| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = + 3000.29080206064 + 0.241703589564587`Yt-1`[t] -0.0637255373607908`Yt-3`[t] -0.105740638589231`Yt-6`[t] + 0.576198585815679`Yt-12 `[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) | 3000.29080206064 | 1347.539397 | 2.2265 | 0.028829 | 0.014415 |
| `Yt-1` | 0.241703589564587 | 0.079842 | 3.0273 | 0.003331 | 0.001666 |
| `Yt-3` | -0.0637255373607908 | 0.07025 | -0.9071 | 0.367098 | 0.183549 |
| `Yt-6` | -0.105740638589231 | 0.0802 | -1.3185 | 0.191158 | 0.095579 |
| `Yt-12 ` | 0.576198585815679 | 0.07139 | 8.0711 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.806187929180415 |
| R-squared | 0.649938977156206 |
| Adjusted R-squared | 0.632214368404622 |
| F-TEST (value) | 36.6687347667465 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 79 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 459.357740870306 |
| Sum Squared Residuals | 16669753.1937002 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10102 | 10657.4945898650 | -555.494589864962 |
| 2 | 8463 | 9302.77132163496 | -839.77132163496 |
| 3 | 9114 | 8726.96965685472 | 387.030343145281 |
| 4 | 8563 | 8524.65925330665 | 38.3407466933546 |
| 5 | 8872 | 8370.48040556903 | 501.519594430971 |
| 6 | 8301 | 8349.81102928618 | -48.8110292861799 |
| 7 | 8301 | 8138.37014436535 | 162.629855634649 |
| 8 | 8278 | 8301.78323592748 | -23.7832359274822 |
| 9 | 7736 | 7964.15091485477 | -228.150914854766 |
| 10 | 7973 | 8256.14436599475 | -283.144365994751 |
| 11 | 8268 | 8432.03157906886 | -164.03157906886 |
| 12 | 9476 | 8734.81034871273 | 741.189651287271 |
| 13 | 11100 | 9725.59538037787 | 1374.40461962213 |
| 14 | 8962 | 9157.36552884498 | -195.36552884498 |
| 15 | 9173 | 8996.03951070543 | 176.960489294573 |
| 16 | 8738 | 8601.00274329954 | 136.997256700456 |
| 17 | 8459 | 8778.95875534954 | -319.958755349541 |
| 18 | 8078 | 8241.33328156135 | -163.333281561351 |
| 19 | 8411 | 8005.24202562028 | 405.757974379723 |
| 20 | 8291 | 8316.32966369896 | -25.3296636989592 |
| 21 | 7810 | 7976.99375443124 | -166.993754431245 |
| 22 | 8616 | 8022.06996653417 | 593.930033465834 |
| 23 | 8312 | 8424.01034518854 | -112.010345188539 |
| 24 | 9692 | 9117.51951239928 | 574.480487600718 |
| 25 | 9911 | 10300.2425536001 | -389.242553600063 |
| 26 | 8915 | 9153.32450322917 | -238.324503229175 |
| 27 | 9452 | 8997.08563523348 | 454.914364766518 |
| 28 | 9112 | 8777.05123061491 | 334.948769385087 |
| 29 | 8472 | 8629.72839406285 | -157.728394062852 |
| 30 | 8230 | 8075.36374072986 | 154.63625927014 |
| 31 | 8384 | 8207.25508398348 | 176.744916016522 |
| 32 | 8625 | 8321.43562642432 | 303.564373575677 |
| 33 | 8221 | 8061.17352885094 | 159.826471149059 |
| 34 | 8649 | 8454.07942320106 | 194.920576798938 |
| 35 | 8625 | 8434.6803436399 | 190.319656360104 |
| 36 | 10443 | 9275.36785754834 | 1167.63214245166 |
| 37 | 10357 | 9797.41388533723 | 559.58611466277 |
| 38 | 8586 | 9178.77950415891 | -592.779504158913 |
| 39 | 8892 | 8987.00727869118 | -95.00727869118 |
| 40 | 8329 | 8825.28446081745 | -496.28446081745 |
| 41 | 8101 | 8435.83394696266 | -334.833946962655 |
| 42 | 7922 | 8029.54897538691 | -107.548975386912 |
| 43 | 8120 | 8119.98978752326 | 0.010212476735866 |
| 44 | 7838 | 8508.50705089842 | -670.507050898419 |
| 45 | 7735 | 8186.61264575095 | -451.612645750948 |
| 46 | 8406 | 8455.2444938832 | -49.2444938832061 |
| 47 | 8209 | 8645.67830355556 | -436.678303555555 |
| 48 | 9451 | 9671.08303007987 | -220.083030079870 |
| 49 | 10041 | 9858.02932792918 | 182.970672070819 |
| 50 | 9411 | 9022.55954123496 | 388.440458765041 |
| 51 | 10405 | 8978.34721544146 | 1426.65278455855 |
| 52 | 8467 | 8785.65074411819 | -318.650744118187 |
| 53 | 8464 | 8246.83390431542 | 217.166095684581 |
| 54 | 8102 | 7948.29618942127 | 153.703810578732 |
| 55 | 7627 | 8035.99992462796 | -408.999924627958 |
| 56 | 7513 | 7825.51049730806 | -312.510497308056 |
| 57 | 7510 | 7656.57028352559 | -146.570283525589 |
| 58 | 8291 | 8277.66941167152 | 13.3305883284799 |
| 59 | 8064 | 8360.51072689067 | -296.510726890672 |
| 60 | 9383 | 9059.75194342397 | 323.248056576032 |
| 61 | 9706 | 9718.97330234202 | -12.9733023420156 |
| 62 | 8579 | 9460.55858248757 | -881.558582487571 |
| 63 | 9474 | 9677.16326948595 | -203.163269485951 |
| 64 | 8318 | 8673.64833552975 | -355.648335529746 |
| 65 | 8213 | 8488.332195801 | -275.332195801003 |
| 66 | 8059 | 8057.86317259434 | 1.13682740565717 |
| 67 | 9111 | 7786.4589864637 | 1324.54101353630 |
| 68 | 7708 | 8100.9054050156 | -392.905405015606 |
| 69 | 7680 | 7675.24253431524 | 4.75746568475654 |
| 70 | 8014 | 8173.68284223508 | -159.682842235079 |
| 71 | 8007 | 8224.12445813855 | -217.124458138550 |
| 72 | 8718 | 9000.50684109132 | -282.506841091322 |
| 73 | 9486 | 9225.94675521583 | 260.053244784167 |
| 74 | 9113 | 8910.99950048938 | 202.000499510617 |
| 75 | 9025 | 9294.1936767038 | -269.193676703800 |
| 76 | 8476 | 8522.5796096373 | -46.5796096373016 |
| 77 | 7952 | 8353.8932973614 | -401.893297361396 |
| 78 | 7759 | 8068.93228746475 | -309.932287464745 |
| 79 | 7835 | 8582.22091653142 | -747.220916531419 |
| 80 | 7600 | 7865.01721320977 | -265.017213209767 |
| 81 | 7651 | 7813.68751416573 | -162.687514165735 |
| 82 | 8319 | 8071.67319464203 | 247.326805357967 |
| 83 | 8812 | 8299.48139827101 | 512.518601728989 |
| 84 | 8630 | 8845.47640328362 | -215.476403283621 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.276335513087138 | 0.552671026174277 | 0.723664486912862 |
| 9 | 0.327824731929404 | 0.655649463858808 | 0.672175268070596 |
| 10 | 0.410114439690031 | 0.820228879380062 | 0.589885560309969 |
| 11 | 0.300240855430904 | 0.600481710861807 | 0.699759144569096 |
| 12 | 0.544338535020122 | 0.911322929959756 | 0.455661464979878 |
| 13 | 0.967327226150502 | 0.0653455476989957 | 0.0326727738494978 |
| 14 | 0.955549583104901 | 0.088900833790198 | 0.044450416895099 |
| 15 | 0.933338684807976 | 0.133322630384049 | 0.0666613151920245 |
| 16 | 0.91348538086579 | 0.173029238268420 | 0.0865146191342102 |
| 17 | 0.897675207971843 | 0.204649584056314 | 0.102324792028157 |
| 18 | 0.855673200921566 | 0.288653598156867 | 0.144326799078434 |
| 19 | 0.853134172614955 | 0.293731654770091 | 0.146865827385045 |
| 20 | 0.80441837535946 | 0.391163249281081 | 0.195581624640540 |
| 21 | 0.762190417231992 | 0.475619165536017 | 0.237809582768008 |
| 22 | 0.762781367427515 | 0.47443726514497 | 0.237218632572485 |
| 23 | 0.710339505640487 | 0.579320988719025 | 0.289660494359513 |
| 24 | 0.704072020545687 | 0.591855958908627 | 0.295927979454314 |
| 25 | 0.672111603663626 | 0.655776792672748 | 0.327888396336374 |
| 26 | 0.617654060969023 | 0.764691878061953 | 0.382345939030977 |
| 27 | 0.609995296492681 | 0.780009407014637 | 0.390004703507319 |
| 28 | 0.586428178493848 | 0.827143643012304 | 0.413571821506152 |
| 29 | 0.527420872361172 | 0.945158255277656 | 0.472579127638828 |
| 30 | 0.462992284561133 | 0.925984569122267 | 0.537007715438867 |
| 31 | 0.400873742412532 | 0.801747484825064 | 0.599126257587468 |
| 32 | 0.353237741798266 | 0.706475483596531 | 0.646762258201734 |
| 33 | 0.295493180734147 | 0.590986361468295 | 0.704506819265853 |
| 34 | 0.245027789741765 | 0.49005557948353 | 0.754972210258235 |
| 35 | 0.199830720825401 | 0.399661441650802 | 0.800169279174599 |
| 36 | 0.489360960141012 | 0.978721920282023 | 0.510639039858988 |
| 37 | 0.551207062158698 | 0.897585875682605 | 0.448792937841302 |
| 38 | 0.575532396160635 | 0.84893520767873 | 0.424467603839365 |
| 39 | 0.517989107587281 | 0.964021784825437 | 0.482010892412719 |
| 40 | 0.512231290320684 | 0.975537419358632 | 0.487768709679316 |
| 41 | 0.498689056715854 | 0.997378113431708 | 0.501310943284146 |
| 42 | 0.435765566543469 | 0.871531133086938 | 0.564234433456531 |
| 43 | 0.374538261824518 | 0.749076523649037 | 0.625461738175481 |
| 44 | 0.475929011209274 | 0.951858022418548 | 0.524070988790726 |
| 45 | 0.485909080066162 | 0.971818160132324 | 0.514090919933838 |
| 46 | 0.427228303521997 | 0.854456607043993 | 0.572771696478003 |
| 47 | 0.424259095354283 | 0.848518190708566 | 0.575740904645717 |
| 48 | 0.376366971712316 | 0.752733943424631 | 0.623633028287684 |
| 49 | 0.330207459792645 | 0.66041491958529 | 0.669792540207355 |
| 50 | 0.309900006146192 | 0.619800012292384 | 0.690099993853808 |
| 51 | 0.860586085640912 | 0.278827828718175 | 0.139413914359088 |
| 52 | 0.828084520574296 | 0.343830958851408 | 0.171915479425704 |
| 53 | 0.802568514194823 | 0.394862971610354 | 0.197431485805177 |
| 54 | 0.778024519827552 | 0.443950960344896 | 0.221975480172448 |
| 55 | 0.762620464611636 | 0.474759070776728 | 0.237379535388364 |
| 56 | 0.731935306961998 | 0.536129386076004 | 0.268064693038002 |
| 57 | 0.696610392529937 | 0.606779214940127 | 0.303389607470063 |
| 58 | 0.629490677232357 | 0.741018645535286 | 0.370509322767643 |
| 59 | 0.595939943080857 | 0.808120113838286 | 0.404060056919143 |
| 60 | 0.575501694764031 | 0.848996610471938 | 0.424498305235969 |
| 61 | 0.528399774455452 | 0.943200451089096 | 0.471600225544548 |
| 62 | 0.66392944546801 | 0.672141109063979 | 0.336070554531990 |
| 63 | 0.644110101074491 | 0.711779797851018 | 0.355889898925509 |
| 64 | 0.590798424199388 | 0.818403151601223 | 0.409201575800612 |
| 65 | 0.515463058455447 | 0.969073883089106 | 0.484536941544553 |
| 66 | 0.430011271054494 | 0.860022542108989 | 0.569988728945506 |
| 67 | 0.95436455300343 | 0.0912708939931406 | 0.0456354469965703 |
| 68 | 0.96655245698608 | 0.0668950860278417 | 0.0334475430139209 |
| 69 | 0.942307353768112 | 0.115385292463776 | 0.0576926462318878 |
| 70 | 0.929974782867829 | 0.140050434264342 | 0.0700252171321708 |
| 71 | 0.898066371823888 | 0.203867256352224 | 0.101933628176112 |
| 72 | 0.836828821240169 | 0.326342357519662 | 0.163171178759831 |
| 73 | 0.946067038558727 | 0.107865922882546 | 0.053932961441273 |
| 74 | 0.905821549292529 | 0.188356901414943 | 0.0941784507074714 |
| 75 | 0.81981539171538 | 0.360369216569239 | 0.180184608284619 |
| 76 | 0.885769109374186 | 0.228461781251627 | 0.114230890625814 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 4 | 0.0579710144927536 | OK |
