| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -2144.95629086107 + 0.0676640923599321Nikkei[t] + 0.393331506519843DJ_Indust[t] + 0.00173978490673361Goudprijs[t] + 3.92037673438888Conjunct_Seizoenzuiver[t] -11.2351720560286Cons_vertrouw[t] -29.5413432798274Alg_consumptie_index_BE[t] + 8.8153605202871Gem_rente_kasbon_1j[t] + 191.789136312232M1[t] + 223.981065857801M2[t] + 171.623779965858M3[t] + 137.037028842043M4[t] + 71.8640671295251M5[t] + 28.2582022074953M6[t] + 32.8134963863037M7[t] + 45.8338192955717M8[t] + 104.698425035446M9[t] + 128.178960193137M10[t] + 80.14170827084M11[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) | -2144.95629086107 | 385.362656 | -5.5661 | 0 | 0 |
| Nikkei | 0.0676640923599321 | 0.017821 | 3.7969 | 0.000237 | 0.000119 |
| DJ_Indust | 0.393331506519843 | 0.039557 | 9.9433 | 0 | 0 |
| Goudprijs | 0.00173978490673361 | 0.00963 | 0.1807 | 0.856957 | 0.428478 |
| Conjunct_Seizoenzuiver | 3.92037673438888 | 8.165837 | 0.4801 | 0.632088 | 0.316044 |
| Cons_vertrouw | -11.2351720560286 | 6.989126 | -1.6075 | 0.110731 | 0.055365 |
| Alg_consumptie_index_BE | -29.5413432798274 | 31.431623 | -0.9399 | 0.349294 | 0.174647 |
| Gem_rente_kasbon_1j | 8.8153605202871 | 45.657969 | 0.1931 | 0.847248 | 0.423624 |
| M1 | 191.789136312232 | 127.897541 | 1.4996 | 0.136519 | 0.068259 |
| M2 | 223.981065857801 | 128.832021 | 1.7386 | 0.084837 | 0.042419 |
| M3 | 171.623779965858 | 128.469866 | 1.3359 | 0.184264 | 0.092132 |
| M4 | 137.037028842043 | 128.72632 | 1.0646 | 0.289344 | 0.144672 |
| M5 | 71.8640671295251 | 126.660828 | 0.5674 | 0.571586 | 0.285793 |
| M6 | 28.2582022074953 | 126.5428 | 0.2233 | 0.823698 | 0.411849 |
| M7 | 32.8134963863037 | 126.516668 | 0.2594 | 0.795829 | 0.397914 |
| M8 | 45.8338192955717 | 126.403528 | 0.3626 | 0.717582 | 0.358791 |
| M9 | 104.698425035446 | 126.468134 | 0.8279 | 0.409492 | 0.204746 |
| M10 | 128.178960193137 | 126.854835 | 1.0104 | 0.314444 | 0.157222 |
| M11 | 80.14170827084 | 126.420214 | 0.6339 | 0.527407 | 0.263703 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.93110913758741 |
| R-squared | 0.86696422609877 |
| Adjusted R-squared | 0.845772686893265 |
| F-TEST (value) | 40.9108662514488 |
| F-TEST (DF numerator) | 18 |
| F-TEST (DF denominator) | 113 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 295.700039428375 |
| Sum Squared Residuals | 9880552.00492752 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2579.45636359244 | 905.283636407559 |
| 2 | 3411.13 | 2656.71408740409 | 754.415912595913 |
| 3 | 3288.18 | 2859.59098489657 | 428.589015103434 |
| 4 | 3280.37 | 3200.64180102325 | 79.7281989767542 |
| 5 | 3173.95 | 3302.67051506728 | -128.720515067284 |
| 6 | 3165.26 | 3354.5579594172 | -189.297959417197 |
| 7 | 3092.71 | 3472.35210478824 | -379.642104788238 |
| 8 | 3053.05 | 3432.33874170369 | -379.288741703687 |
| 9 | 3181.96 | 3341.60356150114 | -159.643561501143 |
| 10 | 2999.93 | 3242.62656716889 | -242.696567168887 |
| 11 | 3249.57 | 3375.95826475764 | -126.388264757642 |
| 12 | 3210.52 | 3460.44554134794 | -249.925541347943 |
| 13 | 3030.29 | 3683.21866722462 | -652.928667224617 |
| 14 | 2803.47 | 3456.82022612727 | -653.350226127274 |
| 15 | 2767.63 | 3366.52757102557 | -598.89757102557 |
| 16 | 2882.6 | 3510.26558272827 | -627.665582728267 |
| 17 | 2863.36 | 3113.46922817847 | -250.109228178474 |
| 18 | 2897.06 | 3033.51288242301 | -136.452882423011 |
| 19 | 3012.61 | 3076.49040451252 | -63.880404512523 |
| 20 | 3142.95 | 3152.90538203494 | -9.95538203494452 |
| 21 | 3032.93 | 3237.11116296212 | -204.181162962117 |
| 22 | 3045.78 | 2954.59378375236 | 91.1862162476395 |
| 23 | 3110.52 | 2955.83609016701 | 154.683909832988 |
| 24 | 3013.24 | 2860.77610223275 | 152.463897767249 |
| 25 | 2987.1 | 3031.44686707431 | -44.3468670743118 |
| 26 | 2995.55 | 3116.68280216051 | -121.132802160511 |
| 27 | 2833.18 | 2749.63687234129 | 83.5431276587118 |
| 28 | 2848.96 | 2828.48402518022 | 20.4759748197811 |
| 29 | 2794.83 | 2926.45462133852 | -131.624621338521 |
| 30 | 2845.26 | 2891.99453701445 | -46.7345370144545 |
| 31 | 2915.02 | 2716.72580366919 | 198.294196330811 |
| 32 | 2892.63 | 2680.02932991049 | 212.600670089507 |
| 33 | 2604.42 | 2168.31698640912 | 436.103013590882 |
| 34 | 2641.65 | 2388.50652397270 | 253.143476027296 |
| 35 | 2659.81 | 2592.21877746132 | 67.5912225386759 |
| 36 | 2638.53 | 2504.93920126638 | 133.590798733624 |
| 37 | 2720.25 | 2572.93897503594 | 147.311024964062 |
| 38 | 2745.88 | 2561.19964471573 | 184.680355284267 |
| 39 | 2735.7 | 2848.65885145413 | -112.958851454135 |
| 40 | 2811.7 | 2735.63990801865 | 76.0600919813515 |
| 41 | 2799.43 | 2662.96710702570 | 136.462892974295 |
| 42 | 2555.28 | 2359.18347506081 | 196.096524939194 |
| 43 | 2304.98 | 1968.7464401317 | 336.233559868299 |
| 44 | 2214.95 | 1982.05277085516 | 232.897229144841 |
| 45 | 2065.81 | 1806.97451917652 | 258.835480823477 |
| 46 | 1940.49 | 1742.75602432244 | 197.733975677561 |
| 47 | 2042 | 1943.28254462502 | 98.7174553749822 |
| 48 | 1995.37 | 1848.86606251371 | 146.503937486285 |
| 49 | 1946.81 | 2019.78209257038 | -72.9720925703787 |
| 50 | 1765.9 | 1860.51912010206 | -94.6191201020627 |
| 51 | 1635.25 | 1843.73527445071 | -208.485274450707 |
| 52 | 1833.42 | 1856.02777959345 | -22.6077795934523 |
| 53 | 1910.43 | 1918.22270717168 | -7.7927071716789 |
| 54 | 1959.67 | 2092.05383014939 | -132.383830149386 |
| 55 | 1969.6 | 2214.58733097342 | -244.987330973424 |
| 56 | 2061.41 | 2276.26024930731 | -214.850249307305 |
| 57 | 2093.48 | 2413.74489181949 | -320.264891819488 |
| 58 | 2120.88 | 2641.04464729918 | -520.164647299178 |
| 59 | 2174.56 | 2490.9594562507 | -316.399456250702 |
| 60 | 2196.72 | 2568.50360909735 | -371.783609097352 |
| 61 | 2350.44 | 2932.15984902518 | -581.719849025183 |
| 62 | 2440.25 | 2958.95074323101 | -518.700743231007 |
| 63 | 2408.64 | 2883.48273114631 | -474.842731146307 |
| 64 | 2472.81 | 2915.08659385683 | -442.276593856826 |
| 65 | 2407.6 | 2667.04638878704 | -259.446388787044 |
| 66 | 2454.62 | 2704.22626833340 | -249.606268333404 |
| 67 | 2448.05 | 2671.88596622675 | -223.835966226745 |
| 68 | 2497.84 | 2583.81295070158 | -85.9729507015778 |
| 69 | 2645.64 | 2726.40670648942 | -80.7667064894167 |
| 70 | 2756.76 | 2682.71791244245 | 74.0420875575543 |
| 71 | 2849.27 | 2805.16285727737 | 44.1071427226338 |
| 72 | 2921.44 | 2824.02057769154 | 97.4194223084617 |
| 73 | 2981.85 | 2990.28747468154 | -8.43747468153495 |
| 74 | 3080.58 | 3055.90437404431 | 24.6756259556898 |
| 75 | 3106.22 | 2976.87017279786 | 129.349827202144 |
| 76 | 3119.31 | 2789.45127110106 | 329.858728898939 |
| 77 | 3061.26 | 2811.75691855993 | 249.503081440072 |
| 78 | 3097.31 | 2823.54184140404 | 273.768158595962 |
| 79 | 3161.69 | 2863.17428686712 | 298.515713132881 |
| 80 | 3257.16 | 2903.84227118056 | 353.317728819438 |
| 81 | 3277.01 | 3065.48173806899 | 211.528261931011 |
| 82 | 3295.32 | 2997.15267626549 | 298.167323734507 |
| 83 | 3363.99 | 3175.85561796069 | 188.134382039313 |
| 84 | 3494.17 | 3187.6754777711 | 306.4945222289 |
| 85 | 3667.03 | 3394.81020208005 | 272.219797919954 |
| 86 | 3813.06 | 3495.58051912550 | 317.479480874497 |
| 87 | 3917.96 | 3581.22615679587 | 336.733843204125 |
| 88 | 3895.51 | 3636.16373300585 | 259.34626699415 |
| 89 | 3801.06 | 3575.15715061151 | 225.902849388493 |
| 90 | 3570.12 | 3268.03627362533 | 302.083726374674 |
| 91 | 3701.61 | 3314.16049180479 | 387.449508195215 |
| 92 | 3862.27 | 3452.34051051968 | 409.929489480321 |
| 93 | 3970.1 | 3637.11851587557 | 332.981484124428 |
| 94 | 4138.52 | 3829.47152166292 | 309.048478337083 |
| 95 | 4199.75 | 3839.33276552868 | 360.417234471317 |
| 96 | 4290.89 | 3983.03642805938 | 307.853571940624 |
| 97 | 4443.91 | 4180.56800892346 | 263.34199107654 |
| 98 | 4502.64 | 4261.97281013844 | 240.667189861562 |
| 99 | 4356.98 | 4043.25522638083 | 313.724773619173 |
| 100 | 4591.27 | 4197.53544176756 | 393.734558232437 |
| 101 | 4696.96 | 4418.28019013005 | 278.679809869947 |
| 102 | 4621.4 | 4449.73439377353 | 171.665606226466 |
| 103 | 4562.84 | 4543.26009792124 | 19.5799020787571 |
| 104 | 4202.52 | 4294.85185672821 | -92.331856728207 |
| 105 | 4296.49 | 4451.49397509008 | -155.003975090081 |
| 106 | 4435.23 | 4614.76282125114 | -179.532821251138 |
| 107 | 4105.18 | 4258.28398726484 | -153.103987264843 |
| 108 | 4116.68 | 4198.58153731595 | -81.9015373159546 |
| 109 | 3844.49 | 3948.93651530707 | -104.446515307073 |
| 110 | 3720.98 | 3884.01335639170 | -163.033356391705 |
| 111 | 3674.4 | 3655.18790180882 | 19.2120981911797 |
| 112 | 3857.62 | 3888.62172065534 | -31.0017206553357 |
| 113 | 3801.06 | 3932.53969974938 | -131.479699749383 |
| 114 | 3504.37 | 3598.55387657899 | -94.1838765789923 |
| 115 | 3032.6 | 3267.05003163803 | -234.450031638030 |
| 116 | 3047.03 | 3343.28541168167 | -296.255411681673 |
| 117 | 2962.34 | 3134.92070421712 | -172.580704217118 |
| 118 | 2197.82 | 2287.67174210778 | -89.8517421077805 |
| 119 | 2014.45 | 2047.69089771185 | -33.2408977118458 |
| 120 | 1862.83 | 1973.38280000864 | -110.552800008640 |
| 121 | 1905.41 | 2028.71498448502 | -123.304984485016 |
| 122 | 1810.99 | 1782.07231655937 | 28.9176834406316 |
| 123 | 1670.07 | 1586.03825690205 | 84.031743097952 |
| 124 | 1864.44 | 1900.09214306953 | -35.652143069534 |
| 125 | 2052.02 | 2033.39547338042 | 18.6245266195780 |
| 126 | 2029.6 | 2124.55466221985 | -94.9546622198514 |
| 127 | 2070.83 | 2164.107041467 | -93.277041467002 |
| 128 | 2293.41 | 2423.50052537671 | -130.090525376711 |
| 129 | 2443.27 | 2590.27723839043 | -147.007238390434 |
| 130 | 2513.17 | 2704.24577975465 | -191.075779754655 |
| 131 | 2466.92 | 2751.43874099488 | -284.518740994878 |
| 132 | 2502.66 | 2832.82266269525 | -330.162662695255 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 22 | 0.0510274732891065 | 0.102054946578213 | 0.948972526710893 |
| 23 | 0.0883763589522277 | 0.176752717904455 | 0.911623641047772 |
| 24 | 0.123070819757911 | 0.246141639515821 | 0.87692918024209 |
| 25 | 0.0734143277092875 | 0.146828655418575 | 0.926585672290712 |
| 26 | 0.0523252924235859 | 0.104650584847172 | 0.947674707576414 |
| 27 | 0.0259707292703970 | 0.0519414585407941 | 0.974029270729603 |
| 28 | 0.0702309459428051 | 0.140461891885610 | 0.929769054057195 |
| 29 | 0.0889534709367527 | 0.177906941873505 | 0.911046529063247 |
| 30 | 0.0841683927475856 | 0.168336785495171 | 0.915831607252414 |
| 31 | 0.0541116035872669 | 0.108223207174534 | 0.945888396412733 |
| 32 | 0.0385620352119432 | 0.0771240704238863 | 0.961437964788057 |
| 33 | 0.0817388275079475 | 0.163477655015895 | 0.918261172492052 |
| 34 | 0.0605573740450505 | 0.121114748090101 | 0.93944262595495 |
| 35 | 0.0418002384452025 | 0.083600476890405 | 0.958199761554797 |
| 36 | 0.0380458951473594 | 0.0760917902947187 | 0.96195410485264 |
| 37 | 0.0260100318637286 | 0.0520200637274571 | 0.973989968136271 |
| 38 | 0.0218320397543041 | 0.0436640795086082 | 0.978167960245696 |
| 39 | 0.020215954996684 | 0.040431909993368 | 0.979784045003316 |
| 40 | 0.0363142438234769 | 0.0726284876469539 | 0.963685756176523 |
| 41 | 0.0294803478102207 | 0.0589606956204413 | 0.97051965218978 |
| 42 | 0.0262458643626894 | 0.0524917287253788 | 0.97375413563731 |
| 43 | 0.0335934926967091 | 0.0671869853934182 | 0.96640650730329 |
| 44 | 0.045717399280412 | 0.091434798560824 | 0.954282600719588 |
| 45 | 0.071275978848584 | 0.142551957697168 | 0.928724021151416 |
| 46 | 0.203077861356087 | 0.406155722712173 | 0.796922138643913 |
| 47 | 0.3121202972316 | 0.6242405944632 | 0.6878797027684 |
| 48 | 0.290862020949354 | 0.581724041898708 | 0.709137979050646 |
| 49 | 0.251747520810866 | 0.503495041621732 | 0.748252479189134 |
| 50 | 0.217180098974335 | 0.434360197948671 | 0.782819901025664 |
| 51 | 0.177835090052731 | 0.355670180105463 | 0.822164909947269 |
| 52 | 0.253202226909487 | 0.506404453818975 | 0.746797773090513 |
| 53 | 0.272046675906266 | 0.544093351812532 | 0.727953324093734 |
| 54 | 0.307106411035642 | 0.614212822071284 | 0.692893588964358 |
| 55 | 0.267412273705906 | 0.534824547411812 | 0.732587726294094 |
| 56 | 0.245813717805062 | 0.491627435610125 | 0.754186282194938 |
| 57 | 0.237897483527851 | 0.475794967055702 | 0.762102516472149 |
| 58 | 0.312541871140639 | 0.625083742281277 | 0.687458128859361 |
| 59 | 0.318517303788091 | 0.637034607576181 | 0.681482696211909 |
| 60 | 0.302350067276619 | 0.604700134553238 | 0.697649932723381 |
| 61 | 0.351002389782485 | 0.70200477956497 | 0.648997610217515 |
| 62 | 0.380709846101733 | 0.761419692203466 | 0.619290153898267 |
| 63 | 0.605601139708833 | 0.788797720582333 | 0.394398860291167 |
| 64 | 0.937291511088827 | 0.125416977822346 | 0.062708488911173 |
| 65 | 0.991333921893806 | 0.0173321562123878 | 0.00866607810619392 |
| 66 | 0.99733609939561 | 0.00532780120877941 | 0.00266390060438971 |
| 67 | 0.999671312223663 | 0.000657375552674587 | 0.000328687776337293 |
| 68 | 0.999871788232852 | 0.000256423534296455 | 0.000128211767148228 |
| 69 | 0.999946316956017 | 0.000107366087965501 | 5.36830439827507e-05 |
| 70 | 0.999976698362829 | 4.66032743417790e-05 | 2.33016371708895e-05 |
| 71 | 0.999986528899143 | 2.6942201715028e-05 | 1.3471100857514e-05 |
| 72 | 0.99998917770835 | 2.16445833012253e-05 | 1.08222916506127e-05 |
| 73 | 0.999996689789958 | 6.62042008388212e-06 | 3.31021004194106e-06 |
| 74 | 0.999999399729427 | 1.20054114659967e-06 | 6.00270573299837e-07 |
| 75 | 0.999999966445296 | 6.71094070998668e-08 | 3.35547035499334e-08 |
| 76 | 0.99999999013879 | 1.97224193762624e-08 | 9.86120968813121e-09 |
| 77 | 0.999999998507687 | 2.98462531900296e-09 | 1.49231265950148e-09 |
| 78 | 0.999999999088507 | 1.82298529599818e-09 | 9.11492647999088e-10 |
| 79 | 0.99999999893013 | 2.13973875416854e-09 | 1.06986937708427e-09 |
| 80 | 0.999999999588766 | 8.22467335491315e-10 | 4.11233667745657e-10 |
| 81 | 0.999999999654112 | 6.91776473647855e-10 | 3.45888236823928e-10 |
| 82 | 0.999999999667615 | 6.64770964451768e-10 | 3.32385482225884e-10 |
| 83 | 0.999999999257197 | 1.48560656561539e-09 | 7.42803282807697e-10 |
| 84 | 0.999999998173098 | 3.65380385217734e-09 | 1.82690192608867e-09 |
| 85 | 0.999999996615135 | 6.7697299322667e-09 | 3.38486496613335e-09 |
| 86 | 0.99999999587275 | 8.25450061269767e-09 | 4.12725030634884e-09 |
| 87 | 0.999999997788087 | 4.42382545404557e-09 | 2.21191272702278e-09 |
| 88 | 0.9999999995218 | 9.56400530839021e-10 | 4.78200265419511e-10 |
| 89 | 0.999999999690933 | 6.18133881016318e-10 | 3.09066940508159e-10 |
| 90 | 0.999999999861415 | 2.77171001815779e-10 | 1.38585500907890e-10 |
| 91 | 0.999999999469943 | 1.06011401170186e-09 | 5.30057005850930e-10 |
| 92 | 0.999999999688375 | 6.23250090768028e-10 | 3.11625045384014e-10 |
| 93 | 0.999999998821499 | 2.35700266382858e-09 | 1.17850133191429e-09 |
| 94 | 0.999999995727858 | 8.54428427075783e-09 | 4.27214213537891e-09 |
| 95 | 0.99999998776963 | 2.44607381196074e-08 | 1.22303690598037e-08 |
| 96 | 0.999999986016074 | 2.79678517551275e-08 | 1.39839258775638e-08 |
| 97 | 0.999999965790834 | 6.84183328353116e-08 | 3.42091664176558e-08 |
| 98 | 0.999999853071824 | 2.93856351688199e-07 | 1.46928175844099e-07 |
| 99 | 0.999999592796384 | 8.14407231359573e-07 | 4.07203615679786e-07 |
| 100 | 0.999998508730088 | 2.98253982492740e-06 | 1.49126991246370e-06 |
| 101 | 0.99999521702495 | 9.56595010163853e-06 | 4.78297505081927e-06 |
| 102 | 0.99998579954688 | 2.84009062391987e-05 | 1.42004531195994e-05 |
| 103 | 0.999961285074688 | 7.74298506231637e-05 | 3.87149253115818e-05 |
| 104 | 0.99987442225303 | 0.000251155493938071 | 0.000125577746969035 |
| 105 | 0.999569666050091 | 0.000860667899817284 | 0.000430333949908642 |
| 106 | 0.999525961430994 | 0.000948077138011742 | 0.000474038569005871 |
| 107 | 0.998237780566248 | 0.00352443886750453 | 0.00176221943375226 |
| 108 | 0.995446241122877 | 0.00910751775424536 | 0.00455375887712268 |
| 109 | 0.990927217967523 | 0.0181455640649539 | 0.00907278203247697 |
| 110 | 0.982669947230076 | 0.034660105539848 | 0.017330052769924 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 43 | 0.48314606741573 | NOK |
| 5% type I error level | 48 | 0.539325842696629 | NOK |
| 10% type I error level | 58 | 0.651685393258427 | NOK |
