| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2850.80433638344 -529.242454901961X[t] + 606.554587799569M1[t] + 626.875762091508M2[t] + 542.308047494557M3[t] + 509.450605664492M4[t] + 460.512891067541M5[t] + 350.105176470591M6[t] + 131.211906318086M7[t] + 79.4308583878024M8[t] + 138.930921568630M9[t] + 95.2054291939026M10[t] + 85.7332701525081M11[t] + 45.3132701525054t + 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) | 2850.80433638344 | 559.729488 | 5.0932 | 2e-06 | 1e-06 |
| X | -529.242454901961 | 476.40413 | -1.1109 | 0.26944 | 0.13472 |
| M1 | 606.554587799569 | 670.050174 | 0.9052 | 0.367654 | 0.183827 |
| M2 | 626.875762091508 | 669.805105 | 0.9359 | 0.351719 | 0.175859 |
| M3 | 542.308047494557 | 669.614433 | 0.8099 | 0.420054 | 0.210027 |
| M4 | 509.450605664492 | 670.001167 | 0.7604 | 0.448935 | 0.224467 |
| M5 | 460.512891067541 | 669.592638 | 0.6878 | 0.493303 | 0.246652 |
| M6 | 350.105176470591 | 669.238378 | 0.5231 | 0.602108 | 0.301054 |
| M7 | 131.211906318086 | 668.938473 | 0.1961 | 0.844917 | 0.422458 |
| M8 | 79.4308583878024 | 668.692996 | 0.1188 | 0.905699 | 0.452849 |
| M9 | 138.930921568630 | 668.502007 | 0.2078 | 0.835816 | 0.417908 |
| M10 | 95.2054291939026 | 668.365553 | 0.1424 | 0.887033 | 0.443517 |
| M11 | 85.7332701525081 | 668.283667 | 0.1283 | 0.898195 | 0.449097 |
| t | 45.3132701525054 | 6.040215 | 7.5019 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.694078414024687 |
| R-squared | 0.481744844815025 |
| Adjusted R-squared | 0.410071259523486 |
| F-TEST (value) | 6.72137221621442 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 94 |
| p-value | 6.17242346123703e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1417.58583194669 |
| Sum Squared Residuals | 188897661.547984 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 4716.99 | 3502.67219433550 | 1214.31780566450 |
| 2 | 4926.65 | 3568.30663877996 | 1358.34336122004 |
| 3 | 4920.1 | 3529.05219433551 | 1391.04780566449 |
| 4 | 5170.09 | 3541.50802265795 | 1628.58197734205 |
| 5 | 5246.24 | 3537.88357821351 | 1708.35642178649 |
| 6 | 5283.61 | 3472.78913376906 | 1810.82086623094 |
| 7 | 4979.05 | 3299.20913376906 | 1679.84086623094 |
| 8 | 4825.2 | 3292.74135599128 | 1532.45864400871 |
| 9 | 4695.12 | 3397.55468932462 | 1297.56531067538 |
| 10 | 4711.54 | 3399.14246710240 | 1312.39753289760 |
| 11 | 4727.22 | 3434.98357821351 | 1292.23642178649 |
| 12 | 4384.96 | 3394.56357821351 | 990.396421786495 |
| 13 | 4378.75 | 4046.43143616558 | 332.318563834421 |
| 14 | 4472.93 | 4112.06588061002 | 360.864119389976 |
| 15 | 4564.07 | 4072.81143616558 | 491.258563834422 |
| 16 | 4310.54 | 4085.26726448802 | 225.272735511982 |
| 17 | 4171.38 | 4081.64282004357 | 89.7371799564272 |
| 18 | 4049.38 | 4016.54837559913 | 32.8316244008712 |
| 19 | 3591.37 | 3842.96837559913 | -251.598375599129 |
| 20 | 3720.46 | 3836.50059782135 | -116.040597821351 |
| 21 | 4107.23 | 3941.31393115468 | 165.916068845316 |
| 22 | 4101.71 | 3942.90170893246 | 158.808291067539 |
| 23 | 4162.34 | 3978.74282004357 | 183.597179956428 |
| 24 | 4136.22 | 3938.32282004357 | 197.897179956430 |
| 25 | 4125.88 | 4590.19067799564 | -464.310677995644 |
| 26 | 4031.48 | 4655.82512244009 | -624.345122440088 |
| 27 | 3761.36 | 4616.57067799564 | -855.210677995644 |
| 28 | 3408.56 | 4629.02650631808 | -1220.46650631808 |
| 29 | 3228.47 | 4625.40206187364 | -1396.93206187364 |
| 30 | 3090.45 | 4560.30761742919 | -1469.85761742919 |
| 31 | 2741.14 | 4386.72761742919 | -1645.58761742919 |
| 32 | 2980.44 | 4380.25983965142 | -1399.81983965142 |
| 33 | 3104.33 | 4485.07317298475 | -1380.74317298475 |
| 34 | 3181.57 | 4486.66095076253 | -1305.09095076253 |
| 35 | 2863.86 | 4522.50206187364 | -1658.64206187364 |
| 36 | 2898.01 | 4482.08206187364 | -1584.07206187364 |
| 37 | 3112.33 | 5133.94991982571 | -2021.61991982571 |
| 38 | 3254.33 | 5199.58436427015 | -1945.25436427015 |
| 39 | 3513.47 | 5160.32991982571 | -1646.85991982571 |
| 40 | 3587.61 | 5172.78574814815 | -1585.17574814815 |
| 41 | 3727.45 | 5169.1613037037 | -1441.71130370370 |
| 42 | 3793.34 | 5104.06685925926 | -1310.72685925926 |
| 43 | 3817.58 | 4930.48685925926 | -1112.90685925926 |
| 44 | 3845.13 | 4924.01908148148 | -1078.88908148148 |
| 45 | 3931.86 | 5028.83241481481 | -1096.97241481481 |
| 46 | 4197.52 | 5030.42019259259 | -832.900192592592 |
| 47 | 4307.13 | 5066.2613037037 | -759.131303703703 |
| 48 | 4229.43 | 5025.8413037037 | -796.4113037037 |
| 49 | 4362.28 | 5677.70916165577 | -1315.42916165577 |
| 50 | 4217.34 | 5743.34360610022 | -1526.00360610022 |
| 51 | 4361.28 | 5704.08916165577 | -1342.80916165577 |
| 52 | 4327.74 | 5716.54498997821 | -1388.80498997821 |
| 53 | 4417.65 | 5712.92054553377 | -1295.27054553377 |
| 54 | 4557.68 | 5647.82610108932 | -1090.14610108932 |
| 55 | 4650.35 | 5474.24610108932 | -823.896101089325 |
| 56 | 4967.18 | 5467.77832331155 | -500.598323311547 |
| 57 | 5123.42 | 5572.59165664488 | -449.17165664488 |
| 58 | 5290.85 | 5574.17943442266 | -283.329434422657 |
| 59 | 5535.66 | 5610.02054553377 | -74.3605455337688 |
| 60 | 5514.06 | 5569.60054553377 | -55.5405455337657 |
| 61 | 5493.88 | 6221.46840348584 | -727.58840348584 |
| 62 | 5694.83 | 6287.10284793028 | -592.272847930284 |
| 63 | 5850.41 | 6247.84840348584 | -397.438403485840 |
| 64 | 6116.64 | 6260.30423180828 | -143.664231808279 |
| 65 | 6175 | 6256.67978736383 | -81.6797873638341 |
| 66 | 6513.58 | 6191.58534291939 | 321.99465708061 |
| 67 | 6383.78 | 6018.00534291939 | 365.77465708061 |
| 68 | 6673.66 | 6011.53756514161 | 662.122434858388 |
| 69 | 6936.61 | 6116.35089847495 | 820.259101525054 |
| 70 | 7300.68 | 6117.93867625272 | 1182.74132374728 |
| 71 | 7392.93 | 6153.77978736383 | 1239.15021263617 |
| 72 | 7497.31 | 6113.35978736383 | 1383.95021263617 |
| 73 | 7584.71 | 6765.2276453159 | 819.482354684095 |
| 74 | 7160.79 | 6830.86208976035 | 329.927910239651 |
| 75 | 7196.19 | 6791.6076453159 | 404.582354684094 |
| 76 | 7245.63 | 6804.06347363835 | 441.566526361654 |
| 77 | 7347.51 | 6800.4390291939 | 547.0709708061 |
| 78 | 7425.75 | 6735.34458474946 | 690.405415250543 |
| 79 | 7778.51 | 6561.76458474946 | 1216.74541525054 |
| 80 | 7822.33 | 6555.29680697168 | 1267.03319302832 |
| 81 | 8181.22 | 6660.11014030501 | 1521.10985969499 |
| 82 | 8371.47 | 6661.69791808279 | 1709.77208191721 |
| 83 | 8347.71 | 6697.5390291939 | 1650.1709708061 |
| 84 | 8672.11 | 6657.1190291939 | 2014.99097080610 |
| 85 | 8802.79 | 7308.98688714597 | 1493.80311285403 |
| 86 | 9138.46 | 7374.62133159042 | 1763.83866840958 |
| 87 | 9123.29 | 7335.36688714597 | 1787.92311285403 |
| 88 | 9023.21 | 6818.58026056645 | 2204.62973943355 |
| 89 | 8850.41 | 6814.955816122 | 2035.45418387800 |
| 90 | 8864.58 | 6749.86137167756 | 2114.71862832244 |
| 91 | 9163.74 | 6576.28137167756 | 2587.45862832244 |
| 92 | 8516.66 | 6569.81359389978 | 1946.84640610022 |
| 93 | 8553.44 | 6674.62692723311 | 1878.81307276689 |
| 94 | 7555.2 | 6676.21470501089 | 878.985294989107 |
| 95 | 7851.22 | 6712.055816122 | 1139.16418387800 |
| 96 | 7442 | 6671.635816122 | 770.364183877999 |
| 97 | 7992.53 | 7323.50367407408 | 669.026325925924 |
| 98 | 8264.04 | 7389.13811851852 | 874.901881481482 |
| 99 | 7517.39 | 7349.88367407407 | 167.506325925926 |
| 100 | 7200.4 | 7362.33950239651 | -161.939502396515 |
| 101 | 7193.69 | 7358.71505795207 | -165.025057952070 |
| 102 | 6193.58 | 7293.62061350763 | -1100.04061350763 |
| 103 | 5104.21 | 7120.04061350763 | -2015.83061350763 |
| 104 | 4800.46 | 7113.57283572985 | -2313.11283572985 |
| 105 | 4461.61 | 7218.38616906318 | -2756.77616906318 |
| 106 | 4398.59 | 7219.97394684096 | -2821.38394684096 |
| 107 | 4243.63 | 7255.81505795207 | -3012.18505795207 |
| 108 | 4293.82 | 7215.39505795207 | -2921.57505795207 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0117929439939733 | 0.0235858879879466 | 0.988207056006027 |
| 18 | 0.00575506919909182 | 0.0115101383981836 | 0.994244930800908 |
| 19 | 0.00307612073067958 | 0.00615224146135917 | 0.99692387926932 |
| 20 | 0.000841991975623328 | 0.00168398395124666 | 0.999158008024377 |
| 21 | 0.000225584979383739 | 0.000451169958767477 | 0.999774415020616 |
| 22 | 5.68447002265703e-05 | 0.000113689400453141 | 0.999943155299774 |
| 23 | 1.4828381508291e-05 | 2.9656763016582e-05 | 0.999985171618492 |
| 24 | 7.53464851654945e-06 | 1.50692970330989e-05 | 0.999992465351483 |
| 25 | 6.56308228762762e-06 | 1.31261645752552e-05 | 0.999993436917712 |
| 26 | 2.01521235059438e-06 | 4.03042470118877e-06 | 0.99999798478765 |
| 27 | 4.69858614814139e-07 | 9.39717229628277e-07 | 0.999999530141385 |
| 28 | 1.72691809052340e-07 | 3.45383618104681e-07 | 0.99999982730819 |
| 29 | 8.38240644685006e-08 | 1.67648128937001e-07 | 0.999999916175936 |
| 30 | 4.54720949931140e-08 | 9.09441899862279e-08 | 0.999999954527905 |
| 31 | 1.88850569637243e-08 | 3.77701139274487e-08 | 0.999999981114943 |
| 32 | 4.53626220556216e-09 | 9.07252441112433e-09 | 0.999999995463738 |
| 33 | 1.05382139537120e-09 | 2.10764279074239e-09 | 0.999999998946179 |
| 34 | 2.24575490603552e-10 | 4.49150981207104e-10 | 0.999999999775425 |
| 35 | 8.52059727667224e-11 | 1.70411945533445e-10 | 0.999999999914794 |
| 36 | 1.92487905036415e-11 | 3.84975810072831e-11 | 0.999999999980751 |
| 37 | 5.69971510789948e-12 | 1.13994302157990e-11 | 0.9999999999943 |
| 38 | 1.84885597585640e-12 | 3.69771195171281e-12 | 0.99999999999815 |
| 39 | 1.65616826533817e-12 | 3.31233653067634e-12 | 0.999999999998344 |
| 40 | 2.64290593981564e-12 | 5.28581187963128e-12 | 0.999999999997357 |
| 41 | 7.34564866092312e-12 | 1.46912973218462e-11 | 0.999999999992654 |
| 42 | 2.05248590858802e-11 | 4.10497181717604e-11 | 0.999999999979475 |
| 43 | 1.74264877568783e-10 | 3.48529755137566e-10 | 0.999999999825735 |
| 44 | 4.95472578730786e-10 | 9.90945157461573e-10 | 0.999999999504527 |
| 45 | 7.81647368940772e-10 | 1.56329473788154e-09 | 0.999999999218353 |
| 46 | 1.75257972048614e-09 | 3.50515944097228e-09 | 0.99999999824742 |
| 47 | 4.55773154935894e-09 | 9.11546309871788e-09 | 0.999999995442268 |
| 48 | 8.79844052317458e-09 | 1.75968810463492e-08 | 0.99999999120156 |
| 49 | 1.77563831468435e-08 | 3.55127662936871e-08 | 0.999999982243617 |
| 50 | 1.91119193110616e-08 | 3.82238386221233e-08 | 0.99999998088808 |
| 51 | 2.12519667052173e-08 | 4.25039334104347e-08 | 0.999999978748033 |
| 52 | 2.68149470385126e-08 | 5.36298940770252e-08 | 0.999999973185053 |
| 53 | 3.72871888366175e-08 | 7.4574377673235e-08 | 0.999999962712811 |
| 54 | 5.79049361282724e-08 | 1.15809872256545e-07 | 0.999999942095064 |
| 55 | 1.39165232473692e-07 | 2.78330464947383e-07 | 0.999999860834768 |
| 56 | 3.63906196869596e-07 | 7.27812393739193e-07 | 0.999999636093803 |
| 57 | 7.84811036818889e-07 | 1.56962207363778e-06 | 0.999999215188963 |
| 58 | 1.45595393884394e-06 | 2.91190787768787e-06 | 0.999998544046061 |
| 59 | 3.24567433991579e-06 | 6.49134867983158e-06 | 0.99999675432566 |
| 60 | 6.83930442177037e-06 | 1.36786088435407e-05 | 0.999993160695578 |
| 61 | 1.85462854846923e-05 | 3.70925709693847e-05 | 0.999981453714515 |
| 62 | 5.99438370845473e-05 | 0.000119887674169095 | 0.999940056162915 |
| 63 | 0.000188375854048618 | 0.000376751708097237 | 0.999811624145951 |
| 64 | 0.000556670533415962 | 0.00111334106683192 | 0.999443329466584 |
| 65 | 0.00159731668456078 | 0.00319463336912155 | 0.99840268331544 |
| 66 | 0.00388326681530248 | 0.00776653363060497 | 0.996116733184698 |
| 67 | 0.00926797949637707 | 0.0185359589927541 | 0.990732020503623 |
| 68 | 0.0173717335593256 | 0.0347434671186512 | 0.982628266440674 |
| 69 | 0.0301274635001488 | 0.0602549270002977 | 0.96987253649985 |
| 70 | 0.04407093437632 | 0.08814186875264 | 0.95592906562368 |
| 71 | 0.0623807077649518 | 0.124761415529904 | 0.937619292235048 |
| 72 | 0.0894297017478393 | 0.178859403495679 | 0.91057029825216 |
| 73 | 0.167809310667641 | 0.335618621335282 | 0.83219068933236 |
| 74 | 0.432250046027118 | 0.864500092054236 | 0.567749953972882 |
| 75 | 0.815252583934237 | 0.369494832131526 | 0.184747416065763 |
| 76 | 0.9113473727565 | 0.177305254487001 | 0.0886526272435004 |
| 77 | 0.974856334331663 | 0.050287331336674 | 0.025143665668337 |
| 78 | 0.993987440227585 | 0.0120251195448306 | 0.00601255977241531 |
| 79 | 0.99778315580063 | 0.0044336883987414 | 0.0022168441993707 |
| 80 | 0.998673892647167 | 0.00265221470566636 | 0.00132610735283318 |
| 81 | 0.998632191277663 | 0.00273561744467302 | 0.00136780872233651 |
| 82 | 0.99737015665496 | 0.00525968669007768 | 0.00262984334503884 |
| 83 | 0.995230190105868 | 0.00953961978826357 | 0.00476980989413178 |
| 84 | 0.99099574330205 | 0.0180085133959001 | 0.00900425669795007 |
| 85 | 0.983550550680676 | 0.0328988986386478 | 0.0164494493193239 |
| 86 | 0.972887865449773 | 0.0542242691004543 | 0.0271121345502271 |
| 87 | 0.948844081135604 | 0.102311837728793 | 0.0511559188643964 |
| 88 | 0.954202101280622 | 0.0915957974387559 | 0.0457978987193779 |
| 89 | 0.989195612341582 | 0.0216087753168365 | 0.0108043876584183 |
| 90 | 0.989690863985992 | 0.0206182720280155 | 0.0103091360140078 |
| 91 | 0.973319805491864 | 0.0533603890162718 | 0.0266801945081359 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 53 | 0.706666666666667 | NOK |
| 5% type I error level | 62 | 0.826666666666667 | NOK |
| 10% type I error level | 68 | 0.906666666666667 | NOK |
