Loaded glmnet 4.1-10
=======================================================================
VALIDATION DATA FOR RUST STATISTICS LIBRARY
=======================================================================
### DATASET 1: Simple Linear Regression ###
# X data (column-major for Rust):
X1 = [ 1.0000000000, 2.0000000000, 3.0000000000, 4.0000000000, 5.0000000000, 6.0000000000, 7.0000000000, 8.0000000000, 9.0000000000, 10.0000000000, 11.0000000000, 12.0000000000, 13.0000000000, 14.0000000000, 15.0000000000, 16.0000000000, 17.0000000000, 18.0000000000, 19.0000000000, 20.0000000000 ]
# Y data:
Y1 = [ 6.1854792236, 8.2176509143, 11.6815642057, 14.8164313025, 17.7021341616, 20.4469377420, 24.2557609987, 26.4526704808, 30.5092118569, 32.4686429505, 36.1524348271, 39.6433226964, 40.8055696494, 44.3606056166, 47.4333393318, 50.8179751990, 53.3578735393, 55.1717722895, 58.2797665357, 63.1600566729 ]
# OLS Results:
intercept = 3.008845227701627
coefficient = 2.960677598286641
r_squared = 0.998773884764589
adj_r_squared = 0.998705767251511
residual_std_error = 0.630518368469364
se_intercept = 0.292895615787820
se_coefficient = 0.024450453598427
t_intercept = 10.272756113499822
t_coefficient = 121.088861863778604
p_intercept = 5.893230752934917e-09
p_coefficient = 1.162241529734109e-27
f_statistic = 14662.512467465243390
log_likelihood = -18.100905691064835
aic = 42.201811382129669
bic = 45.189008202791641
residuals_first5 = [ 0.215956397585084, -0.712549509972986, -0.209313816892890, -0.035124318367676, -0.110099057564337 ]
### DATASET 2: Multiple Regression ###
# X data (row-major):
n2 = 50
X2_col1 = [ 0.0000000000, 0.2040816327, 0.4081632653, 0.6122448980, 0.8163265306, 1.0204081633, 1.2244897959, 1.4285714286, 1.6326530612, 1.8367346939, 2.0408163265, 2.2448979592, 2.4489795918, 2.6530612245, 2.8571428571, 3.0612244898, 3.2653061224, 3.4693877551, 3.6734693878, 3.8775510204, 4.0816326531, 4.2857142857, 4.4897959184, 4.6938775510, 4.8979591837, 5.1020408163, 5.3061224490, 5.5102040816, 5.7142857143, 5.9183673469, 6.1224489796, 6.3265306122, 6.5306122449, 6.7346938776, 6.9387755102, 7.1428571429, 7.3469387755, 7.5510204082, 7.7551020408, 7.9591836735, 8.1632653061, 8.3673469388, 8.5714285714, 8.7755102041, 8.9795918367, 9.1836734694, 9.3877551020, 9.5918367347, 9.7959183673, 10.0000000000 ]
X2_col2 = [ 0.0000000000, 1.0133396827, 1.9846207446, 2.8735302061, 3.6431739173, 4.2616078486, 4.7031639256, 4.9495153819, 4.9904374107, 4.8242315449, 4.4577961521, 3.9063401176, 3.1927516011, 2.3466480639, 1.4031469976, 0.4014083742, -0.6169906868, -1.6097815754, -2.5357585474, -3.3564889678, -4.0379084548, -4.5517347216, -4.8766414303, -4.9991433419, -4.9141560196, -4.6252068587, -4.1442886819, -3.4913619778, -2.6935264419, -1.7838962045, -0.8002254302, 0.2166586668, 1.2245503551, 2.1816171324, 3.0481359825, 3.7881420770, 4.3709214941, 4.7722859987, 4.9755769739, 4.9723568363, 4.7627592377, 4.3554835174, 3.7674336372, 3.0230165825, 2.1531293519, 1.1938765782, 0.1850720074, -0.8314139692, -1.8133921441, -2.7201055544 ]
# Y data:
Y2 = [ 0.6933614059, 2.6668738795, 7.5982714087, 12.0597551133, 15.4573682745, 15.3951707407, 17.3012019858, 16.9425259175, 19.6967157093, 18.5061691466, 18.9104712325, 17.9136536085, 16.5113175090, 12.7371402652, 11.4286818303, 6.6096654232, 4.8951811761, 2.2585231899, -1.6745445167, -1.2782422556, -2.7444614582, -4.4448328918, -3.8921692186, -5.3363797508, -5.3148307360, -2.2387209175, -1.6320143238, 2.9904234915, 3.9165459002, 8.1406939638, 11.1661469337, 13.5191982841, 19.3106030748, 21.6571384579, 24.1117196144, 26.9266912639, 29.4859308494, 30.5087316990, 28.4438449201, 32.1203208094, 31.2475736825, 30.9863749947, 30.0269817818, 29.0198069830, 24.6912796697, 24.2515193055, 20.6665743461, 18.7279376604, 16.0723888706, 13.5605614995 ]
# OLS Results:
intercept = 0.586633340017646
coef1 = 2.078575906332045
coef2 = 3.022440472606421
r_squared = 0.992375515498879
adj_r_squared = 0.992051069349895
se_intercept = 0.290985644377972
se_coef1 = 0.049296453341195
se_coef2 = 0.043745569774467
### DATASET 3: Ridge Regression ###
# Ridge lambda = 0.0:
intercept = 0.586633340017646
coef1 = 2.078575906332045
coef2 = 3.022440472606421
# Ridge lambda = 0.1:
intercept = 0.586913038864145
coef1 = 2.078528971006804
coef2 = 3.022388771310106
# Ridge lambda = 1.0:
intercept = 0.589429767473181
coef1 = 2.078106651096626
coef2 = 3.021923541089428
# Ridge lambda = 10.0:
intercept = 0.614544058598135
coef1 = 2.073892655217044
coef2 = 3.017279253054705
### DATASET 4: Elastic Net ###
# X data dimensions: 100 x 5
# First 10 rows of X:
X4_row1 = [1.3709584471, 1.2009653756, -2.0009292377, -0.0046207678, 1.3349125854]
X4_row2 = [-0.5646981714, 1.0447510872, 0.3337771974, 0.7602421677, -0.8692717639]
X4_row3 = [0.3631284113, -1.0032086468, 1.1713251274, 0.0389909129, 0.0554869547]
X4_row4 = [0.6328626050, 1.8484819017, 2.0595392423, 0.7350721416, 0.0490669132]
X4_row5 = [0.4042683231, -0.6667734088, -1.3768615982, -0.1464726270, -0.5783557284]
X4_row6 = [-0.1061245161, 0.1055138125, -1.1508555656, -0.0578873354, -0.9987386560]
X4_row7 = [1.5115219974, -0.4222558819, -0.7058213948, 0.4823694661, -0.0024327800]
X4_row8 = [-0.0946590384, -0.1223501720, -1.0540557821, 0.9929436368, 0.6555118828]
X4_row9 = [2.0184237139, 0.1881930345, -0.6457437231, -1.2463954980, 1.4768422790]
X4_row10 = [-0.0627140991, 0.1191609580, -0.1853779677, -0.0334875248, -1.9091527883]
# Y first 10:
Y4_first10 = [ 2.2255149499, -3.3262092547, 3.0945743944, -1.7303712123, 2.1862750145, -0.6284633382, 4.8644733530, -0.5227547193, 5.0684785282, -0.0083603612 ]
# Full X4 data (flattened row-major):
X4_flat = [ 1.3709584471, 1.2009653756, -2.0009292377, -0.0046207678, 1.3349125854, -0.5646981714, 1.0447510872, 0.3337771974, 0.7602421677, -0.8692717639, 0.3631284113, -1.0032086468, 1.1713251274, 0.0389909129, 0.0554869547, 0.6328626050, 1.8484819017, 2.0595392423, 0.7350721416, 0.0490669132, 0.4042683231, -0.6667734088, -1.3768615982, -0.1464726270, -0.5783557284, -0.1061245161, 0.1055138125, -1.1508555656, -0.0578873354, -0.9987386560, 1.5115219974, -0.4222558819, -0.7058213948, 0.4823694661, -0.0024327800, -0.0946590384, -0.1223501720, -1.0540557821, 0.9929436368, 0.6555118828, 2.0184237139, 0.1881930345, -0.6457437231, -1.2463954980, 1.4768422790, -0.0627140991, 0.1191609580, -0.1853779677, -0.0334875248, -1.9091527883, 1.3048696542, -0.0250925509, -1.2012220507, -0.0709621812, -0.7024394733, 2.2866453927, 0.1080727279, 2.0369721670, -0.7589206537, -0.3114302180, -1.3888607011, -0.4854352358, 0.1077747449, -1.0343593609, -1.6631570307, -0.2787887668, -0.5042171307, -0.0841081005, -0.6307319540, -0.7505334418, -0.1333213364, -1.6610990799, 0.4956196416, 0.5868077200, -0.7773517592, 0.6359503981, -0.3823337269, 0.0374151861, -0.4163226562, -0.7225696999, -0.2842529214, -0.5126502579, -0.1320880370, -0.7848878095, -2.1888345991, -2.6564554209, 2.7018910003, 1.4767874236, 0.1634163195, 0.2134185503, -2.4404669286, -1.3621162312, -0.2170302101, -1.2367142351, -0.6319229363, 1.3201133457, 0.1372562186, -1.2836022041, 1.0458737762, 1.5204911938, -0.3066385941, -1.4936250673, 0.3856678904, -0.4845954162, 0.7959559494, -1.7813084340, -1.4704357414, -0.3515128735, 0.1891288117, -1.4535295651, -0.1719173558, 0.1247023862, -0.5217960934, 0.0510063316, 0.0983954210, 1.2146746992, -0.9966391349, -1.0681312007, -0.0002406689, -0.5937709842, 1.8951934613, -0.0018226143, 0.4283659033, 1.8093820424, 0.8882811686, -0.4304691316, -0.4282588814, -0.1740182344, -0.8253279571, 0.0530704155, -0.2572693828, -0.6136716064, 0.5156677286, 1.1454704522, -0.5570236258, -1.7631630852, -2.0246778454, -0.2343652773, 0.0315731876, 0.4383970362, 0.4600973548, -1.2247479504, -0.6585034258, -0.8352058053, 0.1526081586, -0.6399948760, 0.1795164411, 1.2502366041, -0.0687636490, -0.1646175817, 0.4554501232, 0.5676205944, -0.2717637151, 0.7467716870, 2.0198906215, 0.7048373372, -0.4928773536, 0.9479519959, -0.4255187344, -0.5293858863, 1.0351035220, 0.0000628841, -1.2015824301, -0.7720822352, -0.4707869730, -0.6089263754, 1.1228896434, -0.4661160964, 0.1527641067, -1.5459369240, 0.5049551233, 1.4398557430, -0.2693513952, 0.9885968452, -0.0405267233, -1.7170086791, -1.0971137684, -0.3909654081, -0.0734583347, 0.8903563055, -0.7844590084, -0.1173195603, 1.3487070120, -1.3870265536, -2.0713878509, -0.8509075942, 1.2014984009, -0.0227647013, -1.3066759044, -0.2500651201, -2.4142076499, -0.4697295806, 0.2442258511, -0.7683953251, -1.1816504267, 0.0361226069, -0.0524694849, -0.9423717079, -0.5271081254, 1.4419372650, 0.2059986002, -0.0861072982, -0.7292172765, -0.0214270650, 1.3578955389, -0.3610572985, -0.8876790179, 0.9980689086, 0.6704980710, 0.3345028473, 0.7581632357, -0.4446840049, 1.2584816646, -0.4346170386, 1.4293380804, -0.7267048271, -0.0294448791, 1.2488636888, -1.1138797833, -0.8673178509, -1.3682810444, -0.4138688491, -1.3806370495, 0.6071059949, 0.9506517250, 0.4328180259, 1.1133860234, 2.0499606936, 0.2754569687, -0.5850115086, -0.8113931762, -0.4809928417, 1.0168728298, 1.1573470694, 0.3209575225, 1.4441012617, -0.4331690326, -0.0267174641, -1.6824808595, -0.2993960167, -0.4314462026, 0.6968625766, 0.7036077788, 0.0873190889, -0.2785430833, 0.6556478834, -1.0563684132, -0.9713852292, 1.3533618939, 0.5461151583, 0.3219252652, -0.0406984752, -1.0961562416, 0.7241738007, -1.3038211536, -0.7838389409, -1.5515448223, 0.0490504509, -0.8325528258, -0.2509144650, 1.5757275198, 1.1671695492, -1.1984958566, 0.7325284868, 0.1710073737, 0.6428993057, -0.2736457014, 0.1900189986, -0.8719268700, -0.4034674787, 0.0897606466, -0.4678453247, 1.2977058996, -0.4533975112, 0.1046594408, 0.2765507473, -1.2382523280, -1.0338737230, 1.1875342786, -0.3188807867, 0.6792888161, -0.0077620338, -0.7384407542, -0.2901453118, 1.6183439359, 0.0898328866, -0.8002821780, 0.0465639395, 0.8285461450, 0.7141886015, -2.9930900832, -0.5334923300, -1.0175961198, -0.2912277088, 2.9658653698, 0.2848829535, 1.2876752456, -0.3832839599, -1.5763624047, -0.7950776046, -0.3672346427, -0.1755258702, 0.8727554117, -0.8488156969, 0.8143659147, 0.1852305649, -1.0717823842, 0.9695450140, -1.0885198620, 2.0980308101, 0.5818237274, 0.1632068825, 0.3838466650, -0.4842905711, 0.3009800552, 1.3997368273, -0.3627384156, -1.8515556631, -0.3363112090, -1.0830751418, -0.7272920595, 0.5900135480, -0.0539967368, -0.1533578907, -1.0063225018, 1.3025426320, 1.4324219277, 1.0647732143, -0.2432472286, -0.0354145649, 0.3358481198, -0.9926925111, 0.8131950374, 1.8922020416, 1.3091243609, 1.0385060987, 0.4546502976, -0.1908164741, -1.3859983373, 0.7504004866, 0.9207285683, 0.0848980587, -2.6999298086, -0.4148243007, -2.1383683276, 0.7208781629, 0.8955655823, 0.0609666388, 0.3490815281, -0.7003541089, -1.0431189386, -0.2297781389, 0.5737516975, 1.6284422658, -0.0090564753, -0.0901863866, 0.8366190685, 0.0458035797, 0.0885218957, -1.4581334872, 0.6235181620, -1.7450558613, 0.1574125402, 1.2391507084, 0.6945296465, -0.9535233578, 1.6894589213, 0.4315653729, -1.6445555358, -2.4613354752, -0.5428288146, 0.8647779785, -0.3965497361, 1.4463565254, 0.1432897640, 0.5809964977, -0.1507759889, 1.3099782258, -0.6905601717, -0.3912221191, 0.7681787378, -1.4490071301, 0.4703933999, -0.2764310855, -0.4911640856, 0.4637675885, 0.6430087000, -1.2426702706, -1.1094187599, -0.2836474525, -0.8857762974, 0.4831938638, 1.3815754564, 0.1338693164, 0.3147948047, -1.0997808986, -0.0063556264, 1.2044589370, 1.7853390517, 0.3963265779, 1.5127070098, 0.1514558929, 0.8240739637, 2.4221633553, -0.2256037110, 0.2579214375, -0.5841089703, -1.6626294022, -1.0768289021, -1.9249504303, 0.0884402292, 0.3688067326, -0.5693063436, 0.4859411104, -1.4392292983, -0.1208965375, 0.2946543397, 0.6355138173, 1.3885217387, -1.4696577740, -1.1943288952, -0.2792593733, 0.0437220076, -0.1956568173, 0.7618634469, 0.6119968980, -1.3362366549, 0.3480123037, -0.2181747977, -0.2436149819, -0.2171398457, 0.7007488184, 2.4595935489, -0.3047779545, 0.2696766074, -0.1827567063, 0.5541966223, -0.8183803244, 0.5978327241, -1.5589275210, 0.9333463286, -0.8363065928, -2.1132001149, 1.3974294108, -0.5355880067, 0.8217731105, -1.5945881620, 0.2736952724, 0.6876197612, 0.5624519732, 1.3921163759, 0.2049585806, -0.6875968412, 0.3201880143, -0.1783261234, -0.4761739231, -0.3450879780, 0.4460410530, -0.3018699258, -0.1151359862, 0.6503485607, 0.2526117034, -0.8123847238, 0.4983486856, -0.0720614721, 1.3911104564, -1.2940024655, 2.2120554803, -0.5495369179, 1.2109098069, -1.1107888794, -0.9591704444, -0.1237059716, -0.2792565036, -0.6148969008, -0.8607925869, 1.0857748537, -0.4773355060, 1.0965134431, 0.6761264583, -1.1317386809, 0.4037749047, -0.1662614915, 0.4420130882, 0.8985996055, -1.4592139995, 0.5864875367, 0.8625633836, 0.2410162940, -1.1893179035, 0.0799825532, 1.8152284462, 0.0973404852, -0.2556076554, 0.1212588498, 0.6532043396, 0.1288214286, -1.6256167392, 0.9310329015, -0.0112216861 ]
# Full Y4 data:
Y4 = [ 2.2255149499, -3.3262092547, 3.0945743944, -1.7303712123, 2.1862750145, -0.6284633382, 4.8644733530, -0.5227547193, 5.0684785282, -0.0083603612, 4.5222799637, 6.4373182958, -3.7602003306, 0.1281022950, 4.0431859973, 3.6931752333, -0.6873584169, -13.5516015915, -3.8305280773, 3.6667055518, 2.8660409736, -2.5698465157, -0.4626638777, 5.7494229869, 7.3037603601, 0.0253366514, -0.1477344700, -1.5420741493, 4.0149056075, -3.2295178335, -0.6710957916, 2.5393554156, 2.9312199945, -3.4531073387, -1.5019448985, -2.8756081426, -2.1510413595, -5.3083381329, -5.6220651543, -0.3349498035, 0.6759936378, 0.5182720999, 3.4299220266, -1.3176074419, -3.0201981721, -0.2371313888, -1.0906453210, 4.8863495780, -2.6472918607, 4.7677200322, 0.2665398528, 0.9139581524, 2.3144483024, 2.9148812503, 1.5800558767, 3.4566835998, 2.7997960743, 1.1073161156, -7.4569268103, -2.5104676445, -0.4567940592, 2.7440776109, 1.9026882456, 4.9640934896, -4.1462531926, 0.0388724487, 3.2634161436, 2.1695294019, 2.3068803907, 0.2159690941, -3.0055080714, -2.0224675228, 4.8950136732, -7.2309926557, -3.4678423029, 2.5671794055, 6.1412152569, 0.1065884635, -3.6640515872, -2.8051403025, 4.2619947520, 1.7245330488, -1.3409414055, -1.5838460919, -2.8213136828, 3.7786370200, -1.5286884890, -2.3298786333, 4.3758668923, 5.6533276770, 3.7600170997, -0.6623721522, 1.7450778412, 6.6982300815, -1.5382935325, -4.6737637705, -4.4195868228, -4.7819108624, -4.4756325209, 2.2154724714 ]
# Elastic Net (alpha=0.5, lambda=0.1):
intercept = -0.001477022967520
coef1 = 2.981170977551803
coef2 = -2.111768548328050
coef3 = 0.054127690181294
coef4 = 0.034078404041139
coef5 = 0.059985687348184
# Lasso (alpha=1.0, lambda=0.1):
intercept = -0.001473113499827
coef1 = 2.981072659072019
coef2 = -2.111504297540462
coef3 = 0.053610091203830
coef4 = 0.033473030457753
coef5 = 0.059671869731005
### DATASET 5: Weighted Least Squares ###
# X data:
X5 = [ 1.0000000000, 2.0000000000, 3.0000000000, 4.0000000000, 5.0000000000, 6.0000000000, 7.0000000000, 8.0000000000, 9.0000000000, 10.0000000000, 11.0000000000, 12.0000000000, 13.0000000000, 14.0000000000, 15.0000000000, 16.0000000000, 17.0000000000, 18.0000000000, 19.0000000000, 20.0000000000, 21.0000000000, 22.0000000000, 23.0000000000, 24.0000000000, 25.0000000000, 26.0000000000, 27.0000000000, 28.0000000000, 29.0000000000, 30.0000000000 ]
# Y data:
Y5 = [ 3.6370958447, 4.8870603657, 6.6089385234, 8.2531450420, 9.7021341616, 10.9363252903, 13.5580653982, 13.9242727693, 17.3165813425, 16.9372859009, 19.9353566196, 22.7439744712, 19.6944810886, 22.6096957265, 24.3000179954, 27.0175206369, 27.0167700336, 24.2183802424, 25.8631128357, 34.6402266915, 32.8560589524, 31.0811214452, 36.1045900818, 40.9152192780, 44.2379836532, 39.8807802578, 41.8053726665, 39.0631433615, 46.8342823290, 45.0800153721 ]
# Weights:
W5 = [ 1.0000000000, 0.2500000000, 0.1111111111, 0.0625000000, 0.0400000000, 0.0277777778, 0.0204081633, 0.0156250000, 0.0123456790, 0.0100000000, 0.0082644628, 0.0069444444, 0.0059171598, 0.0051020408, 0.0044444444, 0.0039062500, 0.0034602076, 0.0030864198, 0.0027700831, 0.0025000000, 0.0022675737, 0.0020661157, 0.0018903592, 0.0017361111, 0.0016000000, 0.0014792899, 0.0013717421, 0.0012755102, 0.0011890606, 0.0011111111 ]
# WLS Results:
intercept = 2.138362439251541
coefficient = 1.488433478007494
r_squared = 0.990301760247167
# OLS (for comparison):
intercept = 2.543172646113784
coefficient = 1.452395331170167
### DATASET 6: Collinearity Test ###
# X6 columns:
X6_col1 = [ 1.3709584471, -0.5646981714, 0.3631284113, 0.6328626050, 0.4042683231, -0.1061245161, 1.5115219974, -0.0946590384, 2.0184237139, -0.0627140991, 1.3048696542, 2.2866453927, -1.3888607011, -0.2787887668, -0.1333213364, 0.6359503981, -0.2842529214, -2.6564554209, -2.4404669286, 1.3201133457, -0.3066385941, -1.7813084340, -0.1719173558, 1.2146746992, 1.8951934613, -0.4304691316, -0.2572693828, -1.7631630852, 0.4600973548, -0.6399948760, 0.4554501232, 0.7048373372, 1.0351035220, -0.6089263754, 0.5049551233, -1.7170086791, -0.7844590084, -0.8509075942, -2.4142076499, 0.0361226069, 0.2059986002, -0.3610572985, 0.7581632357, -0.7267048271, -1.3682810444, 0.4328180259, -0.8113931762, 1.4441012617, -0.4314462026, 0.6556478834 ]
X6_col2 = [ 1.3741776998, -0.5725365608, 0.3788856865, 0.6392915980, 0.4051659296, -0.1033590086, 1.5183148856, -0.0937607095, 1.9884928130, -0.0598652695, 1.3011973078, 2.2884976983, -1.3830424638, -0.2647913985, -0.1405942570, 0.6489758244, -0.2808944402, -2.6460703599, -2.4312596429, 1.3273221274, -0.3170697835, -1.7822102978, -0.1656821741, 1.2051394656, 1.8897651731, -0.4246591666, -0.2495875954, -1.7585254093, 0.4512395919, -0.6509926849, 0.4705771933, 0.7074165516, 1.0359879243, -0.6101353408, 0.4930118343, -1.7108887101, -0.7866304068, -0.8527351612, -2.4048741867, 0.0443403380, 0.2199197640, -0.3658190378, 0.7646667213, -0.7127937225, -1.3793889332, 0.4242101000, -0.8227105630, 1.4295091217, -0.4306463771, 0.6621799268 ]
X6_col3 = [ 1.2009653756, 1.0447510872, -1.0032086468, 1.8484819017, -0.6667734088, 0.1055138125, -0.4222558819, -0.1223501720, 0.1881930345, 0.1191609580, -0.0250925509, 0.1080727279, -0.4854352358, -0.5042171307, -1.6610990799, -0.3823337269, -0.5126502579, 2.7018910003, -1.3621162312, 0.1372562186, -1.4936250673, -1.4704357414, 0.1247023862, -0.9966391349, -0.0018226143, -0.4282588814, -0.6136716064, -2.0246778454, -1.2247479504, 0.1795164411, 0.5676205944, -0.4928773536, 0.0000628841, 1.1228896434, 1.4398557430, -1.0971137684, -0.1173195603, 1.2014984009, -0.4697295806, -0.0524694849, -0.0861072982, -0.8876790179, -0.4446840049, -0.0294448791, -0.4138688491, 1.1133860234, -0.4809928417, -0.4331690326, 0.6968625766, -1.0563684132 ]
# Y6:
Y6 = [ 7.3244637835, 2.2290845075, -0.6997843432, 7.6743480643, -0.4257062423, 0.4851662412, 2.7523953324, 0.0434903183, 5.3346803663, 1.8758922987, 3.4466987207, 5.3616177772, -3.1524236685, -1.2515981335, -3.9549331385, 1.8411105794, -1.6028028720, 4.0200873080, -7.9248335214, 4.4997781383, -4.2090414596, -6.5556145580, 0.1577445164, 1.2841614543, 5.2173080689, -1.2211029019, -2.0800571500, -8.2788553566, -1.5124522095, 0.2553817582, 3.6894899762, 0.6389881286, 3.2547990625, 3.2981433492, 6.1898477889, -6.3934769908, -0.5705022883, 3.1797783255, -5.6557573380, 0.1175426780, 1.2561545960, -2.5576956398, 1.3085803084, -1.1887455242, -3.4577538582, 5.7486815487, -1.8638774250, 2.8819391940, 3.1353095475, -0.7933987584 ]
# VIF values:
vif1 = 16380.503169891922880
vif2 = 16381.055158514855066
vif3 = 1.011449753315868
# OLS coefficients (may be unstable due to collinearity):
intercept = 0.988638267702341
coef1 = 4.328954072200014
coef2 = -2.286004376184118
coef3 = 2.977932718094672
# Ridge (lambda=0.1) on collinear data:
intercept = 0.986139217457542
coef1 = 2.043456948665469
coef2 = 0.003944448099730
coef3 = 2.975606523149180
### DATASET 7: Leverage and Diagnostics ###
# X7:
X7 = [ 1.0000000000, 2.0000000000, 3.0000000000, 4.0000000000, 5.0000000000, 6.0000000000, 7.0000000000, 8.0000000000, 9.0000000000, 10.0000000000, 11.0000000000, 12.0000000000, 13.0000000000, 14.0000000000, 15.0000000000, 16.0000000000, 17.0000000000, 18.0000000000, 19.0000000000, 50.0000000000 ]
# Y7:
Y7 = [ 6.3709584471, 7.4353018286, 11.3631284113, 14.6328626050, 17.4042683231, 19.8938754839, 24.5115219974, 25.9053409616, 31.0184237139, 31.9372859009, 36.3048696542, 40.2866453927, 39.6111392989, 43.7212112332, 46.8666786636, 50.6359503981, 52.7157470786, 53.3435445791, 56.5595330714, 72.0000000000 ]
# Leverage values:
leverage = [ 0.107894736842105, 0.097846889952153, 0.088755980861244, 0.080622009569378, 0.073444976076555, 0.067224880382775, 0.061961722488038, 0.057655502392344, 0.054306220095694, 0.051913875598086, 0.050478468899522, 0.050000000000000, 0.050478468899522, 0.051913875598086, 0.054306220095694, 0.057655502392344, 0.061961722488038, 0.067224880382775, 0.073444976076555, 0.740909090909091 ]
# Cook's distance:
cooks_d = [ 0.099988500014990, 0.095963998298432, 0.053403456864335, 0.031108147236643, 0.019208028826527, 0.012261100886527, 0.001768510463619, 0.001824946194609, 0.000741528861411, 0.000241279027185, 0.004554051285788, 0.012550598309811, 0.005273800699532, 0.014879981631107, 0.024387084914606, 0.042395904663218, 0.051103647051725, 0.047434147201527, 0.071644965041732, 25.321998419048295 ]
# Studentized residuals:
studentized_resid = [ -1.311322751493635, -1.361430364133452, -1.050159481215660, -0.835204523098682, -0.685844912580558, -0.572315427350749, -0.225217690607212, -0.237757140174303, 0.156289390382954, 0.091253914446625, 0.404183176490386, 0.680210428609883, 0.435282470184123, 0.727518757323066, 0.917549901728662, 1.190822668755939, 1.264432251314524, 1.158144626593225, 1.377629705040581, -32.213002554226989 ]
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END OF VALIDATION DATA
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