| Multiple Linear Regression - Estimated Regression Equation |
| Bel20[t] = + 7157.54976019622 -0.145896546986036Goudprijs[t] -1480.75533060803Crisis[t] -25.7971417400726t + 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) | 7157.54976019622 | 1150.081548 | 6.2235 | 0 | 0 |
| Goudprijs | -0.145896546986036 | 0.039329 | -3.7096 | 0.000428 | 0.000214 |
| Crisis | -1480.75533060803 | 196.975377 | -7.5175 | 0 | 0 |
| t | -25.7971417400726 | 11.442122 | -2.2546 | 0.027484 | 0.013742 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.794490138920613 |
| R-squared | 0.631214580842094 |
| Adjusted R-squared | 0.614451607244008 |
| F-TEST (value) | 37.6552869422966 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 66 |
| p-value | 2.65343302885412e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 526.977815912378 |
| Sum Squared Residuals | 18328570.8186095 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2649.2 | 2597.72562777112 | 51.4743722288777 |
| 2 | 2579.4 | 2540.41483188207 | 38.9851681179326 |
| 3 | 2504.6 | 2668.83034030624 | -164.230340306235 |
| 4 | 2462.3 | 2654.1213361371 | -191.821336137100 |
| 5 | 2467.4 | 2296.26365345681 | 171.136346543189 |
| 6 | 2446.7 | 2524.47240001943 | -77.7724000194267 |
| 7 | 2656.3 | 2961.16731222509 | -304.867312225086 |
| 8 | 2626.2 | 3094.54330324678 | -468.343303246779 |
| 9 | 2482.6 | 3170.144261662 | -687.544261662001 |
| 10 | 2539.9 | 3222.40177255946 | -682.501772559457 |
| 11 | 2502.7 | 3229.72314698521 | -727.023146985215 |
| 12 | 2466.9 | 3299.78003661497 | -832.880036614967 |
| 13 | 2513.2 | 2032.49790132396 | 480.702098676036 |
| 14 | 2443.3 | 2098.32379109112 | 344.976208908879 |
| 15 | 2293.4 | 2157.87612933788 | 135.523870662120 |
| 16 | 2070.8 | 2144.33429754463 | -73.5342975446341 |
| 17 | 2029.6 | 2061.05391629206 | -31.4539162920635 |
| 18 | 2052 | 2013.2263959571 | 38.7736040429005 |
| 19 | 1864.4 | 2004.06146057344 | -139.661460573435 |
| 20 | 1670.1 | 1814.42249656804 | -144.322496568045 |
| 21 | 1811 | 1692.62542691116 | 118.374573088839 |
| 22 | 1905.4 | 2070.23223758748 | -164.832237587476 |
| 23 | 1862.8 | 2216.59302129093 | -353.793021290926 |
| 24 | 2014.5 | 2257.1788084295 | -242.678808429499 |
| 25 | 2197.8 | 2165.87411709270 | 31.9258829073037 |
| 26 | 2962.3 | 3790.21819701144 | -827.91819701144 |
| 27 | 3047 | 3823.36326025373 | -776.363260253726 |
| 28 | 3032.6 | 3637.225813376 | -604.625813376 |
| 29 | 3504.4 | 3726.24925411394 | -221.849254113938 |
| 30 | 3801.1 | 3693.15728502456 | 107.942714975437 |
| 31 | 3857.6 | 3646.49693706549 | 211.103062934512 |
| 32 | 3674.4 | 3398.35345771870 | 276.046542281303 |
| 33 | 3721 | 3366.72045409918 | 354.279545900817 |
| 34 | 3844.5 | 3450.92930878658 | 393.570691213419 |
| 35 | 4116.7 | 3665.71557302648 | 450.984426973519 |
| 36 | 4105.2 | 3647.06736208872 | 458.132637911276 |
| 37 | 4435.2 | 3718.14552754738 | 717.054472452621 |
| 38 | 4296.5 | 3779.01093471701 | 517.489065282988 |
| 39 | 4202.5 | 3863.36568595140 | 339.134314048604 |
| 40 | 4562.8 | 3850.55333689308 | 712.24666310692 |
| 41 | 4621.4 | 3807.39450606167 | 814.00549393833 |
| 42 | 4697 | 3748.91653779672 | 948.083462203275 |
| 43 | 4591.3 | 3688.97960406192 | 902.32039593808 |
| 44 | 4357 | 3698.63532323945 | 658.364676760546 |
| 45 | 4502.6 | 3611.56163176525 | 891.038368234754 |
| 46 | 4443.9 | 3697.95893465743 | 745.941065342565 |
| 47 | 4290.9 | 3712.13744679154 | 578.762553208463 |
| 48 | 4199.8 | 3636.29778943525 | 563.502210564747 |
| 49 | 4138.5 | 3711.75285130349 | 426.747148696511 |
| 50 | 3970.1 | 3659.25664146497 | 310.843358535028 |
| 51 | 3862.3 | 3531.0401237407 | 331.259876259298 |
| 52 | 3701.6 | 3474.45881058658 | 227.141189413423 |
| 53 | 3570.12 | 3577.34242328819 | -7.22242328818742 |
| 54 | 3801.06 | 3274.92542846259 | 526.134571537409 |
| 55 | 3895.51 | 3403.63272998073 | 491.87727001927 |
| 56 | 3917.96 | 3541.09382431803 | 376.866175681969 |
| 57 | 3813.06 | 3508.73133796359 | 304.328662036413 |
| 58 | 3667.03 | 3539.39615990711 | 127.633840092890 |
| 59 | 3494.17 | 3620.39529056082 | -126.225290560816 |
| 60 | 3364 | 3708.54335201684 | -344.543352016837 |
| 61 | 3295.3 | 3749.42093224938 | -454.120932249382 |
| 62 | 3277 | 3812.62068417079 | -535.620684170791 |
| 63 | 3257.2 | 3861.66847103456 | -604.468471034555 |
| 64 | 3161.7 | 3851.19046672802 | -689.490466728016 |
| 65 | 3097.3 | 3824.37204915904 | -727.072049159041 |
| 66 | 3061.3 | 3893.55355950688 | -832.253559506878 |
| 67 | 3119.3 | 3875.92662439802 | -756.626624398023 |
| 68 | 3106.22 | 3863.26017188669 | -757.040171886694 |
| 69 | 3080.58 | 3851.03140901632 | -770.451409016322 |
| 70 | 2981.85 | 3833.40447390747 | -851.554473907468 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.00580009291247104 | 0.0116001858249421 | 0.994199907087529 |
| 8 | 0.000785353057328181 | 0.00157070611465636 | 0.999214646942672 |
| 9 | 0.000282828266318656 | 0.000565656532637311 | 0.999717171733681 |
| 10 | 4.78183880289849e-05 | 9.56367760579698e-05 | 0.99995218161197 |
| 11 | 9.95780106716747e-06 | 1.99156021343349e-05 | 0.999990042198933 |
| 12 | 3.96387082263338e-06 | 7.92774164526676e-06 | 0.999996036129177 |
| 13 | 5.85938142354838e-07 | 1.17187628470968e-06 | 0.999999414061858 |
| 14 | 1.03537454062174e-07 | 2.07074908124349e-07 | 0.999999896462546 |
| 15 | 1.09253825038292e-07 | 2.18507650076583e-07 | 0.999999890746175 |
| 16 | 1.23127066435862e-06 | 2.46254132871725e-06 | 0.999998768729336 |
| 17 | 8.13040268361759e-07 | 1.62608053672352e-06 | 0.999999186959732 |
| 18 | 1.87348101574703e-07 | 3.74696203149406e-07 | 0.999999812651898 |
| 19 | 8.9730078333395e-08 | 1.7946015666679e-07 | 0.999999910269922 |
| 20 | 3.80969970527591e-08 | 7.61939941055182e-08 | 0.999999961903003 |
| 21 | 2.08793620137376e-08 | 4.17587240274751e-08 | 0.999999979120638 |
| 22 | 5.43255836247252e-09 | 1.08651167249450e-08 | 0.999999994567442 |
| 23 | 1.19739306867834e-09 | 2.39478613735668e-09 | 0.999999998802607 |
| 24 | 7.55423520161206e-10 | 1.51084704032241e-09 | 0.999999999244576 |
| 25 | 1.67730668969477e-08 | 3.35461337938953e-08 | 0.999999983226933 |
| 26 | 3.57139442792882e-06 | 7.14278885585764e-06 | 0.999996428605572 |
| 27 | 2.89756394780904e-05 | 5.79512789561808e-05 | 0.999971024360522 |
| 28 | 0.000347138311352434 | 0.000694276622704868 | 0.999652861688648 |
| 29 | 0.00892067526007236 | 0.0178413505201447 | 0.991079324739928 |
| 30 | 0.088288045727472 | 0.176576091454944 | 0.911711954272528 |
| 31 | 0.249048218773753 | 0.498096437547506 | 0.750951781226247 |
| 32 | 0.443480549954517 | 0.886961099909034 | 0.556519450045483 |
| 33 | 0.713180586768774 | 0.573638826462452 | 0.286819413231226 |
| 34 | 0.933939910580794 | 0.132120178838413 | 0.0660600894192063 |
| 35 | 0.984982206916234 | 0.0300355861675315 | 0.0150177930837657 |
| 36 | 0.998614113281174 | 0.0027717734376518 | 0.0013858867188259 |
| 37 | 0.999474592566515 | 0.00105081486697082 | 0.000525407433485409 |
| 38 | 0.999847728502987 | 0.000304542994025144 | 0.000152271497012572 |
| 39 | 0.999992495514672 | 1.50089706566349e-05 | 7.50448532831747e-06 |
| 40 | 0.99999242974898 | 1.51405020419357e-05 | 7.57025102096786e-06 |
| 41 | 0.999988123872897 | 2.37522542059033e-05 | 1.18761271029517e-05 |
| 42 | 0.999986657263771 | 2.66854724571332e-05 | 1.33427362285666e-05 |
| 43 | 0.99997804394477 | 4.39121104601649e-05 | 2.19560552300824e-05 |
| 44 | 0.99994917894397 | 0.000101642112060516 | 5.08210560302579e-05 |
| 45 | 0.99993229834514 | 0.000135403309718812 | 6.77016548594058e-05 |
| 46 | 0.999940642156747 | 0.000118715686506010 | 5.93578432530048e-05 |
| 47 | 0.99993716541425 | 0.000125669171499644 | 6.2834585749822e-05 |
| 48 | 0.99993646792641 | 0.000127064147179854 | 6.35320735899268e-05 |
| 49 | 0.999980130251419 | 3.97394971619784e-05 | 1.98697485809892e-05 |
| 50 | 0.99999173892872 | 1.65221425617821e-05 | 8.26107128089107e-06 |
| 51 | 0.99998777656591 | 2.44468681790151e-05 | 1.22234340895075e-05 |
| 52 | 0.999987823781038 | 2.43524379247331e-05 | 1.21762189623665e-05 |
| 53 | 0.99999487711494 | 1.02457701203298e-05 | 5.12288506016489e-06 |
| 54 | 0.99999910204845 | 1.79590310114643e-06 | 8.97951550573213e-07 |
| 55 | 0.999996697792395 | 6.60441521057183e-06 | 3.30220760528591e-06 |
| 56 | 0.999999157393126 | 1.68521374712177e-06 | 8.42606873560887e-07 |
| 57 | 0.999999268873319 | 1.46225336293918e-06 | 7.3112668146959e-07 |
| 58 | 0.999998865890568 | 2.26821886360416e-06 | 1.13410943180208e-06 |
| 59 | 0.999996271734494 | 7.45653101205344e-06 | 3.72826550602672e-06 |
| 60 | 0.999979268732372 | 4.14625352562967e-05 | 2.07312676281483e-05 |
| 61 | 0.999868089520067 | 0.000263820959866972 | 0.000131910479933486 |
| 62 | 0.999316515780306 | 0.00136696843938724 | 0.00068348421969362 |
| 63 | 0.997654044062178 | 0.00469191187564397 | 0.00234595593782198 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 49 | 0.859649122807018 | NOK |
| 5% type I error level | 52 | 0.912280701754386 | NOK |
| 10% type I error level | 52 | 0.912280701754386 | NOK |
