| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1550.70804561538 + 0.086528028444836Nikkei[t] + 0.376273521438822DJ_Indust[t] + 0.0122770847008117Goudprijs[t] -7.74003093034112Conjunct_Seizoenzuiver[t] + 6.90342219860368Cons_vertrouw[t] -184.570093209091Rend_oblig_EUR[t] + 33.8362739714698Alg_consumptie_index_BE[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) | -1550.70804561538 | 354.791303 | -4.3708 | 2.6e-05 | 1.3e-05 |
| Nikkei | 0.086528028444836 | 0.015381 | 5.6258 | 0 | 0 |
| DJ_Indust | 0.376273521438822 | 0.036089 | 10.4263 | 0 | 0 |
| Goudprijs | 0.0122770847008117 | 0.008021 | 1.5306 | 0.128412 | 0.064206 |
| Conjunct_Seizoenzuiver | -7.74003093034112 | 7.007133 | -1.1046 | 0.271475 | 0.135737 |
| Cons_vertrouw | 6.90342219860368 | 6.308425 | 1.0943 | 0.275937 | 0.137968 |
| Rend_oblig_EUR | -184.570093209091 | 45.948764 | -4.0169 | 0.000102 | 5.1e-05 |
| Alg_consumptie_index_BE | 33.8362739714698 | 25.209669 | 1.3422 | 0.181985 | 0.090993 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.935715907429102 |
| R-squared | 0.875564259415868 |
| Adjusted R-squared | 0.868539661157086 |
| F-TEST (value) | 124.642609749433 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 124 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 273.003433972532 |
| Sum Squared Residuals | 9241828.49513854 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2502.66 | 3003.39018820974 | -500.730188209737 |
| 2 | 2466.92 | 2879.74313513525 | -412.823135135255 |
| 3 | 2513.17 | 2736.25078390764 | -223.080783907643 |
| 4 | 2443.27 | 2689.65283601344 | -246.38283601344 |
| 5 | 2293.41 | 2571.56738741295 | -278.157387412954 |
| 6 | 2070.83 | 2177.46109992148 | -106.631099921481 |
| 7 | 2029.6 | 2133.4176626454 | -103.817662645401 |
| 8 | 2052.02 | 2075.23518589116 | -23.2151858911566 |
| 9 | 1864.44 | 1873.92733779985 | -9.48733779985038 |
| 10 | 1670.07 | 1515.41877778054 | 154.651222219463 |
| 11 | 1810.99 | 1720.33582271885 | 90.654177281152 |
| 12 | 1905.41 | 2002.14394105048 | -96.7339410504801 |
| 13 | 1862.83 | 1992.34849837931 | -129.518498379309 |
| 14 | 2014.45 | 1867.95198173867 | 146.498018261327 |
| 15 | 2197.82 | 2075.68954872001 | 122.130451279987 |
| 16 | 2962.34 | 3135.13864949752 | -172.798649497525 |
| 17 | 3047.03 | 3333.97087532574 | -286.940875325745 |
| 18 | 3032.6 | 3226.9780259678 | -194.378025967801 |
| 19 | 3504.37 | 3569.63155080370 | -65.2615508036956 |
| 20 | 3801.06 | 3918.7704091224 | -117.710409122398 |
| 21 | 3857.62 | 3836.63449764519 | 20.9855023548056 |
| 22 | 3674.4 | 3675.48129357721 | -1.08129357721300 |
| 23 | 3720.98 | 3823.44484027478 | -102.464840274783 |
| 24 | 3844.49 | 3817.65162573115 | 26.8383742688539 |
| 25 | 4116.68 | 4246.37385899595 | -129.693858995949 |
| 26 | 4105.18 | 4161.22899196693 | -56.0489919669306 |
| 27 | 4435.23 | 4550.55943371415 | -115.329433714150 |
| 28 | 4296.49 | 4312.55711359523 | -16.0671135952274 |
| 29 | 4202.52 | 4181.76410073105 | 20.7558992689486 |
| 30 | 4562.84 | 4445.29523233311 | 117.544767666889 |
| 31 | 4621.4 | 4378.61759990765 | 242.782400092345 |
| 32 | 4696.96 | 4388.3867539917 | 308.573246008302 |
| 33 | 4591.27 | 4181.19208965739 | 410.07791034261 |
| 34 | 4356.98 | 4002.64630174071 | 354.333698259293 |
| 35 | 4502.64 | 4186.08222141898 | 316.557778581017 |
| 36 | 4443.91 | 4069.09529081717 | 374.814709182827 |
| 37 | 4290.89 | 3951.45637314425 | 339.433626855753 |
| 38 | 4199.75 | 3907.72610903661 | 292.023890963386 |
| 39 | 4138.52 | 3831.94423271205 | 306.575767287955 |
| 40 | 3970.1 | 3614.37185126701 | 355.728148732991 |
| 41 | 3862.27 | 3499.17669542812 | 363.09330457188 |
| 42 | 3701.61 | 3333.91184077139 | 367.698159228613 |
| 43 | 3570.12 | 3326.89435050467 | 243.22564949533 |
| 44 | 3801.06 | 3600.00479694653 | 201.055203053465 |
| 45 | 3895.51 | 3643.44755091068 | 252.062449089318 |
| 46 | 3917.96 | 3559.20292010767 | 358.75707989233 |
| 47 | 3813.06 | 3576.90500054989 | 236.154999450110 |
| 48 | 3667.03 | 3585.08856937863 | 81.9414306213735 |
| 49 | 3494.17 | 3511.36968520873 | -17.1996852087344 |
| 50 | 3363.99 | 3304.57039378218 | 59.4196062178174 |
| 51 | 3295.32 | 3137.93699284063 | 157.383007159373 |
| 52 | 3277.01 | 3212.00465818399 | 65.0053418160117 |
| 53 | 3257.16 | 3176.67123910813 | 80.4887608918678 |
| 54 | 3161.69 | 3133.07957680062 | 28.6104231993798 |
| 55 | 3097.31 | 3077.23485179986 | 20.0751482001423 |
| 56 | 3061.26 | 2957.44747462901 | 103.81252537099 |
| 57 | 3119.31 | 2960.1802453105 | 159.129754689498 |
| 58 | 3106.22 | 3118.00868030601 | -11.7886803060106 |
| 59 | 3080.58 | 3101.58732999367 | -21.0073299936699 |
| 60 | 2981.85 | 2973.71620334155 | 8.13379665844577 |
| 61 | 2921.44 | 3000.09538834788 | -78.6553883478807 |
| 62 | 2849.27 | 2851.77768219881 | -2.50768219881385 |
| 63 | 2756.76 | 2677.97447790977 | 78.7855220902298 |
| 64 | 2645.64 | 2729.07123671718 | -83.4312367171805 |
| 65 | 2497.84 | 2685.23746190292 | -187.397461902915 |
| 66 | 2448.05 | 2698.42945212243 | -250.379452122428 |
| 67 | 2454.62 | 2818.76176459596 | -364.141764595956 |
| 68 | 2407.6 | 2655.19741010511 | -247.597410105109 |
| 69 | 2472.81 | 2893.4737399117 | -420.663739911701 |
| 70 | 2408.64 | 2839.65898710560 | -431.018987105596 |
| 71 | 2440.25 | 2875.44491496144 | -435.194914961435 |
| 72 | 2350.44 | 2894.43310420071 | -543.99310420071 |
| 73 | 2196.72 | 2627.35878391799 | -430.638783917994 |
| 74 | 2174.56 | 2480.03363689223 | -305.473636892232 |
| 75 | 2120.88 | 2461.43759981296 | -340.557599812959 |
| 76 | 2093.48 | 2485.35659070359 | -391.876590703587 |
| 77 | 2061.41 | 2312.17252449898 | -250.762524498983 |
| 78 | 1969.6 | 2295.00770267096 | -325.407702670958 |
| 79 | 1959.67 | 2295.10063205556 | -335.430632055561 |
| 80 | 1910.43 | 1968.62283911142 | -58.1928391114226 |
| 81 | 1833.42 | 1785.79298492778 | 47.6270150722225 |
| 82 | 1635.25 | 1670.36705771811 | -35.1170577181129 |
| 83 | 1765.9 | 1720.25817483313 | 45.6418251668717 |
| 84 | 1946.81 | 1891.29763852223 | 55.5123614777717 |
| 85 | 1995.37 | 1859.64897370778 | 135.721026292218 |
| 86 | 2042 | 1879.97266766233 | 162.027332337666 |
| 87 | 1940.49 | 1670.36917534796 | 270.120824652043 |
| 88 | 2065.81 | 1756.03466110150 | 309.775338898505 |
| 89 | 2214.95 | 1932.83801757163 | 282.111982428373 |
| 90 | 2304.98 | 1917.64454304317 | 387.33545695683 |
| 91 | 2555.28 | 2264.37000383401 | 290.90999616599 |
| 92 | 2799.43 | 2536.57533329 | 262.854666710002 |
| 93 | 2811.7 | 2563.27152205295 | 248.42847794705 |
| 94 | 2735.7 | 2734.35725724899 | 1.34274275100743 |
| 95 | 2745.88 | 2439.41233038517 | 306.467669614827 |
| 96 | 2720.25 | 2491.83154128404 | 228.418458715962 |
| 97 | 2638.53 | 2493.58463544675 | 144.945364553250 |
| 98 | 2659.81 | 2390.83514693340 | 268.974853066597 |
| 99 | 2641.65 | 2209.88724011270 | 431.762759887296 |
| 100 | 2604.42 | 2112.56021057837 | 491.859789421631 |
| 101 | 2892.63 | 2713.33566559789 | 179.294334402113 |
| 102 | 2915.02 | 2798.44071145629 | 116.57928854371 |
| 103 | 2845.26 | 2989.69016603734 | -144.430166037342 |
| 104 | 2794.83 | 2969.44689232447 | -174.616892324469 |
| 105 | 2848.96 | 2794.01475923299 | 54.945240767011 |
| 106 | 2833.18 | 2635.65397809555 | 197.52602190445 |
| 107 | 2995.55 | 2925.20133865871 | 70.3486613412945 |
| 108 | 2987.1 | 2940.79350014004 | 46.3064998599592 |
| 109 | 3013.24 | 2985.71997463777 | 27.5200253622277 |
| 110 | 3110.52 | 2975.45863018740 | 135.061369812605 |
| 111 | 3045.78 | 2947.7526895259 | 98.0273104741005 |
| 112 | 3032.93 | 3185.88454968944 | -152.954549689442 |
| 113 | 3142.95 | 3245.81074999731 | -102.860749997309 |
| 114 | 3012.61 | 3142.74270665803 | -130.132706658026 |
| 115 | 2897.06 | 3131.9064255591 | -234.846425559103 |
| 116 | 2863.36 | 3095.80195009596 | -232.441950095957 |
| 117 | 2882.6 | 3489.99777924289 | -607.397779242891 |
| 118 | 2767.63 | 3327.2355623782 | -559.605562378198 |
| 119 | 2803.47 | 3304.09320449827 | -500.623204498266 |
| 120 | 3030.29 | 3529.97354726504 | -499.683547265035 |
| 121 | 3210.52 | 3518.52154362114 | -308.001543621135 |
| 122 | 3249.57 | 3376.43400347089 | -126.864003470894 |
| 123 | 2999.93 | 3084.13682615803 | -84.2068261580265 |
| 124 | 3181.96 | 3240.37038639344 | -58.4103863934407 |
| 125 | 3053.05 | 3331.50119020751 | -278.451190207512 |
| 126 | 3092.71 | 3477.93225110056 | -385.222251100558 |
| 127 | 3165.26 | 3298.09356676188 | -132.833566761878 |
| 128 | 3173.95 | 3428.73693195226 | -254.78693195226 |
| 129 | 3280.37 | 3316.86255514234 | -36.492555142343 |
| 130 | 3288.18 | 2974.31084614725 | 313.869153852753 |
| 131 | 3411.13 | 2710.07675021468 | 701.053249785323 |
| 132 | 3484.74 | 2701.25075600359 | 783.489243996414 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.00837925485437199 | 0.0167585097087440 | 0.991620745145628 |
| 12 | 0.00138264756008401 | 0.00276529512016803 | 0.998617352439916 |
| 13 | 0.000218769613389439 | 0.000437539226778878 | 0.99978123038661 |
| 14 | 0.00190693972842896 | 0.00381387945685792 | 0.998093060271571 |
| 15 | 0.000480249440218446 | 0.000960498880436891 | 0.999519750559782 |
| 16 | 0.000186660677030363 | 0.000373321354060725 | 0.99981333932297 |
| 17 | 6.16783286402733e-05 | 0.000123356657280547 | 0.99993832167136 |
| 18 | 1.48463054721708e-05 | 2.96926109443415e-05 | 0.999985153694528 |
| 19 | 6.66048854981156e-05 | 0.000133209770996231 | 0.999933395114502 |
| 20 | 0.000165056514690149 | 0.000330113029380299 | 0.99983494348531 |
| 21 | 0.000133191619123800 | 0.000266383238247600 | 0.999866808380876 |
| 22 | 0.000844707109184393 | 0.00168941421836879 | 0.999155292890816 |
| 23 | 0.000490015063497834 | 0.000980030126995667 | 0.999509984936502 |
| 24 | 0.000600544493099973 | 0.00120108898619995 | 0.9993994555069 |
| 25 | 0.000847784449130985 | 0.00169556889826197 | 0.999152215550869 |
| 26 | 0.00113846196934114 | 0.00227692393868228 | 0.998861538030659 |
| 27 | 0.000739191844236883 | 0.00147838368847377 | 0.999260808155763 |
| 28 | 0.000526400182418505 | 0.00105280036483701 | 0.999473599817582 |
| 29 | 0.000452184221984258 | 0.000904368443968516 | 0.999547815778016 |
| 30 | 0.000454558590662444 | 0.000909117181324889 | 0.999545441409338 |
| 31 | 0.000641955283908422 | 0.00128391056781684 | 0.999358044716092 |
| 32 | 0.00122003440146802 | 0.00244006880293605 | 0.998779965598532 |
| 33 | 0.00169907435102891 | 0.00339814870205782 | 0.998300925648971 |
| 34 | 0.00107528327930279 | 0.00215056655860557 | 0.998924716720697 |
| 35 | 0.000590313779224334 | 0.00118062755844867 | 0.999409686220776 |
| 36 | 0.000379491826948297 | 0.000758983653896594 | 0.999620508173052 |
| 37 | 0.000306283422605646 | 0.000612566845211292 | 0.999693716577394 |
| 38 | 0.000166623823829667 | 0.000333247647659334 | 0.99983337617617 |
| 39 | 0.000115617171703129 | 0.000231234343406258 | 0.999884382828297 |
| 40 | 6.93271389727521e-05 | 0.000138654277945504 | 0.999930672861027 |
| 41 | 4.09072253222763e-05 | 8.18144506445526e-05 | 0.999959092774678 |
| 42 | 2.50165820305362e-05 | 5.00331640610723e-05 | 0.99997498341797 |
| 43 | 2.18040145910562e-05 | 4.36080291821124e-05 | 0.999978195985409 |
| 44 | 1.56058261470398e-05 | 3.12116522940796e-05 | 0.999984394173853 |
| 45 | 1.55500980230747e-05 | 3.11001960461495e-05 | 0.999984449901977 |
| 46 | 1.48911661705728e-05 | 2.97823323411456e-05 | 0.99998510883383 |
| 47 | 1.43794770167795e-05 | 2.8758954033559e-05 | 0.999985620522983 |
| 48 | 2.030310008557e-05 | 4.060620017114e-05 | 0.999979696899914 |
| 49 | 2.15719245619662e-05 | 4.31438491239325e-05 | 0.999978428075438 |
| 50 | 1.68886148271296e-05 | 3.37772296542592e-05 | 0.999983111385173 |
| 51 | 2.27168423572026e-05 | 4.54336847144051e-05 | 0.999977283157643 |
| 52 | 2.96680674735825e-05 | 5.9336134947165e-05 | 0.999970331932526 |
| 53 | 2.64450160345815e-05 | 5.2890032069163e-05 | 0.999973554983965 |
| 54 | 2.01523541843326e-05 | 4.03047083686653e-05 | 0.999979847645816 |
| 55 | 1.78481934998145e-05 | 3.5696386999629e-05 | 0.9999821518065 |
| 56 | 1.74240651158559e-05 | 3.48481302317118e-05 | 0.999982575934884 |
| 57 | 1.6393917125737e-05 | 3.2787834251474e-05 | 0.999983606082874 |
| 58 | 1.93068248607007e-05 | 3.86136497214014e-05 | 0.99998069317514 |
| 59 | 2.04165371211879e-05 | 4.08330742423757e-05 | 0.999979583462879 |
| 60 | 2.5989725810406e-05 | 5.1979451620812e-05 | 0.99997401027419 |
| 61 | 3.44632222259375e-05 | 6.8926444451875e-05 | 0.999965536777774 |
| 62 | 6.67116041386617e-05 | 0.000133423208277323 | 0.999933288395861 |
| 63 | 0.000198505555069282 | 0.000397011110138564 | 0.99980149444493 |
| 64 | 0.000496420353369561 | 0.000992840706739121 | 0.99950357964663 |
| 65 | 0.00123141968290464 | 0.00246283936580928 | 0.998768580317095 |
| 66 | 0.00398944461370823 | 0.00797888922741647 | 0.996010555386292 |
| 67 | 0.0111044618014797 | 0.0222089236029595 | 0.98889553819852 |
| 68 | 0.0162973365970406 | 0.0325946731940812 | 0.98370266340296 |
| 69 | 0.0488459357419172 | 0.0976918714838345 | 0.951154064258083 |
| 70 | 0.0727664720378295 | 0.145532944075659 | 0.92723352796217 |
| 71 | 0.0699263981489827 | 0.139852796297965 | 0.930073601851017 |
| 72 | 0.0897611519767056 | 0.179522303953411 | 0.910238848023294 |
| 73 | 0.0841748459451168 | 0.168349691890234 | 0.915825154054883 |
| 74 | 0.0699068623048815 | 0.139813724609763 | 0.930093137695118 |
| 75 | 0.0748203292731258 | 0.149640658546252 | 0.925179670726874 |
| 76 | 0.079069265811445 | 0.15813853162289 | 0.920930734188555 |
| 77 | 0.0669184196638453 | 0.133836839327691 | 0.933081580336155 |
| 78 | 0.0890444700114291 | 0.178088940022858 | 0.91095552998857 |
| 79 | 0.203535543943612 | 0.407071087887224 | 0.796464456056388 |
| 80 | 0.353805481275289 | 0.707610962550578 | 0.646194518724711 |
| 81 | 0.59183072939086 | 0.81633854121828 | 0.40816927060914 |
| 82 | 0.613368543192005 | 0.77326291361599 | 0.386631456807995 |
| 83 | 0.581920394220478 | 0.836159211559044 | 0.418079605779522 |
| 84 | 0.616516361851051 | 0.766967276297898 | 0.383483638148949 |
| 85 | 0.660557557197428 | 0.678884885605145 | 0.339442442802572 |
| 86 | 0.779339073712688 | 0.441321852574624 | 0.220660926287312 |
| 87 | 0.889977147771173 | 0.220045704457655 | 0.110022852228827 |
| 88 | 0.95294762187595 | 0.0941047562480994 | 0.0470523781240497 |
| 89 | 0.986482533538153 | 0.0270349329236945 | 0.0135174664618473 |
| 90 | 0.99711063564082 | 0.00577872871835856 | 0.00288936435917928 |
| 91 | 0.99735866032676 | 0.00528267934648166 | 0.00264133967324083 |
| 92 | 0.996535497736787 | 0.00692900452642529 | 0.00346450226321264 |
| 93 | 0.997371792573701 | 0.00525641485259729 | 0.00262820742629864 |
| 94 | 0.995958968874474 | 0.00808206225105253 | 0.00404103112552627 |
| 95 | 0.995827130643053 | 0.0083457387138942 | 0.0041728693569471 |
| 96 | 0.994428346548995 | 0.0111433069020109 | 0.00557165345100545 |
| 97 | 0.991939038866117 | 0.0161219222677661 | 0.00806096113388304 |
| 98 | 0.990479428261503 | 0.0190411434769937 | 0.00952057173849685 |
| 99 | 0.988726357225786 | 0.0225472855484286 | 0.0112736427742143 |
| 100 | 0.98856709428619 | 0.0228658114276189 | 0.0114329057138095 |
| 101 | 0.982060562136557 | 0.0358788757268865 | 0.0179394378634432 |
| 102 | 0.97626330589224 | 0.0474733882155208 | 0.0237366941077604 |
| 103 | 0.973507467312926 | 0.0529850653741476 | 0.0264925326870738 |
| 104 | 0.976484383218675 | 0.0470312335626507 | 0.0235156167813254 |
| 105 | 0.981752958530994 | 0.0364940829380126 | 0.0182470414690063 |
| 106 | 0.990366574704206 | 0.0192668505915882 | 0.0096334252957941 |
| 107 | 0.989976043912867 | 0.0200479121742667 | 0.0100239560871333 |
| 108 | 0.994380909506003 | 0.0112381809879944 | 0.00561909049399721 |
| 109 | 0.995192708910706 | 0.0096145821785883 | 0.00480729108929415 |
| 110 | 0.991169862542113 | 0.0176602749157745 | 0.00883013745788727 |
| 111 | 0.984905108468663 | 0.0301897830626747 | 0.0150948915313373 |
| 112 | 0.979763810245588 | 0.040472379508823 | 0.0202361897544115 |
| 113 | 0.97540967626136 | 0.0491806474772794 | 0.0245903237386397 |
| 114 | 0.969343774948014 | 0.0613124501039729 | 0.0306562250519864 |
| 115 | 0.967026735496939 | 0.0659465290061228 | 0.0329732645030614 |
| 116 | 0.987926527309034 | 0.0241469453819316 | 0.0120734726909658 |
| 117 | 0.984370856289316 | 0.0312582874213681 | 0.0156291437106840 |
| 118 | 0.99069851247519 | 0.0186029750496201 | 0.00930148752481003 |
| 119 | 0.998381575790776 | 0.00323684841844866 | 0.00161842420922433 |
| 120 | 0.993037819393562 | 0.0139243612128756 | 0.0069621806064378 |
| 121 | 0.973661064968014 | 0.0526778700639716 | 0.0263389350319858 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 63 | 0.567567567567568 | NOK |
| 5% type I error level | 87 | 0.783783783783784 | NOK |
| 10% type I error level | 93 | 0.837837837837838 | NOK |
