| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -2047.16188772809 + 0.0723275143762075Nikkei[t] + 0.386310468950729DJ_Indust[t] + 0.00586235663459956Goudprijs[t] + 1.0731471514904Conjunct_Seizoenzuiver[t] -7.03174420326656Cons_vertrouw[t] -14.6090054577671Alg_consumptie_index_BE[t] -12.9375414285237Gem_rente_kasbon_1j[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) | -2047.16188772809 | 360.12577 | -5.6846 | 0 | 0 |
| Nikkei | 0.0723275143762075 | 0.017005 | 4.2532 | 4.1e-05 | 2.1e-05 |
| DJ_Indust | 0.386310468950729 | 0.038277 | 10.0925 | 0 | 0 |
| Goudprijs | 0.00586235663459956 | 0.009282 | 0.6316 | 0.528817 | 0.264408 |
| Conjunct_Seizoenzuiver | 1.0731471514904 | 7.624152 | 0.1408 | 0.888291 | 0.444145 |
| Cons_vertrouw | -7.03174420326656 | 6.497973 | -1.0821 | 0.281288 | 0.140644 |
| Alg_consumptie_index_BE | -14.6090054577671 | 29.85171 | -0.4894 | 0.625433 | 0.312717 |
| Gem_rente_kasbon_1j | -12.9375414285237 | 43.028156 | -0.3007 | 0.764165 | 0.382082 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.927078632287769 |
| R-squared | 0.85947479044456 |
| Adjusted R-squared | 0.851541915711591 |
| F-TEST (value) | 108.3434214425 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 124 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 290.116655497996 |
| Sum Squared Residuals | 10436791.5508705 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2513.04224716505 | 971.69775283495 |
| 2 | 3411.13 | 2550.17071763697 | 860.959282363034 |
| 3 | 3288.18 | 2810.49576337 | 477.684236630001 |
| 4 | 3280.37 | 3177.6003619873 | 102.769638012696 |
| 5 | 3173.95 | 3331.07162350843 | -157.121623508434 |
| 6 | 3165.26 | 3387.89980780453 | -222.639807804526 |
| 7 | 3092.71 | 3528.24842942687 | -435.53842942687 |
| 8 | 3053.05 | 3465.86605367731 | -412.816053677312 |
| 9 | 3181.96 | 3334.88755464712 | -152.927554647124 |
| 10 | 2999.93 | 3210.359289611 | -210.429289611004 |
| 11 | 3249.57 | 3407.16655639094 | -157.59655639094 |
| 12 | 3210.52 | 3563.67375751684 | -353.153757516838 |
| 13 | 3030.29 | 3605.69489422131 | -575.404894221313 |
| 14 | 2803.47 | 3360.76583188458 | -557.295831884577 |
| 15 | 2767.63 | 3331.50231335007 | -563.87231335007 |
| 16 | 2882.6 | 3501.2915300753 | -618.691530075303 |
| 17 | 2863.36 | 3159.56350979423 | -296.203509794231 |
| 18 | 2897.06 | 3135.14796701341 | -238.087967013415 |
| 19 | 3012.61 | 3172.813349183 | -160.203349182998 |
| 20 | 3142.95 | 3239.48047702933 | -96.530477029331 |
| 21 | 3032.93 | 3245.95237651484 | -213.022376514843 |
| 22 | 3045.78 | 2955.16878318751 | 90.6112168124899 |
| 23 | 3110.52 | 3002.25053557194 | 108.269464428064 |
| 24 | 3013.24 | 2983.37369174739 | 29.8663082526084 |
| 25 | 2987.1 | 2953.76157872875 | 33.3384212712537 |
| 26 | 2995.55 | 2989.55263045666 | 5.99736954334172 |
| 27 | 2833.18 | 2680.18362452632 | 152.996375473685 |
| 28 | 2848.96 | 2805.92013571683 | 43.0398642831692 |
| 29 | 2794.83 | 2971.91891963235 | -177.088919632346 |
| 30 | 2845.26 | 2983.64029736613 | -138.380297366134 |
| 31 | 2915.02 | 2802.26327507224 | 112.756724927764 |
| 32 | 2892.63 | 2735.39858379642 | 157.231416203582 |
| 33 | 2604.42 | 2168.88679605968 | 435.533203940322 |
| 34 | 2641.65 | 2339.59194808802 | 302.058051911981 |
| 35 | 2659.81 | 2569.98227185514 | 89.827728144863 |
| 36 | 2638.53 | 2598.06382120476 | 40.4661787952357 |
| 37 | 2720.25 | 2507.6437578261 | 212.606242173902 |
| 38 | 2745.88 | 2463.79141445968 | 282.088585540318 |
| 39 | 2735.7 | 2796.55898772855 | -60.8589877285517 |
| 40 | 2811.7 | 2696.93745250031 | 114.762547499694 |
| 41 | 2799.43 | 2685.32327400572 | 114.106725994275 |
| 42 | 2555.28 | 2415.46146891726 | 139.818531082738 |
| 43 | 2304.98 | 2030.33596231522 | 274.644037684781 |
| 44 | 2214.95 | 2029.43955394705 | 185.510446052952 |
| 45 | 2065.81 | 1801.27367517313 | 264.536324826869 |
| 46 | 1940.49 | 1715.51599287712 | 224.974007122883 |
| 47 | 2042 | 1950.18925085621 | 91.8107491437909 |
| 48 | 1995.37 | 1929.37217140869 | 65.9978285913104 |
| 49 | 1946.81 | 1913.19615150551 | 33.6138484944906 |
| 50 | 1765.9 | 1718.78346093438 | 47.1165390656171 |
| 51 | 1635.25 | 1742.97103504667 | -107.721035046669 |
| 52 | 1833.42 | 1812.90394305156 | 20.5160569484361 |
| 53 | 1910.43 | 1941.12543797604 | -30.6954379760365 |
| 54 | 1959.67 | 2176.45845413851 | -216.78845413851 |
| 55 | 1969.6 | 2279.63578461636 | -310.035784616361 |
| 56 | 2061.41 | 2330.11408802713 | -268.704088027127 |
| 57 | 2093.48 | 2428.85394532106 | -335.373945321062 |
| 58 | 2120.88 | 2578.37668418935 | -457.496684189354 |
| 59 | 2174.56 | 2509.00753533109 | -334.447535331088 |
| 60 | 2196.72 | 2659.11311376011 | -462.393113760114 |
| 61 | 2350.44 | 2842.00345895263 | -491.563458952635 |
| 62 | 2440.25 | 2838.67345150581 | -398.423451505808 |
| 63 | 2408.64 | 2811.33513337478 | -402.695133374777 |
| 64 | 2472.81 | 2884.35598635747 | -411.545986357472 |
| 65 | 2407.6 | 2692.87348592586 | -285.273485925856 |
| 66 | 2454.62 | 2794.75149363828 | -340.131493638285 |
| 67 | 2448.05 | 2731.04832255857 | -282.99832255857 |
| 68 | 2497.84 | 2644.75810256734 | -146.918102567335 |
| 69 | 2645.64 | 2720.58733136742 | -74.9473313674172 |
| 70 | 2756.76 | 2654.00316572147 | 102.756834278535 |
| 71 | 2849.27 | 2817.91262000126 | 31.3573799987422 |
| 72 | 2921.44 | 2919.85110940607 | 1.58889059393404 |
| 73 | 2981.85 | 2892.12542303066 | 89.7245769693375 |
| 74 | 3080.58 | 2946.75347184702 | 133.826528152979 |
| 75 | 3106.22 | 2935.14288332766 | 171.077116672341 |
| 76 | 3119.31 | 2774.36786522877 | 344.942134771225 |
| 77 | 3061.26 | 2834.25836767093 | 227.001632329068 |
| 78 | 3097.31 | 2899.13047084474 | 198.179529155257 |
| 79 | 3161.69 | 2941.73345391272 | 219.956546087279 |
| 80 | 3257.16 | 2974.9579793867 | 282.202020613305 |
| 81 | 3277.01 | 3056.56814410221 | 220.441855897789 |
| 82 | 3295.32 | 2978.61527504628 | 316.704724953718 |
| 83 | 3363.99 | 3199.05761616041 | 164.932383839592 |
| 84 | 3494.17 | 3313.23561621932 | 180.93438378068 |
| 85 | 3667.03 | 3343.49975080762 | 323.530249192376 |
| 86 | 3813.06 | 3401.84898408881 | 411.211015911192 |
| 87 | 3917.96 | 3506.95114359578 | 411.008856404218 |
| 88 | 3895.51 | 3601.65842015465 | 293.851579845351 |
| 89 | 3801.06 | 3593.51885913975 | 207.541140860253 |
| 90 | 3570.12 | 3327.82072543168 | 242.299274568322 |
| 91 | 3701.61 | 3365.67253968774 | 335.937460312255 |
| 92 | 3862.27 | 3494.15960261278 | 368.110397387219 |
| 93 | 3970.1 | 3611.27802547262 | 358.82197452738 |
| 94 | 4138.52 | 3791.72011426174 | 346.799885738257 |
| 95 | 4199.75 | 3852.66270698186 | 347.087293018141 |
| 96 | 4290.89 | 4036.4790102024 | 254.410989797599 |
| 97 | 4443.91 | 4072.54221845797 | 371.367781542027 |
| 98 | 4502.64 | 4137.42282898134 | 365.217171018658 |
| 99 | 4356.98 | 3962.65876349701 | 394.321236502991 |
| 100 | 4591.27 | 4156.85844065085 | 434.411559349153 |
| 101 | 4696.96 | 4426.09333882031 | 270.866661179692 |
| 102 | 4621.4 | 4485.9714253816 | 135.428574618402 |
| 103 | 4562.84 | 4568.23672396381 | -5.39672396381288 |
| 104 | 4202.52 | 4300.95790338994 | -98.4379033899365 |
| 105 | 4296.49 | 4406.2607467519 | -109.770746751903 |
| 106 | 4435.23 | 4571.34253545309 | -136.112535453087 |
| 107 | 4105.18 | 4245.83162809351 | -140.651628093511 |
| 108 | 4116.68 | 4291.75368311439 | -175.073683114394 |
| 109 | 3844.49 | 3843.3452010813 | 1.14479891869715 |
| 110 | 3720.98 | 3768.77387935548 | -47.7938793554795 |
| 111 | 3674.4 | 3603.45597932261 | 70.9440206773902 |
| 112 | 3857.62 | 3851.76542482941 | 5.85457517059325 |
| 113 | 3801.06 | 3955.5299365064 | -154.469936506402 |
| 114 | 3504.37 | 3668.29571027602 | -163.925710276023 |
| 115 | 3032.6 | 3331.01404974883 | -298.414049748829 |
| 116 | 3047.03 | 3384.30478666795 | -337.274786667948 |
| 117 | 2962.34 | 3141.46433135622 | -179.124331356217 |
| 118 | 2197.82 | 2245.42290890139 | -47.602908901391 |
| 119 | 2014.45 | 2032.05379814711 | -17.6037981471105 |
| 120 | 1862.83 | 2049.36098603662 | -186.530986036618 |
| 121 | 1905.41 | 1953.22083825645 | -47.810838256453 |
| 122 | 1810.99 | 1687.76757234031 | 123.222427659686 |
| 123 | 1670.07 | 1539.2419717546 | 130.828028245398 |
| 124 | 1864.44 | 1888.76129141735 | -24.3212914173478 |
| 125 | 2052.02 | 2081.65021075726 | -29.6302107572624 |
| 126 | 2029.6 | 2201.32254681594 | -171.722546815938 |
| 127 | 2070.83 | 2226.49667183747 | -155.666671837467 |
| 128 | 2293.41 | 2500.17498406255 | -206.764984062554 |
| 129 | 2443.27 | 2601.61720593431 | -158.347205934307 |
| 130 | 2513.17 | 2684.26042005449 | -171.090420054495 |
| 131 | 2466.92 | 2789.33277902907 | -322.412779029072 |
| 132 | 2502.66 | 2937.74226763193 | -435.082267631931 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.0875093044736154 | 0.175018608947231 | 0.912490695526385 |
| 12 | 0.0335760341507567 | 0.0671520683015133 | 0.966423965849243 |
| 13 | 0.0161027002297789 | 0.0322054004595579 | 0.98389729977022 |
| 14 | 0.0152190577885078 | 0.0304381155770156 | 0.984780942211492 |
| 15 | 0.0147186419205087 | 0.0294372838410175 | 0.985281358079491 |
| 16 | 0.0108863946581355 | 0.021772789316271 | 0.989113605341864 |
| 17 | 0.0283987821438733 | 0.0567975642877466 | 0.971601217856127 |
| 18 | 0.028080835878263 | 0.056161671756526 | 0.971919164121737 |
| 19 | 0.0200504336031821 | 0.0401008672063641 | 0.979949566396818 |
| 20 | 0.0169852835421988 | 0.0339705670843975 | 0.9830147164578 |
| 21 | 0.0126071003944452 | 0.0252142007888905 | 0.987392899605555 |
| 22 | 0.00737698932687835 | 0.0147539786537567 | 0.992623010673122 |
| 23 | 0.00411851519345512 | 0.00823703038691024 | 0.995881484806545 |
| 24 | 0.00495613960568621 | 0.00991227921137242 | 0.995043860394314 |
| 25 | 0.0106368931623135 | 0.0212737863246271 | 0.989363106837686 |
| 26 | 0.0112780157341248 | 0.0225560314682496 | 0.988721984265875 |
| 27 | 0.0304101249502902 | 0.0608202499005803 | 0.96958987504971 |
| 28 | 0.0648687210989556 | 0.129737442197911 | 0.935131278901044 |
| 29 | 0.0783765980077411 | 0.156753196015482 | 0.921623401992259 |
| 30 | 0.0730037159455102 | 0.14600743189102 | 0.92699628405449 |
| 31 | 0.0532875962726844 | 0.106575192545369 | 0.946712403727316 |
| 32 | 0.037140973576223 | 0.074281947152446 | 0.962859026423777 |
| 33 | 0.0612311677610991 | 0.122462335522198 | 0.9387688322389 |
| 34 | 0.0499611935351499 | 0.0999223870702999 | 0.95003880646485 |
| 35 | 0.0432218038171936 | 0.0864436076343871 | 0.956778196182806 |
| 36 | 0.0385626186724981 | 0.0771252373449962 | 0.961437381327502 |
| 37 | 0.031630221112162 | 0.0632604422243241 | 0.968369778887838 |
| 38 | 0.0284264486625495 | 0.056852897325099 | 0.97157355133745 |
| 39 | 0.0206466265207482 | 0.0412932530414964 | 0.979353373479252 |
| 40 | 0.01924295347535 | 0.0384859069507 | 0.98075704652465 |
| 41 | 0.0136438644621503 | 0.0272877289243006 | 0.98635613553785 |
| 42 | 0.0138779544800885 | 0.027755908960177 | 0.986122045519912 |
| 43 | 0.0473855309850013 | 0.0947710619700026 | 0.952614469014999 |
| 44 | 0.093668040446088 | 0.187336080892176 | 0.906331959553912 |
| 45 | 0.117210975401526 | 0.234421950803052 | 0.882789024598474 |
| 46 | 0.173169280887331 | 0.346338561774663 | 0.826830719112668 |
| 47 | 0.208701134726393 | 0.417402269452787 | 0.791298865273607 |
| 48 | 0.192991054881407 | 0.385982109762813 | 0.807008945118593 |
| 49 | 0.178885770489806 | 0.357771540979612 | 0.821114229510194 |
| 50 | 0.152984205724443 | 0.305968411448887 | 0.847015794275557 |
| 51 | 0.150801803785728 | 0.301603607571456 | 0.849198196214272 |
| 52 | 0.272337181775393 | 0.544674363550786 | 0.727662818224607 |
| 53 | 0.349649547743651 | 0.699299095487301 | 0.65035045225635 |
| 54 | 0.409701101342564 | 0.819402202685127 | 0.590298898657436 |
| 55 | 0.407462717180001 | 0.814925434360003 | 0.592537282819999 |
| 56 | 0.376273290997003 | 0.752546581994006 | 0.623726709002997 |
| 57 | 0.398009949503583 | 0.796019899007167 | 0.601990050496417 |
| 58 | 0.46221741693315 | 0.924434833866299 | 0.53778258306685 |
| 59 | 0.48659109592812 | 0.97318219185624 | 0.51340890407188 |
| 60 | 0.501008722727964 | 0.997982554544071 | 0.498991277272036 |
| 61 | 0.546449992750308 | 0.907100014499384 | 0.453550007249692 |
| 62 | 0.546215729222555 | 0.90756854155489 | 0.453784270777445 |
| 63 | 0.647870402321688 | 0.704259195356625 | 0.352129597678312 |
| 64 | 0.868235523848527 | 0.263528952302947 | 0.131764476151473 |
| 65 | 0.937231687261455 | 0.125536625477089 | 0.0627683127385445 |
| 66 | 0.98045447510779 | 0.0390910497844212 | 0.0195455248922106 |
| 67 | 0.995137090200594 | 0.00972581959881287 | 0.00486290979940643 |
| 68 | 0.99845353923005 | 0.00309292153989755 | 0.00154646076994877 |
| 69 | 0.999524550132695 | 0.00095089973461071 | 0.000475449867305355 |
| 70 | 0.99987262021895 | 0.000254759562098626 | 0.000127379781049313 |
| 71 | 0.999942475313145 | 0.000115049373709868 | 5.7524686854934e-05 |
| 72 | 0.99996300670436 | 7.39865912818429e-05 | 3.69932956409214e-05 |
| 73 | 0.999975853870006 | 4.82922599885831e-05 | 2.41461299942916e-05 |
| 74 | 0.999983284802715 | 3.34303945696871e-05 | 1.67151972848435e-05 |
| 75 | 0.999989960265864 | 2.00794682716592e-05 | 1.00397341358296e-05 |
| 76 | 0.999992910392062 | 1.4179215875988e-05 | 7.08960793799402e-06 |
| 77 | 0.99999442858421 | 1.11428315800221e-05 | 5.57141579001103e-06 |
| 78 | 0.999995889992927 | 8.22001414596243e-06 | 4.11000707298122e-06 |
| 79 | 0.999996079718208 | 7.84056358475542e-06 | 3.92028179237771e-06 |
| 80 | 0.999996822498 | 6.3550040000917e-06 | 3.17750200004585e-06 |
| 81 | 0.999998224009727 | 3.55198054537045e-06 | 1.77599027268522e-06 |
| 82 | 0.999999104719815 | 1.79056037082588e-06 | 8.9528018541294e-07 |
| 83 | 0.999998828116842 | 2.34376631524907e-06 | 1.17188315762453e-06 |
| 84 | 0.99999875747742 | 2.48504515847819e-06 | 1.2425225792391e-06 |
| 85 | 0.999998957966425 | 2.08406714998244e-06 | 1.04203357499122e-06 |
| 86 | 0.999998629796582 | 2.74040683598103e-06 | 1.37020341799051e-06 |
| 87 | 0.999997952608002 | 4.09478399580471e-06 | 2.04739199790236e-06 |
| 88 | 0.99999736770658 | 5.26458684149547e-06 | 2.63229342074773e-06 |
| 89 | 0.999995485495563 | 9.02900887351383e-06 | 4.51450443675692e-06 |
| 90 | 0.9999945031339 | 1.09937322002118e-05 | 5.49686610010591e-06 |
| 91 | 0.999989817985782 | 2.0364028435404e-05 | 1.0182014217702e-05 |
| 92 | 0.999980982188265 | 3.80356234691745e-05 | 1.90178117345872e-05 |
| 93 | 0.999964669791917 | 7.06604161658346e-05 | 3.53302080829173e-05 |
| 94 | 0.999946465586445 | 0.000107068827110446 | 5.35344135552229e-05 |
| 95 | 0.999895311493606 | 0.000209377012787501 | 0.000104688506393751 |
| 96 | 0.999852331661738 | 0.000295336676524583 | 0.000147668338262292 |
| 97 | 0.999772066649967 | 0.000455866700065753 | 0.000227933350032877 |
| 98 | 0.999574977692224 | 0.000850044615551285 | 0.000425022307775643 |
| 99 | 0.99939190596703 | 0.00121618806593983 | 0.000608094032969913 |
| 100 | 0.999534499832279 | 0.000931000335442373 | 0.000465500167721187 |
| 101 | 0.999682266674026 | 0.000635466651948284 | 0.000317733325974142 |
| 102 | 0.99970616307892 | 0.000587673842159232 | 0.000293836921079616 |
| 103 | 0.999641694910845 | 0.000716610178310125 | 0.000358305089155063 |
| 104 | 0.999472737915908 | 0.00105452416818501 | 0.000527262084092506 |
| 105 | 0.999251374863885 | 0.00149725027222921 | 0.000748625136114606 |
| 106 | 0.998779199742839 | 0.00244160051432196 | 0.00122080025716098 |
| 107 | 0.998707080097089 | 0.00258583980582249 | 0.00129291990291124 |
| 108 | 0.997968901151082 | 0.00406219769783498 | 0.00203109884891749 |
| 109 | 0.998890845742434 | 0.0022183085151313 | 0.00110915425756565 |
| 110 | 0.998995504447728 | 0.00200899110454336 | 0.00100449555227168 |
| 111 | 0.999372527983593 | 0.0012549440328141 | 0.000627472016407048 |
| 112 | 0.99972791315867 | 0.000544173682660498 | 0.000272086841330249 |
| 113 | 0.999929087130073 | 0.00014182573985315 | 7.09128699265752e-05 |
| 114 | 0.999994285069936 | 1.14298601280183e-05 | 5.71493006400913e-06 |
| 115 | 0.999975128728984 | 4.9742542032518e-05 | 2.4871271016259e-05 |
| 116 | 0.999895405640248 | 0.000209188719504279 | 0.000104594359752139 |
| 117 | 0.999704121107972 | 0.000591757784055213 | 0.000295878892027606 |
| 118 | 0.998793721865895 | 0.0024125562682107 | 0.00120627813410535 |
| 119 | 0.999712455790022 | 0.000575088419955293 | 0.000287544209977647 |
| 120 | 0.998254940732999 | 0.00349011853400228 | 0.00174505926700114 |
| 121 | 0.98977364413465 | 0.0204527117307008 | 0.0102263558653504 |
| 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 | 72 | 0.648648648648649 | NOK |
| 10% type I error level | 83 | 0.747747747747748 | NOK |
