| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 209353.868069024 + 5735.54723429517X[t] + 3983.78103921857M1[t] + 3985.98987757529M2[t] + 5357.06728336256M3[t] + 3780.10695867444M4[t] + 4567.97996731963M5[t] + 5422.22403977358M6[t] + 1522.45486384059M7[t] + 1953.34861000709M8[t] + 2057.72025932738M9[t] + 1986.24169349609M10[t] + 2914.60840423528M11[t] + 841.58801269033t + 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) | 209353.868069024 | 15462.823805 | 13.5392 | 0 | 0 |
| X | 5735.54723429517 | 1969.645973 | 2.912 | 0.005212 | 0.002606 |
| M1 | 3983.78103921857 | 5502.990624 | 0.7239 | 0.472233 | 0.236117 |
| M2 | 3985.98987757529 | 5525.544563 | 0.7214 | 0.473791 | 0.236895 |
| M3 | 5357.06728336256 | 5482.78641 | 0.9771 | 0.332891 | 0.166446 |
| M4 | 3780.10695867444 | 5443.439219 | 0.6944 | 0.490387 | 0.245194 |
| M5 | 4567.97996731963 | 5439.253765 | 0.8398 | 0.404714 | 0.202357 |
| M6 | 5422.22403977358 | 5454.429364 | 0.9941 | 0.32461 | 0.162305 |
| M7 | 1522.45486384059 | 5462.216272 | 0.2787 | 0.781521 | 0.39076 |
| M8 | 1953.34861000709 | 5472.586249 | 0.3569 | 0.722533 | 0.361266 |
| M9 | 2057.72025932738 | 5680.924276 | 0.3622 | 0.718605 | 0.359302 |
| M10 | 1986.24169349609 | 5686.135583 | 0.3493 | 0.728213 | 0.364106 |
| M11 | 2914.60840423528 | 5696.571216 | 0.5116 | 0.610987 | 0.305494 |
| t | 841.58801269033 | 61.010651 | 13.7941 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.888249380073616 |
| R-squared | 0.788986961201163 |
| Adjusted R-squared | 0.738187525934777 |
| F-TEST (value) | 15.5314120533782 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 54 |
| p-value | 7.84927678409986e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 8977.46866398717 |
| Sum Squared Residuals | 4352126955.09506 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 269285 | 261210.724442154 | 8074.2755578462 |
| 2 | 269829 | 260907.411846341 | 8921.58815365855 |
| 3 | 270911 | 260252.303647672 | 10658.6963523285 |
| 4 | 266844 | 255502.048271667 | 11341.9517283329 |
| 5 | 271244 | 255410.845122714 | 15833.1548772859 |
| 6 | 269907 | 257680.231931288 | 12226.7680687121 |
| 7 | 271296 | 260357.598002340 | 10938.4019976596 |
| 8 | 270157 | 263924.298654915 | 6232.70134508474 |
| 9 | 271322 | 265443.813040355 | 5878.18695964458 |
| 10 | 267179 | 263919.703593496 | 3259.29640650361 |
| 11 | 264101 | 264542.548870067 | -441.548870066871 |
| 12 | 265518 | 263043.083201951 | 2474.91679804856 |
| 13 | 269419 | 269015.561700719 | 403.438299280631 |
| 14 | 268714 | 269859.358551766 | -1145.35855176644 |
| 15 | 272482 | 272072.023970244 | 409.976029755979 |
| 16 | 268351 | 269615.987487958 | -1264.98748795769 |
| 17 | 268175 | 271245.448509293 | -3070.44850929322 |
| 18 | 270674 | 270647.061700719 | 26.9382992805758 |
| 19 | 272764 | 269883.099431195 | 2880.90056880517 |
| 20 | 272599 | 271155.581190052 | 1443.41880994835 |
| 21 | 270333 | 272675.095575492 | -2342.09557549180 |
| 22 | 270846 | 274018.759745780 | -3172.75974578036 |
| 23 | 270491 | 275788.71446921 | -5297.71446920987 |
| 24 | 269160 | 274862.803524524 | -5702.80352452396 |
| 25 | 274027 | 280835.282023292 | -6808.2820232919 |
| 26 | 273784 | 282252.633597768 | -8468.63359776845 |
| 27 | 276663 | 284465.299016246 | -7802.29901624605 |
| 28 | 274525 | 283729.926704248 | -9204.92670424827 |
| 29 | 271344 | 283638.723555295 | -12294.7235552953 |
| 30 | 271115 | 281893.227299862 | -10778.2272998624 |
| 31 | 270798 | 276540.827242902 | -5742.8272429017 |
| 32 | 273911 | 276092.64483147 | -2181.64483146998 |
| 33 | 273985 | 277612.15921691 | -3627.15921691013 |
| 34 | 271917 | 279529.378110628 | -7612.3781106282 |
| 35 | 273338 | 281872.887557487 | -8534.88755748723 |
| 36 | 270601 | 280373.421889372 | -9772.4218893718 |
| 37 | 273547 | 285772.34566471 | -12225.3456647102 |
| 38 | 275363 | 286042.587792328 | -10679.5877923277 |
| 39 | 281229 | 287108.143763946 | -5879.14376394631 |
| 40 | 277793 | 286946.326175378 | -9153.32617537805 |
| 41 | 279913 | 287428.677749855 | -7515.67774985453 |
| 42 | 282500 | 286830.290941281 | -4330.29094128075 |
| 43 | 280041 | 285492.773948327 | -5451.77394832664 |
| 44 | 282166 | 286191.700983754 | -4025.70098375394 |
| 45 | 290304 | 285990.551198906 | 4313.44880109446 |
| 46 | 283519 | 286187.105922335 | -2668.10592233506 |
| 47 | 287816 | 287383.505922335 | 432.494077664936 |
| 48 | 285226 | 287031.149701079 | -1805.14970107867 |
| 49 | 287595 | 293577.182923276 | -5982.18292327611 |
| 50 | 289741 | 294420.979774323 | -4679.97977432315 |
| 51 | 289148 | 294339.426299083 | -5191.4262990827 |
| 52 | 288301 | 291883.389816796 | -3582.38981679636 |
| 53 | 290155 | 291792.186667843 | -1637.18666784334 |
| 54 | 289648 | 295208.682923276 | -5560.68292327616 |
| 55 | 288225 | 298459.603717758 | -10234.6037177582 |
| 56 | 289351 | 300305.640200045 | -10954.6402000445 |
| 57 | 294735 | 298957.380968337 | -4222.38096833709 |
| 58 | 305333 | 295139.05262776 | 10193.94737224 |
| 59 | 309030 | 295188.343180901 | 13841.6568190990 |
| 60 | 310215 | 295409.541683074 | 14805.4583169259 |
| 61 | 321935 | 305396.903245849 | 16538.0967541514 |
| 62 | 325734 | 309682.028437473 | 16051.9715625272 |
| 63 | 320846 | 313041.803302809 | 7804.19669719057 |
| 64 | 323023 | 311159.321543953 | 11863.6784560474 |
| 65 | 319753 | 311068.118395000 | 8684.88160500044 |
| 66 | 321753 | 313337.505203573 | 8415.49479642665 |
| 67 | 320757 | 313147.097657478 | 7609.90234252172 |
| 68 | 324479 | 314993.134139765 | 9485.86586023536 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0136127042841586 | 0.0272254085683172 | 0.986387295715841 |
| 18 | 0.00314842678082165 | 0.0062968535616433 | 0.996851573219178 |
| 19 | 0.000926553539736921 | 0.00185310707947384 | 0.999073446460263 |
| 20 | 0.00032315919237547 | 0.00064631838475094 | 0.999676840807625 |
| 21 | 0.000134499853789380 | 0.000268999707578759 | 0.99986550014621 |
| 22 | 0.000107940942986832 | 0.000215881885973664 | 0.999892059057013 |
| 23 | 0.000388741641042712 | 0.000777483282085423 | 0.999611258358957 |
| 24 | 0.000168268808250272 | 0.000336537616500544 | 0.99983173119175 |
| 25 | 7.98350298557177e-05 | 0.000159670059711435 | 0.999920164970144 |
| 26 | 3.0192511435412e-05 | 6.0385022870824e-05 | 0.999969807488565 |
| 27 | 1.29134604938512e-05 | 2.58269209877024e-05 | 0.999987086539506 |
| 28 | 8.66212765085053e-06 | 1.73242553017011e-05 | 0.999991337872349 |
| 29 | 3.65358385010062e-06 | 7.30716770020125e-06 | 0.99999634641615 |
| 30 | 1.74393837761806e-06 | 3.48787675523612e-06 | 0.999998256061622 |
| 31 | 2.27324846482756e-06 | 4.54649692965513e-06 | 0.999997726751535 |
| 32 | 4.13727261753147e-06 | 8.27454523506293e-06 | 0.999995862727382 |
| 33 | 2.77690728167555e-06 | 5.5538145633511e-06 | 0.999997223092718 |
| 34 | 8.81442547307764e-07 | 1.76288509461553e-06 | 0.999999118557453 |
| 35 | 6.8750161209482e-07 | 1.37500322418964e-06 | 0.999999312498388 |
| 36 | 2.18355626330723e-07 | 4.36711252661446e-07 | 0.999999781644374 |
| 37 | 8.26575429268427e-08 | 1.65315085853685e-07 | 0.999999917342457 |
| 38 | 2.78229728818504e-08 | 5.56459457637008e-08 | 0.999999972177027 |
| 39 | 3.98039941130153e-08 | 7.96079882260305e-08 | 0.999999960196006 |
| 40 | 2.89059402668932e-08 | 5.78118805337863e-08 | 0.99999997109406 |
| 41 | 4.6528532325386e-08 | 9.3057064650772e-08 | 0.999999953471468 |
| 42 | 4.17072541309245e-07 | 8.3414508261849e-07 | 0.999999582927459 |
| 43 | 1.13542918955451e-06 | 2.27085837910902e-06 | 0.99999886457081 |
| 44 | 3.41279194283345e-05 | 6.8255838856669e-05 | 0.999965872080572 |
| 45 | 0.502661449166827 | 0.994677101666346 | 0.497338550833173 |
| 46 | 0.564045836442472 | 0.871908327115057 | 0.435954163557528 |
| 47 | 0.811200766853801 | 0.377598466292398 | 0.188799233146199 |
| 48 | 0.985606632787531 | 0.0287867344249369 | 0.0143933672124685 |
| 49 | 0.969794829765385 | 0.0604103404692296 | 0.0302051702346148 |
| 50 | 0.953615149968263 | 0.0927697000634734 | 0.0463848500317367 |
| 51 | 0.878020919185846 | 0.243958161628309 | 0.121979080814154 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.771428571428571 | NOK |
| 5% type I error level | 29 | 0.828571428571429 | NOK |
| 10% type I error level | 31 | 0.885714285714286 | NOK |
