| Multiple Linear Regression - Estimated Regression Equation |
| Bel20[t] = + 4594.10216619123 -0.0618369432998312Goudprijs[t] -1261.58799773430Crisis[t] + 247.018444485440M1[t] + 59.9196063764291M2[t] -27.2667429400975M3[t] -46.614056640991M4[t] + 14.7376492088272M5[t] + 108.829245379779M6[t] + 88.2528810544591M7[t] -16.0969452616774M8[t] -2.40546963877111M9[t] -61.3876935415897M10[t] + 43.1494544672859M11[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) | 4594.10216619123 | 347.596503 | 13.2168 | 0 | 0 |
| Goudprijs | -0.0618369432998312 | 0.013008 | -4.7539 | 1.4e-05 | 7e-06 |
| Crisis | -1261.58799773430 | 186.773272 | -6.7546 | 0 | 0 |
| M1 | 247.018444485440 | 356.394922 | 0.6931 | 0.491109 | 0.245555 |
| M2 | 59.9196063764291 | 355.701072 | 0.1685 | 0.866832 | 0.433416 |
| M3 | -27.2667429400975 | 355.464107 | -0.0767 | 0.93913 | 0.469565 |
| M4 | -46.614056640991 | 355.540391 | -0.1311 | 0.89616 | 0.44808 |
| M5 | 14.7376492088272 | 355.645812 | 0.0414 | 0.967093 | 0.483547 |
| M6 | 108.829245379779 | 355.638676 | 0.306 | 0.760731 | 0.380366 |
| M7 | 88.2528810544591 | 355.343092 | 0.2484 | 0.804765 | 0.402382 |
| M8 | -16.0969452616774 | 355.348044 | -0.0453 | 0.96403 | 0.482015 |
| M9 | -2.40546963877111 | 355.367085 | -0.0068 | 0.994623 | 0.497312 |
| M10 | -61.3876935415897 | 355.270008 | -0.1728 | 0.863438 | 0.431719 |
| M11 | 43.1494544672859 | 371.026256 | 0.1163 | 0.907833 | 0.453916 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.782477714108096 |
| R-squared | 0.612271373075831 |
| Adjusted R-squared | 0.522262941825577 |
| F-TEST (value) | 6.80237800582827 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 56 |
| p-value | 1.31955511184501e-07 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 586.60714723922 |
| Sum Squared Residuals | 19270044.9307596 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2649.2 | 2919.41392374781 | -270.213923747811 |
| 2 | 2579.4 | 2718.95830588604 | -139.558305886037 |
| 3 | 2504.6 | 2697.13360563743 | -192.533605637433 |
| 4 | 2462.3 | 2682.48589962733 | -220.185899627326 |
| 5 | 2467.4 | 2603.09672252673 | -135.696722526728 |
| 6 | 2446.7 | 2804.84643698269 | -358.146436982687 |
| 7 | 2656.3 | 2980.29318291783 | -323.993182917831 |
| 8 | 2626.2 | 2943.40746174181 | -317.207461741811 |
| 9 | 2482.6 | 3000.0756129581 | -517.4756129581 |
| 10 | 2539.9 | 2974.17615372069 | -434.276153720691 |
| 11 | 2502.7 | 3092.75028785863 | -590.050287858628 |
| 12 | 2466.9 | 3090.22770513933 | -623.327705139331 |
| 13 | 2513.2 | 2177.07073890219 | 336.12926109781 |
| 14 | 2443.3 | 2028.80550118547 | 414.494498814527 |
| 15 | 2293.4 | 1977.79376369935 | 315.606236300653 |
| 16 | 2070.8 | 1963.64075323564 | 107.159246764360 |
| 17 | 2029.6 | 2000.62870342532 | 28.9712965746754 |
| 18 | 2052 | 2085.382921158 | -33.382921158002 |
| 19 | 1864.4 | 2071.85596836886 | -207.455968368863 |
| 20 | 1670.1 | 1898.06325472702 | -227.963254727016 |
| 21 | 1811 | 1871.06602165863 | -60.0660216586333 |
| 22 | 1905.4 | 1983.06294597985 | -77.6629459798478 |
| 23 | 1862.8 | 2160.56768708252 | -297.767687082524 |
| 24 | 2014.5 | 2145.55404181666 | -131.054041816662 |
| 25 | 2197.8 | 2364.80769876048 | -167.007698760478 |
| 26 | 2962.3 | 3511.08954955687 | -548.789549556875 |
| 27 | 3047 | 3448.88532533348 | -401.88532533348 |
| 28 | 3032.6 | 3361.57921094607 | -328.979210946072 |
| 29 | 3504.4 | 3471.59659117286 | 32.8034088271423 |
| 30 | 3801.1 | 3562.59634017882 | 238.503659821182 |
| 31 | 3857.6 | 3533.17729296162 | 324.422707038378 |
| 32 | 3674.4 | 3334.58796505654 | 339.812034943457 |
| 33 | 3721 | 3345.80596294746 | 375.194037052544 |
| 34 | 3844.5 | 3333.44879429271 | 511.05120570729 |
| 35 | 4116.7 | 3539.95506180301 | 576.744938196992 |
| 36 | 4105.2 | 3499.83561755741 | 605.364382442586 |
| 37 | 4435.2 | 3787.91379239394 | 647.286207606058 |
| 38 | 4296.5 | 3637.54609860503 | 658.95390139497 |
| 39 | 4202.5 | 3597.04664147988 | 605.453358520124 |
| 40 | 4562.8 | 3583.20281573267 | 979.597184267333 |
| 41 | 4621.4 | 3637.19592532981 | 984.204074670194 |
| 42 | 4697 | 3717.43604620160 | 979.563953798404 |
| 43 | 4591.3 | 3682.38983714412 | 908.910162855885 |
| 44 | 4357 | 3593.06638804984 | 763.933611950163 |
| 45 | 4502.6 | 3580.78634748681 | 921.813652513186 |
| 46 | 4443.9 | 3569.35673298157 | 874.543267018434 |
| 47 | 4290.9 | 3690.83720345460 | 600.062796545404 |
| 48 | 4199.8 | 3626.47767743547 | 573.322322564533 |
| 49 | 4138.5 | 3916.41096057099 | 222.089039429009 |
| 50 | 3970.1 | 3717.99596183811 | 252.104038161890 |
| 51 | 3862.3 | 3587.4000783251 | 274.899921674898 |
| 52 | 3701.6 | 3555.00516958794 | 146.594830412056 |
| 53 | 3570.12 | 3670.89705942821 | -100.777059428214 |
| 54 | 3801.06 | 3647.74581110269 | 153.314188897314 |
| 55 | 3895.51 | 3692.65476973189 | 202.855230268113 |
| 56 | 3917.96 | 3657.50048296826 | 260.459517031738 |
| 57 | 3813.06 | 3668.40929614268 | 144.650703857325 |
| 58 | 3667.03 | 3633.35796929689 | 33.6720307031087 |
| 59 | 3494.17 | 3783.15975980124 | -288.989759801243 |
| 60 | 3364 | 3788.30495805113 | -424.304958051126 |
| 61 | 3295.3 | 4063.58288562459 | -768.282885624589 |
| 62 | 3277 | 3914.20458292847 | -637.204582928475 |
| 63 | 3257.2 | 3858.74058552476 | -601.540585524762 |
| 64 | 3161.7 | 3845.88615087035 | -684.186150870351 |
| 65 | 3097.3 | 3906.80499811707 | -809.50499811707 |
| 66 | 3061.3 | 4041.15244437621 | -979.852444376212 |
| 67 | 3119.3 | 4024.03894887568 | -904.738948875682 |
| 68 | 3106.22 | 3925.25444745653 | -819.034447456531 |
| 69 | 3080.58 | 3944.69675880632 | -864.116758806321 |
| 70 | 2981.85 | 3889.17740372829 | -907.327403728294 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00832697044382449 | 0.0166539408876490 | 0.991673029556176 |
| 18 | 0.00262934090427085 | 0.0052586818085417 | 0.99737065909573 |
| 19 | 0.00507512601465159 | 0.0101502520293032 | 0.994924873985348 |
| 20 | 0.00134931977604987 | 0.00269863955209973 | 0.99865068022395 |
| 21 | 0.000823296209056332 | 0.00164659241811266 | 0.999176703790944 |
| 22 | 0.000205713274078097 | 0.000411426548156195 | 0.999794286725922 |
| 23 | 4.82743562881171e-05 | 9.65487125762342e-05 | 0.999951725643712 |
| 24 | 1.55494425979859e-05 | 3.10988851959718e-05 | 0.999984450557402 |
| 25 | 3.46725499256063e-05 | 6.93450998512126e-05 | 0.999965327450074 |
| 26 | 3.65999838853624e-05 | 7.31999677707248e-05 | 0.999963400016115 |
| 27 | 1.99427669307173e-05 | 3.98855338614345e-05 | 0.99998005723307 |
| 28 | 2.68035779060064e-05 | 5.36071558120128e-05 | 0.999973196422094 |
| 29 | 0.000181860915900214 | 0.000363721831800429 | 0.9998181390841 |
| 30 | 0.00197518480017735 | 0.0039503696003547 | 0.998024815199823 |
| 31 | 0.0097367522499022 | 0.0194735044998044 | 0.990263247750098 |
| 32 | 0.0429570647567861 | 0.0859141295135723 | 0.957042935243214 |
| 33 | 0.167039211842333 | 0.334078423684667 | 0.832960788157667 |
| 34 | 0.434890908236749 | 0.869781816473498 | 0.565109091763251 |
| 35 | 0.612038935794627 | 0.775922128410747 | 0.387961064205373 |
| 36 | 0.7064731528167 | 0.5870536943666 | 0.2935268471833 |
| 37 | 0.654444423127536 | 0.691111153744928 | 0.345555576872464 |
| 38 | 0.602495789681933 | 0.795008420636135 | 0.397504210318067 |
| 39 | 0.544071899973263 | 0.911856200053474 | 0.455928100026737 |
| 40 | 0.67610262085937 | 0.64779475828126 | 0.32389737914063 |
| 41 | 0.793043953348569 | 0.413912093302863 | 0.206956046651431 |
| 42 | 0.925523593473874 | 0.148952813052251 | 0.0744764065261255 |
| 43 | 0.95233837297023 | 0.0953232540595415 | 0.0476616270297708 |
| 44 | 0.937038473639594 | 0.125923052720812 | 0.062961526360406 |
| 45 | 0.943070841204063 | 0.113858317591875 | 0.0569291587959373 |
| 46 | 0.977924532558481 | 0.0441509348830378 | 0.0220754674415189 |
| 47 | 0.98987281617473 | 0.0202543676505395 | 0.0101271838252698 |
| 48 | 0.993438163599162 | 0.0131236728016756 | 0.00656183640083779 |
| 49 | 0.999113251098716 | 0.00177349780256892 | 0.00088674890128446 |
| 50 | 0.999055412622103 | 0.00188917475579401 | 0.000944587377897004 |
| 51 | 0.99598040780382 | 0.00803918439235988 | 0.00401959219617994 |
| 52 | 0.989189174512574 | 0.0216216509748522 | 0.0108108254874261 |
| 53 | 0.966853660407695 | 0.0662926791846107 | 0.0331463395923054 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 15 | 0.405405405405405 | NOK |
| 5% type I error level | 22 | 0.594594594594595 | NOK |
| 10% type I error level | 25 | 0.675675675675676 | NOK |
