Multiple Linear Regression - Estimated Regression Equation
Q4 [t] = + 0.865045701430835 + 0.145400006160318Q1[t] + 0.252561146567979Q2[t] + 0.220272402114639Q3[t] -0.0776944496009527M1[t] -0.135576717001389M2[t] + 0.0716598829398656M3[t] + 0.0976981103730005M4[t] + 0.278051810260123M5[t] + 0.0567419658771181M6[t] + 0.133278071817606M7[t] + 0.0873192329729293M8[t] + 0.12122700224052M9[t] + 0.207612182563193M10[t] + 0.230802626594899M11[t] + 0.00207493155891959t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.8650457014308350.2615343.30760.00126e-04
Q10.1454000061603180.0675852.15140.033190.016595
Q20.2525611465679790.0768263.28740.0012820.000641
Q30.2202724021146390.0721133.05460.0027060.001353
M1-0.07769444960095270.258216-0.30090.7639510.381976
M2-0.1355767170013890.259051-0.52340.6015640.300782
M30.07165988293986560.2569190.27890.7807240.390362
M40.09769811037300050.2590710.37710.7066720.353336
M50.2780518102601230.2559521.08630.2792210.139611
M60.05674196587711810.2558130.22180.824790.412395
M70.1332780718176060.257550.51750.6056460.302823
M80.08731923297292930.2651270.32930.7423910.371196
M90.121227002240520.2592430.46760.6407940.320397
M100.2076121825631930.2619860.79250.4294560.214728
M110.2308026265948990.2564840.89990.3697560.184878
t0.002074931558919590.0011861.750.0823330.041166


Multiple Linear Regression - Regression Statistics
Multiple R0.701482221157589
R-squared0.492077306600185
Adjusted R-squared0.436868318187161
F-TEST (value)8.91299262574619
F-TEST (DF numerator)15
F-TEST (DF denominator)138
p-value3.71924713249427e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.646445212137204
Sum Squared Residuals57.6690148967258


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
133.0420880006459-0.042088000645902
221.970085957233160.0299140427668448
342.684519781869291.31548021813071
412.23979939217872-1.23979939217872
522.86277282785404-0.862772827854045
621.918143219779360.0818567802206368
733.63118251969294-0.631182519692938
822.74879265544961-0.748792655449606
923.47788130707337-1.47788130707337
1021.857040760586480.142959239413523
1143.591606794545590.408393205454409
1232.599245538506360.400754461493641
1343.287259581467580.712740418532421
1422.79090744139678-0.790907441396783
1531.806335514712071.19366448528793
1633.02833213188901-0.0283321318890123
1732.780510866153420.219489133846581
1843.211798252625610.788201747374392
1922.12881457639347-0.128814576393467
2022.48289182183601-0.482891821836005
2122.15320211438756-0.153202114387559
2233.33867945109402-0.338679451094022
2343.363944826684650.636055173315352
2422.00591116237046-0.0059111623704582
2533.31215876017461-0.312158760174614
2643.401751430493410.598248569506586
2733.46566295583327-0.465662955833271
2833.27350371271069-0.273503712710687
2933.45593234415673-0.455932344156728
3022.22050272376141-0.220502723761412
3122.29911376126082-0.299113761260819
3243.051152159431660.948847840568345
3333.27511851791946-0.275118517919465
3432.159400264568530.840599735431475
3522.99088285266339-0.990882852663387
3643.412677456923680.587322543076318
3732.278279579809440.721720420190565
3822.04478349335426-0.0447834933542608
3933.27028973242567-0.270289732425667
4043.518675293532360.481324706467639
4143.082870370135470.917129629864532
4221.627168347625510.372831652374489
4312.54428534208249-1.54428534208249
4422.57092904500273-0.570929045002733
4532.095839331393970.904160668606032
4633.27536654680111-0.275366546801114
4743.413743184098720.586256815901282
4821.835437117669890.164562882330111
4932.711434818292410.288565181707591
5043.306149781747170.693850218252833
5121.660760648718540.339239351281465
5223.79613561880737-1.79613561880737
5333.07548080438916-0.0754808043891635
5422.37746222158314-0.377462221583143
5543.149179209879810.850820790120193
5633.32122291896036-0.321222918960364
5732.884372071104260.115627928895743
5843.665938133783110.334061866216893
5942.454736399687861.54526360031214
6043.209914667769770.790085332230226
6122.15038918660985-0.150389186609848
6243.33104896045420.668951039545798
6344.15859404679731-0.158594046797312
6443.170512498218140.829487501781865
6522.04160162402398-0.0416016240239844
6633.05883382088577-0.0588338208857702
6733.61027840706780-0.610278407067795
6822.10965498798153-0.109654987981528
6942.984143645765611.01585635423439
7011.83613664796134-0.836136647961335
7133.46354154151279-0.463541541512788
7232.982252699908830.0177473000911697
7322.7186495242055-0.718649524205497
7423.35594813916124-1.35594813916124
7532.947026115818480.0529738841815237
7633.59337282965347-0.593372829653466
7733.63040145493919-0.63040145493919
7833.15860539554713-0.158605395547127
7932.178438073974320.82156192602568
8021.956865416074910.0431345839250939
8122.17053686751507-0.170536867515074
8233.24290294251456-0.242902942514559
8333.37532945851284-0.375329458512845
8422.67971833609357-0.679718336093565
8521.581953989180980.418046010819017
8632.762613763025340.237386236974663
8722.35369173968258-0.353691739682576
8832.747477306949590.252522693050413
8933.54813949323856-0.548139493238565
9022.49039862345691-0.490398623456905
9132.569009660956310.430990339043687
9233.14335930851349-0.143359308513491
9343.652175558022620.347824441977381
9443.740635669904210.259364330095788
9532.969978740038240.0300212599617556
9622.30070624077299-0.300706240772987
9711.60685316788802-0.606853167888018
9822.02387938072912-0.0238793807291185
9933.36249688150750-0.362496881507503
10032.879537626064280.120462373935717
10153.825599818513581.17440018148642
10243.460964899529180.539035100470824
10353.610103547234581.38989645276542
10422.82237407220085-0.822374072200847
10510.7816288854933540.218371114506646
10632.845133126836640.154866873163363
10732.309511382597910.690488617402086
10844.64794705416629-0.647947054166285
10922.26470617580247-0.264706175802468
11021.946851255985260.0531487440147399
11132.308348078798930.691651921201068
11244.46863188137442-0.468631881374425
11322.15843053571391-0.158430535713911
11432.984480426645340.0155195733546601
11532.193157665927560.80684233407244
11643.411173903116050.588826096883946
11744.55396691763241-0.553966917632411
11822.81569940290891-0.815699402908907
11934.18901055514463-1.18901055514463
12021.893118634987960.106881365012041
12132.455544853989380.544455146010622
12244.64866167791832-0.64866167791832
12321.440408397913630.559591602086372
12443.655125773813010.344874226186990
12544.0217350006894-0.0217350006893962
12622.51450189848833-0.514501898488332
12733.69089039331721-0.690890393317214
12832.635805990618170.364194009381829
12931.960632541496511.03936745850349
13032.400053777386660.599946222613336
13143.961348587283690.0386514127163119
13233.29978425885206-0.299784258852059
13321.641938075738840.358061924261162
13433.21692201551397-0.216922015513970
13532.481401613502770.518598386497229
13632.647736208066710.352263791933295
13744.20822889312798-0.208228893127981
13832.614273473149690.385726526850311
13943.242956023341630.757043976658369
14043.751772272850760.248227727149241
14144.58767123816437-0.587671238164373
14233.64522535820834-0.645225358208338
14333.79826410832942-0.798264108329423
14421.470083443719410.529916556280588
14533.65064254687464-0.650642546874641
14611.47818763321775-0.478187633217751
14721.522495499781040.477504500218962
14843.925196533341720.074803466658281
14944.0877280656747-0.0877280656746981
15033.16633910317411-0.166339103174106
15132.488127604163310.511872395836695
15244.68560434803224-0.685604348032241
15322.67012453691537-0.670124536915373
15443.71600214662880.283997853371202
1553NANA
1563NANA


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.6619287447148340.6761425105703320.338071255285166
200.5318880071747010.9362239856505990.468111992825299
210.556761726947910.886476546104180.44323827305209
220.4713865354953190.9427730709906380.528613464504681
230.3682479783112050.736495956622410.631752021688795
240.3937281394934270.7874562789868540.606271860506573
250.458793277370910.917586554741820.54120672262909
260.4706584788550720.9413169577101440.529341521144928
270.768737012821310.4625259743573790.231262987178690
280.7164158238399520.5671683523200960.283584176160048
290.6602665950498180.6794668099003640.339733404950182
300.6685651245154940.6628697509690120.331434875484506
310.6003141661855120.7993716676289750.399685833814488
320.7220683605453920.5558632789092160.277931639454608
330.6831018733685740.6337962532628520.316898126631426
340.6483971632369290.7032056735261420.351602836763071
350.8007364295113350.3985271409773290.199263570488665
360.7614386564157320.4771226871685360.238561343584268
370.7234908080027260.5530183839945480.276509191997274
380.6663120525108070.6673758949783870.333687947489193
390.7258916797989010.5482166404021980.274108320201099
400.757690646761320.4846187064773590.242309353238680
410.7905610369775050.4188779260449910.209438963022495
420.7515556242603490.4968887514793020.248444375739651
430.8766683044871780.2466633910256450.123331695512822
440.8645930036801230.2708139926397550.135406996319877
450.8934813534945780.2130372930108430.106518646505422
460.8792460369666960.2415079260666080.120753963033304
470.8581803327334360.2836393345331270.141819667266564
480.8448240833244630.3103518333510730.155175916675537
490.8108780924982140.3782438150035720.189121907501786
500.8091182982744720.3817634034510560.190881701725528
510.7894473977475150.4211052045049710.210552602252485
520.9364733445328130.1270533109343740.0635266554671868
530.9180384018268020.1639231963463960.081961598173198
540.905594280274290.1888114394514210.0944057197257105
550.9498869425715120.1002261148569770.0501130574284885
560.9396106323980130.1207787352039740.0603893676019871
570.9224027121396810.1551945757206380.0775972878603188
580.9043002315111050.191399536977790.095699768488895
590.9604096899956480.07918062000870360.0395903100043518
600.964527765546550.07094446890689820.0354722344534491
610.960844886903360.07831022619328120.0391551130966406
620.9604030110647630.07919397787047330.0395969889352367
630.9536336707266240.09273265854675260.0463663292733763
640.9688676270244770.06226474595104590.0311323729755230
650.9607023352954480.07859532940910460.0392976647045523
660.9497643685294250.100471262941150.050235631470575
670.9502473565575020.09950528688499620.0497526434424981
680.936951644068250.1260967118634990.0630483559317495
690.9571809522827030.08563809543459480.0428190477172974
700.9703611081310880.05927778373782440.0296388918689122
710.970523545834920.05895290833015940.0294764541650797
720.9636376492343990.07272470153120220.0363623507656011
730.9688681310061790.06226373798764230.0311318689938212
740.990879071170930.01824185765813960.00912092882906981
750.9882942246976560.02341155060468720.0117057753023436
760.9911029147920740.01779417041585150.00889708520792575
770.992018265296690.01596346940662090.00798173470331045
780.9889056407012260.02218871859754750.0110943592987738
790.990790686872660.01841862625468130.00920931312734064
800.9871268279717410.02574634405651710.0128731720282586
810.9828220378005770.03435592439884550.0171779621994227
820.9790315445825820.04193691083483680.0209684554174184
830.9754518394529040.04909632109419230.0245481605470961
840.9763681021561040.04726379568779250.0236318978438962
850.9745653305658510.0508693388682980.025434669434149
860.966230153444890.06753969311022190.0337698465551110
870.9591470679002530.08170586419949310.0408529320997466
880.9512896125013690.09742077499726250.0487103874986313
890.9591516590231190.08169668195376220.0408483409768811
900.9564600066988450.08707998660231020.0435399933011551
910.9485320507660150.102935898467970.051467949233985
920.944607914294220.1107841714115600.0553920857057798
930.9305402693647540.1389194612704920.0694597306352459
940.9138480438967090.1723039122065820.0861519561032911
950.9010329323029570.1979341353940870.0989670676970435
960.8809774694134420.2380450611731160.119022530586558
970.872623508825350.2547529823493000.127376491174650
980.8427812565939490.3144374868121030.157218743406051
990.8160329388371120.3679341223257760.183967061162888
1000.7879615218249530.4240769563500950.212038478175047
1010.8333134127174270.3333731745651470.166686587282573
1020.819992635937240.3600147281255190.180007364062760
1030.8953653437434580.2092693125130840.104634656256542
1040.913880959291910.1722380814161800.0861190407080898
1050.8909152162744050.2181695674511910.109084783725595
1060.8664528169156750.2670943661686500.133547183084325
1070.8982396692492820.2035206615014360.101760330750718
1080.9067949648828480.1864100702343040.0932050351171518
1090.9015131080498710.1969737839002570.0984868919501287
1100.873255562584330.2534888748313390.126744437415670
1110.854359595846410.291280808307180.14564040415359
1120.850027044277330.2999459114453390.149972955722669
1130.8131732495589970.3736535008820070.186826750441003
1140.7676903251514920.4646193496970150.232309674848508
1150.744620499346640.5107590013067190.255379500653360
1160.7933969628890830.4132060742218340.206603037110917
1170.797639370867610.4047212582647790.202360629132389
1180.7875745766222310.4248508467555380.212425423377769
1190.8314597403358920.3370805193282150.168540259664108
1200.7802467346047940.4395065307904130.219753265395206
1210.7746186208764810.4507627582470380.225381379123519
1220.7298925699620160.5402148600759680.270107430037984
1230.6699755670334520.6600488659330970.330024432966548
1240.5952584218118090.8094831563763820.404741578188191
1250.5146822160784860.9706355678430280.485317783921514
1260.5807327287400250.838534542519950.419267271259975
1270.8022736881082760.3954526237834470.197726311891723
1280.7305355399665690.5389289200668620.269464460033431
1290.8911090991669850.217781801666030.108890900833015
1300.9596638267237870.08067234655242690.0403361732762134
1310.9295009618357980.1409980763284040.0704990381642022
1320.9194603851366650.1610792297266700.0805396148633351
1330.906679428476620.1866411430467580.0933205715233792
1340.8421075913769550.3157848172460890.157892408623045
1350.7525110589529420.4949778820941160.247488941047058
1360.556576835373950.8868463292520990.443423164626049
1370.59181223167530.81637553664940.4081877683247


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level110.092436974789916NOK
10% type I error level310.260504201680672NOK