| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 46071.1845929129 + 0.626558835163595X[t] + 0.336631429022401`yt-1`[t] -0.0518462980042751`yt-2`[t] + 0.0698520891405935`yt-3`[t] -0.0690390803881129`yt-4`[t] -0.0228142693555400`yt-5`[t] -0.243418679323981`yt-6`[t] -16257.540984572M1[t] -29962.1038916211M2[t] -30104.4363888772M3[t] -26010.3620742694M4[t] -21521.0979193019M5[t] -14857.4290050065M6[t] -9613.76497647236M7[t] -6977.30610908971M8[t] -5770.32808988139M9[t] -3321.17746051666M10[t] -1454.50789014262M11[t] -481.174713519072t + 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) | 46071.1845929129 | 13809.716823 | 3.3361 | 0.001688 | 0.000844 |
| X | 0.626558835163595 | 0.067925 | 9.2243 | 0 | 0 |
| `yt-1` | 0.336631429022401 | 0.113768 | 2.9589 | 0.004864 | 0.002432 |
| `yt-2` | -0.0518462980042751 | 0.124676 | -0.4158 | 0.679455 | 0.339728 |
| `yt-3` | 0.0698520891405935 | 0.124737 | 0.56 | 0.578199 | 0.2891 |
| `yt-4` | -0.0690390803881129 | 0.123304 | -0.5599 | 0.578259 | 0.289129 |
| `yt-5` | -0.0228142693555400 | 0.122964 | -0.1855 | 0.853625 | 0.426812 |
| `yt-6` | -0.243418679323981 | 0.087382 | -2.7857 | 0.007733 | 0.003866 |
| M1 | -16257.540984572 | 3917.093507 | -4.1504 | 0.000142 | 7.1e-05 |
| M2 | -29962.1038916211 | 4202.85066 | -7.129 | 0 | 0 |
| M3 | -30104.4363888772 | 4208.413418 | -7.1534 | 0 | 0 |
| M4 | -26010.3620742694 | 3692.10032 | -7.0449 | 0 | 0 |
| M5 | -21521.0979193019 | 2663.7328 | -8.0793 | 0 | 0 |
| M6 | -14857.4290050065 | 2857.27529 | -5.1999 | 4e-06 | 2e-06 |
| M7 | -9613.76497647236 | 2292.691171 | -4.1932 | 0.000124 | 6.2e-05 |
| M8 | -6977.30610908971 | 2142.876229 | -3.256 | 0.002124 | 0.001062 |
| M9 | -5770.32808988139 | 2018.424177 | -2.8588 | 0.00637 | 0.003185 |
| M10 | -3321.17746051666 | 2022.570357 | -1.6421 | 0.107398 | 0.053699 |
| M11 | -1454.50789014262 | 1657.246921 | -0.8777 | 0.384687 | 0.192343 |
| t | -481.174713519072 | 84.364183 | -5.7035 | 1e-06 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.996201542618571 |
| R-squared | 0.992417513515621 |
| Adjusted R-squared | 0.989285616924248 |
| F-TEST (value) | 316.874291523239 |
| F-TEST (DF numerator) | 19 |
| F-TEST (DF denominator) | 46 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2531.77697481877 |
| Sum Squared Residuals | 294855153.910234 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 337302 | 334182.393685091 | 3119.60631490889 |
| 2 | 349420 | 348213.448417159 | 1206.55158284101 |
| 3 | 336923 | 341900.468061574 | -4977.46806157396 |
| 4 | 330758 | 332279.700038611 | -1521.70003861141 |
| 5 | 321002 | 323166.254835277 | -2164.25483527702 |
| 6 | 320820 | 321929.166038643 | -1109.16603864280 |
| 7 | 327032 | 326836.598873915 | 195.401126084623 |
| 8 | 324047 | 323806.749403543 | 240.250596456604 |
| 9 | 316735 | 319479.040238083 | -2744.04023808320 |
| 10 | 315710 | 318101.459009824 | -2391.45900982406 |
| 11 | 313427 | 317014.503459581 | -3587.50345958097 |
| 12 | 310527 | 313888.55918022 | -3361.55918022006 |
| 13 | 330962 | 328292.681907067 | 2669.31809293342 |
| 14 | 339015 | 338017.323828611 | 997.676171389256 |
| 15 | 341332 | 342842.360036983 | -1510.36003698263 |
| 16 | 339092 | 342421.208319436 | -3329.20831943553 |
| 17 | 323308 | 325374.687756089 | -2066.68775608868 |
| 18 | 325849 | 326257.511723956 | -408.511723956002 |
| 19 | 330675 | 330340.823332562 | 334.176667438436 |
| 20 | 332225 | 330123.189240064 | 2101.81075993640 |
| 21 | 331735 | 329264.626805992 | 2470.37319400763 |
| 22 | 328047 | 326297.505130347 | 1749.49486965282 |
| 23 | 326165 | 325936.595958109 | 228.404041890979 |
| 24 | 327081 | 326162.887375317 | 918.112624682797 |
| 25 | 346764 | 346754.773227326 | 9.22677267383943 |
| 26 | 344190 | 344133.128830415 | 56.8711695849656 |
| 27 | 343333 | 340630.890941356 | 2702.10905864447 |
| 28 | 345777 | 343590.47990966 | 2186.52009034034 |
| 29 | 344094 | 341508.430554620 | 2585.56944537954 |
| 30 | 348609 | 348322.530233225 | 286.469766775032 |
| 31 | 354846 | 354529.1133241 | 316.886675900142 |
| 32 | 356427 | 357559.466306435 | -1132.46630643475 |
| 33 | 353467 | 354645.014911777 | -1178.01491177684 |
| 34 | 355996 | 354597.023574505 | 1398.97642549531 |
| 35 | 352487 | 351792.189410360 | 694.810589640337 |
| 36 | 355178 | 353726.703428013 | 1451.29657198703 |
| 37 | 374556 | 375969.728003829 | -1413.72800382922 |
| 38 | 375021 | 373941.263173298 | 1079.73682670212 |
| 39 | 375787 | 372483.729808698 | 3303.27019130241 |
| 40 | 372720 | 369113.110518116 | 3606.88948188375 |
| 41 | 364431 | 360183.195877919 | 4247.80412208104 |
| 42 | 370490 | 367322.737678734 | 3167.26232126571 |
| 43 | 376974 | 374282.30863082 | 2691.69136918042 |
| 44 | 377632 | 376886.579680783 | 745.420319217177 |
| 45 | 378205 | 374916.868583927 | 3288.13141607309 |
| 46 | 370861 | 370662.490357632 | 198.509642368109 |
| 47 | 369167 | 366677.396483769 | 2489.60351623071 |
| 48 | 371551 | 369629.977804921 | 1921.02219507947 |
| 49 | 382842 | 383469.928717746 | -627.928717746472 |
| 50 | 381903 | 383974.434894233 | -2071.43489423252 |
| 51 | 384502 | 383920.116739475 | 581.883260525253 |
| 52 | 392058 | 390099.395683978 | 1958.60431602236 |
| 53 | 384359 | 385279.304395970 | -920.304395970423 |
| 54 | 388884 | 388693.171047198 | 190.828952802351 |
| 55 | 386586 | 390124.155838604 | -3538.15583860362 |
| 56 | 387495 | 389450.015369175 | -1955.01536917543 |
| 57 | 385705 | 387541.449460221 | -1836.44946022068 |
| 58 | 378670 | 379625.521927692 | -955.521927692172 |
| 59 | 377367 | 377192.314688181 | 174.685311818939 |
| 60 | 376911 | 377839.872211529 | -928.872211529229 |
| 61 | 389827 | 393583.494458940 | -3756.49445894046 |
| 62 | 387820 | 389089.400856285 | -1269.40085628483 |
| 63 | 387267 | 387366.434411916 | -99.4344119155428 |
| 64 | 380575 | 383476.105530200 | -2901.10553019951 |
| 65 | 372402 | 374084.126580124 | -1682.12658012445 |
| 66 | 376740 | 378866.883278244 | -2126.88327824429 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 23 | 0.00586519273735834 | 0.0117303854747167 | 0.994134807262642 |
| 24 | 0.00143593005455180 | 0.00287186010910360 | 0.998564069945448 |
| 25 | 0.807930899391102 | 0.384138201217797 | 0.192069100608898 |
| 26 | 0.942260542818733 | 0.115478914362535 | 0.0577394571812674 |
| 27 | 0.927329161350543 | 0.145341677298913 | 0.0726708386494567 |
| 28 | 0.879096468235683 | 0.241807063528635 | 0.120903531764317 |
| 29 | 0.81852812519786 | 0.36294374960428 | 0.18147187480214 |
| 30 | 0.845724893947049 | 0.308550212105903 | 0.154275106052951 |
| 31 | 0.817405884135103 | 0.365188231729794 | 0.182594115864897 |
| 32 | 0.736671337052723 | 0.526657325894553 | 0.263328662947277 |
| 33 | 0.765192860230504 | 0.469614279538992 | 0.234807139769496 |
| 34 | 0.705966627892352 | 0.588066744215297 | 0.294033372107648 |
| 35 | 0.704689363909763 | 0.590621272180475 | 0.295310636090237 |
| 36 | 0.732451760497433 | 0.535096479005135 | 0.267548239502567 |
| 37 | 0.856411275337693 | 0.287177449324615 | 0.143588724662307 |
| 38 | 0.874780763343867 | 0.250438473312267 | 0.125219236656133 |
| 39 | 0.792074806312982 | 0.415850387374035 | 0.207925193687018 |
| 40 | 0.691701365999353 | 0.616597268001294 | 0.308298634000647 |
| 41 | 0.599700549249419 | 0.800598901501162 | 0.400299450750581 |
| 42 | 0.513131437687633 | 0.973737124624734 | 0.486868562312367 |
| 43 | 0.363351924088236 | 0.726703848176472 | 0.636648075911764 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0476190476190476 | NOK |
| 5% type I error level | 2 | 0.0952380952380952 | NOK |
| 10% type I error level | 2 | 0.0952380952380952 | OK |
