| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1829.91346353290 + 0.0932493209745398Nikkei[t] + 0.340625474153254DJ_Indust[t] -0.0461339961375057Goudprijs[t] -3.13234058387437Conjunct_Seizoenzuiver[t] -3.40204073251154Cons_vertrouw[t] -40.6029474729970Alg_consumptie_index_BE[t] + 46.1458989103431Gem_rente_kasbon_1j[t] + 166.234384975720M1[t] + 211.441636202194M2[t] + 145.674425778467M3[t] + 104.382150990713M4[t] + 55.5711165024448M5[t] -4.54850954972528M6[t] -9.27999423012134M7[t] -1.80540573459105M8[t] + 65.0922035015173M9[t] + 102.426980918673M10[t] + 78.1752424408722M11[t] + 7.05246043891046t + 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) | -1829.91346353290 | 396.703255 | -4.6128 | 1.1e-05 | 5e-06 |
| Nikkei | 0.0932493209745398 | 0.020151 | 4.6275 | 1e-05 | 5e-06 |
| DJ_Indust | 0.340625474153254 | 0.043937 | 7.7526 | 0 | 0 |
| Goudprijs | -0.0461339961375057 | 0.021183 | -2.1779 | 0.031512 | 0.015756 |
| Conjunct_Seizoenzuiver | -3.13234058387437 | 8.45438 | -0.3705 | 0.71171 | 0.355855 |
| Cons_vertrouw | -3.40204073251154 | 7.501817 | -0.4535 | 0.651069 | 0.325535 |
| Alg_consumptie_index_BE | -40.6029474729970 | 31.022759 | -1.3088 | 0.193277 | 0.096639 |
| Gem_rente_kasbon_1j | 46.1458989103431 | 47.00212 | 0.9818 | 0.328323 | 0.164161 |
| M1 | 166.234384975720 | 125.376334 | 1.3259 | 0.187576 | 0.093788 |
| M2 | 211.441636202194 | 125.977555 | 1.6784 | 0.096056 | 0.048028 |
| M3 | 145.674425778467 | 125.946402 | 1.1566 | 0.249881 | 0.124941 |
| M4 | 104.382150990713 | 126.440595 | 0.8255 | 0.410818 | 0.205409 |
| M5 | 55.5711165024448 | 123.926442 | 0.4484 | 0.654716 | 0.327358 |
| M6 | -4.54850954972528 | 124.324802 | -0.0366 | 0.97088 | 0.48544 |
| M7 | -9.27999423012134 | 124.738355 | -0.0744 | 0.940828 | 0.470414 |
| M8 | -1.80540573459105 | 124.942163 | -0.0144 | 0.988497 | 0.494248 |
| M9 | 65.0922035015173 | 124.563236 | 0.5226 | 0.60231 | 0.301155 |
| M10 | 102.426980918673 | 124.367276 | 0.8236 | 0.411926 | 0.205963 |
| M11 | 78.1752424408722 | 123.525367 | 0.6329 | 0.52811 | 0.264055 |
| t | 7.05246043891046 | 2.795793 | 2.5225 | 0.013056 | 0.006528 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.934941793727624 |
| R-squared | 0.874116157658626 |
| Adjusted R-squared | 0.852760862975715 |
| F-TEST (value) | 40.932057863762 |
| F-TEST (DF numerator) | 19 |
| F-TEST (DF denominator) | 112 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 288.923167774606 |
| Sum Squared Residuals | 9349378.85021425 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2534.02114712633 | 950.718852873674 |
| 2 | 3411.13 | 2608.47459422049 | 802.655405779515 |
| 3 | 3288.18 | 2801.49323261313 | 486.686767386874 |
| 4 | 3280.37 | 3084.88324623281 | 195.486753767186 |
| 5 | 3173.95 | 3184.69794168707 | -10.7479416870737 |
| 6 | 3165.26 | 3193.785816389 | -28.5258163889966 |
| 7 | 3092.71 | 3384.73266462838 | -292.022664628377 |
| 8 | 3053.05 | 3337.36663672685 | -284.316636726849 |
| 9 | 3181.96 | 3277.35744518876 | -95.3974451887568 |
| 10 | 2999.93 | 3168.8389390444 | -168.908939044399 |
| 11 | 3249.57 | 3357.25266260533 | -107.682662605332 |
| 12 | 3210.52 | 3417.82120965294 | -207.301209652936 |
| 13 | 3030.29 | 3658.79478612352 | -628.50478612352 |
| 14 | 2803.47 | 3487.00921576899 | -683.539215768993 |
| 15 | 2767.63 | 3410.92774799485 | -643.297747994851 |
| 16 | 2882.6 | 3524.22935742517 | -641.629357425168 |
| 17 | 2863.36 | 3126.80591151088 | -263.445911510876 |
| 18 | 2897.06 | 3039.12287284004 | -142.062872840037 |
| 19 | 3012.61 | 3078.60718789925 | -65.9971878992468 |
| 20 | 3142.95 | 3150.64062278773 | -7.6906227877324 |
| 21 | 3032.93 | 3176.30910125195 | -143.379101251949 |
| 22 | 3045.78 | 2964.45493270193 | 81.3250672980713 |
| 23 | 3110.52 | 2979.24232169379 | 131.277678306210 |
| 24 | 3013.24 | 2902.5991972917 | 110.640802708298 |
| 25 | 2987.1 | 3051.6343875118 | -64.5343875117993 |
| 26 | 2995.55 | 3109.55371282317 | -114.003712823174 |
| 27 | 2833.18 | 2754.88446768889 | 78.2955323111083 |
| 28 | 2848.96 | 2839.49838530974 | 9.4616146902643 |
| 29 | 2794.83 | 2933.93648470224 | -139.106484702244 |
| 30 | 2845.26 | 2850.05605188813 | -4.79605188812484 |
| 31 | 2915.02 | 2686.73642490625 | 228.283575093747 |
| 32 | 2892.63 | 2626.10126646834 | 266.528733531663 |
| 33 | 2604.42 | 2121.19596131122 | 483.224038688777 |
| 34 | 2641.65 | 2299.05784858478 | 342.592151415219 |
| 35 | 2659.81 | 2480.17418366772 | 179.635816332280 |
| 36 | 2638.53 | 2453.56456329165 | 184.965436708353 |
| 37 | 2720.25 | 2517.19035019666 | 203.05964980334 |
| 38 | 2745.88 | 2514.41301750447 | 231.466982495533 |
| 39 | 2735.7 | 2797.79835498630 | -62.0983549863025 |
| 40 | 2811.7 | 2679.8979854921 | 131.802014507899 |
| 41 | 2799.43 | 2644.01113865752 | 155.418861342482 |
| 42 | 2555.28 | 2348.67071174700 | 206.609288253004 |
| 43 | 2304.98 | 2010.83414680724 | 294.145853192756 |
| 44 | 2214.95 | 1991.2180815781 | 223.731918421901 |
| 45 | 2065.81 | 1830.89276859119 | 234.917231408806 |
| 46 | 1940.49 | 1791.83042103848 | 148.659578961518 |
| 47 | 2042 | 1982.58354969615 | 59.416450303854 |
| 48 | 1995.37 | 1857.72597228793 | 137.644027712072 |
| 49 | 1946.81 | 1993.81250060264 | -47.0025006026429 |
| 50 | 1765.9 | 1838.89297939166 | -72.9929793916587 |
| 51 | 1635.25 | 1814.84101277089 | -179.591012770887 |
| 52 | 1833.42 | 1890.77697325789 | -57.3569732578883 |
| 53 | 1910.43 | 1958.42336958905 | -47.9933695890542 |
| 54 | 1959.67 | 2117.66138002378 | -157.991380023775 |
| 55 | 1969.6 | 2216.31774557692 | -246.717745576917 |
| 56 | 2061.41 | 2254.13152166134 | -192.721521661344 |
| 57 | 2093.48 | 2416.70330871334 | -323.223308713343 |
| 58 | 2120.88 | 2597.23667872717 | -476.356678727169 |
| 59 | 2174.56 | 2495.02958803531 | -320.469588035314 |
| 60 | 2196.72 | 2563.62674243379 | -366.906742433792 |
| 61 | 2350.44 | 2934.02667244014 | -583.586672440137 |
| 62 | 2440.25 | 2990.70106878267 | -550.451068782671 |
| 63 | 2408.64 | 2903.76169847032 | -495.121698470325 |
| 64 | 2472.81 | 2900.43142873969 | -427.621428739685 |
| 65 | 2407.6 | 2669.06550322987 | -261.465503229871 |
| 66 | 2454.62 | 2746.57851880803 | -291.958518808029 |
| 67 | 2448.05 | 2665.6779765628 | -217.627976562798 |
| 68 | 2497.84 | 2600.56767631484 | -102.727676314841 |
| 69 | 2645.64 | 2748.01841625171 | -102.378416251705 |
| 70 | 2756.76 | 2689.56356005696 | 67.1964399430367 |
| 71 | 2849.27 | 2826.22269804069 | 23.0473019593099 |
| 72 | 2921.44 | 2878.74503547568 | 42.6949645243168 |
| 73 | 2981.85 | 3042.11576961814 | -60.2657696181366 |
| 74 | 3080.58 | 3153.26314225632 | -72.6831422563204 |
| 75 | 3106.22 | 3079.27143318082 | 26.948566819183 |
| 76 | 3119.31 | 2896.81616927087 | 222.493830729126 |
| 77 | 3061.26 | 2889.47106478781 | 171.788935212188 |
| 78 | 3097.31 | 2852.49225484560 | 244.817745154395 |
| 79 | 3161.69 | 2895.27782162376 | 266.412178376245 |
| 80 | 3257.16 | 2947.30052442882 | 309.859475571180 |
| 81 | 3277.01 | 3061.78557865143 | 215.224421348566 |
| 82 | 3295.32 | 3049.03014569472 | 246.289854305285 |
| 83 | 3363.99 | 3233.94162174953 | 130.048378250467 |
| 84 | 3494.17 | 3273.1038096405 | 221.066190359502 |
| 85 | 3667.03 | 3469.59436554623 | 197.435634453773 |
| 86 | 3813.06 | 3551.59897984671 | 261.461020153290 |
| 87 | 3917.96 | 3613.58137426977 | 304.378625730234 |
| 88 | 3895.51 | 3635.03947158522 | 260.470528414775 |
| 89 | 3801.06 | 3511.31668029212 | 289.743319707881 |
| 90 | 3570.12 | 3296.57809190852 | 273.541908091477 |
| 91 | 3701.61 | 3292.539780215 | 409.070219784997 |
| 92 | 3862.27 | 3456.6463434808 | 405.623656519201 |
| 93 | 3970.1 | 3693.417149394 | 276.682850606002 |
| 94 | 4138.52 | 3929.60727773035 | 208.912722269645 |
| 95 | 4199.75 | 3911.98732717343 | 287.762672826574 |
| 96 | 4290.89 | 4009.28330579892 | 281.606694201080 |
| 97 | 4443.91 | 4249.84639433541 | 194.063605664587 |
| 98 | 4502.64 | 4347.72760198227 | 154.912398017730 |
| 99 | 4356.98 | 4140.16728673163 | 216.812713268371 |
| 100 | 4591.27 | 4275.46543564731 | 315.804564352688 |
| 101 | 4696.96 | 4501.35724635082 | 195.602753649178 |
| 102 | 4621.4 | 4531.61533166643 | 89.7846683335693 |
| 103 | 4562.84 | 4612.75642372264 | -49.9164237226385 |
| 104 | 4202.52 | 4356.34248836437 | -153.822488364367 |
| 105 | 4296.49 | 4465.59284961735 | -169.102849617354 |
| 106 | 4435.23 | 4636.2088858338 | -200.978885833801 |
| 107 | 4105.18 | 4216.15173970512 | -110.971739705118 |
| 108 | 4116.68 | 4196.54296930608 | -79.8629693060819 |
| 109 | 3844.49 | 3823.10345843720 | 21.3865415627959 |
| 110 | 3720.98 | 3759.29648754651 | -38.3164875465073 |
| 111 | 3674.4 | 3497.55663226248 | 176.843367737517 |
| 112 | 3857.62 | 3806.1896936347 | 51.4303063652964 |
| 113 | 3801.06 | 3855.63915298752 | -54.5791529875167 |
| 114 | 3504.37 | 3560.90942307378 | -56.5394230737847 |
| 115 | 3032.6 | 3209.19378241135 | -176.59378241135 |
| 116 | 3047.03 | 3346.12310492481 | -299.093104924814 |
| 117 | 2962.34 | 3186.03912753891 | -223.699127538906 |
| 118 | 2197.82 | 2318.32840662910 | -120.508406629096 |
| 119 | 2014.45 | 2178.30728940516 | -163.857289405160 |
| 120 | 1862.83 | 2103.58222525945 | -240.752225259453 |
| 121 | 1905.41 | 2088.18016806193 | -182.770168061932 |
| 122 | 1810.99 | 1729.49919987674 | 81.490800123258 |
| 123 | 1670.07 | 1579.92675903092 | 90.1432409690804 |
| 124 | 1864.44 | 1924.78185340449 | -60.3418534044938 |
| 125 | 2052.02 | 2087.23550620509 | -35.2155062050931 |
| 126 | 2029.6 | 2162.4795468097 | -132.879546809699 |
| 127 | 2070.83 | 2219.86604564642 | -149.036045646417 |
| 128 | 2293.41 | 2458.78173326400 | -165.371733263996 |
| 129 | 2443.27 | 2596.13829349014 | -152.868293490137 |
| 130 | 2513.17 | 2641.39290395831 | -128.222903958309 |
| 131 | 2466.92 | 2575.12701822777 | -108.207018227771 |
| 132 | 2502.66 | 2586.45496956136 | -83.7949695613586 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 23 | 0.171201136977058 | 0.342402273954116 | 0.828798863022942 |
| 24 | 0.0779723137856717 | 0.155944627571343 | 0.922027686214328 |
| 25 | 0.0444801723490121 | 0.0889603446980242 | 0.955519827650988 |
| 26 | 0.0196782365506479 | 0.0393564731012958 | 0.980321763449352 |
| 27 | 0.00803252779852416 | 0.0160650555970483 | 0.991967472201476 |
| 28 | 0.00319344116587403 | 0.00638688233174806 | 0.996806558834126 |
| 29 | 0.00180028522530496 | 0.00360057045060993 | 0.998199714774695 |
| 30 | 0.000742583506381132 | 0.00148516701276226 | 0.999257416493619 |
| 31 | 0.000284796591511973 | 0.000569593183023947 | 0.999715203408488 |
| 32 | 9.23169701472007e-05 | 0.000184633940294401 | 0.999907683029853 |
| 33 | 8.74074571100918e-05 | 0.000174814914220184 | 0.99991259254289 |
| 34 | 3.22256377037297e-05 | 6.44512754074594e-05 | 0.999967774362296 |
| 35 | 1.47821129305409e-05 | 2.95642258610819e-05 | 0.99998521788707 |
| 36 | 7.36243329036599e-06 | 1.47248665807320e-05 | 0.99999263756671 |
| 37 | 2.64384878591697e-06 | 5.28769757183394e-06 | 0.999997356151214 |
| 38 | 1.81169348658725e-06 | 3.6233869731745e-06 | 0.999998188306513 |
| 39 | 1.46464270762981e-06 | 2.92928541525961e-06 | 0.999998535357292 |
| 40 | 1.80146198055577e-05 | 3.60292396111153e-05 | 0.999981985380194 |
| 41 | 0.000147090551491254 | 0.000294181102982508 | 0.999852909448509 |
| 42 | 7.57608683876598e-05 | 0.000151521736775320 | 0.999924239131612 |
| 43 | 3.99819601600853e-05 | 7.99639203201706e-05 | 0.99996001803984 |
| 44 | 3.80725861247481e-05 | 7.61451722494961e-05 | 0.999961927413875 |
| 45 | 4.44751874736872e-05 | 8.89503749473744e-05 | 0.999955524812526 |
| 46 | 6.02384948960904e-05 | 0.000120476989792181 | 0.999939761505104 |
| 47 | 0.000135499183546814 | 0.000270998367093628 | 0.999864500816453 |
| 48 | 0.000168906657031833 | 0.000337813314063667 | 0.999831093342968 |
| 49 | 0.000306030347062808 | 0.000612060694125617 | 0.999693969652937 |
| 50 | 0.000195783922554726 | 0.000391567845109452 | 0.999804216077445 |
| 51 | 0.000101148436240234 | 0.000202296872480468 | 0.99989885156376 |
| 52 | 8.75825791807284e-05 | 0.000175165158361457 | 0.99991241742082 |
| 53 | 0.000189898165397236 | 0.000379796330794471 | 0.999810101834603 |
| 54 | 0.000263425845778141 | 0.000526851691556282 | 0.999736574154222 |
| 55 | 0.000317992238531903 | 0.000635984477063806 | 0.999682007761468 |
| 56 | 0.000685833956803706 | 0.00137166791360741 | 0.999314166043196 |
| 57 | 0.000548665644336396 | 0.00109733128867279 | 0.999451334355664 |
| 58 | 0.00191857977758245 | 0.00383715955516489 | 0.998081420222418 |
| 59 | 0.00162703793271758 | 0.00325407586543516 | 0.998372962067282 |
| 60 | 0.00132786142134343 | 0.00265572284268687 | 0.998672138578657 |
| 61 | 0.00148704451386995 | 0.00297408902773989 | 0.99851295548613 |
| 62 | 0.00187621651522464 | 0.00375243303044927 | 0.998123783484775 |
| 63 | 0.0117777326197297 | 0.0235554652394595 | 0.98822226738027 |
| 64 | 0.121887956230068 | 0.243775912460135 | 0.878112043769932 |
| 65 | 0.424843139380452 | 0.849686278760904 | 0.575156860619548 |
| 66 | 0.64608928787568 | 0.70782142424864 | 0.35391071212432 |
| 67 | 0.823085101594466 | 0.353829796811069 | 0.176914898405534 |
| 68 | 0.904106371950703 | 0.191787256098595 | 0.0958936280492974 |
| 69 | 0.973552616927925 | 0.0528947661441493 | 0.0264473830720746 |
| 70 | 0.992145936801713 | 0.0157081263965740 | 0.00785406319828702 |
| 71 | 0.99826654308608 | 0.00346691382784194 | 0.00173345691392097 |
| 72 | 0.999804809523008 | 0.000390380953984355 | 0.000195190476992177 |
| 73 | 0.999985123793035 | 2.97524139291884e-05 | 1.48762069645942e-05 |
| 74 | 0.9999985364302 | 2.92713960125355e-06 | 1.46356980062678e-06 |
| 75 | 0.999999942972909 | 1.14054183072453e-07 | 5.70270915362265e-08 |
| 76 | 0.99999998901819 | 2.19636210976787e-08 | 1.09818105488393e-08 |
| 77 | 0.999999998214833 | 3.57033419681764e-09 | 1.78516709840882e-09 |
| 78 | 0.999999998985349 | 2.02930261770487e-09 | 1.01465130885243e-09 |
| 79 | 0.99999999875694 | 2.48612222058396e-09 | 1.24306111029198e-09 |
| 80 | 0.999999999335786 | 1.32842806664082e-09 | 6.64214033320408e-10 |
| 81 | 0.999999999403403 | 1.19319302796948e-09 | 5.96596513984742e-10 |
| 82 | 0.999999999394566 | 1.21086798880362e-09 | 6.0543399440181e-10 |
| 83 | 0.999999998624918 | 2.75016349222907e-09 | 1.37508174611454e-09 |
| 84 | 0.999999996645332 | 6.70933669451476e-09 | 3.35466834725738e-09 |
| 85 | 0.99999999403352 | 1.19329606682527e-08 | 5.96648033412636e-09 |
| 86 | 0.99999999145118 | 1.70976397591806e-08 | 8.5488198795903e-09 |
| 87 | 0.99999999471408 | 1.05718405349796e-08 | 5.28592026748981e-09 |
| 88 | 0.999999998965526 | 2.06894714538849e-09 | 1.03447357269425e-09 |
| 89 | 0.999999999878849 | 2.42302823955694e-10 | 1.21151411977847e-10 |
| 90 | 0.999999999980058 | 3.98849026661947e-11 | 1.99424513330974e-11 |
| 91 | 0.999999999941596 | 1.16807648829504e-10 | 5.8403824414752e-11 |
| 92 | 0.999999999794076 | 4.11848942936719e-10 | 2.05924471468359e-10 |
| 93 | 0.999999999089523 | 1.8209540439428e-09 | 9.104770219714e-10 |
| 94 | 0.999999998125887 | 3.74822513059431e-09 | 1.87411256529715e-09 |
| 95 | 0.999999991999762 | 1.60004754459736e-08 | 8.00023772298682e-09 |
| 96 | 0.999999972649137 | 5.47017251086111e-08 | 2.73508625543055e-08 |
| 97 | 0.999999901907827 | 1.96184346855913e-07 | 9.80921734279566e-08 |
| 98 | 0.999999580410647 | 8.39178706135815e-07 | 4.19589353067908e-07 |
| 99 | 0.999998575962715 | 2.84807456906469e-06 | 1.42403728453235e-06 |
| 100 | 0.999994961820986 | 1.00763580274477e-05 | 5.03817901372386e-06 |
| 101 | 0.999984194283636 | 3.16114327278508e-05 | 1.58057163639254e-05 |
| 102 | 0.999957488633105 | 8.50227337893005e-05 | 4.25113668946502e-05 |
| 103 | 0.999924640802347 | 0.000150718395305150 | 7.53591976525749e-05 |
| 104 | 0.999732248793858 | 0.000535502412284193 | 0.000267751206142096 |
| 105 | 0.999285354962 | 0.00142929007600078 | 0.000714645038000389 |
| 106 | 0.998804877559575 | 0.00239024488084963 | 0.00119512244042482 |
| 107 | 0.996452819278296 | 0.00709436144340855 | 0.00354718072170427 |
| 108 | 0.98652602538967 | 0.0269479492206603 | 0.0134739746103301 |
| 109 | 0.964613104188494 | 0.0707737916230125 | 0.0353868958115063 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 72 | 0.827586206896552 | NOK |
| 5% type I error level | 77 | 0.885057471264368 | NOK |
| 10% type I error level | 80 | 0.919540229885057 | NOK |
