Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 2.97800660075982 -0.0178884775131215X[t] + 1.13770027938383Y1[t] -0.189411036310105Y2[t] + 0.0135050512884166Y3[t] -0.0350137447939528Y4[t] -0.00610584212118887M1[t] -0.0165912030097572M2[t] -0.0290877279644277M3[t] -0.0262203834456709M4[t] -0.0363526671664465M5[t] -0.0528874969185614M6[t] -0.0144954812421030M7[t] -0.0228599371456861M8[t] -0.0554478823797208M9[t] -0.0148607415103697M10[t] -0.0222110183577529M11[t] + 0.00667066163419205t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2.978006600759823.5397720.84130.4011750.200588
X-0.01788847751312150.02285-0.78290.4346310.217316
Y11.137700279383830.07140615.932900
Y2-0.1894110363101050.109253-1.73370.0844990.042249
Y30.01350505128841660.1086970.12420.9012450.450622
Y4-0.03501374479395280.075492-0.46380.6432840.321642
M1-0.006105842121188870.12356-0.04940.9606370.480318
M2-0.01659120300975720.123516-0.13430.893280.44664
M3-0.02908772796442770.123525-0.23550.8140750.407037
M4-0.02622038344567090.123576-0.21220.832180.41609
M5-0.03635266716644650.125872-0.28880.7730250.386513
M6-0.05288749691856140.126127-0.41930.6754290.337715
M7-0.01449548124210300.126396-0.11470.908810.454405
M8-0.02285993714568610.126652-0.18050.8569450.428473
M9-0.05544788237972080.127066-0.43640.6630330.331516
M10-0.01486074151036970.125978-0.1180.9062140.453107
M11-0.02221101835775290.125466-0.1770.8596640.429832
t0.006670661634192050.008750.76240.4467350.223367


Multiple Linear Regression - Regression Statistics
Multiple R0.934225822739988
R-squared0.872777887874208
Adjusted R-squared0.862071076457681
F-TEST (value)81.5161352825347
F-TEST (DF numerator)17
F-TEST (DF denominator)202
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.375339855393874
Sum Squared Residuals28.4577614235130


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
13.222.741391720205310.478608279794694
23.623.18207838995490.437921610045099
33.823.589132994424730.230867005575270
43.543.76402745148004-0.224027451480041
52.533.38868065243283-0.858680652432829
62.222.26252556588761-0.0425255658876074
72.852.126477901186370.72352209881363
82.782.89104990767199-0.111049907671993
92.282.68482003372321-0.404820033723214
102.262.181538130263880.0784618697361195
112.712.210128689543250.499871310456749
122.772.739729065967620.0302709340323820
132.772.736980011772690.0330199882273122
142.642.72678935056406-0.0867893505640593
152.562.55632772109240.00367227890760273
162.072.49558346717600-0.425583467176004
172.321.930157456915540.389842543084463
182.162.28847921489648-0.128479214896478
192.232.098551865129070.131448134870930
202.42.225547006245990.174452993754008
212.842.367076905443750.472923094556254
222.772.87495972545018-0.104959725450181
232.932.705778588033190.224221411966807
242.912.91026364595576-0.000263645955755940
252.692.83247305401538-0.142473054015377
262.382.57603119785661-0.19603119785661
272.582.247949832468630.332050167531370
283.192.536107936112970.653892063887032
292.823.18870003964114-0.368700039641137
302.722.648745916140590.0712540838594077
312.532.64956713352343-0.119567133523431
322.72.422507288749780.277492711250216
332.422.63580288223772-0.215802882237722
342.52.322507058567800.177492941432202
352.312.46588278734546-0.155882787345463
362.412.235826302860820.174173697139178
372.562.397033499856510.162966500143491
382.762.537776831799070.222223168200931
392.712.73908248554853-0.0290824855485330
402.442.64522226267889-0.205222262678888
412.462.330767979004890.129232020995106
422.122.37459886049598-0.254598860495979
431.992.02537069773044-0.0353706977304384
441.861.94989943160672-0.0898994316067203
451.881.793623706322040.0863762936779588
461.821.88588603143684-0.065886031436839
471.741.80879691788489-0.0687969178848873
481.711.74674949579190-0.0367494957919047
491.381.72503676410371-0.345036764103705
501.271.36858335408834-0.0985833540883417
511.191.29356781130628-0.103567811306280
521.281.224152211267340.0558477887326618
531.191.33399469535989-0.14399469535989
541.221.218194703161650.00180529683835325
551.471.318451936321200.151548063678805
561.461.58934534140973-0.129345341409733
571.961.506465836757320.453534163242678
581.882.09996102352448-0.219961023524484
592.031.892149446834980.137850553165023
602.042.09784208496964-0.0578420849696427
611.92.06099612757861-0.160996127578607
621.81.89904728837286-0.0990472883728599
631.921.799063083239890.120936916760107
641.921.96182538192159-0.0418253819215934
651.971.937397006868800.0326029931312032
662.461.987750985602760.472249014397242
672.362.57124805536677-0.211248055366770
682.532.360070382428840.169929617571160
692.312.55137003784689-0.241370037846885
701.982.28152703287358-0.301527032873581
711.461.94214090014250-0.482140900142502
721.261.42226754243089-0.162267542430894
731.581.293454706375250.286545293624747
741.741.688962821892500.0510371781074968
751.891.811119369932820.0788806300671848
761.851.97054216980349-0.120542169803493
771.621.88232844321581-0.262328443215810
781.31.61300436306693-0.313004363066929
791.421.328197530052820.0918024699471758
801.151.51656714567021-0.366567145670212
810.421.16268415941853-0.742684159418527
820.740.4183428737459070.321657126254093
831.020.8996274569595860.120372543040414
841.511.168160229700470.341839770299528
851.861.699467050553980.160532949446024
861.591.99182420956737-0.401824209567368
871.031.60755018694242-0.577550186942424
880.441.01332050619213-0.573320506192129
890.820.4269958773256780.393004122674322
900.860.961312361418113-0.101312361418114
910.580.991546572930725-0.411546572930725
920.590.687721440148176-0.0977214401481764
930.950.7134512285388360.236548771461164
940.981.14889427509444-0.168894275094444
951.231.113363507738450.116636492261552
961.171.39151150022801-0.221511500228007
970.841.25352866080541-0.413528660805411
980.740.879019143254701-0.139019143254701
990.650.803420915945821-0.153420915945821
1000.910.7199957673424460.190004232657554
1011.191.034220698562800.155779301437205
1021.31.283429724835970.0165702751640306
1031.531.407266893078460.122733106921544
1041.941.641086789787560.298913210212437
1051.792.02974378948319-0.239743789483185
1061.951.817209588553140.132790411446861
1072.262.015513344456960.244486655543043
1082.042.34681725668687-0.306817256686865
1092.162.045783463404530.114216536595467
1102.752.218747592396820.531252407603184
1112.792.84761019738601-0.0576101973860074
1122.882.785916551290130.0940834487098701
1133.362.868515909521390.491484090478607
1142.973.36221643160897-0.392216431608967
1153.12.868895911852650.231104088147351
1162.493.08693810239714-0.596938102397144
1172.22.31853779839796-0.11853779839796
1182.252.150714639404680.0992853605953172
1192.092.24011513182490-0.150115131824905
1202.792.071681113983540.718318886016456
1213.142.89367150366770.246328496332297
1222.933.13903074707556-0.209030747075564
1232.652.83231661093700-0.182316610936996
1242.672.543292003082770.126707996917227
1252.262.59158436654568-0.331584366545684
1262.352.113257487448850.236742512551150
1272.132.34486796885664-0.214867968856639
1282.182.066018078428140.113981921571859
1292.92.148860783513260.751139216486745
1302.632.99430334378881-0.364303343788807
1312.672.547713896909920.122286103090076
1321.812.66690673555841-0.856906735558415
1331.331.64546122224415-0.315461222244153
1340.881.26486009775551-0.384860097755509
1351.280.8124495779821760.467550422017824
1361.261.38235436262994-0.122354362629939
1371.261.28215940609639-0.0221594060963866
1381.291.295452816626-0.00545281662599885
1391.11.35321551236957-0.253215512369566
1401.371.128587761072510.241412238927489
1411.211.43550971483600-0.225509714836002
1421.741.244189272994470.495810727005526
1431.761.88530669927174-0.125306699271741
1441.481.82315116855518-0.343151168555181
1451.041.49982078345391-0.459820783453905
1461.621.019432781214570.600567218785426
1471.491.74696570340259-0.256965703402591
1481.791.497239354897250.292760645102752
1491.81.87937253330012-0.079372533300124
1501.581.79842073293240-0.218420732932396
1511.861.590954301868680.269045698131319
1521.741.93017370213312-0.190173702133123
1531.591.70600950285506-0.116009502855064
1541.261.61145948276974-0.351459482769735
1551.131.24695943285554-0.116959432855543
1561.921.183677371435380.736322628564624
1572.612.104866545673210.505133454326791
1582.262.73012956986139-0.470129569861393
1592.412.201691532287100.208308467712897
1602.262.42089183130139-0.160891831301388
1612.032.18411071674800-0.154110716748005
1622.861.949901164935530.910098835064474
1632.552.96838640206848-0.418386402068475
1642.272.45536256547284-0.185362565472843
1652.262.179924740017090.0800752599829052
1662.572.23022611256130.339773887438698
1673.072.584045149840320.485954850159681
1682.763.11305102103304-0.353051021033036
1692.512.66181570037279-0.151815700372787
1702.872.426402769535360.443597230464644
1713.142.84149754556370.2985024544363
1723.113.093926956640040.0160730433599578
1733.163.015230905527910.144769094472091
1742.473.05360895493659-0.583608954936594
1752.572.287173634018630.282826365981371
1762.892.528091452147210.361908547852793
1772.632.83086143843654-0.200861438436539
1782.382.53648253920985-0.156482539209849
1791.692.28176764025979-0.591767640259792
1801.961.551117783880120.408882216119881
1812.191.988127213699800.201872786300197
1821.872.18712215870421-0.317122158704212
1831.61.79789581988266-0.197895819882660
1841.631.545574494166620.0844255058333843
1851.221.60964353929644-0.389643539296437
1861.211.126253721271470.0837462787285282
1871.491.242090240054510.247909759945489
1881.641.548892607749690.091107392250313
1891.661.653027012991910.00697298700808624
1901.771.693392174191380.0766078258086229
1911.821.802715582632540.0172844173674633
1921.781.86087625415493-0.080876254154925
1931.281.80367009592029-0.523670095920292
1941.291.230038895809550.0599611041904451
1951.371.322638120892800.0473618791072038
1961.121.41415721542959-0.294157215429588
1971.511.125181867999480.384818132000524
1982.241.596370748066030.643629251933967
1992.942.388329267257690.551670732742306
2003.093.046254083992390.0437459160076078
2013.463.051029748351330.408970251648672
2023.643.455041175718240.184958824281755
2034.393.529015860919340.860984139080655
2044.154.36072394140915-0.210723941409154
2055.213.91955861053381.29044138946620
2065.85.167413475041490.632586524958512
2075.915.595398166158820.314601833841176
2085.395.62852741047812-0.238527410478118
2095.464.970957905637220.489042094362779
2104.725.11647624666809-0.396476246668091
2113.144.27940817633388-1.13940817633388
2122.632.63588691288794-0.00588691288793656
2132.322.311200680829360.00879931917063523
2141.932.10336551985128-0.173365519851277
2150.621.75897896654663-1.13897896654663
2160.60.3796474853982680.220352514601732
217-0.370.596863265762979-0.966863265762979
218-1.1-0.52329067474488-0.57670932525512
219-1.68-1.13567767539438-0.544322324605621
220-0.78-1.672657333890740.892657333890744


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.9215164394356970.1569671211286050.0784835605643025
220.8524445963839780.2951108072320430.147555403616022
230.7638188883912390.4723622232175220.236181111608761
240.6648382273128050.670323545374390.335161772687195
250.5560161020406320.8879677959187360.443983897959368
260.4469332710316820.8938665420633650.553066728968318
270.3830521469156840.7661042938313670.616947853084316
280.5410721264693440.9178557470613110.458927873530656
290.454650503246280.909301006492560.54534949675372
300.5351370933468490.9297258133063020.464862906653151
310.4764348973778740.952869794755750.523565102622126
320.4068943837417420.8137887674834840.593105616258258
330.3895929825980070.7791859651960140.610407017401993
340.3193338479888010.6386676959776020.680666152011199
350.3112050211029670.6224100422059340.688794978897033
360.2525263134188900.5050526268377810.74747368658111
370.2071384890905540.4142769781811080.792861510909446
380.1777349412384190.3554698824768370.822265058761581
390.1360317710903260.2720635421806520.863968228909674
400.1045421968906380.2090843937812760.895457803109362
410.0982374996148130.1964749992296260.901762500385187
420.07966160120298950.1593232024059790.92033839879701
430.06559194330381670.1311838866076330.934408056696183
440.0504320915403270.1008641830806540.949567908459673
450.03641588675994240.07283177351988490.963584113240058
460.02772027608789040.05544055217578080.97227972391211
470.02106573450725210.04213146901450430.978934265492748
480.01448362932579900.02896725865159790.9855163706742
490.01371033376896620.02742066753793240.986289666231034
500.00929482015599450.0185896403119890.990705179844006
510.006384549174631780.01276909834926360.993615450825368
520.004501712030560420.009003424061120840.99549828796944
530.003251412454109150.006502824908218290.99674858754589
540.003790614383885020.007581228767770040.996209385616115
550.003829198814357620.007658397628715240.996170801185642
560.002688948443032670.005377896886065330.997311051556967
570.007644800084005110.01528960016801020.992355199915995
580.005218457693881090.01043691538776220.994781542306119
590.004196014121629660.008392028243259320.99580398587837
600.002950333258727950.00590066651745590.997049666741272
610.001951986575899990.003903973151799980.9980480134241
620.001269187543751140.002538375087502270.99873081245625
630.0008754210287566890.001750842057513380.999124578971243
640.0005609568883481780.001121913776696360.999439043111652
650.0004748955408007090.0009497910816014170.9995251044592
660.001370917266492960.002741834532985910.998629082733507
670.0009517306196793320.001903461239358660.99904826938032
680.0009047335951720340.001809467190344070.999095266404828
690.0006398618679944560.001279723735988910.999360138132006
700.0005440855720990230.001088171144198050.9994559144279
710.0009329090541040840.001865818108208170.999067090945896
720.0007303130436532420.001460626087306480.999269686956347
730.0005827096671608930.001165419334321790.99941729033284
740.0003859841844469860.0007719683688939720.999614015815553
750.0002630201630366270.0005260403260732540.999736979836963
760.0001720546061894360.0003441092123788730.99982794539381
770.0001144310628478160.0002288621256956320.999885568937152
788.6933330786413e-050.0001738666615728260.999913066669214
795.56724362407067e-050.0001113448724814130.99994432756376
805.57077159013673e-050.0001114154318027350.999944292284099
810.0002534557006760300.0005069114013520590.999746544299324
820.0002339372226486940.0004678744452973890.999766062777351
830.0001590904494991790.0003181808989983580.9998409095505
840.0001654727705698340.0003309455411396670.99983452722943
850.0001506157036016030.0003012314072032050.999849384296398
860.0001139466116501220.0002278932233002440.99988605338835
870.0001462523806559340.0002925047613118680.999853747619344
880.0002100233165174810.0004200466330349620.999789976683483
890.0002322433039133730.0004644866078267460.999767756696087
900.0001685832119620290.0003371664239240590.999831416788038
910.0001979737238078610.0003959474476157220.999802026276192
920.0001346477506221710.0002692955012443420.999865352249378
930.0001159184656094420.0002318369312188850.99988408153439
947.90556784341398e-050.0001581113568682800.999920944321566
956.08835880740868e-050.0001217671761481740.999939116411926
964.0065436854982e-058.0130873709964e-050.999959934563145
973.60494659249742e-057.20989318499484e-050.999963950534075
982.3206797962799e-054.6413595925598e-050.999976793202037
991.57026138666035e-053.14052277332070e-050.999984297386133
1001.23292948607548e-052.46585897215097e-050.99998767070514
1019.99619765774281e-061.99923953154856e-050.999990003802342
1026.9739809762315e-061.3947961952463e-050.999993026019024
1036.03072971240190e-061.20614594248038e-050.999993969270288
1049.40780404759356e-061.88156080951871e-050.999990592195952
1056.1599594211869e-061.23199188423738e-050.999993840040579
1066.1447604175878e-061.22895208351756e-050.999993855239582
1076.35291396091382e-061.27058279218276e-050.99999364708604
1084.31425941105944e-068.62851882211887e-060.99999568574059
1093.69388416991716e-067.38776833983431e-060.99999630611583
1101.05306275721846e-052.10612551443693e-050.999989469372428
1116.67654774756987e-061.33530954951397e-050.999993323452252
1125.79838336603088e-061.15967667320618e-050.999994201616634
1131.16644214710618e-052.33288429421235e-050.99998833557853
1141.17507956507553e-052.35015913015106e-050.99998824920435
1159.03579320194948e-061.80715864038990e-050.999990964206798
1161.99354542363491e-053.98709084726982e-050.999980064545764
1171.41085383065957e-052.82170766131914e-050.999985891461693
1188.89770255283898e-061.77954051056780e-050.999991102297447
1196.79902135635606e-061.35980427127121e-050.999993200978644
1202.53573775597269e-055.07147551194538e-050.99997464262244
1212.14161226822689e-054.28322453645379e-050.999978583877318
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1239.7257458622417e-061.94514917244834e-050.999990274254138
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1256.35210793996486e-061.27042158799297e-050.99999364789206
1264.70360975161386e-069.40721950322772e-060.999995296390248
1273.74876761022917e-067.49753522045833e-060.99999625123239
1282.37796336719768e-064.75592673439535e-060.999997622036633
1291.09213489944080e-052.18426979888159e-050.999989078651006
1309.45731079337781e-061.89146215867556e-050.999990542689207
1316.61200869114593e-061.32240173822919e-050.999993387991309
1323.17653797937762e-056.35307595875524e-050.999968234620206
1333.18902509196824e-056.37805018393649e-050.99996810974908
1343.74970222274626e-057.49940444549252e-050.999962502977773
1354.27915914321057e-058.55831828642114e-050.999957208408568
1362.95373427798412e-055.90746855596825e-050.99997046265722
1371.89417402507514e-053.78834805015028e-050.99998105825975
1381.20421868055271e-052.40843736110542e-050.999987957813194
1398.81429359582e-061.762858719164e-050.999991185706404
1406.82366976053194e-061.36473395210639e-050.99999317633024
1414.70914384724795e-069.4182876944959e-060.999995290856153
1427.10039255040312e-061.42007851008062e-050.99999289960745
1434.37773045012308e-068.75546090024615e-060.99999562226955
1443.85816465018212e-067.71632930036423e-060.99999614183535
1454.64627205320642e-069.29254410641285e-060.999995353727947
1468.56662386570902e-061.71332477314180e-050.999991433376134
1476.19387655397951e-061.23877531079590e-050.999993806123446
1484.8698349098634e-069.7396698197268e-060.99999513016509
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1502.23619777186206e-064.47239554372412e-060.999997763802228
1511.78890118512571e-063.57780237025142e-060.999998211098815
1521.16291213823851e-062.32582427647702e-060.999998837087862
1537.07457187098803e-071.41491437419761e-060.999999292542813
1546.64672149065831e-071.32934429813166e-060.999999335327851
1554.10415738636009e-078.20831477272017e-070.999999589584261
1561.29063218720680e-062.58126437441359e-060.999998709367813
1571.91095198171495e-063.8219039634299e-060.999998089048018
1582.20795022584366e-064.41590045168731e-060.999997792049774
1591.65417922893378e-063.30835845786756e-060.999998345820771
1601.14778542970548e-062.29557085941096e-060.99999885221457
1617.40916722146151e-071.48183344429230e-060.999999259083278
1626.31644521155898e-061.26328904231180e-050.999993683554788
1635.92721258359694e-061.18544251671939e-050.999994072787416
1644.16259948584106e-068.32519897168211e-060.999995837400514
1652.48203726264974e-064.96407452529947e-060.999997517962737
1662.00490227793163e-064.00980455586327e-060.999997995097722
1673.51331782180361e-067.02663564360722e-060.999996486682178
1683.22295424983807e-066.44590849967613e-060.99999677704575
1692.06332843977796e-064.12665687955591e-060.99999793667156
1702.08198229800661e-064.16396459601322e-060.999997918017702
1711.99498241834682e-063.98996483669364e-060.999998005017582
1721.08591247580098e-062.17182495160196e-060.999998914087524
1736.2704754067323e-071.25409508134646e-060.99999937295246
1741.26936847799313e-062.53873695598626e-060.999998730631522
1759.74576598902521e-071.94915319780504e-060.9999990254234
1768.84448116827963e-071.76889623365593e-060.999999115551883
1775.52677853914556e-071.10535570782911e-060.999999447322146
1783.20086505137867e-076.40173010275734e-070.999999679913495
1794.47799896486332e-078.95599792972664e-070.999999552200104
1804.80371783067018e-079.60743566134036e-070.999999519628217
1814.00615889135638e-078.01231778271276e-070.999999599384111
1822.68256079395785e-075.3651215879157e-070.99999973174392
1831.45140203042927e-072.90280406085853e-070.999999854859797
1846.7136633768207e-081.34273267536414e-070.999999932863366
1851.07626588205392e-072.15253176410783e-070.999999892373412
1865.19802465906873e-081.03960493181375e-070.999999948019753
1873.71027812409579e-087.42055624819157e-080.999999962897219
1881.53876251153675e-083.07752502307351e-080.999999984612375
1891.64704506729820e-083.29409013459641e-080.99999998352955
1901.87805428263500e-083.75610856527000e-080.999999981219457
1911.21013772843429e-082.42027545686857e-080.999999987898623
1921.60445964719372e-083.20891929438745e-080.999999983955403
1932.46749181323483e-074.93498362646966e-070.999999753250819
1941.59037006745192e-073.18074013490383e-070.999999840962993
1955.77384715309238e-081.15476943061848e-070.999999942261528
1962.56294680177683e-075.12589360355366e-070.99999974370532
1979.43311907783696e-061.88662381556739e-050.999990566880922
1980.0004126375363595430.0008252750727190860.99958736246364
1990.0002472761709700420.0004945523419400840.99975272382903


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1460.815642458100559NOK
5% type I error level1530.854748603351955NOK
10% type I error level1550.865921787709497NOK