| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -204.722456427373 + 0.177400378019995Nikkei[t] + 0.220142962023709DJ_Indust[t] -0.0793121795843404Goudprijs[t] + 8.83568088071237Conjunct_Seizoenzuiver[t] -8.23572530490068Cons_vertrouw[t] + 18.5328439084293Alg_consumptie_index_BE[t] -280.1553727945Gem_rente_kasbon_5j[t] + 161.090413781246M1[t] + 247.445572641716M2[t] + 189.272612931734M3[t] + 111.726785113516M4[t] + 83.0601724822622M5[t] -3.16898498687954M6[t] + 12.8625451025933M7[t] + 4.30907126374565M8[t] + 35.700574039436M9[t] + 112.037528681405M10[t] + 84.5376550919719M11[t] + 22.318614447017t + 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) | -204.722456427373 | 567.980524 | -0.3604 | 0.719979 | 0.359989 |
| Nikkei | 0.177400378019995 | 0.015 | 11.8267 | 0 | 0 |
| DJ_Indust | 0.220142962023709 | 0.038735 | 5.6833 | 1e-06 | 0 |
| Goudprijs | -0.0793121795843404 | 0.025185 | -3.1492 | 0.002713 | 0.001356 |
| Conjunct_Seizoenzuiver | 8.83568088071237 | 7.893963 | 1.1193 | 0.268158 | 0.134079 |
| Cons_vertrouw | -8.23572530490068 | 8.790611 | -0.9369 | 0.353153 | 0.176576 |
| Alg_consumptie_index_BE | 18.5328439084293 | 18.131434 | 1.0221 | 0.311447 | 0.155724 |
| Gem_rente_kasbon_5j | -280.1553727945 | 57.69116 | -4.8561 | 1.1e-05 | 6e-06 |
| M1 | 161.090413781246 | 93.476107 | 1.7233 | 0.090771 | 0.045385 |
| M2 | 247.445572641716 | 100.677285 | 2.4578 | 0.017348 | 0.008674 |
| M3 | 189.272612931734 | 94.80828 | 1.9964 | 0.051142 | 0.025571 |
| M4 | 111.726785113516 | 92.897672 | 1.2027 | 0.234545 | 0.117273 |
| M5 | 83.0601724822622 | 87.502124 | 0.9492 | 0.346892 | 0.173446 |
| M6 | -3.16898498687954 | 90.438848 | -0.035 | 0.972182 | 0.486091 |
| M7 | 12.8625451025933 | 91.498011 | 0.1406 | 0.888747 | 0.444374 |
| M8 | 4.30907126374565 | 94.313348 | 0.0457 | 0.963733 | 0.481867 |
| M9 | 35.700574039436 | 91.773 | 0.389 | 0.698858 | 0.349429 |
| M10 | 112.037528681405 | 92.275599 | 1.2142 | 0.230171 | 0.115086 |
| M11 | 84.5376550919719 | 88.055742 | 0.96 | 0.341474 | 0.170737 |
| t | 22.318614447017 | 5.836967 | 3.8237 | 0.000354 | 0.000177 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.988447189712945 |
| R-squared | 0.97702784685142 |
| Adjusted R-squared | 0.968634175508669 |
| F-TEST (value) | 116.400536422631 |
| F-TEST (DF numerator) | 19 |
| F-TEST (DF denominator) | 52 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 149.766092731832 |
| Sum Squared Residuals | 1166353.89167231 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2350.44 | 2457.19413196077 | -106.754131960772 |
| 2 | 2440.25 | 2549.12448662837 | -108.874486628374 |
| 3 | 2408.64 | 2625.97178134145 | -217.331781341454 |
| 4 | 2472.81 | 2747.03073202865 | -274.22073202865 |
| 5 | 2407.6 | 2562.79767991999 | -155.197679919987 |
| 6 | 2454.62 | 2574.70138828411 | -120.081388284106 |
| 7 | 2448.05 | 2556.89086760979 | -108.840867609793 |
| 8 | 2497.84 | 2450.72649477586 | 47.1135052241398 |
| 9 | 2645.64 | 2558.13306496033 | 87.5069350396716 |
| 10 | 2756.76 | 2612.99804019027 | 143.761959809726 |
| 11 | 2849.27 | 2685.56989857376 | 163.700101426239 |
| 12 | 2921.44 | 2700.82327186014 | 220.616728139856 |
| 13 | 2981.85 | 2970.40997695728 | 11.4400230427194 |
| 14 | 3080.58 | 3154.54727189964 | -73.9672718996395 |
| 15 | 3106.22 | 3147.43852908107 | -41.2185290810652 |
| 16 | 3119.31 | 2924.76125570302 | 194.548744296976 |
| 17 | 3061.26 | 2921.63048091606 | 139.629519083944 |
| 18 | 3097.31 | 2929.66638572503 | 167.643614274971 |
| 19 | 3161.69 | 3059.96349556821 | 101.726504431785 |
| 20 | 3257.16 | 3128.60208016773 | 128.557919832274 |
| 21 | 3277.01 | 3353.1645764035 | -76.1545764034988 |
| 22 | 3295.32 | 3384.93807770034 | -89.6180777003413 |
| 23 | 3363.99 | 3577.88541387396 | -213.895413873962 |
| 24 | 3494.17 | 3654.62023521827 | -160.450235218271 |
| 25 | 3667.03 | 3812.5768870342 | -145.546887034203 |
| 26 | 3813.06 | 3976.84952769536 | -163.78952769536 |
| 27 | 3917.96 | 4003.99128282905 | -86.031282829049 |
| 28 | 3895.51 | 3985.23019143339 | -89.7201914333885 |
| 29 | 3801.06 | 3740.09181366709 | 60.9681863329113 |
| 30 | 3570.12 | 3477.08325846111 | 93.0367415388856 |
| 31 | 3701.61 | 3457.93546917912 | 243.674530820884 |
| 32 | 3862.27 | 3631.36036248836 | 230.90963751164 |
| 33 | 3970.1 | 3836.65793640225 | 133.44206359775 |
| 34 | 4138.52 | 4124.85245039267 | 13.6675496073332 |
| 35 | 4199.75 | 4050.88530692903 | 148.864693070973 |
| 36 | 4290.89 | 4261.58696403532 | 29.3030359646797 |
| 37 | 4443.91 | 4441.6502731501 | 2.25972684989876 |
| 38 | 4502.64 | 4485.98977698646 | 16.6502230135373 |
| 39 | 4356.98 | 4301.5762650501 | 55.4037349498997 |
| 40 | 4591.27 | 4395.30283486492 | 195.967165135077 |
| 41 | 4696.96 | 4585.94842480073 | 111.011575199273 |
| 42 | 4621.4 | 4555.7874283284 | 65.6125716715979 |
| 43 | 4562.84 | 4597.77025661072 | -34.9302566107224 |
| 44 | 4202.52 | 4240.52368549951 | -38.0036854995115 |
| 45 | 4296.49 | 4285.91149260098 | 10.5785073990201 |
| 46 | 4435.23 | 4509.52120170601 | -74.2912017060101 |
| 47 | 4105.18 | 4158.55265483927 | -53.3726548392649 |
| 48 | 4116.68 | 4097.4761433975 | 19.2038566024962 |
| 49 | 3844.49 | 3653.92798637897 | 190.562013621027 |
| 50 | 3720.98 | 3664.35861272375 | 56.6213872762538 |
| 51 | 3674.4 | 3524.29355076329 | 150.106449236707 |
| 52 | 3857.62 | 3842.89534489995 | 14.7246551000516 |
| 53 | 3801.06 | 3978.68360376993 | -177.623603769927 |
| 54 | 3504.37 | 3631.39353313422 | -127.023533134216 |
| 55 | 3032.6 | 3152.21281263012 | -119.612812630116 |
| 56 | 3047.03 | 3251.44229105332 | -204.412291053316 |
| 57 | 2962.34 | 3068.07875184762 | -105.738751847617 |
| 58 | 2197.82 | 2117.63595509976 | 80.184044900241 |
| 59 | 2014.45 | 1969.42429064433 | 45.025709355671 |
| 60 | 1862.83 | 1834.11773222056 | 28.7122677794436 |
| 61 | 1905.41 | 1857.37074451867 | 48.0392554813297 |
| 62 | 1810.99 | 1537.63032406642 | 273.359675933582 |
| 63 | 1670.07 | 1530.99859093504 | 139.071409064962 |
| 64 | 1864.44 | 1905.73964107007 | -41.2996410700661 |
| 65 | 2052.02 | 2030.80799692621 | 21.2120030737858 |
| 66 | 2029.6 | 2108.78800606713 | -79.188006067132 |
| 67 | 2070.83 | 2152.84709840204 | -82.0170984020375 |
| 68 | 2293.41 | 2457.57508601523 | -164.165086015227 |
| 69 | 2443.27 | 2492.90417778533 | -49.6341777853266 |
| 70 | 2513.17 | 2586.87427491095 | -73.7042749109487 |
| 71 | 2466.92 | 2557.24243513966 | -90.322435139655 |
| 72 | 2502.66 | 2640.04565326821 | -137.385653268205 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 23 | 0.0199077415538393 | 0.0398154831076786 | 0.98009225844616 |
| 24 | 0.0287406105091539 | 0.0574812210183079 | 0.971259389490846 |
| 25 | 0.0261961990211743 | 0.0523923980423487 | 0.973803800978826 |
| 26 | 0.02105502897394 | 0.0421100579478801 | 0.97894497102606 |
| 27 | 0.013064701427931 | 0.026129402855862 | 0.98693529857207 |
| 28 | 0.098501067572858 | 0.197002135145716 | 0.901498932427142 |
| 29 | 0.377927279507537 | 0.755854559015074 | 0.622072720492463 |
| 30 | 0.89464735434311 | 0.21070529131378 | 0.10535264565689 |
| 31 | 0.86114189566001 | 0.277716208679979 | 0.13885810433999 |
| 32 | 0.811811311370217 | 0.376377377259565 | 0.188188688629783 |
| 33 | 0.741153883182425 | 0.517692233635149 | 0.258846116817574 |
| 34 | 0.756442761444181 | 0.487114477111637 | 0.243557238555819 |
| 35 | 0.709692932377164 | 0.580614135245672 | 0.290307067622836 |
| 36 | 0.627915847600644 | 0.744168304798711 | 0.372084152399356 |
| 37 | 0.592671158735817 | 0.814657682528366 | 0.407328841264183 |
| 38 | 0.633870455774966 | 0.732259088450069 | 0.366129544225034 |
| 39 | 0.697138685846532 | 0.605722628306937 | 0.302861314153468 |
| 40 | 0.608617306015579 | 0.782765387968842 | 0.391382693984421 |
| 41 | 0.5366390446716 | 0.9267219106568 | 0.4633609553284 |
| 42 | 0.513319342451182 | 0.973361315097635 | 0.486680657548818 |
| 43 | 0.535230888688171 | 0.929538222623657 | 0.464769111311829 |
| 44 | 0.86084784384436 | 0.27830431231128 | 0.13915215615564 |
| 45 | 0.90797837654516 | 0.184043246909679 | 0.0920216234548395 |
| 46 | 0.910362566296719 | 0.179274867406561 | 0.0896374337032807 |
| 47 | 0.945238893300655 | 0.109522213398691 | 0.0547611066993455 |
| 48 | 0.892001695304251 | 0.215996609391498 | 0.107998304695749 |
| 49 | 0.776095664231486 | 0.447808671537028 | 0.223904335768514 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 3 | 0.111111111111111 | NOK |
| 10% type I error level | 5 | 0.185185185185185 | NOK |
