| Multiple Linear Regression - Estimated Regression Equation |
| BEL20[t] = -6.52694269803798 + 0.38134548609792Eonia[t] + 0.0066331019909006Werkloosheid[t] + 0.0339479944182582Consumentenvertrouwen[t] -0.0176233167337368Goudprijs[t] + 0.00861723790694973Olieprijs[t] + 0.0406391768418570CPI[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) | -6.52694269803798 | 2.38488 | -2.7368 | 0.007116 | 0.003558 |
| Eonia | 0.38134548609792 | 0.064267 | 5.9338 | 0 | 0 |
| Werkloosheid | 0.0066331019909006 | 0.001316 | 5.0403 | 2e-06 | 1e-06 |
| Consumentenvertrouwen | 0.0339479944182582 | 0.006971 | 4.8699 | 3e-06 | 2e-06 |
| Goudprijs | -0.0176233167337368 | 0.022191 | -0.7942 | 0.42861 | 0.214305 |
| Olieprijs | 0.00861723790694973 | 0.003943 | 2.1856 | 0.030722 | 0.015361 |
| CPI | 0.0406391768418570 | 0.024786 | 1.6396 | 0.103616 | 0.051808 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.821004574068137 |
| R-squared | 0.674048510640803 |
| Adjusted R-squared | 0.658276664381487 |
| F-TEST (value) | 42.7374512506842 |
| F-TEST (DF numerator) | 6 |
| F-TEST (DF denominator) | 124 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.443811783973242 |
| Sum Squared Residuals | 24.4241435495955 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3.03 | 2.52886246710014 | 0.501137532899857 |
| 2 | 2.803 | 2.63160663973489 | 0.171393360265108 |
| 3 | 2.768 | 2.67884624251629 | 0.0891537574837057 |
| 4 | 2.883 | 2.65217313820033 | 0.230826861799671 |
| 5 | 2.863 | 2.73182577203769 | 0.131174227962309 |
| 6 | 2.897 | 2.94231092612984 | -0.0453109261298374 |
| 7 | 3.013 | 3.20823999158108 | -0.195239991581082 |
| 8 | 3.143 | 3.57895333402728 | -0.435953334027283 |
| 9 | 3.033 | 3.35529564464951 | -0.322295644649509 |
| 10 | 3.046 | 3.42821612369081 | -0.382216123690813 |
| 11 | 3.111 | 3.34020458700085 | -0.229204587000851 |
| 12 | 3.013 | 4.3083665810325 | -1.29536658103250 |
| 13 | 2.987 | 3.24243715217481 | -0.255437152174809 |
| 14 | 2.996 | 3.14683270316400 | -0.150832703163997 |
| 15 | 2.833 | 2.94397538811202 | -0.110975388112018 |
| 16 | 2.849 | 2.91563616907485 | -0.0666361690748498 |
| 17 | 2.795 | 2.75821311754354 | 0.0367868824564586 |
| 18 | 2.845 | 2.71271927135099 | 0.132280728649011 |
| 19 | 2.915 | 3.03301895613899 | -0.118018956138994 |
| 20 | 2.893 | 3.07113642599380 | -0.178136425993797 |
| 21 | 2.604 | 2.77570109006415 | -0.171701090064148 |
| 22 | 2.642 | 2.31507110139011 | 0.326928898609894 |
| 23 | 2.66 | 1.77538290259360 | 0.884617097406401 |
| 24 | 2.639 | 2.0427433243853 | 0.596256675614701 |
| 25 | 2.72 | 2.32074396121330 | 0.399256038786698 |
| 26 | 2.746 | 2.37858323440516 | 0.367416765594839 |
| 27 | 2.736 | 2.41997665455607 | 0.316023345443931 |
| 28 | 2.812 | 2.32754457691911 | 0.484455423080892 |
| 29 | 2.799 | 2.32068242989377 | 0.478317570106226 |
| 30 | 2.555 | 2.29091897230156 | 0.264081027698440 |
| 31 | 2.305 | 2.67672989992180 | -0.371729899921805 |
| 32 | 2.215 | 2.66082224946506 | -0.445822249465058 |
| 33 | 2.066 | 2.68646593848017 | -0.620465938480174 |
| 34 | 1.94 | 2.63971624795032 | -0.699716247950316 |
| 35 | 2.042 | 2.51314735381025 | -0.471147353810252 |
| 36 | 1.995 | 2.34075676879281 | -0.345756768792811 |
| 37 | 1.947 | 2.27731516979939 | -0.330315169799387 |
| 38 | 1.766 | 2.16750911477274 | -0.401509114772736 |
| 39 | 1.635 | 1.94932252581049 | -0.314322525810488 |
| 40 | 1.833 | 2.06133507586850 | -0.228335075868503 |
| 41 | 1.91 | 2.06531652356652 | -0.155316523566523 |
| 42 | 1.96 | 1.96783418640435 | -0.00783418640434615 |
| 43 | 1.97 | 2.24318894228212 | -0.273188942282121 |
| 44 | 2.061 | 2.40753719200839 | -0.346537192008392 |
| 45 | 2.093 | 2.54982783286232 | -0.456827832862316 |
| 46 | 2.121 | 2.13125322539307 | -0.0102532253930704 |
| 47 | 2.175 | 2.30269572913065 | -0.127695729130647 |
| 48 | 2.197 | 2.39521749977699 | -0.198217499776989 |
| 49 | 2.35 | 2.55283678509818 | -0.202836785098181 |
| 50 | 2.44 | 2.63824164372342 | -0.198241643723416 |
| 51 | 2.409 | 2.54239917372659 | -0.133399173726592 |
| 52 | 2.473 | 2.48727537695453 | -0.0142753769545326 |
| 53 | 2.408 | 2.41205113061827 | -0.00405113061826799 |
| 54 | 2.455 | 2.64208456826422 | -0.187084568264222 |
| 55 | 2.448 | 2.8938820671105 | -0.445882067110501 |
| 56 | 2.498 | 3.10151427871375 | -0.60351427871375 |
| 57 | 2.646 | 3.12993179137956 | -0.483931791379559 |
| 58 | 2.757 | 3.0772604088016 | -0.320260408801600 |
| 59 | 2.849 | 2.87701643611857 | -0.0280164361185700 |
| 60 | 2.921 | 2.85342411070563 | 0.0675758892943694 |
| 61 | 2.982 | 2.88973361096918 | 0.0922663890308174 |
| 62 | 3.081 | 3.01535605812902 | 0.0656439418709842 |
| 63 | 3.106 | 3.10986675820726 | -0.00386675820725781 |
| 64 | 3.119 | 2.95103797346697 | 0.167962026533034 |
| 65 | 3.061 | 2.69707852713291 | 0.363921472867087 |
| 66 | 3.097 | 2.73984893339747 | 0.357151066602535 |
| 67 | 3.162 | 3.13919013770657 | 0.0228098622934251 |
| 68 | 3.257 | 3.27800536751436 | -0.0210053675143613 |
| 69 | 3.277 | 3.1420321005045 | 0.134967899495502 |
| 70 | 3.295 | 3.17246104419478 | 0.122538955805216 |
| 71 | 3.364 | 2.99799396374254 | 0.366006036257458 |
| 72 | 3.494 | 3.21613360312913 | 0.27786639687087 |
| 73 | 3.667 | 3.38493811406359 | 0.282061885936408 |
| 74 | 3.813 | 3.33743267116482 | 0.47556732883518 |
| 75 | 3.918 | 3.24445629209607 | 0.673543707903935 |
| 76 | 3.896 | 3.32895502916185 | 0.567044970838153 |
| 77 | 3.801 | 3.2681595671291 | 0.532840432870902 |
| 78 | 3.57 | 3.46266672569636 | 0.107333274303636 |
| 79 | 3.702 | 3.85764514853185 | -0.155645148531854 |
| 80 | 3.862 | 3.96758405557747 | -0.105584055577467 |
| 81 | 3.97 | 3.86608594539865 | 0.103914054601354 |
| 82 | 4.139 | 3.83792827718991 | 0.301071722810089 |
| 83 | 4.2 | 3.67199631415098 | 0.52800368584902 |
| 84 | 4.291 | 3.41051099303483 | 0.880489006965169 |
| 85 | 4.444 | 3.63088505813174 | 0.81311494186826 |
| 86 | 4.503 | 3.66470368917874 | 0.838296310821256 |
| 87 | 4.357 | 3.56846432133214 | 0.788535678667865 |
| 88 | 4.591 | 3.74753046033778 | 0.843469539662219 |
| 89 | 4.697 | 3.63488006261796 | 1.06211993738204 |
| 90 | 4.621 | 3.61228197144169 | 1.00871802855831 |
| 91 | 4.563 | 4.01994528937295 | 0.543054710627052 |
| 92 | 4.203 | 4.00793265948259 | 0.195067340517414 |
| 93 | 4.296 | 3.88130591979074 | 0.41469408020926 |
| 94 | 4.435 | 3.84307933643781 | 0.591920663562193 |
| 95 | 4.105 | 3.65206317241614 | 0.452936827583862 |
| 96 | 4.117 | 3.75712488355986 | 0.359875116440137 |
| 97 | 3.844 | 3.76782140566508 | 0.0761785943349186 |
| 98 | 3.721 | 3.85309626671009 | -0.132096266710090 |
| 99 | 3.674 | 3.88954341116678 | -0.215543411166777 |
| 100 | 3.858 | 3.79347512693928 | 0.0645248730607213 |
| 101 | 3.801 | 3.76684792776853 | 0.0341520722314743 |
| 102 | 3.504 | 3.86283777376056 | -0.358837773760565 |
| 103 | 3.033 | 4.2358899442194 | -1.2028899442194 |
| 104 | 3.047 | 4.20228495580579 | -1.15528495580579 |
| 105 | 2.962 | 4.02778282004451 | -1.06578282004451 |
| 106 | 2.198 | 3.25381164883254 | -1.05581164883254 |
| 107 | 2.014 | 2.60415942852153 | -0.590159428521525 |
| 108 | 1.863 | 2.22344393493199 | -0.360443934931989 |
| 109 | 1.905 | 2.21079346409249 | -0.305793464092489 |
| 110 | 1.811 | 1.85654968154084 | -0.0455496815408419 |
| 111 | 1.67 | 1.8116048573789 | -0.141604857378901 |
| 112 | 1.864 | 1.86393738779001 | 6.26122099874546e-05 |
| 113 | 2.052 | 1.90893604083542 | 0.143063959164578 |
| 114 | 2.03 | 2.08139440319924 | -0.0513944031992398 |
| 115 | 2.071 | 2.29810846050504 | -0.227108460505042 |
| 116 | 2.293 | 2.64124405962976 | -0.348244059629764 |
| 117 | 2.443 | 2.47677443292429 | -0.0337744329242888 |
| 118 | 2.513 | 2.36314204383208 | 0.149857956167918 |
| 119 | 2.467 | 2.41176816408873 | 0.0552318359112712 |
| 120 | 2.503 | 2.32940611752455 | 0.173593882475448 |
| 121 | 2.54 | 2.39599373999704 | 0.144006260002959 |
| 122 | 2.483 | 2.34932085260560 | 0.133679147394396 |
| 123 | 2.626 | 2.39554497625331 | 0.230455023746685 |
| 124 | 2.656 | 2.54069648842171 | 0.115303511578291 |
| 125 | 2.447 | 2.16836987759470 | 0.278630122405305 |
| 126 | 2.467 | 2.31021806504714 | 0.156781934952857 |
| 127 | 2.462 | 2.83746925148891 | -0.375469251488915 |
| 128 | 2.505 | 2.95937767668005 | -0.454377676680048 |
| 129 | 2.579 | 2.85115799954385 | -0.272157999543846 |
| 130 | 2.649 | 2.92893610743094 | -0.279936107430943 |
| 131 | 2.637 | 2.86283904555191 | -0.225839045551909 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 10 | 0.000878723581651672 | 0.00175744716330334 | 0.999121276418348 |
| 11 | 0.000615358272501805 | 0.00123071654500361 | 0.999384641727498 |
| 12 | 0.000206265559376606 | 0.000412531118753212 | 0.999793734440623 |
| 13 | 0.000221007060854818 | 0.000442014121709636 | 0.999778992939145 |
| 14 | 4.71259844848096e-05 | 9.42519689696192e-05 | 0.999952874015515 |
| 15 | 9.00616697596201e-06 | 1.80123339519240e-05 | 0.999990993833024 |
| 16 | 1.73030505214405e-06 | 3.46061010428809e-06 | 0.999998269694948 |
| 17 | 3.65545430783622e-07 | 7.31090861567244e-07 | 0.99999963445457 |
| 18 | 1.39548733097121e-07 | 2.79097466194241e-07 | 0.999999860451267 |
| 19 | 2.30153054991982e-08 | 4.60306109983964e-08 | 0.999999976984695 |
| 20 | 7.47544960303117e-09 | 1.49508992060623e-08 | 0.99999999252455 |
| 21 | 3.98377021393674e-08 | 7.96754042787349e-08 | 0.999999960162298 |
| 22 | 8.79613583082916e-09 | 1.75922716616583e-08 | 0.999999991203864 |
| 23 | 8.67518727119655e-09 | 1.73503745423931e-08 | 0.999999991324813 |
| 24 | 2.80595923888905e-09 | 5.6119184777781e-09 | 0.99999999719404 |
| 25 | 1.44509635548742e-09 | 2.89019271097484e-09 | 0.999999998554904 |
| 26 | 5.04217689203774e-10 | 1.00843537840755e-09 | 0.999999999495782 |
| 27 | 1.31953193165719e-10 | 2.63906386331437e-10 | 0.999999999868047 |
| 28 | 5.76717683575943e-11 | 1.15343536715189e-10 | 0.999999999942328 |
| 29 | 1.76875382461664e-11 | 3.53750764923327e-11 | 0.999999999982312 |
| 30 | 1.66760542193812e-11 | 3.33521084387624e-11 | 0.999999999983324 |
| 31 | 4.14879514602423e-10 | 8.29759029204845e-10 | 0.99999999958512 |
| 32 | 1.18712006636003e-09 | 2.37424013272006e-09 | 0.99999999881288 |
| 33 | 6.46080540198683e-09 | 1.29216108039737e-08 | 0.999999993539195 |
| 34 | 5.17214660795943e-08 | 1.03442932159189e-07 | 0.999999948278534 |
| 35 | 8.67148857002095e-08 | 1.73429771400419e-07 | 0.999999913285114 |
| 36 | 7.22392259002392e-08 | 1.44478451800478e-07 | 0.999999927760774 |
| 37 | 2.98424106293431e-08 | 5.96848212586862e-08 | 0.99999997015759 |
| 38 | 1.17777933364393e-08 | 2.35555866728786e-08 | 0.999999988222207 |
| 39 | 4.73820144124059e-09 | 9.47640288248118e-09 | 0.999999995261799 |
| 40 | 4.88743918498313e-09 | 9.77487836996627e-09 | 0.99999999511256 |
| 41 | 2.84311663633253e-09 | 5.68623327266506e-09 | 0.999999997156883 |
| 42 | 1.03235783760647e-08 | 2.06471567521294e-08 | 0.999999989676422 |
| 43 | 4.55525824298141e-08 | 9.11051648596281e-08 | 0.999999954447418 |
| 44 | 1.21866330095137e-07 | 2.43732660190273e-07 | 0.99999987813367 |
| 45 | 1.35009733581721e-07 | 2.70019467163442e-07 | 0.999999864990266 |
| 46 | 2.2333647090806e-07 | 4.4667294181612e-07 | 0.999999776663529 |
| 47 | 3.06822292808928e-07 | 6.13644585617855e-07 | 0.999999693177707 |
| 48 | 4.48516944038307e-07 | 8.97033888076613e-07 | 0.999999551483056 |
| 49 | 2.1088194129996e-06 | 4.2176388259992e-06 | 0.999997891180587 |
| 50 | 1.47882523602673e-05 | 2.95765047205347e-05 | 0.99998521174764 |
| 51 | 5.15177380113457e-05 | 0.000103035476022691 | 0.999948482261989 |
| 52 | 0.000164565775424614 | 0.000329131550849227 | 0.999835434224575 |
| 53 | 0.00049394746016683 | 0.00098789492033366 | 0.999506052539833 |
| 54 | 0.00158062897915926 | 0.00316125795831852 | 0.99841937102084 |
| 55 | 0.0047459748477082 | 0.0094919496954164 | 0.995254025152292 |
| 56 | 0.016438106073818 | 0.032876212147636 | 0.983561893926182 |
| 57 | 0.0526395731298754 | 0.105279146259751 | 0.947360426870125 |
| 58 | 0.101002542836081 | 0.202005085672162 | 0.898997457163919 |
| 59 | 0.179453009278977 | 0.358906018557954 | 0.820546990721023 |
| 60 | 0.335138832842899 | 0.670277665685799 | 0.664861167157101 |
| 61 | 0.498660151648292 | 0.997320303296584 | 0.501339848351708 |
| 62 | 0.65258496565341 | 0.69483006869318 | 0.34741503434659 |
| 63 | 0.773989474203105 | 0.45202105159379 | 0.226010525796895 |
| 64 | 0.857539910984313 | 0.284920178031374 | 0.142460089015687 |
| 65 | 0.880038952926756 | 0.239922094146487 | 0.119961047073244 |
| 66 | 0.898177818759918 | 0.203644362480164 | 0.101822181240082 |
| 67 | 0.877017538100424 | 0.245964923799152 | 0.122982461899576 |
| 68 | 0.848782527213123 | 0.302434945573754 | 0.151217472786877 |
| 69 | 0.829055092251293 | 0.341889815497414 | 0.170944907748707 |
| 70 | 0.80963961931093 | 0.38072076137814 | 0.19036038068907 |
| 71 | 0.79240614714809 | 0.415187705703819 | 0.207593852851909 |
| 72 | 0.803719474337616 | 0.392561051324768 | 0.196280525662384 |
| 73 | 0.872830717258066 | 0.254338565483868 | 0.127169282741934 |
| 74 | 0.878518191946193 | 0.242963616107613 | 0.121481808053807 |
| 75 | 0.860692190136325 | 0.278615619727349 | 0.139307809863675 |
| 76 | 0.864444671980724 | 0.271110656038551 | 0.135555328019276 |
| 77 | 0.892639959372465 | 0.214720081255070 | 0.107360040627535 |
| 78 | 0.986035992345747 | 0.0279280153085061 | 0.0139640076542530 |
| 79 | 0.996012425082256 | 0.00797514983548776 | 0.00398757491774388 |
| 80 | 0.997625560359799 | 0.00474887928040306 | 0.00237443964020153 |
| 81 | 0.99805761573492 | 0.00388476853015968 | 0.00194238426507984 |
| 82 | 0.999460814934272 | 0.00107837013145645 | 0.000539185065728224 |
| 83 | 0.999832534068288 | 0.000334931863423922 | 0.000167465931711961 |
| 84 | 0.999810158629765 | 0.000379682740469761 | 0.000189841370234880 |
| 85 | 0.999839222400774 | 0.000321555198452334 | 0.000160777599226167 |
| 86 | 0.999797627413853 | 0.000404745172293666 | 0.000202372586146833 |
| 87 | 0.999657305314763 | 0.000685389370474297 | 0.000342694685237149 |
| 88 | 0.999468365632934 | 0.00106326873413212 | 0.000531634367066058 |
| 89 | 0.999399541861348 | 0.00120091627730413 | 0.000600458138652066 |
| 90 | 0.999134451368837 | 0.00173109726232502 | 0.000865548631162511 |
| 91 | 0.99951945211794 | 0.00096109576412044 | 0.00048054788206022 |
| 92 | 0.999318349988928 | 0.00136330002214366 | 0.00068165001107183 |
| 93 | 0.99907733106634 | 0.00184533786731935 | 0.000922668933659677 |
| 94 | 0.999226854041798 | 0.00154629191640355 | 0.000773145958201775 |
| 95 | 0.999610205003309 | 0.00077958999338241 | 0.000389794996691205 |
| 96 | 0.999831590283322 | 0.000336819433356223 | 0.000168409716678112 |
| 97 | 0.999910446257232 | 0.000179107485536182 | 8.95537427680908e-05 |
| 98 | 0.999953594958624 | 9.28100827521577e-05 | 4.64050413760788e-05 |
| 99 | 0.999971933527522 | 5.6132944955891e-05 | 2.80664724779455e-05 |
| 100 | 0.99999082247386 | 1.83550522807422e-05 | 9.1775261403711e-06 |
| 101 | 0.99999952845077 | 9.43098461443915e-07 | 4.71549230721957e-07 |
| 102 | 0.999999789030433 | 4.21939134837489e-07 | 2.10969567418744e-07 |
| 103 | 0.99999996576447 | 6.84710584228158e-08 | 3.42355292114079e-08 |
| 104 | 0.99999995339989 | 9.32002214404243e-08 | 4.66001107202121e-08 |
| 105 | 0.999999957520574 | 8.49588514838488e-08 | 4.24794257419244e-08 |
| 106 | 0.999999989934453 | 2.01310944525951e-08 | 1.00655472262975e-08 |
| 107 | 0.999999981524716 | 3.69505688458387e-08 | 1.84752844229194e-08 |
| 108 | 0.99999994330389 | 1.13392221562619e-07 | 5.66961107813096e-08 |
| 109 | 0.99999993595287 | 1.28094260290691e-07 | 6.40471301453456e-08 |
| 110 | 0.999999936273068 | 1.27453864478889e-07 | 6.37269322394447e-08 |
| 111 | 0.99999971111534 | 5.77769320118724e-07 | 2.88884660059362e-07 |
| 112 | 0.999998805002148 | 2.38999570331684e-06 | 1.19499785165842e-06 |
| 113 | 0.99999896243481 | 2.07513037799125e-06 | 1.03756518899562e-06 |
| 114 | 0.999996546619171 | 6.90676165800907e-06 | 3.45338082900453e-06 |
| 115 | 0.999998704238816 | 2.59152236717197e-06 | 1.29576118358599e-06 |
| 116 | 0.999999936871317 | 1.26257366764203e-07 | 6.31286833821014e-08 |
| 117 | 0.999999297635776 | 1.40472844721956e-06 | 7.02364223609781e-07 |
| 118 | 0.999995325479443 | 9.34904111482786e-06 | 4.67452055741393e-06 |
| 119 | 0.99997938151032 | 4.12369793587486e-05 | 2.06184896793743e-05 |
| 120 | 0.999770801046404 | 0.000458397907191199 | 0.000229198953595599 |
| 121 | 0.997942672799135 | 0.00411465440172924 | 0.00205732720086462 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 89 | 0.794642857142857 | NOK |
| 5% type I error level | 91 | 0.8125 | NOK |
| 10% type I error level | 91 | 0.8125 | NOK |
