| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1453.14454612382 + 0.0993347391427635Nikkei[t] + 0.361604121076399DJ_Indust[t] + 0.0162644412155995Goudprijs[t] -11.6779957473965Conjunct_Seizoenzuiver[t] + 14.3554763933654Cons_vertrouw[t] + 35.0865681640742Alg_consumptie_index_BE[t] -268.749364521601Gem_rente_kasbon_5j[t] + 1.10899673297789t + 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) | -1453.14454612382 | 338.602291 | -4.2916 | 3.6e-05 | 1.8e-05 |
| Nikkei | 0.0993347391427635 | 0.017443 | 5.6949 | 0 | 0 |
| DJ_Indust | 0.361604121076399 | 0.038764 | 9.3283 | 0 | 0 |
| Goudprijs | 0.0162644412155995 | 0.019416 | 0.8377 | 0.403827 | 0.201913 |
| Conjunct_Seizoenzuiver | -11.6779957473965 | 7.124337 | -1.6392 | 0.103733 | 0.051867 |
| Cons_vertrouw | 14.3554763933654 | 6.636792 | 2.163 | 0.032474 | 0.016237 |
| Alg_consumptie_index_BE | 35.0865681640742 | 23.017286 | 1.5244 | 0.129987 | 0.064993 |
| Gem_rente_kasbon_5j | -268.749364521601 | 56.100374 | -4.7905 | 5e-06 | 2e-06 |
| t | 1.10899673297789 | 2.560983 | 0.433 | 0.665747 | 0.332874 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.941733009782613 |
| R-squared | 0.88686106171422 |
| Adjusted R-squared | 0.87950243158181 |
| F-TEST (value) | 120.519858418804 |
| F-TEST (DF numerator) | 8 |
| F-TEST (DF denominator) | 123 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 261.372491501888 |
| Sum Squared Residuals | 8402816.25561026 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2766.99599832661 | 717.744001673388 |
| 2 | 3411.13 | 2760.59989806861 | 650.530101931395 |
| 3 | 3288.18 | 2996.74891689690 | 291.431083103104 |
| 4 | 3280.37 | 3372.75180740797 | -92.381807407968 |
| 5 | 3173.95 | 3475.3089051621 | -301.358905162098 |
| 6 | 3165.26 | 3218.84075572269 | -53.5807557226873 |
| 7 | 3092.71 | 3411.14699445041 | -318.436994450408 |
| 8 | 3053.05 | 3262.28189469402 | -209.231894694022 |
| 9 | 3181.96 | 3188.39890736132 | -6.43890736132138 |
| 10 | 2999.93 | 2994.92754528548 | 5.00245471452145 |
| 11 | 3249.57 | 3356.05328457189 | -106.483284571890 |
| 12 | 3210.52 | 3422.10184302329 | -211.581843023293 |
| 13 | 3030.29 | 3493.91575380119 | -463.625753801187 |
| 14 | 2803.47 | 3276.43004090908 | -472.96004090908 |
| 15 | 2767.63 | 3292.32814656694 | -524.698146566943 |
| 16 | 2882.6 | 3477.27165405098 | -594.671654050984 |
| 17 | 2863.36 | 3046.67442890199 | -183.314428901991 |
| 18 | 2897.06 | 3075.96473293187 | -178.904732931872 |
| 19 | 3012.61 | 3102.70505215217 | -90.0950521521658 |
| 20 | 3142.95 | 3193.86656105645 | -50.9165610564549 |
| 21 | 3032.93 | 3090.13224952553 | -57.2022495255266 |
| 22 | 3045.78 | 2876.42244796443 | 169.357552035571 |
| 23 | 3110.52 | 2952.79039961938 | 157.72960038062 |
| 24 | 3013.24 | 3038.34774116808 | -25.1077411680752 |
| 25 | 2987.1 | 2995.86151343951 | -8.7615134395138 |
| 26 | 2995.55 | 2938.39896690172 | 57.151033098277 |
| 27 | 2833.18 | 2664.17003993411 | 169.009960065889 |
| 28 | 2848.96 | 2827.43437942738 | 21.5256205726154 |
| 29 | 2794.83 | 2985.64305393771 | -190.81305393771 |
| 30 | 2845.26 | 3003.57214507104 | -158.312145071043 |
| 31 | 2915.02 | 2807.97066733130 | 107.049332668695 |
| 32 | 2892.63 | 2658.22484954271 | 234.405150457292 |
| 33 | 2604.42 | 2101.61162828999 | 502.808371710012 |
| 34 | 2641.65 | 2160.4405028459 | 481.2094971541 |
| 35 | 2659.81 | 2350.4261249428 | 309.383875057199 |
| 36 | 2638.53 | 2443.52235378826 | 195.007646211741 |
| 37 | 2720.25 | 2500.40131322504 | 219.848686774959 |
| 38 | 2745.88 | 2435.14903390667 | 310.730966093326 |
| 39 | 2735.7 | 2698.82878310695 | 36.8712168930473 |
| 40 | 2811.7 | 2505.23423181217 | 306.465768187828 |
| 41 | 2799.43 | 2503.86944411747 | 295.560555882533 |
| 42 | 2555.28 | 2234.55068270027 | 320.729317299735 |
| 43 | 2304.98 | 1918.15498204515 | 386.825017954852 |
| 44 | 2214.95 | 1950.02393840442 | 264.926061595576 |
| 45 | 2065.81 | 1785.46616340905 | 280.343836590952 |
| 46 | 1940.49 | 1703.82579405983 | 236.664205940171 |
| 47 | 2042 | 1878.41750714963 | 163.582492850369 |
| 48 | 1995.37 | 1812.83170590496 | 182.538294095044 |
| 49 | 1946.81 | 1882.6189924228 | 64.1910075771997 |
| 50 | 1765.9 | 1707.04805663169 | 58.8519433683129 |
| 51 | 1635.25 | 1672.5761125114 | -37.3261125114003 |
| 52 | 1833.42 | 1812.55667564440 | 20.8633243556049 |
| 53 | 1910.43 | 2069.30894539421 | -158.878945394211 |
| 54 | 1959.67 | 2428.55343196377 | -468.883431963775 |
| 55 | 1969.6 | 2385.9292455825 | -416.329245582502 |
| 56 | 2061.41 | 2349.62035802939 | -288.210358029395 |
| 57 | 2093.48 | 2557.12926686677 | -463.649266866769 |
| 58 | 2120.88 | 2416.32504033649 | -295.445040336487 |
| 59 | 2174.56 | 2503.06966170582 | -328.509661705824 |
| 60 | 2196.72 | 2627.1482968952 | -430.428296895199 |
| 61 | 2350.44 | 2841.6957946944 | -491.255794694401 |
| 62 | 2440.25 | 2850.45174241149 | -410.201742411485 |
| 63 | 2408.64 | 2825.65221943099 | -417.01221943099 |
| 64 | 2472.81 | 2951.19003843712 | -478.380038437125 |
| 65 | 2407.6 | 2685.62274814555 | -278.022748145552 |
| 66 | 2454.62 | 2910.07999334351 | -455.459993343510 |
| 67 | 2448.05 | 2684.10744605480 | -236.057446054796 |
| 68 | 2497.84 | 2686.83283914415 | -188.992839144146 |
| 69 | 2645.64 | 2746.62255540934 | -100.982555409336 |
| 70 | 2756.76 | 2631.44916975138 | 125.310830248617 |
| 71 | 2849.27 | 2789.8357292938 | 59.4342707062021 |
| 72 | 2921.44 | 2930.43082828954 | -8.9908282895366 |
| 73 | 2981.85 | 2922.57357495929 | 59.2764250407144 |
| 74 | 3080.58 | 3126.51298782886 | -45.9329878288583 |
| 75 | 3106.22 | 3181.83309590241 | -75.6130959024082 |
| 76 | 3119.31 | 2982.38727777720 | 136.922722222796 |
| 77 | 3061.26 | 2911.52610162273 | 149.733898377267 |
| 78 | 3097.31 | 3032.38636654856 | 64.9236334514366 |
| 79 | 3161.69 | 3125.20451998752 | 36.485480012479 |
| 80 | 3257.16 | 3165.57095299068 | 91.5890470093196 |
| 81 | 3277.01 | 3153.41500478357 | 123.594995216432 |
| 82 | 3295.32 | 3167.71154467449 | 127.608455325514 |
| 83 | 3363.99 | 3347.11429505407 | 16.8757049459335 |
| 84 | 3494.17 | 3558.78494180609 | -64.6149418060879 |
| 85 | 3667.03 | 3653.55758175301 | 13.4724182469878 |
| 86 | 3813.06 | 3694.60315973038 | 118.456840269625 |
| 87 | 3917.96 | 3668.40051437262 | 249.559485627384 |
| 88 | 3895.51 | 3743.08366498578 | 152.426335014223 |
| 89 | 3801.06 | 3641.92529581188 | 159.134704188118 |
| 90 | 3570.12 | 3393.84336546784 | 176.276634532159 |
| 91 | 3701.61 | 3382.55303153513 | 319.056968464874 |
| 92 | 3862.27 | 3529.39833496757 | 332.871665032427 |
| 93 | 3970.1 | 3655.44302808518 | 314.656971914825 |
| 94 | 4138.52 | 3905.42625764075 | 233.093742359249 |
| 95 | 4199.75 | 3974.79763465317 | 224.952365346829 |
| 96 | 4290.89 | 3964.48676149641 | 326.403238503586 |
| 97 | 4443.91 | 4145.46477375467 | 298.445226245325 |
| 98 | 4502.64 | 4213.92831940261 | 288.711680597393 |
| 99 | 4356.98 | 4000.21858938473 | 356.761410615274 |
| 100 | 4591.27 | 4240.71722728879 | 350.552772711214 |
| 101 | 4696.96 | 4467.93176180266 | 229.028238197345 |
| 102 | 4621.4 | 4407.46739411615 | 213.932605883853 |
| 103 | 4562.84 | 4415.41773882690 | 147.422261173104 |
| 104 | 4202.52 | 4127.75376291685 | 74.7662370831509 |
| 105 | 4296.49 | 4267.38233528758 | 29.1076647124179 |
| 106 | 4435.23 | 4530.31687238 | -95.0868723799948 |
| 107 | 4105.18 | 4106.26083258733 | -1.08083258732591 |
| 108 | 4116.68 | 4283.6965492157 | -167.016549215705 |
| 109 | 3844.49 | 3758.67275656259 | 85.8172434374094 |
| 110 | 3720.98 | 3802.86261229744 | -81.882612297439 |
| 111 | 3674.4 | 3741.10135503184 | -66.7013550318403 |
| 112 | 3857.62 | 3962.33544481343 | -104.715444813430 |
| 113 | 3801.06 | 3989.28702924991 | -188.227029249910 |
| 114 | 3504.37 | 3596.07062259521 | -91.7006225952081 |
| 115 | 3032.6 | 3125.33911141335 | -92.7391114133531 |
| 116 | 3047.03 | 3176.78805032003 | -129.758050320029 |
| 117 | 2962.34 | 3137.48724704799 | -175.147247047995 |
| 118 | 2197.82 | 2088.75824631426 | 109.061753685742 |
| 119 | 2014.45 | 1889.62177411535 | 124.82822588465 |
| 120 | 1862.83 | 1928.41603708707 | -65.5860370870748 |
| 121 | 1905.41 | 1945.94402890318 | -40.534028903176 |
| 122 | 1810.99 | 1711.01245408028 | 99.9775459197183 |
| 123 | 1670.07 | 1591.55824004996 | 78.5117599500431 |
| 124 | 1864.44 | 1940.30180012867 | -75.861800128671 |
| 125 | 2052.02 | 2114.29123165485 | -62.2712316548458 |
| 126 | 2029.6 | 2160.53269950454 | -130.932699504540 |
| 127 | 2070.83 | 2147.97412065966 | -77.1441206596634 |
| 128 | 2293.41 | 2544.51899788509 | -251.108997885092 |
| 129 | 2443.27 | 2615.2261978545 | -171.956197854502 |
| 130 | 2513.17 | 2628.69965800967 | -115.529658009673 |
| 131 | 2466.92 | 2797.07993264529 | -330.159932645292 |
| 132 | 2502.66 | 2866.84394707277 | -364.183947072775 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 12 | 0.0476575070204963 | 0.0953150140409926 | 0.952342492979504 |
| 13 | 0.0202109127514776 | 0.0404218255029552 | 0.979789087248522 |
| 14 | 0.0339508026815418 | 0.0679016053630836 | 0.966049197318458 |
| 15 | 0.0318080318474295 | 0.063616063694859 | 0.96819196815257 |
| 16 | 0.0208554908500961 | 0.0417109817001922 | 0.979144509149904 |
| 17 | 0.0134067541007297 | 0.0268135082014595 | 0.98659324589927 |
| 18 | 0.0079009532827308 | 0.0158019065654616 | 0.99209904671727 |
| 19 | 0.00818063351419734 | 0.0163612670283947 | 0.991819366485803 |
| 20 | 0.00719295204310093 | 0.0143859040862019 | 0.992807047956899 |
| 21 | 0.00473845692748019 | 0.00947691385496038 | 0.99526154307252 |
| 22 | 0.00405827491768405 | 0.0081165498353681 | 0.995941725082316 |
| 23 | 0.00244928873912834 | 0.00489857747825669 | 0.997550711260872 |
| 24 | 0.00127419485341924 | 0.00254838970683847 | 0.99872580514658 |
| 25 | 0.000617315235008265 | 0.00123463047001653 | 0.999382684764992 |
| 26 | 0.00028105034362414 | 0.00056210068724828 | 0.999718949656376 |
| 27 | 0.000120276164678915 | 0.000240552329357831 | 0.999879723835321 |
| 28 | 6.26728633115159e-05 | 0.000125345726623032 | 0.999937327136688 |
| 29 | 5.27441511857481e-05 | 0.000105488302371496 | 0.999947255848814 |
| 30 | 3.58548924674708e-05 | 7.17097849349417e-05 | 0.999964145107533 |
| 31 | 2.78812692165773e-05 | 5.57625384331546e-05 | 0.999972118730783 |
| 32 | 1.45281700170890e-05 | 2.90563400341779e-05 | 0.999985471829983 |
| 33 | 8.30034695056207e-06 | 1.66006939011241e-05 | 0.99999169965305 |
| 34 | 6.76560623678206e-06 | 1.35312124735641e-05 | 0.999993234393763 |
| 35 | 4.27770718206606e-06 | 8.55541436413212e-06 | 0.999995722292818 |
| 36 | 1.93118332393193e-06 | 3.86236664786385e-06 | 0.999998068816676 |
| 37 | 8.75721984740245e-07 | 1.75144396948049e-06 | 0.999999124278015 |
| 38 | 6.43131381251995e-07 | 1.28626276250399e-06 | 0.999999356868619 |
| 39 | 3.51726586945225e-07 | 7.0345317389045e-07 | 0.999999648273413 |
| 40 | 3.19698350180899e-06 | 6.39396700361798e-06 | 0.999996803016498 |
| 41 | 6.99883321185139e-06 | 1.39976664237028e-05 | 0.999993001166788 |
| 42 | 3.94928057510057e-06 | 7.89856115020114e-06 | 0.999996050719425 |
| 43 | 2.36821782852202e-06 | 4.73643565704404e-06 | 0.999997631782171 |
| 44 | 2.43961072146233e-06 | 4.87922144292466e-06 | 0.999997560389279 |
| 45 | 2.89631760488448e-06 | 5.79263520976896e-06 | 0.999997103682395 |
| 46 | 9.58847870474431e-06 | 1.91769574094886e-05 | 0.999990411521295 |
| 47 | 2.39219962583601e-05 | 4.78439925167203e-05 | 0.999976078003742 |
| 48 | 4.63647264392903e-05 | 9.27294528785807e-05 | 0.99995363527356 |
| 49 | 8.22842318976783e-05 | 0.000164568463795357 | 0.999917715768102 |
| 50 | 8.68382479638484e-05 | 0.000173676495927697 | 0.999913161752036 |
| 51 | 6.90242134638745e-05 | 0.000138048426927749 | 0.999930975786536 |
| 52 | 0.000156303055250604 | 0.000312606110501209 | 0.99984369694475 |
| 53 | 0.000233163092222457 | 0.000466326184444914 | 0.999766836907778 |
| 54 | 0.000237379600558971 | 0.000474759201117942 | 0.99976262039944 |
| 55 | 0.000437623616451563 | 0.000875247232903126 | 0.999562376383548 |
| 56 | 0.00101316937627049 | 0.00202633875254098 | 0.99898683062373 |
| 57 | 0.00147541285097299 | 0.00295082570194598 | 0.998524587149027 |
| 58 | 0.00615352668311002 | 0.0123070533662200 | 0.99384647331689 |
| 59 | 0.00750370300617507 | 0.0150074060123501 | 0.992496296993825 |
| 60 | 0.00636131087681125 | 0.0127226217536225 | 0.993638689123189 |
| 61 | 0.00733715076990603 | 0.0146743015398121 | 0.992662849230094 |
| 62 | 0.00888990609276702 | 0.0177798121855340 | 0.991110093907233 |
| 63 | 0.0256840460341197 | 0.0513680920682395 | 0.97431595396588 |
| 64 | 0.161311508653545 | 0.322623017307089 | 0.838688491346455 |
| 65 | 0.378779611405421 | 0.757559222810841 | 0.62122038859458 |
| 66 | 0.695784642746379 | 0.608430714507242 | 0.304215357253621 |
| 67 | 0.871683037875539 | 0.256633924248922 | 0.128316962124461 |
| 68 | 0.95624528367655 | 0.087509432646901 | 0.0437547163234505 |
| 69 | 0.988499362937142 | 0.0230012741257155 | 0.0115006370628577 |
| 70 | 0.99766205914719 | 0.00467588170561885 | 0.00233794085280943 |
| 71 | 0.999291812385651 | 0.00141637522869722 | 0.000708187614348611 |
| 72 | 0.999852305083643 | 0.000295389832713169 | 0.000147694916356584 |
| 73 | 0.999969374445153 | 6.12511096947673e-05 | 3.06255548473837e-05 |
| 74 | 0.999992876767177 | 1.42464656451399e-05 | 7.12323282256996e-06 |
| 75 | 0.999998130685534 | 3.73862893208016e-06 | 1.86931446604008e-06 |
| 76 | 0.999999297931661 | 1.40413667753727e-06 | 7.02068338768634e-07 |
| 77 | 0.999999562179329 | 8.75641342515923e-07 | 4.37820671257961e-07 |
| 78 | 0.999999584464032 | 8.31071935920193e-07 | 4.15535967960096e-07 |
| 79 | 0.999999472218051 | 1.05556389811456e-06 | 5.27781949057281e-07 |
| 80 | 0.999999362668235 | 1.27466353017977e-06 | 6.37331765089884e-07 |
| 81 | 0.999999203612848 | 1.59277430462590e-06 | 7.9638715231295e-07 |
| 82 | 0.99999898521265 | 2.02957469974918e-06 | 1.01478734987459e-06 |
| 83 | 0.99999879448179 | 2.41103642036709e-06 | 1.20551821018355e-06 |
| 84 | 0.99999968588276 | 6.28234480159581e-07 | 3.14117240079791e-07 |
| 85 | 0.999999927411276 | 1.45177447640092e-07 | 7.25887238200459e-08 |
| 86 | 0.999999952817983 | 9.43640336154442e-08 | 4.71820168077221e-08 |
| 87 | 0.999999934822133 | 1.3035573479117e-07 | 6.5177867395585e-08 |
| 88 | 0.999999975792037 | 4.84159261112242e-08 | 2.42079630556121e-08 |
| 89 | 0.999999996907562 | 6.18487627510569e-09 | 3.09243813755285e-09 |
| 90 | 0.999999999418483 | 1.16303350765796e-09 | 5.81516753828979e-10 |
| 91 | 0.99999999944746 | 1.10508165918326e-09 | 5.52540829591632e-10 |
| 92 | 0.999999999553546 | 8.92908118445662e-10 | 4.46454059222831e-10 |
| 93 | 0.999999999658185 | 6.836306062013e-10 | 3.41815303100650e-10 |
| 94 | 0.99999999994169 | 1.16619021726663e-10 | 5.83095108633314e-11 |
| 95 | 0.999999999994972 | 1.00565369558518e-11 | 5.0282684779259e-12 |
| 96 | 0.999999999994622 | 1.07570015620056e-11 | 5.37850078100281e-12 |
| 97 | 0.999999999995685 | 8.63037439632665e-12 | 4.31518719816333e-12 |
| 98 | 0.999999999989831 | 2.03377044008344e-11 | 1.01688522004172e-11 |
| 99 | 0.99999999996734 | 6.53210895503978e-11 | 3.26605447751989e-11 |
| 100 | 0.999999999899761 | 2.00477861183788e-10 | 1.00238930591894e-10 |
| 101 | 0.99999999968181 | 6.36380913404988e-10 | 3.18190456702494e-10 |
| 102 | 0.999999999131579 | 1.73684199806065e-09 | 8.68420999030325e-10 |
| 103 | 0.999999998242456 | 3.51508765695705e-09 | 1.75754382847853e-09 |
| 104 | 0.999999993688262 | 1.26234752767366e-08 | 6.31173763836831e-09 |
| 105 | 0.999999977066974 | 4.58660512138252e-08 | 2.29330256069126e-08 |
| 106 | 0.999999929679193 | 1.40641614874939e-07 | 7.03208074374695e-08 |
| 107 | 0.999999775408498 | 4.491830040018e-07 | 2.245915020009e-07 |
| 108 | 0.999999589818983 | 8.20362034704074e-07 | 4.10181017352037e-07 |
| 109 | 0.99999914874328 | 1.70251344176004e-06 | 8.5125672088002e-07 |
| 110 | 0.999998425937336 | 3.14812532838379e-06 | 1.57406266419189e-06 |
| 111 | 0.999998005859362 | 3.98828127691557e-06 | 1.99414063845779e-06 |
| 112 | 0.999992228294707 | 1.55434105854535e-05 | 7.77170529272677e-06 |
| 113 | 0.999978270330297 | 4.34593394055065e-05 | 2.17296697027533e-05 |
| 114 | 0.999955438995916 | 8.9122008167321e-05 | 4.45610040836605e-05 |
| 115 | 0.999816638732102 | 0.000366722535795326 | 0.000183361267897663 |
| 116 | 0.999315423196271 | 0.00136915360745775 | 0.000684576803728874 |
| 117 | 0.998050811184074 | 0.00389837763185158 | 0.00194918881592579 |
| 118 | 0.992795453747004 | 0.0144090925059930 | 0.00720454625299652 |
| 119 | 0.999241542859685 | 0.0015169142806301 | 0.00075845714031505 |
| 120 | 0.99471589457329 | 0.0105682108534191 | 0.00528410542670957 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 86 | 0.788990825688073 | NOK |
| 5% type I error level | 100 | 0.91743119266055 | NOK |
| 10% type I error level | 105 | 0.963302752293578 | NOK |
