| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1471.55250880347 + 0.0954355312113703Nikkei[t] + 0.369163039198861DJ_Indust[t] + 0.0238744986798515Goudprijs[t] -10.6388338055077Conjunct_Seizoenzuiver[t] + 13.4082779421853Cons_vertrouw[t] + 36.2029927235425Alg_consumptie_index_BE[t] -278.729546599587Gem_rente_kasbon_5j[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) | -1471.55250880347 | 334.820996 | -4.395 | 2.4e-05 | 1.2e-05 |
| Nikkei | 0.0954355312113703 | 0.01489 | 6.4094 | 0 | 0 |
| DJ_Indust | 0.369163039198861 | 0.034498 | 10.7009 | 0 | 0 |
| Goudprijs | 0.0238744986798515 | 0.008227 | 2.9019 | 0.004391 | 0.002195 |
| Conjunct_Seizoenzuiver | -10.6388338055077 | 6.686008 | -1.5912 | 0.114109 | 0.057054 |
| Cons_vertrouw | 13.4082779421853 | 6.24542 | 2.1469 | 0.033748 | 0.016874 |
| Alg_consumptie_index_BE | 36.2029927235425 | 22.797387 | 1.588 | 0.114826 | 0.057413 |
| Gem_rente_kasbon_5j | -278.729546599587 | 50.979851 | -5.4674 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.941641426248589 |
| R-squared | 0.886688575627476 |
| Adjusted R-squared | 0.880291962961286 |
| F-TEST (value) | 138.618456658170 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 124 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 260.514793987770 |
| Sum Squared Residuals | 8415626.77792477 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2782.9062769675 | 701.8337230325 |
| 2 | 3411.13 | 2778.20485107048 | 632.925148929522 |
| 3 | 3288.18 | 3011.41592595034 | 276.764074049664 |
| 4 | 3280.37 | 3395.42294505136 | -115.052945051356 |
| 5 | 3173.95 | 3500.73185001672 | -326.781850016719 |
| 6 | 3165.26 | 3241.30139670025 | -76.0413967002547 |
| 7 | 3092.71 | 3419.42382524288 | -326.713825242876 |
| 8 | 3053.05 | 3268.99781322394 | -215.947813223945 |
| 9 | 3181.96 | 3191.80915380501 | -9.84915380500932 |
| 10 | 2999.93 | 3001.50298236305 | -1.57298236304665 |
| 11 | 3249.57 | 3361.08175818603 | -111.511758186028 |
| 12 | 3210.52 | 3428.88766156591 | -218.367661565914 |
| 13 | 3030.29 | 3493.32683474948 | -463.036834749478 |
| 14 | 2803.47 | 3269.58921825948 | -466.119218259476 |
| 15 | 2767.63 | 3281.56010261961 | -513.930102619609 |
| 16 | 2882.6 | 3471.57983976385 | -588.979839763845 |
| 17 | 2863.36 | 3043.87167181946 | -180.511671819459 |
| 18 | 2897.06 | 3072.03963437298 | -174.979634372979 |
| 19 | 3012.61 | 3097.24993334053 | -84.6399333405251 |
| 20 | 3142.95 | 3189.40437583695 | -46.4543758369476 |
| 21 | 3032.93 | 3094.17421316021 | -61.2442131602135 |
| 22 | 3045.78 | 2873.31410599627 | 172.465894003733 |
| 23 | 3110.52 | 2952.50485978835 | 158.015140211654 |
| 24 | 3013.24 | 3039.72840480046 | -26.4884048004578 |
| 25 | 2987.1 | 2996.52224692528 | -9.42224692528093 |
| 26 | 2995.55 | 2943.91454449975 | 51.6354555002539 |
| 27 | 2833.18 | 2666.48140967185 | 166.698590328153 |
| 28 | 2848.96 | 2826.51939823056 | 22.4406017694427 |
| 29 | 2794.83 | 2987.19462930827 | -192.364629308267 |
| 30 | 2845.26 | 3009.92204066049 | -164.662040660487 |
| 31 | 2915.02 | 2810.96679487084 | 104.053205129165 |
| 32 | 2892.63 | 2663.17527363360 | 229.454726366404 |
| 33 | 2604.42 | 2106.36423852480 | 498.055761475196 |
| 34 | 2641.65 | 2171.90268293308 | 469.747317066924 |
| 35 | 2659.81 | 2369.79939967285 | 290.010600327151 |
| 36 | 2638.53 | 2451.67492933541 | 186.855070664595 |
| 37 | 2720.25 | 2506.44299736808 | 213.807002631916 |
| 38 | 2745.88 | 2442.06806342782 | 303.81193657218 |
| 39 | 2735.7 | 2702.38180906088 | 33.318190939116 |
| 40 | 2811.7 | 2508.4193965516 | 303.2806034484 |
| 41 | 2799.43 | 2504.98174463288 | 294.448255367116 |
| 42 | 2555.28 | 2233.7353243904 | 321.544675609602 |
| 43 | 2304.98 | 1908.80279944558 | 396.177200554424 |
| 44 | 2214.95 | 1945.60573095747 | 269.344269042525 |
| 45 | 2065.81 | 1781.77926015096 | 284.030739849039 |
| 46 | 1940.49 | 1698.34022526250 | 242.149774737498 |
| 47 | 2042 | 1877.29997118634 | 164.700028813658 |
| 48 | 1995.37 | 1815.57251427901 | 179.797485720992 |
| 49 | 1946.81 | 1888.86428465092 | 57.9457153490768 |
| 50 | 1765.9 | 1715.18955333380 | 50.7104466662039 |
| 51 | 1635.25 | 1678.39048532208 | -43.1404853220774 |
| 52 | 1833.42 | 1806.95305272367 | 26.4669472763262 |
| 53 | 1910.43 | 2069.59072607337 | -159.160726073366 |
| 54 | 1959.67 | 2429.16326929088 | -469.493269290875 |
| 55 | 1969.6 | 2385.04093186342 | -415.440931863422 |
| 56 | 2061.41 | 2348.56867776170 | -287.158677761696 |
| 57 | 2093.48 | 2554.86041680655 | -461.380416806548 |
| 58 | 2120.88 | 2419.67942614705 | -298.799426147051 |
| 59 | 2174.56 | 2504.58264818782 | -330.022648187820 |
| 60 | 2196.72 | 2630.18922282629 | -433.46922282629 |
| 61 | 2350.44 | 2839.07854317997 | -488.638543179968 |
| 62 | 2440.25 | 2845.13567181262 | -404.885671812615 |
| 63 | 2408.64 | 2820.44757767273 | -411.807577672728 |
| 64 | 2472.81 | 2950.71515592222 | -477.905155922219 |
| 65 | 2407.6 | 2683.68606159096 | -276.086061590964 |
| 66 | 2454.62 | 2901.20733260169 | -446.587332601692 |
| 67 | 2448.05 | 2679.27996319084 | -231.229963190844 |
| 68 | 2497.84 | 2678.89964407652 | -181.059644076521 |
| 69 | 2645.64 | 2739.8367105046 | -94.196710504604 |
| 70 | 2756.76 | 2626.74520724389 | 130.014792756113 |
| 71 | 2849.27 | 2787.08769118939 | 62.1823088106102 |
| 72 | 2921.44 | 2923.54360488827 | -2.10360488827106 |
| 73 | 2981.85 | 2913.08507269532 | 68.7649273046758 |
| 74 | 3080.58 | 3114.46573186389 | -33.8857318638916 |
| 75 | 3106.22 | 3167.1284348135 | -60.9084348135003 |
| 76 | 3119.31 | 2965.75729212929 | 153.552707870711 |
| 77 | 3061.26 | 2900.64980171626 | 160.610198283741 |
| 78 | 3097.31 | 3026.99739807435 | 70.3126019256458 |
| 79 | 3161.69 | 3118.26656397278 | 43.4234360272214 |
| 80 | 3257.16 | 3155.36489682314 | 101.795103176863 |
| 81 | 3277.01 | 3151.04445248029 | 125.965547519714 |
| 82 | 3295.32 | 3161.33003187036 | 133.989968129645 |
| 83 | 3363.99 | 3342.80352269739 | 21.1864773026068 |
| 84 | 3494.17 | 3551.49276747278 | -57.3227674727801 |
| 85 | 3667.03 | 3644.79645752556 | 22.2335424744379 |
| 86 | 3813.06 | 3691.5772318172 | 121.482768182800 |
| 87 | 3917.96 | 3667.16351586527 | 250.796484134733 |
| 88 | 3895.51 | 3745.20465282433 | 150.305347175671 |
| 89 | 3801.06 | 3655.53164839026 | 145.528351609735 |
| 90 | 3570.12 | 3391.76836134461 | 178.351638655387 |
| 91 | 3701.61 | 3385.78426232281 | 315.825737677191 |
| 92 | 3862.27 | 3527.54239550801 | 334.727604491992 |
| 93 | 3970.1 | 3648.06199939585 | 322.038000604154 |
| 94 | 4138.52 | 3894.07420353413 | 244.445796465871 |
| 95 | 4199.75 | 3971.26211885784 | 228.487881142157 |
| 96 | 4290.89 | 3965.84238011712 | 325.047619882884 |
| 97 | 4443.91 | 4138.07831343244 | 305.831686567559 |
| 98 | 4502.64 | 4204.27990036321 | 298.360099636787 |
| 99 | 4356.98 | 3986.66242748394 | 370.317572516063 |
| 100 | 4591.27 | 4229.92187701452 | 361.348122985484 |
| 101 | 4696.96 | 4459.37535235478 | 237.58464764522 |
| 102 | 4621.4 | 4394.54378002604 | 226.856219973956 |
| 103 | 4562.84 | 4400.90134647826 | 161.938653521738 |
| 104 | 4202.52 | 4114.35597350577 | 88.164026494235 |
| 105 | 4296.49 | 4262.63786482052 | 33.8521351794845 |
| 106 | 4435.23 | 4526.11710050783 | -90.8871005078348 |
| 107 | 4105.18 | 4114.62359388622 | -9.4435938862209 |
| 108 | 4116.68 | 4287.37207046046 | -170.692070460459 |
| 109 | 3844.49 | 3777.55590824415 | 66.9340917558457 |
| 110 | 3720.98 | 3824.85307235633 | -103.873072356332 |
| 111 | 3674.4 | 3768.15519271046 | -93.7551927104564 |
| 112 | 3857.62 | 3977.54863426004 | -119.928634260039 |
| 113 | 3801.06 | 4003.90475196433 | -202.844751964330 |
| 114 | 3504.37 | 3598.54192114657 | -94.1719211465738 |
| 115 | 3032.6 | 3125.94758607654 | -93.3475860765388 |
| 116 | 3047.03 | 3168.46584407277 | -121.435844072772 |
| 117 | 2962.34 | 3127.76341408423 | -165.423414084230 |
| 118 | 2197.82 | 2084.53038087081 | 113.289619129190 |
| 119 | 2014.45 | 1877.3927155733 | 137.057284426701 |
| 120 | 1862.83 | 1914.68332931617 | -51.85332931617 |
| 121 | 1905.41 | 1936.5534971336 | -31.1434971335989 |
| 122 | 1810.99 | 1720.49172292983 | 90.4982770701676 |
| 123 | 1670.07 | 1592.63583850985 | 77.434161490152 |
| 124 | 1864.44 | 1933.83156176222 | -69.3915617622216 |
| 125 | 2052.02 | 2105.87220617235 | -53.8522061723506 |
| 126 | 2029.6 | 2151.18336073787 | -121.583360737874 |
| 127 | 2070.83 | 2134.4529743431 | -63.6229743431011 |
| 128 | 2293.41 | 2533.19956917905 | -239.78956917905 |
| 129 | 2443.27 | 2609.58390893535 | -166.313908935353 |
| 130 | 2513.17 | 2634.04289735311 | -120.872897353108 |
| 131 | 2466.92 | 2824.88267013467 | -357.962670134671 |
| 132 | 2502.66 | 2904.13932919437 | -401.479329194367 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.0323997973529295 | 0.0647995947058591 | 0.96760020264707 |
| 12 | 0.0152863264020716 | 0.0305726528041432 | 0.984713673597928 |
| 13 | 0.0057931028295234 | 0.0115862056590468 | 0.994206897170477 |
| 14 | 0.0149237053522376 | 0.0298474107044752 | 0.985076294647762 |
| 15 | 0.0183047728546225 | 0.036609545709245 | 0.981695227145377 |
| 16 | 0.0142997800608265 | 0.0285995601216531 | 0.985700219939173 |
| 17 | 0.0445191450343003 | 0.0890382900686007 | 0.9554808549657 |
| 18 | 0.0395729103560355 | 0.079145820712071 | 0.960427089643965 |
| 19 | 0.0293433678596913 | 0.0586867357193827 | 0.970656632140309 |
| 20 | 0.0243308205282003 | 0.0486616410564005 | 0.9756691794718 |
| 21 | 0.0174315822609719 | 0.0348631645219438 | 0.982568417739028 |
| 22 | 0.0100580981388315 | 0.0201161962776630 | 0.989941901861169 |
| 23 | 0.00555452086107098 | 0.0111090417221420 | 0.994445479138929 |
| 24 | 0.0085884671821004 | 0.0171769343642008 | 0.9914115328179 |
| 25 | 0.0175702265808783 | 0.0351404531617566 | 0.982429773419122 |
| 26 | 0.0190867112256686 | 0.0381734224513372 | 0.980913288774331 |
| 27 | 0.040983855088241 | 0.081967710176482 | 0.959016144911759 |
| 28 | 0.0738656381311821 | 0.147731276262364 | 0.926134361868818 |
| 29 | 0.0852814512733487 | 0.170562902546697 | 0.914718548726651 |
| 30 | 0.0795956615649018 | 0.159191323129804 | 0.920404338435098 |
| 31 | 0.0618332931997419 | 0.123666586399484 | 0.938166706800258 |
| 32 | 0.0432863407645455 | 0.086572681529091 | 0.956713659235454 |
| 33 | 0.0468844897445634 | 0.0937689794891268 | 0.953115510255437 |
| 34 | 0.0399177469397642 | 0.0798354938795285 | 0.960082253060236 |
| 35 | 0.0334056195080551 | 0.0668112390161102 | 0.966594380491945 |
| 36 | 0.0244593597061334 | 0.0489187194122668 | 0.975540640293867 |
| 37 | 0.0185120084008586 | 0.0370240168017172 | 0.981487991599141 |
| 38 | 0.0191343857746929 | 0.0382687715493858 | 0.980865614225307 |
| 39 | 0.0138170208347216 | 0.0276340416694432 | 0.986182979165278 |
| 40 | 0.0157039067489941 | 0.0314078134979882 | 0.984296093251006 |
| 41 | 0.0117229977489005 | 0.0234459954978009 | 0.9882770022511 |
| 42 | 0.0127973403975877 | 0.0255946807951754 | 0.987202659602412 |
| 43 | 0.0462388817752009 | 0.0924777635504018 | 0.953761118224799 |
| 44 | 0.111904818028657 | 0.223809636057314 | 0.888095181971343 |
| 45 | 0.179435367514818 | 0.358870735029636 | 0.820564632485182 |
| 46 | 0.298014518338853 | 0.596029036677706 | 0.701985481661147 |
| 47 | 0.40020604897569 | 0.80041209795138 | 0.59979395102431 |
| 48 | 0.434650696455188 | 0.869301392910377 | 0.565349303544812 |
| 49 | 0.450983314569762 | 0.901966629139525 | 0.549016685430238 |
| 50 | 0.414873421083487 | 0.829746842166974 | 0.585126578916513 |
| 51 | 0.42769611237162 | 0.85539222474324 | 0.57230388762838 |
| 52 | 0.660397133223179 | 0.679205733553642 | 0.339602866776821 |
| 53 | 0.770506991615273 | 0.458986016769453 | 0.229493008384727 |
| 54 | 0.883201437800972 | 0.233597124398056 | 0.116798562199028 |
| 55 | 0.915391216270125 | 0.169217567459751 | 0.0846087837298755 |
| 56 | 0.902879798630227 | 0.194240402739545 | 0.0971202013697726 |
| 57 | 0.914623813432267 | 0.170752373135467 | 0.0853761865677333 |
| 58 | 0.92724853037646 | 0.145502939247079 | 0.0727514696235395 |
| 59 | 0.918582560689141 | 0.162834878621718 | 0.081417439310859 |
| 60 | 0.92007472187445 | 0.159850556251098 | 0.0799252781255492 |
| 61 | 0.934684867081114 | 0.130630265837772 | 0.0653151329188861 |
| 62 | 0.931747433823418 | 0.136505132353165 | 0.0682525661765824 |
| 63 | 0.954696691251993 | 0.0906066174960132 | 0.0453033087480066 |
| 64 | 0.99181097093703 | 0.0163780581259405 | 0.00818902906297025 |
| 65 | 0.995975290186268 | 0.0080494196274635 | 0.00402470981373175 |
| 66 | 0.999285333466716 | 0.00142933306656857 | 0.000714666533284283 |
| 67 | 0.99981891243832 | 0.000362175123360832 | 0.000181087561680416 |
| 68 | 0.999932643917329 | 0.000134712165341802 | 6.73560826709012e-05 |
| 69 | 0.999975022882783 | 4.99542344347484e-05 | 2.49771172173742e-05 |
| 70 | 0.999992098365133 | 1.58032697344862e-05 | 7.90163486724312e-06 |
| 71 | 0.999995992629006 | 8.0147419883021e-06 | 4.00737099415105e-06 |
| 72 | 0.999996771851818 | 6.45629636470691e-06 | 3.22814818235346e-06 |
| 73 | 0.999997391447691 | 5.21710461742972e-06 | 2.60855230871486e-06 |
| 74 | 0.999997809315034 | 4.38136993116523e-06 | 2.19068496558262e-06 |
| 75 | 0.999998418572012 | 3.16285597597775e-06 | 1.58142798798887e-06 |
| 76 | 0.999998661375182 | 2.67724963630439e-06 | 1.33862481815219e-06 |
| 77 | 0.999998895676051 | 2.20864789754283e-06 | 1.10432394877142e-06 |
| 78 | 0.999998976512405 | 2.04697519069756e-06 | 1.02348759534878e-06 |
| 79 | 0.999998702443574 | 2.59511285117537e-06 | 1.29755642558768e-06 |
| 80 | 0.99999849470719 | 3.01058562045257e-06 | 1.50529281022628e-06 |
| 81 | 0.999998547563251 | 2.90487349773240e-06 | 1.45243674886620e-06 |
| 82 | 0.999998516772241 | 2.96645551698758e-06 | 1.48322775849379e-06 |
| 83 | 0.999998320580046 | 3.3588399073991e-06 | 1.67941995369955e-06 |
| 84 | 0.999999551975966 | 8.96048068353057e-07 | 4.48024034176528e-07 |
| 85 | 0.999999876711967 | 2.46576065540835e-07 | 1.23288032770418e-07 |
| 86 | 0.999999934008467 | 1.31983066215823e-07 | 6.59915331079114e-08 |
| 87 | 0.999999924119762 | 1.51760475101662e-07 | 7.58802375508312e-08 |
| 88 | 0.99999996840833 | 6.31833410290195e-08 | 3.15916705145098e-08 |
| 89 | 0.999999973725554 | 5.25488928073461e-08 | 2.62744464036730e-08 |
| 90 | 0.999999983818538 | 3.23629239456539e-08 | 1.61814619728270e-08 |
| 91 | 0.9999999670528 | 6.58943995559013e-08 | 3.29471997779507e-08 |
| 92 | 0.999999932474177 | 1.35051645973568e-07 | 6.75258229867841e-08 |
| 93 | 0.999999873953766 | 2.52092468638194e-07 | 1.26046234319097e-07 |
| 94 | 0.999999891815646 | 2.16368708985461e-07 | 1.08184354492731e-07 |
| 95 | 0.99999983788189 | 3.24236222101166e-07 | 1.62118111050583e-07 |
| 96 | 0.999999695180636 | 6.09638726899165e-07 | 3.04819363449582e-07 |
| 97 | 0.999999460816466 | 1.07836706715209e-06 | 5.39183533576043e-07 |
| 98 | 0.999998632535137 | 2.73492972584283e-06 | 1.36746486292141e-06 |
| 99 | 0.999996614633194 | 6.77073361146977e-06 | 3.38536680573488e-06 |
| 100 | 0.99999330885259 | 1.33822948188023e-05 | 6.69114740940116e-06 |
| 101 | 0.99998665195061 | 2.66960987830777e-05 | 1.33480493915389e-05 |
| 102 | 0.999975180202826 | 4.96395943488386e-05 | 2.48197971744193e-05 |
| 103 | 0.999958199961569 | 8.36000768627274e-05 | 4.18000384313637e-05 |
| 104 | 0.999915598799105 | 0.000168802401790387 | 8.44012008951936e-05 |
| 105 | 0.999876672647504 | 0.000246654704991923 | 0.000123327352495962 |
| 106 | 0.999795378277164 | 0.000409243445671717 | 0.000204621722835859 |
| 107 | 0.99978438068514 | 0.000431238629720175 | 0.000215619314860088 |
| 108 | 0.999609741649499 | 0.000780516701002793 | 0.000390258350501396 |
| 109 | 0.999970517552914 | 5.89648941717101e-05 | 2.94824470858551e-05 |
| 110 | 0.999975905570835 | 4.81888583306757e-05 | 2.40944291653379e-05 |
| 111 | 0.9999516839502 | 9.66320995995522e-05 | 4.83160497997761e-05 |
| 112 | 0.999948156073069 | 0.000103687853862716 | 5.18439269313579e-05 |
| 113 | 0.999924755863848 | 0.000150488272303158 | 7.52441361515789e-05 |
| 114 | 0.99998479006817 | 3.04198636579714e-05 | 1.52099318289857e-05 |
| 115 | 0.999936433633428 | 0.000127132733144618 | 6.35663665723088e-05 |
| 116 | 0.999743598292943 | 0.000512803414113466 | 0.000256401707056733 |
| 117 | 0.999483164503985 | 0.00103367099203054 | 0.000516835496015269 |
| 118 | 0.997972044780435 | 0.00405591043913022 | 0.00202795521956511 |
| 119 | 0.999485588313663 | 0.00102882337267464 | 0.000514411686337322 |
| 120 | 0.997292038061522 | 0.0054159238769559 | 0.00270796193847795 |
| 121 | 0.986326697448695 | 0.027346605102609 | 0.0136733025513045 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 56 | 0.504504504504504 | NOK |
| 5% type I error level | 77 | 0.693693693693694 | NOK |
| 10% type I error level | 88 | 0.792792792792793 | NOK |
