| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -203.213533723905 + 0.0883416305203353Nikkei[t] + 0.136821877484492DJ_Indust[t] -0.00815216372016688Goudprijs[t] -7.96149871283661Conjunct_Seizoenzuiver[t] + 9.82043023620331Cons_vertrouw[t] -8.46487453756446Alg_consumptie_index_BE[t] -242.695105335560Gem_rente_kasbon_5j[t] + 0.448559634759112Y1[t] -0.0614225929551998Y2[t] + 0.0748163256792463Y3[t] + 0.0777147845854144Y4[t] + 3.31975176170273t + 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) | -203.213533723905 | 364.963374 | -0.5568 | 0.579961 | 0.28998 |
| Nikkei | 0.0883416305203353 | 0.012873 | 6.8626 | 0 | 0 |
| DJ_Indust | 0.136821877484492 | 0.0279 | 4.9041 | 9e-06 | 4e-06 |
| Goudprijs | -0.00815216372016688 | 0.01353 | -0.6025 | 0.549348 | 0.274674 |
| Conjunct_Seizoenzuiver | -7.96149871283661 | 4.120919 | -1.932 | 0.058617 | 0.029308 |
| Cons_vertrouw | 9.82043023620331 | 4.577992 | 2.1451 | 0.036457 | 0.018228 |
| Alg_consumptie_index_BE | -8.46487453756446 | 11.338721 | -0.7465 | 0.458576 | 0.229288 |
| Gem_rente_kasbon_5j | -242.695105335560 | 40.289138 | -6.0238 | 0 | 0 |
| Y1 | 0.448559634759112 | 0.095333 | 4.7052 | 1.8e-05 | 9e-06 |
| Y2 | -0.0614225929551998 | 0.111788 | -0.5495 | 0.584958 | 0.292479 |
| Y3 | 0.0748163256792463 | 0.110224 | 0.6788 | 0.500185 | 0.250093 |
| Y4 | 0.0777147845854144 | 0.076327 | 1.0182 | 0.31313 | 0.156565 |
| t | 3.31975176170273 | 3.587279 | 0.9254 | 0.358863 | 0.179432 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.995516590819115 |
| R-squared | 0.991053282596114 |
| Adjusted R-squared | 0.989065123173029 |
| F-TEST (value) | 498.477773506692 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 54 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 88.5147247296587 |
| Sum Squared Residuals | 423082.250674232 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2454.62 | 2659.41920362837 | -204.799203628373 |
| 2 | 2448.05 | 2541.93556256269 | -93.8855625626862 |
| 3 | 2497.84 | 2555.91613445387 | -58.0761344538721 |
| 4 | 2645.64 | 2608.99244986361 | 36.6475501363918 |
| 5 | 2756.76 | 2583.70190270218 | 173.058097297817 |
| 6 | 2849.27 | 2704.03979724598 | 145.230202754016 |
| 7 | 2921.44 | 2842.78645399472 | 78.6535460052832 |
| 8 | 2981.85 | 2918.04978651937 | 63.8002134806256 |
| 9 | 3080.58 | 3080.18552436485 | 0.394475635151281 |
| 10 | 3106.22 | 3166.28843998531 | -60.0684399853104 |
| 11 | 3119.31 | 3092.74315548307 | 26.5668445169261 |
| 12 | 3061.26 | 3056.82589415939 | 4.434105840607 |
| 13 | 3097.31 | 3100.19504336697 | -2.88504336697123 |
| 14 | 3161.69 | 3187.7893931429 | -26.0993931429015 |
| 15 | 3257.16 | 3243.55605369406 | 13.6039463059389 |
| 16 | 3277.01 | 3281.93014502248 | -4.92014502247929 |
| 17 | 3295.32 | 3347.25156043464 | -51.9315604346404 |
| 18 | 3363.99 | 3450.2886889283 | -86.2986889282974 |
| 19 | 3494.17 | 3615.31060874214 | -121.140608742139 |
| 20 | 3667.03 | 3734.99754659932 | -67.9675465993223 |
| 21 | 3813.06 | 3838.11036554343 | -25.050365543431 |
| 22 | 3917.96 | 3894.86521947672 | 23.0947805232830 |
| 23 | 3895.51 | 3972.03584861159 | -76.5258486115918 |
| 24 | 3801.06 | 3847.75211774549 | -46.6921177454914 |
| 25 | 3570.12 | 3714.74121197296 | -144.621211972964 |
| 26 | 3701.61 | 3603.46725960944 | 98.1427403905601 |
| 27 | 3862.27 | 3761.76937591638 | 100.500624083617 |
| 28 | 3970.1 | 3894.18212616223 | 75.917873837766 |
| 29 | 4138.52 | 4065.57244798251 | 72.9475520174938 |
| 30 | 4199.75 | 4152.29035403403 | 47.4596459659651 |
| 31 | 4290.89 | 4180.74605303013 | 110.143946969868 |
| 32 | 4443.91 | 4343.89356144805 | 100.016438551948 |
| 33 | 4502.64 | 4434.40355447463 | 68.2364455253744 |
| 34 | 4356.98 | 4354.98570935479 | 1.99429064520637 |
| 35 | 4591.27 | 4421.81018660151 | 169.459813398486 |
| 36 | 4696.96 | 4663.55804512789 | 33.4019548721148 |
| 37 | 4621.4 | 4636.3311982691 | -14.9311982691006 |
| 38 | 4562.84 | 4576.68871303656 | -13.8487130365623 |
| 39 | 4202.52 | 4415.51234255912 | -212.992342559122 |
| 40 | 4296.49 | 4294.35415271497 | 2.13584728502725 |
| 41 | 4435.23 | 4471.02998433135 | -35.7999843313469 |
| 42 | 4105.18 | 4229.14070327235 | -123.960703272347 |
| 43 | 4116.68 | 4147.34408845802 | -30.664088458021 |
| 44 | 3844.49 | 3843.16521232370 | 1.32478767630371 |
| 45 | 3720.98 | 3740.23749408303 | -19.2574940830285 |
| 46 | 3674.4 | 3636.9857864662 | 37.4142135338013 |
| 47 | 3857.62 | 3762.81994038574 | 94.800059614259 |
| 48 | 3801.06 | 3789.29676478551 | 11.7632352144877 |
| 49 | 3504.37 | 3508.77366761102 | -4.40366761102274 |
| 50 | 3032.6 | 3086.16492879333 | -53.5649287933256 |
| 51 | 3047.03 | 2952.45109207508 | 94.5789079249208 |
| 52 | 2962.34 | 2975.40150003758 | -13.0615000375790 |
| 53 | 2197.82 | 2319.6498329147 | -121.829832914701 |
| 54 | 2014.45 | 1946.76607366469 | 67.6839263353147 |
| 55 | 1862.83 | 1948.58907253136 | -85.7590725313615 |
| 56 | 1905.41 | 1856.68702295079 | 48.7229770492113 |
| 57 | 1810.99 | 1692.54657881721 | 118.443421182787 |
| 58 | 1670.07 | 1668.85437627914 | 1.21562372086194 |
| 59 | 1864.44 | 1800.73897813541 | 63.7010218645875 |
| 60 | 2052.02 | 2007.22681279366 | 44.7931872063417 |
| 61 | 2029.6 | 2106.75674890070 | -77.1567489006961 |
| 62 | 2070.83 | 2095.46278865392 | -24.6327886539187 |
| 63 | 2293.41 | 2327.02320810613 | -33.6132081061270 |
| 64 | 2443.27 | 2457.91506716159 | -14.6450671615913 |
| 65 | 2513.17 | 2475.49937611897 | 37.6706238810282 |
| 66 | 2466.92 | 2534.16777929508 | -67.247779295082 |
| 67 | 2502.66 | 2552.28193248797 | -49.621932487967 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0447137874999940 | 0.0894275749999879 | 0.955286212500006 |
| 17 | 0.061757068406472 | 0.123514136812944 | 0.938242931593528 |
| 18 | 0.040667329611643 | 0.081334659223286 | 0.959332670388357 |
| 19 | 0.0281458271947754 | 0.0562916543895507 | 0.971854172805225 |
| 20 | 0.0153592209311108 | 0.0307184418622217 | 0.98464077906889 |
| 21 | 0.00786178427128056 | 0.0157235685425611 | 0.99213821572872 |
| 22 | 0.0033243110952363 | 0.0066486221904726 | 0.996675688904764 |
| 23 | 0.00564916844256068 | 0.0112983368851214 | 0.99435083155744 |
| 24 | 0.00579593022632133 | 0.0115918604526427 | 0.994204069773679 |
| 25 | 0.0335891409288954 | 0.0671782818577908 | 0.966410859071105 |
| 26 | 0.486502654773996 | 0.973005309547992 | 0.513497345226004 |
| 27 | 0.448537037423198 | 0.897074074846397 | 0.551462962576802 |
| 28 | 0.532422533525277 | 0.935154932949447 | 0.467577466474723 |
| 29 | 0.496174563549343 | 0.992349127098685 | 0.503825436450657 |
| 30 | 0.616651276336791 | 0.766697447326418 | 0.383348723663209 |
| 31 | 0.63681864730105 | 0.726362705397899 | 0.363181352698950 |
| 32 | 0.656854213157489 | 0.686291573685022 | 0.343145786842511 |
| 33 | 0.613672464474116 | 0.772655071051767 | 0.386327535525884 |
| 34 | 0.614032041834531 | 0.771935916330937 | 0.385967958165469 |
| 35 | 0.803667495903999 | 0.392665008192002 | 0.196332504096001 |
| 36 | 0.771227857851337 | 0.457544284297326 | 0.228772142148663 |
| 37 | 0.774400498427645 | 0.451199003144709 | 0.225599501572355 |
| 38 | 0.84900093228862 | 0.301998135422759 | 0.150999067711380 |
| 39 | 0.968676335591503 | 0.0626473288169948 | 0.0313236644084974 |
| 40 | 0.95263339082761 | 0.0947332183447816 | 0.0473666091723908 |
| 41 | 0.93853644056616 | 0.122927118867679 | 0.0614635594338396 |
| 42 | 0.953527123744608 | 0.0929457525107846 | 0.0464728762553923 |
| 43 | 0.97067560856031 | 0.0586487828793783 | 0.0293243914396891 |
| 44 | 0.969737457042438 | 0.0605250859151244 | 0.0302625429575622 |
| 45 | 0.970485602580258 | 0.0590287948394842 | 0.0295143974197421 |
| 46 | 0.941883756738354 | 0.116232486523293 | 0.0581162432616464 |
| 47 | 0.89530855205419 | 0.209382895891621 | 0.104691447945811 |
| 48 | 0.824230435664718 | 0.351539128670563 | 0.175769564335282 |
| 49 | 0.713621893797073 | 0.572756212405853 | 0.286378106202927 |
| 50 | 0.885103114975875 | 0.22979377004825 | 0.114896885024125 |
| 51 | 0.811012178222632 | 0.377975643554735 | 0.188987821777368 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0277777777777778 | NOK |
| 5% type I error level | 5 | 0.138888888888889 | NOK |
| 10% type I error level | 15 | 0.416666666666667 | NOK |
