| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 243.301929501305 -1.54574360309231X[t] + 0.889239136592848`Yt-1`[t] + 0.0310888319576515`Yt-2`[t] + 0.0174977223073751`Yt-3`[t] -0.347038931375699`Yt-4`[t] + 0.266291251496857`Yt-5`[t] -0.0304035045744285t + 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) | 243.301929501305 | 35.203991 | 6.9112 | 0 | 0 |
| X | -1.54574360309231 | 0.228481 | -6.7653 | 0 | 0 |
| `Yt-1` | 0.889239136592848 | 0.099542 | 8.9333 | 0 | 0 |
| `Yt-2` | 0.0310888319576515 | 0.162016 | 0.1919 | 0.848489 | 0.424245 |
| `Yt-3` | 0.0174977223073751 | 0.150517 | 0.1163 | 0.907848 | 0.453924 |
| `Yt-4` | -0.347038931375699 | 0.147972 | -2.3453 | 0.022394 | 0.011197 |
| `Yt-5` | 0.266291251496857 | 0.091754 | 2.9022 | 0.005202 | 0.002601 |
| t | -0.0304035045744285 | 0.100142 | -0.3036 | 0.762499 | 0.381249 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.955334021847317 |
| R-squared | 0.91266309329897 |
| Adjusted R-squared | 0.902301087419188 |
| F-TEST (value) | 88.077839743329 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12.6291749440012 |
| Sum Squared Residuals | 9410.26752620514 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 507 | 510.784212755440 | -3.78421275544049 |
| 2 | 569 | 544.151941321968 | 24.8480586780318 |
| 3 | 580 | 593.919556662604 | -13.9195566626042 |
| 4 | 578 | 577.453000073742 | 0.54699992625841 |
| 5 | 565 | 569.921477784468 | -4.92147778446847 |
| 6 | 547 | 558.79183774985 | -11.7918377498499 |
| 7 | 555 | 557.636372999469 | -2.63637299946930 |
| 8 | 562 | 570.338433337187 | -8.33843333718706 |
| 9 | 561 | 577.508466201906 | -16.508466201906 |
| 10 | 555 | 555.463167089655 | -0.463167089655524 |
| 11 | 544 | 557.767457322074 | -13.7674573220736 |
| 12 | 537 | 555.954039910277 | -18.9540399102772 |
| 13 | 543 | 529.822666212736 | 13.1773337872642 |
| 14 | 594 | 573.631389569606 | 20.3686104303935 |
| 15 | 611 | 606.705921833945 | 4.29407816605457 |
| 16 | 613 | 596.241804834801 | 16.7581951651985 |
| 17 | 611 | 601.338326927387 | 9.66167307261248 |
| 18 | 594 | 593.680605161379 | 0.319394838620695 |
| 19 | 595 | 589.742356395491 | 5.25764360450893 |
| 20 | 591 | 604.690765073956 | -13.6907650739560 |
| 21 | 589 | 600.054226257468 | -11.0542262574675 |
| 22 | 584 | 589.903022497365 | -5.90302249736505 |
| 23 | 573 | 583.357177395735 | -10.3571773957347 |
| 24 | 567 | 582.27414569577 | -15.2741456957694 |
| 25 | 569 | 551.685005536472 | 17.3149944635276 |
| 26 | 621 | 605.266223423887 | 15.7337765761125 |
| 27 | 629 | 631.042413014094 | -2.04241301409448 |
| 28 | 628 | 611.880054076349 | 16.1199459236511 |
| 29 | 612 | 621.111106581668 | -9.11110658166762 |
| 30 | 595 | 584.965671460599 | 10.0343285394013 |
| 31 | 597 | 590.421450647247 | 6.57854935275301 |
| 32 | 593 | 598.939374549215 | -5.93937454921535 |
| 33 | 590 | 597.775298408217 | -7.77529840821684 |
| 34 | 580 | 573.749814094319 | 6.25018590568094 |
| 35 | 574 | 582.319738026282 | -8.31973802628186 |
| 36 | 573 | 564.290415295699 | 8.709584704301 |
| 37 | 573 | 555.720219293318 | 17.2797807066821 |
| 38 | 620 | 603.360969392503 | 16.6390306074967 |
| 39 | 626 | 621.185900252077 | 4.81409974792284 |
| 40 | 620 | 604.597264567244 | 15.4027354327560 |
| 41 | 588 | 597.346296806551 | -9.34629680655128 |
| 42 | 566 | 558.032541469579 | 7.9674585304215 |
| 43 | 557 | 564.621108509276 | -7.62110850927655 |
| 44 | 561 | 552.840678043328 | 8.15932195667174 |
| 45 | 549 | 566.29200052395 | -17.2920005239500 |
| 46 | 532 | 533.803601007945 | -1.80360100794540 |
| 47 | 526 | 535.248943695753 | -9.24894369575297 |
| 48 | 511 | 520.413466041783 | -9.41346604178298 |
| 49 | 499 | 499.578738935411 | -0.578738935411133 |
| 50 | 555 | 529.190180790318 | 25.8098192096819 |
| 51 | 565 | 557.791719273468 | 7.20828072653168 |
| 52 | 542 | 558.96287361275 | -16.9628736127505 |
| 53 | 527 | 524.637967468772 | 2.36203253122816 |
| 54 | 510 | 502.165502616491 | 7.83449738350896 |
| 55 | 514 | 518.149564388598 | -4.14956438859846 |
| 56 | 517 | 514.990492836027 | 2.00950716397332 |
| 57 | 508 | 513.28952440955 | -5.28952440954997 |
| 58 | 493 | 511.961749930953 | -18.9617499309533 |
| 59 | 490 | 480.857269032648 | 9.14273096735224 |
| 60 | 469 | 490.234481895381 | -21.2344818953809 |
| 61 | 478 | 464.585491827717 | 13.4145081722828 |
| 62 | 528 | 505.422142323146 | 22.5778576768537 |
| 63 | 534 | 540.938965297302 | -6.93896529730173 |
| 64 | 518 | 528.167220262763 | -10.1672202627633 |
| 65 | 506 | 507.955260979404 | -1.95526097940416 |
| 66 | 502 | 507.101848283329 | -5.10184828332873 |
| 67 | 516 | 521.977080054333 | -5.97708005433252 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.543857726186619 | 0.912284547626762 | 0.456142273813381 |
| 12 | 0.555126598611576 | 0.889746802776849 | 0.444873401388424 |
| 13 | 0.798717393139307 | 0.402565213721385 | 0.201282606860692 |
| 14 | 0.818806420866328 | 0.362387158267343 | 0.181193579133671 |
| 15 | 0.759677384496011 | 0.480645231007978 | 0.240322615503989 |
| 16 | 0.763887937742368 | 0.472224124515264 | 0.236112062257632 |
| 17 | 0.682954393581388 | 0.634091212837224 | 0.317045606418612 |
| 18 | 0.60927822859636 | 0.78144354280728 | 0.39072177140364 |
| 19 | 0.53282007057327 | 0.93435985885346 | 0.46717992942673 |
| 20 | 0.530820720544797 | 0.938358558910405 | 0.469179279455203 |
| 21 | 0.52637169993283 | 0.94725660013434 | 0.47362830006717 |
| 22 | 0.481314117698492 | 0.962628235396984 | 0.518685882301508 |
| 23 | 0.554481823478491 | 0.891036353043018 | 0.445518176521509 |
| 24 | 0.765554206213763 | 0.468891587572474 | 0.234445793786237 |
| 25 | 0.730820691597873 | 0.538358616804255 | 0.269179308402127 |
| 26 | 0.66679962654676 | 0.66640074690648 | 0.33320037345324 |
| 27 | 0.63873006082824 | 0.722539878343521 | 0.361269939171761 |
| 28 | 0.580959336364687 | 0.838081327270626 | 0.419040663635313 |
| 29 | 0.650513529748457 | 0.698972940503087 | 0.349486470251543 |
| 30 | 0.580035120614413 | 0.839929758771173 | 0.419964879385587 |
| 31 | 0.508824074838579 | 0.982351850322843 | 0.491175925161421 |
| 32 | 0.477281916367058 | 0.954563832734116 | 0.522718083632942 |
| 33 | 0.497450643754483 | 0.994901287508965 | 0.502549356245517 |
| 34 | 0.422552081035271 | 0.845104162070542 | 0.577447918964729 |
| 35 | 0.577260176347932 | 0.845479647304137 | 0.422739823652068 |
| 36 | 0.499859741198009 | 0.999719482396018 | 0.500140258801991 |
| 37 | 0.449802954126582 | 0.899605908253163 | 0.550197045873418 |
| 38 | 0.372507021680055 | 0.74501404336011 | 0.627492978319945 |
| 39 | 0.306004798622369 | 0.612009597244738 | 0.693995201377631 |
| 40 | 0.420063745427429 | 0.840127490854858 | 0.579936254572571 |
| 41 | 0.417519359062853 | 0.835038718125706 | 0.582480640937147 |
| 42 | 0.438400302193004 | 0.876800604386007 | 0.561599697806996 |
| 43 | 0.392783843041273 | 0.785567686082546 | 0.607216156958727 |
| 44 | 0.490610396505209 | 0.981220793010418 | 0.509389603494791 |
| 45 | 0.544874872666805 | 0.91025025466639 | 0.455125127333195 |
| 46 | 0.539987236205005 | 0.92002552758999 | 0.460012763794995 |
| 47 | 0.54538257224731 | 0.90923485550538 | 0.45461742775269 |
| 48 | 0.56008110519405 | 0.8798377896119 | 0.43991889480595 |
| 49 | 0.467955589667521 | 0.935911179335042 | 0.532044410332479 |
| 50 | 0.455620547611068 | 0.911241095222136 | 0.544379452388932 |
| 51 | 0.365429117466023 | 0.730858234932045 | 0.634570882533977 |
| 52 | 0.351879722674795 | 0.70375944534959 | 0.648120277325205 |
| 53 | 0.253192084706822 | 0.506384169413645 | 0.746807915293177 |
| 54 | 0.231227457516012 | 0.462454915032024 | 0.768772542483988 |
| 55 | 0.191806753299484 | 0.383613506598969 | 0.808193246700516 |
| 56 | 0.132570136502891 | 0.265140273005782 | 0.86742986349711 |
| 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 |
