| Multiple Linear Regression - Estimated Regression Equation |
| S&P[t] = + 3228.51499047869 -0.0358664385477845month[t] -0.143337992426391Bel20[t] -0.134850414826532Nikkei225[t] + 0.00307994776017903DAX[t] -0.047311126005587HangSeng[t] + 37.6855360142645t + 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) | 3228.51499047869 | 1240.665784 | 2.6022 | 0.011459 | 0.005729 |
| month | -0.0358664385477845 | 0.156162 | -0.2297 | 0.819066 | 0.409533 |
| Bel20 | -0.143337992426391 | 0.132368 | -1.0829 | 0.282866 | 0.141433 |
| Nikkei225 | -0.134850414826532 | 0.11438 | -1.179 | 0.242707 | 0.121353 |
| DAX | 0.00307994776017903 | 0.121581 | 0.0253 | 0.979867 | 0.489934 |
| HangSeng | -0.047311126005587 | 0.073961 | -0.6397 | 0.524632 | 0.262316 |
| t | 37.6855360142645 | 22.632631 | 1.6651 | 0.100707 | 0.050353 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.489007957167126 |
| R-squared | 0.239128782172766 |
| Adjusted R-squared | 0.168894515911791 |
| F-TEST (value) | 3.40473097966475 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 65 |
| p-value | 0.0055410281396141 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1776.52131573894 |
| Sum Squared Residuals | 205141819.042863 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1221.53 | 431.437685358542 | 790.092314641458 |
| 2 | 1180.55 | 536.320208344990 | 644.22979165501 |
| 3 | 1183.26 | 643.865187806063 | 539.394812193937 |
| 4 | 1141.2 | 705.661761380223 | 435.538238619777 |
| 5 | 1049.33 | 921.12510668435 | 128.204893315649 |
| 6 | 1101.6 | 831.434987481996 | 270.165012518003 |
| 7 | 1030.71 | 950.813536420986 | 79.8964635790141 |
| 8 | 1089.41 | 944.101998815085 | 145.308001184915 |
| 9 | 1186.69 | 734.076460210492 | 452.613539789508 |
| 10 | 1169.43 | 769.093191742964 | 400.336808257036 |
| 11 | 1104.49 | 957.64523432911 | 146.844765670891 |
| 12 | 1073.87 | 1015.16488206799 | 58.7051179320082 |
| 13 | 1115.1 | 959.718499674154 | 155.381500325846 |
| 14 | 1095.63 | 1169.47439265095 | -73.8443926509476 |
| 15 | 1036.19 | 1136.65893914294 | -100.468939142935 |
| 16 | 1057.08 | 1193.84720545716 | -136.767205457156 |
| 17 | 1020.62 | 1257.60772025170 | -236.987720251705 |
| 18 | 987.48 | 1302.39517566745 | -314.915175667451 |
| 19 | 919.32 | 1503.53278904737 | -584.212789047373 |
| 20 | 919.14 | 1581.10521420105 | -661.96521420105 |
| 21 | 872.81 | 1836.06677518619 | -963.256775186193 |
| 22 | 797.87 | 2064.51505423660 | -1266.64505423660 |
| 23 | 735.09 | 2179.27914021851 | -1444.18914021851 |
| 24 | 825.88 | 2057.05807130337 | -1231.17807130337 |
| 25 | 903.25 | 1860.12699367616 | -956.876993676163 |
| 26 | 896.24 | 1988.16619628181 | -1091.92619628181 |
| 27 | 968.75 | 1989.41937368322 | -1020.66937368322 |
| 28 | 1166.36 | 1392.86288640964 | -226.502886409641 |
| 29 | 1282.83 | 1009.41979689359 | 273.410203106413 |
| 30 | 1267.38 | 966.33586865462 | 301.04413134538 |
| 31 | 1280 | 1014.14079497181 | 265.859205028189 |
| 32 | 1400.38 | 828.345979021076 | 572.034020978925 |
| 33 | 1385.59 | 815.581446178638 | 570.008553821362 |
| 34 | 1322.7 | 1163.10294313434 | 159.597056865660 |
| 35 | 1330.63 | 946.007749270379 | 384.622250729622 |
| 36 | 1378.55 | 1043.61537864604 | 334.934621353959 |
| 37 | 1468.36 | 643.54884054745 | 824.81115945255 |
| 38 | 1481.14 | 586.244194765567 | 894.895805234433 |
| 39 | 1549.38 | 317.186515570651 | 1232.19348442935 |
| 40 | 1526.75 | 538.746774195778 | 988.003225804222 |
| 41 | 1473.99 | 766.324436735117 | 707.665563264883 |
| 42 | 1455.27 | 770.532269611176 | 684.737730388824 |
| 43 | 1503.35 | 780.279199837335 | 723.070800162665 |
| 44 | 1530.62 | 888.487258159224 | 642.132741840776 |
| 45 | 1482.37 | 1010.23016828862 | 472.139831711376 |
| 46 | 1420.86 | 1121.73278069811 | 299.127219301894 |
| 47 | 1406.82 | 1122.64159514045 | 284.178404859553 |
| 48 | 1438.24 | 1179.37875580835 | 258.861244191652 |
| 49 | 1418.3 | 1267.65069027816 | 150.649309721841 |
| 50 | 1400.63 | 1496.08930721538 | -95.4593072153769 |
| 51 | 1377.94 | 1560.18997859837 | -182.249978598374 |
| 52 | 1335.85 | 1674.65899322706 | -338.80899322706 |
| 53 | 1303.82 | 1683.56908945558 | -379.749089455585 |
| 54 | 1276.66 | 1832.71423432557 | -556.054234325567 |
| 55 | 1270.2 | 1907.67880852277 | -637.47880852277 |
| 56 | 1270.09 | 1983.48114117953 | -713.39114117953 |
| 57 | 1310.61 | 1818.13786279297 | -507.527862792975 |
| 58 | 1294.87 | 1897.79033413742 | -602.920334137421 |
| 59 | 1280.66 | 2063.41873666159 | -782.758736661586 |
| 60 | 1280.08 | 2039.40993597971 | -759.329935979712 |
| 61 | 1248.29 | 2204.98695434495 | -956.696954344946 |
| 62 | 1249.48 | 2405.71411073895 | -1156.23411073895 |
| 63 | 1207.01 | 2655.86203696329 | -1448.85203696329 |
| 64 | 1228.81 | 2657.7412324134 | -1428.9312324134 |
| 65 | 1220.33 | 2877.87432236572 | -1657.54432236572 |
| 66 | 1234.18 | 2973.83028815660 | -1739.65028815660 |
| 67 | 1191.33 | 3088.09430769680 | -1896.76430769680 |
| 68 | 1191.5 | 3615.59113603547 | -2424.09113603547 |
| 69 | 11008.9 | 3256.00214508583 | 7752.89785491417 |
| 70 | 4348.77 | 2958.47270862990 | 1390.29729137010 |
| 71 | 14195.35 | 5422.48481556862 | 8772.86518443138 |
| 72 | 12 | 4623.84941576698 | -4611.84941576698 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 4.87468363857662e-07 | 9.74936727715325e-07 | 0.999999512531636 |
| 11 | 3.12091892860340e-09 | 6.24183785720681e-09 | 0.999999996879081 |
| 12 | 2.99971876783194e-11 | 5.99943753566387e-11 | 0.999999999970003 |
| 13 | 1.62094173540876e-13 | 3.24188347081751e-13 | 0.999999999999838 |
| 14 | 5.75651669508389e-14 | 1.15130333901678e-13 | 0.999999999999942 |
| 15 | 6.95481730455344e-16 | 1.39096346091069e-15 | 1 |
| 16 | 6.27756798343442e-18 | 1.25551359668688e-17 | 1 |
| 17 | 5.40960239270589e-20 | 1.08192047854118e-19 | 1 |
| 18 | 4.28573071765793e-22 | 8.57146143531587e-22 | 1 |
| 19 | 8.1715484372114e-24 | 1.63430968744228e-23 | 1 |
| 20 | 7.23659460762464e-26 | 1.44731892152493e-25 | 1 |
| 21 | 8.71493621517294e-28 | 1.74298724303459e-27 | 1 |
| 22 | 1.24851151672813e-29 | 2.49702303345627e-29 | 1 |
| 23 | 1.11317502942603e-30 | 2.22635005885206e-30 | 1 |
| 24 | 1.04128761791383e-31 | 2.08257523582766e-31 | 1 |
| 25 | 2.51048493904311e-33 | 5.02096987808621e-33 | 1 |
| 26 | 4.02852875411891e-35 | 8.05705750823781e-35 | 1 |
| 27 | 2.46562233873463e-36 | 4.93124467746927e-36 | 1 |
| 28 | 6.47323413989503e-38 | 1.29464682797901e-37 | 1 |
| 29 | 3.43385083210430e-39 | 6.86770166420861e-39 | 1 |
| 30 | 3.57357031749248e-40 | 7.14714063498496e-40 | 1 |
| 31 | 8.10852722717705e-42 | 1.62170544543541e-41 | 1 |
| 32 | 1.35567544327289e-43 | 2.71135088654577e-43 | 1 |
| 33 | 2.50852148748147e-45 | 5.01704297496294e-45 | 1 |
| 34 | 2.29544544152612e-46 | 4.59089088305224e-46 | 1 |
| 35 | 1.34532349848433e-46 | 2.69064699696866e-46 | 1 |
| 36 | 1.4274517182839e-45 | 2.8549034365678e-45 | 1 |
| 37 | 1.72360626794935e-45 | 3.44721253589870e-45 | 1 |
| 38 | 1.22997231242873e-46 | 2.45994462485747e-46 | 1 |
| 39 | 1.02329088226278e-46 | 2.04658176452555e-46 | 1 |
| 40 | 4.66330295234030e-48 | 9.32660590468059e-48 | 1 |
| 41 | 9.51267085054787e-50 | 1.90253417010957e-49 | 1 |
| 42 | 2.09668822335721e-51 | 4.19337644671442e-51 | 1 |
| 43 | 6.36821614616219e-53 | 1.27364322923244e-52 | 1 |
| 44 | 5.32825222291956e-54 | 1.06565044458391e-53 | 1 |
| 45 | 2.23656191293479e-55 | 4.47312382586958e-55 | 1 |
| 46 | 6.63685763042185e-57 | 1.32737152608437e-56 | 1 |
| 47 | 1.25593080939809e-58 | 2.51186161879618e-58 | 1 |
| 48 | 1.21723645619164e-59 | 2.43447291238329e-59 | 1 |
| 49 | 5.08365303499555e-60 | 1.01673060699911e-59 | 1 |
| 50 | 1.48883566250658e-59 | 2.97767132501317e-59 | 1 |
| 51 | 2.70242693629776e-60 | 5.40485387259551e-60 | 1 |
| 52 | 3.1506289605069e-61 | 6.3012579210138e-61 | 1 |
| 53 | 9.07602962651386e-63 | 1.81520592530277e-62 | 1 |
| 54 | 2.74776642812588e-63 | 5.49553285625175e-63 | 1 |
| 55 | 3.28756691686456e-62 | 6.57513383372912e-62 | 1 |
| 56 | 1.99551809903069e-52 | 3.99103619806137e-52 | 1 |
| 57 | 5.62934474285537e-53 | 1.12586894857107e-52 | 1 |
| 58 | 2.34938268061243e-54 | 4.69876536122485e-54 | 1 |
| 59 | 2.16774599118958e-54 | 4.33549198237915e-54 | 1 |
| 60 | 2.09672681768252e-52 | 4.19345363536504e-52 | 1 |
| 61 | 4.53481723576286e-49 | 9.06963447152572e-49 | 1 |
| 62 | 7.50166439480947e-46 | 1.50033287896189e-45 | 1 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 53 | 1 | NOK |
| 5% type I error level | 53 | 1 | NOK |
| 10% type I error level | 53 | 1 | NOK |
