| Multiple Linear Regression - Estimated Regression Equation |
| S&P[t] = + 3901.66133003445 + 0.679202303098418Bel20[t] + 0.0093168895553967Nikkei225[t] -0.815900090317011DAX[t] + 0.0111161931322036HangSeng[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) | 3901.66133003445 | 1240.443424 | 3.1454 | 0.002474 | 0.001237 |
| Bel20 | 0.679202303098418 | 0.262972 | 2.5828 | 0.01199 | 0.005995 |
| Nikkei225 | 0.0093168895553967 | 0.067189 | 0.1387 | 0.890129 | 0.445065 |
| DAX | -0.815900090317011 | 0.26881 | -3.0352 | 0.00342 | 0.00171 |
| HangSeng | 0.0111161931322036 | 0.063968 | 0.1738 | 0.862563 | 0.431282 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.419785427527184 |
| R-squared | 0.176219805164180 |
| Adjusted R-squared | 0.127038898009803 |
| F-TEST (value) | 3.58309383377236 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 67 |
| p-value | 0.0104409700206471 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1812.90836227926 |
| Sum Squared Residuals | 220204660.911477 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1221.53 | 357.955115289487 | 863.574884710513 |
| 2 | 1180.55 | 495.034567425437 | 685.515432574563 |
| 3 | 1183.26 | 677.714829032561 | 505.545170967439 |
| 4 | 1141.2 | 914.184864809546 | 227.015135190454 |
| 5 | 1049.33 | 1046.88667020629 | 2.44332979370736 |
| 6 | 1101.6 | 917.917409608057 | 183.682590391942 |
| 7 | 1030.71 | 966.504456674227 | 64.2055433257735 |
| 8 | 1089.41 | 1012.42606704106 | 76.9839329589371 |
| 9 | 1186.69 | 951.361781690657 | 235.328218309343 |
| 10 | 1169.43 | 901.524580513672 | 267.905419486328 |
| 11 | 1104.49 | 1372.92817641194 | -268.438176411944 |
| 12 | 1073.87 | 1329.19637169705 | -255.32637169705 |
| 13 | 1115.1 | 896.91186150793 | 218.18813849207 |
| 14 | 1095.63 | 1114.37656627719 | -18.7465662771854 |
| 15 | 1036.19 | 1198.34293891511 | -162.152938915115 |
| 16 | 1057.08 | 1005.52983892298 | 51.5501610770234 |
| 17 | 1020.62 | 1092.18146842085 | -71.561468420854 |
| 18 | 987.48 | 1064.10660887841 | -76.6266088784103 |
| 19 | 919.32 | 1427.69576095184 | -508.375760951844 |
| 20 | 919.14 | 1451.70377608517 | -532.563776085168 |
| 21 | 872.81 | 1561.40557388708 | -688.595573887076 |
| 22 | 797.87 | 2073.26649794152 | -1275.39649794152 |
| 23 | 735.09 | 2404.93062949618 | -1669.84062949618 |
| 24 | 825.88 | 2399.04839530752 | -1573.16839530752 |
| 25 | 903.25 | 2349.47468650333 | -1446.22468650333 |
| 26 | 896.24 | 2359.34684221854 | -1463.10684221854 |
| 27 | 968.75 | 2219.02768615725 | -1250.27768615725 |
| 28 | 1166.36 | 1997.27643916016 | -830.916439160158 |
| 29 | 1282.83 | 1686.01703820086 | -403.187038200863 |
| 30 | 1267.38 | 1518.60785032155 | -251.227850321548 |
| 31 | 1280 | 1588.09275965233 | -308.092759652332 |
| 32 | 1400.38 | 1045.84241035678 | 354.537589643219 |
| 33 | 1385.59 | 1450.84586636828 | -65.2558663682768 |
| 34 | 1322.7 | 1767.65349638071 | -444.95349638071 |
| 35 | 1330.63 | 1809.96920542103 | -479.339205421033 |
| 36 | 1378.55 | 1636.44289344723 | -257.892893447225 |
| 37 | 1468.36 | 726.419654324607 | 741.940345675393 |
| 38 | 1481.14 | 922.548444366672 | 558.591555633328 |
| 39 | 1549.38 | 1014.33415735923 | 535.04584264077 |
| 40 | 1526.75 | 1136.36330108647 | 390.38669891353 |
| 41 | 1473.99 | 1225.01807133746 | 248.971928662538 |
| 42 | 1455.27 | 1169.35007158938 | 285.919928410624 |
| 43 | 1503.35 | 703.633318736995 | 799.716681263005 |
| 44 | 1530.62 | 877.102379180439 | 653.517620819561 |
| 45 | 1482.37 | 1225.45071522196 | 256.919284778038 |
| 46 | 1420.86 | 1451.33531162696 | -30.4753116269564 |
| 47 | 1406.82 | 1619.87129069039 | -213.051290690387 |
| 48 | 1438.24 | 1512.77527142158 | -74.5352714215836 |
| 49 | 1418.3 | 1554.62753310622 | -136.327533106215 |
| 50 | 1400.63 | 1694.57794631895 | -293.947946318949 |
| 51 | 1377.94 | 1658.64072798274 | -280.700727982741 |
| 52 | 1335.85 | 1844.61058005421 | -508.760580054208 |
| 53 | 1303.82 | 2120.9561079593 | -817.136107959299 |
| 54 | 1276.66 | 2255.63716502283 | -978.977165022828 |
| 55 | 1270.2 | 2197.56968522333 | -927.369685223326 |
| 56 | 1270.09 | 2120.60443535990 | -850.514435359897 |
| 57 | 1310.61 | 1751.57401685293 | -440.96401685293 |
| 58 | 1294.87 | 1670.61506904796 | -375.745069047958 |
| 59 | 1280.66 | 1717.70178002432 | -437.041780024319 |
| 60 | 1280.08 | 1863.28993985208 | -583.209939852076 |
| 61 | 1248.29 | 1994.27383160702 | -745.983831607025 |
| 62 | 1249.48 | 2161.44393949087 | -911.963939490869 |
| 63 | 1207.01 | 2280.96590213628 | -1073.95590213628 |
| 64 | 1228.81 | 2156.84132071685 | -928.031320716848 |
| 65 | 1220.33 | 2307.02173592291 | -1086.69173592291 |
| 66 | 1234.18 | 2314.01490805587 | -1079.83490805587 |
| 67 | 1191.33 | 2535.47285390333 | -1344.14285390333 |
| 68 | 1191.5 | 301.022528781206 | 890.477471218794 |
| 69 | 11008.9 | 6040.07344767483 | 4968.82655232517 |
| 70 | 4348.77 | 3562.77545169209 | 785.99454830791 |
| 71 | 14195.35 | 1491.08000980255 | 12704.2699901975 |
| 72 | 1221.53 | 357.955115289489 | 863.574884710511 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 5.36273322959642e-07 | 1.07254664591928e-06 | 0.999999463726677 |
| 9 | 3.15527804493776e-09 | 6.31055608987552e-09 | 0.999999996844722 |
| 10 | 1.79494028428203e-11 | 3.58988056856406e-11 | 0.99999999998205 |
| 11 | 1.04130978981112e-13 | 2.08261957962223e-13 | 0.999999999999896 |
| 12 | 1.69155465453844e-15 | 3.38310930907689e-15 | 0.999999999999998 |
| 13 | 2.70526922025508e-17 | 5.41053844051015e-17 | 1 |
| 14 | 5.56578304165071e-18 | 1.11315660833014e-17 | 1 |
| 15 | 1.84468942640024e-19 | 3.68937885280048e-19 | 1 |
| 16 | 1.63058770792088e-21 | 3.26117541584175e-21 | 1 |
| 17 | 1.38687527344559e-23 | 2.77375054689118e-23 | 1 |
| 18 | 1.35855314024320e-25 | 2.71710628048639e-25 | 1 |
| 19 | 1.32544241649339e-27 | 2.65088483298678e-27 | 1 |
| 20 | 9.82195934084636e-30 | 1.96439186816927e-29 | 1 |
| 21 | 4.44804048810969e-31 | 8.89608097621937e-31 | 1 |
| 22 | 1.04873714870125e-32 | 2.09747429740251e-32 | 1 |
| 23 | 2.62750697505035e-34 | 5.25501395010071e-34 | 1 |
| 24 | 9.17111452502764e-36 | 1.83422290500553e-35 | 1 |
| 25 | 1.05802366763262e-36 | 2.11604733526525e-36 | 1 |
| 26 | 1.41365010644719e-38 | 2.82730021289437e-38 | 1 |
| 27 | 6.27802954579363e-40 | 1.25560590915873e-39 | 1 |
| 28 | 9.19973329948479e-42 | 1.83994665989696e-41 | 1 |
| 29 | 2.79269319753747e-43 | 5.58538639507494e-43 | 1 |
| 30 | 2.26869897788983e-44 | 4.53739795577965e-44 | 1 |
| 31 | 2.79079508823505e-46 | 5.58159017647010e-46 | 1 |
| 32 | 2.77467256855098e-48 | 5.54934513710197e-48 | 1 |
| 33 | 4.01943873964431e-50 | 8.03887747928863e-50 | 1 |
| 34 | 5.43999990118575e-52 | 1.08799998023715e-51 | 1 |
| 35 | 3.81008557387632e-53 | 7.62017114775264e-53 | 1 |
| 36 | 4.54084950442022e-55 | 9.08169900884043e-55 | 1 |
| 37 | 1.96134261175591e-54 | 3.92268522351183e-54 | 1 |
| 38 | 1.88462165447589e-55 | 3.76924330895179e-55 | 1 |
| 39 | 8.51355491308592e-57 | 1.70271098261718e-56 | 1 |
| 40 | 1.21138050960024e-58 | 2.42276101920049e-58 | 1 |
| 41 | 1.54276271900177e-60 | 3.08552543800354e-60 | 1 |
| 42 | 2.26365496577007e-62 | 4.52730993154015e-62 | 1 |
| 43 | 4.59705866633819e-64 | 9.19411733267637e-64 | 1 |
| 44 | 3.05901795840702e-65 | 6.11803591681404e-65 | 1 |
| 45 | 1.63920497744831e-66 | 3.27840995489663e-66 | 1 |
| 46 | 6.34194580966901e-68 | 1.26838916193380e-67 | 1 |
| 47 | 2.13139586892324e-69 | 4.26279173784648e-69 | 1 |
| 48 | 2.83217813915127e-70 | 5.66435627830255e-70 | 1 |
| 49 | 4.60690595704502e-71 | 9.21381191409003e-71 | 1 |
| 50 | 4.26953699749887e-71 | 8.53907399499775e-71 | 1 |
| 51 | 5.97032935514885e-72 | 1.19406587102977e-71 | 1 |
| 52 | 3.09015698871613e-73 | 6.18031397743225e-73 | 1 |
| 53 | 6.43141343624823e-75 | 1.28628268724965e-74 | 1 |
| 54 | 1.15044798584418e-76 | 2.30089597168837e-76 | 1 |
| 55 | 1.66635811039386e-78 | 3.33271622078772e-78 | 1 |
| 56 | 2.37617786841222e-80 | 4.75235573682445e-80 | 1 |
| 57 | 6.66009072526662e-82 | 1.33201814505332e-81 | 1 |
| 58 | 2.29455760689867e-83 | 4.58911521379733e-83 | 1 |
| 59 | 7.23210479023434e-85 | 1.44642095804687e-84 | 1 |
| 60 | 1.54057096113466e-85 | 3.08114192226932e-85 | 1 |
| 61 | 8.46689505415489e-86 | 1.69337901083098e-85 | 1 |
| 62 | 3.36748534633244e-85 | 6.73497069266489e-85 | 1 |
| 63 | 1.16534381872894e-85 | 2.33068763745788e-85 | 1 |
| 64 | 7.02047072427143e-86 | 1.40409414485429e-85 | 1 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 57 | 1 | NOK |
| 5% type I error level | 57 | 1 | NOK |
| 10% type I error level | 57 | 1 | NOK |
