| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1619.34491058766 + 0.097090018535330Nikkei[t] + 0.377623204905491DJ_Indust[t] + 0.0224418967318068Goudprijs[t] -11.9978133248867Conjunct_Seizoenzuiver[t] + 13.1960386198306Cons_vertrouw[t] + 35.1584463072643Alg_consumptie_index_BE[t] -281.151660194821Gem_rente_kasbon_5j[t] + 101.669511969855M1[t] + 111.675876231966M2[t] + 66.9582047439335M3[t] + 27.0773094453436M4[t] + 9.19557078440676M5[t] -8.26816866526923M6[t] + 43.5191316121944M7[t] + 54.7982173057046M8[t] + 90.3544111508069M9[t] + 154.637115270349M10[t] + 85.9311944465136M11[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) | -1619.34491058766 | 360.842489 | -4.4877 | 1.7e-05 | 9e-06 |
| Nikkei | 0.097090018535330 | 0.015819 | 6.1374 | 0 | 0 |
| DJ_Indust | 0.377623204905491 | 0.035999 | 10.4898 | 0 | 0 |
| Goudprijs | 0.0224418967318068 | 0.008695 | 2.5811 | 0.011128 | 0.005564 |
| Conjunct_Seizoenzuiver | -11.9978133248867 | 7.307075 | -1.6419 | 0.103382 | 0.051691 |
| Cons_vertrouw | 13.1960386198306 | 6.991986 | 1.8873 | 0.061684 | 0.030842 |
| Alg_consumptie_index_BE | 35.1584463072643 | 24.31066 | 1.4462 | 0.150885 | 0.075442 |
| Gem_rente_kasbon_5j | -281.151660194821 | 56.829501 | -4.9473 | 3e-06 | 1e-06 |
| M1 | 101.669511969855 | 116.822167 | 0.8703 | 0.385985 | 0.192993 |
| M2 | 111.675876231966 | 117.85931 | 0.9475 | 0.345388 | 0.172694 |
| M3 | 66.9582047439335 | 117.419158 | 0.5702 | 0.569641 | 0.28482 |
| M4 | 27.0773094453436 | 117.575576 | 0.2303 | 0.818277 | 0.409139 |
| M5 | 9.19557078440676 | 115.390203 | 0.0797 | 0.936624 | 0.468312 |
| M6 | -8.26816866526923 | 114.916944 | -0.0719 | 0.94277 | 0.471385 |
| M7 | 43.5191316121944 | 114.74208 | 0.3793 | 0.705193 | 0.352597 |
| M8 | 54.7982173057046 | 114.627044 | 0.4781 | 0.633533 | 0.316767 |
| M9 | 90.3544111508069 | 114.685489 | 0.7878 | 0.432437 | 0.216218 |
| M10 | 154.637115270349 | 115.096969 | 1.3435 | 0.18179 | 0.090895 |
| M11 | 85.9311944465136 | 114.558184 | 0.7501 | 0.454748 | 0.227374 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.94372311410716 |
| R-squared | 0.890613316100117 |
| Adjusted R-squared | 0.873188888576242 |
| F-TEST (value) | 51.1129169024226 |
| F-TEST (DF numerator) | 18 |
| F-TEST (DF denominator) | 113 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 268.132458734677 |
| Sum Squared Residuals | 8124136.74326266 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2824.94932725762 | 659.79067274238 |
| 2 | 3411.13 | 2831.67944896253 | 579.450551037465 |
| 3 | 3288.18 | 3026.34361786074 | 261.836382139262 |
| 4 | 3280.37 | 3371.16595702633 | -90.7959570263253 |
| 5 | 3173.95 | 3460.59456225228 | -286.644562252277 |
| 6 | 3165.26 | 3186.09006272444 | -20.8300627244404 |
| 7 | 3092.71 | 3416.53562046413 | -323.825620464133 |
| 8 | 3053.05 | 3275.75311444174 | -222.70311444174 |
| 9 | 3181.96 | 3226.47236691210 | -44.5123669120959 |
| 10 | 2999.93 | 3090.11186975507 | -90.1818697550748 |
| 11 | 3249.57 | 3385.55429526564 | -135.984295265644 |
| 12 | 3210.52 | 3367.06124372353 | -156.541243723530 |
| 13 | 3030.29 | 3536.91507305959 | -506.625073059586 |
| 14 | 2803.47 | 3314.27051443885 | -510.800514438848 |
| 15 | 2767.63 | 3278.90181337856 | -511.27181337856 |
| 16 | 2882.6 | 3434.23459844578 | -551.634598445783 |
| 17 | 2863.36 | 2981.53971781858 | -118.179717818577 |
| 18 | 2897.06 | 2989.65626779428 | -92.5962677942793 |
| 19 | 3012.61 | 3070.89015368888 | -58.2801536888809 |
| 20 | 3142.95 | 3175.44209763084 | -32.4920976308441 |
| 21 | 3032.93 | 3114.56308713044 | -81.6330871304413 |
| 22 | 3045.78 | 2953.58419646163 | 92.1958035383672 |
| 23 | 3110.52 | 2966.14395016107 | 144.376049838927 |
| 24 | 3013.24 | 2968.46511074246 | 44.7748892575436 |
| 25 | 2987.1 | 3029.90319403906 | -42.8031940390629 |
| 26 | 2995.55 | 2990.54142188693 | 5.00857811306545 |
| 27 | 2833.18 | 2664.59635271701 | 168.583647282989 |
| 28 | 2848.96 | 2794.88723600528 | 54.0727639947217 |
| 29 | 2794.83 | 2939.84732636752 | -145.017326367522 |
| 30 | 2845.26 | 2946.22098484891 | -100.960984848915 |
| 31 | 2915.02 | 2797.29075293645 | 117.729247063550 |
| 32 | 2892.63 | 2660.34624676337 | 232.283753236633 |
| 33 | 2604.42 | 2132.61689243756 | 471.803107562441 |
| 34 | 2641.65 | 2271.92859150958 | 369.721408490422 |
| 35 | 2659.81 | 2407.31788325785 | 252.492116742151 |
| 36 | 2638.53 | 2399.32144294878 | 239.208557051219 |
| 37 | 2720.25 | 2548.91463235998 | 171.335367640016 |
| 38 | 2745.88 | 2492.10523568421 | 253.774764315794 |
| 39 | 2735.7 | 2709.69673962339 | 26.0032603766056 |
| 40 | 2811.7 | 2472.99135095788 | 338.708649042122 |
| 41 | 2799.43 | 2449.88175063835 | 349.548249361649 |
| 42 | 2555.28 | 2156.51035095622 | 398.769649043779 |
| 43 | 2304.98 | 1878.2034968129 | 426.776503187098 |
| 44 | 2214.95 | 1929.12242698476 | 285.827573015238 |
| 45 | 2065.81 | 1795.90033131494 | 269.909668685061 |
| 46 | 1940.49 | 1776.75680346372 | 163.733196536281 |
| 47 | 2042 | 1891.28608291027 | 150.713917089728 |
| 48 | 1995.37 | 1743.94856603094 | 251.421433969057 |
| 49 | 1946.81 | 1921.68390785491 | 25.1260921450883 |
| 50 | 1765.9 | 1753.67211643368 | 12.2278835663206 |
| 51 | 1635.25 | 1679.23165110453 | -43.9816511045273 |
| 52 | 1833.42 | 1771.17849040016 | 62.2415095998413 |
| 53 | 1910.43 | 2017.38506129133 | -106.955061291331 |
| 54 | 1959.67 | 2369.02970769841 | -409.359707698409 |
| 55 | 1969.6 | 2376.18941793250 | -406.589417932497 |
| 56 | 2061.41 | 2345.81140615421 | -284.401406154209 |
| 57 | 2093.48 | 2584.35994753175 | -490.879947531753 |
| 58 | 2120.88 | 2515.97294061163 | -395.092940611629 |
| 59 | 2174.56 | 2525.63302147816 | -351.073021478160 |
| 60 | 2196.72 | 2567.71439975515 | -370.994399755147 |
| 61 | 2350.44 | 2882.44325306799 | -532.003253067986 |
| 62 | 2440.25 | 2897.72556474247 | -457.475564742468 |
| 63 | 2408.64 | 2826.54859490051 | -417.908594900511 |
| 64 | 2472.81 | 2915.55822575873 | -442.748225758727 |
| 65 | 2407.6 | 2624.86826017711 | -217.268260177112 |
| 66 | 2454.62 | 2827.44797155566 | -372.827971555662 |
| 67 | 2448.05 | 2650.93711425795 | -202.887114257947 |
| 68 | 2497.84 | 2663.55323750216 | -165.713237502159 |
| 69 | 2645.64 | 2760.68167711004 | -115.041677110037 |
| 70 | 2756.76 | 2710.38474250976 | 46.3752574902388 |
| 71 | 2849.27 | 2808.55571393923 | 40.7142860607731 |
| 72 | 2921.44 | 2864.60926941584 | 56.8307305841598 |
| 73 | 2981.85 | 2953.88030397927 | 27.9696960207345 |
| 74 | 3080.58 | 3168.90350949230 | -88.323509492304 |
| 75 | 3106.22 | 3176.90368584923 | -70.6836858492261 |
| 76 | 3119.31 | 2936.13144867646 | 183.178551323542 |
| 77 | 3061.26 | 2856.49322090725 | 204.766779092751 |
| 78 | 3097.31 | 2965.06967595899 | 132.240324041010 |
| 79 | 3161.69 | 3110.11319464421 | 51.5768053557948 |
| 80 | 3257.16 | 3158.00157654276 | 99.1584234572418 |
| 81 | 3277.01 | 3185.12892124683 | 91.8810787531733 |
| 82 | 3295.32 | 3254.47344789792 | 40.8465521020795 |
| 83 | 3363.99 | 3369.74779724366 | -5.75779724366406 |
| 84 | 3494.17 | 3491.93053071749 | 2.23946928250979 |
| 85 | 3667.03 | 3685.70754337421 | -18.6775433742065 |
| 86 | 3813.06 | 3741.42921322358 | 71.6307867764211 |
| 87 | 3917.96 | 3673.72249825942 | 244.237501740584 |
| 88 | 3895.51 | 3708.68404932705 | 186.825950672954 |
| 89 | 3801.06 | 3598.57749367387 | 202.482506326132 |
| 90 | 3570.12 | 3313.32176750317 | 256.798232496835 |
| 91 | 3701.61 | 3356.59519517905 | 345.014804820952 |
| 92 | 3862.27 | 3514.41553114797 | 347.854468852029 |
| 93 | 3970.1 | 3676.07256246039 | 294.027437539608 |
| 94 | 4138.52 | 3988.45623625326 | 150.063763746744 |
| 95 | 4199.75 | 3998.73254195989 | 201.017458040108 |
| 96 | 4290.89 | 3910.76716303597 | 380.122836964035 |
| 97 | 4443.91 | 4185.42827991608 | 258.481720083922 |
| 98 | 4502.64 | 4262.80160010089 | 239.838399899109 |
| 99 | 4356.98 | 3998.90291842320 | 358.077081576795 |
| 100 | 4591.27 | 4203.17891811961 | 388.091081880395 |
| 101 | 4696.96 | 4420.0950882854 | 276.864911714602 |
| 102 | 4621.4 | 4336.48201019186 | 284.917989808139 |
| 103 | 4562.84 | 4398.03746831465 | 164.802531685346 |
| 104 | 4202.52 | 4120.1316944217 | 82.3883055783028 |
| 105 | 4296.49 | 4305.34034454639 | -8.85034454639469 |
| 106 | 4435.23 | 4638.5329817899 | -203.302981789899 |
| 107 | 4105.18 | 4150.08985488328 | -44.9098548832834 |
| 108 | 4116.68 | 4240.72854501824 | -124.048545018241 |
| 109 | 3844.49 | 3817.23190931791 | 27.2580906820945 |
| 110 | 3720.98 | 3872.06691585994 | -151.086915859942 |
| 111 | 3674.4 | 3766.79191888594 | -92.3919188859348 |
| 112 | 3857.62 | 3950.20310536987 | -92.5831053698668 |
| 113 | 3801.06 | 3956.74444591671 | -155.684445916706 |
| 114 | 3504.37 | 3528.70311771171 | -24.333117711709 |
| 115 | 3032.6 | 3100.94100226371 | -68.3410022637077 |
| 116 | 3047.03 | 3157.2452875544 | -110.215287554398 |
| 117 | 2962.34 | 3153.97241587285 | -191.632415872854 |
| 118 | 2197.82 | 2162.61237058675 | 35.2076294132463 |
| 119 | 2014.45 | 1896.19368260242 | 118.256317397579 |
| 120 | 1862.83 | 1857.37789164693 | 5.45210835307332 |
| 121 | 1905.41 | 1975.26257577339 | -69.8525757733936 |
| 122 | 1810.99 | 1765.23445917461 | 45.7555408253865 |
| 123 | 1670.07 | 1592.57020899748 | 77.4997910025243 |
| 124 | 1864.44 | 1899.79661991287 | -35.3566199128735 |
| 125 | 2052.02 | 2055.93307267161 | -3.91307267160933 |
| 126 | 2029.6 | 2081.41808305635 | -51.8180830563478 |
| 127 | 2070.83 | 2116.80658350557 | -45.9765835055748 |
| 128 | 2293.41 | 2525.39738085609 | -231.987380856094 |
| 129 | 2443.27 | 2638.34145343671 | -195.071453436706 |
| 130 | 2513.17 | 2722.73581916078 | -209.565819160776 |
| 131 | 2466.92 | 2836.76517629852 | -369.845176298515 |
| 132 | 2502.66 | 2831.12583696468 | -328.465836964683 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 22 | 0.0545682816817718 | 0.109136563363544 | 0.945431718318228 |
| 23 | 0.0603585562786019 | 0.120717112557204 | 0.939641443721398 |
| 24 | 0.116817775494850 | 0.233635550989701 | 0.88318222450515 |
| 25 | 0.0682951066519698 | 0.136590213303940 | 0.93170489334803 |
| 26 | 0.0484346028710521 | 0.0968692057421042 | 0.951565397128948 |
| 27 | 0.0239107039007436 | 0.0478214078014871 | 0.976089296099256 |
| 28 | 0.0321787988874815 | 0.0643575977749631 | 0.967821201112518 |
| 29 | 0.0351437952238826 | 0.0702875904477651 | 0.964856204776117 |
| 30 | 0.0216220160199059 | 0.0432440320398118 | 0.978377983980094 |
| 31 | 0.0115459397125865 | 0.023091879425173 | 0.988454060287413 |
| 32 | 0.00650009185348118 | 0.0130001837069624 | 0.993499908146519 |
| 33 | 0.00996663191904888 | 0.0199332638380978 | 0.99003336808095 |
| 34 | 0.00690028291906368 | 0.0138005658381274 | 0.993099717080936 |
| 35 | 0.00386541070337018 | 0.00773082140674035 | 0.99613458929663 |
| 36 | 0.00207445372836406 | 0.00414890745672812 | 0.997925546271636 |
| 37 | 0.00110637473477159 | 0.00221274946954318 | 0.998893625265228 |
| 38 | 0.00249077079047962 | 0.00498154158095925 | 0.99750922920952 |
| 39 | 0.00445124183939195 | 0.0089024836787839 | 0.995548758160608 |
| 40 | 0.0181031915995776 | 0.0362063831991552 | 0.981896808400422 |
| 41 | 0.0150081513710780 | 0.0300163027421561 | 0.984991848628922 |
| 42 | 0.0170157699297252 | 0.0340315398594503 | 0.982984230070275 |
| 43 | 0.0272887498827037 | 0.0545774997654075 | 0.972711250117296 |
| 44 | 0.0539235983644967 | 0.107847196728993 | 0.946076401635503 |
| 45 | 0.108917189670311 | 0.217834379340623 | 0.891082810329689 |
| 46 | 0.324582121162863 | 0.649164242325726 | 0.675417878837137 |
| 47 | 0.511228729345633 | 0.977542541308734 | 0.488771270654367 |
| 48 | 0.544241752940389 | 0.911516494119221 | 0.455758247059611 |
| 49 | 0.512953272342962 | 0.974093455314076 | 0.487046727657038 |
| 50 | 0.458804100521952 | 0.917608201043903 | 0.541195899478048 |
| 51 | 0.40489238695706 | 0.80978477391412 | 0.59510761304294 |
| 52 | 0.553447765741959 | 0.893104468516082 | 0.446552234258041 |
| 53 | 0.645364213755895 | 0.709271572488211 | 0.354635786244105 |
| 54 | 0.819990638068178 | 0.360018723863645 | 0.180009361931822 |
| 55 | 0.834594007766029 | 0.330811984467942 | 0.165405992233971 |
| 56 | 0.806931874716124 | 0.386136250567751 | 0.193068125283876 |
| 57 | 0.825645828158399 | 0.348708343683202 | 0.174354171841601 |
| 58 | 0.86856016435226 | 0.262879671295479 | 0.131439835647740 |
| 59 | 0.848632482900715 | 0.30273503419857 | 0.151367517099285 |
| 60 | 0.82393623213127 | 0.352127535737461 | 0.176063767868731 |
| 61 | 0.85510607190866 | 0.289787856182680 | 0.144893928091340 |
| 62 | 0.869927346537851 | 0.260145306924299 | 0.130072653462149 |
| 63 | 0.937484966911952 | 0.125030066176095 | 0.0625150330880476 |
| 64 | 0.994615026044495 | 0.0107699479110093 | 0.00538497395550463 |
| 65 | 0.998719057992453 | 0.00256188401509327 | 0.00128094200754664 |
| 66 | 0.999640652436452 | 0.000718695127097004 | 0.000359347563548502 |
| 67 | 0.999951873670318 | 9.62526593631777e-05 | 4.81263296815888e-05 |
| 68 | 0.999977336201047 | 4.53275979066333e-05 | 2.26637989533167e-05 |
| 69 | 0.999987186236277 | 2.56275274460655e-05 | 1.28137637230328e-05 |
| 70 | 0.999992308566895 | 1.53828662102570e-05 | 7.69143310512852e-06 |
| 71 | 0.99999425601817 | 1.14879636609501e-05 | 5.74398183047504e-06 |
| 72 | 0.999994444238163 | 1.11115236739173e-05 | 5.55576183695865e-06 |
| 73 | 0.999997302988666 | 5.3940226676377e-06 | 2.69701133381885e-06 |
| 74 | 0.999999041947625 | 1.91610475042714e-06 | 9.58052375213569e-07 |
| 75 | 0.99999990086932 | 1.98261362079871e-07 | 9.91306810399357e-08 |
| 76 | 0.999999953442636 | 9.31147276026831e-08 | 4.65573638013415e-08 |
| 77 | 0.999999990405507 | 1.91889869745944e-08 | 9.59449348729721e-09 |
| 78 | 0.99999999328991 | 1.34201782143454e-08 | 6.71008910717268e-09 |
| 79 | 0.999999989638075 | 2.07238497873747e-08 | 1.03619248936873e-08 |
| 80 | 0.999999991063407 | 1.78731856735111e-08 | 8.93659283675553e-09 |
| 81 | 0.99999998619668 | 2.76066403345250e-08 | 1.38033201672625e-08 |
| 82 | 0.999999972194669 | 5.56106621715987e-08 | 2.78053310857993e-08 |
| 83 | 0.999999963360269 | 7.32794625114006e-08 | 3.66397312557003e-08 |
| 84 | 0.999999939170575 | 1.21658850164832e-07 | 6.08294250824162e-08 |
| 85 | 0.999999941197996 | 1.17604007257742e-07 | 5.88020036288711e-08 |
| 86 | 0.999999971502233 | 5.69955344438824e-08 | 2.84977672219412e-08 |
| 87 | 0.99999999251632 | 1.49673589763533e-08 | 7.48367948817664e-09 |
| 88 | 0.999999998982198 | 2.03560455669455e-09 | 1.01780227834727e-09 |
| 89 | 0.99999999947134 | 1.05732020661709e-09 | 5.28660103308545e-10 |
| 90 | 0.999999999817286 | 3.65428758537997e-10 | 1.82714379268999e-10 |
| 91 | 0.999999999354749 | 1.29050230571643e-09 | 6.45251152858214e-10 |
| 92 | 0.999999999452017 | 1.09596565757279e-09 | 5.47982828786394e-10 |
| 93 | 0.999999997833977 | 4.33204625386485e-09 | 2.16602312693242e-09 |
| 94 | 0.999999994484268 | 1.10314635139605e-08 | 5.51573175698023e-09 |
| 95 | 0.999999978859906 | 4.22801877642693e-08 | 2.11400938821346e-08 |
| 96 | 0.999999942656755 | 1.14686490986503e-07 | 5.73432454932513e-08 |
| 97 | 0.999999775600657 | 4.48798686708328e-07 | 2.24399343354164e-07 |
| 98 | 0.99999969284137 | 6.14317259871989e-07 | 3.07158629935994e-07 |
| 99 | 0.999999806461154 | 3.87077692299481e-07 | 1.93538846149740e-07 |
| 100 | 0.99999918240609 | 1.63518782144992e-06 | 8.17593910724959e-07 |
| 101 | 0.999996761368098 | 6.47726380356991e-06 | 3.23863190178495e-06 |
| 102 | 0.999990161772387 | 1.96764552260977e-05 | 9.83822761304886e-06 |
| 103 | 0.999965206454302 | 6.95870913961568e-05 | 3.47935456980784e-05 |
| 104 | 0.999878830841586 | 0.00024233831682857 | 0.000121169158414285 |
| 105 | 0.99956508648047 | 0.000869827039059782 | 0.000434913519529891 |
| 106 | 0.999004154322534 | 0.00199169135493203 | 0.000995845677466013 |
| 107 | 0.997177660335526 | 0.00564467932894811 | 0.00282233966447406 |
| 108 | 0.991346272693665 | 0.0173074546126695 | 0.00865372730633476 |
| 109 | 0.993063062068661 | 0.0138738758626779 | 0.00693693793133896 |
| 110 | 0.984626325325907 | 0.0307473493481855 | 0.0153736746740927 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 48 | 0.539325842696629 | NOK |
| 5% type I error level | 61 | 0.685393258426966 | NOK |
| 10% type I error level | 65 | 0.730337078651685 | NOK |
