| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 405212.376212214 + 14.2876090146007DJIA[t] + 0.433366643601294Y1[t] + 0.117304164406053Y2[t] + 0.00146315681682760Y3[t] + 0.198193232954481Y4[t] -20549.0296296705M1[t] -58844.700821326M2[t] + 122216.654744061M3[t] -135295.969565926M4[t] -196839.08413439M5[t] -314012.44835748M6[t] -562394.662160664M7[t] -520562.784357975M8[t] -489669.430133837M9[t] -377128.669217277M10[t] -98765.5693057837M11[t] + 737.570519139868t + 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) | 405212.376212214 | 74469.218399 | 5.4413 | 3e-06 | 2e-06 |
| DJIA | 14.2876090146007 | 3.482476 | 4.1027 | 0.000208 | 0.000104 |
| Y1 | 0.433366643601294 | 0.153249 | 2.8279 | 0.007438 | 0.003719 |
| Y2 | 0.117304164406053 | 0.168455 | 0.6964 | 0.490445 | 0.245223 |
| Y3 | 0.00146315681682760 | 0.166695 | 0.0088 | 0.993043 | 0.496521 |
| Y4 | 0.198193232954481 | 0.148377 | 1.3357 | 0.189578 | 0.094789 |
| M1 | -20549.0296296705 | 41758.628709 | -0.4921 | 0.625486 | 0.312743 |
| M2 | -58844.700821326 | 61514.799407 | -0.9566 | 0.344819 | 0.172409 |
| M3 | 122216.654744061 | 53218.606555 | 2.2965 | 0.027252 | 0.013626 |
| M4 | -135295.969565926 | 46548.744748 | -2.9065 | 0.006067 | 0.003033 |
| M5 | -196839.08413439 | 63011.720563 | -3.1238 | 0.003409 | 0.001705 |
| M6 | -314012.44835748 | 67733.758776 | -4.636 | 4.1e-05 | 2.1e-05 |
| M7 | -562394.662160664 | 66408.528594 | -8.4687 | 0 | 0 |
| M8 | -520562.784357975 | 85788.088171 | -6.068 | 0 | 0 |
| M9 | -489669.430133837 | 86000.973134 | -5.6938 | 1e-06 | 1e-06 |
| M10 | -377128.669217277 | 72659.905333 | -5.1903 | 7e-06 | 4e-06 |
| M11 | -98765.5693057837 | 44491.573327 | -2.2199 | 0.032469 | 0.016235 |
| t | 737.570519139868 | 341.719637 | 2.1584 | 0.037278 | 0.018639 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.996597096381513 |
| R-squared | 0.993205772516062 |
| Adjusted R-squared | 0.9901662496943 |
| F-TEST (value) | 326.763716135021 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 38 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 26131.9690148321 |
| Sum Squared Residuals | 25949432574.5016 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1469798 | 1467376.27035185 | 2421.72964815017 |
| 2 | 1498721 | 1493800.75047243 | 4920.24952756512 |
| 3 | 1761769 | 1744957.29958051 | 16811.7004194935 |
| 4 | 1653214 | 1635366.99605114 | 17847.0039488613 |
| 5 | 1599104 | 1579670.12208000 | 19433.8779200041 |
| 6 | 1421179 | 1431330.31392723 | -10151.3139272284 |
| 7 | 1163995 | 1157433.49017591 | 6561.509824087 |
| 8 | 1037735 | 1044819.99435049 | -7084.99435048725 |
| 9 | 1015407 | 982686.146506649 | 32720.853493351 |
| 10 | 1039210 | 1037674.28436873 | 1535.71563126705 |
| 11 | 1258049 | 1274970.42379117 | -16921.423791174 |
| 12 | 1469445 | 1450730.36195842 | 18714.6380415762 |
| 13 | 1552346 | 1540970.36758902 | 11375.6324109812 |
| 14 | 1549144 | 1568915.75262806 | -19771.7526280553 |
| 15 | 1785895 | 1803240.02427383 | -17345.0242738306 |
| 16 | 1662335 | 1693500.70155881 | -31165.7015588062 |
| 17 | 1629440 | 1627602.54990807 | 1837.45009193418 |
| 18 | 1467430 | 1487867.60805326 | -20437.6080532646 |
| 19 | 1202209 | 1214913.58318302 | -12704.5831830183 |
| 20 | 1076982 | 1102450.219886 | -25468.2198860006 |
| 21 | 1039367 | 1044208.95726232 | -4841.95726232361 |
| 22 | 1063449 | 1088954.82497912 | -25505.8249791178 |
| 23 | 1335135 | 1322555.93444543 | 12579.0655545659 |
| 24 | 1491602 | 1527873.09070757 | -36271.090707575 |
| 25 | 1591972 | 1608387.94815593 | -16415.9481559265 |
| 26 | 1641248 | 1634722.22472636 | 6525.7752736366 |
| 27 | 1898849 | 1900915.43440801 | -2066.43440801189 |
| 28 | 1798580 | 1794796.31802505 | 3783.68197495404 |
| 29 | 1762444 | 1748405.11936344 | 14038.8806365614 |
| 30 | 1622044 | 1615181.50576964 | 6862.49423035942 |
| 31 | 1368955 | 1345384.71893368 | 23570.281066323 |
| 32 | 1262973 | 1240351.47679698 | 22621.5232030184 |
| 33 | 1195650 | 1180218.44213451 | 15431.5578654944 |
| 34 | 1269530 | 1218206.44903519 | 51323.5509648063 |
| 35 | 1479279 | 1471061.37678225 | 8217.623217747 |
| 36 | 1607819 | 1656987.37632816 | -49168.3763281587 |
| 37 | 1712466 | 1701652.80157463 | 10813.1984253682 |
| 38 | 1721766 | 1721066.03950806 | 699.960491935596 |
| 39 | 1949843 | 1961329.90679539 | -11486.9067953871 |
| 40 | 1821326 | 1832480.64676173 | -11154.6467617347 |
| 41 | 1757802 | 1753588.6968792 | 4213.30312079985 |
| 42 | 1590367 | 1574927.16000081 | 15439.8399991883 |
| 43 | 1260647 | 1285199.19503061 | -24552.1950306141 |
| 44 | 1149235 | 1138921.78294903 | 10313.2170509651 |
| 45 | 1016367 | 1059677.45409652 | -43310.4540965218 |
| 46 | 1027885 | 1055238.44161696 | -27353.4416169555 |
| 47 | 1262159 | 1266034.26498114 | -3875.26498113887 |
| 48 | 1520854 | 1454129.17100584 | 66724.8289941574 |
| 49 | 1544144 | 1552338.61232857 | -8194.61232857302 |
| 50 | 1564709 | 1557083.23266508 | 7625.76733491793 |
| 51 | 1821776 | 1807689.33494226 | 14086.6650577361 |
| 52 | 1741365 | 1720675.33760327 | 20689.6623967256 |
| 53 | 1623386 | 1662909.5117693 | -39523.5117692996 |
| 54 | 1498658 | 1490371.41224905 | 8286.58775094537 |
| 55 | 1241822 | 1234697.01267678 | 7124.98732322246 |
| 56 | 1136029 | 1136410.52601750 | -381.526017495626 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.0236986683364031 | 0.0473973366728061 | 0.976301331663597 |
| 22 | 0.0059233635521012 | 0.0118467271042024 | 0.994076636447899 |
| 23 | 0.0210508896911284 | 0.0421017793822569 | 0.978949110308872 |
| 24 | 0.0130742884427536 | 0.0261485768855072 | 0.986925711557246 |
| 25 | 0.0219285548727814 | 0.0438571097455627 | 0.978071445127219 |
| 26 | 0.0565886331844631 | 0.113177266368926 | 0.943411366815537 |
| 27 | 0.0696811703255266 | 0.139362340651053 | 0.930318829674473 |
| 28 | 0.0533617053747738 | 0.106723410749548 | 0.946638294625226 |
| 29 | 0.0263116783419665 | 0.052623356683933 | 0.973688321658034 |
| 30 | 0.0357112444771493 | 0.0714224889542986 | 0.96428875552285 |
| 31 | 0.0240352988435742 | 0.0480705976871484 | 0.975964701156426 |
| 32 | 0.112290892529011 | 0.224581785058022 | 0.887709107470989 |
| 33 | 0.236166916885292 | 0.472333833770584 | 0.763833083114708 |
| 34 | 0.296619422405108 | 0.593238844810216 | 0.703380577594892 |
| 35 | 0.498793083801226 | 0.997586167602452 | 0.501206916198774 |
| 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 | 6 | 0.4 | NOK |
| 10% type I error level | 8 | 0.533333333333333 | NOK |
