999999999, 0.642000000000000015, 0.357499999999999984, 0.353999999999999981, 9),
	(2433, 'F', 0.609999999999999987, 0.484999999999999987, 0.165000000000000008, 1.08699999999999997, 0.425499999999999989, 0.232000000000000012, 0.380000000000000004, 11),
	(552, 'I', 0.614999999999999991, 0.489999999999999991, 0.154999999999999999, 0.988500000000000045, 0.41449999999999998, 0.195000000000000007, 0.344999999999999973, 13),
	(1425, 'F', 0.729999999999999982, 0.57999999999999996, 0.190000000000000002, 1.73750000000000004, 0.678499999999999992, 0.434499999999999997, 0.520000000000000018, 11),
	(2402, 'F', 0.584999999999999964, 0.41499999999999998, 0.154999999999999999, 0.69850000000000001, 0.299999999999999989, 0.145999999999999991, 0.195000000000000007, 12),
	(1748, 'F', 0.699999999999999956, 0.535000000000000031, 0.174999999999999989, 1.77299999999999991, 0.680499999999999994, 0.479999999999999982, 0.512000000000000011, 15),
	(3983, 'I', 0.57999999999999996, 0.434999999999999998, 0.149999999999999994, 0.891499999999999959, 0.362999999999999989, 0.192500000000000004, 0.251500000000000001, 6),
	(335, 'F', 0.739999999999999991, 0.599999999999999978, 0.195000000000000007, 1.97399999999999998, 0.597999999999999976, 0.408499999999999974, 0.709999999999999964, 16),
	(1587, 'I', 0.515000000000000013, 0.349999999999999978, 0.104999999999999996, 0.474499999999999977, 0.212999999999999995, 0.122999999999999998, 0.127500000000000002, 10),
	(2448, 'I', 0.275000000000000022, 0.204999999999999988, 0.0800000000000000017, 0.096000000000000002, 0.0359999999999999973, 0.0184999999999999991, 0.0299999999999999989, 6),
	(1362, 'F', 0.604999999999999982, 0.474999999999999978, 0.174999999999999989, 1.07600000000000007, 0.463000000000000023, 0.219500000000000001, 0.33500000000000002, 9),
	(2799, 'M', 0.640000000000000013, 0.484999999999999987, 0.149999999999999994, 1.09800000000000009, 0.519499999999999962, 0.222000000000000003, 0.317500000000000004, 10),
	(1413, 'F', 0.67000000000000004, 0.505000000000000004, 0.174999999999999989, 1.01449999999999996, 0.4375, 0.271000000000000019, 0.3745, 10),
	(1739, 'F', 0.67000000000000004, 0.540000000000000036, 0.195000000000000007, 1.61899999999999999, 0.739999999999999991, 0.330500000000000016, 0.465000000000000024, 11),
	(1152, 'M', 0.584999999999999964, 0.465000000000000024, 0.160000000000000003, 0.955500000000000016, 0.45950000000000002, 0.235999999999999988, 0.265000000000000013, 7),
	(2427, 'I', 0.564999999999999947, 0.434999999999999998, 0.154999999999999999, 0.782000000000000028, 0.271500000000000019, 0.16800000000000001, 0.284999999999999976, 14),
	(1777, 'M', 0.484999999999999987, 0.369999999999999996, 0.154999999999999999, 0.967999999999999972, 0.418999999999999984, 0.245499999999999996, 0.236499999999999988, 9),
	(3294, 'M', 0.574999999999999956, 0.455000000000000016, 0.184999999999999998, 1.15599999999999992, 0.552499999999999991, 0.242999999999999994, 0.294999999999999984, 13),
	(1403, 'M', 0.650000000000000022, 0.510000000000000009, 0.190000000000000002, 1.54200000000000004, 0.715500000000000025, 0.373499999999999999, 0.375, 9),
	(2256, 'M', 0.510000000000000009, 0.395000000000000018, 0.14499999999999999, 0.61850000000000005, 0.215999999999999998, 0.138500000000000012, 0.239999999999999991, 12),
	(3984, 'F', 0.584999999999999964, 0.450000000000000011, 0.125, 0.873999999999999999, 0.354499999999999982, 0.20749999999999999, 0.225000000000000006, 6),
	(1116, 'M', 0.525000000000000022, 0.405000000000000027, 0.119999999999999996, 0.755499999999999949, 0.3755, 0.155499999999999999, 0.201000000000000012, 9),
	(1366, 'M', 0.609999999999999987, 0.474999999999999978, 0.170000000000000012, 1.02649999999999997, 0.434999999999999998, 0.233500000000000013, 0.303499999999999992, 10),
	(3759, 'I', 0.525000000000000022, 0.400000000000000022, 0.140000000000000013, 0.605500000000000038, 0.260500000000000009, 0.107999999999999999, 0.209999999999999992, 9);


	DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
	SELECT glm(
	'abalone',
	'abalone_out',
	'rings',
	'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
	'family=gaussian, link=identity'
	);

	SELECT
	assert(relative_error(ARRAY[0.997553983448236, -2.00220770198294, -2.38237621266428, 88.6791075055313, 11.8100239757845, -25.3192976658248, -9.4550584312097, -3.72450665767602], coef) < 1e-4, 'wrong coef'),
	assert(relative_error(-119.506940681, log_likelihood) < 1e-4, 'wrong log_likelihood'),
	assert(relative_error(ARRAY[1.78323811632271, 12.5513613314091, 15.7314928158976, 20.2562380620116, 5.89920538789372, 6.76993998744087, 10.0832608221583, 9.93889730891343], std_err) < 1e-4, 'wrong std_err'),
	assert(relative_error(ARRAY[0.559405933687272, -0.159521158631017, -0.151439932658949, 4.37786657295658, 2.00196860411418, -3.73995895278178, -0.937698488412787, -0.374740430644735], t_stats) < 1e-4, 'wrong t_stats'),
	assert(relative_error(ARRAY[0.578286340104612, 0.873876297316166, 0.880214691535476, 5.80912431853212e-05, 0.0505170037034926, 0.000460004387928058, 0.352734399919449, 0.709377533942504], p_values) < 1e-4, 'wrong p_values'),
	assert(relative_error(3.62838797857, dispersion) < 1e-4, 'wrong dispersion')
	FROM abalone_out;

	------------------------------------------------------------

	DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
	SELECT glm(
	'abalone',
	'abalone_out',
	'rings',
	'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
	'family=gaussian, link=inverse'
	);

	SELECT
	assert(relative_error(ARRAY[0.207505893301398, 0.121692677273364, -0.13743526302674, -0.973758981785658, -0.0881650764717561, 0.201488111012545, 0.0486202647973386, 0.0915246696608111], coef) < 1e-4, 'wrong coef'),
	assert(relative_error(-124.390370629, log_likelihood) < 1e-4, 'wrong log_likelihood'),
	assert(relative_error(ARRAY[0.0340567087639318, 0.144909354770801, 0.185838850959084, 0.209563197751552, 0.0473915910403184, 0.0658474252895474, 0.0929236924714683, 0.0973507352624716], std_err) < 1e-4, 'wrong std_err'),
	assert(relative_error(ARRAY[6.09295204477186, 0.839784825940617, -0.739539995633092, -4.64661253613861, -1.86035274478862, 3.05992390934881, 0.523227860454073, 0.94015386133497], t_stats) < 1e-4, 'wrong t_stats'),
	assert(relative_error(ARRAY[1.37277829098147e-07, 0.404873600352569, 0.462904806101211, 2.33957307776227e-05, 0.0684951360271206, 0.0034969162088071, 0.603038329735201, 0.351485606551847], p_values) < 1e-4, 'wrong p_values'),
	assert(relative_error(4.26991902085, dispersion) < 1e-4, 'wrong dispersion')
	FROM abalone_out;

	------------------------------------------------------------

	DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
	SELECT glm(
	'abalone',
	'abalone_out',
	'rings',
	'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
	'family=gaussian, link=log'
	);

	SELECT
	assert(relative_error(ARRAY[1.24642691358571, -0.710823591814181, 0.631879078261415, 9.7633031368507, 1.00681604973084, -2.31553977293938, -0.62212281355569, -0.681150079395847], coef) < 1e-4, 'wrong coef'),
	assert(relative_error(-121.439926239, log_likelihood) < 1e-4, 'wrong log_likelihood'),
	assert(relative_error(ARRAY[0.274311389188441, 1.36956583660479, 1.73245430104351, 2.10363764593199, 0.511047771609972, 0.649645203994886, 0.94355127671166, 0.965386925520628], std_err) < 1e-4, 'wrong std_err'),
	assert(relative_error(ARRAY[4.54383945658728, -0.519013816507238, 0.364730589361472, 4.64115250824255, 1.97010163366731, -3.56431442686, -0.659341817356054, -0.705572099009428], t_stats) < 1e-4, 'wrong t_stats'),
	assert(relative_error(ARRAY[3.32026977680014e-05, 0.605953093865339, 0.716791689842453, 2.38365422133465e-05, 0.0541628180005122, 0.000792113263000157, 0.51258581879907, 0.48360324365538], p_values) < 1e-4, 'wrong p_values'),
	assert(relative_error(3.86987789994, dispersion) < 1e-4, 'wrong dispersion')
	FROM abalone_out;

	------------------------------------------------------------
	-- Grouping support

	DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
	SELECT glm(
	'abalone',
	'abalone_out',
	'rings',
	'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
	'family=gaussian, link=identity',
	'sex'
	);

	SELECT
	assert(relative_error(ARRAY[0.209710168944741, 19.0036159909532, -21.5653997488975, 106.856474437712, 35.0095220501715, -41.750182394032, -63.884749494387, -37.377686641516], coef) < 1e-4, 'wrong coef'),
	assert(relative_error(-38.2338243376, log_likelihood) < 1e-4, 'wrong log_likelihood'),
	assert(relative_error(ARRAY[8.45728488507485, 40.2935117639766, 48.4372582378544, 42.1844318159701, 16.0440013310081, 20.8141398246576, 23.0878072228745, 34.994310628607], std_err) < 1e-4, 'wrong std_err'),
	assert(relative_error(ARRAY[0.0247963940903576, 0.471629678303267, -0.44522337831343, 2.53307843291273, 2.18209418759577, -2.0058567274816, -2.76703408330144, -1.06810752862669], t_stats) < 1e-4, 'wrong t_stats'),
	assert(relative_error(ARRAY[0.980624944052056, 0.645650692577156, 0.664083467030224, 0.0262703800464156, 0.0497070449993228, 0.0679529287394978, 0.0170553935436379, 0.306488464561412], p_values) < 1e-4, 'wrong p_values'),
	assert(relative_error(4.46527584187, dispersion) < 1e-4, 'wrong dispersion')
	FROM abalone_out where sex = 'M';

	------------------------------------------------------------

	DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
	SELECT glm(
	'abalone',
	'abalone_out',
	'rings',
	'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
	'family=gaussian, link=inverse',
	'sex'
	);

	SELECT
	assert(relative_error(ARRAY[0.184074822293059, 0.0631806170942958, -0.00650837763786568, -1.20067479469727, -0.240597039447159, 0.294074324448698, 0.587970076573244, 0.200570270495788], coef) < 1e-4, 'wrong coef'),
	assert(relative_error(-35.3262201512, log_likelihood) < 1e-4, 'wrong log_likelihood'),
	assert(relative_error(ARRAY[0.0694466050297355, 0.264723907580007, 0.382477169907492, 0.34807791627604, 0.096508309661607, 0.153781362466539, 0.23420835627635, 0.232015594885046], std_err) < 1e-4, 'wrong std_err'),
	assert(relative_error(ARRAY[2.65059497457423, 0.238666079206317, -0.017016382022069, -3.44944260624992, -2.49301889433956, 1.9122884576646, 2.51045729503981, 0.864468918975739], t_stats) < 1e-4, 'wrong t_stats'),
	assert(relative_error(ARRAY[0.0211557834211453, 0.815391641340597, 0.986703199019439, 0.00480992607214596, 0.0282751471734034, 0.0800034483814998, 0.0273848180365069, 0.404279997259952], p_values) < 1e-3, 'wrong p_values'),
	assert(relative_error(3.33866317325, dispersion) < 1e-4, 'wrong dispersion')
	FROM abalone_out where sex = 'M';

	------------------------------------------------------------

	DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
	SELECT glm(
	'abalone',
	'abalone_out',
	'rings',
	'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
	'family=gaussian, link=log',
	'sex'
	);

	SELECT
	assert(relative_error(ARRAY[1.39427729177307, 0.486930615615555, -0.855747900922272, 11.3639612621932, 2.85472895058833, -3.47679916783533, -5.96248073440894, -2.78828800807937], coef) < 1e-4, 'wrong coef'),
	assert(relative_error(-37.1607275903, log_likelihood) < 1e-4, 'wrong log_likelihood'),
	assert(relative_error(ARRAY[0.769986839024755, 3.3952158034843, 4.40195784717915, 3.93519362383163, 1.27601166566703, 1.802330542242, 2.27259663876784, 2.90100018116101], std_err) < 1e-4, 'wrong std_err'),
	assert(relative_error(ARRAY[1.81078067975684, 0.143416690955505, -0.194401657314972, 2.88777690464144, 2.23722794030729, -1.92905745441698, -2.62364232732548, -0.961147133387448], t_stats) < 1e-4, 'wrong t_stats'),
	assert(relative_error(ARRAY[0.0952657004232437, 0.88834126296204, 0.849113623796413, 0.0136322946375411, 0.0450212457473478, 0.0777087160148953, 0.0222349991922514, 0.355445860304514], p_values) < 1e-4, 'wrong p_values'),
	assert(relative_error(4.0109424558, dispersion) < 1e-4, 'wrong dispersion')
	FROM abalone_out where sex = 'M';