| Multiple Linear Regression - Estimated Regression Equation |
| Bel20[t] = + 4613.22177600925 -0.061195865360757Goudprijs[t] -1244.06723492356Crisis[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) | 4613.22177600925 | 228.323382 | 20.2048 | 0 | 0 |
| Goudprijs | -0.061195865360757 | 0.011986 | -5.1058 | 3e-06 | 1e-06 |
| Crisis | -1244.06723492356 | 171.671535 | -7.2468 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.776409600774211 |
| R-squared | 0.60281186817437 |
| Adjusted R-squared | 0.590955506030321 |
| F-TEST (value) | 50.8429028103661 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 67 |
| p-value | 3.68594044175552e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 542.797901831124 |
| Sum Squared Residuals | 19740180.6695622 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2649.2 | 2711.43786819299 | -62.2378681929893 |
| 2 | 2579.4 | 2698.21956127507 | -118.819561275075 |
| 3 | 2504.6 | 2762.90359096140 | -258.303590961396 |
| 4 | 2462.3 | 2767.55447672881 | -305.254476728812 |
| 5 | 2467.4 | 2628.27268716773 | -160.872687167729 |
| 6 | 2446.7 | 2734.81468876081 | -288.114688760807 |
| 7 | 2656.3 | 2928.80558195441 | -272.505581954407 |
| 8 | 2626.2 | 2995.57027106299 | -369.370271062993 |
| 9 | 2482.6 | 3038.10139748872 | -555.501397488719 |
| 10 | 2539.9 | 3070.84118545672 | -530.941185456724 |
| 11 | 2502.7 | 3084.73264689362 | -582.032646893616 |
| 12 | 2466.9 | 3124.93833043563 | -658.038330435633 |
| 13 | 2513.2 | 1981.23231470371 | 531.967685296285 |
| 14 | 2443.3 | 2019.66331815027 | 423.63668184973 |
| 15 | 2293.4 | 2055.46289938631 | 237.937100613687 |
| 16 | 2070.8 | 2060.60335207662 | 10.1966479233834 |
| 17 | 2029.6 | 2036.49218112448 | -6.89218112447866 |
| 18 | 2052 | 2027.25160545500 | 24.7483945449957 |
| 19 | 1864.4 | 2034.22793410613 | -169.827934106130 |
| 20 | 1670.1 | 1965.504977306 | -295.404977306000 |
| 21 | 1811 | 1925.23809789862 | -114.238097898622 |
| 22 | 1905.4 | 2094.44466562112 | -189.044665621115 |
| 23 | 1862.8 | 2166.65578674681 | -303.855786746809 |
| 24 | 2014.5 | 2194.49990548595 | -179.999905485953 |
| 25 | 2197.8 | 2167.02296193897 | 30.7770380610269 |
| 26 | 2962.3 | 3482.13859654637 | -519.838596546372 |
| 27 | 3047 | 3506.86172615212 | -459.861726152118 |
| 28 | 3032.6 | 3439.60747012065 | -407.007470120646 |
| 29 | 3504.4 | 3487.76861615956 | 16.6313838404383 |
| 30 | 3801.1 | 3484.70882289152 | 316.391177108476 |
| 31 | 3857.6 | 3475.95781414494 | 381.642185855064 |
| 32 | 3674.4 | 3382.69531533514 | 291.704684664858 |
| 33 | 3721 | 3380.24748072071 | 340.752519279288 |
| 34 | 3844.5 | 3426.38916320272 | 418.110836797277 |
| 35 | 4116.7 | 3527.30114518261 | 589.398854817389 |
| 36 | 4105.2 | 3530.29974258529 | 574.900257414712 |
| 37 | 4435.2 | 3570.93379718483 | 864.266202815169 |
| 38 | 4296.5 | 3607.28414120912 | 689.21585879088 |
| 39 | 4202.5 | 3653.48701955649 | 549.012980443508 |
| 40 | 4562.8 | 3658.9334515736 | 903.8665484264 |
| 41 | 4621.4 | 3651.65114359567 | 969.74885640433 |
| 42 | 4697 | 3637.94326975486 | 1059.05673024514 |
| 43 | 4591.3 | 3623.62343726044 | 967.676562739558 |
| 44 | 4357 | 3638.49403254311 | 718.505967456894 |
| 45 | 4502.6 | 3612.79176909159 | 889.808230908412 |
| 46 | 4443.9 | 3659.85138955401 | 784.04861044599 |
| 47 | 4290.9 | 3676.61905666286 | 614.280943337142 |
| 48 | 4199.8 | 3655.62887484412 | 544.171125155882 |
| 49 | 4138.5 | 3698.09880540448 | 440.401194595516 |
| 50 | 3970.1 | 3686.89996204347 | 283.200037956535 |
| 51 | 3862.3 | 3643.94046456021 | 218.359535439786 |
| 52 | 3701.6 | 3631.02813696909 | 70.571863030906 |
| 53 | 3570.12 | 3685.00289021728 | -114.882890217282 |
| 54 | 3801.06 | 3568.97552949329 | 232.084470506714 |
| 55 | 3895.51 | 3633.78195091033 | 261.728049089672 |
| 56 | 3917.96 | 3702.26012424902 | 215.699875750985 |
| 57 | 3813.06 | 3699.50631030778 | 113.553689692219 |
| 58 | 3667.03 | 3723.18911020239 | -56.1591102023939 |
| 59 | 3494.17 | 3767.98448364647 | -273.814483646468 |
| 60 | 3364 | 3815.77845449322 | -451.778454493220 |
| 61 | 3295.3 | 3843.74496496309 | -548.444964963085 |
| 62 | 3277 | 3881.07444283315 | -604.074442833147 |
| 63 | 3257.2 | 3912.46792176322 | -655.267921763216 |
| 64 | 3161.7 | 3918.89348762610 | -757.193487626095 |
| 65 | 3097.3 | 3918.46511656857 | -821.16511656857 |
| 66 | 3061.3 | 3958.30362491842 | -897.003624918422 |
| 67 | 3119.3 | 3961.73059337862 | -842.430593378625 |
| 68 | 3106.22 | 3967.23822126109 | -861.018221261093 |
| 69 | 3080.58 | 3972.92943673964 | -892.349436739644 |
| 70 | 2981.85 | 3976.35640519985 | -994.506405199846 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.00834308216163476 | 0.0166861643232695 | 0.991656917838365 |
| 7 | 0.00181870479547208 | 0.00363740959094417 | 0.998181295204528 |
| 8 | 0.000287093837567836 | 0.000574187675135673 | 0.999712906162432 |
| 9 | 0.000130813154128263 | 0.000261626308256525 | 0.999869186845872 |
| 10 | 2.83167245240797e-05 | 5.66334490481594e-05 | 0.999971683275476 |
| 11 | 8.96072240673996e-06 | 1.79214448134799e-05 | 0.999991039277593 |
| 12 | 6.17076556960727e-06 | 1.23415311392145e-05 | 0.99999382923443 |
| 13 | 1.14132862579632e-06 | 2.28265725159264e-06 | 0.999998858671374 |
| 14 | 2.47740234932889e-07 | 4.95480469865778e-07 | 0.999999752259765 |
| 15 | 2.25508338966473e-07 | 4.51016677932945e-07 | 0.999999774491661 |
| 16 | 2.79817927913522e-06 | 5.59635855827044e-06 | 0.99999720182072 |
| 17 | 5.9667641580142e-06 | 1.19335283160284e-05 | 0.999994033235842 |
| 18 | 4.41520009213631e-06 | 8.83040018427263e-06 | 0.999995584799908 |
| 19 | 1.37092569093677e-05 | 2.74185138187354e-05 | 0.99998629074309 |
| 20 | 0.000121411950686569 | 0.000242823901373137 | 0.999878588049314 |
| 21 | 0.000125200404214631 | 0.000250400808429262 | 0.999874799595785 |
| 22 | 6.9985338021111e-05 | 0.000139970676042222 | 0.999930014661979 |
| 23 | 4.2335594481768e-05 | 8.4671188963536e-05 | 0.999957664405518 |
| 24 | 1.67333450080796e-05 | 3.34666900161591e-05 | 0.999983266654992 |
| 25 | 8.03100132330144e-06 | 1.60620026466029e-05 | 0.999991968998677 |
| 26 | 2.42468854819470e-05 | 4.84937709638941e-05 | 0.999975753114518 |
| 27 | 5.1792041030865e-05 | 0.00010358408206173 | 0.99994820795897 |
| 28 | 0.000189206032140015 | 0.000378412064280029 | 0.99981079396786 |
| 29 | 0.00161203656621969 | 0.00322407313243938 | 0.99838796343378 |
| 30 | 0.0135414358660923 | 0.0270828717321847 | 0.986458564133908 |
| 31 | 0.0422006853602082 | 0.0844013707204164 | 0.957799314639792 |
| 32 | 0.122121490978540 | 0.244242981957079 | 0.87787850902146 |
| 33 | 0.358427402890646 | 0.716854805781293 | 0.641572597109354 |
| 34 | 0.685226558933815 | 0.62954688213237 | 0.314773441066185 |
| 35 | 0.787378728682815 | 0.425242542634370 | 0.212621271317185 |
| 36 | 0.855805695311808 | 0.288388609376383 | 0.144194304688192 |
| 37 | 0.894947043649216 | 0.210105912701569 | 0.105052956350784 |
| 38 | 0.887047605471798 | 0.225904789056405 | 0.112952394528202 |
| 39 | 0.858847072169265 | 0.282305855661469 | 0.141152927830735 |
| 40 | 0.908341051217773 | 0.183317897564455 | 0.0916589487822273 |
| 41 | 0.953403174468308 | 0.0931936510633843 | 0.0465968255316922 |
| 42 | 0.985687036712341 | 0.0286259265753174 | 0.0143129632876587 |
| 43 | 0.993562973788406 | 0.0128740524231877 | 0.00643702621159387 |
| 44 | 0.993691161643892 | 0.0126176767122158 | 0.00630883835610792 |
| 45 | 0.996591951844382 | 0.00681609631123648 | 0.00340804815561824 |
| 46 | 0.999321426616543 | 0.00135714676691351 | 0.000678573383456754 |
| 47 | 0.999870381405835 | 0.000259237188329146 | 0.000129618594164573 |
| 48 | 0.999953448815001 | 9.31023699974298e-05 | 4.65511849987149e-05 |
| 49 | 0.999998169451667 | 3.66109666536169e-06 | 1.83054833268085e-06 |
| 50 | 0.999999504102624 | 9.91794753074006e-07 | 4.95897376537003e-07 |
| 51 | 0.999998673440692 | 2.65311861499514e-06 | 1.32655930749757e-06 |
| 52 | 0.99999788315778 | 4.23368443959049e-06 | 2.11684221979524e-06 |
| 53 | 0.999998088003702 | 3.82399259632428e-06 | 1.91199629816214e-06 |
| 54 | 0.999999822944024 | 3.54111952755872e-07 | 1.77055976377936e-07 |
| 55 | 0.999999264283637 | 1.47143272569921e-06 | 7.35716362849604e-07 |
| 56 | 0.999999841894848 | 3.16210303397375e-07 | 1.58105151698687e-07 |
| 57 | 0.999999883819624 | 2.32360752082446e-07 | 1.16180376041223e-07 |
| 58 | 0.999999719481291 | 5.61037417310413e-07 | 2.80518708655207e-07 |
| 59 | 0.99999849642362 | 3.00715275923046e-06 | 1.50357637961523e-06 |
| 60 | 0.999992201960986 | 1.55960780276960e-05 | 7.79803901384798e-06 |
| 61 | 0.999966268063373 | 6.74638732543073e-05 | 3.37319366271536e-05 |
| 62 | 0.999806451778569 | 0.000387096442862755 | 0.000193548221431377 |
| 63 | 0.999574506361485 | 0.000850987277029142 | 0.000425493638514571 |
| 64 | 0.997236750687917 | 0.00552649862416655 | 0.00276324931208328 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 43 | 0.728813559322034 | NOK |
| 5% type I error level | 48 | 0.813559322033898 | NOK |
| 10% type I error level | 50 | 0.847457627118644 | NOK |
