Multiple Linear Regression - Estimated Regression Equation
YT[t] = + 1.29605226452594 + 0.0689248642585393X1[t] + 0.252916716305925X2[t] + 0.363828375948588X3[t] -0.118420136069921X4[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.296052264525940.4319793.00030.0031530.001577
X10.06892486425853930.0736190.93620.3506340.175317
X20.2529167163059250.08263.06190.0026010.001301
X30.3638283759485880.0724445.02221e-061e-06
X4-0.1184201360699210.089782-1.3190.1891630.094582


Multiple Linear Regression - Regression Statistics
Multiple R0.456901675014126
R-squared0.208759140630714
Adjusted R-squared0.187937012752575
F-TEST (value)10.0258312624181
F-TEST (DF numerator)4
F-TEST (DF denominator)152
p-value3.15112685944641e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.866596311038476
Sum Squared Residuals114.150353278435


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
143.798538670157230.201461329842773
243.300213713972640.699786286027362
353.074235066541131.92576493345887
432.936385338024050.0636146619759458
542.499476769670741.50052323032926
633.32715178284706-0.327151782847056
743.62205529453710.377944705462896
833.12373033835251-0.123730338352512
922.38856511002808-0.388565110028079
1042.936385338024051.06361466197595
1123.07423506654113-1.07423506654113
1222.75239348597667-0.752393485976667
1312.75239348597667-1.75239348597667
1443.074235066541130.925764933458869
1543.081743542968390.918256457031611
1623.00531020228259-1.00531020228259
1722.61789690574066-0.617896905740663
1833.36913857823118-0.369138578231179
1933.80189181843831-0.801891818438307
2033.66404208992123-0.664042089921228
2143.633976410557000.366023589442996
2233.80189181843831-0.801891818438307
2323.42720181778139-1.42720181778139
2423.25822691858852-1.25822691858852
2543.074235066541130.925764933458869
2643.801891818438310.198108181561693
2733.00531020228259-0.00531020228259128
2843.438063442489720.561936557510281
2923.07423506654113-1.07423506654113
3043.595117225662690.404882774337312
3143.31964330641980.680356693580202
3253.3649832500851.63501674991500
3352.936385338024052.06361466197595
3443.074235066541130.925764933458869
3543.867463534415770.132536465584229
3644.0439469100359-0.0439469100358984
3723.19265520261105-1.19265520261105
3843.617899966390920.382100033609078
3943.683471682368390.316528317631614
4044.3002167746229-0.300216774622899
4133.43806344248972-0.438063442489719
4223.00531020228259-1.00531020228259
4333.69098015879564-0.690980158795644
4442.936385338024051.06361466197595
4532.825473678381390.174526321618612
4623.07423506654113-1.07423506654113
4743.427201817781390.572798182218614
4843.565051546298460.434948453701535
4933.54897510213238-0.548975102132382
5043.476697089592770.523302910407233
5133.07423506654113-0.0742350665411309
5242.936385338024051.06361466197595
5322.11621880127500-0.116218801274996
5443.430554966062460.569445033937539
5543.021386646448670.978613353551326
5643.664042089921230.335957910078772
5743.074235066541130.925764933458869
5833.37664705465844-0.376647054658437
5912.31964024576954-1.31964024576954
6033.18930205432998-0.189302054329976
6133.00531020228259-0.00531020228259128
6243.189302054329980.810697945670024
6322.86746047376551-0.867460473765512
6432.759901962403920.240098037596076
6554.280787182175740.719212817824259
6643.250718442161260.749281557838742
6743.005310202282590.99468979771741
6833.01281867870985-0.0128186787098493
6942.936385338024051.06361466197595
7023.243209965734-1.243209965734
7132.936385338024050.0636146619759482
7244.3002167746229-0.300216774622899
7333.81796826260439-0.81796826260439
7443.690980158795640.309019841204356
7542.699545065884211.30045493411579
7633.12373033835251-0.123730338352512
7733.32715178284706-0.327151782847056
7823.25822691858852-1.25822691858852
7943.565051546298460.434948453701535
8033.07088191826006-0.0708819182600554
8122.75239348597667-0.752393485976667
8223.73296695417977-1.73296695417977
8333.80189181843831-0.801891818438307
8422.81796520195413-0.81796520195413
8523.07423506654113-1.07423506654113
8643.300213713972640.69978628602736
8743.30772219039990.692277809600103
8843.801891818438310.198108181561693
8923.00531020228259-1.00531020228259
9023.56505154629846-1.56505154629846
9142.943893814451311.05610618554869
9222.68346862171813-0.683468621718127
9333.11622186192525-0.116221861925255
9433.25822691858852-0.258226918588516
9553.886893126862931.11310687313707
9632.699545065884210.300454934115790
9743.250718442161260.749281557838742
9833.07423506654113-0.0742350665411309
9922.88689006621267-0.88689006621267
10043.074235066541130.925764933458869
10133.12373033835251-0.123730338352512
10233.00531020228259-0.00531020228259128
10332.936385338024050.0636146619759482
10443.62205529453710.377944705462896
10512.19371163327236-1.19371163327236
10633.00531020228259-0.00531020228259128
10723.03978852123946-1.03978852123946
10833.3196433064198-0.319643306419798
10923.18930205432998-1.18930205432998
11022.57591011035654-0.575910110356539
11122.83739479440129-0.837394794401289
11242.614543757459591.38545624254041
11354.234645058645430.765354941354565
11452.690977098145382.30902290185462
11533.00531020228259-0.00531020228259128
11642.568401633929281.43159836607072
11742.108710324847741.89128967515226
11833.02473979472975-0.0247397947297494
11922.87081362204659-0.870813622046588
12043.978375194058430.0216248059415657
12122.75239348597667-0.752393485976667
12232.633973349906750.366026650093254
12323.3077221903999-1.30772219039990
12422.93638533802405-0.936385338024052
12522.70289821416528-0.702898214165285
12643.192655202611050.807344797388948
12743.369138578231180.630861421768821
12843.005310202282590.99468979771741
12943.614546818109850.385453181890154
13033.54897510213238-0.548975102132382
13123.00531020228259-1.00531020228259
13243.801891818438310.198108181561693
13333.80189181843831-0.801891818438307
13422.93638533802405-0.936385338024052
13543.801891818438310.198108181561693
13632.928876861596790.0711231384032061
13733.07423506654113-0.0742350665411309
13833.00531020228259-0.00531020228259128
13932.744885009549410.255114990450591
14033.15820865730938-0.158208657309378
14143.664042089921230.335957910078772
14253.847231762103511.15276823789649
14323.05480547409397-1.05480547409397
14443.132298306091340.867701693908663
14533.72545847775251-0.72545847775251
14632.381056633600820.61894336639918
14712.49947676967074-1.49947676967074
14823.07423506654113-1.07423506654113
14942.821318350235211.17868164976479
15042.837394794401291.16260520559871
15154.047300058316970.952699941683026
15222.81380987380795-0.813809873807948
15343.396076647105600.603923352894405
15433.00531020228259-0.00531020228259128
15523.36913857823118-1.36913857823118
15643.31964330641980.680356693580202
15722.46605794202544-0.466057942025443


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.4722296176606850.944459235321370.527770382339315
90.4172436076145470.8344872152290930.582756392385453
100.5815136204449510.8369727591100970.418486379555049
110.7734984992513510.4530030014972980.226501500748649
120.8399073860076920.3201852279846150.160092613992308
130.9585673737704670.08286525245906540.0414326262295327
140.953679335029140.09264132994172170.0463206649708608
150.9447368771599660.1105262456800670.0552631228400336
160.9500541099489240.09989178010215160.0499458900510758
170.937640459578180.1247190808436380.0623595404218189
180.9165927445097120.1668145109805770.0834072554902883
190.89671407025460.2065718594907980.103285929745399
200.8680596721727460.2638806556545090.131940327827254
210.8327059125751180.3345881748497640.167294087424882
220.7953580608131850.4092838783736300.204641939186815
230.8396606803482030.3206786393035940.160339319651797
240.8868690222486610.2262619555026780.113130977751339
250.8809990363652170.2380019272695650.119000963634783
260.8530517236516790.2938965526966430.146948276348321
270.812691236521850.3746175269563010.187308763478151
280.7849274191599220.4301451616801560.215072580840078
290.813795564193610.3724088716127800.186204435806390
300.7990037405133660.4019925189732680.200996259486634
310.7862680219323280.4274639561353450.213731978067672
320.8478407093884670.3043185812230650.152159290611533
330.9532372388003190.09352552239936240.0467627611996812
340.9502236077193920.09955278456121640.0497763922806082
350.9350280020508010.1299439958983980.0649719979491991
360.9166627425875250.1666745148249510.0833372574124753
370.9348527227014190.1302945545971620.065147277298581
380.9177114090815310.1645771818369380.0822885909184688
390.8968714680160460.2062570639679080.103128531983954
400.8733890699595930.2532218600808140.126610930040407
410.8521763972699450.2956472054601090.147823602730055
420.8598521084392390.2802957831215230.140147891560762
430.8443157184716630.3113685630566740.155684281528337
440.8565778868733510.2868442262532980.143422113126649
450.826734744696390.3465305106072190.173265255303610
460.8421921679089720.3156156641820550.157807832091028
470.8188314518958150.362337096208370.181168548104185
480.7883265267635310.4233469464729370.211673473236469
490.7659994274143060.4680011451713870.234000572585693
500.7366663446842640.5266673106314710.263333655315736
510.6943854157007250.6112291685985510.305614584299276
520.7063250014188970.5873499971622060.293674998581103
530.6691647750036650.6616704499926690.330835224996335
540.6364854291097330.7270291417805330.363514570890266
550.6273151387668550.7453697224662890.372684861233145
560.5896551068537090.8206897862925820.410344893146291
570.5902476209382510.8195047581234980.409752379061749
580.546650655654430.906698688691140.45334934434557
590.6306153031257990.7387693937484020.369384696874201
600.5856567692315920.8286864615368160.414343230768408
610.5381185831823340.9237628336353320.461881416817666
620.5328273371656510.9343453256686980.467172662834349
630.5323456315416490.9353087369167030.467654368458351
640.4895595812019660.9791191624039320.510440418798034
650.4823489498982360.9646978997964710.517651050101764
660.4647519868166710.9295039736333410.535248013183329
670.475478251391850.95095650278370.52452174860815
680.4286587977832530.8573175955665050.571341202216747
690.4491082184699970.8982164369399950.550891781530003
700.5124172357258190.9751655285483610.487582764274181
710.4660861997247190.9321723994494390.533913800275281
720.4251352701485570.8502705402971150.574864729851443
730.4213549857971590.8427099715943180.578645014202841
740.3820351790590190.7640703581180370.617964820940981
750.4310999418992740.8621998837985480.568900058100726
760.3861946627909850.772389325581970.613805337209015
770.3483381811560950.696676362312190.651661818843905
780.3928492166100690.7856984332201380.607150783389931
790.3592820931069640.7185641862139270.640717906893036
800.3186275884439370.6372551768878740.681372411556063
810.3110964704011630.6221929408023250.688903529598837
820.4297237020094060.8594474040188120.570276297990594
830.4207126249773460.8414252499546920.579287375022654
840.4174348772200910.8348697544401820.582565122779909
850.4431550214636740.8863100429273470.556844978536326
860.4287067423565880.8574134847131760.571293257643412
870.4149690650368040.8299381300736070.585030934963196
880.3725989959088070.7451979918176140.627401004091193
890.3861072203833830.7722144407667660.613892779616617
900.4867031476280420.9734062952560830.513296852371959
910.5168017459129690.9663965081740620.483198254087031
920.4946232522518180.9892465045036350.505376747748182
930.4481507347913540.8963014695827080.551849265208646
940.4045036021556720.8090072043113450.595496397844328
950.428687045783850.85737409156770.57131295421615
960.3947200441594870.7894400883189740.605279955840513
970.3879263702325820.7758527404651630.612073629767419
980.3429540557826980.6859081115653960.657045944217302
990.3376524062572290.6753048125144590.662347593742771
1000.3405008573429960.6810017146859920.659499142657004
1010.2976115089872240.5952230179744490.702388491012776
1020.2566845034047640.5133690068095280.743315496595236
1030.2202188229650770.4404376459301550.779781177034923
1040.1952064046867300.3904128093734610.80479359531327
1050.2191536986535810.4383073973071630.780846301346419
1060.1843094192616860.3686188385233710.815690580738314
1070.2036925996815980.4073851993631960.796307400318402
1080.1732357251466310.3464714502932630.826764274853369
1090.1875169051976430.3750338103952860.812483094802357
1100.1704654488744490.3409308977488990.82953455112555
1110.1660053222098690.3320106444197380.833994677790131
1120.2222080578895400.4444161157790810.77779194211046
1130.2076836804999270.4153673609998550.792316319500073
1140.5668591735613060.8662816528773880.433140826438694
1150.5163180697519830.9673638604960350.483681930248017
1160.5873185810755170.8253628378489660.412681418924483
1170.879088047951620.2418239040967610.120911952048381
1180.8577063905596690.2845872188806620.142293609440331
1190.8365533935095020.3268932129809970.163446606490498
1200.8005420861198690.3989158277602630.199457913880131
1210.7723749144637990.4552501710724020.227625085536201
1220.7454239300488090.5091521399023830.254576069951191
1230.7499593393385050.500081321322990.250040660661495
1240.7246897756342670.5506204487314660.275310224365733
1250.7158959048010930.5682081903978130.284104095198907
1260.7222723999956350.5554552000087310.277727600004365
1270.7105272006754840.5789455986490320.289472799324516
1280.7807181419839570.4385637160320860.219281858016043
1290.7347161396905580.5305677206188830.265283860309442
1300.7158742598061470.5682514803877070.284125740193853
1310.6979811237213640.6040377525572720.302018876278636
1320.6353724771634320.7292550456731350.364627522836568
1330.678460024344350.64307995131130.32153997565565
1340.6308751702925350.738249659414930.369124829707465
1350.5638491095253870.8723017809492270.436150890474613
1360.5060108429226590.9879783141546810.493989157077341
1370.4311525146849840.8623050293699680.568847485315016
1380.3618461047888530.7236922095777060.638153895211147
1390.3079120555086690.6158241110173370.692087944491331
1400.2582399237077950.516479847415590.741760076292205
1410.2509930827849630.5019861655699250.749006917215037
1420.2607728065395060.5215456130790130.739227193460494
1430.1991847630475460.3983695260950910.800815236952454
1440.1731594432958150.3463188865916290.826840556704185
1450.1257388797654760.2514777595309520.874261120234524
1460.2027311996591770.4054623993183530.797268800340823
1470.1418615859295780.2837231718591550.858138414070422
1480.1866465598064570.3732931196129150.813353440193542
1490.3670527223575740.7341054447151490.632947277642426


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level50.0352112676056338OK