| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = + 3540.69197220561 + 0.130932028247944`Yt-1`[t] + 0.201818490077343`Yt-2`[t] + 0.264823448542267`Yt-3`[t] + 385.773255960307M1[t] -436.30006975701M2[t] + 469.50316191611M3[t] + 72.8939494758238M4[t] + 333.401103073757M5[t] + 79.6860766985089M6[t] + 718.477094565068M7[t] + 477.862169357032M8[t] + 160.8783375403M9[t] + 134.048534247597M10[t] -554.848198896826M11[t] + 5.16340774563452t + 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) | 3540.69197220561 | 1487.891151 | 2.3797 | 0.020759 | 0.01038 |
| `Yt-1` | 0.130932028247944 | 0.133903 | 0.9778 | 0.332371 | 0.166186 |
| `Yt-2` | 0.201818490077343 | 0.129049 | 1.5639 | 0.123476 | 0.061738 |
| `Yt-3` | 0.264823448542267 | 0.134251 | 1.9726 | 0.053486 | 0.026743 |
| M1 | 385.773255960307 | 200.187808 | 1.9271 | 0.059052 | 0.029526 |
| M2 | -436.30006975701 | 220.764862 | -1.9763 | 0.053053 | 0.026527 |
| M3 | 469.50316191611 | 159.044028 | 2.952 | 0.004605 | 0.002303 |
| M4 | 72.8939494758238 | 235.72034 | 0.3092 | 0.758287 | 0.379144 |
| M5 | 333.401103073757 | 212.06604 | 1.5722 | 0.121548 | 0.060774 |
| M6 | 79.6860766985089 | 183.358501 | 0.4346 | 0.665529 | 0.332764 |
| M7 | 718.477094565068 | 182.264961 | 3.9419 | 0.000227 | 0.000113 |
| M8 | 477.862169357032 | 222.742583 | 2.1454 | 0.036275 | 0.018138 |
| M9 | 160.8783375403 | 205.873838 | 0.7814 | 0.437834 | 0.218917 |
| M10 | 134.048534247597 | 177.712911 | 0.7543 | 0.45383 | 0.226915 |
| M11 | -554.848198896826 | 184.793507 | -3.0025 | 0.003996 | 0.001998 |
| t | 5.16340774563452 | 2.422649 | 2.1313 | 0.037467 | 0.018733 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.881471388071222 |
| R-squared | 0.776991807988208 |
| Adjusted R-squared | 0.717257470842192 |
| F-TEST (value) | 13.0074567679376 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 56 |
| p-value | 3.57713858534225e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 268.914224668373 |
| Sum Squared Residuals | 4049632.17282355 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9743 | 9522.5163397682 | 220.483660231804 |
| 2 | 8587 | 8628.5703692345 | -41.5703692344936 |
| 3 | 9731 | 9521.97243930522 | 209.027560694778 |
| 4 | 9563 | 9221.52935298616 | 341.470647013836 |
| 5 | 9998 | 9389.9477797177 | 608.052220282304 |
| 6 | 9437 | 9467.4041121753 | -30.4041121752984 |
| 7 | 10038 | 10081.2063737689 | -43.2063737689387 |
| 8 | 9918 | 9926.42303246605 | -8.42303246604785 |
| 9 | 9252 | 9571.61772290947 | -319.617722909469 |
| 10 | 9737 | 9597.6912703139 | 139.308729686109 |
| 11 | 9035 | 8811.27005039877 | 223.729949601227 |
| 12 | 9133 | 9200.87692416954 | -67.8769241695381 |
| 13 | 9487 | 9591.40771915248 | -104.407719152483 |
| 14 | 8700 | 8654.71989033148 | 45.2801096685198 |
| 15 | 9627 | 9560.03946696363 | 66.9605330363746 |
| 16 | 8947 | 9224.88400154791 | -277.884001547911 |
| 17 | 9283 | 9380.19046998181 | -97.1904699818096 |
| 18 | 8829 | 9283.88677638959 | -454.886776389593 |
| 19 | 9947 | 9756.12912883447 | 190.870871165534 |
| 20 | 9628 | 9664.41470316835 | -36.4147031683539 |
| 21 | 9318 | 9416.23018835444 | -98.230188354443 |
| 22 | 9605 | 9585.6673811861 | 19.3326188139060 |
| 23 | 8640 | 8792.4691358855 | -152.469135885506 |
| 24 | 9214 | 9201.9579728728 | 12.0420271272052 |
| 25 | 9567 | 9549.29910760005 | 17.7008923999494 |
| 26 | 8547 | 8638.897381061 | -91.8973810609994 |
| 27 | 9185 | 9639.56393812742 | -454.563938127415 |
| 28 | 9470 | 9219.28058491148 | 250.719415088518 |
| 29 | 9123 | 9380.90705346195 | -257.907053461946 |
| 30 | 9278 | 9313.3976508723 | -35.3976508723051 |
| 31 | 10170 | 9983.09020764064 | 186.909792359363 |
| 32 | 9434 | 9803.81818869322 | -369.818188693224 |
| 33 | 9655 | 9616.70151950468 | 38.2984804953184 |
| 34 | 9429 | 9711.65520960319 | -282.655209603186 |
| 35 | 8739 | 8848.02307400035 | -109.023074000347 |
| 36 | 9552 | 9330.60658452209 | 221.393415477913 |
| 37 | 9687 | 9628.88612966969 | 58.1138703303121 |
| 38 | 9019 | 8811.0022884502 | 207.997711549807 |
| 39 | 9672 | 9877.05329282463 | -205.053292824626 |
| 40 | 9206 | 9472.04251675742 | -266.042516757423 |
| 41 | 9069 | 9631.58416333172 | -562.584163331719 |
| 42 | 9788 | 9443.9771523542 | 344.022847645804 |
| 43 | 10312 | 10031.0148461154 | 280.985153884632 |
| 44 | 10105 | 9972.99839337021 | 132.001606629791 |
| 45 | 9863 | 9930.2359877542 | -67.2359877542051 |
| 46 | 9656 | 9973.87510096127 | -317.875100961272 |
| 47 | 9295 | 9159.38031726819 | 135.619682731807 |
| 48 | 9946 | 9566.2617597199 | 379.738240280093 |
| 49 | 9701 | 9914.7602450491 | -213.760245049090 |
| 50 | 9049 | 9101.55455227325 | -52.5545522732525 |
| 51 | 10190 | 10050.1080442064 | 139.891955793585 |
| 52 | 9706 | 9611.58828331938 | 94.4117166806158 |
| 53 | 9765 | 9871.49775171964 | -106.497751719637 |
| 54 | 9893 | 9835.15452834595 | 57.845471654055 |
| 55 | 9994 | 10379.6009953940 | -385.600995393981 |
| 56 | 10433 | 10198.8309629785 | 234.169037021484 |
| 57 | 10073 | 9998.77076821949 | 74.2292317805122 |
| 58 | 10112 | 10045.3143279499 | 66.6856720501176 |
| 59 | 9266 | 9410.29018913498 | -144.290189134975 |
| 60 | 9820 | 9772.06777951748 | 47.9322204825248 |
| 61 | 10097 | 10075.1304587605 | 21.8695412395063 |
| 62 | 9115 | 9182.25551864958 | -67.2555186495814 |
| 63 | 10411 | 10167.2628185727 | 243.737181427304 |
| 64 | 9678 | 9820.67526047764 | -142.675260477636 |
| 65 | 10408 | 9991.87278178719 | 416.127218212808 |
| 66 | 10153 | 10034.1797798627 | 118.820220137337 |
| 67 | 10368 | 10597.9584482466 | -229.958448246609 |
| 68 | 10581 | 10532.5147193236 | 48.4852806763516 |
| 69 | 10597 | 10224.4438132577 | 372.556186742286 |
| 70 | 10680 | 10304.7967099857 | 375.203290014326 |
| 71 | 9738 | 9691.5672333122 | 46.4327666877946 |
| 72 | 9556 | 10149.2289791982 | -593.228979198198 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.724299647848351 | 0.551400704303297 | 0.275700352151649 |
| 20 | 0.63801872896644 | 0.723962542067119 | 0.361981271033559 |
| 21 | 0.576243413776385 | 0.84751317244723 | 0.423756586223615 |
| 22 | 0.46824636956869 | 0.93649273913738 | 0.53175363043131 |
| 23 | 0.377151798888824 | 0.754303597777648 | 0.622848201111176 |
| 24 | 0.456071486919627 | 0.912142973839254 | 0.543928513080373 |
| 25 | 0.402916691174363 | 0.805833382348725 | 0.597083308825637 |
| 26 | 0.31644303204329 | 0.63288606408658 | 0.68355696795671 |
| 27 | 0.282430381833860 | 0.564860763667721 | 0.71756961816614 |
| 28 | 0.542854502599966 | 0.914290994800068 | 0.457145497400034 |
| 29 | 0.499987254005359 | 0.999974508010719 | 0.500012745994641 |
| 30 | 0.445781647396238 | 0.891563294792477 | 0.554218352603762 |
| 31 | 0.679376031946832 | 0.641247936106336 | 0.320623968053168 |
| 32 | 0.715444183258559 | 0.569111633482883 | 0.284555816741441 |
| 33 | 0.738157894403984 | 0.523684211192032 | 0.261842105596016 |
| 34 | 0.670567578949318 | 0.658864842101364 | 0.329432421050682 |
| 35 | 0.69383164136063 | 0.61233671727874 | 0.30616835863937 |
| 36 | 0.714734304364504 | 0.570531391270992 | 0.285265695635496 |
| 37 | 0.672545520010682 | 0.654908959978635 | 0.327454479989317 |
| 38 | 0.685205951650274 | 0.629588096699453 | 0.314794048349726 |
| 39 | 0.608290217583566 | 0.783419564832868 | 0.391709782416434 |
| 40 | 0.552676505919095 | 0.89464698816181 | 0.447323494080905 |
| 41 | 0.782817392073497 | 0.434365215853007 | 0.217182607926503 |
| 42 | 0.826191377730364 | 0.347617244539272 | 0.173808622269636 |
| 43 | 0.810940497621126 | 0.378119004757747 | 0.189059502378874 |
| 44 | 0.805258967974178 | 0.389482064051644 | 0.194741032025822 |
| 45 | 0.740707286300687 | 0.518585427398626 | 0.259292713699313 |
| 46 | 0.67569233972825 | 0.648615320543499 | 0.324307660271750 |
| 47 | 0.588327678901877 | 0.823344642196246 | 0.411672321098123 |
| 48 | 0.780907954874467 | 0.438184090251065 | 0.219092045125533 |
| 49 | 0.695057528969951 | 0.609884942060098 | 0.304942471030049 |
| 50 | 0.700441050762417 | 0.599117898475167 | 0.299558949237583 |
| 51 | 0.721353335955171 | 0.557293328089658 | 0.278646664044829 |
| 52 | 0.772065792931168 | 0.455868414137663 | 0.227934207068832 |
| 53 | 0.629287079623463 | 0.741425840753074 | 0.370712920376537 |
| 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 | 0 | 0 | OK |
