Multiple Linear Regression - Estimated Regression Equation
Y[t] = -25.4133631689989 + 0.179229739292978X[t] + 0.095280873041429M1[t] + 0.0421340272055563M2[t] -0.0422355774266983M3[t] -0.132143448451306M4[t] -0.132177275468981M5[t] -0.124486492861985M6[t] -0.132564913920593M7[t] -0.139372069077023M8[t] + 0.00123723721385846M9[t] -0.0336295549066252M10[t] -0.0235177431578595M11[t] -0.0695730755602266t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-25.41336316899897.882439-3.2240.0014660.000733
X0.1792297392929780.0511433.50450.0005590.00028
M10.0952808730414290.3358730.28370.7769340.388467
M20.04213402720555630.3357190.12550.9002450.450122
M3-0.04223557742669830.336122-0.12570.9001250.450062
M4-0.1321434484513060.337958-0.3910.696190.348095
M5-0.1321772754689810.337897-0.39120.6960630.348032
M6-0.1244864928619850.337376-0.3690.7125110.356256
M7-0.1325649139205930.337046-0.39330.6944870.347243
M8-0.1393720690770230.336799-0.41380.6794330.339716
M90.001237237213858460.3407010.00360.9971060.498553
M10-0.03362955490662520.340469-0.09880.9214120.460706
M11-0.02351774315785950.340263-0.06910.9449630.472481
t-0.06957307556022660.019631-3.5440.0004860.000243


Multiple Linear Regression - Regression Statistics
Multiple R0.243310752051549
R-squared0.0592001220638905
Adjusted R-squared0.000960129620226513
F-TEST (value)1.01648574424448
F-TEST (DF numerator)13
F-TEST (DF denominator)210
p-value0.436507145272958
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.02046354510624
Sum Squared Residuals218.682627847067


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
13.882.088263662095741.79173633790426
23.982.180619427851191.79938057214881
33.292.152137565163811.13786243483619
42.882.297347175377040.582652824622961
53.222.245663246728430.974336753271567
63.622.255472849492401.36452715050760
73.822.141975405014961.67802459498504
83.542.11936409608621.42063590391380
92.532.280015196463340.249984803536656
102.222.26519019842912-0.0451901984291231
112.852.295343804264150.554656195735849
122.782.303057393649680.47694260635032
132.282.45422600863596-0.174226008635964
142.262.47488987867425-0.214889878674251
152.712.518099911704040.191900088295957
162.772.466156808694990.303843191305007
172.772.432395853975680.337604146024316
182.642.388436534951760.251563465048243
192.562.328708012262220.231291987737782
202.072.27025075547486-0.200250755474859
212.322.52051672549849-0.200516725498491
222.162.54153767532286-0.381537675322863
232.232.49999938544070-0.269999385440704
242.42.47186702696763-0.0718670269676341
252.842.515497798378130.324502201621867
262.772.536161668416420.233838331583582
272.932.435987910011830.494012089988174
282.912.473659676649270.436340323350734
292.692.493667643717850.196332356282147
302.382.53932319434041-0.159323194340413
312.582.515440619509470.0645593804905305
323.192.492829310580710.697170689419292
332.822.599711489169960.220288510830043
342.722.566963517206440.153036482793562
352.532.525425227324270.00457477267572591
362.72.497292868851200.202707131148797
372.422.54092364026171-0.120923640261707
382.52.52574156244139-0.0257415624413933
392.312.4614137518954-0.151413751895402
402.412.48116254460354-0.071162544603544
412.562.411555642025640.148444357974358
422.762.367596323001710.392403676998291
432.712.289944826382870.420055173617126
442.442.285256491383410.15474350861659
452.462.46383056568985-0.0038305656898506
462.122.48485151551422-0.364851515514222
471.992.44331322563206-0.453313225632063
481.862.39725789322970-0.537257893229696
491.882.44088866464019-0.560888664640195
501.822.44362956074918-0.623629560749178
511.742.36137877627389-0.621378776273889
521.712.36320459505274-0.653204595052735
531.382.31152066640413-0.93152066640413
541.272.08833160808722-0.818331608087219
551.192.10029498111487-0.910294981114872
561.282.07768367218611-0.797683672186112
571.192.29210369435115-1.10210369435115
581.222.08012598309465-0.86012598309465
591.472.02066471928319-0.550664719283189
601.461.99253236081012-0.532532360810118
611.962.03616313222062-0.0761631322206229
621.882.18228781976399-0.30228781976399
632.032.15380595707659-0.123805957076591
642.042.15563177585544-0.115631775855437
651.92.10394784720683-0.203947847206832
661.82.0599885281829-0.259988528182898
671.922.00026000549336-0.0802600054933604
681.921.92387977477670-0.00387977477670409
691.972.01283897943666-0.0428389794366607
702.461.926322085685250.533677914314753
712.361.920629743661680.439370256338324
722.531.910420359117910.619579640882092
732.311.936128156599110.37387184340089
741.981.974715000566690.00528499943330803
751.461.92831016395000-0.468310163949996
761.261.87636706094095-0.616367060940947
771.581.84260610622164-0.262606106221639
781.741.8524157089856-0.112415708985600
791.891.864379082013250.0256209179867456
801.851.805921825225890.0440781747741052
811.621.89488102988585-0.274881029885851
821.31.80836413613444-0.508364136134438
831.421.78474882018157-0.364748820181570
841.151.7924624095671-0.642462409567099
850.421.83609318097760-1.41609318097760
860.741.96429489459167-1.22429489459167
871.021.93581303190427-0.91581303190427
881.511.95556182461241-0.445561824612412
891.861.92180086989311-0.0618008698931087
901.591.87784155086918-0.287841550869175
911.031.81811302817964-0.788113028179637
920.441.79550171925088-1.35550171925088
930.821.88446092391083-1.06446092391083
940.861.79794403015941-0.937944030159414
950.581.73848276634795-1.15848276634795
960.591.71035040787488-1.12035040787488
970.951.73605820535609-0.786058205356085
980.981.75672207539437-0.77672207539437
991.231.71031723877767-0.480317238777674
1001.171.89137279684950-0.721372796849498
1010.841.92930373784738-1.08930373784738
1020.741.95703631454064-1.21703631454064
1030.651.96899968756829-1.31899968756829
1040.911.96431135256883-1.05431135256883
1051.192.08911650508738-0.899116505087375
1061.32.11013745491175-0.810137454911752
1071.532.05067619110029-0.520676191100291
1081.942.00462085869792-0.0646208586979243
1091.792.03032865617913-0.240328656179127
1101.952.01514657835881-0.065146578358813
1112.261.950818767812820.309181232187179
1122.041.827183769086580.212816230913421
1132.161.757576866508680.402423133491323
1142.751.695694573555451.05430542644455
1152.791.618043076936611.17195692306339
1162.881.685046637654341.19495336234566
1173.361.881543685890081.47845631410992
1182.971.830872739997261.13912726000274
1193.11.807257424044391.29274257595561
1202.491.814971013429920.675028986570077
1212.21.858601784840420.341398215159578
1222.251.897188628808000.352811371191996
1232.091.832860818262010.257139181737988
1242.791.906378532758050.88362146724195
1253.141.998078395543821.14192160445618
1262.932.061656920095680.86834307990432
1272.652.091543267052630.558456732947368
1282.672.015163036335970.654836963664025
1292.262.175814136713120.0841858632868812
1302.352.089297242961710.260702757038295
1312.132.065681927008840.0643180729911573
1322.182.055472542465070.124527457534931
1332.92.134949261734170.765050738265833
1342.632.065998262125960.564001737874042
1352.672.019593425509260.650406574490738
1361.812.00349627035881-0.193496270358812
1371.332.0055812634981-0.675581263498101
1380.881.97954491840346-1.09954491840346
1391.282.02735423928972-0.747354239289718
1401.261.98681995643166-0.726819956431655
1411.262.1474710568088-0.887471056808798
1421.292.06095416305738-0.770954163057385
1431.12.07318479496312-0.973184794963116
1441.372.04505243649005-0.675052436490045
1451.212.17829807754703-0.968298077547034
1461.742.07350113008024-0.333501130080236
1471.761.93748142381705-0.177481423817052
1481.481.79592345116151-0.315923451161514
1491.041.86970034001800-0.829700340017996
1501.621.91535589064055-0.295355890640551
1511.491.89147331580961-0.401473315809607
1521.791.86886200688085-0.0788620068808458
1531.81.97574418547009-0.175744185470093
1541.581.90715026564798-0.327150265647982
1551.861.93730387148301-0.0773038714830098
1561.741.98086340872713-0.240863408727131
1571.592.06034012799622-0.470340127996224
1581.261.99138912838802-0.73138912838802
1591.131.89121536998343-0.761215369983435
1601.921.821349293045090.0986507069549115
1612.611.787588338325780.82241166167422
1622.261.887012810736230.372987189263769
1632.411.898976183763880.511023816236115
1642.261.912210822693720.347789177306283
1652.032.03701597521226-0.00701597521226226
1662.861.986345029319450.873654970680553
1672.551.998575661225180.551424338774821
1682.271.988366276681400.281633723318596
1692.262.103688943809100.156311056190903
1702.572.034737944200890.535262055799107
1713.071.952487159725601.11751284027440
1722.761.990158926363040.769841073636957
1732.512.010166893431630.499833106568371
1742.871.966207574407700.903792425592304
1753.142.031939869223241.10806013077676
1763.111.991405586365181.11859441363482
1773.162.098287764954431.06171223504557
1782.472.047616819061620.422383180938384
1792.572.059847450967350.510152549032653
1802.892.049638066423570.840361933576427
1812.632.129114785692670.500885214307329
1822.382.113932707872360.266067292127643
1831.692.15714274090215-0.46714274090215
1841.962.06935369003451-0.109353690034508
1852.192.07143868317380.118561316826202
1861.872.08124828593776-0.211248285937759
1871.62.03944273717752-0.439442737177518
1881.632.05267737610735-0.422677376107351
1891.222.1774825286259-0.957482528625901
1901.212.16265753059168-0.95265753059168
1911.492.15696518856811-0.666965188568109
1921.642.16467877795364-0.524678777953637
1931.662.20830954936414-0.548309549364137
1941.772.13935854975593-0.369358549755932
1951.822.02126181742205-0.201261817422045
1961.781.87970384476651-0.0997038447665063
1971.281.84594289004720-0.565942890047203
1981.291.83782951888186-0.547829518881863
1991.371.81394694405092-0.443946944050924
2001.121.75548968726356-0.635489687263563
2011.511.86237186585281-0.352371865852812
2022.241.865469841747890.374530158252107
2032.941.841854525795031.09814547420497
2043.091.921260010897741.16873998910226
2053.461.982813756237541.47718624376246
2063.642.057246548063721.58275345193628
2074.392.279686320386492.11031367961351
2084.152.281512139165331.86848786083467
2095.212.373212001951112.83678799804889
2105.82.347175656856483.45282434314352
2115.912.341216055954833.56878394404517
2125.392.390296642743262.99970335725674
2135.462.5867936909792.873206309021
2144.722.518199771156882.20180022884312
2153.142.620045272709100.519954727290896
2162.632.609835888165330.0201641118346695
2172.322.68931260743443-0.369312607434429
2181.932.60243863389692-0.672438633896922
2190.622.52018784942163-1.90018784942163
2200.62.41447582462469-1.81447582462469
221-0.372.48825271348117-2.85825271348117
222-1.12.55183123803303-3.65183123803303
223-1.682.52794866320208-4.20794866320208
224-0.782.57702924999051-3.35702924999051


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1055691615149260.2111383230298520.894430838485074
180.05831220610667940.1166244122133590.94168779389332
190.02940251401672720.05880502803345440.970597485983273
200.01848728597989370.03697457195978740.981512714020106
210.01409197603205250.0281839520641050.985908023967948
220.01234890363870070.02469780727740150.9876510963613
230.005341217355902180.01068243471180440.994658782644098
240.002455583331249410.004911166662498830.99754441666875
250.001922522979705220.003845045959410450.998077477020295
260.0008969970110730610.001793994022146120.999103002988927
270.0003756376925567520.0007512753851135030.999624362307443
280.0001570716034588440.0003141432069176880.999842928396541
295.85799754359013e-050.0001171599508718030.999941420024564
302.27264862028407e-054.54529724056813e-050.999977273513797
318.44764101096282e-061.68952820219256e-050.99999155235899
323.52649078479996e-057.05298156959992e-050.999964735092152
333.38566903511268e-056.77133807022536e-050.99996614330965
342.79890554237129e-055.59781108474258e-050.999972010944576
351.1448409369302e-052.2896818738604e-050.99998855159063
364.64761704384565e-069.2952340876913e-060.999995352382956
372.71666113619686e-065.43332227239371e-060.999997283338864
381.66632083897859e-063.33264167795719e-060.99999833367916
391.32958304833509e-062.65916609667017e-060.999998670416952
406.65412812802654e-071.33082562560531e-060.999999334587187
413.09328146785560e-076.18656293571119e-070.999999690671853
421.30548614817264e-072.61097229634527e-070.999999869451385
436.06131650654585e-081.21226330130917e-070.999999939386835
443.09919078898864e-086.19838157797728e-080.999999969008092
451.19737900412192e-082.39475800824385e-080.99999998802621
464.41998024589396e-098.83996049178792e-090.99999999558002
472.09520721737462e-094.19041443474924e-090.999999997904793
481.50044632037613e-093.00089264075227e-090.999999998499554
491.09958605447830e-092.19917210895661e-090.999999998900414
508.95715942187337e-101.79143188437467e-090.999999999104284
516.9246695786768e-101.38493391573536e-090.999999999307533
524.42573908266205e-108.8514781653241e-100.999999999557426
536.50414549481049e-101.30082909896210e-090.999999999349585
541.02781036956121e-092.05562073912242e-090.99999999897219
551.40015266211776e-092.80030532423553e-090.999999998599847
569.2537831103017e-101.85075662206034e-090.999999999074622
574.53294894538617e-109.06589789077234e-100.999999999546705
581.83054463894812e-103.66108927789624e-100.999999999816946
597.71256933508241e-111.54251386701648e-100.999999999922874
603.06808424460704e-116.13616848921409e-110.999999999969319
611.94788377984282e-113.89576755968565e-110.999999999980521
629.15826709799255e-121.83165341959851e-110.999999999990842
635.80364021499214e-121.16072804299843e-110.999999999994196
643.97694921272862e-127.95389842545724e-120.999999999996023
652.03388368837039e-124.06776737674078e-120.999999999997966
668.74671210972071e-131.74934242194414e-120.999999999999125
674.09047105278113e-138.18094210556227e-130.99999999999959
682.04529359709146e-134.09058719418291e-130.999999999999795
691.6300845607625e-133.260169121525e-130.999999999999837
709.06840849910715e-131.81368169982143e-120.999999999999093
711.43575146826882e-122.87150293653763e-120.999999999998564
722.86025089291462e-125.72050178582923e-120.99999999999714
732.02028555369731e-124.04057110739463e-120.99999999999798
748.98465435341542e-131.79693087068308e-120.999999999999102
754.08004635386087e-138.16009270772174e-130.999999999999592
762.23052207106661e-134.46104414213321e-130.999999999999777
778.86418511474694e-141.77283702294939e-130.999999999999911
783.58091840827335e-147.16183681654671e-140.999999999999964
791.58688494174678e-143.17376988349356e-140.999999999999984
806.91703500979581e-151.38340700195916e-140.999999999999993
812.7036105022098e-155.4072210044196e-150.999999999999997
821.04795676226988e-152.09591352453975e-150.999999999999999
833.92244174883461e-167.84488349766922e-161
841.89663061228806e-163.79326122457612e-161
858.64932013690124e-161.72986402738025e-151
868.20501202783818e-161.64100240556764e-151
873.71957175675032e-167.43914351350065e-161
881.56721488441748e-163.13442976883497e-161
891.06497629006968e-162.12995258013937e-161
904.53575303915952e-179.07150607831905e-171
912.10432033356265e-174.2086406671253e-171
923.21357703021077e-176.42715406042154e-171
931.64207347390141e-173.28414694780283e-171
947.49490765405992e-181.49898153081198e-171
955.76392312817392e-181.15278462563478e-171
964.32495854429692e-188.64991708859383e-181
971.9095245127049e-183.8190490254098e-181
988.27711203092661e-191.65542240618532e-181
993.54871195198804e-197.09742390397608e-191
1001.47819861262597e-192.95639722525193e-191
1016.564851408498e-201.3129702816996e-191
1023.17933675240047e-206.35867350480094e-201
1031.68533087448815e-203.3706617489763e-201
1047.49855194606341e-211.49971038921268e-201
1055.47402683644425e-211.09480536728885e-201
1065.76531840203866e-211.15306368040773e-201
1077.9775186200676e-211.59550372401352e-201
1083.32336665762621e-206.64673331525243e-201
1095.62777153427498e-201.12555430685500e-191
1101.29737272154566e-192.59474544309132e-191
1117.54369234855256e-191.50873846971051e-181
1121.67435343832858e-183.34870687665716e-181
1134.34583498138839e-188.69166996277678e-181
1148.61213357610963e-171.72242671522193e-161
1151.22820020556069e-152.45640041112138e-150.999999999999999
1161.91386527010659e-143.82773054021318e-140.99999999999998
1171.15777325290436e-122.31554650580871e-120.999999999998842
1181.03481182033721e-112.06962364067442e-110.999999999989652
1197.90332009277555e-111.58066401855511e-100.999999999920967
1201.15437078057088e-102.30874156114175e-100.999999999884563
1219.8991249595998e-111.97982499191996e-100.999999999901009
1228.52955733418688e-111.70591146683738e-100.999999999914704
1236.05131734654685e-111.21026346930937e-100.999999999939487
1241.12011198651809e-102.24022397303618e-100.999999999887989
1253.4844639607776e-106.9689279215552e-100.999999999651554
1265.79856088169844e-101.15971217633969e-090.999999999420144
1275.80597418529365e-101.16119483705873e-090.999999999419403
1286.15396830002977e-101.23079366000595e-090.999999999384603
1293.86802678010283e-107.73605356020565e-100.999999999613197
1302.73892944694178e-105.47785889388356e-100.999999999726107
1311.58457997720567e-103.16915995441134e-100.999999999841542
1329.32529492271335e-111.86505898454267e-100.999999999906747
1331.05320783396260e-102.10641566792521e-100.999999999894679
1348.79011687102461e-111.75802337420492e-100.999999999912099
1357.9849320328525e-111.5969864065705e-100.99999999992015
1364.13566461597519e-118.27132923195039e-110.999999999958643
1372.43237537234584e-114.86475074469168e-110.999999999975676
1382.11854265504617e-114.23708531009234e-110.999999999978815
1391.27111846628271e-112.54223693256541e-110.999999999987289
1407.35736066219996e-121.47147213243999e-110.999999999992643
1414.57653813975035e-129.1530762795007e-120.999999999995423
1422.68570021000332e-125.37140042000663e-120.999999999997314
1431.85912374984060e-123.71824749968121e-120.99999999999814
1441.02876961776939e-122.05753923553878e-120.999999999998971
1456.85955555623753e-131.37191111124751e-120.999999999999314
1463.29798457299554e-136.59596914599107e-130.99999999999967
1471.55437306353259e-133.10874612706519e-130.999999999999845
1487.56711091522304e-141.51342218304461e-130.999999999999924
1494.99946304889092e-149.99892609778184e-140.99999999999995
1502.35382980071706e-144.70765960143413e-140.999999999999976
1511.12642514907938e-142.25285029815877e-140.999999999999989
1525.22321100614032e-151.04464220122806e-140.999999999999995
1532.84827008446185e-155.6965401689237e-150.999999999999997
1541.67220448921215e-153.34440897842429e-150.999999999999998
1558.80613367648499e-161.76122673529700e-151
1564.5397890548242e-169.0795781096484e-161
1572.43719737426711e-164.87439474853422e-161
1581.71635745751694e-163.43271491503389e-161
1591.25849240836846e-162.51698481673692e-161
1606.3297963575885e-171.26595927151770e-161
1615.72267608762334e-171.14453521752467e-161
1623.06660738576770e-176.13321477153539e-171
1631.78498621153908e-173.56997242307817e-171
1648.93874038715898e-181.78774807743180e-171
1655.37496917779563e-181.07499383555913e-171
1665.73710680388486e-181.14742136077697e-171
1673.66881974775862e-187.33763949551724e-181
1681.92721223264974e-183.85442446529948e-181
1699.173480123934e-191.83469602478680e-181
1705.0799312621858e-191.01598625243716e-181
1715.49666840435996e-191.09933368087199e-181
1723.36860987149096e-196.73721974298193e-191
1731.51562482778953e-193.03124965557907e-191
1741.03699673771848e-192.07399347543696e-191
1751.00573774369087e-192.01147548738174e-191
1769.88556134672596e-201.97711226934519e-191
1778.06198328374075e-201.61239665674815e-191
1783.36460386354377e-206.72920772708754e-201
1791.36669474994476e-202.73338949988952e-201
1807.21257540233168e-211.44251508046634e-201
1812.71214626866744e-215.42429253733489e-211
1829.07824035514116e-221.81564807102823e-211
1833.92826012831211e-227.85652025662422e-221
1841.28890602551098e-222.57781205102195e-221
1853.93173388011845e-237.86346776023689e-231
1861.27381881558634e-232.54763763117268e-231
1874.73428924244326e-249.46857848488651e-241
1881.74050712048236e-243.48101424096473e-241
1895.43234818385883e-241.08646963677177e-231
1904.37040665714175e-238.74081331428349e-231
1912.30210142941914e-224.60420285883828e-221
1922.18953563241501e-214.37907126483001e-211
1931.89572250623896e-193.79144501247791e-191
1941.88521690660393e-163.77043381320785e-161
1951.9219719249649e-143.8439438499298e-140.99999999999998
1961.01045020935834e-122.02090041871667e-120.99999999999899
1973.76972645864679e-117.53945291729358e-110.999999999962303
1982.55865874322735e-095.1173174864547e-090.999999997441341
1994.37581582106050e-078.75163164212101e-070.999999562418418
2006.91675890738798e-050.0001383351781477600.999930832410926
2010.001634947215779250.003269894431558500.99836505278422
2020.03873247392480210.07746494784960420.961267526075198
2030.02515255763877450.05030511527754910.974847442361225
2040.01658335047201290.03316670094402570.983416649527987
2050.01005632568751200.02011265137502410.989943674312488
2060.01153689937544330.02307379875088650.988463100624557
2070.2273868817221050.4547737634442110.772613118277895


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1780.931937172774869NOK
5% type I error level1850.968586387434555NOK
10% type I error level1880.984293193717278NOK