| Multiple Linear Regression - Estimated Regression Equation |
| BEL20[t] = + 33.6449842417089 + 0.464260281041345Eonia[t] + 0.00349273190392421Werkloosheid[t] + 0.0201133517056931Consumentenvertrouwen[t] -0.000543752892766527Goudprijs[t] + 0.0181403452647249Olieprijs[t] -0.33406999136402CPI[t] + 0.071913678995696t + 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) | 33.6449842417089 | 5.739412 | 5.8621 | 0 | 0 |
| Eonia | 0.464260281041345 | 0.054682 | 8.4902 | 0 | 0 |
| Werkloosheid | 0.00349273190392421 | 0.001174 | 2.9741 | 0.003538 | 0.001769 |
| Consumentenvertrouwen | 0.0201133517056931 | 0.006096 | 3.2992 | 0.001268 | 0.000634 |
| Goudprijs | -0.000543752892766527 | 0.018628 | -0.0292 | 0.976761 | 0.48838 |
| Olieprijs | 0.0181403452647249 | 0.003524 | 5.1477 | 1e-06 | 1e-06 |
| CPI | -0.33406999136402 | 0.054304 | -6.1518 | 0 | 0 |
| t | 0.071913678995696 | 0.009639 | 7.4606 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.88067962642104 |
| R-squared | 0.775596604393103 |
| Adjusted R-squared | 0.762825679439865 |
| F-TEST (value) | 60.7314354467686 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 123 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.369739069066535 |
| Sum Squared Residuals | 16.8149584408851 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3.03 | 2.48086161308435 | 0.549138386915652 |
| 2 | 2.803 | 2.57073689206409 | 0.232263107935912 |
| 3 | 2.768 | 2.58345459752394 | 0.184545402476058 |
| 4 | 2.883 | 2.55638424215106 | 0.326615757848936 |
| 5 | 2.863 | 2.70693378703709 | 0.156066212962913 |
| 6 | 2.897 | 2.85601869487859 | 0.0409813051214084 |
| 7 | 3.013 | 2.98077226957404 | 0.0322277304259561 |
| 8 | 3.143 | 3.31272029475665 | -0.169720294756646 |
| 9 | 3.033 | 3.07904736278463 | -0.0460473627846305 |
| 10 | 3.046 | 3.32059675862638 | -0.27459675862638 |
| 11 | 3.111 | 3.25096489181336 | -0.139964891813355 |
| 12 | 3.013 | 3.91925153577151 | -0.906251535771515 |
| 13 | 2.987 | 3.36406174522654 | -0.377061745226538 |
| 14 | 2.996 | 3.29578454004121 | -0.299784540041206 |
| 15 | 2.833 | 3.09363218079515 | -0.260632180795145 |
| 16 | 2.849 | 2.87756280357171 | -0.0285628035717093 |
| 17 | 2.795 | 2.56507951217733 | 0.229920487822671 |
| 18 | 2.845 | 2.50810591357675 | 0.336894086423252 |
| 19 | 2.915 | 2.73666734391097 | 0.178332656089031 |
| 20 | 2.893 | 2.82293891461431 | 0.0700610853856927 |
| 21 | 2.604 | 2.49611129101611 | 0.107888708983892 |
| 22 | 2.642 | 2.29689908694573 | 0.345100913054268 |
| 23 | 2.66 | 1.87689180185815 | 0.78310819814185 |
| 24 | 2.639 | 2.15005922724702 | 0.488940772752978 |
| 25 | 2.72 | 2.14545091618383 | 0.57454908381617 |
| 26 | 2.746 | 2.19876190622345 | 0.547238093776547 |
| 27 | 2.736 | 2.2388886322308 | 0.497111367769197 |
| 28 | 2.812 | 2.28698746040853 | 0.525012539591471 |
| 29 | 2.799 | 2.29006208013389 | 0.508937919866113 |
| 30 | 2.555 | 2.45052776133524 | 0.104472238664756 |
| 31 | 2.305 | 2.58895506212718 | -0.283955062127175 |
| 32 | 2.215 | 2.66302268744789 | -0.448022687447893 |
| 33 | 2.066 | 2.67952964391377 | -0.613529643913767 |
| 34 | 1.94 | 2.75298012693505 | -0.81298012693505 |
| 35 | 2.042 | 2.74774266540487 | -0.705742665404869 |
| 36 | 1.995 | 2.68641812856085 | -0.691418128560847 |
| 37 | 1.947 | 2.50978028586011 | -0.562780285860113 |
| 38 | 1.766 | 2.26122835521364 | -0.495228355213641 |
| 39 | 1.635 | 2.05226421084548 | -0.417264210845476 |
| 40 | 1.833 | 2.17635172653929 | -0.343351726539289 |
| 41 | 1.91 | 2.37842256105382 | -0.468422561053817 |
| 42 | 1.96 | 2.21113522467887 | -0.251135224678874 |
| 43 | 1.97 | 2.32277152314176 | -0.352771523141764 |
| 44 | 2.061 | 2.4064611698153 | -0.345461169815299 |
| 45 | 2.093 | 2.39671818493358 | -0.303718184933581 |
| 46 | 2.121 | 2.37993050653204 | -0.258930506532038 |
| 47 | 2.175 | 2.47530420583926 | -0.300304205839265 |
| 48 | 2.197 | 2.65541010771124 | -0.458410107711241 |
| 49 | 2.35 | 2.70348526526969 | -0.353485265269685 |
| 50 | 2.44 | 2.67334930460244 | -0.233349304602443 |
| 51 | 2.409 | 2.6568207384519 | -0.247820738451901 |
| 52 | 2.473 | 2.50822064984165 | -0.0352206498416507 |
| 53 | 2.408 | 2.41239825104509 | -0.00439825104509185 |
| 54 | 2.455 | 2.61840407860452 | -0.163404078604522 |
| 55 | 2.448 | 2.71634085538346 | -0.268340855383456 |
| 56 | 2.498 | 2.90127632840411 | -0.403276328404106 |
| 57 | 2.646 | 2.97800389802161 | -0.332003898021611 |
| 58 | 2.757 | 2.91564261828691 | -0.158642618286909 |
| 59 | 2.849 | 2.86333890088732 | -0.0143389008873174 |
| 60 | 2.921 | 2.98773304022167 | -0.066733040221674 |
| 61 | 2.982 | 3.0255625254386 | -0.0435625254385994 |
| 62 | 3.081 | 2.91032790602562 | 0.170672093974376 |
| 63 | 3.106 | 2.87088501450873 | 0.235114985491272 |
| 64 | 3.119 | 2.7608991162046 | 0.3581008837954 |
| 65 | 3.061 | 2.60322643795181 | 0.457773562048193 |
| 66 | 3.097 | 2.62035500634724 | 0.476644993652763 |
| 67 | 3.162 | 2.68687972617366 | 0.475120273826342 |
| 68 | 3.257 | 2.8769643395703 | 0.380035660429696 |
| 69 | 3.277 | 2.82836427864529 | 0.448635721354707 |
| 70 | 3.295 | 2.945144465504 | 0.349855534495999 |
| 71 | 3.364 | 2.90166191456493 | 0.462338085435071 |
| 72 | 3.494 | 3.17906309525127 | 0.314936904748728 |
| 73 | 3.667 | 3.44424894667615 | 0.22275105332385 |
| 74 | 3.813 | 3.28809543106726 | 0.524904568932735 |
| 75 | 3.918 | 3.38063570106254 | 0.537364298937457 |
| 76 | 3.896 | 3.40219150179543 | 0.493808498204573 |
| 77 | 3.801 | 3.32610573026569 | 0.474894269734314 |
| 78 | 3.57 | 3.50053641791751 | 0.0694635820824871 |
| 79 | 3.702 | 3.73476284973515 | -0.0327628497351461 |
| 80 | 3.862 | 3.85046757065559 | 0.0115324293444066 |
| 81 | 3.97 | 3.86485250577405 | 0.105147494225947 |
| 82 | 4.139 | 4.02412078917276 | 0.11487921082724 |
| 83 | 4.2 | 3.91099286300552 | 0.28900713699448 |
| 84 | 4.291 | 3.85162080242572 | 0.439379197574276 |
| 85 | 4.444 | 3.95063432439014 | 0.493365675609858 |
| 86 | 4.503 | 3.86446332585935 | 0.63853667414065 |
| 87 | 4.357 | 3.95431520515095 | 0.40268479484905 |
| 88 | 4.591 | 4.04603993553927 | 0.544960064460728 |
| 89 | 4.697 | 4.10241677478432 | 0.594583225215682 |
| 90 | 4.621 | 4.24221877215946 | 0.37878122784054 |
| 91 | 4.563 | 4.43224918606564 | 0.130750813934359 |
| 92 | 4.203 | 4.49510021537037 | -0.292100215370371 |
| 93 | 4.296 | 4.52948812117335 | -0.233488121173351 |
| 94 | 4.435 | 4.41026381149716 | 0.024736188502843 |
| 95 | 4.105 | 4.13215522661303 | -0.0271552266130301 |
| 96 | 4.117 | 4.08026496930281 | 0.0367350306971933 |
| 97 | 3.844 | 4.049063698524 | -0.205063698523998 |
| 98 | 3.721 | 3.88719350859549 | -0.166193508595492 |
| 99 | 3.674 | 3.78507018775872 | -0.111070187758724 |
| 100 | 3.858 | 3.74801738654477 | 0.109982613455234 |
| 101 | 3.801 | 3.59610113608821 | 0.204898863911789 |
| 102 | 3.504 | 3.57879277567125 | -0.0747927756712535 |
| 103 | 3.033 | 3.69768554661102 | -0.664685546611017 |
| 104 | 3.047 | 3.79161411335089 | -0.74461411335089 |
| 105 | 2.962 | 3.4978125443806 | -0.535812544380601 |
| 106 | 2.198 | 2.76816883146949 | -0.570168831469492 |
| 107 | 2.014 | 2.3046264828118 | -0.290626482811797 |
| 108 | 1.863 | 1.94009952518179 | -0.0770995251817943 |
| 109 | 1.905 | 1.82175414159858 | 0.0832458584014193 |
| 110 | 1.811 | 1.40362100383087 | 0.407378996169125 |
| 111 | 1.67 | 1.70367740341148 | -0.0336774034114783 |
| 112 | 1.864 | 1.69270883222404 | 0.171291167775957 |
| 113 | 2.052 | 1.90785658347214 | 0.144143416527859 |
| 114 | 2.03 | 2.2880863461164 | -0.258086346116403 |
| 115 | 2.071 | 2.36511266205473 | -0.294112662054733 |
| 116 | 2.293 | 2.58935710226036 | -0.296357102260359 |
| 117 | 2.443 | 2.63904873543087 | -0.196048735430866 |
| 118 | 2.513 | 2.69888621513693 | -0.185886215136926 |
| 119 | 2.467 | 2.75476199743275 | -0.28776199743275 |
| 120 | 2.503 | 2.67132907130013 | -0.168329071300131 |
| 121 | 2.54 | 2.59936748789993 | -0.059367487899927 |
| 122 | 2.483 | 2.41834496154234 | 0.0646550384576649 |
| 123 | 2.626 | 2.42691942086076 | 0.199080579139238 |
| 124 | 2.656 | 2.51806556901304 | 0.137934430986956 |
| 125 | 2.447 | 2.12106762989885 | 0.325932370101146 |
| 126 | 2.467 | 2.26687180923024 | 0.200128190769759 |
| 127 | 2.462 | 2.60726362771483 | -0.145263627714833 |
| 128 | 2.505 | 2.73647771294044 | -0.231477712940444 |
| 129 | 2.579 | 2.62887380098885 | -0.0498738009888447 |
| 130 | 2.649 | 2.81992046513924 | -0.170920465139243 |
| 131 | 2.637 | 2.81915051673211 | -0.182150516732106 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.00226865293627894 | 0.00453730587255789 | 0.99773134706372 |
| 12 | 0.000323813933571711 | 0.000647627867143422 | 0.999676186066428 |
| 13 | 0.00225271557849577 | 0.00450543115699155 | 0.997747284421504 |
| 14 | 0.00054385423095881 | 0.00108770846191762 | 0.999456145769041 |
| 15 | 0.000112436896583701 | 0.000224873793167402 | 0.999887563103416 |
| 16 | 2.1966615653425e-05 | 4.39332313068499e-05 | 0.999978033384347 |
| 17 | 6.81983318514308e-06 | 1.36396663702862e-05 | 0.999993180166815 |
| 18 | 3.62037029353353e-06 | 7.24074058706706e-06 | 0.999996379629706 |
| 19 | 6.91785781221209e-07 | 1.38357156244242e-06 | 0.999999308214219 |
| 20 | 2.25953748836903e-07 | 4.51907497673806e-07 | 0.999999774046251 |
| 21 | 5.77994829872174e-07 | 1.15598965974435e-06 | 0.99999942200517 |
| 22 | 1.47710783286933e-07 | 2.95421566573866e-07 | 0.999999852289217 |
| 23 | 3.25921265994698e-07 | 6.51842531989395e-07 | 0.999999674078734 |
| 24 | 1.60948143545646e-07 | 3.21896287091291e-07 | 0.999999839051856 |
| 25 | 1.18796103685547e-07 | 2.37592207371093e-07 | 0.999999881203896 |
| 26 | 6.1672891316429e-08 | 1.23345782632858e-07 | 0.999999938327109 |
| 27 | 2.42707384809939e-08 | 4.85414769619877e-08 | 0.999999975729261 |
| 28 | 1.47681781329152e-08 | 2.95363562658304e-08 | 0.999999985231822 |
| 29 | 8.95388918508898e-09 | 1.7907778370178e-08 | 0.99999999104611 |
| 30 | 2.64549157268988e-08 | 5.29098314537976e-08 | 0.999999973545084 |
| 31 | 4.94583212609509e-07 | 9.89166425219018e-07 | 0.999999505416787 |
| 32 | 1.01494639595963e-06 | 2.02989279191925e-06 | 0.999998985053604 |
| 33 | 3.24974790478932e-06 | 6.49949580957863e-06 | 0.999996750252095 |
| 34 | 1.08639834225282e-05 | 2.17279668450564e-05 | 0.999989136016577 |
| 35 | 8.89219326593396e-06 | 1.77843865318679e-05 | 0.999991107806734 |
| 36 | 4.8973188656034e-06 | 9.7946377312068e-06 | 0.999995102681134 |
| 37 | 2.29694857715806e-06 | 4.59389715431612e-06 | 0.999997703051423 |
| 38 | 1.06249077876106e-06 | 2.12498155752212e-06 | 0.999998937509221 |
| 39 | 4.50841964984938e-07 | 9.01683929969876e-07 | 0.999999549158035 |
| 40 | 3.66368559036476e-07 | 7.32737118072951e-07 | 0.99999963363144 |
| 41 | 4.32588324388048e-07 | 8.65176648776096e-07 | 0.999999567411676 |
| 42 | 1.87419460036724e-06 | 3.74838920073448e-06 | 0.9999981258054 |
| 43 | 6.47114869296222e-06 | 1.29422973859244e-05 | 0.999993528851307 |
| 44 | 1.47716984243331e-05 | 2.95433968486661e-05 | 0.999985228301576 |
| 45 | 1.09539063384154e-05 | 2.19078126768307e-05 | 0.999989046093662 |
| 46 | 5.15315630583993e-05 | 0.000103063126116799 | 0.999948468436942 |
| 47 | 0.000120063933811744 | 0.000240127867623487 | 0.999879936066188 |
| 48 | 0.000438329099000169 | 0.000876658198000338 | 0.999561670901 |
| 49 | 0.00226176559045543 | 0.00452353118091086 | 0.997738234409545 |
| 50 | 0.00786999239289116 | 0.0157399847857823 | 0.99213000760711 |
| 51 | 0.0209574938204985 | 0.0419149876409971 | 0.979042506179502 |
| 52 | 0.0361886795785084 | 0.0723773591570168 | 0.963811320421492 |
| 53 | 0.0493885303939758 | 0.0987770607879516 | 0.950611469606024 |
| 54 | 0.0711314884070467 | 0.142262976814093 | 0.928868511592953 |
| 55 | 0.104986205244026 | 0.209972410488051 | 0.895013794755974 |
| 56 | 0.188626753656638 | 0.377253507313277 | 0.811373246343362 |
| 57 | 0.349744274900269 | 0.699488549800537 | 0.650255725099731 |
| 58 | 0.477418546897052 | 0.954837093794105 | 0.522581453102948 |
| 59 | 0.671038646428254 | 0.657922707143492 | 0.328961353571746 |
| 60 | 0.915073152736143 | 0.169853694527714 | 0.084926847263857 |
| 61 | 0.985606805224838 | 0.028786389550325 | 0.0143931947751625 |
| 62 | 0.993697176933417 | 0.0126056461331665 | 0.00630282306658327 |
| 63 | 0.99542560334017 | 0.00914879331966152 | 0.00457439665983076 |
| 64 | 0.996334589801791 | 0.00733082039641748 | 0.00366541019820874 |
| 65 | 0.996335811784165 | 0.00732837643167004 | 0.00366418821583502 |
| 66 | 0.996058127861218 | 0.00788374427756454 | 0.00394187213878227 |
| 67 | 0.994742503676982 | 0.0105149926460351 | 0.00525749632301754 |
| 68 | 0.993276099504867 | 0.0134478009902659 | 0.00672390049513294 |
| 69 | 0.9941729180341 | 0.0116541639318004 | 0.0058270819659002 |
| 70 | 0.99214156496863 | 0.0157168700627405 | 0.00785843503137027 |
| 71 | 0.991101341594114 | 0.0177973168117727 | 0.00889865840588633 |
| 72 | 0.989974659998604 | 0.0200506800027917 | 0.0100253400013959 |
| 73 | 0.992098729769037 | 0.0158025404619266 | 0.0079012702309633 |
| 74 | 0.98932314030111 | 0.0213537193977811 | 0.0106768596988905 |
| 75 | 0.98662460147549 | 0.0267507970490221 | 0.0133753985245111 |
| 76 | 0.9821146086602 | 0.0357707826796016 | 0.0178853913398008 |
| 77 | 0.981211618097709 | 0.0375767638045825 | 0.0187883819022913 |
| 78 | 0.994461773771057 | 0.0110764524578868 | 0.00553822622894342 |
| 79 | 0.99682266591366 | 0.00635466817268157 | 0.00317733408634079 |
| 80 | 0.996671349045593 | 0.00665730190881353 | 0.00332865095440676 |
| 81 | 0.996634396334947 | 0.00673120733010623 | 0.00336560366505311 |
| 82 | 0.998942401265229 | 0.0021151974695416 | 0.0010575987347708 |
| 83 | 0.999709202483023 | 0.00058159503395367 | 0.000290797516976835 |
| 84 | 0.999726428515031 | 0.000547142969937293 | 0.000273571484968647 |
| 85 | 0.999777948782705 | 0.000444102434590565 | 0.000222051217295282 |
| 86 | 0.999709581475445 | 0.000580837049109359 | 0.000290418524554679 |
| 87 | 0.999521656284252 | 0.000956687431496716 | 0.000478343715748358 |
| 88 | 0.999251285623542 | 0.00149742875291672 | 0.000748714376458362 |
| 89 | 0.9991861518576 | 0.00162769628480171 | 0.000813848142400854 |
| 90 | 0.998838613589464 | 0.00232277282107155 | 0.00116138641053578 |
| 91 | 0.999403642514316 | 0.00119271497136886 | 0.000596357485684429 |
| 92 | 0.999132029803016 | 0.0017359403939677 | 0.00086797019698385 |
| 93 | 0.998732821884183 | 0.00253435623163368 | 0.00126717811581684 |
| 94 | 0.998826552601106 | 0.00234689479778777 | 0.00117344739889388 |
| 95 | 0.9993410174652 | 0.00131796506959969 | 0.000658982534799843 |
| 96 | 0.999707856019072 | 0.000584287961856772 | 0.000292143980928386 |
| 97 | 0.99984853061499 | 0.000302938770018914 | 0.000151469385009457 |
| 98 | 0.999917204381037 | 0.000165591237925285 | 8.27956189626427e-05 |
| 99 | 0.999936207569461 | 0.000127584861077484 | 6.3792430538742e-05 |
| 100 | 0.999977910858954 | 4.41782820916607e-05 | 2.20891410458303e-05 |
| 101 | 0.999999291882942 | 1.41623411536778e-06 | 7.08117057683889e-07 |
| 102 | 0.999999863249575 | 2.73500850653814e-07 | 1.36750425326907e-07 |
| 103 | 0.999999926749726 | 1.4650054837389e-07 | 7.32502741869448e-08 |
| 104 | 0.999999855500015 | 2.88999970725167e-07 | 1.44499985362584e-07 |
| 105 | 0.999999948980435 | 1.02039129323568e-07 | 5.10195646617842e-08 |
| 106 | 0.99999988246964 | 2.35060720305119e-07 | 1.17530360152559e-07 |
| 107 | 0.999999597731312 | 8.04537376012204e-07 | 4.02268688006102e-07 |
| 108 | 0.99999853831204 | 2.92337591999203e-06 | 1.46168795999602e-06 |
| 109 | 0.999998518873466 | 2.96225306718417e-06 | 1.48112653359208e-06 |
| 110 | 0.999999939561734 | 1.20876531664664e-07 | 6.0438265832332e-08 |
| 111 | 0.99999978308173 | 4.33836539636767e-07 | 2.16918269818384e-07 |
| 112 | 0.999999038737713 | 1.92252457422294e-06 | 9.6126228711147e-07 |
| 113 | 0.999999409810234 | 1.18037953194212e-06 | 5.90189765971062e-07 |
| 114 | 0.99999696900965 | 6.06198069992919e-06 | 3.0309903499646e-06 |
| 115 | 0.999999122841316 | 1.75431736705341e-06 | 8.77158683526707e-07 |
| 116 | 0.99999837718971 | 3.24562058169918e-06 | 1.62281029084959e-06 |
| 117 | 0.999985984306324 | 2.80313873513958e-05 | 1.40156936756979e-05 |
| 118 | 0.999917945560616 | 0.000164108878767984 | 8.2054439383992e-05 |
| 119 | 0.999544985548285 | 0.000910028903430571 | 0.000455014451715286 |
| 120 | 0.99611936413917 | 0.00776127172165928 | 0.00388063586082964 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 85 | 0.772727272727273 | NOK |
| 5% type I error level | 101 | 0.918181818181818 | NOK |
| 10% type I error level | 103 | 0.936363636363636 | NOK |
