| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2387.29973592068 -878.654280869877D[t] + 223.634513555660X[t] + 543.264022856550M1[t] + 543.152359649053M2[t] + 437.654841966989M3[t] + 433.375893362571M4[t] + 396.556587128177M5[t] + 286.340106837481M6[t] + 75.5895203620973M7[t] + 42.8843989938796M8[t] + 115.745284501462M9[t] + 72.7079920186672M10[t] + 63.6755500763662M11[t] + 46.3644498104495t + 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) | 2387.29973592068 | 641.075447 | 3.7239 | 0.000336 | 0.000168 |
| D | -878.654280869877 | 530.938571 | -1.6549 | 0.101314 | 0.050657 |
| X | 223.634513555660 | 153.615233 | 1.4558 | 0.148813 | 0.074406 |
| M1 | 543.264022856550 | 667.513103 | 0.8139 | 0.417803 | 0.208901 |
| M2 | 543.152359649053 | 668.331207 | 0.8127 | 0.418466 | 0.209233 |
| M3 | 437.654841966989 | 669.53306 | 0.6537 | 0.514936 | 0.257468 |
| M4 | 433.375893362571 | 668.093929 | 0.6487 | 0.518147 | 0.259073 |
| M5 | 396.556587128177 | 667.089194 | 0.5945 | 0.553649 | 0.276825 |
| M6 | 286.340106837481 | 666.729146 | 0.4295 | 0.668575 | 0.334287 |
| M7 | 75.5895203620973 | 666.087429 | 0.1135 | 0.909892 | 0.454946 |
| M8 | 42.8843989938796 | 665.220554 | 0.0645 | 0.948737 | 0.474369 |
| M9 | 115.745284501462 | 664.747654 | 0.1741 | 0.86215 | 0.431075 |
| M10 | 72.7079920186672 | 664.600884 | 0.1094 | 0.91312 | 0.45656 |
| M11 | 63.6755500763662 | 664.512548 | 0.0958 | 0.923867 | 0.461934 |
| t | 46.3644498104495 | 6.047827 | 7.6663 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.702347657036743 |
| R-squared | 0.493292231345002 |
| Adjusted R-squared | 0.417013642515218 |
| F-TEST (value) | 6.46698161191448 |
| F-TEST (DF numerator) | 14 |
| F-TEST (DF denominator) | 93 |
| p-value | 6.66057253795316e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1409.21994924357 |
| Sum Squared Residuals | 184688780.477183 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 4716.99 | 3433.14261624122 | 1283.84738375878 |
| 2 | 4926.65 | 3506.23154447086 | 1420.41845552914 |
| 3 | 4920.1 | 3579.04283959708 | 1341.05716040292 |
| 4 | 5170.09 | 3630.07372134534 | 1540.01627865466 |
| 5 | 5246.24 | 3659.74597114140 | 1586.49402885860 |
| 6 | 5283.61 | 3703.23850716787 | 1580.37149283213 |
| 7 | 4979.05 | 3451.63491021623 | 1527.41508978377 |
| 8 | 4825.2 | 3494.3667254207 | 1330.8332745793 |
| 9 | 4695.12 | 3477.17500746978 | 1217.94499253022 |
| 10 | 4711.54 | 3415.64815586629 | 1295.89184413371 |
| 11 | 4727.22 | 3464.16188941222 | 1263.05811058778 |
| 12 | 4384.96 | 3411.0692669774 | 973.890733022598 |
| 13 | 4378.75 | 4157.24189913336 | 221.508100866638 |
| 14 | 4472.93 | 4281.76676548080 | 191.163234519205 |
| 15 | 4564.07 | 4175.67044976249 | 388.39955023751 |
| 16 | 4310.54 | 4155.13828717294 | 155.401712827060 |
| 17 | 4171.38 | 4169.15612102011 | 2.22387897989208 |
| 18 | 4049.38 | 4013.61393998204 | 35.766060017958 |
| 19 | 3591.37 | 3869.35490953712 | -277.984909537118 |
| 20 | 3720.46 | 3833.8146449971 | -113.354644997104 |
| 21 | 4107.23 | 3964.22170599292 | 143.008294007082 |
| 22 | 4101.71 | 4128.56571308065 | -26.855713080648 |
| 23 | 4162.34 | 4105.51640228877 | 56.8235977112316 |
| 24 | 4136.22 | 4097.15068256508 | 39.0693174349219 |
| 25 | 4125.88 | 4494.45347357421 | -368.57347357421 |
| 26 | 4031.48 | 4433.36169367045 | -401.881693670447 |
| 27 | 3761.36 | 4273.59309469878 | -512.233094698785 |
| 28 | 3408.56 | 4405.13240132708 | -996.57240132708 |
| 29 | 3228.47 | 4410.20485463202 | -1181.73485463202 |
| 30 | 3090.45 | 4346.35282415178 | -1255.90282415178 |
| 31 | 2741.14 | 4188.67572289351 | -1447.53572289351 |
| 32 | 2980.44 | 4159.84449376017 | -1179.40449376017 |
| 33 | 3104.33 | 4339.45114773823 | -1235.12114773823 |
| 34 | 3181.57 | 4306.99678289698 | -1125.42678289698 |
| 35 | 2863.86 | 4462.85508294963 | -1598.99508294963 |
| 36 | 2898.01 | 4450.01667295482 | -1552.00667295482 |
| 37 | 3112.33 | 4977.02748182624 | -1864.69748182624 |
| 38 | 3254.33 | 4924.8810824647 | -1670.5510824647 |
| 39 | 3513.47 | 4995.45603245537 | -1481.98603245537 |
| 40 | 3587.61 | 5008.46904689916 | -1420.85904689916 |
| 41 | 3727.45 | 5085.10454454192 | -1357.65454454192 |
| 42 | 3793.34 | 5023.48885919723 | -1230.14885919723 |
| 43 | 3817.58 | 4809.90312955005 | -992.323129550047 |
| 44 | 3845.13 | 4886.18012178786 | -1041.05012178786 |
| 45 | 3931.86 | 4978.56931547922 | -1046.70931547922 |
| 46 | 4197.52 | 4948.35129577352 | -750.831295773522 |
| 47 | 4307.13 | 4911.8839141683 | -604.753914168304 |
| 48 | 4229.43 | 4865.50032714015 | -636.070327140151 |
| 49 | 4362.28 | 5631.80006551612 | -1269.52006551612 |
| 50 | 4217.34 | 5832.36066647248 | -1615.02066647248 |
| 51 | 4361.28 | 5694.95551885638 | -1333.67551885638 |
| 52 | 4327.74 | 5770.58619709576 | -1442.84619709576 |
| 53 | 4417.65 | 5746.58616363847 | -1328.93616363847 |
| 54 | 4557.68 | 5631.29819504042 | -1073.61819504042 |
| 55 | 4650.35 | 5652.52870462669 | -1002.17870462669 |
| 56 | 4967.18 | 5596.86133386666 | -629.681333866663 |
| 57 | 5123.42 | 5653.46900538911 | -530.04900538911 |
| 58 | 5290.85 | 5654.55981758121 | -363.709817581209 |
| 59 | 5535.66 | 5761.21852465161 | -225.558524651612 |
| 60 | 5514.06 | 5855.72468116353 | -341.664681163525 |
| 61 | 5493.88 | 6376.02645462827 | -882.146454628269 |
| 62 | 5694.83 | 6366.37061284231 | -671.540612842308 |
| 63 | 5850.41 | 6387.74596985073 | -537.335969850731 |
| 64 | 6116.64 | 6490.21278971679 | -373.572789716790 |
| 65 | 6175 | 6493.04889788618 | -318.048897886176 |
| 66 | 6513.58 | 6440.37859308371 | 73.2014069162872 |
| 67 | 6383.78 | 6121.68464206537 | 262.095357934626 |
| 68 | 6673.66 | 6157.70742186317 | 515.952578136829 |
| 69 | 6936.61 | 6348.49580151901 | 588.114198480986 |
| 70 | 7300.68 | 6293.6779853222 | 1007.00201467780 |
| 71 | 7392.93 | 6275.10136480143 | 1117.82863519857 |
| 72 | 7497.31 | 6103.4824501821 | 1393.82754981789 |
| 73 | 7584.71 | 6753.49224150914 | 831.217758490863 |
| 74 | 7160.79 | 6851.18096622989 | 309.609033770109 |
| 75 | 7196.19 | 6720.48485402047 | 475.705145979534 |
| 76 | 7245.63 | 6702.18903656647 | 543.440963433531 |
| 77 | 7347.51 | 6718.4432155492 | 629.066784450806 |
| 78 | 7425.75 | 6562.90103451113 | 862.848965488872 |
| 79 | 7778.51 | 6396.27855271064 | 1382.23144728936 |
| 80 | 7822.33 | 6472.55554494845 | 1349.77445505155 |
| 81 | 8181.22 | 6625.32605729983 | 1555.89394270017 |
| 82 | 8371.47 | 6633.1259048986 | 1738.34409510140 |
| 83 | 8347.71 | 6695.05770925787 | 1652.65229074213 |
| 84 | 8672.11 | 6688.92833466974 | 1983.18166533026 |
| 85 | 8802.79 | 7269.61142679451 | 1533.17857320549 |
| 86 | 9138.46 | 7204.04695661964 | 1934.41304338036 |
| 87 | 9123.29 | 7147.15023388358 | 1976.13976611642 |
| 88 | 9023.21 | 6328.47221530418 | 2694.73778469582 |
| 89 | 8850.41 | 6282.10873049132 | 2568.30126950868 |
| 90 | 8864.58 | 6305.47416029779 | 2559.10583970221 |
| 91 | 9163.74 | 6304.34121852848 | 2859.39878147152 |
| 92 | 8516.66 | 6474.54470645968 | 2042.11529354032 |
| 93 | 8553.44 | 6627.31521881106 | 1926.12478118894 |
| 94 | 7555.2 | 6713.3871461543 | 841.812853845694 |
| 95 | 7851.22 | 6790.97336646247 | 1060.24663353753 |
| 96 | 7442 | 6941.3881513633 | 500.611848636699 |
| 97 | 7992.53 | 7477.34434077694 | 515.185659223058 |
| 98 | 8264.04 | 7760.6497117489 | 503.390288251107 |
| 99 | 7517.39 | 7833.46100687512 | -316.071006875119 |
| 100 | 7200.4 | 7900.14630457227 | -699.746304572273 |
| 101 | 7193.69 | 7793.40150109938 | -599.711501099385 |
| 102 | 6193.58 | 7745.20388656804 | -1551.62388656804 |
| 103 | 5104.21 | 7415.32820987191 | -2311.11820987191 |
| 104 | 4800.46 | 7075.6450068962 | -2275.18500689620 |
| 105 | 4461.61 | 7080.81674030085 | -2619.20674030085 |
| 106 | 4398.59 | 7014.81719842625 | -2616.22719842625 |
| 107 | 4243.63 | 6964.93174600769 | -2721.30174600769 |
| 108 | 4293.82 | 6654.65943298386 | -2360.83943298386 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 18 | 0.0030811154926611 | 0.0061622309853222 | 0.99691888450734 |
| 19 | 0.000747343659587178 | 0.00149468731917436 | 0.999252656340413 |
| 20 | 0.000115666602749818 | 0.000231333205499635 | 0.99988433339725 |
| 21 | 3.35524518534347e-05 | 6.71049037068694e-05 | 0.999966447548147 |
| 22 | 5.57919346142384e-06 | 1.11583869228477e-05 | 0.999994420806539 |
| 23 | 7.52414027533098e-07 | 1.50482805506620e-06 | 0.999999247585972 |
| 24 | 1.74353533400300e-07 | 3.48707066800601e-07 | 0.999999825646467 |
| 25 | 3.93353090776349e-06 | 7.86706181552697e-06 | 0.999996066469092 |
| 26 | 3.34097666986377e-06 | 6.68195333972754e-06 | 0.99999665902333 |
| 27 | 8.86854488278339e-07 | 1.77370897655668e-06 | 0.999999113145512 |
| 28 | 2.26883003121655e-07 | 4.53766006243309e-07 | 0.999999773116997 |
| 29 | 6.81462455844138e-08 | 1.36292491168828e-07 | 0.999999931853754 |
| 30 | 2.20469487729194e-08 | 4.40938975458387e-08 | 0.999999977953051 |
| 31 | 6.46512118423835e-09 | 1.29302423684767e-08 | 0.999999993534879 |
| 32 | 1.24910111564773e-09 | 2.49820223129546e-09 | 0.999999998750899 |
| 33 | 2.55536967812456e-10 | 5.11073935624912e-10 | 0.999999999744463 |
| 34 | 4.66567231157054e-11 | 9.33134462314107e-11 | 0.999999999953343 |
| 35 | 2.43274481627763e-11 | 4.86548963255527e-11 | 0.999999999975673 |
| 36 | 5.83773301677305e-12 | 1.16754660335461e-11 | 0.999999999994162 |
| 37 | 1.27705917578554e-12 | 2.55411835157108e-12 | 0.999999999998723 |
| 38 | 4.18709741397976e-13 | 8.37419482795951e-13 | 0.999999999999581 |
| 39 | 2.18794688647469e-13 | 4.37589377294938e-13 | 0.999999999999781 |
| 40 | 2.93114259939357e-13 | 5.86228519878713e-13 | 0.999999999999707 |
| 41 | 4.74837041142902e-13 | 9.49674082285804e-13 | 0.999999999999525 |
| 42 | 8.75735672325688e-13 | 1.75147134465138e-12 | 0.999999999999124 |
| 43 | 8.65123178824129e-12 | 1.73024635764826e-11 | 0.999999999991349 |
| 44 | 1.19922103844743e-11 | 2.39844207689485e-11 | 0.999999999988008 |
| 45 | 1.02347824680385e-11 | 2.04695649360770e-11 | 0.999999999989765 |
| 46 | 2.18887659019661e-11 | 4.37775318039322e-11 | 0.999999999978111 |
| 47 | 1.46458998763724e-10 | 2.92917997527448e-10 | 0.99999999985354 |
| 48 | 6.22969282295352e-10 | 1.24593856459070e-09 | 0.999999999377031 |
| 49 | 5.04895119404522e-10 | 1.00979023880904e-09 | 0.999999999495105 |
| 50 | 2.11088117393548e-10 | 4.22176234787095e-10 | 0.999999999788912 |
| 51 | 1.05848106421362e-10 | 2.11696212842724e-10 | 0.999999999894152 |
| 52 | 5.9214174270297e-11 | 1.18428348540594e-10 | 0.999999999940786 |
| 53 | 4.42794062575415e-11 | 8.8558812515083e-11 | 0.99999999995572 |
| 54 | 5.42458558005329e-11 | 1.08491711601066e-10 | 0.999999999945754 |
| 55 | 3.2670897607302e-11 | 6.5341795214604e-11 | 0.99999999996733 |
| 56 | 3.41130557340597e-11 | 6.82261114681193e-11 | 0.999999999965887 |
| 57 | 4.46777729124025e-11 | 8.9355545824805e-11 | 0.999999999955322 |
| 58 | 5.72577554279959e-11 | 1.14515510855992e-10 | 0.999999999942742 |
| 59 | 5.93846009871806e-11 | 1.18769201974361e-10 | 0.999999999940615 |
| 60 | 2.98883836249650e-11 | 5.97767672499299e-11 | 0.999999999970112 |
| 61 | 4.16897699299085e-11 | 8.33795398598169e-11 | 0.99999999995831 |
| 62 | 1.48641359592048e-10 | 2.97282719184096e-10 | 0.999999999851359 |
| 63 | 3.67391194290627e-10 | 7.34782388581253e-10 | 0.999999999632609 |
| 64 | 6.03119123293528e-10 | 1.20623824658706e-09 | 0.999999999396881 |
| 65 | 1.28816239965197e-09 | 2.57632479930395e-09 | 0.999999998711838 |
| 66 | 2.58079467522846e-09 | 5.16158935045692e-09 | 0.999999997419205 |
| 67 | 3.76221722505714e-08 | 7.52443445011428e-08 | 0.999999962377828 |
| 68 | 2.22619630967982e-07 | 4.45239261935964e-07 | 0.999999777380369 |
| 69 | 5.03818279130444e-07 | 1.00763655826089e-06 | 0.99999949618172 |
| 70 | 1.72831772654722e-06 | 3.45663545309445e-06 | 0.999998271682274 |
| 71 | 9.81812629538812e-06 | 1.96362525907762e-05 | 0.999990181873705 |
| 72 | 0.000201708868271788 | 0.000403417736543576 | 0.999798291131728 |
| 73 | 0.00190160195177574 | 0.00380320390355149 | 0.998098398048224 |
| 74 | 0.0259063975781780 | 0.0518127951563559 | 0.974093602421822 |
| 75 | 0.265315970510391 | 0.530631941020781 | 0.73468402948961 |
| 76 | 0.530420789070716 | 0.939158421858567 | 0.469579210929284 |
| 77 | 0.832858204772426 | 0.334283590455148 | 0.167141795227574 |
| 78 | 0.96129355690094 | 0.0774128861981189 | 0.0387064430990595 |
| 79 | 0.989058396971742 | 0.0218832060565156 | 0.0109416030282578 |
| 80 | 0.995457499260618 | 0.0090850014787648 | 0.0045425007393824 |
| 81 | 0.9969339578343 | 0.00613208433140097 | 0.00306604216570048 |
| 82 | 0.995140710651775 | 0.00971857869645037 | 0.00485928934822518 |
| 83 | 0.993509870398785 | 0.012980259202429 | 0.0064901296012145 |
| 84 | 0.98881505591546 | 0.0223698881690802 | 0.0111849440845401 |
| 85 | 0.982998285492788 | 0.0340034290144246 | 0.0170017145072123 |
| 86 | 0.97514008689755 | 0.0497198262048995 | 0.0248599131024497 |
| 87 | 0.951739236342469 | 0.0965215273150621 | 0.0482607636575311 |
| 88 | 0.92414141271025 | 0.151717174579502 | 0.0758585872897508 |
| 89 | 0.957682216913172 | 0.0846355661736555 | 0.0423177830868278 |
| 90 | 0.985688642686075 | 0.0286227146278503 | 0.0143113573139252 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 59 | 0.808219178082192 | NOK |
| 5% type I error level | 65 | 0.89041095890411 | NOK |
| 10% type I error level | 69 | 0.945205479452055 | NOK |
