| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 575726.747205707 -66470.4227110583X[t] -804.875142026716M1[t] -4823.62574976884M2[t] -13212.7096908442M3[t] -19500.6269652530M4[t] -30145.3775729951M5[t] -16548.5577288942M6[t] + 34425.1916633637M7[t] + 43581.1077222883M8[t] + 33498.1904478795M9[t] + 13192.5678821509M10[t] -2456.51605892456M11[t] + 192.08394107544t + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | 575726.747205707 | 11286.27915 | 51.0112 | 0 | 0 |
| X | -66470.4227110583 | 10150.669975 | -6.5484 | 0 | 0 |
| M1 | -804.875142026716 | 13039.571626 | -0.0617 | 0.951005 | 0.475503 |
| M2 | -4823.62574976884 | 13029.148789 | -0.3702 | 0.712642 | 0.356321 |
| M3 | -13212.7096908442 | 13023.484952 | -1.0145 | 0.314773 | 0.157386 |
| M4 | -19500.6269652530 | 13022.586324 | -1.4974 | 0.139995 | 0.069997 |
| M5 | -30145.3775729951 | 13026.453891 | -2.3142 | 0.02442 | 0.01221 |
| M6 | -16548.5577288942 | 13057.021954 | -1.2674 | 0.21035 | 0.105175 |
| M7 | 34425.1916633637 | 13042.907515 | 2.6394 | 0.010785 | 0.005392 |
| M8 | 43581.1077222883 | 13033.54145 | 3.3438 | 0.001493 | 0.000746 |
| M9 | 33498.1904478795 | 13028.933999 | 2.5711 | 0.012874 | 0.006437 |
| M10 | 13192.5678821509 | 13605.469765 | 0.9697 | 0.336465 | 0.168233 |
| M11 | -2456.51605892456 | 13598.62417 | -0.1806 | 0.857311 | 0.428655 |
| t | 192.08394107544 | 249.150699 | 0.771 | 0.444033 | 0.222017 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.878227212463633 |
| R-squared | 0.771283036711643 |
| Adjusted R-squared | 0.717222663570759 |
| F-TEST (value) | 14.2670683145608 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 55 |
| p-value | 3.20965476419133e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21497.7035540613 |
| Sum Squared Residuals | 25418319195.4065 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 562325 | 575113.956004756 | -12788.9560047564 |
| 2 | 560854 | 571287.28933809 | -10433.2893380897 |
| 3 | 555332 | 563090.28933809 | -7758.28933808959 |
| 4 | 543599 | 556994.456004756 | -13395.4560047562 |
| 5 | 536662 | 546541.789338090 | -9879.78933808959 |
| 6 | 542722 | 560330.693123266 | -17608.6931232660 |
| 7 | 593530 | 611496.526456599 | -17966.5264565993 |
| 8 | 610763 | 620844.526456599 | -10081.5264565993 |
| 9 | 612613 | 610953.693123266 | 1659.30687673404 |
| 10 | 611324 | 590840.154498613 | 20483.8455013873 |
| 11 | 594167 | 575383.154498613 | 18783.8455013872 |
| 12 | 595454 | 578031.754498613 | 17422.2455013872 |
| 13 | 590865 | 577418.963297662 | 13446.0367023385 |
| 14 | 589379 | 573592.296630995 | 15786.7033690052 |
| 15 | 584428 | 565395.296630995 | 19032.7033690052 |
| 16 | 573100 | 559299.463297662 | 13800.5367023385 |
| 17 | 567456 | 548846.796630995 | 18609.2033690052 |
| 18 | 569028 | 562635.700416171 | 6392.29958382878 |
| 19 | 620735 | 613801.533749505 | 6933.46625049545 |
| 20 | 628884 | 623149.533749505 | 5734.46625049545 |
| 21 | 628232 | 613258.700416171 | 14973.2995838288 |
| 22 | 612117 | 593145.161791518 | 18971.8382084820 |
| 23 | 595404 | 577688.161791518 | 17715.8382084820 |
| 24 | 597141 | 580336.761791518 | 16804.2382084820 |
| 25 | 593408 | 579723.970590567 | 13684.0294094333 |
| 26 | 590072 | 575897.3039239 | 14174.6960760999 |
| 27 | 579799 | 567700.3039239 | 12098.6960760999 |
| 28 | 574205 | 561604.470590567 | 12600.5294094332 |
| 29 | 572775 | 551151.8039239 | 21623.1960760999 |
| 30 | 572942 | 564940.707709076 | 8001.2922909235 |
| 31 | 619567 | 616106.54104241 | 3460.45895759017 |
| 32 | 625809 | 625454.54104241 | 354.458957590171 |
| 33 | 619916 | 615563.707709076 | 4352.2922909235 |
| 34 | 587625 | 595450.169084423 | -7825.16908442332 |
| 35 | 565742 | 579993.169084423 | -14251.1690844233 |
| 36 | 557274 | 582641.769084423 | -25367.7690844233 |
| 37 | 560576 | 582028.977883472 | -21452.9778834720 |
| 38 | 548854 | 578202.311216805 | -29348.3112168054 |
| 39 | 531673 | 570005.311216805 | -38332.3112168054 |
| 40 | 525919 | 563909.477883472 | -37990.4778834721 |
| 41 | 511038 | 553456.811216805 | -42418.8112168054 |
| 42 | 498662 | 500775.292290923 | -2113.2922909235 |
| 43 | 555362 | 551941.125624257 | 3420.87437574317 |
| 44 | 564591 | 561289.125624257 | 3301.87437574316 |
| 45 | 541657 | 551398.292290924 | -9741.2922909235 |
| 46 | 527070 | 531284.75366627 | -4214.75366627031 |
| 47 | 509846 | 515827.75366627 | -5981.75366627032 |
| 48 | 514258 | 518476.35366627 | -4218.35366627032 |
| 49 | 516922 | 517863.562465319 | -941.562465319028 |
| 50 | 507561 | 514036.895798652 | -6475.89579865238 |
| 51 | 492622 | 505839.895798652 | -13217.8957986524 |
| 52 | 490243 | 499744.062465319 | -9501.06246531906 |
| 53 | 469357 | 489291.395798652 | -19934.3957986524 |
| 54 | 477580 | 503080.299583829 | -25500.2995838288 |
| 55 | 528379 | 554246.132917162 | -25867.1329171621 |
| 56 | 533590 | 563594.132917162 | -30004.1329171621 |
| 57 | 517945 | 553703.299583829 | -35758.2995838288 |
| 58 | 506174 | 533589.760959176 | -27415.7609591756 |
| 59 | 501866 | 518132.760959176 | -16266.7609591756 |
| 60 | 516141 | 520781.360959176 | -4640.36095917559 |
| 61 | 528222 | 520168.569758224 | 8053.4302417757 |
| 62 | 532638 | 516341.903091558 | 16296.0969084423 |
| 63 | 536322 | 508144.903091558 | 28177.0969084423 |
| 64 | 536535 | 502049.069758224 | 34485.9302417757 |
| 65 | 523597 | 491596.403091558 | 32000.5969084423 |
| 66 | 536214 | 505385.306876734 | 30828.6931232659 |
| 67 | 586570 | 556551.140210067 | 30018.8597899326 |
| 68 | 596594 | 565899.140210067 | 30694.8597899326 |
| 69 | 580523 | 556008.306876734 | 24514.6931232659 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 4.75383306438665e-05 | 9.5076661287733e-05 | 0.999952461669356 |
| 18 | 1.19706509980433e-05 | 2.39413019960866e-05 | 0.999988029349002 |
| 19 | 7.67216069366232e-07 | 1.53443213873246e-06 | 0.99999923278393 |
| 20 | 1.72037544255747e-05 | 3.44075088511493e-05 | 0.999982796245574 |
| 21 | 2.54757208751506e-05 | 5.09514417503011e-05 | 0.999974524279125 |
| 22 | 0.000522803680025649 | 0.00104560736005130 | 0.999477196319974 |
| 23 | 0.00100751787159313 | 0.00201503574318627 | 0.998992482128407 |
| 24 | 0.00116930484583806 | 0.00233860969167612 | 0.998830695154162 |
| 25 | 0.00075059313307377 | 0.00150118626614754 | 0.999249406866926 |
| 26 | 0.000503064609366793 | 0.00100612921873359 | 0.999496935390633 |
| 27 | 0.000456867087111288 | 0.000913734174222577 | 0.99954313291289 |
| 28 | 0.000257466978091438 | 0.000514933956182875 | 0.999742533021909 |
| 29 | 0.000218493807874308 | 0.000436987615748616 | 0.999781506192126 |
| 30 | 0.000115518209266206 | 0.000231036418532412 | 0.999884481790734 |
| 31 | 7.08576702481385e-05 | 0.000141715340496277 | 0.999929142329752 |
| 32 | 7.17790928857272e-05 | 0.000143558185771454 | 0.999928220907114 |
| 33 | 0.000231922292189748 | 0.000463844584379497 | 0.99976807770781 |
| 34 | 0.00613920346572203 | 0.0122784069314441 | 0.993860796534278 |
| 35 | 0.0375052359899874 | 0.0750104719799749 | 0.962494764010013 |
| 36 | 0.119701609899286 | 0.239403219798571 | 0.880298390100714 |
| 37 | 0.144086045004329 | 0.288172090008659 | 0.85591395499567 |
| 38 | 0.179870631161577 | 0.359741262323154 | 0.820129368838423 |
| 39 | 0.227971066662546 | 0.455942133325092 | 0.772028933337454 |
| 40 | 0.229551074850393 | 0.459102149700786 | 0.770448925149607 |
| 41 | 0.248199393945709 | 0.496398787891418 | 0.751800606054291 |
| 42 | 0.200697042146355 | 0.401394084292709 | 0.799302957853645 |
| 43 | 0.18496830953507 | 0.36993661907014 | 0.81503169046493 |
| 44 | 0.201227018394088 | 0.402454036788177 | 0.798772981605911 |
| 45 | 0.24364706163685 | 0.4872941232737 | 0.75635293836315 |
| 46 | 0.422967102681411 | 0.845934205362821 | 0.577032897318589 |
| 47 | 0.609626778782343 | 0.780746442435315 | 0.390373221217657 |
| 48 | 0.791692967961256 | 0.416614064077489 | 0.208307032038744 |
| 49 | 0.937423953284224 | 0.125152093431553 | 0.0625760467157764 |
| 50 | 0.989593831670816 | 0.0208123366583679 | 0.0104061683291840 |
| 51 | 0.988617156448487 | 0.0227656871030267 | 0.0113828435515133 |
| 52 | 0.993416769515177 | 0.0131664609696456 | 0.00658323048482278 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 17 | 0.472222222222222 | NOK |
| 5% type I error level | 21 | 0.583333333333333 | NOK |
| 10% type I error level | 22 | 0.611111111111111 | NOK |
