Multiple Linear Regression - Estimated Regression Equation
I1[t] = + 5.09223733152745 + 0.366890283715879I2[t] + 0.250958877450976I3[t] + 0.268713785619825E1[t] -0.120117396410981E2[t] + 0.0271668030106582E3[t] -0.212280176771546A[t] + 0.0471967180591655Happiness[t] + 0.110270616085803Depression[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)5.092237331527452.8632181.77850.0773070.038654
I20.3668902837158790.0634725.780300
I30.2509588774509760.0502294.99632e-061e-06
E10.2687137856198250.0749913.58330.0004550.000228
E2-0.1201173964109810.05898-2.03660.0434160.021708
E30.02716680301065820.0615980.4410.6598130.329906
A-0.2122801767715460.083969-2.52810.0124830.006241
Happiness0.04719671805916550.1015670.46470.6428160.321408
Depression0.1102706160858030.0752161.46610.1446840.072342


Multiple Linear Regression - Regression Statistics
Multiple R0.746185770527199
R-squared0.556793204137269
Adjusted R-squared0.533618992588891
F-TEST (value)24.0264141446589
F-TEST (DF numerator)8
F-TEST (DF denominator)153
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.49748657128081
Sum Squared Residuals954.328193580378


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12623.96520825431762.03479174568238
22020.8907332037711-0.890733203771068
31921.6626101879212-2.66261018792116
41918.0704899369310.929510063069016
52019.04152810207740.958471897922561
62524.11225491803190.887745081968066
72520.43738649892274.56261350107731
82219.84561325164422.15438674835584
92622.03417339679913.96582660320089
102220.41139463131541.58860536868463
111719.8083707833056-2.80837078330562
122222.5690704314685-0.569070431468473
131920.8234393471561-1.82343934715608
142422.74222734160471.25777265839535
152626.5647281359707-0.564728135970706
162118.97195987778622.02804012221385
171316.2086300873893-3.20863008738929
182627.0957815207233-1.09578152072327
192022.2668291703878-2.26682917038779
202218.75093286379783.24906713620225
211417.588496675924-3.58849667592397
222120.26778537059610.732214629403893
23713.8304577794511-6.83045777945105
242321.61996934329351.38003065670654
251718.9005310455531-1.90053104555306
262522.40992515513532.59007484486468
272522.96084341372112.03915658627891
281916.26157708165082.73842291834916
292016.58100628918013.41899371081986
302321.18803068522091.81196931477907
312223.7418370641793-1.74183706417929
322221.9764041156150.0235958843850454
332117.71631996714473.28368003285535
341517.5210747232382-2.52107472323815
352015.88048049674314.11951950325689
362221.19418111968490.805818880315064
371816.97084759871711.02915240128293
382020.7118960955753-0.711896095575301
392827.33831057430860.661689425691444
402223.7175483496274-1.71754834962743
411821.2395577449253-3.2395577449253
422320.7537358103192.24626418968102
432021.1609804252111-1.16098042521113
442524.57444385736940.425556142630585
452621.8429110709924.15708892900799
461514.17391556185290.826084438147061
471717.3789998488856-0.378999848885643
482315.05450571384537.94549428615471
492122.302872904222-1.30287290422197
501315.90643128166-2.90643128165997
511819.8565600472041-1.85656004720413
521919.2406040928175-0.240604092817517
532222.2434819675067-0.243481967506741
541617.4288545185238-1.42885451852378
552422.81186175906121.1881382409388
561819.8691698826436-1.86916988264355
572021.5334075872987-1.53340758729872
582420.37843090077843.62156909922164
591417.9127727298442-3.91277272984424
602220.35875209513031.64124790486965
612418.53371419715915.46628580284089
621818.3605318118787-0.360531811878674
632124.3554796199263-3.35547961992625
642321.87249765806951.12750234193046
651718.5748363425418-1.57483634254184
662222.3207678272668-0.320767827266801
672425.2590171242802-1.25901712428022
682122.7688028102993-1.76880281029932
692222.1182440054422-0.118244005442171
701617.2486182575932-1.24861825759321
712125.1796195495478-4.1796195495478
722324.263002981095-1.26300298109499
732219.49295451462452.50704548537549
742422.36126613149311.6387338685069
752424.4849618845725-0.484961884572511
761618.1224349377702-2.12243493777017
771617.6683158387533-1.66831583875332
782123.3888335243808-2.38883352438084
792626.0964437669551-0.0964437669551022
801516.9225919951072-1.92259199510716
812523.23950995373171.7604900462683
821817.8566697412780.143330258722003
832320.5251834665882.47481653341201
842021.3437552958354-1.34375529583537
851720.7488067016638-3.74880670166379
862524.98269601518860.0173039848114381
872422.60293232756751.39706767243252
881714.56843102392662.43156897607343
891918.86796979378010.13203020621986
902020.9443489142159-0.944348914215891
911516.7042331594518-1.70423315945181
922724.88750565792782.11249434207225
932219.64554918649542.35445081350461
942323.0848870581306-0.0848870581306487
951620.409841069822-4.40984106982195
961920.9291034359179-1.92910343591788
972520.76692871821794.23307128178214
981919.4670586309858-0.467058630985763
991919.3686432851059-0.368643285105885
1002625.08432350170530.915676498294669
1012118.72333610667242.27666389332759
1022020.2304187335718-0.230418733571775
1032419.99931286226044.0006871377396
1042223.6689828959576-1.66898289595756
1052021.5986899184348-1.59868991843481
1061819.6197927323201-1.61979273232014
1071816.85090352663731.14909647336267
1082421.61759559514652.38240440485349
1092421.47240793079722.52759206920277
1102224.5959171343994-2.59591713439942
1112320.09370531955932.90629468044066
1122220.12248645028131.87751354971866
1132018.08797246196041.91202753803959
1141820.0251124161435-2.02511241614353
1152524.82700729206280.172992707937245
1161818.3695320346283-0.369532034628311
1171617.8258933172296-1.82589331722957
1182020.0862096749033-0.0862096749032655
1191918.38779821408470.612201785915303
1201516.0293200776177-1.02932007761771
1211919.2553106030243-0.255310603024328
1221922.2351639569958-3.23516395699583
1231617.5888813904541-1.58888139045409
1241717.6459508068338-0.645950806833832
1252823.53547098649014.46452901350994
1262322.96509251635110.034907483648874
1272523.54223201832511.45776798167485
1282018.85029393841371.14970606158625
1291720.3837873569714-3.38378735697139
1302322.9561530754050.0438469245949504
1311620.0051078044499-4.00510780444994
1322324.0912999293888-1.09129992938878
1331116.0946841948914-5.09468419489143
1341820.6496907716558-2.64969077165583
1352423.25622352390850.743776476091495
1362319.19117839648363.80882160351644
1372121.8587297673922-0.858729767392159
1381619.7634722283455-3.76347222834555
1392425.1831734275095-1.1831734275095
1402321.68729330656141.31270669343861
1411815.9251666795712.07483332042904
1422020.9163477430383-0.916347743038341
143918.9289624035991-9.92896240359914
1442420.51217933580883.48782066419123
1452524.94402707245170.0559729275483377
1462018.47191614261431.52808385738571
1472119.21616225585551.7838377441445
1482522.97367674332222.02632325667784
1492222.3733756902121-0.373375690212053
1502121.5007175807685-0.500717580768493
1512120.4274628797640.572537120235958
1522220.6380607227651.361939277235
1532723.40549302975293.59450697024707
1542421.68225800025722.31774199974279
1552424.4763142155386-0.476314215538606
1562120.67094526907450.329054730925513
1571820.9721577637822-2.97215776378223
1581616.3274460588286-0.327446058828595
1592219.61379482656042.38620517343955
1602019.88118761802250.118812381977475
1611819.64358720748-1.64358720748002
1622021.4327296641483-1.43272966414833


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.8759520124470420.2480959751059160.124047987552958
130.9068589791202030.1862820417595930.0931410208797966
140.8494317422959810.3011365154080390.150568257704019
150.7891508851385350.421698229722930.210849114861465
160.7115109950188750.5769780099622510.288489004981125
170.6405667903315140.7188664193369720.359433209668486
180.566957924179340.8660841516413210.43304207582066
190.4976991572873630.9953983145747270.502300842712637
200.4798731556979530.9597463113959050.520126844302047
210.4513724808015880.9027449616031770.548627519198412
220.3695815912382010.7391631824764020.630418408761799
230.5041462319197630.9917075361604730.495853768080237
240.4502912249251570.9005824498503150.549708775074843
250.385999531554180.771999063108360.61400046844582
260.429354731656120.858709463312240.57064526834388
270.3717843486829710.7435686973659430.628215651317029
280.5761359954165370.8477280091669260.423864004583463
290.6255625549034160.7488748901931680.374437445096584
300.5836120366328710.8327759267342570.416387963367129
310.5464377956448540.9071244087102910.453562204355146
320.5036107052011010.9927785895977980.496389294798899
330.4710887935921110.9421775871842230.528911206407889
340.5310221255314620.9379557489370750.468977874468538
350.6910655048379130.6178689903241730.308934495162087
360.6444888318646880.7110223362706250.355511168135312
370.5924323323996290.8151353352007410.407567667600371
380.5357560891436140.9284878217127720.464243910856386
390.4780570478545930.9561140957091870.521942952145407
400.4496213425008350.899242685001670.550378657499165
410.4532481422867820.9064962845735640.546751857713218
420.4249047409543940.8498094819087880.575095259045606
430.377329830228420.7546596604568410.62267016977158
440.3474957653396460.6949915306792910.652504234660354
450.4085031943116520.8170063886233050.591496805688348
460.3577681781673530.7155363563347050.642231821832647
470.3173933279028260.6347866558056520.682606672097174
480.7410778851974270.5178442296051460.258922114802573
490.7283779795754610.5432440408490780.271622020424539
500.7600889688345330.4798220623309340.239911031165467
510.7428937940118330.5142124119763340.257106205988167
520.7016663914728090.5966672170543820.298333608527191
530.6842287658979670.6315424682040660.315771234102033
540.6569661181626810.6860677636746380.343033881837319
550.6164338648670310.7671322702659380.383566135132969
560.6083887605355770.7832224789288450.391611239464423
570.5838375319455050.832324936108990.416162468054495
580.6865130780393990.6269738439212020.313486921960601
590.7402877214540980.5194245570918040.259712278545902
600.7168175531908750.566364893618250.283182446809125
610.8194371410767360.3611257178465290.180562858923264
620.7879016105527590.4241967788944820.212098389447241
630.837675028696750.3246499426065010.16232497130325
640.8108226635963720.3783546728072560.189177336403628
650.8354593340920260.3290813318159480.164540665907974
660.8058604119124720.3882791761750560.194139588087528
670.8018572687801640.3962854624396730.198142731219836
680.7865815045367470.4268369909265060.213418495463253
690.7505268380637650.4989463238724710.249473161936235
700.7215762638023620.5568474723952750.278423736197638
710.7985022839813050.4029954320373910.201497716018695
720.7780529019213560.4438941961572880.221947098078644
730.7765829795962530.4468340408074940.223417020403747
740.7526073806050930.4947852387898140.247392619394907
750.7156250516443640.5687498967112730.284374948355636
760.7395892573026120.5208214853947760.260410742697388
770.7226190526129680.5547618947740640.277380947387032
780.7286600269438340.5426799461123320.271339973056166
790.6903105772307980.6193788455384040.309689422769202
800.6753726605924850.649254678815030.324627339407515
810.6447012012008820.7105975975982350.355298798799118
820.6052287669415770.7895424661168460.394771233058423
830.6080498903326170.7839002193347650.391950109667382
840.5787891644675650.842421671064870.421210835532435
850.6396708649095760.7206582701808490.360329135090424
860.5953896462252020.8092207075495950.404610353774798
870.5624206942982420.8751586114035150.437579305701758
880.5763998736351730.8472002527296530.423600126364827
890.5310212305095930.9379575389808150.468978769490407
900.5132037310426680.9735925379146640.486796268957332
910.4867722459206860.9735444918413720.513227754079314
920.4630583830799330.9261167661598660.536941616920067
930.4520720790222260.9041441580444530.547927920977774
940.4088316625109320.8176633250218650.591168337489068
950.5166804485124620.9666391029750760.483319551487538
960.5014784719809920.9970430560380150.498521528019008
970.6028485763187060.7943028473625890.397151423681294
980.5575767752613630.8848464494772740.442423224738637
990.5124936935756950.9750126128486110.487506306424305
1000.4671455444798560.9342910889597120.532854455520144
1010.4549054841609950.909810968321990.545094515839005
1020.4099008231756610.8198016463513220.590099176824339
1030.5033875688105730.9932248623788540.496612431189427
1040.4920547193989730.9841094387979470.507945280601027
1050.4602924090088030.9205848180176060.539707590991197
1060.4303587194720780.8607174389441560.569641280527922
1070.3964076381897830.7928152763795660.603592361810217
1080.4043933914917360.8087867829834720.595606608508264
1090.3846149099301370.7692298198602740.615385090069863
1100.3715332281326370.7430664562652740.628466771867363
1110.3890058387011390.7780116774022780.610994161298861
1120.3777458128905980.7554916257811950.622254187109402
1130.3721745504761610.7443491009523220.627825449523839
1140.3412749872110750.682549974422150.658725012788925
1150.2972014842221290.5944029684442580.702798515777871
1160.2558983730118380.5117967460236760.744101626988162
1170.2253686901264350.4507373802528710.774631309873565
1180.1869155705588810.3738311411177620.813084429441119
1190.1592022511081720.3184045022163440.840797748891828
1200.1377750123198810.2755500246397620.862224987680119
1210.110125962115360.220251924230720.88987403788464
1220.1183408061058650.236681612211730.881659193894135
1230.09643259685108380.1928651937021680.903567403148916
1240.07572526773459110.1514505354691820.924274732265409
1250.1380345811929130.2760691623858250.861965418807087
1260.112609698409510.225219396819020.88739030159049
1270.09127362678262990.182547253565260.90872637321737
1280.07053840519001890.1410768103800380.929461594809981
1290.0831392827386060.1662785654772120.916860717261394
1300.06216698784574150.1243339756914830.937833012154259
1310.08986012813209240.1797202562641850.910139871867908
1320.06945588660418060.1389117732083610.930544113395819
1330.1995593329359570.3991186658719130.800440667064043
1340.202338177879570.404676355759140.79766182212043
1350.182656067964030.365312135928060.81734393203597
1360.1547493868952520.3094987737905040.845250613104748
1370.1297524414526690.2595048829053380.870247558547331
1380.1549631018598340.3099262037196690.845036898140166
1390.1152131350114540.2304262700229090.884786864988546
1400.08478463102619210.1695692620523840.915215368973808
1410.06079062384844010.121581247696880.93920937615156
1420.05420735641360850.1084147128272170.945792643586392
1430.8989860349950180.2020279300099650.101013965004982
1440.995262859645070.009474280709860030.00473714035493001
1450.9913990593954070.01720188120918650.00860094060459324
1460.9799748934383270.04005021312334640.0200251065616732
1470.9582825489355910.08343490212881730.0417174510644087
1480.920560044226760.158879911546480.0794399557732401
1490.8512442649054880.2975114701890250.148755735094512
1500.7659217924589890.4681564150820220.234078207541011


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.00719424460431655OK
5% type I error level30.0215827338129496OK
10% type I error level40.0287769784172662OK