| Multiple Linear Regression - Estimated Regression Equation |
| BEL20[t] = + 3339.86513177408 + 1304.98832890692`X `[t] -22.5208594318981t + 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) | 3339.86513177408 | 134.536134 | 24.825 | 0 | 0 |
| `X ` | 1304.98832890692 | 124.828528 | 10.4542 | 0 | 0 |
| t | -22.5208594318981 | 3.585925 | -6.2803 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.835206925173309 |
| R-squared | 0.697570607857453 |
| Adjusted R-squared | 0.686959050238417 |
| F-TEST (value) | 65.7368722765109 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 57 |
| p-value | 1.55431223447522e-15 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 475.167067871291 |
| Sum Squared Residuals | 12869673.3161958 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2756.76 | 3317.34427234219 | -560.584272342194 |
| 2 | 2849.27 | 3294.82341291029 | -445.553412910291 |
| 3 | 2921.44 | 3272.30255347839 | -350.862553478391 |
| 4 | 2981.85 | 3249.78169404649 | -267.931694046493 |
| 5 | 3080.58 | 3227.26083461459 | -146.680834614595 |
| 6 | 3106.22 | 3204.73997518270 | -98.5199751826969 |
| 7 | 3119.31 | 3182.2191157508 | -62.9091157507986 |
| 8 | 3061.26 | 3159.6982563189 | -98.4382563189002 |
| 9 | 3097.31 | 3137.177396887 | -39.8673968870024 |
| 10 | 3161.69 | 3114.65653745510 | 47.0334625448959 |
| 11 | 3257.16 | 3092.13567802321 | 165.024321976794 |
| 12 | 3277.01 | 3069.61481859131 | 207.395181408692 |
| 13 | 3295.32 | 3047.09395915941 | 248.226040840590 |
| 14 | 3363.99 | 3024.57309972751 | 339.416900272488 |
| 15 | 3494.17 | 3002.05224029561 | 492.117759704387 |
| 16 | 3667.03 | 4284.51970977064 | -617.489709770638 |
| 17 | 3813.06 | 4261.99885033874 | -448.93885033874 |
| 18 | 3917.96 | 4239.47799090684 | -321.517990906842 |
| 19 | 3895.51 | 4216.95713147494 | -321.447131474943 |
| 20 | 3801.06 | 4194.43627204305 | -393.376272043046 |
| 21 | 3570.12 | 2866.92708370422 | 703.192916295775 |
| 22 | 3701.61 | 4149.39455317925 | -447.784553179249 |
| 23 | 3862.27 | 4126.87369374735 | -264.603693747351 |
| 24 | 3970.1 | 4104.35283431545 | -134.252834315453 |
| 25 | 4138.52 | 4081.83197488355 | 56.6880251164455 |
| 26 | 4199.75 | 4059.31111545166 | 140.438884548343 |
| 27 | 4290.89 | 4036.79025601976 | 254.099743980242 |
| 28 | 4443.91 | 4014.26939658786 | 429.640603412139 |
| 29 | 4502.64 | 3991.74853715596 | 510.891462844038 |
| 30 | 4356.98 | 3969.22767772406 | 387.752322275935 |
| 31 | 4591.27 | 3946.70681829217 | 644.563181707834 |
| 32 | 4696.96 | 3924.18595886027 | 772.774041139732 |
| 33 | 4621.4 | 3901.66509942837 | 719.73490057163 |
| 34 | 4562.84 | 3879.14423999647 | 683.695760003529 |
| 35 | 4202.52 | 3856.62338056457 | 345.896619435427 |
| 36 | 4296.49 | 3834.10252113268 | 462.387478867324 |
| 37 | 4435.23 | 3811.58166170078 | 623.648338299222 |
| 38 | 4105.18 | 3789.06080226888 | 316.119197731121 |
| 39 | 4116.68 | 3766.53994283698 | 350.140057163019 |
| 40 | 3844.49 | 3744.01908340508 | 100.470916594917 |
| 41 | 3720.98 | 3721.49822397318 | -0.518223973184703 |
| 42 | 3674.4 | 3698.97736454129 | -24.5773645412865 |
| 43 | 3857.62 | 3676.45650510939 | 181.163494890611 |
| 44 | 3801.06 | 3653.93564567749 | 147.124354322510 |
| 45 | 3504.37 | 3631.41478624559 | -127.044786245592 |
| 46 | 3032.6 | 3608.89392681369 | -576.293926813694 |
| 47 | 3047.03 | 2281.38473847487 | 765.645261525127 |
| 48 | 2962.34 | 3563.8522079499 | -601.512207949898 |
| 49 | 2197.82 | 3541.331348518 | -1343.511348518 |
| 50 | 2014.45 | 3518.8104890861 | -1504.3604890861 |
| 51 | 1862.83 | 2191.30130074728 | -328.471300747281 |
| 52 | 1905.41 | 2168.78044131538 | -263.370441315382 |
| 53 | 1810.99 | 2146.25958188348 | -335.269581883484 |
| 54 | 1670.07 | 2123.73872245159 | -453.668722451586 |
| 55 | 1864.44 | 2101.21786301969 | -236.777863019688 |
| 56 | 2052.02 | 2078.69700358779 | -26.6770035877898 |
| 57 | 2029.6 | 2056.17614415589 | -26.5761441558916 |
| 58 | 2070.83 | 2033.65528472399 | 37.1747152760064 |
| 59 | 2293.41 | 2011.13442529210 | 282.275574707905 |
| 60 | 2443.27 | 1988.61356586020 | 454.656434139803 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.000124209146068425 | 0.000248418292136851 | 0.999875790853932 |
| 7 | 5.54915922406518e-05 | 0.000110983184481304 | 0.99994450840776 |
| 8 | 0.000125180127005182 | 0.000250360254010364 | 0.999874819872995 |
| 9 | 3.64016714144054e-05 | 7.28033428288108e-05 | 0.999963598328586 |
| 10 | 5.39546348968978e-06 | 1.07909269793796e-05 | 0.99999460453651 |
| 11 | 6.84196580268048e-07 | 1.36839316053610e-06 | 0.99999931580342 |
| 12 | 7.69511262090618e-08 | 1.53902252418124e-07 | 0.999999923048874 |
| 13 | 8.73703521956666e-09 | 1.74740704391333e-08 | 0.999999991262965 |
| 14 | 8.88558719092688e-10 | 1.77711743818538e-09 | 0.999999999111441 |
| 15 | 3.06631004237721e-10 | 6.13262008475442e-10 | 0.99999999969337 |
| 16 | 4.59790369025354e-11 | 9.19580738050708e-11 | 0.999999999954021 |
| 17 | 1.61353527280524e-11 | 3.22707054561048e-11 | 0.999999999983865 |
| 18 | 8.8016062624149e-12 | 1.76032125248298e-11 | 0.999999999991198 |
| 19 | 1.48587334604746e-12 | 2.97174669209492e-12 | 0.999999999998514 |
| 20 | 2.13675350796598e-12 | 4.27350701593197e-12 | 0.999999999997863 |
| 21 | 6.07973410896417e-13 | 1.21594682179283e-12 | 0.999999999999392 |
| 22 | 6.97497282635232e-11 | 1.39499456527046e-10 | 0.99999999993025 |
| 23 | 6.16946446089152e-11 | 1.23389289217830e-10 | 0.999999999938305 |
| 24 | 3.36728872938233e-11 | 6.73457745876466e-11 | 0.999999999966327 |
| 25 | 3.71620200587646e-11 | 7.43240401175292e-11 | 0.999999999962838 |
| 26 | 4.53255388543792e-11 | 9.06510777087585e-11 | 0.999999999954674 |
| 27 | 8.15161214116907e-11 | 1.63032242823381e-10 | 0.999999999918484 |
| 28 | 4.7808271913803e-10 | 9.5616543827606e-10 | 0.999999999521917 |
| 29 | 1.14954052233281e-09 | 2.29908104466562e-09 | 0.99999999885046 |
| 30 | 5.23545498595001e-10 | 1.04709099719000e-09 | 0.999999999476455 |
| 31 | 5.44911830431442e-10 | 1.08982366086288e-09 | 0.999999999455088 |
| 32 | 7.1852006141997e-10 | 1.43704012283994e-09 | 0.99999999928148 |
| 33 | 2.24089271327725e-10 | 4.48178542655450e-10 | 0.99999999977591 |
| 34 | 6.403631128786e-11 | 1.2807262257572e-10 | 0.999999999935964 |
| 35 | 2.87751789060804e-09 | 5.75503578121607e-09 | 0.999999997122482 |
| 36 | 7.82228092667963e-09 | 1.56445618533593e-08 | 0.999999992177719 |
| 37 | 6.98647747021682e-09 | 1.39729549404336e-08 | 0.999999993013523 |
| 38 | 1.56956868939592e-07 | 3.13913737879185e-07 | 0.99999984304313 |
| 39 | 1.01446168510863e-06 | 2.02892337021725e-06 | 0.999998985538315 |
| 40 | 2.37600546629739e-05 | 4.75201093259477e-05 | 0.999976239945337 |
| 41 | 0.000233414248863525 | 0.000466828497727049 | 0.999766585751136 |
| 42 | 0.000936452793840267 | 0.00187290558768053 | 0.99906354720616 |
| 43 | 0.00234455292420612 | 0.00468910584841224 | 0.997655447075794 |
| 44 | 0.0103590732120489 | 0.0207181464240977 | 0.989640926787951 |
| 45 | 0.0540845483564334 | 0.108169096712867 | 0.945915451643567 |
| 46 | 0.176298843656041 | 0.352597687312082 | 0.823701156343959 |
| 47 | 0.742600935130472 | 0.514798129739055 | 0.257399064869528 |
| 48 | 0.9978828266335 | 0.00423434673299958 | 0.00211717336649979 |
| 49 | 0.999210907721384 | 0.00157818455723265 | 0.000789092278616324 |
| 50 | 0.998901992690212 | 0.00219601461957596 | 0.00109800730978798 |
| 51 | 0.99820743916395 | 0.00358512167210126 | 0.00179256083605063 |
| 52 | 0.998901170129479 | 0.00219765974104289 | 0.00109882987052144 |
| 53 | 0.998399892633088 | 0.00320021473382482 | 0.00160010736691241 |
| 54 | 0.992158454902455 | 0.0156830901950897 | 0.00784154509754487 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 44 | 0.897959183673469 | NOK |
| 5% type I error level | 46 | 0.938775510204082 | NOK |
| 10% type I error level | 46 | 0.938775510204082 | NOK |
