| Multiple Linear Regression - Estimated Regression Equation |
| Nikkei225[t] = + 1.76136822710579 -0.960255268334286month[t] -0.155257413606003`S&P`[t] -0.195263524204028Bel20[t] -0.186413495406639DAX[t] + 0.477200864515611HangSeng[t] + 164.108594105633t + 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) | 1.76136822710579 | 1398.861404 | 0.0013 | 0.998999 | 0.4995 |
| month | -0.960255268334286 | 0.117957 | -8.1407 | 0 | 0 |
| `S&P` | -0.155257413606003 | 0.131689 | -1.179 | 0.242707 | 0.121353 |
| Bel20 | -0.195263524204028 | 0.141245 | -1.3824 | 0.171568 | 0.085784 |
| DAX | -0.186413495406639 | 0.128392 | -1.4519 | 0.151337 | 0.075668 |
| HangSeng | 0.477200864515611 | 0.053238 | 8.9635 | 0 | 0 |
| t | 164.108594105633 | 14.162482 | 11.5876 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.893053076885623 |
| R-squared | 0.797543798134879 |
| Adjusted R-squared | 0.77885553334733 |
| F-TEST (value) | 42.6761824707350 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 65 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1906.20872451305 |
| Sum Squared Residuals | 236186060.591628 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10168.52 | 9346.437303184 | 822.082696816002 |
| 2 | 9937.04 | 9379.37875181487 | 557.66124818513 |
| 3 | 9202.45 | 9568.64947580461 | -366.19947580461 |
| 4 | 9369.35 | 9474.8585421197 | -105.508542119701 |
| 5 | 8824.06 | 8867.34354546186 | -43.2835454618575 |
| 6 | 9537.3 | 9206.50164491928 | 330.798355080720 |
| 7 | 9382.64 | 9012.25036286792 | 370.389637132077 |
| 8 | 9768.7 | 8981.77034565418 | 786.929654345822 |
| 9 | 11057.4 | 9725.96506025347 | 1331.43493974653 |
| 10 | 11089.94 | 9963.43072407693 | 1126.50927592307 |
| 11 | 10126.03 | 9931.19409745465 | 194.835902545351 |
| 12 | 10198.04 | 9875.61970324647 | 322.420296753529 |
| 13 | 10546.44 | 10842.1446761993 | -295.704676199250 |
| 14 | 9345.55 | 11059.5459373377 | -1713.99593733765 |
| 15 | 10034.74 | 11267.4019839445 | -1232.66198394453 |
| 16 | 10133.23 | 10992.2110671459 | -858.981067145916 |
| 17 | 10492.53 | 10638.9968047986 | -146.466804798617 |
| 18 | 10356.83 | 11277.8435557134 | -921.013555713358 |
| 19 | 9958.44 | 10514.0021434006 | -555.562143400607 |
| 20 | 9522.5 | 10515.5917878896 | -993.091787889585 |
| 21 | 8828.26 | 9453.5428278368 | -625.282827836796 |
| 22 | 8109.53 | 8835.0480210873 | -725.518021087306 |
| 23 | 7568.42 | 8647.2890726575 | -1078.86907265750 |
| 24 | 7994.05 | 8817.04649278948 | -822.996492789479 |
| 25 | 8859.56 | 9309.40218550052 | -449.842185500521 |
| 26 | 8512.27 | 9291.2144136543 | -778.944413654305 |
| 27 | 8576.98 | 9390.08391176119 | -813.103911761187 |
| 28 | 11259.86 | 11184.9302988109 | 74.9297011891261 |
| 29 | 13072.87 | 12736.5552891172 | 336.314710882844 |
| 30 | 13376.81 | 13634.6638232082 | -257.853823208185 |
| 31 | 13481.38 | 13501.6450861130 | -20.2650861129508 |
| 32 | 14338.54 | 14688.4886219005 | -349.948621900509 |
| 33 | 13849.99 | 15387.5579554255 | -1537.56795542551 |
| 34 | 12525.54 | 14245.8807949503 | -1720.34079495028 |
| 35 | 13603.02 | 15022.8775103913 | -1419.85751039126 |
| 36 | 13592.47 | 14765.9497633315 | -1173.47976333153 |
| 37 | 15307.78 | 16753.0874167666 | -1445.30741676663 |
| 38 | 15680.67 | 17342.8244177144 | -1662.15441771440 |
| 39 | 16737.63 | 18712.5231101385 | -1974.89311013845 |
| 40 | 16785.69 | 16890.0214698121 | -104.331469812120 |
| 41 | 16569.09 | 15613.9838828278 | 955.10611717218 |
| 42 | 17248.89 | 15438.5963041693 | 1810.29369583072 |
| 43 | 18138.36 | 14875.9018369313 | 3262.45816306867 |
| 44 | 17875.75 | 14491.6655091055 | 3384.08449089449 |
| 45 | 17400.41 | 14610.8597841871 | 2789.55021581294 |
| 46 | 17287.65 | 14678.4204874036 | 2609.22951259642 |
| 47 | 17604.12 | 14811.1482190489 | 2792.97178095107 |
| 48 | 17383.42 | 15189.060638939 | 2194.35936106100 |
| 49 | 17225.83 | 15346.0832759837 | 1879.7467240163 |
| 50 | 16274.33 | 15109.8065967231 | 1164.52340327686 |
| 51 | 16399.39 | 15000.4227720336 | 1398.96722796641 |
| 52 | 16127.58 | 14853.8861694359 | 1273.69383056407 |
| 53 | 16140.76 | 14933.0230883069 | 1207.73691169314 |
| 54 | 15456.81 | 14934.3093844185 | 522.500615581504 |
| 55 | 15505.18 | 14778.5757053962 | 726.604294603792 |
| 56 | 15467.33 | 14764.8337086467 | 702.496291353258 |
| 57 | 16906.23 | 15286.0513910921 | 1620.17860890790 |
| 58 | 17059.66 | 15082.6644263975 | 1976.99557360249 |
| 59 | 16205.43 | 15361.8773809537 | 843.552619046337 |
| 60 | 16649.82 | 15458.2555217915 | 1191.56447820850 |
| 61 | 16111.43 | 15268.4031780952 | 843.026821904754 |
| 62 | 14872.15 | 15501.5240272523 | -629.374027252293 |
| 63 | 13606.5 | 15482.1238707915 | -1875.6238707915 |
| 64 | 13574.3 | 16131.6184339976 | -2557.31843399759 |
| 65 | 12413.6 | 16089.7957259637 | -3676.19572596370 |
| 66 | 11899.6 | 16214.5688334325 | -4314.96883343248 |
| 67 | 11584.01 | 16121.532501987 | -4537.52250198701 |
| 68 | 4460.63 | 6186.34839206256 | -1725.71839206256 |
| 69 | 13908.97 | 8250.84243521844 | 5658.12756478156 |
| 70 | 2 | 2347.91702144229 | -2345.91702144229 |
| 71 | 1181.27 | 5179.37965986182 | -3998.10965986182 |
| 72 | 2617.2 | -174.500160151262 | 2791.70016015126 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.00139849166263179 | 0.00279698332526358 | 0.998601508337368 |
| 11 | 0.000127666623403460 | 0.000255333246806919 | 0.999872333376597 |
| 12 | 1.15113724470530e-05 | 2.30227448941059e-05 | 0.999988488627553 |
| 13 | 8.1252197446408e-07 | 1.62504394892816e-06 | 0.999999187478026 |
| 14 | 1.2562674907016e-05 | 2.5125349814032e-05 | 0.999987437325093 |
| 15 | 2.76349928548576e-06 | 5.52699857097151e-06 | 0.999997236500714 |
| 16 | 6.6470298007684e-07 | 1.32940596015368e-06 | 0.99999933529702 |
| 17 | 8.94268684915812e-08 | 1.78853736983162e-07 | 0.999999910573132 |
| 18 | 1.94912985266597e-08 | 3.89825970533194e-08 | 0.999999980508701 |
| 19 | 2.50249375321250e-09 | 5.00498750642499e-09 | 0.999999997497506 |
| 20 | 4.03657889385012e-10 | 8.07315778770024e-10 | 0.999999999596342 |
| 21 | 1.25937870742972e-10 | 2.51875741485945e-10 | 0.999999999874062 |
| 22 | 1.59839856798861e-11 | 3.19679713597723e-11 | 0.999999999984016 |
| 23 | 9.41731645539445e-12 | 1.88346329107889e-11 | 0.999999999990583 |
| 24 | 1.99098694482422e-12 | 3.98197388964845e-12 | 0.99999999999801 |
| 25 | 9.92005524288206e-12 | 1.98401104857641e-11 | 0.99999999999008 |
| 26 | 1.91818227289869e-12 | 3.83636454579739e-12 | 0.999999999998082 |
| 27 | 3.50124867618276e-12 | 7.00249735236552e-12 | 0.999999999996499 |
| 28 | 8.66688000622474e-13 | 1.73337600124495e-12 | 0.999999999999133 |
| 29 | 1.93782918965663e-13 | 3.87565837931325e-13 | 0.999999999999806 |
| 30 | 5.03343169456475e-14 | 1.00668633891295e-13 | 0.99999999999995 |
| 31 | 1.69020359059318e-14 | 3.38040718118636e-14 | 0.999999999999983 |
| 32 | 5.95224423951687e-14 | 1.19044884790337e-13 | 0.99999999999994 |
| 33 | 1.67748413412453e-13 | 3.35496826824906e-13 | 0.999999999999832 |
| 34 | 2.20352140219590e-11 | 4.40704280439181e-11 | 0.999999999977965 |
| 35 | 2.69136507523061e-10 | 5.38273015046121e-10 | 0.999999999730864 |
| 36 | 1.28985546040823e-06 | 2.57971092081647e-06 | 0.99999871014454 |
| 37 | 3.04618267732667e-06 | 6.09236535465333e-06 | 0.999996953817323 |
| 38 | 3.86589261617849e-06 | 7.73178523235698e-06 | 0.999996134107384 |
| 39 | 4.32381048732104e-06 | 8.64762097464208e-06 | 0.999995676189513 |
| 40 | 5.33674959548963e-06 | 1.06734991909793e-05 | 0.999994663250405 |
| 41 | 9.4176359374454e-06 | 1.88352718748908e-05 | 0.999990582364063 |
| 42 | 1.76451294800549e-05 | 3.52902589601097e-05 | 0.99998235487052 |
| 43 | 8.99725269701675e-06 | 1.79945053940335e-05 | 0.999991002747303 |
| 44 | 4.67870480103442e-06 | 9.35740960206885e-06 | 0.999995321295199 |
| 45 | 1.89409299079649e-06 | 3.78818598159298e-06 | 0.99999810590701 |
| 46 | 1.19104557909618e-06 | 2.38209115819236e-06 | 0.99999880895442 |
| 47 | 1.18879997784957e-06 | 2.37759995569913e-06 | 0.999998811200022 |
| 48 | 4.92673790875094e-07 | 9.85347581750187e-07 | 0.99999950732621 |
| 49 | 2.06842773584476e-07 | 4.13685547168953e-07 | 0.999999793157226 |
| 50 | 1.96864125208238e-07 | 3.93728250416475e-07 | 0.999999803135875 |
| 51 | 1.30065694753860e-07 | 2.60131389507720e-07 | 0.999999869934305 |
| 52 | 1.43917230846644e-07 | 2.87834461693289e-07 | 0.99999985608277 |
| 53 | 1.34407330355721e-07 | 2.68814660711442e-07 | 0.99999986559267 |
| 54 | 1.00693531302901e-06 | 2.01387062605802e-06 | 0.999998993064687 |
| 55 | 6.40937212841204e-05 | 0.000128187442568241 | 0.999935906278716 |
| 56 | 0.210296483333892 | 0.420592966667783 | 0.789703516666108 |
| 57 | 0.218034165646400 | 0.436068331292799 | 0.7819658343536 |
| 58 | 0.167983144801215 | 0.33596628960243 | 0.832016855198785 |
| 59 | 0.223537372056238 | 0.447074744112476 | 0.776462627943762 |
| 60 | 0.277057680850726 | 0.554115361701452 | 0.722942319149274 |
| 61 | 0.352693509872883 | 0.705387019745765 | 0.647306490127117 |
| 62 | 0.380298670332748 | 0.760597340665496 | 0.619701329667252 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 46 | 0.867924528301887 | NOK |
| 5% type I error level | 46 | 0.867924528301887 | NOK |
| 10% type I error level | 46 | 0.867924528301887 | NOK |
