| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -98.9823530336727 -368.123436426008X[t] + 1.01130602561975Y1[t] + 0.163239051318856Y2[t] -0.210238226465953Y3[t] + 0.0225486848879357Y4[t] + 99.0580758997808M1[t] + 32.162636746199M2[t] -87.15409126129M3[t] + 89.5300852830297M4[t] + 212.316131005456M5[t] + 70.6363792115456M6[t] + 87.0167479026612M7[t] + 28.9732274452039M8[t] + 175.445037331277M9[t] + 104.148942223657M10[t] -24.9058248936815M11[t] + 3.29961068075524t + 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) | -98.9823530336727 | 128.460069 | -0.7705 | 0.443097 | 0.221549 |
| X | -368.123436426008 | 114.42225 | -3.2172 | 0.001825 | 0.000913 |
| Y1 | 1.01130602561975 | 0.106837 | 9.4659 | 0 | 0 |
| Y2 | 0.163239051318856 | 0.150892 | 1.0818 | 0.282355 | 0.141178 |
| Y3 | -0.210238226465953 | 0.150955 | -1.3927 | 0.167294 | 0.083647 |
| Y4 | 0.0225486848879357 | 0.110149 | 0.2047 | 0.838282 | 0.419141 |
| M1 | 99.0580758997808 | 127.617861 | 0.7762 | 0.439755 | 0.219878 |
| M2 | 32.162636746199 | 129.021558 | 0.2493 | 0.803738 | 0.401869 |
| M3 | -87.15409126129 | 128.571304 | -0.6779 | 0.499677 | 0.249838 |
| M4 | 89.5300852830297 | 128.842694 | 0.6949 | 0.489004 | 0.244502 |
| M5 | 212.316131005456 | 130.911752 | 1.6218 | 0.108501 | 0.054251 |
| M6 | 70.6363792115456 | 132.800481 | 0.5319 | 0.596168 | 0.298084 |
| M7 | 87.0167479026612 | 128.226643 | 0.6786 | 0.499203 | 0.249601 |
| M8 | 28.9732274452039 | 127.545217 | 0.2272 | 0.820838 | 0.410419 |
| M9 | 175.445037331277 | 132.187026 | 1.3272 | 0.187939 | 0.09397 |
| M10 | 104.148942223657 | 133.407951 | 0.7807 | 0.437134 | 0.218567 |
| M11 | -24.9058248936815 | 133.701838 | -0.1863 | 0.852665 | 0.426332 |
| t | 3.29961068075524 | 1.526913 | 2.161 | 0.033478 | 0.016739 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.991889576646781 |
| R-squared | 0.98384493226053 |
| Adjusted R-squared | 0.980651488637612 |
| F-TEST (value) | 308.082762194323 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 86 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 261.115658716006 |
| Sum Squared Residuals | 5863599.30149564 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 5246.24 | 5105.66272264824 | 140.577277351759 |
| 2 | 5283.61 | 5165.99059612251 | 117.619403877489 |
| 3 | 4979.05 | 5047.49149061088 | -68.4414906108815 |
| 4 | 4825.2 | 4915.19946281074 | -89.999462810743 |
| 5 | 4695.12 | 4829.84008153384 | -134.720081533839 |
| 6 | 4711.54 | 4599.66772316939 | 111.872276830607 |
| 7 | 4727.22 | 4640.1969353587 | 87.023064641299 |
| 8 | 4384.96 | 4627.86936261506 | -242.909362615056 |
| 9 | 4378.75 | 4427.68552656915 | -48.9355265691532 |
| 10 | 4472.93 | 4294.61234803367 | 178.317651966329 |
| 11 | 4564.07 | 4335.39797735055 | 228.672022649453 |
| 12 | 4310.54 | 4464.73576444979 | -154.195764449786 |
| 13 | 4171.38 | 4305.63437799043 | -134.254377990430 |
| 14 | 4049.38 | 4042.88172949413 | 6.49827050587184 |
| 15 | 3591.37 | 3836.12571535685 | -244.755715356853 |
| 16 | 3720.46 | 3556.54604904229 | 163.913950957711 |
| 17 | 4107.23 | 3760.92727103802 | 346.302728961984 |
| 18 | 4101.71 | 4128.30276113591 | -26.592761135906 |
| 19 | 4162.34 | 4168.06912330494 | -5.72912330493626 |
| 20 | 4136.22 | 4095.33658918023 | 40.8834108197734 |
| 21 | 4125.88 | 4238.47154990353 | -112.591549903529 |
| 22 | 4031.48 | 4142.88314474009 | -111.403144740094 |
| 23 | 3761.36 | 3926.83135693442 | -165.471356934416 |
| 24 | 3408.56 | 3668.03793403633 | -259.477934036331 |
| 25 | 3228.47 | 3389.12605741261 | -160.656057412614 |
| 26 | 3090.45 | 3140.4743433602 | -50.024343360197 |
| 27 | 2741.14 | 2923.56024316067 | -182.420243160672 |
| 28 | 2980.44 | 2757.66109488927 | 222.778905110727 |
| 29 | 3104.33 | 3093.68753756243 | 10.6424624375658 |
| 30 | 3181.57 | 3189.9873503425 | -8.41735034250093 |
| 31 | 2863.86 | 3249.81780448963 | -385.957804489627 |
| 32 | 2898.01 | 2865.72992805396 | 32.2800719460411 |
| 33 | 3112.33 | 2984.72952635972 | 127.600473640275 |
| 34 | 3254.33 | 3207.58721029746 | 46.7427897025351 |
| 35 | 3513.47 | 3246.07932486798 | 267.390675132015 |
| 36 | 3587.61 | 3515.24633010154 | 72.3636698984587 |
| 37 | 3727.45 | 3709.86281916731 | 17.5871808326886 |
| 38 | 3793.34 | 3748.51134782963 | 44.8286521703705 |
| 39 | 3817.58 | 3712.21273755908 | 105.367262440915 |
| 40 | 3845.13 | 3899.73844984517 | -54.608449845174 |
| 41 | 3931.86 | 4046.94311321104 | -115.083113211036 |
| 42 | 4197.52 | 3997.16033780145 | 200.359662198552 |
| 43 | 4307.13 | 4294.41611584289 | 12.7138841571073 |
| 44 | 4229.43 | 4376.27480079501 | -146.844800795008 |
| 45 | 4362.28 | 4411.46413578363 | -49.1841357836284 |
| 46 | 4217.34 | 4448.08205419727 | -230.742054197267 |
| 47 | 4361.28 | 4216.24158192204 | 145.038418077961 |
| 48 | 4327.74 | 4336.67235752423 | -8.9323575242332 |
| 49 | 4417.65 | 4462.07499038366 | -44.4249903836563 |
| 50 | 4557.68 | 4450.4007521879 | 107.279247812100 |
| 51 | 4650.35 | 4500.97068855122 | 149.379311448784 |
| 52 | 4967.18 | 4777.87176769396 | 189.308232306042 |
| 53 | 5123.42 | 5212.08456848621 | -88.66456848621 |
| 54 | 5290.85 | 5267.1046253435 | 23.7453746565051 |
| 55 | 5535.66 | 5417.0918513003 | 118.568148699704 |
| 56 | 5514.06 | 5611.55336334789 | -97.4933633478846 |
| 57 | 5493.88 | 5747.7659461844 | -253.885946184393 |
| 58 | 5694.83 | 5608.14224874169 | 86.6877512583095 |
| 59 | 5850.41 | 5692.37616333686 | 158.033836663138 |
| 60 | 6116.64 | 5914.47903355625 | 202.160966443753 |
| 61 | 6175 | 6268.77105087234 | -93.7710508723453 |
| 62 | 6513.58 | 6279.47646964196 | 234.103530358036 |
| 63 | 6383.78 | 6462.93037886737 | -79.150378867368 |
| 64 | 6673.66 | 6560.6497554437 | 113.010244556301 |
| 65 | 6936.61 | 6888.83785622556 | 47.7721437744357 |
| 66 | 7300.68 | 7098.62382627007 | 202.056173729930 |
| 67 | 7392.93 | 7465.54302254721 | -72.6130225472122 |
| 68 | 7497.31 | 7514.77680617368 | -17.4668061736802 |
| 69 | 7584.71 | 7714.55489776069 | -129.844897760686 |
| 70 | 7160.79 | 7740.80027546532 | -580.010275465315 |
| 71 | 7196.19 | 7180.73481183567 | 15.4551881643284 |
| 72 | 7245.63 | 7159.51899281744 | 86.1110071825638 |
| 73 | 7347.51 | 7408.74925574395 | -61.2392557439527 |
| 74 | 7425.75 | 7439.25455214388 | -13.5045521438826 |
| 75 | 7778.51 | 7409.39685833856 | 369.113141661441 |
| 76 | 7822.33 | 7938.59651900495 | -116.266519004953 |
| 77 | 8181.22 | 8152.43003437172 | 28.7899656282821 |
| 78 | 8371.47 | 8311.75122035953 | 59.7187796404691 |
| 79 | 8347.71 | 8581.15866923071 | -233.448669230713 |
| 80 | 8672.11 | 8458.97804407412 | 213.131955925881 |
| 81 | 8802.79 | 8901.03325442694 | -98.243254426944 |
| 82 | 9138.46 | 9027.43413723667 | 111.025862763333 |
| 83 | 9123.29 | 9193.73911622772 | -70.4491162277178 |
| 84 | 9023.21 | 8873.11491726677 | 150.095082733225 |
| 85 | 8850.41 | 8804.1607570581 | 46.2492429418934 |
| 86 | 8864.58 | 8560.23251405402 | 304.347485945982 |
| 87 | 9163.74 | 8451.03647319738 | 712.703526802619 |
| 88 | 8516.66 | 8969.94816155378 | -453.288161553781 |
| 89 | 8553.44 | 8483.59702107383 | 69.8429789261756 |
| 90 | 7555.2 | 8214.20863729087 | -659.008637290867 |
| 91 | 7851.22 | 7373.15303810825 | 478.066961891751 |
| 92 | 7442 | 7432.50082246027 | 9.49917753973168 |
| 93 | 7992.53 | 7427.44516301194 | 565.084836988058 |
| 94 | 8264.04 | 7764.65858128783 | 499.38141871217 |
| 95 | 7517.39 | 8096.05966752476 | -578.669667524761 |
| 96 | 7200.4 | 7288.52467024765 | -88.1246702476514 |
| 97 | 7193.69 | 6903.75796872334 | 289.932031276658 |
| 98 | 6193.58 | 6944.72769516577 | -751.14769516577 |
| 99 | 5104.21 | 5866.00541435798 | -761.795414357984 |
| 100 | 4800.46 | 4775.30873971613 | 25.1512602838692 |
| 101 | 4461.61 | 4626.49251649736 | -164.882516497358 |
| 102 | 4398.59 | 4302.32351828679 | 96.2664817132106 |
| 103 | 4243.63 | 4242.25343981737 | 1.37656018262728 |
| 104 | 4293.82 | 4084.9002832998 | 208.919716700202 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.240184539492171 | 0.480369078984342 | 0.759815460507829 |
| 22 | 0.118660392582154 | 0.237320785164308 | 0.881339607417846 |
| 23 | 0.0791328230079827 | 0.158265646015965 | 0.920867176992017 |
| 24 | 0.0446035432221474 | 0.0892070864442949 | 0.955396456777853 |
| 25 | 0.0215575496888775 | 0.043115099377755 | 0.978442450311122 |
| 26 | 0.0095821229186285 | 0.019164245837257 | 0.990417877081371 |
| 27 | 0.00411183430929289 | 0.00822366861858577 | 0.995888165690707 |
| 28 | 0.00163029670824957 | 0.00326059341649915 | 0.99836970329175 |
| 29 | 0.00149239666616301 | 0.00298479333232602 | 0.998507603333837 |
| 30 | 0.00059386821870568 | 0.00118773643741136 | 0.999406131781294 |
| 31 | 0.00720247437531529 | 0.0144049487506306 | 0.992797525624685 |
| 32 | 0.00502935771738632 | 0.0100587154347726 | 0.994970642282614 |
| 33 | 0.00273817030606261 | 0.00547634061212522 | 0.997261829693937 |
| 34 | 0.00153548930825939 | 0.00307097861651879 | 0.99846451069174 |
| 35 | 0.00193598831738365 | 0.0038719766347673 | 0.998064011682616 |
| 36 | 0.00276908946732009 | 0.00553817893464019 | 0.99723091053268 |
| 37 | 0.00260144173382442 | 0.00520288346764883 | 0.997398558266176 |
| 38 | 0.00144932399549945 | 0.00289864799099889 | 0.9985506760045 |
| 39 | 0.00197019777650634 | 0.00394039555301267 | 0.998029802223494 |
| 40 | 0.00137458226051199 | 0.00274916452102398 | 0.998625417739488 |
| 41 | 0.000713365548970888 | 0.00142673109794178 | 0.99928663445103 |
| 42 | 0.000626039362506551 | 0.00125207872501310 | 0.999373960637493 |
| 43 | 0.000352458665090636 | 0.000704917330181272 | 0.99964754133491 |
| 44 | 0.000194179909916493 | 0.000388359819832986 | 0.999805820090083 |
| 45 | 9.4531137611683e-05 | 0.000189062275223366 | 0.999905468862388 |
| 46 | 8.43522245156038e-05 | 0.000168704449031208 | 0.999915647775484 |
| 47 | 5.88068766096973e-05 | 0.000117613753219395 | 0.99994119312339 |
| 48 | 3.11412180882889e-05 | 6.22824361765778e-05 | 0.999968858781912 |
| 49 | 1.61440557484732e-05 | 3.22881114969465e-05 | 0.999983855944252 |
| 50 | 7.75850748540692e-06 | 1.55170149708138e-05 | 0.999992241492515 |
| 51 | 6.26725837215696e-06 | 1.25345167443139e-05 | 0.999993732741628 |
| 52 | 3.1189535070213e-06 | 6.2379070140426e-06 | 0.999996881046493 |
| 53 | 1.56955638066552e-06 | 3.13911276133104e-06 | 0.99999843044362 |
| 54 | 6.42529010218063e-07 | 1.28505802043613e-06 | 0.99999935747099 |
| 55 | 3.60598839384855e-07 | 7.2119767876971e-07 | 0.99999963940116 |
| 56 | 1.89305559594072e-07 | 3.78611119188143e-07 | 0.99999981069444 |
| 57 | 1.83482921663495e-07 | 3.66965843326989e-07 | 0.999999816517078 |
| 58 | 1.02703685548449e-07 | 2.05407371096897e-07 | 0.999999897296314 |
| 59 | 4.35301331137472e-08 | 8.70602662274943e-08 | 0.999999956469867 |
| 60 | 5.73681277284943e-08 | 1.14736255456989e-07 | 0.999999942631872 |
| 61 | 3.29437749995893e-08 | 6.58875499991786e-08 | 0.999999967056225 |
| 62 | 2.74254697362237e-08 | 5.48509394724474e-08 | 0.99999997257453 |
| 63 | 1.44591816674560e-08 | 2.89183633349121e-08 | 0.999999985540818 |
| 64 | 6.0472472556768e-09 | 1.20944945113536e-08 | 0.999999993952753 |
| 65 | 2.10631599440343e-09 | 4.21263198880686e-09 | 0.999999997893684 |
| 66 | 1.22825959185453e-09 | 2.45651918370905e-09 | 0.99999999877174 |
| 67 | 4.97186915874119e-10 | 9.94373831748237e-10 | 0.999999999502813 |
| 68 | 1.90063812775519e-10 | 3.80127625551038e-10 | 0.999999999809936 |
| 69 | 1.52579864702703e-10 | 3.05159729405407e-10 | 0.99999999984742 |
| 70 | 2.49229821744063e-07 | 4.98459643488125e-07 | 0.999999750770178 |
| 71 | 2.17724393338283e-07 | 4.35448786676567e-07 | 0.999999782275607 |
| 72 | 1.23993445019537e-07 | 2.47986890039073e-07 | 0.999999876006555 |
| 73 | 2.66488933722338e-07 | 5.32977867444676e-07 | 0.999999733511066 |
| 74 | 2.90483673902845e-07 | 5.80967347805689e-07 | 0.999999709516326 |
| 75 | 6.7700106639264e-07 | 1.35400213278528e-06 | 0.999999322998934 |
| 76 | 6.20623046116621e-07 | 1.24124609223324e-06 | 0.999999379376954 |
| 77 | 2.84614531294319e-07 | 5.69229062588639e-07 | 0.999999715385469 |
| 78 | 1.25139566825248e-07 | 2.50279133650495e-07 | 0.999999874860433 |
| 79 | 6.77540030295558e-08 | 1.35508006059112e-07 | 0.999999932245997 |
| 80 | 4.25570312147019e-08 | 8.51140624294038e-08 | 0.999999957442969 |
| 81 | 3.26976979221641e-08 | 6.53953958443282e-08 | 0.999999967302302 |
| 82 | 5.09504805328779e-08 | 1.01900961065756e-07 | 0.99999994904952 |
| 83 | 1.43850597059107e-08 | 2.87701194118214e-08 | 0.99999998561494 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 55 | 0.873015873015873 | NOK |
| 5% type I error level | 59 | 0.936507936507937 | NOK |
| 10% type I error level | 60 | 0.952380952380952 | NOK |
