| Multiple Linear Regression - Estimated Regression Equation |
| X[t] = + 15346.807084182 + 0.289096682910106Y_1[t] + 0.27664390031443Y_2[t] + 149.900108370174M1[t] -3544.55214943836M2[t] -8210.6550195411M3[t] -4712.60659211193M4[t] -9776.45674052903M5[t] -9728.54466247162M6[t] -6124.88659935529M7[t] -3321.58788455124M8[t] -9310.67591569469M9[t] -14255.1507298011M10[t] + 5343.75696282205M11[t] + 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) | 15346.807084182 | 3027.53376 | 5.0691 | 3e-06 | 1e-06 |
| Y_1 | 0.289096682910106 | 0.109067 | 2.6506 | 0.009725 | 0.004863 |
| Y_2 | 0.27664390031443 | 0.108496 | 2.5498 | 0.012738 | 0.006369 |
| M1 | 149.900108370174 | 2189.494949 | 0.0685 | 0.945592 | 0.472796 |
| M2 | -3544.55214943836 | 1814.798347 | -1.9531 | 0.05439 | 0.027195 |
| M3 | -8210.6550195411 | 2325.469822 | -3.5308 | 0.000699 | 0.00035 |
| M4 | -4712.60659211193 | 2254.619156 | -2.0902 | 0.039858 | 0.019929 |
| M5 | -9776.45674052903 | 1777.365147 | -5.5005 | 0 | 0 |
| M6 | -9728.54466247162 | 2295.267893 | -4.2385 | 6.1e-05 | 3.1e-05 |
| M7 | -6124.88659935529 | 1936.716249 | -3.1625 | 0.002229 | 0.001114 |
| M8 | -3321.58788455124 | 1717.701493 | -1.9337 | 0.056773 | 0.028386 |
| M9 | -9310.67591569469 | 1646.975538 | -5.6532 | 0 | 0 |
| M10 | -14255.1507298011 | 2197.023644 | -6.4884 | 0 | 0 |
| M11 | 5343.75696282205 | 2374.202453 | 2.2508 | 0.027217 | 0.013608 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.948917019856188 |
| R-squared | 0.900443510572749 |
| Adjusted R-squared | 0.883850762334874 |
| F-TEST (value) | 54.2672918110916 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 78 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1936.43101832706 |
| Sum Squared Residuals | 292481676.921655 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 29462 | 32040.9993701206 | -2578.99937012064 |
| 2 | 26105 | 27808.6484320532 | -1703.64843205316 |
| 3 | 22397 | 22833.503563073 | -436.503563073006 |
| 4 | 23843 | 24330.8879169159 | -487.887916915945 |
| 5 | 21705 | 18659.275989621 | 3045.72401037905 |
| 6 | 18089 | 18489.1264394712 | -400.126439471226 |
| 7 | 20764 | 20455.9462383124 | 308.053761687636 |
| 8 | 25316 | 23032.234236364 | 2283.76576363604 |
| 9 | 17704 | 19099.1367391684 | -1395.13673916842 |
| 10 | 15548 | 13213.3410089816 | 2334.65899101844 |
| 11 | 28029 | 30083.1428840571 | -2054.14288405709 |
| 12 | 29383 | 27751.1573715582 | 1631.84262844184 |
| 13 | 36438 | 31745.286908413 | 4692.71309158698 |
| 14 | 32034 | 30464.987589561 | 1569.01241043898 |
| 15 | 22679 | 26477.4256446405 | -3798.42564464049 |
| 16 | 24319 | 26052.6348664609 | -1733.63486646085 |
| 17 | 18004 | 18874.8995905748 | -870.899590574837 |
| 18 | 17537 | 17550.8621125706 | -13.8621125705934 |
| 19 | 20366 | 19272.5057942823 | 1093.49420571772 |
| 20 | 22782 | 22764.4663235922 | 17.5336764078221 |
| 21 | 19169 | 18256.4614723491 | 912.538527650936 |
| 22 | 13807 | 12935.8520060481 | 871.1479939519 |
| 23 | 29743 | 29985.1088730712 | -242.108873071237 |
| 24 | 25591 | 27765.0320556187 | -2174.03205561866 |
| 25 | 29096 | 31123.1999319568 | -2027.19993195683 |
| 26 | 26482 | 27293.4060736427 | -811.406073642702 |
| 27 | 22405 | 22841.241345015 | -436.241345015035 |
| 28 | 27044 | 24437.4954407978 | 2606.50455920223 |
| 29 | 17970 | 19586.8876228187 | -1616.88762281872 |
| 30 | 18730 | 18294.8874537085 | 435.112546291524 |
| 31 | 19684 | 19607.9922443833 | 76.0077556166566 |
| 32 | 19785 | 22897.3385589226 | -3112.3385589226 |
| 33 | 18479 | 17201.367573653 | 1277.63242634697 |
| 34 | 10698 | 11907.2735255978 | -1209.27352559778 |
| 35 | 31956 | 28895.4229946868 | 3060.57700531324 |
| 36 | 29506 | 27544.7171288212 | 1961.28287117885 |
| 37 | 34506 | 32867.2263969457 | 1638.77360305427 |
| 38 | 27165 | 29940.4799979174 | -2775.47999791737 |
| 39 | 26736 | 24535.3378801437 | 2200.66211985629 |
| 40 | 23691 | 25878.5209583962 | -2187.52095839619 |
| 41 | 18157 | 19815.6911772829 | -1658.69117728294 |
| 42 | 17328 | 17421.3615356584 | -93.3615356583782 |
| 43 | 18205 | 19254.4111043022 | -1049.41110430218 |
| 44 | 20995 | 22081.9098166577 | -1086.90981665772 |
| 45 | 17382 | 17142.0182314092 | 239.981768590783 |
| 46 | 9367 | 11924.8735838259 | -2557.87358382585 |
| 47 | 31124 | 28207.1569510885 | 2916.84304891152 |
| 48 | 26551 | 26935.9756573214 | -384.975657321442 |
| 49 | 30651 | 31782.7779738848 | -1131.77797388476 |
| 50 | 25859 | 28008.5295598698 | -2149.52955986977 |
| 51 | 25100 | 23091.315376551 | 2008.68462344902 |
| 52 | 25778 | 25044.2618513446 | 733.738148655385 |
| 53 | 20418 | 19966.4465336019 | 451.553466398084 |
| 54 | 18688 | 18652.3649556743 | 35.6350443256525 |
| 55 | 20424 | 20273.0744516708 | 150.925548329155 |
| 56 | 24776 | 23099.6510604629 | 1676.34893953713 |
| 57 | 19814 | 18848.96560429 | 965.03439570995 |
| 58 | 12738 | 13673.9473037521 | -935.947303752092 |
| 59 | 31566 | 29854.4998347431 | 1711.50016525686 |
| 60 | 30111 | 27996.3229791277 | 2114.67702087235 |
| 61 | 30019 | 32934.2387689837 | -2915.23876898372 |
| 62 | 31934 | 28810.67274139 | 3123.32725861004 |
| 63 | 25826 | 24672.7387802311 | 1153.26121976885 |
| 64 | 26835 | 26934.7577375475 | -99.7577375475158 |
| 65 | 20205 | 20472.8651990662 | -267.865199066176 |
| 66 | 17789 | 18883.1999648468 | -1094.19996484684 |
| 67 | 20520 | 19954.2513829677 | 565.748617032315 |
| 68 | 22518 | 22878.7014756396 | -360.701475639571 |
| 69 | 15572 | 18222.7431087092 | -2650.74310870922 |
| 70 | 11509 | 11822.9372479374 | -313.937247937439 |
| 71 | 25447 | 28325.6765863128 | -2878.67658631281 |
| 72 | 24090 | 25887.3450229143 | -1797.34502291428 |
| 73 | 27786 | 29500.803615158 | -1714.80361515797 |
| 74 | 26195 | 26499.4469246585 | -304.446924658505 |
| 75 | 20516 | 22395.8670876079 | -1879.86708760793 |
| 76 | 22759 | 23811.9950073903 | -1052.99500739034 |
| 77 | 19028 | 17825.528008855 | 1202.47199114504 |
| 78 | 16971 | 17415.33263138 | -444.332631380031 |
| 79 | 20036 | 19392.1604256771 | 643.839574322866 |
| 80 | 22485 | 22512.4839706539 | -27.4839706538754 |
| 81 | 18730 | 18079.307270421 | 650.692729579 |
| 82 | 14538 | 12726.7753238572 | 1811.22467614282 |
| 83 | 27561 | 30074.9918760405 | -2513.99187604049 |
| 84 | 25985 | 27336.4497846387 | -1351.44978463865 |
| 85 | 34670 | 30633.4670345373 | 4036.53296546267 |
| 86 | 32066 | 29013.8286809075 | 3052.17131909248 |
| 87 | 27186 | 25997.5703227377 | 1188.4296772623 |
| 88 | 29586 | 27364.4462211468 | 2221.55377885323 |
| 89 | 21359 | 21644.4058781795 | -285.405878179502 |
| 90 | 21553 | 19977.8649066901 | 1575.1350933099 |
| 91 | 19573 | 21361.6583584042 | -1788.65835840418 |
| 92 | 24256 | 23646.2145577072 | 609.785442292785 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.872779588206698 | 0.254440823586603 | 0.127220411793302 |
| 18 | 0.854667402932053 | 0.290665194135893 | 0.145332597067947 |
| 19 | 0.790319792196051 | 0.419360415607898 | 0.209680207803949 |
| 20 | 0.753995288575988 | 0.492009422848025 | 0.246004711424012 |
| 21 | 0.758626161847582 | 0.482747676304836 | 0.241373838152418 |
| 22 | 0.77785172452224 | 0.444296550955519 | 0.22214827547776 |
| 23 | 0.76827863239911 | 0.463442735201779 | 0.23172136760089 |
| 24 | 0.854824326712867 | 0.290351346574266 | 0.145175673287133 |
| 25 | 0.854665875257014 | 0.290668249485972 | 0.145334124742986 |
| 26 | 0.804556507275848 | 0.390886985448303 | 0.195443492724152 |
| 27 | 0.748133047105861 | 0.503733905788279 | 0.251866952894139 |
| 28 | 0.764347860530691 | 0.471304278938617 | 0.235652139469309 |
| 29 | 0.786290329505886 | 0.427419340988229 | 0.213709670494114 |
| 30 | 0.751018055574037 | 0.497963888851926 | 0.248981944425963 |
| 31 | 0.698058760778141 | 0.603882478443718 | 0.301941239221859 |
| 32 | 0.780590661784816 | 0.438818676430369 | 0.219409338215184 |
| 33 | 0.744028325395568 | 0.511943349208865 | 0.255971674604432 |
| 34 | 0.779935431727507 | 0.440129136544986 | 0.220064568272493 |
| 35 | 0.842634291580508 | 0.314731416838985 | 0.157365708419492 |
| 36 | 0.82880165455173 | 0.34239669089654 | 0.17119834544827 |
| 37 | 0.815192966312105 | 0.36961406737579 | 0.184807033687895 |
| 38 | 0.846870173079204 | 0.306259653841591 | 0.153129826920796 |
| 39 | 0.87672178986537 | 0.246556420269262 | 0.123278210134631 |
| 40 | 0.873940863402343 | 0.252118273195314 | 0.126059136597657 |
| 41 | 0.857276411020767 | 0.285447177958466 | 0.142723588979233 |
| 42 | 0.813896308470807 | 0.372207383058386 | 0.186103691529193 |
| 43 | 0.779640723910372 | 0.440718552179255 | 0.220359276089628 |
| 44 | 0.740980190385194 | 0.518039619229612 | 0.259019809614806 |
| 45 | 0.685468975854404 | 0.629062048291193 | 0.314531024145596 |
| 46 | 0.724106896882415 | 0.551786206235171 | 0.275893103117585 |
| 47 | 0.798897195390973 | 0.402205609218053 | 0.201102804609027 |
| 48 | 0.750035684554144 | 0.499928630891712 | 0.249964315445856 |
| 49 | 0.711709949856726 | 0.576580100286548 | 0.288290050143274 |
| 50 | 0.776849943498016 | 0.446300113003968 | 0.223150056501984 |
| 51 | 0.78037388312536 | 0.439252233749281 | 0.219626116874641 |
| 52 | 0.72999331265002 | 0.540013374699961 | 0.270006687349981 |
| 53 | 0.67179801561785 | 0.6564039687643 | 0.32820198438215 |
| 54 | 0.602974509752846 | 0.794050980494309 | 0.397025490247154 |
| 55 | 0.531221396235142 | 0.937557207529716 | 0.468778603764858 |
| 56 | 0.505995100147101 | 0.988009799705799 | 0.494004899852899 |
| 57 | 0.458784598377408 | 0.917569196754815 | 0.541215401622592 |
| 58 | 0.423619734948548 | 0.847239469897096 | 0.576380265051452 |
| 59 | 0.527978318770018 | 0.944043362459965 | 0.472021681229982 |
| 60 | 0.559557370970512 | 0.880885258058975 | 0.440442629029488 |
| 61 | 0.799185933808027 | 0.401628132383947 | 0.200814066191973 |
| 62 | 0.812953298687126 | 0.374093402625748 | 0.187046701312874 |
| 63 | 0.768929106972722 | 0.462141786054557 | 0.231070893027278 |
| 64 | 0.718581566875318 | 0.562836866249364 | 0.281418433124682 |
| 65 | 0.652959421624593 | 0.694081156750813 | 0.347040578375407 |
| 66 | 0.609683375957244 | 0.780633248085513 | 0.390316624042756 |
| 67 | 0.544862737627628 | 0.910274524744744 | 0.455137262372372 |
| 68 | 0.452751112261341 | 0.905502224522682 | 0.547248887738659 |
| 69 | 0.512132983048984 | 0.975734033902033 | 0.487867016951016 |
| 70 | 0.437691515578409 | 0.875383031156818 | 0.562308484421591 |
| 71 | 0.380750682587749 | 0.761501365175499 | 0.619249317412251 |
| 72 | 0.293638130029898 | 0.587276260059796 | 0.706361869970102 |
| 73 | 0.538301867342846 | 0.923396265314307 | 0.461698132657154 |
| 74 | 0.570132004296937 | 0.859735991406127 | 0.429867995703063 |
| 75 | 0.499160750451448 | 0.998321500902896 | 0.500839249548552 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
