| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1599.03720837273 + 0.101061464791887Nikkei[t] + 0.369872254147376DJ_Indust[t] + 0.0144742968554702Goudprijs[t] -13.0075815890662Conjunct_Seizoenzuiver[t] + 14.0577880911957Cons_vertrouw[t] + 33.7278234341511Alg_consumptie_index_BE[t] -269.764154997347Gem_rente_kasbon_5j[t] + 99.4975226309243M1[t] + 111.784180391219M2[t] + 64.7722526051577M3[t] + 23.7198433389575M4[t] + 8.23471602593218M5[t] -12.6633778006483M6[t] + 36.2211969330588M7[t] + 46.5102316274506M8[t] + 84.1335508449912M9[t] + 149.910334438272M10[t] + 86.0422081747543M11[t] + 1.14348517765727t + 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) | -1599.03720837273 | 365.422654 | -4.3759 | 2.7e-05 | 1.4e-05 |
| Nikkei | 0.101061464791887 | 0.018511 | 5.4596 | 0 | 0 |
| DJ_Indust | 0.369872254147376 | 0.040625 | 9.1045 | 0 | 0 |
| Goudprijs | 0.0144742968554702 | 0.020991 | 0.6895 | 0.491914 | 0.245957 |
| Conjunct_Seizoenzuiver | -13.0075815890662 | 7.722738 | -1.6843 | 0.094904 | 0.047452 |
| Cons_vertrouw | 14.0577880911957 | 7.315156 | 1.9217 | 0.05718 | 0.02859 |
| Alg_consumptie_index_BE | 33.7278234341511 | 24.639609 | 1.3688 | 0.173787 | 0.086893 |
| Gem_rente_kasbon_5j | -269.764154997347 | 63.228974 | -4.2665 | 4.2e-05 | 2.1e-05 |
| M1 | 99.4975226309243 | 117.36685 | 0.8477 | 0.398386 | 0.199193 |
| M2 | 111.784180391219 | 118.292641 | 0.945 | 0.346703 | 0.173352 |
| M3 | 64.7722526051577 | 117.966928 | 0.5491 | 0.58405 | 0.292025 |
| M4 | 23.7198433389575 | 118.281489 | 0.2005 | 0.841424 | 0.420712 |
| M5 | 8.23471602593218 | 115.837061 | 0.0711 | 0.943454 | 0.471727 |
| M6 | -12.6633778006483 | 115.818998 | -0.1093 | 0.91313 | 0.456565 |
| M7 | 36.2211969330588 | 116.483753 | 0.311 | 0.756413 | 0.378206 |
| M8 | 46.5102316274506 | 116.749653 | 0.3984 | 0.691112 | 0.345556 |
| M9 | 84.1335508449912 | 116.068017 | 0.7249 | 0.470047 | 0.235024 |
| M10 | 149.910334438272 | 116.073767 | 1.2915 | 0.199186 | 0.099593 |
| M11 | 86.0422081747543 | 114.979409 | 0.7483 | 0.455831 | 0.227916 |
| t | 1.14348517765727 | 2.739961 | 0.4173 | 0.677231 | 0.338616 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.943813094641892 |
| R-squared | 0.890783157617505 |
| Adjusted R-squared | 0.872255300427617 |
| F-TEST (value) | 48.0780453178196 |
| F-TEST (DF numerator) | 19 |
| F-TEST (DF denominator) | 112 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 269.117649405580 |
| Sum Squared Residuals | 8111522.63281751 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3484.74 | 2808.62255748293 | 676.117442517073 |
| 2 | 3411.13 | 2816.14460449073 | 594.985395509268 |
| 3 | 3288.18 | 3011.68750543237 | 276.492494567625 |
| 4 | 3280.37 | 3347.12570049667 | -66.75570049667 |
| 5 | 3173.95 | 3436.34346903232 | -262.393469032320 |
| 6 | 3165.26 | 3163.08884094277 | 2.17115905723315 |
| 7 | 3092.71 | 3404.89334452617 | -312.183344526174 |
| 8 | 3053.05 | 3265.13347760171 | -212.083477601714 |
| 9 | 3181.96 | 3220.9491968528 | -38.9891968527991 |
| 10 | 2999.93 | 3083.03015493371 | -83.1001549337123 |
| 11 | 3249.57 | 3384.18225754057 | -134.612257540572 |
| 12 | 3210.52 | 3364.11886361002 | -153.598863610019 |
| 13 | 3030.29 | 3539.27759960481 | -508.987599604814 |
| 14 | 2803.47 | 3325.24114318235 | -521.771143182348 |
| 15 | 2767.63 | 3291.41608457393 | -523.78608457393 |
| 16 | 2882.6 | 3440.27775944428 | -557.677759444277 |
| 17 | 2863.36 | 2987.19267340104 | -123.832673401042 |
| 18 | 2897.06 | 2992.7343023541 | -95.6743023541023 |
| 19 | 3012.61 | 3072.71635019271 | -60.1063501927108 |
| 20 | 3142.95 | 3175.01334970606 | -32.0633497060587 |
| 21 | 3032.93 | 3107.98789687846 | -75.0578968784617 |
| 22 | 3045.78 | 2955.44552357251 | 90.334476427491 |
| 23 | 3110.52 | 2969.77080150319 | 140.749198496806 |
| 24 | 3013.24 | 2969.85328337957 | 43.3867166204268 |
| 25 | 2987.1 | 3029.97120326318 | -42.8712032631799 |
| 26 | 2995.55 | 2988.34564398673 | 7.20435601326654 |
| 27 | 2833.18 | 2663.28164303577 | 169.898356964234 |
| 28 | 2848.96 | 2795.60817755712 | 53.3518224428814 |
| 29 | 2794.83 | 2940.41724116218 | -145.587241162180 |
| 30 | 2845.26 | 2938.26566647897 | -93.0056664789676 |
| 31 | 2915.02 | 2789.94204359655 | 125.077956403453 |
| 32 | 2892.63 | 2650.4283830932 | 242.201616906799 |
| 33 | 2604.42 | 2124.96132957595 | 479.458670424053 |
| 34 | 2641.65 | 2259.55215326141 | 382.097846738591 |
| 35 | 2659.81 | 2391.89166008817 | 267.918339911832 |
| 36 | 2638.53 | 2394.81886575890 | 243.711134241104 |
| 37 | 2720.25 | 2543.56670488732 | 176.683295112677 |
| 38 | 2745.88 | 2488.13647858727 | 257.743521412726 |
| 39 | 2735.7 | 2707.26648155643 | 28.4335184435654 |
| 40 | 2811.7 | 2470.28859715743 | 341.411402842567 |
| 41 | 2799.43 | 2451.71990910627 | 347.710090893729 |
| 42 | 2555.28 | 2156.96171915732 | 398.318280842685 |
| 43 | 2304.98 | 1884.31788708140 | 420.662112918596 |
| 44 | 2214.95 | 1929.01329304077 | 285.93670695923 |
| 45 | 2065.81 | 1796.82707486377 | 268.982925136225 |
| 46 | 1940.49 | 1780.9854445357 | 159.504555464300 |
| 47 | 2042 | 1896.11900096138 | 145.880999038625 |
| 48 | 1995.37 | 1744.93884517396 | 250.431154826039 |
| 49 | 1946.81 | 1916.52569765169 | 30.2843023483113 |
| 50 | 1765.9 | 1748.8691241306 | 17.0308758694006 |
| 51 | 1635.25 | 1674.88519054437 | -39.635190544373 |
| 52 | 1833.42 | 1776.96787284007 | 56.4521271599324 |
| 53 | 1910.43 | 2018.95454320583 | -108.524543205828 |
| 54 | 1959.67 | 2366.29066720967 | -406.620667209671 |
| 55 | 1969.6 | 2372.83446355801 | -403.234463558007 |
| 56 | 2061.41 | 2341.92555286725 | -280.515552867254 |
| 57 | 2093.48 | 2583.21889902119 | -489.738899021194 |
| 58 | 2120.88 | 2512.05612354128 | -391.176123541277 |
| 59 | 2174.56 | 2527.51597035947 | -352.955970359474 |
| 60 | 2196.72 | 2568.03298054503 | -371.312980545027 |
| 61 | 2350.44 | 2886.24202052657 | -535.802020526574 |
| 62 | 2440.25 | 2906.51247428389 | -466.262474283886 |
| 63 | 2408.64 | 2833.03251273144 | -424.392512731436 |
| 64 | 2472.81 | 2915.77110094659 | -442.961100946592 |
| 65 | 2407.6 | 2629.32047198321 | -221.720471983214 |
| 66 | 2454.62 | 2834.98632654039 | -380.366326540391 |
| 67 | 2448.05 | 2652.21085686839 | -204.160856868388 |
| 68 | 2497.84 | 2666.58111973673 | -168.741119736731 |
| 69 | 2645.64 | 2764.68137646383 | -119.041376463833 |
| 70 | 2756.76 | 2713.96608140969 | 42.7939185903105 |
| 71 | 2849.27 | 2814.98607472351 | 34.2839252764931 |
| 72 | 2921.44 | 2875.0298243142 | 46.4101756858017 |
| 73 | 2981.85 | 2964.79231409996 | 17.0576859000381 |
| 74 | 3080.58 | 3184.00178564041 | -103.421785640410 |
| 75 | 3106.22 | 3192.1191489299 | -85.899148929897 |
| 76 | 3119.31 | 2952.39283719018 | 166.917162809819 |
| 77 | 3061.26 | 2869.9037232058 | 191.356276794202 |
| 78 | 3097.31 | 2969.09655585297 | 128.21344414703 |
| 79 | 3161.69 | 3112.62466496433 | 49.0653350356719 |
| 80 | 3257.16 | 3162.86636866311 | 94.2936313368915 |
| 81 | 3277.01 | 3184.51983303367 | 92.4901669663344 |
| 82 | 3295.32 | 3259.02114752499 | 36.2988524750109 |
| 83 | 3363.99 | 3377.21330917197 | -13.2233091719671 |
| 84 | 3494.17 | 3501.86223964972 | -7.69223964971827 |
| 85 | 3667.03 | 3694.60984705601 | -27.5798470560133 |
| 86 | 3813.06 | 3746.80043132041 | 66.2595686795931 |
| 87 | 3917.96 | 3675.65776147452 | 242.302238525481 |
| 88 | 3895.51 | 3706.01865950118 | 189.491340498825 |
| 89 | 3801.06 | 3586.76707792798 | 214.292922072024 |
| 90 | 3570.12 | 3314.18140378979 | 255.938596210209 |
| 91 | 3701.61 | 3349.25910807833 | 352.350891921674 |
| 92 | 3862.27 | 3511.29728185908 | 350.972718140922 |
| 93 | 3970.1 | 3680.75923189107 | 289.340768108933 |
| 94 | 4138.52 | 3998.38115866742 | 140.138841332576 |
| 95 | 4199.75 | 4005.30591265847 | 194.444087341531 |
| 96 | 4290.89 | 3913.29420654587 | 377.595793454128 |
| 97 | 4443.91 | 4194.01683732498 | 249.893162675018 |
| 98 | 4502.64 | 4275.88370420499 | 226.756295795007 |
| 99 | 4356.98 | 4013.94715652773 | 343.032843472272 |
| 100 | 4591.27 | 4213.93221133105 | 377.337788668951 |
| 101 | 4696.96 | 4431.15397063312 | 265.806029366885 |
| 102 | 4621.4 | 4349.20243048809 | 272.197569511910 |
| 103 | 4562.84 | 4409.84056454571 | 152.999435454289 |
| 104 | 4202.52 | 4129.83331065031 | 72.6866893496911 |
| 105 | 4296.49 | 4307.92401769693 | -11.4340176969336 |
| 106 | 4435.23 | 4641.52263044847 | -206.292630448468 |
| 107 | 4105.18 | 4145.41452511886 | -40.2345251188606 |
| 108 | 4116.68 | 4240.07740634523 | -123.397406345227 |
| 109 | 3844.49 | 3798.90759393396 | 45.5824060660444 |
| 110 | 3720.98 | 3852.17118176078 | -131.191181760783 |
| 111 | 3674.4 | 3738.85546496286 | -64.4554649628629 |
| 112 | 3857.62 | 3933.65824339979 | -76.0382433997869 |
| 113 | 3801.06 | 3943.5865605569 | -142.526560556897 |
| 114 | 3504.37 | 3525.13660820987 | -20.7666082098690 |
| 115 | 3032.6 | 3096.90468604373 | -64.3046860437313 |
| 116 | 3047.03 | 3161.49679542101 | -114.466795421005 |
| 117 | 2962.34 | 3160.73838475211 | -198.398384752110 |
| 118 | 2197.82 | 2165.89717742234 | 31.9228225776631 |
| 119 | 2014.45 | 1912.72507459910 | 101.724925400897 |
| 120 | 1862.83 | 1875.25624960617 | -12.4262496061659 |
| 121 | 1905.41 | 1985.78762416858 | -80.377624168581 |
| 122 | 1810.99 | 1758.32342841183 | 52.6665715881659 |
| 123 | 1670.07 | 1592.06105023068 | 78.008949769321 |
| 124 | 1864.44 | 1905.96884013565 | -41.5288401356504 |
| 125 | 2052.02 | 2066.60035978536 | -14.5803597853576 |
| 126 | 2029.6 | 2090.00547897607 | -60.405478976066 |
| 127 | 2070.83 | 2126.99603054467 | -56.1660305446732 |
| 128 | 2293.41 | 2531.63106736077 | -238.221067360769 |
| 129 | 2443.27 | 2640.88275897021 | -197.612758970214 |
| 130 | 2513.17 | 2715.69240468249 | -202.522404682485 |
| 131 | 2466.92 | 2810.89541327531 | -343.975413275310 |
| 132 | 2502.66 | 2795.76723507134 | -293.107235071345 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 23 | 0.143247789393016 | 0.286495578786031 | 0.856752210606984 |
| 24 | 0.0732187004096181 | 0.146437400819236 | 0.926781299590382 |
| 25 | 0.0419992370665825 | 0.083998474133165 | 0.958000762933418 |
| 26 | 0.0191903994248866 | 0.0383807988497733 | 0.980809600575113 |
| 27 | 0.00786426484181974 | 0.0157285296836395 | 0.99213573515818 |
| 28 | 0.00308691176632982 | 0.00617382353265963 | 0.99691308823367 |
| 29 | 0.00167644886891851 | 0.00335289773783703 | 0.998323551131082 |
| 30 | 0.000686318851684574 | 0.00137263770336915 | 0.999313681148315 |
| 31 | 0.000283745001087341 | 0.000567490002174683 | 0.999716254998913 |
| 32 | 9.16980217966155e-05 | 0.000183396043593231 | 0.999908301978203 |
| 33 | 8.15818149243974e-05 | 0.000163163629848795 | 0.999918418185076 |
| 34 | 2.94520390031158e-05 | 5.89040780062315e-05 | 0.999970547960997 |
| 35 | 1.32053104965165e-05 | 2.6410620993033e-05 | 0.999986794689503 |
| 36 | 4.98916633374654e-06 | 9.97833266749309e-06 | 0.999995010833666 |
| 37 | 1.68930743681456e-06 | 3.37861487362912e-06 | 0.999998310692563 |
| 38 | 1.70186631587016e-06 | 3.40373263174032e-06 | 0.999998298133684 |
| 39 | 1.71965361642185e-06 | 3.43930723284371e-06 | 0.999998280346384 |
| 40 | 1.69902256589049e-05 | 3.39804513178098e-05 | 0.999983009774341 |
| 41 | 0.000191004184415169 | 0.000382008368830337 | 0.999808995815585 |
| 42 | 0.000106593380326529 | 0.000213186760653059 | 0.999893406619673 |
| 43 | 6.664122640398e-05 | 0.00013328245280796 | 0.999933358773596 |
| 44 | 7.18558563335686e-05 | 0.000143711712667137 | 0.999928144143666 |
| 45 | 7.80155308520417e-05 | 0.000156031061704083 | 0.999921984469148 |
| 46 | 0.000149738141610941 | 0.000299476283221882 | 0.99985026185839 |
| 47 | 0.000751761738458942 | 0.00150352347691788 | 0.99924823826154 |
| 48 | 0.00186148654607147 | 0.00372297309214294 | 0.998138513453928 |
| 49 | 0.00272656236577629 | 0.00545312473155259 | 0.997273437634224 |
| 50 | 0.00221787743648747 | 0.00443575487297494 | 0.997782122563513 |
| 51 | 0.00137993554129367 | 0.00275987108258734 | 0.998620064458706 |
| 52 | 0.00230708897519843 | 0.00461417795039685 | 0.997692911024802 |
| 53 | 0.00490470654700325 | 0.0098094130940065 | 0.995095293452997 |
| 54 | 0.00591821378480476 | 0.0118364275696095 | 0.994081786215195 |
| 55 | 0.0067121456382241 | 0.0134242912764482 | 0.993287854361776 |
| 56 | 0.0111048519645621 | 0.0222097039291241 | 0.988895148035438 |
| 57 | 0.00899337271409132 | 0.0179867454281826 | 0.991006627285909 |
| 58 | 0.0225153324008424 | 0.0450306648016848 | 0.977484667599158 |
| 59 | 0.0199142521041237 | 0.0398285042082475 | 0.980085747895876 |
| 60 | 0.0172518703787952 | 0.0345037407575904 | 0.982748129621205 |
| 61 | 0.0178832581758222 | 0.0357665163516444 | 0.982116741824178 |
| 62 | 0.0196510882206221 | 0.0393021764412442 | 0.980348911779378 |
| 63 | 0.059822687814717 | 0.119645375629434 | 0.940177312185283 |
| 64 | 0.294389233261681 | 0.588778466523361 | 0.705610766738319 |
| 65 | 0.717130186194287 | 0.565739627611426 | 0.282869813805713 |
| 66 | 0.878549364860064 | 0.242901270279873 | 0.121450635139936 |
| 67 | 0.950939041020576 | 0.0981219179588488 | 0.0490609589794244 |
| 68 | 0.974348368734017 | 0.051303262531967 | 0.0256516312659835 |
| 69 | 0.988811744590947 | 0.0223765108181061 | 0.0111882554090531 |
| 70 | 0.996438643060433 | 0.00712271387913469 | 0.00356135693956735 |
| 71 | 0.99881954906655 | 0.00236090186689779 | 0.00118045093344890 |
| 72 | 0.999736010364855 | 0.000527979270288991 | 0.000263989635144495 |
| 73 | 0.999955249419973 | 8.95011600547486e-05 | 4.47505800273743e-05 |
| 74 | 0.999991821979787 | 1.63560404269183e-05 | 8.17802021345915e-06 |
| 75 | 0.999999447949086 | 1.10410182817721e-06 | 5.52050914088607e-07 |
| 76 | 0.999999865998808 | 2.68002383356715e-07 | 1.34001191678358e-07 |
| 77 | 0.999999979805916 | 4.03881671518795e-08 | 2.01940835759397e-08 |
| 78 | 0.999999986667262 | 2.66654758810450e-08 | 1.33327379405225e-08 |
| 79 | 0.999999977865618 | 4.42687631609296e-08 | 2.21343815804648e-08 |
| 80 | 0.999999977214162 | 4.55716763995504e-08 | 2.27858381997752e-08 |
| 81 | 0.999999959396677 | 8.12066455311474e-08 | 4.06033227655737e-08 |
| 82 | 0.999999912264889 | 1.75470222245799e-07 | 8.77351111228994e-08 |
| 83 | 0.999999879994226 | 2.40011547178971e-07 | 1.20005773589486e-07 |
| 84 | 0.999999803053181 | 3.93893637745505e-07 | 1.96946818872752e-07 |
| 85 | 0.999999808670733 | 3.82658533651996e-07 | 1.91329266825998e-07 |
| 86 | 0.99999987530396 | 2.49392082151797e-07 | 1.24696041075899e-07 |
| 87 | 0.999999955571951 | 8.8856097620371e-08 | 4.44280488101855e-08 |
| 88 | 0.999999992641132 | 1.47177356644605e-08 | 7.35886783223024e-09 |
| 89 | 0.999999998360742 | 3.27851516313736e-09 | 1.63925758156868e-09 |
| 90 | 0.99999999979845 | 4.03098284684173e-10 | 2.01549142342086e-10 |
| 91 | 0.999999999430083 | 1.13983382385728e-09 | 5.6991691192864e-10 |
| 92 | 0.999999998284002 | 3.43199576747599e-09 | 1.71599788373799e-09 |
| 93 | 0.999999994139588 | 1.17208237361543e-08 | 5.86041186807713e-09 |
| 94 | 0.999999993537153 | 1.29256948434256e-08 | 6.46284742171282e-09 |
| 95 | 0.999999982049185 | 3.59016296426999e-08 | 1.79508148213500e-08 |
| 96 | 0.999999935271894 | 1.29456211224920e-07 | 6.47281056124602e-08 |
| 97 | 0.999999852787932 | 2.94424135901040e-07 | 1.47212067950520e-07 |
| 98 | 0.999999748986427 | 5.02027145903405e-07 | 2.51013572951703e-07 |
| 99 | 0.999999382101446 | 1.23579710809519e-06 | 6.17898554047593e-07 |
| 100 | 0.999997558830858 | 4.88233828503801e-06 | 2.44116914251901e-06 |
| 101 | 0.99999065437025 | 1.86912595016216e-05 | 9.34562975081078e-06 |
| 102 | 0.9999764503599 | 4.70992801995718e-05 | 2.35496400997859e-05 |
| 103 | 0.999945499661665 | 0.000109000676670785 | 5.45003383353927e-05 |
| 104 | 0.999780154010238 | 0.000439691979523398 | 0.000219845989761699 |
| 105 | 0.999366997717847 | 0.00126600456430651 | 0.000633002282153255 |
| 106 | 0.99889255877815 | 0.00221488244369992 | 0.00110744122184996 |
| 107 | 0.99852509786321 | 0.00294980427357802 | 0.00147490213678901 |
| 108 | 0.993753085995501 | 0.0124938280089973 | 0.00624691400449863 |
| 109 | 0.973807972256099 | 0.0523840554878024 | 0.0261920277439012 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 64 | 0.735632183908046 | NOK |
| 5% type I error level | 77 | 0.885057471264368 | NOK |
| 10% type I error level | 81 | 0.93103448275862 | NOK |
