| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1881.92093448974 + 0.191100321953382Nikkei[t] + 0.289259310027567DJ_Indust[t] + 0.0145639845361721Goudprijs[t] -9.42821394015824Conjunct_Seizoenzuiver[t] -3.35520018942041Cons_vertrouw[t] + 32.6392820980445Alg_consumptie_index_BE[t] -254.219100476035Gem_rente_kasbon_5j[t] -1.32190944304161Maand[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) | -1881.92093448974 | 272.991974 | -6.8937 | 0 | 0 |
| Nikkei | 0.191100321953382 | 0.015432 | 12.3835 | 0 | 0 |
| DJ_Indust | 0.289259310027567 | 0.03376 | 8.5682 | 0 | 0 |
| Goudprijs | 0.0145639845361721 | 0.008322 | 1.7501 | 0.084975 | 0.042487 |
| Conjunct_Seizoenzuiver | -9.42821394015824 | 6.642913 | -1.4193 | 0.160744 | 0.080372 |
| Cons_vertrouw | -3.35520018942041 | 8.724572 | -0.3846 | 0.701852 | 0.350926 |
| Alg_consumptie_index_BE | 32.6392820980445 | 18.498163 | 1.7645 | 0.082502 | 0.041251 |
| Gem_rente_kasbon_5j | -254.219100476035 | 57.058457 | -4.4554 | 3.5e-05 | 1.8e-05 |
| Maand | -1.32190944304161 | 6.377068 | -0.2073 | 0.836451 | 0.418226 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.983716693372244 |
| R-squared | 0.96769853281922 |
| Adjusted R-squared | 0.963596759208963 |
| F-TEST (value) | 235.921975410639 |
| F-TEST (DF numerator) | 8 |
| F-TEST (DF denominator) | 63 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 161.344873074614 |
| Sum Squared Residuals | 1640026.58825019 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2502.66 | 2707.67994551663 | -205.019945516626 |
| 2 | 2466.92 | 2516.97706924377 | -50.0570692437716 |
| 3 | 2513.17 | 2449.18616376271 | 63.9838362372944 |
| 4 | 2443.27 | 2451.40226291509 | -8.13226291509133 |
| 5 | 2293.41 | 2412.62913109455 | -119.219131094554 |
| 6 | 2070.83 | 2099.50131485049 | -28.6713148504925 |
| 7 | 2029.6 | 2144.89554104893 | -115.295541048933 |
| 8 | 2052.02 | 2074.61294122374 | -22.5929412237412 |
| 9 | 1864.44 | 1929.17218579978 | -64.7321857997813 |
| 10 | 1670.07 | 1573.19983875250 | 96.8701612474971 |
| 11 | 1810.99 | 1657.15518938415 | 153.834810615853 |
| 12 | 1905.41 | 1846.80857765675 | 58.6014223432489 |
| 13 | 1862.83 | 1902.31990399739 | -39.4899039973921 |
| 14 | 2014.45 | 1834.30236372566 | 180.147636274342 |
| 15 | 2197.82 | 1979.00581391919 | 218.814186080813 |
| 16 | 2962.34 | 3038.01345391172 | -75.6734539117243 |
| 17 | 3047.03 | 3182.33655457386 | -135.306554573857 |
| 18 | 3032.6 | 3196.36506079008 | -163.765060790078 |
| 19 | 3504.37 | 3664.26620772756 | -159.896207727562 |
| 20 | 3801.06 | 3959.35323829092 | -158.293238290915 |
| 21 | 3857.62 | 3845.20043287096 | 12.4195671290381 |
| 22 | 3674.4 | 3526.62581228835 | 147.774187711654 |
| 23 | 3720.98 | 3667.21055535645 | 53.7694446435532 |
| 24 | 3844.49 | 3691.14506122603 | 153.344938773970 |
| 25 | 4116.68 | 4268.14222608313 | -151.462226083132 |
| 26 | 4105.18 | 4186.3025012722 | -81.1225012721991 |
| 27 | 4435.23 | 4567.10274279444 | -131.872742794436 |
| 28 | 4296.49 | 4295.70212830935 | 0.787871690651293 |
| 29 | 4202.52 | 4206.01681959499 | -3.49681959499111 |
| 30 | 4562.84 | 4591.18955058552 | -28.3495505855178 |
| 31 | 4621.4 | 4567.00897914014 | 54.3910208598633 |
| 32 | 4696.96 | 4572.62547954475 | 124.334520455245 |
| 33 | 4591.27 | 4377.82315737226 | 213.446842627739 |
| 34 | 4356.98 | 4193.71028777419 | 163.269712225814 |
| 35 | 4502.64 | 4406.17204489626 | 96.4679551037408 |
| 36 | 4443.91 | 4342.51306538464 | 101.396934615356 |
| 37 | 4290.89 | 4235.42587031606 | 55.4641296839441 |
| 38 | 4199.75 | 4037.66127687256 | 162.088723127439 |
| 39 | 4138.52 | 4012.51476357641 | 126.00523642359 |
| 40 | 3970.1 | 3809.55824857668 | 160.541751423318 |
| 41 | 3862.27 | 3693.79587479137 | 168.474125208635 |
| 42 | 3701.61 | 3508.57633496669 | 193.033665033308 |
| 43 | 3570.12 | 3506.70160827661 | 63.4183917233942 |
| 44 | 3801.06 | 3927.45022691712 | -126.390226917115 |
| 45 | 3895.51 | 4078.65670013303 | -183.146700133032 |
| 46 | 3917.96 | 3940.35999441493 | -22.3999944149300 |
| 47 | 3813.06 | 3911.68623431729 | -98.6262343172928 |
| 48 | 3667.03 | 3852.86926536805 | -185.839265368054 |
| 49 | 3494.17 | 3775.72657397467 | -281.556573974671 |
| 50 | 3363.99 | 3527.35301809864 | -163.363018098644 |
| 51 | 3295.32 | 3266.74859776635 | 28.5714022336481 |
| 52 | 3277.01 | 3303.63485148703 | -26.6248514870341 |
| 53 | 3257.16 | 3166.85811840313 | 90.301881596873 |
| 54 | 3161.69 | 3100.15097264666 | 61.5390273533421 |
| 55 | 3097.31 | 2988.54797975787 | 108.762020242126 |
| 56 | 3061.26 | 2851.19789412654 | 210.062105873457 |
| 57 | 3119.31 | 2856.04379988562 | 263.26620011438 |
| 58 | 3106.22 | 3019.68328332930 | 86.5367166707018 |
| 59 | 3080.58 | 2960.16765850692 | 120.412341493079 |
| 60 | 2981.85 | 2818.62664994969 | 163.223350050313 |
| 61 | 2921.44 | 2771.31165379598 | 150.128346204023 |
| 62 | 2849.27 | 2664.91029184400 | 184.359708155996 |
| 63 | 2756.76 | 2530.5747812473 | 226.185218752702 |
| 64 | 2645.64 | 2569.93281266683 | 75.70718733317 |
| 65 | 2497.84 | 2514.72623002729 | -16.8862300272921 |
| 66 | 2448.05 | 2584.63066430323 | -136.580664303231 |
| 67 | 2454.62 | 2730.34588266038 | -275.725882660376 |
| 68 | 2407.6 | 2589.29918247106 | -181.699182471058 |
| 69 | 2472.81 | 2878.36232326484 | -405.552323264843 |
| 70 | 2408.64 | 2698.24117148639 | -289.601171486394 |
| 71 | 2440.25 | 2595.6434602399 | -155.393460239898 |
| 72 | 2350.44 | 2650.34214685445 | -299.902146854452 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 12 | 0.0181248920453580 | 0.0362497840907159 | 0.981875107954642 |
| 13 | 0.0145253859466247 | 0.0290507718932494 | 0.985474614053375 |
| 14 | 0.0402136461046304 | 0.0804272922092608 | 0.95978635389537 |
| 15 | 0.0172033280403929 | 0.0344066560807857 | 0.982796671959607 |
| 16 | 0.0120453350520615 | 0.0240906701041230 | 0.987954664947938 |
| 17 | 0.00454280300315557 | 0.00908560600631114 | 0.995457196996844 |
| 18 | 0.00167005323363354 | 0.00334010646726709 | 0.998329946766366 |
| 19 | 0.00651930625397917 | 0.0130386125079583 | 0.99348069374602 |
| 20 | 0.00436271303512712 | 0.00872542607025424 | 0.995637286964873 |
| 21 | 0.00339545451314511 | 0.00679090902629022 | 0.996604545486855 |
| 22 | 0.00164665163143871 | 0.00329330326287743 | 0.99835334836856 |
| 23 | 0.000966723676538598 | 0.00193344735307720 | 0.999033276323461 |
| 24 | 0.000979019705114744 | 0.00195803941022949 | 0.999020980294885 |
| 25 | 0.00316134017593127 | 0.00632268035186254 | 0.996838659824069 |
| 26 | 0.00659004143790365 | 0.0131800828758073 | 0.993409958562096 |
| 27 | 0.0119068436090170 | 0.0238136872180340 | 0.988093156390983 |
| 28 | 0.0180566011911639 | 0.0361132023823277 | 0.981943398808836 |
| 29 | 0.0136772448206461 | 0.0273544896412922 | 0.986322755179354 |
| 30 | 0.0121186342061726 | 0.0242372684123452 | 0.987881365793827 |
| 31 | 0.0111202288716439 | 0.0222404577432877 | 0.988879771128356 |
| 32 | 0.0112564763552908 | 0.0225129527105817 | 0.98874352364471 |
| 33 | 0.0104560214818918 | 0.0209120429637836 | 0.989543978518108 |
| 34 | 0.00738119019312186 | 0.0147623803862437 | 0.992618809806878 |
| 35 | 0.00433883937729519 | 0.00867767875459038 | 0.995661160622705 |
| 36 | 0.00373870856010668 | 0.00747741712021337 | 0.996261291439893 |
| 37 | 0.00216292026159969 | 0.00432584052319937 | 0.9978370797384 |
| 38 | 0.00163805972979537 | 0.00327611945959073 | 0.998361940270205 |
| 39 | 0.00124108600509434 | 0.00248217201018868 | 0.998758913994906 |
| 40 | 0.00154118115275632 | 0.00308236230551263 | 0.998458818847244 |
| 41 | 0.00174383055769052 | 0.00348766111538103 | 0.99825616944231 |
| 42 | 0.00132744290718193 | 0.00265488581436386 | 0.998672557092818 |
| 43 | 0.00318442601334118 | 0.00636885202668236 | 0.99681557398666 |
| 44 | 0.0112412326041063 | 0.0224824652082126 | 0.988758767395894 |
| 45 | 0.0149128352144064 | 0.0298256704288128 | 0.985087164785594 |
| 46 | 0.0283909735368529 | 0.0567819470737058 | 0.971609026463147 |
| 47 | 0.0323875488094735 | 0.064775097618947 | 0.967612451190527 |
| 48 | 0.0601679196955994 | 0.120335839391199 | 0.9398320803044 |
| 49 | 0.0521190784677275 | 0.104238156935455 | 0.947880921532273 |
| 50 | 0.0419667548951798 | 0.0839335097903596 | 0.95803324510482 |
| 51 | 0.0659438229610741 | 0.131887645922148 | 0.934056177038926 |
| 52 | 0.048473024841417 | 0.096946049682834 | 0.951526975158583 |
| 53 | 0.0328086403856169 | 0.0656172807712337 | 0.967191359614383 |
| 54 | 0.0295480117278258 | 0.0590960234556516 | 0.970451988272174 |
| 55 | 0.0552847884166502 | 0.110569576833300 | 0.94471521158335 |
| 56 | 0.0424297702554532 | 0.0848595405109064 | 0.957570229744547 |
| 57 | 0.0420662166893334 | 0.0841324333786668 | 0.957933783310667 |
| 58 | 0.0348674605825541 | 0.0697349211651082 | 0.965132539417446 |
| 59 | 0.0270167406323069 | 0.0540334812646137 | 0.972983259367693 |
| 60 | 0.832276910663795 | 0.335446178672410 | 0.167723089336205 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 17 | 0.346938775510204 | NOK |
| 5% type I error level | 33 | 0.673469387755102 | NOK |
| 10% type I error level | 44 | 0.897959183673469 | NOK |
