| Multiple Linear Regression - Estimated Regression Equation |
| BEL20[t] = + 2126.50790173381 -0.0990811328413003GoudkoersTeBrussel[t] -1106.20333386995EurosPerUSdollar[t] + 0.283036267354236Uitvoer[t] -0.0609199263782027Invoer[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) | 2126.50790173381 | 2243.300481 | 0.9479 | 0.347234 | 0.173617 |
| GoudkoersTeBrussel | -0.0990811328413003 | 0.028498 | -3.4768 | 0.000988 | 0.000494 |
| EurosPerUSdollar | -1106.20333386995 | 1919.932206 | -0.5762 | 0.56681 | 0.283405 |
| Uitvoer | 0.283036267354236 | 0.118886 | 2.3807 | 0.020705 | 0.010352 |
| Invoer | -0.0609199263782027 | 0.119544 | -0.5096 | 0.612332 | 0.306166 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.730564570458489 |
| R-squared | 0.533724591609197 |
| Adjusted R-squared | 0.500419205295568 |
| F-TEST (value) | 16.0251734233989 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 56 |
| p-value | 8.40611757979559e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 609.675684924554 |
| Sum Squared Residuals | 20815448.6841406 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2981.85 | 3491.69245704366 | -509.842457043663 |
| 2 | 3080.58 | 3599.17462068913 | -518.594620689127 |
| 3 | 3106.22 | 4128.07817242405 | -1021.85817242405 |
| 4 | 3119.31 | 3840.15141718048 | -720.841417180484 |
| 5 | 3061.26 | 3663.23007342307 | -601.970073423068 |
| 6 | 3097.31 | 3900.38861851738 | -803.078618517376 |
| 7 | 3161.69 | 3419.51384450949 | -257.823844509491 |
| 8 | 3257.16 | 3073.97427795321 | 183.18572204679 |
| 9 | 3277.01 | 3959.18257802101 | -682.172578021007 |
| 10 | 3295.32 | 3598.36468023977 | -303.04468023977 |
| 11 | 3363.99 | 3760.05435533608 | -396.064355336079 |
| 12 | 3494.17 | 3401.44755883288 | 92.7224411671194 |
| 13 | 3667.03 | 3301.66681319501 | 365.36318680499 |
| 14 | 3813.06 | 3353.81219116679 | 459.24780883321 |
| 15 | 3917.96 | 4036.96166390746 | -119.001663907462 |
| 16 | 3895.51 | 3142.1817327607 | 753.328267239302 |
| 17 | 3801.06 | 3578.79439018193 | 222.265609818066 |
| 18 | 3570.12 | 3824.55922006526 | -254.439220065256 |
| 19 | 3701.61 | 3318.61635806202 | 382.993641937976 |
| 20 | 3862.27 | 2924.61864952066 | 937.651350479335 |
| 21 | 3970.1 | 3834.86589376569 | 135.234106234307 |
| 22 | 4138.52 | 3876.75017832836 | 261.769821671644 |
| 23 | 4199.75 | 3837.67090543143 | 362.079094568567 |
| 24 | 4290.89 | 3303.19218753388 | 987.697812466121 |
| 25 | 4443.91 | 3605.45297666172 | 838.457023338282 |
| 26 | 4502.64 | 3507.89561148535 | 994.744388514652 |
| 27 | 4356.98 | 4115.35589467224 | 241.624105327764 |
| 28 | 4591.27 | 3554.93666827801 | 1036.33333172199 |
| 29 | 4696.96 | 3812.00283216163 | 884.957167838372 |
| 30 | 4621.4 | 4082.74535036678 | 538.654649633219 |
| 31 | 4562.84 | 3818.92135693719 | 743.918643062815 |
| 32 | 4202.52 | 3341.72093931951 | 860.799060680491 |
| 33 | 4296.49 | 3793.55090174177 | 502.939098258232 |
| 34 | 4435.23 | 4203.00104284636 | 232.228957153635 |
| 35 | 4105.18 | 3789.55241228801 | 315.627587711986 |
| 36 | 4116.68 | 3144.3097598985 | 972.370240101498 |
| 37 | 3844.49 | 3471.48509690339 | 373.004903096607 |
| 38 | 3720.98 | 3545.7930486161 | 175.186951383899 |
| 39 | 3674.4 | 3571.60593024483 | 102.794069755165 |
| 40 | 3857.62 | 4024.79151367235 | -167.171513672355 |
| 41 | 3801.06 | 3803.78508205521 | -2.72508205520833 |
| 42 | 3504.37 | 4070.85601076157 | -566.486010761566 |
| 43 | 3032.6 | 3946.52269130104 | -913.922691301042 |
| 44 | 3047.03 | 3036.03969323544 | 10.9903067645572 |
| 45 | 2962.34 | 3940.35790751334 | -978.017907513341 |
| 46 | 2197.82 | 3670.6998219487 | -1472.87982194871 |
| 47 | 2014.45 | 2734.68162527474 | -720.231625274737 |
| 48 | 1862.83 | 2454.40061487941 | -591.570614879405 |
| 49 | 1905.41 | 2179.65675688753 | -274.246756887528 |
| 50 | 1810.99 | 2027.64721827998 | -216.65721827998 |
| 51 | 1670.07 | 2304.02529054005 | -633.955290540054 |
| 52 | 1864.44 | 2276.07413621696 | -411.634136216964 |
| 53 | 2052.02 | 2142.39950867821 | -90.379508678213 |
| 54 | 2029.6 | 2601.97783931905 | -572.377839319046 |
| 55 | 2070.83 | 2549.27995731465 | -478.449957314651 |
| 56 | 2293.41 | 1972.6331898815 | 320.776810118504 |
| 57 | 2443.27 | 2811.06670269913 | -367.796702699129 |
| 58 | 2513.17 | 2651.68395967311 | -138.513959673107 |
| 59 | 2466.92 | 2544.90625618239 | -77.9862561823906 |
| 60 | 2502.66 | 2361.23023794517 | 141.429762054834 |
| 61 | 2539.91 | 2106.55132522967 | 433.358674770326 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.00200150107243051 | 0.00400300214486102 | 0.99799849892757 |
| 9 | 0.000369775484847073 | 0.000739550969694147 | 0.999630224515153 |
| 10 | 9.68028442223821e-05 | 0.000193605688444764 | 0.999903197155778 |
| 11 | 1.72796670310799e-05 | 3.45593340621597e-05 | 0.999982720332969 |
| 12 | 2.16622342106512e-06 | 4.33244684213024e-06 | 0.999997833776579 |
| 13 | 2.64712031015177e-07 | 5.29424062030354e-07 | 0.999999735287969 |
| 14 | 1.06634301383587e-07 | 2.13268602767175e-07 | 0.999999893365699 |
| 15 | 2.01274553837463e-07 | 4.02549107674925e-07 | 0.999999798725446 |
| 16 | 6.33046971270559e-08 | 1.26609394254112e-07 | 0.999999936695303 |
| 17 | 6.33611911159278e-07 | 1.26722382231856e-06 | 0.999999366388089 |
| 18 | 3.31650321016458e-07 | 6.63300642032916e-07 | 0.999999668349679 |
| 19 | 7.28786800985332e-08 | 1.45757360197066e-07 | 0.99999992712132 |
| 20 | 1.85243215939975e-08 | 3.70486431879951e-08 | 0.999999981475678 |
| 21 | 1.53552775999554e-07 | 3.07105551999108e-07 | 0.999999846447224 |
| 22 | 2.46068110841061e-06 | 4.92136221682121e-06 | 0.999997539318892 |
| 23 | 3.50527145825437e-06 | 7.01054291650875e-06 | 0.999996494728542 |
| 24 | 1.26694638635042e-05 | 2.53389277270084e-05 | 0.999987330536137 |
| 25 | 3.60322259794863e-05 | 7.20644519589726e-05 | 0.999963967774021 |
| 26 | 5.60096659322045e-05 | 0.000112019331864409 | 0.999943990334068 |
| 27 | 2.35974562441209e-05 | 4.71949124882419e-05 | 0.999976402543756 |
| 28 | 2.84192433610592e-05 | 5.68384867221184e-05 | 0.999971580756639 |
| 29 | 4.43318507143945e-05 | 8.86637014287889e-05 | 0.999955668149286 |
| 30 | 4.36917163420033e-05 | 8.73834326840066e-05 | 0.999956308283658 |
| 31 | 3.60887523877406e-05 | 7.21775047754811e-05 | 0.999963911247612 |
| 32 | 3.73479172854842e-05 | 7.46958345709684e-05 | 0.999962652082715 |
| 33 | 0.000111471805940187 | 0.000222943611880374 | 0.99988852819406 |
| 34 | 0.00131559391324297 | 0.00263118782648593 | 0.998684406086757 |
| 35 | 0.024031649971436 | 0.048063299942872 | 0.975968350028564 |
| 36 | 0.166823121999434 | 0.333646243998868 | 0.833176878000566 |
| 37 | 0.5685293576822 | 0.862941284635601 | 0.4314706423178 |
| 38 | 0.961686036582387 | 0.0766279268352254 | 0.0383139634176127 |
| 39 | 0.982372981322152 | 0.0352540373556969 | 0.0176270186778484 |
| 40 | 0.986243020805081 | 0.0275139583898376 | 0.0137569791949188 |
| 41 | 0.999144182830736 | 0.00171163433852705 | 0.000855817169263526 |
| 42 | 0.999795612590022 | 0.000408774819956486 | 0.000204387409978243 |
| 43 | 0.999831548327665 | 0.000336903344670844 | 0.000168451672335422 |
| 44 | 0.9997469089712 | 0.000506182057600691 | 0.000253091028800345 |
| 45 | 0.999928396965193 | 0.000143206069613177 | 7.16030348065887e-05 |
| 46 | 0.999959365774229 | 8.12684515419015e-05 | 4.06342257709508e-05 |
| 47 | 0.999998473590941 | 3.05281811897867e-06 | 1.52640905948934e-06 |
| 48 | 0.999994289647552 | 1.14207048952812e-05 | 5.71035244764059e-06 |
| 49 | 0.999973067243083 | 5.38655138344795e-05 | 2.69327569172397e-05 |
| 50 | 0.999910616832648 | 0.000178766334704231 | 8.93831673521154e-05 |
| 51 | 0.999859980115253 | 0.00028003976949483 | 0.000140019884747415 |
| 52 | 0.998957353599666 | 0.00208529280066733 | 0.00104264640033366 |
| 53 | 0.992778473896551 | 0.0144430522068988 | 0.00722152610344942 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 39 | 0.847826086956522 | NOK |
| 5% type I error level | 43 | 0.934782608695652 | NOK |
| 10% type I error level | 44 | 0.956521739130435 | NOK |
