| Multiple Linear Regression - Estimated Regression Equation |
| MVG[t] = -351.343556830821 + 1.08525691228605VVG[t] + 1.34991956196839MWG[t] -1.4473742694076VWG[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) | -351.343556830821 | 116.053031 | -3.0274 | 0.003091 | 0.001545 |
| VVG | 1.08525691228605 | 0.024216 | 44.8163 | 0 | 0 |
| MWG | 1.34991956196839 | 0.026425 | 51.0843 | 0 | 0 |
| VWG | -1.4473742694076 | 0.054987 | -26.3221 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.99950480804335 |
| R-squared | 0.999009861301776 |
| Adjusted R-squared | 0.998982100403695 |
| F-TEST (value) | 35986.2227217913 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 107 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 529.364893669255 |
| Sum Squared Residuals | 29984309.3994924 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 33024 | 32749.468224778 | 274.531775222003 |
| 2 | 32526 | 32676.2854579039 | -150.285457903912 |
| 3 | 31455 | 31329.4325869681 | 125.567413031927 |
| 4 | 31524 | 31654.6168014827 | -130.616801482703 |
| 5 | 31856 | 31772.3096322231 | 83.6903677769173 |
| 6 | 32696 | 33146.493803536 | -450.493803535949 |
| 7 | 32584 | 33282.3809253076 | -698.380925307554 |
| 8 | 33498 | 33617.0143316202 | -119.014331620154 |
| 9 | 34175 | 34459.8673001519 | -284.8673001519 |
| 10 | 34172 | 34910.5093841849 | -738.50938418487 |
| 11 | 34379 | 34630.9904750984 | -251.990475098367 |
| 12 | 34988 | 35050.8668997278 | -62.8668997278104 |
| 13 | 36158 | 37194.6099549252 | -1036.60995492521 |
| 14 | 37411 | 37812.5058301938 | -401.505830193784 |
| 15 | 38015 | 37747.2899129177 | 267.71008708226 |
| 16 | 37577 | 37719.663351394 | -142.663351394008 |
| 17 | 36354 | 36345.5698630444 | 8.43013695558487 |
| 18 | 36030 | 36282.7515805127 | -252.751580512701 |
| 19 | 35636 | 35620.2832954647 | 15.7167045353505 |
| 20 | 35669 | 35969.9115547184 | -300.911554718448 |
| 21 | 34635 | 35154.3202698853 | -519.320269885304 |
| 22 | 35496 | 35816.9405241828 | -320.940524182776 |
| 23 | 36376 | 38468.1108186942 | -2092.11081869418 |
| 24 | 37635 | 37823.2408897628 | -188.240889762824 |
| 25 | 38875 | 38342.3647672889 | 532.635232711092 |
| 26 | 38372 | 39366.5535423293 | -994.553542329292 |
| 27 | 38897 | 39374.3683992779 | -477.36839927785 |
| 28 | 38018 | 39066.0356512668 | -1048.03565126682 |
| 29 | 37325 | 38347.6587130677 | -1022.65871306773 |
| 30 | 36893 | 37166.2929221499 | -273.292922149936 |
| 31 | 36117 | 35901.8055065911 | 215.194493408874 |
| 32 | 37599 | 37941.4926365088 | -342.492636508786 |
| 33 | 39037 | 39163.341938498 | -126.341938497995 |
| 34 | 40809 | 41366.4940672794 | -557.494067279429 |
| 35 | 42508 | 43188.913696123 | -680.913696122991 |
| 36 | 44021 | 44556.7526942894 | -535.75269428938 |
| 37 | 44088 | 44177.5682239557 | -89.5682239557128 |
| 38 | 44510 | 44053.5538268098 | 456.446173190221 |
| 39 | 45786 | 45200.6096748497 | 585.390325150271 |
| 40 | 47349 | 47149.4035034424 | 199.596496557651 |
| 41 | 48696 | 48666.5482179821 | 29.4517820178684 |
| 42 | 50598 | 50564.4721086701 | 33.5278913299034 |
| 43 | 50066 | 49522.3539082912 | 543.6460917088 |
| 44 | 49367 | 48644.588634794 | 722.411365205996 |
| 45 | 48784 | 48655.5251265387 | 128.474873461321 |
| 46 | 47841 | 48446.9199321674 | -605.919932167405 |
| 47 | 48300 | 47794.4297493811 | 505.570250618879 |
| 48 | 47518 | 46326.3958181333 | 1191.60418186674 |
| 49 | 46504 | 45859.8098226337 | 644.190177366305 |
| 50 | 45147 | 44788.495547488 | 358.504452511944 |
| 51 | 44404 | 43843.6841804956 | 560.315819504371 |
| 52 | 43455 | 42661.1416098873 | 793.858390112672 |
| 53 | 42299 | 41349.6653626651 | 949.334637334933 |
| 54 | 42105 | 41081.1683908663 | 1023.83160913367 |
| 55 | 40152 | 38815.2958281501 | 1336.70417184995 |
| 56 | 39519 | 39485.989927979 | 33.0100720209537 |
| 57 | 39633 | 38929.6940477566 | 703.305952243433 |
| 58 | 39376 | 38719.5422334163 | 656.457766583661 |
| 59 | 38850 | 38628.7467252689 | 221.253274731108 |
| 60 | 39657 | 38310.3007256983 | 1346.6992743017 |
| 61 | 34804 | 34090.3221761978 | 713.677823802196 |
| 62 | 34372 | 34210.8215729304 | 161.178427069602 |
| 63 | 32678 | 32336.819269479 | 341.180730520952 |
| 64 | 28420 | 28094.6131052027 | 325.386894797291 |
| 65 | 25420 | 25334.4128273079 | 85.5871726920797 |
| 66 | 27683 | 27946.0860851201 | -263.086085120114 |
| 67 | 29904 | 30173.9881070548 | -269.988107054818 |
| 68 | 30546 | 30116.2530607939 | 429.746939206129 |
| 69 | 29142 | 29495.027067201 | -353.027067200997 |
| 70 | 27724 | 27897.1701121426 | -173.170112142579 |
| 71 | 27069 | 27062.6735385311 | 6.32646146889145 |
| 72 | 26665 | 27252.354240425 | -587.35424042499 |
| 73 | 26004 | 26517.14068941 | -513.140689410028 |
| 74 | 25767 | 26272.8165667968 | -505.816566796782 |
| 75 | 24915 | 25192.1963130666 | -277.196313066641 |
| 76 | 23689 | 23784.6165741159 | -95.6165741158532 |
| 77 | 20915 | 21378.3579261974 | -463.357926197426 |
| 78 | 19414 | 19493.3825672318 | -79.3825672318416 |
| 79 | 17824 | 17905.5371791963 | -81.5371791962547 |
| 80 | 16348 | 17018.6562595456 | -670.656259545596 |
| 81 | 15571 | 15149.1178545471 | 421.882145452894 |
| 82 | 13929 | 13968.8847570182 | -39.8847570181557 |
| 83 | 12480 | 12920.7433554902 | -440.743355490184 |
| 84 | 10837 | 10622.4811464187 | 214.518853581315 |
| 85 | 9473 | 9245.92255719018 | 227.077442809823 |
| 86 | 8051 | 7868.79447317318 | 182.205526826818 |
| 87 | 5278 | 5411.83373418216 | -133.833734182159 |
| 88 | 3008 | 3157.59257210614 | -149.592572106138 |
| 89 | 2404 | 2545.46089455325 | -141.460894553252 |
| 90 | 2298 | 2767.27254522524 | -469.272545225242 |
| 91 | 2260 | 2400.55900913542 | -140.559009135421 |
| 92 | 1938 | 2180.01170533972 | -242.01170533972 |
| 93 | 1371 | 2065.25753403841 | -694.257534038408 |
| 94 | 1009 | 1336.35647262124 | -327.356472621243 |
| 95 | 686 | 738.35016004123 | -52.3501600412297 |
| 96 | 493 | 502.544883263154 | -9.54488326315354 |
| 97 | 285 | 191.583760941839 | 93.4162390581607 |
| 98 | 192 | 62.383523760209 | 129.616476239791 |
| 99 | 129 | -85.8818921774391 | 214.881892177439 |
| 100 | 60 | -212.310329513305 | 272.310329513305 |
| 101 | 54 | -226.72570628055 | 280.72570628055 |
| 102 | 26 | -274.344301349018 | 300.344301349018 |
| 103 | 11 | -337.281536148059 | 348.281536148059 |
| 104 | 3 | -325.764629114054 | 328.764629114054 |
| 105 | 0 | -339.773323948175 | 339.773323948175 |
| 106 | 2 | -348.089976412109 | 350.089976412109 |
| 107 | 1 | -354.963635242947 | 355.963635242947 |
| 108 | 0 | -349.897277720479 | 349.897277720479 |
| 109 | 0 | -349.173043006238 | 349.173043006238 |
| 110 | 0 | -351.343556830809 | 351.343556830809 |
| 111 | 0 | -350.258299918524 | 350.258299918524 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.182755549285556 | 0.365511098571113 | 0.817244450714444 |
| 8 | 0.100451328722154 | 0.200902657444308 | 0.899548671277846 |
| 9 | 0.0448263408588657 | 0.0896526817177314 | 0.955173659141134 |
| 10 | 0.0213890270461417 | 0.0427780540922834 | 0.978610972953858 |
| 11 | 0.0083027524093041 | 0.0166055048186082 | 0.991697247590696 |
| 12 | 0.0144929080948065 | 0.0289858161896131 | 0.985507091905193 |
| 13 | 0.00930586645323366 | 0.0186117329064673 | 0.990694133546766 |
| 14 | 0.0199572252639985 | 0.0399144505279969 | 0.980042774736002 |
| 15 | 0.0383364397065924 | 0.0766728794131848 | 0.961663560293408 |
| 16 | 0.0257640660115046 | 0.0515281320230091 | 0.974235933988495 |
| 17 | 0.0160827276668748 | 0.0321654553337496 | 0.983917272333125 |
| 18 | 0.00910453473315556 | 0.0182090694663111 | 0.990895465266844 |
| 19 | 0.00517274915707267 | 0.0103454983141453 | 0.994827250842927 |
| 20 | 0.00285594379168034 | 0.00571188758336068 | 0.99714405620832 |
| 21 | 0.0060846752784665 | 0.012169350556933 | 0.993915324721534 |
| 22 | 0.00383645390745665 | 0.0076729078149133 | 0.996163546092543 |
| 23 | 0.0455755542443395 | 0.0911511084886789 | 0.95442444575566 |
| 24 | 0.0423984476282716 | 0.0847968952565431 | 0.957601552371728 |
| 25 | 0.055842362426217 | 0.111684724852434 | 0.944157637573783 |
| 26 | 0.0767278664036399 | 0.15345573280728 | 0.92327213359636 |
| 27 | 0.116870216977246 | 0.233740433954492 | 0.883129783022754 |
| 28 | 0.137354506554965 | 0.274709013109929 | 0.862645493445035 |
| 29 | 0.211332679316812 | 0.422665358633623 | 0.788667320683188 |
| 30 | 0.188440325222672 | 0.376880650445343 | 0.811559674777328 |
| 31 | 0.156555276939174 | 0.313110553878348 | 0.843444723060826 |
| 32 | 0.180656613282742 | 0.361313226565484 | 0.819343386717258 |
| 33 | 0.173824875408977 | 0.347649750817955 | 0.826175124591023 |
| 34 | 0.272192041136291 | 0.544384082272582 | 0.727807958863709 |
| 35 | 0.437871772851259 | 0.875743545702519 | 0.562128227148741 |
| 36 | 0.558221184263562 | 0.883557631472875 | 0.441778815736438 |
| 37 | 0.612755770077939 | 0.774488459844122 | 0.387244229922061 |
| 38 | 0.653257706477594 | 0.693484587044812 | 0.346742293522406 |
| 39 | 0.82703689157882 | 0.34592621684236 | 0.17296310842118 |
| 40 | 0.839634565974837 | 0.320730868050326 | 0.160365434025163 |
| 41 | 0.853587358856204 | 0.292825282287592 | 0.146412641143796 |
| 42 | 0.845456935509324 | 0.309086128981353 | 0.154543064490676 |
| 43 | 0.848564904724235 | 0.30287019055153 | 0.151435095275765 |
| 44 | 0.87114082718065 | 0.257718345638701 | 0.12885917281935 |
| 45 | 0.85666016228073 | 0.286679675438541 | 0.14333983771927 |
| 46 | 0.95507559292475 | 0.0898488141505 | 0.04492440707525 |
| 47 | 0.940974495573428 | 0.118051008853144 | 0.059025504426572 |
| 48 | 0.961029715945662 | 0.0779405681086753 | 0.0389702840543376 |
| 49 | 0.953674538681226 | 0.0926509226375473 | 0.0463254613187736 |
| 50 | 0.947044471706473 | 0.105911056587054 | 0.0529555282935272 |
| 51 | 0.934680771140754 | 0.130638457718491 | 0.0653192288592456 |
| 52 | 0.915560485165457 | 0.168879029669086 | 0.0844395148345431 |
| 53 | 0.90093049010053 | 0.198139019798939 | 0.0990695098994695 |
| 54 | 0.899384946523166 | 0.201230106953669 | 0.100615053476834 |
| 55 | 0.929379984264164 | 0.141240031471672 | 0.0706200157358361 |
| 56 | 0.967166262844574 | 0.065667474310853 | 0.0328337371554265 |
| 57 | 0.956163485173469 | 0.0876730296530626 | 0.0438365148265313 |
| 58 | 0.961783253642557 | 0.0764334927148865 | 0.0382167463574433 |
| 59 | 0.997627354439395 | 0.004745291121211 | 0.0023726455606055 |
| 60 | 0.998283685302016 | 0.00343262939596841 | 0.0017163146979842 |
| 61 | 0.99859903373365 | 0.00280193253269957 | 0.00140096626634978 |
| 62 | 0.997820219941787 | 0.00435956011642661 | 0.0021797800582133 |
| 63 | 0.998314394662664 | 0.00337121067467128 | 0.00168560533733564 |
| 64 | 0.99856834957143 | 0.00286330085714108 | 0.00143165042857054 |
| 65 | 0.997996906351562 | 0.00400618729687535 | 0.00200309364843767 |
| 66 | 0.999406116565595 | 0.00118776686881029 | 0.000593883434405145 |
| 67 | 0.999813683069865 | 0.000372633860270395 | 0.000186316930135197 |
| 68 | 0.999986957267347 | 2.60854653059891e-05 | 1.30427326529946e-05 |
| 69 | 0.99998703441677 | 2.59311664602551e-05 | 1.29655832301275e-05 |
| 70 | 0.999994540560705 | 1.09188785901976e-05 | 5.4594392950988e-06 |
| 71 | 0.99999997289009 | 5.42198182870976e-08 | 2.71099091435488e-08 |
| 72 | 0.999999994490635 | 1.10187308576981e-08 | 5.50936542884904e-09 |
| 73 | 0.999999999213561 | 1.57287715293645e-09 | 7.86438576468223e-10 |
| 74 | 0.999999999850087 | 2.9982669695332e-10 | 1.4991334847666e-10 |
| 75 | 0.999999999964294 | 7.1412888707531e-11 | 3.57064443537655e-11 |
| 76 | 0.999999999999987 | 2.66430679181423e-14 | 1.33215339590712e-14 |
| 77 | 0.999999999999994 | 1.19220319197378e-14 | 5.96101595986889e-15 |
| 78 | 1 | 1.68964081114166e-16 | 8.44820405570829e-17 |
| 79 | 1 | 4.39027249365828e-16 | 2.19513624682914e-16 |
| 80 | 1 | 1.68610418014427e-18 | 8.43052090072134e-19 |
| 81 | 1 | 1.60493923563001e-18 | 8.02469617815004e-19 |
| 82 | 1 | 5.77582918742823e-18 | 2.88791459371411e-18 |
| 83 | 1 | 3.24606163176517e-17 | 1.62303081588259e-17 |
| 84 | 1 | 2.41336966758559e-16 | 1.20668483379279e-16 |
| 85 | 1 | 1.56192328537736e-15 | 7.8096164268868e-16 |
| 86 | 1 | 2.7437963031234e-17 | 1.3718981515617e-17 |
| 87 | 1 | 1.99434484873553e-16 | 9.97172424367765e-17 |
| 88 | 1 | 1.48214323429178e-15 | 7.41071617145892e-16 |
| 89 | 0.999999999999997 | 6.23868365648438e-15 | 3.11934182824219e-15 |
| 90 | 0.999999999999976 | 4.70600043424628e-14 | 2.35300021712314e-14 |
| 91 | 1 | 3.16791550422452e-21 | 1.58395775211226e-21 |
| 92 | 1 | 9.06987347570455e-20 | 4.53493673785227e-20 |
| 93 | 1 | 1.69267057989323e-18 | 8.46335289946614e-19 |
| 94 | 1 | 2.37303995075023e-17 | 1.18651997537512e-17 |
| 95 | 1 | 1.90982443912188e-22 | 9.5491221956094e-23 |
| 96 | 1 | 8.3871040439931e-23 | 4.19355202199655e-23 |
| 97 | 1 | 8.56421868982582e-21 | 4.28210934491291e-21 |
| 98 | 1 | 1.0328139508292e-18 | 5.16406975414602e-19 |
| 99 | 1 | 5.8123006977893e-18 | 2.90615034889465e-18 |
| 100 | 1 | 3.2522464123824e-16 | 1.6261232061912e-16 |
| 101 | 0.999999999999972 | 5.65522513927536e-14 | 2.82761256963768e-14 |
| 102 | 0.999999999999976 | 4.77499530443323e-14 | 2.38749765221662e-14 |
| 103 | 0.999999999987442 | 2.51159742339512e-11 | 1.25579871169756e-11 |
| 104 | 0.999999991618517 | 1.67629649229508e-08 | 8.3814824614754e-09 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 48 | 0.489795918367347 | NOK |
| 5% type I error level | 57 | 0.581632653061224 | NOK |
| 10% type I error level | 68 | 0.693877551020408 | NOK |
