Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 9.70088005689665 -0.456471979607422X[t] + 0.0348269533680547M1[t] -0.0633075600436983M2[t] -0.221132793979825M3[t] -0.201956308484031M4[t] -0.158803388178143M5[t] -0.241583211166381M6[t] -0.407825233936127M7[t] -0.574006708775354M8[t] -0.751926034518773M9[t] -0.862685731180946M10[t] -0.374067256705873M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)9.700880056896650.35123527.619400
X-0.4564719796074220.114858-3.97420.0001085.4e-05
M10.03482695336805470.3794610.09180.9269910.463496
M2-0.06330756004369830.379426-0.16690.8677050.433852
M3-0.2211327939798250.37943-0.58280.5608730.280436
M4-0.2019563084840310.379426-0.53230.5953030.297651
M5-0.1588033881781430.379432-0.41850.676140.33807
M6-0.2415832111663810.379429-0.63670.5252580.262629
M7-0.4078252339361270.379431-1.07480.2841190.14206
M8-0.5740067087753540.379428-1.51280.1323610.06618
M9-0.7519260345187730.379428-1.98170.0492770.024639
M10-0.8626857311809460.379428-2.27360.024360.01218
M11-0.3740672567058730.379434-0.98590.325740.16287


Multiple Linear Regression - Regression Statistics
Multiple R0.392575980636937
R-squared0.154115900573052
Adjusted R-squared0.0886280993270953
F-TEST (value)2.35335280221470
F-TEST (DF numerator)12
F-TEST (DF denominator)155
p-value0.00836047978231136
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.00386642039645
Sum Squared Residuals156.200907449936


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
17.68.6766920175754-1.07669201757540
27.68.65159302090092-1.05159302090092
37.68.46181474839227-0.861814748392272
47.88.4033909973548-0.603390997354804
588.24569624663343-0.245696246633427
688.1948694622177-0.194869462217708
787.955591922710770.0444080772892252
87.97.79853988746370.101460112536306
97.97.721044397233910.178955602766089
1087.751791014250040.248208985749963
118.58.149115092803620.350884907196376
129.28.244734441948970.955265558051026
139.48.448456027771770.951543972228227
149.58.395968712320761.10403128767924
159.58.324873154510041.17512684548996
169.68.266449403472581.33355059652742
179.78.437414478068541.26258552193146
189.78.318116896711711.38188310328829
199.68.238604550067381.36139544993262
209.58.02677587726741.47322412273259
219.47.780385754582881.61961424541713
229.37.578331661999221.72166833800078
239.68.089773735454661.51022626454534
2410.28.587088426654541.61291157334546
2510.28.612785940430441.58721405956956
2610.18.669851900085211.43014809991479
279.98.571368023498051.32863197650195
289.88.649885866342811.15011413365719
299.88.683909347056551.11609065294345
309.78.628517842844761.07148215715524
319.58.498793578443611.00120642155639
329.38.34630626299260.953693737007399
339.18.319022690519630.780977309480367
3498.258474911614280.741525088385726
359.58.783611144457940.716388855542058
36109.116595922999150.883404077000853
3710.29.192505354531871.00749464546813
3810.19.08067668173191.01932331826811
39108.80873345289391.19126654710609
409.98.832474658185781.06752534181422
41108.647391588687961.35260841131204
429.98.601129524068311.29887047593169
439.78.366416704357451.33358329564255
449.58.195670509722151.30432949027785
459.28.081657261123771.11834273887623
4698.016544762422340.98345523757766
479.38.450386599344520.849613400655476
489.88.82445385605040.975546143949604
499.88.836457210438080.96354278956192
509.68.514651427018691.08534857298131
519.48.40247339104330.997526608956693
529.38.344049640005840.955950359994162
539.28.487626395825360.71237360417464
549.28.555482326107570.644517673892428
5598.626605732733680.373394267266316
568.88.551718653815940.248281346184059
578.78.227728294598150.472271705401851
588.78.043933081198790.656066918801213
599.18.464080758732750.635919241267252
609.78.856406894622920.843593105377083
619.88.996222403300680.803777596699323
629.69.04415892336330.5558410766367
639.48.831557051874280.568442948125718
649.48.973980971864080.42601902813592
659.59.350358437283390.149641562716613
669.49.121507580820770.278492419179227
679.38.827453403760950.472546596239051
689.28.437600658914090.762399341085913
6998.099916140308070.90008385969193
708.98.11240387813990.787596121860101
719.28.856646661195130.34335333880487
729.89.500032385869380.299967614130620
739.99.361399986986620.538600013013385
749.69.245006594390570.354993405609434
759.29.21499351474452-0.0149935147445172
769.19.22960528044424-0.129605280444237
779.19.10842828809145-0.00842828809145349
7899.011954305715-0.0119543057149924
798.98.731594288043390.168405711956609
808.78.592801131980610.10719886801939
818.58.56551755950764-0.0655175595076403
828.38.5004050608062-0.200405060806207
838.59.03010601344595-0.53010601344595
848.79.2854905554539-0.585490555453894
858.49.19250535453187-0.792505354531869
868.19.0441589233633-0.9441589233633
877.88.78134513411747-0.981345134117466
887.78.61336810797422-0.913368107974217
897.58.72499182522122-1.22499182522122
907.28.56917648549579-1.36917648549579
916.88.26142814904775-1.46142814904775
926.78.19567050972215-1.49567050972215
936.47.96297454642584-1.56297454642584
946.37.58289638179529-1.28289638179529
956.88.05325597708607-1.25325597708607
967.38.38624075562727-1.08624075562727
977.18.20196115878376-1.10196115878376
9878.2818507174189-1.28185071741891
996.88.06468412613381-1.26468412613381
1006.68.36230851919013-1.76230851919014
1016.38.53783831358218-2.23783831358218
1026.18.43223489161357-2.33223489161357
1036.18.339028385581-2.23902838558101
1046.37.85331652501659-1.55331652501659
1056.37.51563200641057-1.21563200641057
10667.50073142546595-1.50073142546595
1076.28.1171620542311-1.91716205423111
1086.48.48209987134483-2.08209987134483
1096.88.70408033635193-1.90408033635193
1107.58.56486334477551-1.06486334477551
1117.58.50746194635301-1.00746194635301
1127.68.50381483286844-0.903814832868437
1137.68.21830792785698-0.618307927856982
1147.48.25877553936275-0.858775539362747
1157.38.0742746374087-0.774274637408704
1167.18.30065906503186-1.20065906503186
1176.98.3418462895-1.44184628950000
1186.88.43649898366117-1.63649898366117
1197.58.74252866629327-1.24252866629327
1207.69.1257253625913-1.52572536259130
1217.89.16055231595935-1.36055231595935
12289.04872364315937-1.04872364315937
1238.18.97762808534866-0.877628085348658
1248.28.87355713635045-0.673557136350448
1258.38.98974557339352-0.689745573393523
1268.28.66503560121335-0.465035601213353
12788.48966413885146-0.489664138851458
1287.98.4512948183023-0.551294818302308
1297.68.47422316358616-0.874223163586156
1307.68.09870971875168-0.498709718751677
1318.38.64666955057572-0.346669550575715
1328.48.88379521339936-0.483795213399362
1338.48.91405744697134-0.514057446971342
1348.48.91634676907322-0.516346769073222
1358.48.63070938084702-0.230709380847017
1368.68.7046625038957-0.104662503895702
1378.98.81628622114270.083713778857297
1388.88.88414215142491-0.0841421514249136
1398.38.77724148600413-0.477241486004133
1407.58.25044714727504-0.750447147275043
1417.27.7575621556025-0.557562155602504
1427.47.80656765180293-0.406567651802927
1438.88.226715329336890.573284670663113
1449.38.669253382983870.630746617016127
1459.38.809068891661640.490931108338365
1468.78.332062635175720.367937364824276
1478.28.3157437149179-0.115743714917897
1488.38.46273235470377-0.162732354703768
1498.58.51044999480573-0.0104499948057310
1508.68.286163858139190.313836141860807
1518.57.891685845565740.608314154434265
1528.27.867010684404810.33298931559519
1538.17.803209353563250.296790646436753
1547.97.52811974424240.371880255757601
1558.67.893490784223470.70650921577653
1568.78.281252200317570.418747799682434
1578.78.293255554705250.40674444529475
1588.58.51008670722262-0.0100867072226169
1598.48.306614275325750.0933857246742524
1608.58.179719727347170.320280272652833
1618.78.341555362350980.358444637649014
1628.78.37289353426460.327106465735397
1638.68.521617177423980.0783828225760224
1648.58.232188268090750.267811731909254
1658.37.949280387037620.350719612962379
16687.984591723849820.0154082761501785
1678.28.5964576328189-0.3964576328189
1688.18.95683073013655-0.85683073013655


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.07530811385787470.1506162277157490.924691886142125
170.7114715150913630.5770569698172750.288528484908637
180.8149624476234270.3700751047531450.185037552376573
190.8830384282181260.2339231435637490.116961571781874
200.8921872722641920.2156254554716160.107812727735808
210.8900213567292720.2199572865414560.109978643270728
220.8817293660580860.2365412678838280.118270633941914
230.8649874531099990.2700250937800020.135012546890001
240.8518688591044510.2962622817910980.148131140895549
250.8840832598357930.2318334803284150.115916740164207
260.8953972021745710.2092055956508580.104602797825429
270.891255618466380.2174887630672390.108744381533620
280.867436712101540.2651265757969200.132563287898460
290.835718000670550.3285639986589010.164281999329451
300.7979404290459650.404119141908070.202059570954035
310.7555166884808120.4889666230383760.244483311519188
320.7106950463898370.5786099072203250.289304953610163
330.6681897632944050.663620473411190.331810236705595
340.6243301008000040.7513397983999930.375669899199997
350.5748318119598960.8503363760802080.425168188040104
360.5343914993585830.9312170012828340.465608500641417
370.4908156584358870.9816313168717740.509184341564113
380.4486904657429790.8973809314859580.551309534257021
390.4209548119305470.8419096238610930.579045188069453
400.3834060423569930.7668120847139850.616593957643008
410.372120873494060.744241746988120.62787912650594
420.3557613611977490.7115227223954980.644238638802251
430.345397228955750.69079445791150.65460277104425
440.3337074719035230.6674149438070460.666292528096477
450.3101534315292410.6203068630584810.68984656847076
460.2821123299957110.5642246599914210.71788767000429
470.2522917080570260.5045834161140520.747708291942974
480.2341202318096750.4682404636193510.765879768190325
490.2160433865989420.4320867731978850.783956613401058
500.2148543923775580.4297087847551160.785145607622442
510.2061498530626440.4122997061252870.793850146937356
520.1980052956692890.3960105913385790.80199470433071
530.1812988209093020.3625976418186030.818701179090699
540.1645355402403660.3290710804807320.835464459759634
550.1536907314640800.3073814629281610.84630926853592
560.1475239689653550.2950479379307100.852476031034645
570.1331851125277540.2663702250555070.866814887472246
580.1202288289798890.2404576579597790.879771171020111
590.1075034115962460.2150068231924920.892496588403754
600.1042415647576390.2084831295152780.895758435242361
610.09610511970536320.1922102394107260.903894880294637
620.08425657705139520.1685131541027900.915743422948605
630.07501513291217660.1500302658243530.924984867087823
640.06620501764114240.1324100352822850.933794982358858
650.06053801607788790.1210760321557760.939461983922112
660.05316883593256950.1063376718651390.94683116406743
670.04653758468544920.09307516937089850.95346241531455
680.04413378976414490.08826757952828980.955866210235855
690.04538661236702130.09077322473404250.954613387632979
700.04504309110111070.09008618220222130.95495690889889
710.03973283837566280.07946567675132570.960267161624337
720.03796052159217330.07592104318434650.962039478407827
730.03548468061541560.07096936123083110.964515319384584
740.03175585777722420.06351171555444830.968244142222776
750.02837490195966770.05674980391933540.971625098040332
760.02541952128920040.05083904257840080.9745804787108
770.02269249474847350.04538498949694690.977307505251527
780.02054305567923660.04108611135847330.979456944320763
790.01898707425073550.0379741485014710.981012925749265
800.01795136750480890.03590273500961780.982048632495191
810.01729182659295960.03458365318591930.98270817340704
820.01711642416430050.03423284832860100.9828835758357
830.01699579034503330.03399158069006660.983004209654967
840.02055730017897970.04111460035795950.97944269982102
850.02421996257104350.04843992514208710.975780037428956
860.03104770380340320.06209540760680640.968952296196597
870.04160335690105430.08320671380210860.958396643098946
880.05503822732992430.1100764546598490.944961772670076
890.0857793733202740.1715587466405480.914220626679726
900.1432680944123360.2865361888246730.856731905587664
910.2420746888171140.4841493776342280.757925311182886
920.3499645598551210.6999291197102410.650035440144879
930.4783885427881210.9567770855762420.521611457211879
940.5733136803990590.8533726392018820.426686319600941
950.6459159314651730.7081681370696540.354084068534827
960.6899782969474360.6200434061051270.310021703052564
970.7238066111567150.552386777686570.276193388843285
980.7656818078407620.4686363843184770.234318192159238
990.8034477010034560.3931045979930890.196552298996544
1000.8758246135299380.2483507729401230.124175386470062
1010.9556419416684240.08871611666315280.0443580583315764
1020.990144321645350.0197113567092980.009855678354649
1030.9980348537599480.003930292480103240.00196514624005162
1040.9991054614481880.001789077103624760.00089453855181238
1050.9994483496033430.001103300793315020.000551650396657508
1060.9998006421292510.0003987157414977690.000199357870748885
1070.9999849671917823.00656164359253e-051.50328082179627e-05
1080.9999995637365398.72526922771188e-074.36263461385594e-07
1090.9999999782191984.35616030708711e-082.17808015354355e-08
1100.9999999857292792.8541442002165e-081.42707210010825e-08
1110.9999999871348722.57302565359173e-081.28651282679587e-08
1120.9999999885866382.28267249572991e-081.14133624786495e-08
1130.9999999965164086.96718342187662e-093.48359171093831e-09
1140.999999999541189.17639466206874e-104.58819733103437e-10
1150.9999999999497871.00426710720140e-105.02133553600698e-11
1160.9999999999777484.45037601128243e-112.22518800564121e-11
1170.9999999999845953.08110428554927e-111.54055214277463e-11
1180.9999999999871082.57838055735224e-111.28919027867612e-11
1190.9999999999927121.45764207887791e-117.28821039438956e-12
1200.9999999999975884.82311086390031e-122.41155543195016e-12
1210.999999999999091.81791885634490e-129.08959428172449e-13
1220.9999999999982323.53547660562221e-121.76773830281111e-12
1230.9999999999943871.12265601533974e-115.61328007669871e-12
1240.9999999999823513.52974443081515e-111.76487221540757e-11
1250.999999999954119.17799832585065e-114.58899916292532e-11
1260.9999999999175551.64889334460912e-108.24446672304561e-11
1270.9999999998459583.08084112503882e-101.54042056251941e-10
1280.9999999994962681.00746412739362e-095.03732063696808e-10
1290.999999998500072.99985883692546e-091.49992941846273e-09
1300.9999999952434879.51302655673712e-094.75651327836856e-09
1310.9999999856115932.87768135447240e-081.43884067723620e-08
1320.9999999620177357.59645300299054e-083.79822650149527e-08
1330.9999999428860551.14227889877026e-075.7113944938513e-08
1340.9999998328177173.34364566785149e-071.67182283392575e-07
1350.9999994903643481.01927130372902e-065.0963565186451e-07
1360.9999985894706822.82105863642764e-061.41052931821382e-06
1370.9999966345456476.73090870664508e-063.36545435332254e-06
1380.999991088925431.78221491388640e-058.91107456943202e-06
1390.9999757695718354.84608563295021e-052.42304281647510e-05
1400.999981897261943.62054761213177e-051.81027380606588e-05
1410.9999953197357659.36052847061514e-064.68026423530757e-06
1420.9999933127561251.33744877503761e-056.68724387518807e-06
1430.999985540738672.89185226586929e-051.44592613293464e-05
1440.999998298437973.40312406070350e-061.70156203035175e-06
1450.99999944385061.11229880066019e-065.56149400330097e-07
1460.9999971133471155.77330577013622e-062.88665288506811e-06
1470.9999867865443542.64269112921486e-051.32134556460743e-05
1480.9999312418109770.0001375163780450686.8758189022534e-05
1490.999673167571960.0006536648560777350.000326832428038867
1500.9984427929982920.003114414003416420.00155720700170821
1510.9947563589770170.01048728204596500.00524364102298251
1520.9899784766729560.02004304665408840.0100215233270442


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level480.35036496350365NOK
5% type I error level600.437956204379562NOK
10% type I error level730.532846715328467NOK