| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1770.68500382969 + 0.0955963133515418Nikkei[t] + 0.337085778067862DJ_Indust[t] -0.0386263036901069Goudprijs[t] -5.28252498489441Conjunct_Seizoenzuiver[t] + 0.206420080151677Cons_vertrouw[t] -25.1205354165253Alg_consumptie_index_BE[t] + 22.2266428401259Gem_rente_kasbon_1j[t] + 6.5800042346992t + 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) | -1770.68500382969 | 370.631391 | -4.7775 | 5e-06 | 2e-06 |
| Nikkei | 0.0955963133515418 | 0.019184 | 4.9832 | 2e-06 | 1e-06 |
| DJ_Indust | 0.337085778067862 | 0.042559 | 7.9204 | 0 | 0 |
| Goudprijs | -0.0386263036901069 | 0.020299 | -1.9029 | 0.059392 | 0.029696 |
| Conjunct_Seizoenzuiver | -5.28252498489441 | 7.911318 | -0.6677 | 0.505565 | 0.252782 |
| Cons_vertrouw | 0.206420080151677 | 7.021271 | 0.0294 | 0.976594 | 0.488297 |
| Alg_consumptie_index_BE | -25.1205354165253 | 29.578485 | -0.8493 | 0.397373 | 0.198687 |
| Gem_rente_kasbon_1j | 22.2266428401259 | 44.555426 | 0.4989 | 0.618773 | 0.309387 |
| t | 6.5800042346992 | 2.683661 | 2.4519 | 0.015615 | 0.007808 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.930603564293447 |
| R-squared | 0.866022993875667 |
| Adjusted R-squared | 0.857309042257825 |
| F-TEST (value) | 99.3834980793776 |
| F-TEST (DF numerator) | 8 |
| F-TEST (DF denominator) | 123 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 284.425783203429 |
| Sum Squared Residuals | 9950457.21655872 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2468.71455555045 | 1016.02544444955 |
| 2 | 3411.13 | 2491.00918289771 | 920.120817102292 |
| 3 | 3288.18 | 2753.73094448663 | 534.449055513375 |
| 4 | 3280.37 | 3073.6951787986 | 206.674821201404 |
| 5 | 3173.95 | 3210.2622287939 | -36.312228793896 |
| 6 | 3165.26 | 3242.6864447545 | -77.4264447545041 |
| 7 | 3092.71 | 3459.09421113822 | -366.384211138219 |
| 8 | 3053.05 | 3395.36952165827 | -342.319521658273 |
| 9 | 3181.96 | 3285.88768465306 | -103.927684653061 |
| 10 | 2999.93 | 3140.44624024474 | -140.516240244737 |
| 11 | 3249.57 | 3365.74299722522 | -116.172997225225 |
| 12 | 3210.52 | 3498.57959835751 | -288.059598357507 |
| 13 | 3030.29 | 3580.56164121704 | -550.271641217043 |
| 14 | 2803.47 | 3374.36675514193 | -570.896755141931 |
| 15 | 2767.63 | 3370.88135323919 | -603.251353239194 |
| 16 | 2882.6 | 3518.59490158866 | -635.99490158866 |
| 17 | 2863.36 | 3162.42799676657 | -299.067996766571 |
| 18 | 2897.06 | 3146.27942214748 | -249.219422147481 |
| 19 | 3012.61 | 3188.91823607622 | -176.308236076219 |
| 20 | 3142.95 | 3256.88260724284 | -113.932607242838 |
| 21 | 3032.93 | 3201.87282664477 | -168.942826644766 |
| 22 | 3045.78 | 2964.09656724815 | 81.6834327518455 |
| 23 | 3110.52 | 3001.80809449923 | 108.711905500765 |
| 24 | 3013.24 | 2998.46840999894 | 14.7715900010552 |
| 25 | 2987.1 | 2972.62411742156 | 14.4758825784437 |
| 26 | 2995.55 | 2971.01382495345 | 24.5361750465484 |
| 27 | 2833.18 | 2685.70549232266 | 147.474507677338 |
| 28 | 2848.96 | 2821.54856374373 | 27.4114362562711 |
| 29 | 2794.83 | 2968.75357735117 | -173.92357735117 |
| 30 | 2845.26 | 2950.12693347642 | -104.866933476424 |
| 31 | 2915.02 | 2788.78620736817 | 126.233792631829 |
| 32 | 2892.63 | 2705.2557797642 | 187.374220235804 |
| 33 | 2604.42 | 2137.94410699397 | 466.475893006025 |
| 34 | 2641.65 | 2255.80599253319 | 385.844007466809 |
| 35 | 2659.81 | 2443.11883260993 | 216.691167390067 |
| 36 | 2638.53 | 2525.71096542434 | 112.819034575655 |
| 37 | 2720.25 | 2455.15855377993 | 265.091446220066 |
| 38 | 2745.88 | 2407.8514146226 | 338.028585377399 |
| 39 | 2735.7 | 2749.16151724167 | -13.4615172416718 |
| 40 | 2811.7 | 2651.81789514717 | 159.882104852827 |
| 41 | 2799.43 | 2659.40358717499 | 140.026412825012 |
| 42 | 2555.28 | 2413.38016399667 | 141.899836003335 |
| 43 | 2304.98 | 2085.8981706409 | 219.081829359097 |
| 44 | 2214.95 | 2059.51215995094 | 155.437840049061 |
| 45 | 2065.81 | 1837.88605229075 | 227.923947709246 |
| 46 | 1940.49 | 1762.70251523031 | 177.78748476969 |
| 47 | 2042 | 1966.35372283479 | 75.6462771652112 |
| 48 | 1995.37 | 1915.38744711184 | 79.9825528881582 |
| 49 | 1946.81 | 1890.28589575923 | 56.5241042407695 |
| 50 | 1765.9 | 1688.04693928482 | 77.8530607151772 |
| 51 | 1635.25 | 1717.51575976165 | -82.2657597616549 |
| 52 | 1833.42 | 1852.419929748 | -18.9999297480023 |
| 53 | 1910.43 | 1970.61333655813 | -60.1833365581281 |
| 54 | 1959.67 | 2206.478234715 | -246.808234715003 |
| 55 | 1969.6 | 2296.17238305763 | -326.572383057631 |
| 56 | 2061.41 | 2330.07375851178 | -268.663758511778 |
| 57 | 2093.48 | 2444.64333478101 | -351.163334781011 |
| 58 | 2120.88 | 2538.54779191912 | -417.667791919117 |
| 59 | 2174.56 | 2491.93479481776 | -317.374794817759 |
| 60 | 2196.72 | 2631.99491748651 | -435.274917486515 |
| 61 | 2350.44 | 2844.37128760197 | -493.931287601966 |
| 62 | 2440.25 | 2856.95039631174 | -416.700396311742 |
| 63 | 2408.64 | 2831.347824097 | -422.707824097003 |
| 64 | 2472.81 | 2878.05973887039 | -405.249738870391 |
| 65 | 2407.6 | 2687.67136954634 | -280.071369546336 |
| 66 | 2454.62 | 2841.86431968284 | -387.244319682844 |
| 67 | 2448.05 | 2742.69319306098 | -294.64319306098 |
| 68 | 2497.84 | 2682.54772946135 | -184.707729461347 |
| 69 | 2645.64 | 2755.61628880492 | -109.976288804916 |
| 70 | 2756.76 | 2662.36421486626 | 94.3957851337415 |
| 71 | 2849.27 | 2817.07635769541 | 32.1936423045897 |
| 72 | 2921.44 | 2948.03235238953 | -26.5923523895317 |
| 73 | 2981.85 | 2941.52933555163 | 40.320664448373 |
| 74 | 3080.58 | 3025.7421227731 | 54.8378772268966 |
| 75 | 3106.22 | 3030.91047583626 | 75.3095241637409 |
| 76 | 3119.31 | 2880.96614117017 | 238.34385882983 |
| 77 | 3061.26 | 2898.33861547214 | 162.921384527856 |
| 78 | 3097.31 | 2933.05115452246 | 164.258845477541 |
| 79 | 3161.69 | 2986.84847084399 | 174.841529156007 |
| 80 | 3257.16 | 3035.62329450069 | 221.536705499311 |
| 81 | 3277.01 | 3066.5122513349 | 210.497748665096 |
| 82 | 3295.32 | 3027.53637079026 | 267.783629209742 |
| 83 | 3363.99 | 3231.40060970402 | 132.589390295977 |
| 84 | 3494.17 | 3368.55170897259 | 125.618291027413 |
| 85 | 3667.03 | 3412.46641404139 | 254.563585958608 |
| 86 | 3813.06 | 3441.6408431349 | 371.419156865098 |
| 87 | 3917.96 | 3537.76692973619 | 380.193070263807 |
| 88 | 3895.51 | 3607.5488274552 | 287.961172544804 |
| 89 | 3801.06 | 3526.55618788865 | 274.503812111354 |
| 90 | 3570.12 | 3362.9455446265 | 207.1744553735 |
| 91 | 3701.61 | 3363.08191816122 | 338.528081838776 |
| 92 | 3862.27 | 3520.23986375816 | 342.03013624184 |
| 93 | 3970.1 | 3678.02100558691 | 292.07899441309 |
| 94 | 4138.52 | 3886.06779144087 | 252.452208559133 |
| 95 | 4199.75 | 3899.28611587892 | 300.46388412108 |
| 96 | 4290.89 | 4038.38464818643 | 252.505351813567 |
| 97 | 4443.91 | 4137.56686536448 | 306.34313463552 |
| 98 | 4502.64 | 4205.11896320073 | 297.521036799268 |
| 99 | 4356.98 | 4053.49884470001 | 303.481155299992 |
| 100 | 4591.27 | 4236.3311205109 | 354.938879489104 |
| 101 | 4696.96 | 4495.28120707454 | 201.678792925455 |
| 102 | 4621.4 | 4569.72456847136 | 51.6754315286372 |
| 103 | 4562.84 | 4648.93764585881 | -86.0976458588118 |
| 104 | 4202.52 | 4379.94304627355 | -177.423046273549 |
| 105 | 4296.49 | 4433.63150010792 | -137.141500107917 |
| 106 | 4435.23 | 4591.57555783358 | -156.345557833586 |
| 107 | 4105.18 | 4185.89231052842 | -80.7123105284217 |
| 108 | 4116.68 | 4266.55060215488 | -149.870602154877 |
| 109 | 3844.49 | 3728.43351691644 | 116.056483083563 |
| 110 | 3720.98 | 3642.6625638392 | 78.317436160804 |
| 111 | 3674.4 | 3459.58790269405 | 214.812097305948 |
| 112 | 3857.62 | 3783.08646903874 | 74.5335309612638 |
| 113 | 3801.06 | 3876.9142213784 | -75.8542213784019 |
| 114 | 3504.37 | 3641.43386318247 | -137.063863182466 |
| 115 | 3032.6 | 3294.42288067018 | -261.822880670183 |
| 116 | 3047.03 | 3409.52552472784 | -362.495524727842 |
| 117 | 2962.34 | 3203.53675335188 | -241.196753351877 |
| 118 | 2197.82 | 2276.99463047801 | -79.1746304780064 |
| 119 | 2014.45 | 2133.83760186707 | -119.387601867068 |
| 120 | 1862.83 | 2147.64479067156 | -284.814790671562 |
| 121 | 1905.41 | 2009.29424770509 | -103.884247705087 |
| 122 | 1810.99 | 1627.39543520662 | 183.594564793377 |
| 123 | 1670.07 | 1534.5582815353 | 135.511718464701 |
| 124 | 1864.44 | 1918.55819287984 | -54.1181928798359 |
| 125 | 2052.02 | 2123.41356931459 | -71.3935693145946 |
| 126 | 2029.6 | 2244.23144403825 | -214.631444038255 |
| 127 | 2070.83 | 2294.93099992802 | -224.100999928024 |
| 128 | 2293.41 | 2554.60918294172 | -261.199182941717 |
| 129 | 2443.27 | 2621.43149784129 | -178.161497841285 |
| 130 | 2513.17 | 2628.06484580727 | -114.894845807275 |
| 131 | 2466.92 | 2606.50088840556 | -139.58088840556 |
| 132 | 2502.66 | 2687.96447898928 | -185.304478989281 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 12 | 0.0990976857229863 | 0.198195371445973 | 0.900902314277014 |
| 13 | 0.0414616592784865 | 0.082923318556973 | 0.958538340721514 |
| 14 | 0.0322130380364041 | 0.0644260760728083 | 0.967786961963596 |
| 15 | 0.0255257996150365 | 0.051051599230073 | 0.974474200384964 |
| 16 | 0.0161520267273909 | 0.0323040534547819 | 0.98384797327261 |
| 17 | 0.00980774320138044 | 0.0196154864027609 | 0.99019225679862 |
| 18 | 0.0051831514510138 | 0.0103663029020276 | 0.994816848548986 |
| 19 | 0.0064190560598237 | 0.0128381121196474 | 0.993580943940176 |
| 20 | 0.00559216613311079 | 0.0111843322662216 | 0.99440783386689 |
| 21 | 0.00378458263491537 | 0.00756916526983073 | 0.996215417365085 |
| 22 | 0.0037032116922296 | 0.0074064233844592 | 0.99629678830777 |
| 23 | 0.00217939557071937 | 0.00435879114143874 | 0.99782060442928 |
| 24 | 0.00110645459262126 | 0.00221290918524253 | 0.998893545407379 |
| 25 | 0.000535862102901426 | 0.00107172420580285 | 0.999464137897099 |
| 26 | 0.000242429224736151 | 0.000484858449472302 | 0.999757570775264 |
| 27 | 0.000103207574348619 | 0.000206415148697238 | 0.999896792425651 |
| 28 | 5.26061444810564e-05 | 0.000105212288962113 | 0.999947393855519 |
| 29 | 4.29943774621196e-05 | 8.59887549242392e-05 | 0.999957005622538 |
| 30 | 2.74690990932213e-05 | 5.49381981864426e-05 | 0.999972530900907 |
| 31 | 2.18424763754517e-05 | 4.36849527509033e-05 | 0.999978157523625 |
| 32 | 1.14224795834013e-05 | 2.28449591668026e-05 | 0.999988577520417 |
| 33 | 6.45289282490208e-06 | 1.29057856498042e-05 | 0.999993547107175 |
| 34 | 4.95596221558763e-06 | 9.91192443117526e-06 | 0.999995044037784 |
| 35 | 2.98457122730728e-06 | 5.96914245461456e-06 | 0.999997015428773 |
| 36 | 1.29113565243568e-06 | 2.58227130487136e-06 | 0.999998708864348 |
| 37 | 5.86947829496836e-07 | 1.17389565899367e-06 | 0.99999941305217 |
| 38 | 4.43489869954533e-07 | 8.86979739909065e-07 | 0.99999955651013 |
| 39 | 2.3823255094251e-07 | 4.7646510188502e-07 | 0.99999976176745 |
| 40 | 2.26364511286907e-06 | 4.52729022573813e-06 | 0.999997736354887 |
| 41 | 3.69076424499174e-06 | 7.38152848998348e-06 | 0.999996309235755 |
| 42 | 1.90082341875233e-06 | 3.80164683750466e-06 | 0.999998099176581 |
| 43 | 9.28213005344426e-07 | 1.85642601068885e-06 | 0.999999071786995 |
| 44 | 7.74275363284999e-07 | 1.54855072657e-06 | 0.999999225724637 |
| 45 | 7.78365429325444e-07 | 1.55673085865089e-06 | 0.99999922163457 |
| 46 | 1.81213087436266e-06 | 3.62426174872533e-06 | 0.999998187869126 |
| 47 | 2.73541781479087e-06 | 5.47083562958174e-06 | 0.999997264582185 |
| 48 | 2.69811875237728e-06 | 5.39623750475457e-06 | 0.999997301881248 |
| 49 | 3.75995799827355e-06 | 7.51991599654709e-06 | 0.999996240042002 |
| 50 | 2.70196554626032e-06 | 5.40393109252065e-06 | 0.999997298034454 |
| 51 | 1.75920946057267e-06 | 3.51841892114534e-06 | 0.99999824079054 |
| 52 | 2.00763851042682e-06 | 4.01527702085364e-06 | 0.99999799236149 |
| 53 | 2.93883244372723e-06 | 5.87766488745445e-06 | 0.999997061167556 |
| 54 | 2.56703110884539e-06 | 5.13406221769078e-06 | 0.999997432968891 |
| 55 | 4.4837717801403e-06 | 8.9675435602806e-06 | 0.99999551622822 |
| 56 | 1.37902941357407e-05 | 2.75805882714815e-05 | 0.999986209705864 |
| 57 | 2.0407760488999e-05 | 4.08155209779979e-05 | 0.999979592239511 |
| 58 | 0.000133938803890482 | 0.000267877607780964 | 0.99986606119611 |
| 59 | 0.000161073317290982 | 0.000322146634581964 | 0.999838926682709 |
| 60 | 0.000130321350371654 | 0.000260642700743308 | 0.999869678649628 |
| 61 | 0.000184922255537839 | 0.000369844511075678 | 0.999815077744462 |
| 62 | 0.000261107784486482 | 0.000522215568972963 | 0.999738892215513 |
| 63 | 0.00155533198642716 | 0.00311066397285432 | 0.998444668013573 |
| 64 | 0.0235344923520682 | 0.0470689847041364 | 0.976465507647932 |
| 65 | 0.0878104376552862 | 0.175620875310572 | 0.912189562344714 |
| 66 | 0.306182462936411 | 0.612364925872822 | 0.693817537063589 |
| 67 | 0.604401188381685 | 0.791197623236631 | 0.395598811618315 |
| 68 | 0.837015578001921 | 0.325968843996157 | 0.162984421998079 |
| 69 | 0.96482640929066 | 0.0703471814186785 | 0.0351735907093393 |
| 70 | 0.992160427834438 | 0.0156791443311248 | 0.00783957216556241 |
| 71 | 0.998483540290495 | 0.00303291941900977 | 0.00151645970950489 |
| 72 | 0.999870698532588 | 0.000258602934823722 | 0.000129301467411861 |
| 73 | 0.999987863558458 | 2.42728830832355e-05 | 1.21364415416177e-05 |
| 74 | 0.999998658033348 | 2.68393330413679e-06 | 1.34196665206839e-06 |
| 75 | 0.99999977616832 | 4.47663359554303e-07 | 2.23831679777151e-07 |
| 76 | 0.999999932586958 | 1.34826084755486e-07 | 6.7413042377743e-08 |
| 77 | 0.999999962503721 | 7.49925573968967e-08 | 3.74962786984483e-08 |
| 78 | 0.99999997481809 | 5.03638215886201e-08 | 2.518191079431e-08 |
| 79 | 0.99999997380535 | 5.23893023009443e-08 | 2.61946511504721e-08 |
| 80 | 0.99999997433522 | 5.1329561366762e-08 | 2.5664780683381e-08 |
| 81 | 0.999999985996912 | 2.80061753710593e-08 | 1.40030876855297e-08 |
| 82 | 0.99999999329013 | 1.34197386569586e-08 | 6.70986932847929e-09 |
| 83 | 0.999999989937958 | 2.01240849077008e-08 | 1.00620424538504e-08 |
| 84 | 0.999999989323617 | 2.13527664259053e-08 | 1.06763832129527e-08 |
| 85 | 0.99999999281098 | 1.43780413210656e-08 | 7.18902066053279e-09 |
| 86 | 0.999999989967474 | 2.00650527623577e-08 | 1.00325263811789e-08 |
| 87 | 0.999999982902903 | 3.41941941234846e-08 | 1.70970970617423e-08 |
| 88 | 0.99999998567979 | 2.86404183059871e-08 | 1.43202091529936e-08 |
| 89 | 0.999999997406262 | 5.18747549547235e-09 | 2.59373774773618e-09 |
| 90 | 0.999999998970184 | 2.05963242172522e-09 | 1.02981621086261e-09 |
| 91 | 0.999999999260728 | 1.47854481760665e-09 | 7.39272408803325e-10 |
| 92 | 0.99999999943007 | 1.13985832410793e-09 | 5.69929162053963e-10 |
| 93 | 0.999999999306821 | 1.38635747407843e-09 | 6.93178737039216e-10 |
| 94 | 0.99999999965804 | 6.83917811613035e-10 | 3.41958905806517e-10 |
| 95 | 0.999999999916986 | 1.66028081317776e-10 | 8.30140406588878e-11 |
| 96 | 0.99999999984484 | 3.10317831194975e-10 | 1.55158915597487e-10 |
| 97 | 0.999999999656812 | 6.86376073058275e-10 | 3.43188036529137e-10 |
| 98 | 0.999999998973835 | 2.05233108064312e-09 | 1.02616554032156e-09 |
| 99 | 0.99999999657913 | 6.84174049060072e-09 | 3.42087024530036e-09 |
| 100 | 0.999999994051276 | 1.18974485227981e-08 | 5.94872426139904e-09 |
| 101 | 0.999999993060247 | 1.38795067949803e-08 | 6.93975339749015e-09 |
| 102 | 0.999999994690192 | 1.06196151243148e-08 | 5.30980756215742e-09 |
| 103 | 0.999999995663167 | 8.6736664673341e-09 | 4.33683323366705e-09 |
| 104 | 0.999999985643003 | 2.87139932394678e-08 | 1.43569966197339e-08 |
| 105 | 0.999999953770503 | 9.24589941915615e-08 | 4.62294970957807e-08 |
| 106 | 0.999999864979467 | 2.7004106504741e-07 | 1.35020532523705e-07 |
| 107 | 0.999999579175501 | 8.41648997106693e-07 | 4.20824498553346e-07 |
| 108 | 0.999999392555288 | 1.2148894230568e-06 | 6.07444711528402e-07 |
| 109 | 0.999997858256944 | 4.28348611108864e-06 | 2.14174305554432e-06 |
| 110 | 0.99999712660171 | 5.74679658138078e-06 | 2.87339829069039e-06 |
| 111 | 0.999996519651336 | 6.96069732886509e-06 | 3.48034866443254e-06 |
| 112 | 0.999987070340863 | 2.58593182746013e-05 | 1.29296591373007e-05 |
| 113 | 0.999950889329713 | 9.82213405748964e-05 | 4.91106702874482e-05 |
| 114 | 0.999973979942822 | 5.2040114355683e-05 | 2.60200571778415e-05 |
| 115 | 0.999896590697436 | 0.000206818605128584 | 0.000103409302564292 |
| 116 | 0.999585863248895 | 0.000828273502209836 | 0.000414136751104918 |
| 117 | 0.998680872703142 | 0.0026382545937152 | 0.0013191272968576 |
| 118 | 0.99509254634478 | 0.00981490731044078 | 0.00490745365522039 |
| 119 | 0.998604287300985 | 0.0027914253980302 | 0.0013957126990151 |
| 120 | 0.993040403572347 | 0.0139191928553066 | 0.0069595964276533 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 92 | 0.844036697247706 | NOK |
| 5% type I error level | 100 | 0.91743119266055 | NOK |
| 10% type I error level | 104 | 0.954128440366973 | NOK |
