Multiple Linear Regression - Estimated Regression Equation
X5[t] = + 16.1343805179710 -0.0706755178434469Y[t] + 0.218173666171411X1[t] -0.148953465580740X2[t] -0.255161534021277X3[t] + 0.422756959732833X4[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)16.13438051797102.0016118.060700
Y-0.07067551784344690.062922-1.12320.2631030.131551
X10.2181736661714110.1126221.93720.054560.02728
X2-0.1489534655807400.104267-1.42860.1551640.077582
X3-0.2551615340212770.130412-1.95660.0522180.026109
X40.4227569597328330.0756165.590800


Multiple Linear Regression - Regression Statistics
Multiple R0.47156352837492
R-squared0.222372161293404
Adjusted R-squared0.196959486825868
F-TEST (value)8.75044307428092
F-TEST (DF numerator)5
F-TEST (DF denominator)153
p-value2.54750247341562e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.49936004674520
Sum Squared Residuals1873.56467272376


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12622.93833992007253.06166007992751
22324.2523603618558-1.25236036185575
32524.35114631660300.64885368339697
42321.98186049779211.01813950220793
51921.8243682471222-2.82436824712216
62922.91238968319456.08761031680554
72524.81239655866370.187603441336281
82122.6816276385943-1.68162763859431
92221.96629584587180.0337041541281613
102522.48817740620882.51182259379117
112420.23019657633823.76980342366183
121819.7297104221437-1.72971042214370
132218.40548387133463.59451612866544
141520.7135896185936-5.71358961859356
152223.5177877585016-1.51778775850159
162824.31845876152553.68154123847446
172022.2773757565055-2.27737575650545
181219.0584541223919-7.05845412239185
192421.44857295157412.55142704842588
202021.3822950759724-1.38229507597240
212123.2872146750446-2.28721467504459
222020.6121484697385-0.612148469738471
232119.24369141331811.75630858668185
242321.07666913843721.92333086156276
252821.96681480792936.0331851920707
262421.94161584579972.05838415420033
272423.48808596212680.511914037873207
282420.4132910149843.58670898501601
292322.00953989906250.990460100937506
302322.72974856762010.270251432379886
312924.31727835040894.68272164959114
322422.08620525888731.91379474111272
331824.9997091636193-6.99970916361932
342526.0675322875889-1.06753228758892
352122.6367209824318-1.63672098243182
362626.7519440436211-0.75194404362108
372225.1676432351877-3.16764323518775
382222.8299965031316-0.829996503131629
392222.5849420248483-0.584942024848278
402325.6719560730761-2.67195607307607
413022.89812505929837.10187494070167
422322.73020378995680.269796210043192
431718.6869610388814-1.68696103888138
442323.8063205840977-0.80632058409767
452324.3634608478922-1.36346084789218
462522.46769054547452.5323094545255
472420.74796290434963.25203709565035
482427.5131920726333-3.51319207263331
492323.0067172964068-0.00671729640684679
502123.8138592742707-2.81385927427075
512425.7455923226503-1.74559232265028
522421.8749464875822.12505351241798
532821.52901215833376.4709878416663
541621.0929792851445-5.09297928514446
552019.90545028534740.0945497146525683
562923.45050788871865.54949211128141
572723.92420288104383.07579711895619
582223.2081353553336-1.20813535533363
592824.05082268602153.94917731397848
601620.3584383722737-4.3584383722737
612522.95873135060272.04126864939731
622423.51073408188340.489265918116596
632823.68431745031114.3156825496889
642424.3565643597678-0.356564359767847
652322.72744844467990.272551555320089
663026.97377771978133.02622228021869
672421.30970151475942.69029848524063
682124.1918592625548-3.19185926255483
692523.34643689259711.65356310740295
702524.009924088750.990075911249979
712220.78242221726461.21757778273542
722322.50629290050210.49370709949793
732622.86136010109423.13863989890584
742321.59286631225001.40713368775004
752523.06403285506611.93596714493389
762121.3169856048034-0.316985604803362
772523.68056201011811.31943798988188
782422.1871294271161.81287057288401
792923.60221281888005.39778718112005
802223.6569360828835-1.65693608288352
812723.64418853452993.35581146547012
822619.67835111571726.3216488842828
832221.32297354751950.677026452480496
842422.10031269428951.89968730571047
852723.12822177414303.87177822585704
862421.335857978362.66414202164002
872424.9093164665318-0.909316466531828
882924.47021568817734.5297843118227
892222.2324709996082-0.232470999608159
902120.58657833099990.413421669000073
912420.41147590559873.58852409440132
922421.82827897654382.1717210234562
932321.97396201548651.02603798451355
942022.2966377134128-2.29663771341281
952721.44290136727685.55709863272324
962623.4634376525382.53656234746198
972521.93031195363433.06968804636567
982120.05584352642020.944156473579804
992120.79116162456140.208838375438651
1001920.3931937376004-1.3931937376004
1012121.6280730192171-0.628073019217087
1022121.3154348573464-0.315434857346426
1031619.7578411650546-3.75784116505456
1042220.69958935662581.30041064337417
1052921.82831066702727.17168933297281
1061521.6944964222482-6.69449642224818
1071720.7295438538645-3.72954385386453
1081519.9461029274324-4.94610292743238
1092121.6814981544617-0.681498154461726
1102121.0102716459281-0.0102716459280739
1111919.3060132265193-0.306013226519286
1122418.06528676536965.93471323463043
1132022.3943929417572-2.39439294175716
1141725.2032625710465-8.20326257104646
1152325.0688900877806-2.06889008778061
1162422.41465499358061.58534500641941
1171422.0960104822520-8.09601048225197
1181922.9163958428202-3.91639584282023
1192422.19182122250431.80817877749572
1201320.4043471047833-7.40434710478335
1212225.4130613862999-3.4130613862999
1221621.1581295863886-5.15812958638857
1231923.3107490527713-4.31074905277131
1242522.85008627673512.14991372326489
1252524.20964277450270.790357225497337
1262321.42517545633421.57482454366575
1272423.61010940192040.389890598079628
1282623.58716712901722.41283287098281
1292621.54005168857074.45994831142933
1302524.16842031503230.831579684967724
1311822.382424560105-4.38242456010498
1322119.90251272460471.09748727539525
1332623.70557399253572.29442600746430
1342321.99735951072631.00264048927367
1352319.76730880155893.23269119844108
1362222.5940710154958-0.594071015495778
1372022.4124503008446-2.41245030084455
1381322.1253524864942-9.12535248649424
1392421.47228680523282.52771319476722
1401521.6118883705203-6.61188837052032
1411423.1549213865043-9.15492138650432
1422224.1062334850528-2.10623348505278
1431017.6923817161542-7.69238171615418
1442424.4822138610477-0.482213861047676
1452221.87087658823550.129123411764544
1462425.8205497465243-1.82054974652427
1471921.6472637326236-2.64726373262356
1482022.1377104514971-2.13771045149714
1491317.1108094321865-4.11080943218647
1502020.1430837911000-0.143083791099952
1512223.3048248497759-1.30482484977593
1522423.36786398922300.632136010777035
1532923.19441948471325.80558051528681
1541220.9591466336236-8.95914663362364
1552020.9707782686841-0.97077826868414
1562121.4614776884216-0.461477688421614
1572423.67628398478380.323716015216156
1582221.93051257584190.0694874241580666
1592017.70838604865042.29161395134965


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.7253213230516890.5493573538966230.274678676948311
100.5986464109906280.8027071780187440.401353589009372
110.4893260815124570.9786521630249140.510673918487543
120.4448558931257080.8897117862514160.555144106874292
130.4529542350626240.9059084701252480.547045764937376
140.6934241689605640.6131516620788730.306575831039436
150.6248974246066110.7502051507867780.375102575393389
160.5729424577337610.8541150845324770.427057542266239
170.5069267630769470.9861464738461060.493073236923053
180.6370262446452040.7259475107095930.362973755354796
190.5620112594482650.875977481103470.437988740551735
200.5671281596137120.8657436807725770.432871840386288
210.5193104347340460.9613791305319090.480689565265954
220.4501751285470530.9003502570941060.549824871452947
230.3911539944686670.7823079889373330.608846005531333
240.3917981325239550.783596265047910.608201867476045
250.5356100160442410.9287799679115180.464389983955759
260.4730091818059330.9460183636118670.526990818194067
270.4094422667417840.8188845334835680.590557733258216
280.4027316330340320.8054632660680650.597268366965968
290.341805978531840.683611957063680.65819402146816
300.2850955636159940.5701911272319890.714904436384006
310.3093019969060430.6186039938120860.690698003093957
320.2607093695950450.5214187391900890.739290630404955
330.4851696443745190.9703392887490390.514830355625481
340.4387744161561090.8775488323122180.561225583843891
350.4039992529929880.8079985059859760.596000747007012
360.3483307111290370.6966614222580740.651669288870963
370.3256998806582530.6513997613165060.674300119341747
380.2763769321200340.5527538642400680.723623067879966
390.2315472767686270.4630945535372530.768452723231373
400.2082515204833980.4165030409667950.791748479516602
410.3597762817531770.7195525635063540.640223718246823
420.3096548314381430.6193096628762850.690345168561857
430.2778920360950280.5557840721900570.722107963904971
440.2360066800676730.4720133601353460.763993319932327
450.2034017647918780.4068035295837560.796598235208122
460.1825159284631400.3650318569262800.81748407153686
470.1702110977033420.3404221954066840.829788902296658
480.1572886639464290.3145773278928580.842711336053571
490.1282078965977010.2564157931954030.871792103402299
500.1187592016217540.2375184032435070.881240798378246
510.09794402906116630.1958880581223330.902055970938834
520.08290365208950970.1658073041790190.91709634791049
530.1389319756170390.2778639512340780.86106802438296
540.1704714021562140.3409428043124280.829528597843786
550.1626988732964300.3253977465928610.83730112670357
560.2180702478481350.436140495696270.781929752151865
570.2089855486336580.4179710972673160.791014451366342
580.1792270568938270.3584541137876530.820772943106173
590.1896994798377920.3793989596755840.810300520162208
600.2180149631526890.4360299263053790.78198503684731
610.1919676148889610.3839352297779220.808032385111039
620.1611003174793170.3222006349586340.838899682520683
630.1758507000633790.3517014001267590.82414929993662
640.1482046373359970.2964092746719930.851795362664003
650.1222079712085620.2444159424171250.877792028791438
660.1184502503507660.2369005007015320.881549749649234
670.1082576603192050.2165153206384110.891742339680795
680.1085019288495910.2170038576991810.89149807115041
690.09211217258322620.1842243451664520.907887827416774
700.07513723641491220.1502744728298240.924862763585088
710.06109322106867070.1221864421373410.93890677893133
720.04826785448029350.0965357089605870.951732145519707
730.04535881619747620.09071763239495240.954641183802524
740.03638188762707380.07276377525414760.963618112372926
750.03030369776676700.06060739553353410.969696302233233
760.02328125942289890.04656251884579780.976718740577101
770.01828192098089200.03656384196178410.981718079019108
780.01463971263164880.02927942526329760.985360287368351
790.02194933684826360.04389867369652720.978050663151736
800.01752216151261680.03504432302523350.982477838487383
810.01714476519056150.03428953038112290.982855234809439
820.03084101231130640.06168202462261280.969158987688694
830.02381464956867620.04762929913735240.976185350431324
840.01990621709143690.03981243418287390.980093782908563
850.02189410335593110.04378820671186210.978105896644069
860.01947244916664400.03894489833328800.980527550833356
870.01484039730079640.02968079460159290.985159602699204
880.01943350331768890.03886700663537780.980566496682311
890.01533147971946560.03066295943893110.984668520280534
900.01150008661395740.02300017322791480.988499913386043
910.01162048896555190.02324097793110370.988379511034448
920.01018872277322680.02037744554645350.989811277226773
930.00783804546403510.01567609092807020.992161954535965
940.00650194667191560.01300389334383120.993498053328084
950.01198228179901940.02396456359803880.98801771820098
960.01089621894148890.02179243788297780.989103781058511
970.01040965815261190.02081931630522380.989590341847388
980.007997340608936080.01599468121787220.992002659391064
990.005925453757017710.01185090751403540.994074546242982
1000.004556769167675270.009113538335350550.995443230832325
1010.003383169856387380.006766339712774770.996616830143613
1020.002419194710520940.004838389421041870.997580805289479
1030.002601225399170790.005202450798341580.99739877460083
1040.002048888400231970.004097776800463940.997951111599768
1050.008725193417262050.01745038683452410.991274806582738
1060.01960001469256310.03920002938512610.980399985307437
1070.01953572455027220.03907144910054440.980464275449728
1080.02469949423416480.04939898846832970.975300505765835
1090.01917553290921230.03835106581842460.980824467090788
1100.01410168239392240.02820336478784480.985898317606078
1110.01028275208783190.02056550417566380.989717247912168
1120.02519172254264470.05038344508528930.974808277457355
1130.02298616611819330.04597233223638660.977013833881807
1140.06364683233832080.1272936646766420.936353167661679
1150.05462994370801080.1092598874160220.94537005629199
1160.04462449768458830.08924899536917650.955375502315412
1170.1293870327738960.2587740655477910.870612967226104
1180.1248358165085560.2496716330171110.875164183491444
1190.1114840173132070.2229680346264150.888515982686793
1200.1923122146633510.3846244293267030.807687785336649
1210.1843714475124840.3687428950249680.815628552487516
1220.2193672087559920.4387344175119840.780632791244008
1230.2131188919553970.4262377839107940.786881108044603
1240.2128450293108430.4256900586216860.787154970689157
1250.1948864589243870.3897729178487740.805113541075613
1260.1606852247092380.3213704494184760.839314775290762
1270.1274968038756050.254993607751210.872503196124395
1280.1320290717841190.2640581435682380.867970928215881
1290.1873664260081720.3747328520163440.812633573991828
1300.1634486246872260.3268972493744520.836551375312774
1310.1448021004267170.2896042008534350.855197899573283
1320.1271100958706160.2542201917412310.872889904129384
1330.1178731028370170.2357462056740340.882126897162983
1340.0979158935363090.1958317870726180.902084106463691
1350.1327893835190790.2655787670381580.867210616480921
1360.1009094895401070.2018189790802150.899090510459893
1370.07555835546564420.1511167109312880.924441644534356
1380.1852116197493420.3704232394986830.814788380250658
1390.2584735023210920.5169470046421830.741526497678908
1400.2391685034379860.4783370068759730.760831496562014
1410.4833561337163060.9667122674326120.516643866283694
1420.4353646171717630.8707292343435250.564635382828237
1430.7471173137231120.5057653725537760.252882686276888
1440.6969707961532350.606058407693530.303029203846765
1450.5979879813347130.8040240373305730.402012018665287
1460.5351808653361350.929638269327730.464819134663865
1470.558078277329840.883843445340320.44192172267016
1480.4307892752804900.8615785505609810.56921072471951
1490.3379112269752260.6758224539504520.662088773024774
1500.2418616446089060.4837232892178130.758138355391094


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.0352112676056338NOK
5% type I error level360.253521126760563NOK
10% type I error level430.302816901408451NOK