| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 129656.217228832 + 12.4358918340159DJIA[t] + 0.524824953147275Y1[t] + 0.222560731502311Y2[t] + 221392.319599041M1[t] + 273538.387148335M2[t] + 206489.247472616M3[t] + 146948.49845131M4[t] + 362848.209945268M5[t] + 116948.288333272M6[t] + 55546.0535751213M7[t] -40727.3840958933M8[t] -219577.429709325M9[t] -158224.026404345M10[t] -97473.7128923078M11[t] + 874.612157839409t + 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) | 129656.217228832 | 57637.816627 | 2.2495 | 0.029781 | 0.014891 |
| DJIA | 12.4358918340159 | 3.079322 | 4.0385 | 0.000224 | 0.000112 |
| Y1 | 0.524824953147275 | 0.145834 | 3.5988 | 0.000837 | 0.000418 |
| Y2 | 0.222560731502311 | 0.132311 | 1.6821 | 0.099971 | 0.049985 |
| M1 | 221392.319599041 | 21753.826268 | 10.1772 | 0 | 0 |
| M2 | 273538.387148335 | 44595.776518 | 6.1337 | 0 | 0 |
| M3 | 206489.247472616 | 45965.934225 | 4.4922 | 5.4e-05 | 2.7e-05 |
| M4 | 146948.49845131 | 43381.094588 | 3.3874 | 0.001543 | 0.000771 |
| M5 | 362848.209945268 | 41606.347274 | 8.721 | 0 | 0 |
| M6 | 116948.288333272 | 67849.313808 | 1.7236 | 0.092127 | 0.046063 |
| M7 | 55546.0535751213 | 49809.624871 | 1.1152 | 0.271119 | 0.13556 |
| M8 | -40727.3840958933 | 45260.145545 | -0.8999 | 0.37333 | 0.186665 |
| M9 | -219577.429709325 | 37915.746689 | -5.7912 | 1e-06 | 0 |
| M10 | -158224.026404345 | 35261.391135 | -4.4872 | 5.5e-05 | 2.8e-05 |
| M11 | -97473.7128923078 | 20490.289028 | -4.7571 | 2.3e-05 | 1.2e-05 |
| t | 874.612157839409 | 330.178509 | 2.6489 | 0.01133 | 0.005665 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.996234563754612 |
| R-squared | 0.992483306019343 |
| Adjusted R-squared | 0.989798772454822 |
| F-TEST (value) | 369.704189635123 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 42 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 26380.5966643776 |
| Sum Squared Residuals | 29229306975.4799 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1207763 | 1231934.84623924 | -24171.8462392447 |
| 2 | 1368839 | 1389986.73089028 | -21147.7308902834 |
| 3 | 1469798 | 1456143.23103228 | 13654.7689677218 |
| 4 | 1498721 | 1483918.05546411 | 14802.9445358923 |
| 5 | 1761769 | 1742892.19038527 | 18876.8096147344 |
| 6 | 1653214 | 1640376.99731576 | 12837.0026842425 |
| 7 | 1599104 | 1582504.32340551 | 16599.6765944936 |
| 8 | 1421179 | 1432947.51070269 | -11768.5107026891 |
| 9 | 1163995 | 1154098.88550966 | 9896.11449033933 |
| 10 | 1037735 | 1040652.24230833 | -2917.24230833081 |
| 11 | 1015407 | 980606.263243803 | 34800.7367561969 |
| 12 | 1039210 | 1040734.41267586 | -1524.41267585885 |
| 13 | 1258049 | 1271965.861002 | -13916.8610020010 |
| 14 | 1469445 | 1448342.54335553 | 21102.4566444735 |
| 15 | 1552346 | 1539346.25118104 | 12999.7488189553 |
| 16 | 1549144 | 1571012.11087183 | -21868.1108718256 |
| 17 | 1785895 | 1804997.42895035 | -19102.4289503532 |
| 18 | 1662335 | 1685943.15629329 | -23608.1562932917 |
| 19 | 1629440 | 1616964.53912120 | 12475.4608788035 |
| 20 | 1467430 | 1481796.99310387 | -14366.9931038669 |
| 21 | 1202209 | 1213229.48165308 | -11020.4816530790 |
| 22 | 1076982 | 1103205.61993474 | -26223.6199347369 |
| 23 | 1039367 | 1042052.09771843 | -2685.09771843052 |
| 24 | 1063449 | 1088397.90346119 | -24948.9034611854 |
| 25 | 1335135 | 1315998.05247231 | 19136.9475276891 |
| 26 | 1491602 | 1525777.60745416 | -34175.6074541639 |
| 27 | 1591972 | 1609210.42197474 | -17238.4219747393 |
| 28 | 1641248 | 1635320.66660515 | 5927.3333948493 |
| 29 | 1898849 | 1897849.41585780 | 999.58414220199 |
| 30 | 1798580 | 1800798.97299965 | -2218.97299964819 |
| 31 | 1762444 | 1751668.68602654 | 10775.3139734618 |
| 32 | 1622044 | 1615416.38998068 | 6627.61001931874 |
| 33 | 1368955 | 1348770.24445763 | 20184.7555423690 |
| 34 | 1262973 | 1245593.91381338 | 17379.0861866209 |
| 35 | 1195650 | 1187627.81022728 | 8022.18977271624 |
| 36 | 1269530 | 1222280.90412311 | 47249.095876888 |
| 37 | 1479279 | 1468294.92167016 | 10984.0783298362 |
| 38 | 1607819 | 1654769.67368396 | -46950.6736839629 |
| 39 | 1712466 | 1700477.06702117 | 11988.9329788306 |
| 40 | 1721766 | 1709318.95964833 | 12447.0403516682 |
| 41 | 1949843 | 1954612.79756419 | -4769.79756419246 |
| 42 | 1821326 | 1833416.31692726 | -12090.3169272630 |
| 43 | 1757802 | 1747584.04468930 | 10217.9553106956 |
| 44 | 1590367 | 1571270.58294535 | 19096.4170546472 |
| 45 | 1260647 | 1285115.30627868 | -24468.3062786766 |
| 46 | 1149235 | 1136378.83240563 | 12856.1675943738 |
| 47 | 1016367 | 1056504.82881048 | -40137.8288104827 |
| 48 | 1027885 | 1048660.77973984 | -20775.7797398437 |
| 49 | 1262159 | 1254191.31861628 | 7967.68138372035 |
| 50 | 1520854 | 1439682.44461606 | 81171.5553839367 |
| 51 | 1544144 | 1565549.02879077 | -21405.0287907684 |
| 52 | 1564709 | 1576018.20741058 | -11309.2074105842 |
| 53 | 1821776 | 1817780.16724239 | 3995.83275760925 |
| 54 | 1741365 | 1716284.55646404 | 25080.4435359603 |
| 55 | 1623386 | 1673454.40675745 | -50068.4067574546 |
| 56 | 1498658 | 1498246.52326741 | 411.476732590057 |
| 57 | 1241822 | 1236414.08210095 | 5407.9178990472 |
| 58 | 1136029 | 1137123.39153793 | -1094.39153792697 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.127475651195992 | 0.254951302391985 | 0.872524348804008 |
| 20 | 0.109202513177519 | 0.218405026355039 | 0.89079748682248 |
| 21 | 0.065791358952582 | 0.131582717905164 | 0.934208641047418 |
| 22 | 0.0292884674890476 | 0.0585769349780952 | 0.970711532510952 |
| 23 | 0.0153251702974933 | 0.0306503405949865 | 0.984674829702507 |
| 24 | 0.00679884630722808 | 0.0135976926144562 | 0.993201153692772 |
| 25 | 0.0098190405776762 | 0.0196380811553524 | 0.990180959422324 |
| 26 | 0.0158512285403045 | 0.0317024570806089 | 0.984148771459695 |
| 27 | 0.02505444097409 | 0.05010888194818 | 0.97494555902591 |
| 28 | 0.0318888589537789 | 0.0637777179075578 | 0.968111141046221 |
| 29 | 0.0232122243361216 | 0.0464244486722431 | 0.976787775663878 |
| 30 | 0.0268890288559927 | 0.0537780577119853 | 0.973110971144007 |
| 31 | 0.0157151084924536 | 0.0314302169849072 | 0.984284891507546 |
| 32 | 0.0292799888803841 | 0.0585599777607682 | 0.970720011119616 |
| 33 | 0.0234225320350922 | 0.0468450640701843 | 0.976577467964908 |
| 34 | 0.164931240911555 | 0.32986248182311 | 0.835068759088445 |
| 35 | 0.193152001268936 | 0.386304002537871 | 0.806847998731064 |
| 36 | 0.194751374570672 | 0.389502749141345 | 0.805248625429328 |
| 37 | 0.278883599078344 | 0.557767198156687 | 0.721116400921656 |
| 38 | 0.480762534704821 | 0.961525069409642 | 0.519237465295179 |
| 39 | 0.341184747234269 | 0.682369494468537 | 0.658815252765731 |
| 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 | 7 | 0.333333333333333 | NOK |
| 10% type I error level | 12 | 0.571428571428571 | NOK |
