| Multiple Linear Regression - Estimated Regression Equation |
| yt[t] = + 28119.1565018716 + 0.224247526251785`yt-1`[t] + 0.36519346283177`yt-2`[t] + 0.602694136336523`yt-3`[t] -0.327862168171322`yt-4`[t] + 28942.8988936196M1[t] + 32090.1133255437M2[t] + 29065.2556587176M3[t] + 68882.0166486343M4[t] + 70753.4096217564M5[t] + 60369.6909960785M6[t] + 56577.5193671499M7[t] + 36920.8165999598M8[t] + 113460.268012881M9[t] + 86862.5721223365M10[t] + 73028.5702156483M11[t] + 126.260004778667t + 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) | 28119.1565018716 | 60431.815341 | 0.4653 | 0.643318 | 0.321659 |
| `yt-1` | 0.224247526251785 | 0.119916 | 1.87 | 0.066126 | 0.033063 |
| `yt-2` | 0.36519346283177 | 0.093545 | 3.9039 | 0.000233 | 0.000117 |
| `yt-3` | 0.602694136336523 | 0.095701 | 6.2977 | 0 | 0 |
| `yt-4` | -0.327862168171322 | 0.119846 | -2.7357 | 0.008076 | 0.004038 |
| M1 | 28942.8988936196 | 15665.724366 | 1.8475 | 0.069366 | 0.034683 |
| M2 | 32090.1133255437 | 16529.470762 | 1.9414 | 0.056687 | 0.028344 |
| M3 | 29065.2556587176 | 16712.487525 | 1.7391 | 0.086896 | 0.043448 |
| M4 | 68882.0166486343 | 15934.791092 | 4.3227 | 5.6e-05 | 2.8e-05 |
| M5 | 70753.4096217564 | 15101.587834 | 4.6852 | 1.5e-05 | 8e-06 |
| M6 | 60369.6909960785 | 14042.509519 | 4.2991 | 6.1e-05 | 3e-05 |
| M7 | 56577.5193671499 | 12446.950333 | 4.5455 | 2.5e-05 | 1.3e-05 |
| M8 | 36920.8165999598 | 13809.908601 | 2.6735 | 0.009548 | 0.004774 |
| M9 | 113460.268012881 | 14552.847121 | 7.7964 | 0 | 0 |
| M10 | 86862.5721223365 | 13958.840078 | 6.2228 | 0 | 0 |
| M11 | 73028.5702156483 | 14126.114306 | 5.1698 | 3e-06 | 1e-06 |
| t | 126.260004778667 | 111.420586 | 1.1332 | 0.261431 | 0.130716 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.900321315396772 |
| R-squared | 0.810578470957773 |
| Adjusted R-squared | 0.762471415962922 |
| F-TEST (value) | 16.8494718923145 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 63 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 20435.3029081579 |
| Sum Squared Residuals | 26308901111.7345 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 600969 | 621290.265763368 | -20321.2657633677 |
| 2 | 625568 | 599929.293405066 | 25638.7065949337 |
| 3 | 558110 | 550731.62178043 | 7378.37821957008 |
| 4 | 630577 | 620912.201853115 | 9664.79814688512 |
| 5 | 628654 | 624718.488185848 | 3935.51181415225 |
| 6 | 603184 | 591772.653719161 | 11411.3462808394 |
| 7 | 656255 | 647485.252690752 | 8769.74730924792 |
| 8 | 600730 | 605636.204330678 | -4906.20433067765 |
| 9 | 670326 | 674511.613416094 | -4185.61341609392 |
| 10 | 678423 | 683705.771276453 | -5282.77127645277 |
| 11 | 641502 | 646365.200786738 | -4863.20078673821 |
| 12 | 625311 | 628290.067127864 | -2979.06712786447 |
| 13 | 628177 | 622307.245453374 | 5869.75454662613 |
| 14 | 589767 | 595403.795760241 | -5636.79576024121 |
| 15 | 582471 | 587285.273428967 | -4814.27342896724 |
| 16 | 636248 | 618600.841324363 | 17647.1586756365 |
| 17 | 599885 | 605904.267266021 | -6019.26726602116 |
| 18 | 621694 | 615327.434159482 | 6366.56584051846 |
| 19 | 637406 | 638075.771895152 | -669.771895152296 |
| 20 | 595994 | 590485.999798753 | 5508.00020124721 |
| 21 | 696308 | 688669.300787903 | 7638.69921209665 |
| 22 | 674201 | 671888.823812241 | 2312.17618775881 |
| 23 | 648861 | 659747.518917714 | -10886.5189177137 |
| 24 | 649605 | 647125.532209575 | 2479.4677904254 |
| 25 | 672392 | 620894.604109418 | 51497.3958905824 |
| 26 | 598396 | 621525.490400163 | -23129.4904001626 |
| 27 | 613177 | 619111.568002031 | -5934.5680020313 |
| 28 | 638104 | 648835.998038136 | -10731.9980381355 |
| 29 | 615632 | 609753.443138554 | 5878.55686144636 |
| 30 | 634465 | 636728.782580927 | -2263.78258092714 |
| 31 | 638686 | 639256.723150642 | -570.723150641723 |
| 32 | 604243 | 605834.154784289 | -1591.15478428887 |
| 33 | 706669 | 695035.847574683 | 11633.1524253171 |
| 34 | 677185 | 675324.174108774 | 1860.82589122598 |
| 35 | 644328 | 670267.523417174 | -25939.5234171737 |
| 36 | 644825 | 652253.854444847 | -7428.85444484675 |
| 37 | 605707 | 618083.858402667 | -12376.8584026668 |
| 38 | 600136 | 602630.686187234 | -2494.68618723375 |
| 39 | 612166 | 595269.273922749 | 16896.7260772511 |
| 40 | 599659 | 612136.363154024 | -12477.3631540241 |
| 41 | 634210 | 625190.332939955 | 9019.66706004503 |
| 42 | 618234 | 627190.306557955 | -8956.3065579551 |
| 43 | 613576 | 621077.538342445 | -7501.53834244518 |
| 44 | 627200 | 619592.477082434 | 7607.52291756552 |
| 45 | 668973 | 676655.658353318 | -7682.6583533185 |
| 46 | 651479 | 666957.686830938 | -15478.6868309383 |
| 47 | 619661 | 674320.472120442 | -54659.4721204424 |
| 48 | 644260 | 608603.907658534 | 35656.0923414662 |
| 49 | 579936 | 607330.288282727 | -27394.2882827267 |
| 50 | 601752 | 591721.757573042 | 10030.242426958 |
| 51 | 595376 | 595482.23116713 | -106.231167130079 |
| 52 | 588902 | 595129.731419025 | -6227.73141902504 |
| 53 | 634341 | 627584.913776726 | 6756.08622327394 |
| 54 | 594305 | 614157.357148702 | -19852.3571487016 |
| 55 | 606200 | 616296.104666766 | -10096.1046667657 |
| 56 | 610926 | 614320.599288923 | -3394.59928892287 |
| 57 | 633685 | 657362.889254167 | -23677.8892541667 |
| 58 | 639696 | 658016.343640338 | -18320.3436403384 |
| 59 | 659451 | 652916.403637245 | 6534.59636275483 |
| 60 | 593248 | 598806.520454667 | -5558.52045466652 |
| 61 | 606677 | 616405.196598967 | -9728.1965989671 |
| 62 | 599434 | 608448.631416304 | -9014.63141630372 |
| 63 | 569578 | 562452.914893871 | 7125.08510612881 |
| 64 | 629873 | 622854.744169812 | 7018.25583018813 |
| 65 | 613438 | 618702.0110309 | -5264.0110309006 |
| 66 | 604172 | 611159.053707096 | -6987.0537070965 |
| 67 | 658328 | 645541.405786391 | 12786.594213609 |
| 68 | 612633 | 605097.701868491 | 7535.29813150853 |
| 69 | 707372 | 691097.690613835 | 16274.3093861654 |
| 70 | 739770 | 704861.200331255 | 34908.7996687446 |
| 71 | 777535 | 687720.881120687 | 89814.1188793132 |
| 72 | 685030 | 707199.118104514 | -22169.1181045139 |
| 73 | 730234 | 717780.54138948 | 12453.4586105198 |
| 74 | 714154 | 709547.34525795 | 4606.65474204973 |
| 75 | 630872 | 651417.116804821 | -20545.1168048214 |
| 76 | 719492 | 724385.120041525 | -4893.12004152498 |
| 77 | 677023 | 691329.543661996 | -14306.5436619958 |
| 78 | 679272 | 658990.412126677 | 20281.5878733225 |
| 79 | 718317 | 721035.203467852 | -2718.20346785207 |
| 80 | 645672 | 656430.862846432 | -10758.8628464319 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.1734070770017 | 0.3468141540034 | 0.8265929229983 |
| 21 | 0.0905598261171926 | 0.181119652234385 | 0.909440173882808 |
| 22 | 0.0422410208296392 | 0.0844820416592783 | 0.95775897917036 |
| 23 | 0.0176546391513303 | 0.0353092783026607 | 0.98234536084867 |
| 24 | 0.00693177527421705 | 0.0138635505484341 | 0.993068224725783 |
| 25 | 0.153193851949193 | 0.306387703898386 | 0.846806148050807 |
| 26 | 0.129153277907362 | 0.258306555814725 | 0.870846722092637 |
| 27 | 0.0794178599995427 | 0.158835719999085 | 0.920582140000457 |
| 28 | 0.134731863901623 | 0.269463727803245 | 0.865268136098377 |
| 29 | 0.0891623579377328 | 0.178324715875466 | 0.910837642062267 |
| 30 | 0.0586686662922547 | 0.117337332584509 | 0.941331333707745 |
| 31 | 0.0423934296875102 | 0.0847868593750204 | 0.95760657031249 |
| 32 | 0.0248223611527363 | 0.0496447223054727 | 0.975177638847264 |
| 33 | 0.0161014635121073 | 0.0322029270242146 | 0.983898536487893 |
| 34 | 0.0093334201066413 | 0.0186668402132826 | 0.990666579893359 |
| 35 | 0.007066879240364 | 0.014133758480728 | 0.992933120759636 |
| 36 | 0.00412104295864532 | 0.00824208591729063 | 0.995878957041355 |
| 37 | 0.0075554984535945 | 0.015110996907189 | 0.992444501546406 |
| 38 | 0.00400188190503342 | 0.00800376381006683 | 0.995998118094967 |
| 39 | 0.00324775481272437 | 0.00649550962544874 | 0.996752245187276 |
| 40 | 0.00241960468892603 | 0.00483920937785207 | 0.997580395311074 |
| 41 | 0.00166673586452616 | 0.00333347172905232 | 0.998333264135474 |
| 42 | 0.00123789364938660 | 0.00247578729877320 | 0.998762106350613 |
| 43 | 0.000678219738495163 | 0.00135643947699033 | 0.999321780261505 |
| 44 | 0.000506097886612760 | 0.00101219577322552 | 0.999493902113387 |
| 45 | 0.00038908599337222 | 0.00077817198674444 | 0.999610914006628 |
| 46 | 0.000198903767035528 | 0.000397807534071055 | 0.999801096232964 |
| 47 | 0.0104754695283159 | 0.0209509390566318 | 0.989524530471684 |
| 48 | 0.0847344296777147 | 0.169468859355429 | 0.915265570322285 |
| 49 | 0.0684975988527447 | 0.136995197705489 | 0.931502401147255 |
| 50 | 0.0535883755177341 | 0.107176751035468 | 0.946411624482266 |
| 51 | 0.0521103493324116 | 0.104220698664823 | 0.947889650667588 |
| 52 | 0.0318213927624854 | 0.0636427855249709 | 0.968178607237514 |
| 53 | 0.0347253905764277 | 0.0694507811528554 | 0.965274609423572 |
| 54 | 0.0216942253993951 | 0.0433884507987902 | 0.978305774600605 |
| 55 | 0.0123140847304930 | 0.0246281694609859 | 0.987685915269507 |
| 56 | 0.0764534804065407 | 0.152906960813081 | 0.92354651959346 |
| 57 | 0.0530612027342133 | 0.106122405468427 | 0.946938797265787 |
| 58 | 0.0446639804680606 | 0.0893279609361213 | 0.95533601953194 |
| 59 | 0.173237249258584 | 0.346474498517167 | 0.826762750741416 |
| 60 | 0.100772000129629 | 0.201544000259257 | 0.899227999870371 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 10 | 0.24390243902439 | NOK |
| 5% type I error level | 20 | 0.48780487804878 | NOK |
| 10% type I error level | 25 | 0.609756097560976 | NOK |
