Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 9.70561896019673 -0.441040701132333X[t] -0.0985342606738392M1[t] -0.256094958407542M2[t] -0.237083808038267M3[t] -0.193699418555253M4[t] -0.276578442619401M5[t] -0.44275433133854M6[t] -0.609354655164949M7[t] -0.787296025591902M8[t] -0.897691984975736M9[t] -0.408930220057678M10[t] -0.0351936336048432M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)9.705618960196730.34831627.864400
X-0.4410407011323330.114508-3.85160.0001718.6e-05
M1-0.09853426067383920.379431-0.25970.7954480.397724
M2-0.2560949584075420.379415-0.6750.5006990.250349
M3-0.2370838080382670.379424-0.62490.5329870.266494
M4-0.1936994185552530.379413-0.51050.610410.305205
M5-0.2765784426194010.379417-0.7290.4671280.233564
M6-0.442754331338540.379414-1.16690.2450260.122513
M7-0.6093546551649490.379442-1.60590.1103260.055163
M8-0.7872960255919020.379444-2.07490.0396520.019826
M9-0.8976919849757360.379417-2.3660.0192190.00961
M10-0.4089302200576780.379412-1.07780.2827970.141399
M11-0.03519363360484320.379429-0.09280.9262190.463109


Multiple Linear Regression - Regression Statistics
Multiple R0.388941212446403
R-squared0.151275266739278
Adjusted R-squared0.0855675454545772
F-TEST (value)2.30224490792835
F-TEST (DF numerator)12
F-TEST (DF denominator)155
p-value0.00997026602697082
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.00382229268530
Sum Squared Residuals156.187175270256


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
17.68.65443678507697-1.05443678507697
27.68.46600323826408-0.866003238264084
37.88.41003746944086-0.61003746944086
488.25936395042565-0.259363950425649
588.20735777544076-0.207357775440761
687.970615374540450.0293846254595509
77.97.812835864736690.087164135263311
87.97.731923448558850.168076551441152
987.758250106526040.241749893473963
108.58.158803731217630.341196268782372
119.28.263505489979740.93649451002026
129.48.461884183003550.938115816996453
139.58.407453992442941.09254600755706
149.58.333691027924381.16630897207562
159.68.277725259101161.32227474089884
169.78.444601044901231.25539895509877
179.78.32643876474651.37356123525351
189.68.24406060924251.35593939075750
199.58.033356215302861.46664378469714
209.47.789258739706051.61074126029395
219.37.590654640095751.70934535990425
229.68.101468440070431.49853155992957
2310.28.5942860158291.60571398417101
2410.28.620658835411191.57934116458881
2510.18.672078413122341.42792158687766
269.98.571853006535841.32814699346416
279.88.648199448052321.15180055194768
289.88.682763023512691.11723697648731
299.78.626346441516481.07365355848352
309.58.495453808887931.00454619111207
319.38.342084706095490.957915293904513
329.18.30968676704220.790313232957795
3398.247805284782930.752194715217072
349.58.771850305791570.728149694208429
35109.10589322914250.894106770857504
3610.29.180780525849251.01921947415075
3710.19.069015044141441.03098495585856
38108.801194171124651.19880582887535
399.98.824615728505251.07538427149475
40108.64747976742211.3525202325779
419.98.599883999448541.30011600055146
429.78.367552005559551.33244799444045
439.58.196541274721821.30345872527818
449.28.08034560245341.11965439754661
4598.014053713182790.985946286817209
469.38.449890593964970.850109406035033
479.88.82362718041780.976372819582197
489.88.836768778966030.96323122103397
499.68.522124574737351.07787542526265
509.48.408667947116880.991332052883123
519.38.352702178293660.947297821706344
529.28.493115522025780.706884477974215
539.28.55577992933530.644220070664695
5498.618945205204980.381054794795020
558.88.540553021605040.259446978394963
568.78.221478626815740.478521373184261
578.78.040516155250730.659483844749268
589.18.463121814998940.636878185001062
599.78.854500029497070.845499970502932
609.88.991133024362350.808866975637654
619.69.033731788050850.566268211949146
629.48.823246206181270.57675379381873
639.48.961338345856280.438661654143725
649.59.32668244716590.173317552834107
659.49.10267039873940.297329601260603
669.38.81300311370320.486996886296795
679.28.430292846321950.769707153678045
6898.097987230498680.902012769501316
698.98.106672260420580.79332773957942
709.28.842416817972740.357583182027255
719.89.476367418093660.323632581906345
729.99.343965585268210.556034414731788
739.69.227789696549080.37221030345092
749.29.193720395132430.00627960486756947
759.19.20832113849038-0.108321138490382
769.19.092930875565760.0070691244342427
7798.996820630467640.00317936953236231
788.98.720384566465420.179615433534584
798.78.580246684706950.119753315293052
808.58.54784874565366-0.0478487456536638
818.38.48155685638306-0.181556856383063
828.59.01001228440303-0.51001228440303
838.79.26907828856146-0.56907828856146
848.49.18078052584925-0.780780525849249
858.19.03373178805085-0.933731788050854
867.88.77473172905671-0.974731729056714
877.78.61291619196173-0.912916191961733
887.58.7224566866146-1.22245668661460
897.28.56901115036928-1.36901115036928
906.88.26611264429911-1.46611264429911
916.78.19654127472182-1.49654127472182
926.47.96567502015898-1.56567502015898
936.37.59506504710708-1.29506504710708
946.88.06618518397984-1.26618518397984
957.38.40022810733076-1.10022810733076
967.18.22372220439209-1.12372220439209
9778.29719381715986-1.29719381715986
986.88.08229782827895-1.28229782827895
996.68.37034380633895-1.77034380633895
1006.38.54162999915034-2.24162999915034
1016.18.43669894002957-2.33669894002957
1026.18.34108956349161-2.24108956349161
1036.37.86576074887257-1.56576074887257
1046.37.5334551330493-1.23345513304930
10567.51567772090325-1.51567772090325
1066.28.12793088213837-1.92793088213837
1076.48.49284665456855-2.09284665456855
1086.88.70886697563765-1.90886697563765
1097.58.5706390518619-1.07063905186190
1107.58.51010730837731-1.01010730837731
1117.68.50706642368997-0.907066423689973
1127.68.2329015083577-0.632901508357709
1137.48.26910347359929-0.869103473599288
1147.38.08528595683486-0.785285956834857
1157.18.29798063598225-1.19798063598226
1166.98.33173880209882-1.43173880209882
1176.88.41981115822454-1.61981115822454
1187.58.73215664268966-1.23215664268966
1197.69.11471404316514-1.51471404316514
1207.89.14990767676999-1.34990767676999
12189.03814219506218-1.03814219506218
1228.18.96437923054362-0.864379230543617
1238.28.86430939160716-0.664309391607163
1248.38.97826029327135-0.67826029327135
1258.28.66162969760707-0.461629697607066
12688.48663299486528-0.48663299486528
1277.98.44352406735592-0.543524067355924
1287.68.4596406054272-0.859640605427198
1297.68.09344103938661-0.493441039386611
1308.38.63953809545187-0.33953809545187
1318.48.880962471565-0.480962471565007
1328.48.91174569815853-0.511745698158526
1338.48.9102403917338-0.5102403917338
1348.48.62918829768304-0.229188297683044
1358.68.7011243321882-0.101124332188200
1368.98.810664826841060.0893351731589363
1378.88.87332923415059-0.0733292341505839
1388.38.76448863657865-0.464488636578649
1397.58.2494661588577-0.749466158857698
1407.27.76720670464943-0.567206704649435
1417.47.81117499066192-0.411174990661918
1428.88.233780650410130.566219349589876
1439.38.673673342032810.62632665796719
1449.38.810306336898090.489693663101911
1458.78.345708294284410.354291705715585
1468.28.32487021390173-0.124870213901735
1478.38.46737276058806-0.167372760588062
1488.58.5151675570824-0.0151675570824012
1498.68.295565915667230.304434084332771
1508.57.908869676381920.591130323618076
1518.27.878991969906540.32100803009346
1528.17.811310774762670.288689225237331
1537.97.54214016297120.357859837028805
1548.67.911820938583520.688179061416478
1558.78.298788746070330.401211253929671
1568.78.311930344618550.388069655381446
1578.58.51771416772602-0.0177141677260242
1588.48.316049399879090.0839506001209126
1598.58.193927525886020.306072474113983
1608.78.351982497663440.348017502336561
1618.78.379363648882370.320636351117627
1628.68.517505843944540.0824941560554566
1638.58.23182453081240.268175469187595
1648.37.952443799125010.347556200874986
16587.983180864103530.0168191358964721
1668.28.59102361832731-0.391023618327315
1678.18.95152898374618-0.85152898374618
1688.19.16754930481528-1.06754930481528


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.8126180921311260.3747638157377480.187381907868874
170.8664206719732460.2671586560535080.133579328026754
180.8881438484561480.2237123030877040.111856151543852
190.8767101851586850.246579629682630.123289814841315
200.8681798395224160.2636403209551680.131820160477584
210.8688482320605690.2623035358788620.131151767939431
220.851524081215740.2969518375685200.148475918784260
230.820917844852750.35816431029450.17908215514725
240.786126522312360.427746955375280.21387347768764
250.7961104707743020.4077790584513960.203889529225698
260.7803133702133530.4393732595732930.219686629786647
270.7326460884266190.5347078231467620.267353911573381
280.6781731952736360.6436536094527290.321826804726364
290.6208678243926720.7582643512146560.379132175607328
300.5644950226792770.8710099546414460.435504977320723
310.5111743142134360.9776513715731280.488825685786564
320.4713846904551730.9427693809103460.528615309544827
330.4312504276038860.8625008552077730.568749572396114
340.3853387252277330.7706774504554660.614661274772267
350.3507865287306050.701573057461210.649213471269395
360.3107099539970280.6214199079940560.689290046002972
370.2737797949831330.5475595899662660.726220205016867
380.250616510293970.501233020587940.74938348970603
390.2194402127002220.4388804254004450.780559787299778
400.2099604543385280.4199209086770560.790039545661472
410.1964084049767540.3928168099535080.803591595023246
420.1874026926326320.3748053852652630.812597307367368
430.1773638016665540.3547276033331090.822636198333446
440.1591055267074580.3182110534149160.840894473292542
450.1386694302675860.2773388605351710.861330569732414
460.1183100329342260.2366200658684520.881689967065774
470.1059582070232170.2119164140464340.894041792976783
480.09530517030614150.1906103406122830.904694829693859
490.09392261994942150.1878452398988430.906077380050578
500.087966804841470.175933609682940.91203319515853
510.0823269164996140.1646538329992280.917673083500386
520.07250340091501280.1450068018300260.927496599084987
530.06333609107204880.1266721821440980.936663908927951
540.05819511911525980.1163902382305200.94180488088474
550.05573994003578820.1114798800715760.944260059964212
560.04880441955028640.09760883910057280.951195580449714
570.04249349724364040.08498699448728080.95750650275636
580.03653568902742870.07307137805485740.963464310972571
590.03472887499483370.06945774998966750.965271125005166
600.03299903153908830.06599806307817660.967000968460912
610.02771879846153950.0554375969230790.97228120153846
620.02375082968458280.04750165936916560.976249170315417
630.02016503988533370.04033007977066740.979834960114666
640.01792122095297140.03584244190594270.982078779047029
650.01517398453612510.03034796907225020.984826015463875
660.01277486371890930.02554972743781850.98722513628109
670.01183841065291740.02367682130583490.988161589347083
680.01208971635495970.02417943270991940.98791028364504
690.01183738550969000.02367477101938010.98816261449031
700.01010124619303900.02020249238607800.98989875380696
710.009538098979462140.01907619795892430.990461901020538
720.00945537758064220.01891075516128440.990544622419358
730.008196228373503560.01639245674700710.991803771626496
740.007117965190070410.01423593038014080.99288203480993
750.006225540046838940.01245108009367790.993774459953161
760.00543890003228540.01087780006457080.994561099967715
770.00484404303078830.00968808606157660.995155956969212
780.004413318937687210.008826637875374430.995586681062313
790.00414193887402850.0082838777480570.995858061125972
800.003986404313220310.007972808626440620.99601359568678
810.003993443305008740.007986886610017480.996006556694991
820.0040618961811830.0081237923623660.995938103818817
830.005405568105653170.01081113621130630.994594431894347
840.00945203237316980.01890406474633960.99054796762683
850.01324389905508080.02648779811016160.98675610094492
860.01962703531807780.03925407063615570.980372964681922
870.02869166882040480.05738333764080970.971308331179595
880.05058597147261240.1011719429452250.949414028527388
890.09630369343694340.1926073868738870.903696306563057
900.1847293635861090.3694587271722190.81527063641389
910.2899519756799410.5799039513598810.71004802432006
920.4234055679131190.8468111358262380.576594432086881
930.5293331902569790.9413336194860420.470666809743021
940.6119559429931610.7760881140136780.388044057006839
950.6643345634789550.671330873042090.335665436521045
960.7182312028433150.5635375943133690.281768797156685
970.7636890392119290.4726219215761420.236310960788071
980.8042670039919350.3914659920161310.195732996008065
990.8784881169535030.2430237660929950.121511883046497
1000.9579329579561730.08413408408765430.0420670420438271
1010.9910756974890780.01784860502184490.00892430251092246
1020.9983080319756250.003383936048750360.00169196802437518
1030.9992574027595710.001485194480857680.000742597240428841
1040.9995552305093820.0008895389812353020.000444769490617651
1050.9998460306902120.0003079386195764320.000153969309788216
1060.9999892947992482.14104015047177e-051.07052007523588e-05
1070.9999997206199185.58760163823678e-072.79380081911839e-07
1080.9999999872224562.55550883143679e-081.27775441571839e-08
1090.999999991837521.63249617520293e-088.16248087601466e-09
1100.999999992752911.44941798697542e-087.24708993487712e-09
1110.9999999936682891.26634228280509e-086.33171141402543e-09
1120.9999999981819943.63601283856146e-091.81800641928073e-09
1130.9999999997781854.43629708030892e-102.21814854015446e-10
1140.9999999999777754.44501874759462e-112.22250937379731e-11
1150.9999999999904551.90896277900824e-119.54481389504121e-12
1160.9999999999934681.30640916750116e-116.53204583750581e-12
1170.9999999999945131.09742808319523e-115.48714041597614e-12
1180.9999999999968876.22555606579576e-123.11277803289788e-12
1190.999999999998962.08013082624772e-121.04006541312386e-12
1200.9999999999993561.28831180615842e-126.44155903079211e-13
1210.999999999998672.65765677546652e-121.32882838773326e-12
1220.9999999999958068.38727004856295e-124.19363502428147e-12
1230.9999999999867022.65953570925540e-111.32976785462770e-11
1240.9999999999639837.20334507345692e-113.60167253672846e-11
1250.999999999932811.34381429479520e-106.71907147397598e-11
1260.9999999998713222.57354996294906e-101.28677498147453e-10
1270.9999999995823268.35348728000453e-104.17674364000227e-10
1280.9999999987381062.52378730206586e-091.26189365103293e-09
1290.999999996018197.96361838443215e-093.98180919221608e-09
1300.9999999877992752.44014491374323e-081.22007245687162e-08
1310.9999999671796866.56406272752546e-083.28203136376273e-08
1320.9999999157206551.68558689377557e-078.42793446887787e-08
1330.999999752348734.95302540284036e-072.47651270142018e-07
1340.9999993038275021.39234499587402e-066.96172497937012e-07
1350.9999982692646633.46147067317826e-061.73073533658913e-06
1360.999996354166787.29166643876348e-063.64583321938174e-06
1370.999991645311941.67093761213426e-058.35468806067132e-06
1380.9999770718543554.58562912908313e-052.29281456454156e-05
1390.9999783343511494.33312977018524e-052.16656488509262e-05
1400.9999934988511751.30022976495694e-056.5011488247847e-06
1410.9999896373120332.07253759337577e-051.03626879668788e-05
1420.9999773813363264.52373273478891e-052.26186636739445e-05
1430.9999944201829031.11596341948312e-055.57981709741558e-06
1440.9999998350047083.29990584769918e-071.64995292384959e-07
1450.9999991191692381.76166152458454e-068.8083076229227e-07
1460.9999959931664888.01366702409177e-064.00683351204588e-06
1470.9999784823344414.30353311175083e-052.15176655587542e-05
1480.9998954187984860.0002091624030287740.000104581201514387
1490.9995131233335250.000973753332950290.000486876666475145
1500.9987245473901170.002550905219766490.00127545260988325
1510.9982449684164590.003510063167082640.00175503158354132
1520.9937221621893220.01255567562135640.00627783781067818


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level560.408759124087591NOK
5% type I error level770.562043795620438NOK
10% type I error level850.62043795620438NOK