| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 239.710507892753 -1.50323568329146X[t] + 0.913782838019183`Yt-1`[t] -0.311051463965936`Yt-4`[t] + 0.253189547911919`Yt-5`[t] -0.0368144501848631t + 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) | 239.710507892753 | 32.721781 | 7.3257 | 0 | 0 |
| X | -1.50323568329146 | 0.187441 | -8.0198 | 0 | 0 |
| `Yt-1` | 0.913782838019183 | 0.052815 | 17.3017 | 0 | 0 |
| `Yt-4` | -0.311051463965936 | 0.086816 | -3.5829 | 0.000675 | 0.000338 |
| `Yt-5` | 0.253189547911919 | 0.082149 | 3.0821 | 0.003084 | 0.001542 |
| t | -0.0368144501848631 | 0.096896 | -0.3799 | 0.705311 | 0.352655 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.955223117147497 |
| R-squared | 0.912451203532981 |
| Adjusted R-squared | 0.905275072675029 |
| F-TEST (value) | 127.15085909029 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 61 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12.4354714485818 |
| Sum Squared Residuals | 9433.09795905813 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 507 | 510.98253488212 | -3.98253488211976 |
| 2 | 569 | 543.804728796271 | 25.1952712037293 |
| 3 | 580 | 595.203085723629 | -15.2030857236291 |
| 4 | 578 | 577.538714557971 | 0.461285442029296 |
| 5 | 565 | 568.926361466403 | -3.92636146640275 |
| 6 | 547 | 558.93670409467 | -11.9367040946702 |
| 7 | 555 | 557.283485088649 | -2.28348508864914 |
| 8 | 562 | 570.669945527505 | -8.66994552750537 |
| 9 | 561 | 577.710753080934 | -16.7107530809343 |
| 10 | 555 | 555.466817793586 | -0.466817793586271 |
| 11 | 544 | 557.633192437401 | -13.6331924374006 |
| 12 | 537 | 555.660719162641 | -18.6607191626415 |
| 13 | 543 | 530.265503579591 | 12.7344964204087 |
| 14 | 594 | 573.4021617924 | 20.5978382075997 |
| 15 | 611 | 607.740285474408 | 3.25971452559218 |
| 16 | 613 | 596.624077170337 | 16.3759228296627 |
| 17 | 611 | 600.48848837352 | 10.5115116264807 |
| 18 | 594 | 593.90032924557 | 0.0996707544298384 |
| 19 | 595 | 589.411440676717 | 5.58855932328347 |
| 20 | 591 | 604.493178234162 | -13.4931782341618 |
| 21 | 589 | 599.975508067377 | -10.9755080673770 |
| 22 | 584 | 589.664149719786 | -5.66414971978602 |
| 23 | 573 | 583.29929509929 | -10.2992950992905 |
| 24 | 567 | 581.77347254614 | -14.7734725461401 |
| 25 | 569 | 552.112182008119 | 16.8878179918807 |
| 26 | 621 | 604.558589006597 | 16.4414109934032 |
| 27 | 629 | 631.946212384762 | -2.94621238476152 |
| 28 | 628 | 611.994259937894 | 16.0057400621059 |
| 29 | 612 | 619.876042922314 | -7.87604292231431 |
| 30 | 595 | 585.191022551872 | 9.8089774481275 |
| 31 | 597 | 590.068376576448 | 6.9316234235517 |
| 32 | 593 | 599.156373404425 | -6.15637340442491 |
| 33 | 590 | 597.632560816111 | -7.63256081611087 |
| 34 | 580 | 573.843351859985 | 6.15664814001493 |
| 35 | 574 | 581.990271899887 | -7.99027189988747 |
| 36 | 573 | 564.391577086994 | 8.60842291300633 |
| 37 | 573 | 556.29616828757 | 16.7038317124301 |
| 38 | 620 | 602.504781785419 | 17.4952182145808 |
| 39 | 626 | 622.051315209111 | 3.94868479088863 |
| 40 | 620 | 604.792841692468 | 15.2071583075318 |
| 41 | 588 | 596.464640004661 | -8.4646400046608 |
| 42 | 566 | 557.979004391312 | 8.02099560868765 |
| 43 | 557 | 564.257836420647 | -7.25783642064696 |
| 44 | 561 | 553.369479766391 | 7.63052023360927 |
| 45 | 549 | 566.474571206025 | -17.4745712060251 |
| 46 | 532 | 533.919747649244 | -1.91974764924447 |
| 47 | 526 | 534.669011252166 | -8.66901125216623 |
| 48 | 511 | 520.816233800263 | -9.81623380026258 |
| 49 | 499 | 499.942490641026 | -0.942490641026338 |
| 50 | 555 | 528.319803824388 | 26.6801961756118 |
| 51 | 565 | 559.42905727806 | 5.5709427219395 |
| 52 | 542 | 559.199849708766 | -17.1998497087659 |
| 53 | 527 | 523.198771068467 | 3.8012289315332 |
| 54 | 510 | 502.677502208911 | 7.32249779108894 |
| 55 | 514 | 518.167514143585 | -4.16751414358458 |
| 56 | 517 | 515.387288384594 | 1.61271161540645 |
| 57 | 508 | 513.777439871069 | -5.77743987106908 |
| 58 | 493 | 511.516318597328 | -18.5163185973281 |
| 59 | 490 | 480.950065781803 | 9.04993421819686 |
| 60 | 469 | 490.578039220301 | -21.5780392203006 |
| 61 | 478 | 464.68881434476 | 13.3111856552399 |
| 62 | 528 | 505.17750156253 | 22.8224984374703 |
| 63 | 534 | 542.252844590015 | -8.25284459001547 |
| 64 | 518 | 527.91623265154 | -9.9162326515398 |
| 65 | 506 | 506.796008362825 | -0.796008362824866 |
| 66 | 502 | 507.022674226971 | -5.02267422697108 |
| 67 | 516 | 521.790399021296 | -5.79039902129627 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.712108896972123 | 0.575782206055753 | 0.287891103027877 |
| 10 | 0.561425591631916 | 0.877148816736167 | 0.438574408368084 |
| 11 | 0.590602473296887 | 0.818795053406226 | 0.409397526703113 |
| 12 | 0.601095590905031 | 0.797808818189939 | 0.398904409094969 |
| 13 | 0.666369338388266 | 0.667261323223467 | 0.333630661611734 |
| 14 | 0.739050636915397 | 0.521898726169207 | 0.260949363084603 |
| 15 | 0.656772457859618 | 0.686455084280764 | 0.343227542140382 |
| 16 | 0.690323503057309 | 0.619352993885382 | 0.309676496942691 |
| 17 | 0.615209534369939 | 0.769580931260122 | 0.384790465630061 |
| 18 | 0.539564108553364 | 0.920871782893273 | 0.460435891446636 |
| 19 | 0.488022743577816 | 0.976045487155632 | 0.511977256422184 |
| 20 | 0.490096607561469 | 0.980193215122938 | 0.509903392438531 |
| 21 | 0.474551951160005 | 0.94910390232001 | 0.525448048839995 |
| 22 | 0.438970063053194 | 0.877940126106389 | 0.561029936946806 |
| 23 | 0.520611350603148 | 0.958777298793705 | 0.479388649396852 |
| 24 | 0.733693551435243 | 0.532612897129515 | 0.266306448564757 |
| 25 | 0.691739273074455 | 0.61652145385109 | 0.308260726925545 |
| 26 | 0.631746815789238 | 0.736506368421524 | 0.368253184210762 |
| 27 | 0.618250031472568 | 0.763499937054863 | 0.381749968527432 |
| 28 | 0.573159786577676 | 0.853680426844648 | 0.426840213422324 |
| 29 | 0.664957378660158 | 0.670085242679685 | 0.335042621339842 |
| 30 | 0.603382589971294 | 0.793234820057413 | 0.396617410028706 |
| 31 | 0.533533362882448 | 0.932933274235104 | 0.466466637117552 |
| 32 | 0.507259334688283 | 0.985481330623433 | 0.492740665311717 |
| 33 | 0.522846499212314 | 0.954307001575372 | 0.477153500787686 |
| 34 | 0.455052324761254 | 0.910104649522507 | 0.544947675238746 |
| 35 | 0.609404229056974 | 0.781191541886052 | 0.390595770943026 |
| 36 | 0.536946672106336 | 0.926106655787328 | 0.463053327893664 |
| 37 | 0.487543997463489 | 0.975087994926977 | 0.512456002536511 |
| 38 | 0.414657338878849 | 0.829314677757699 | 0.585342661121151 |
| 39 | 0.35590251720789 | 0.71180503441578 | 0.64409748279211 |
| 40 | 0.438786850798575 | 0.87757370159715 | 0.561213149201425 |
| 41 | 0.475733160609389 | 0.951466321218777 | 0.524266839390611 |
| 42 | 0.474127301456535 | 0.94825460291307 | 0.525872698543465 |
| 43 | 0.440848425928476 | 0.881696851856953 | 0.559151574071524 |
| 44 | 0.544885638940199 | 0.910228722119602 | 0.455114361059801 |
| 45 | 0.590890964185492 | 0.818218071629017 | 0.409109035814508 |
| 46 | 0.594264481990312 | 0.811471036019375 | 0.405735518009688 |
| 47 | 0.587583960036525 | 0.82483207992695 | 0.412416039963475 |
| 48 | 0.597990766522693 | 0.804018466954615 | 0.402009233477307 |
| 49 | 0.520797916219647 | 0.958404167560707 | 0.479202083780354 |
| 50 | 0.504283636689072 | 0.991432726621856 | 0.495716363310928 |
| 51 | 0.471116535816456 | 0.942233071632911 | 0.528883464183544 |
| 52 | 0.460188054665737 | 0.920376109331475 | 0.539811945334263 |
| 53 | 0.381525892599445 | 0.76305178519889 | 0.618474107400555 |
| 54 | 0.379351644449645 | 0.758703288899289 | 0.620648355550355 |
| 55 | 0.293481755092537 | 0.586963510185075 | 0.706518244907463 |
| 56 | 0.304691926314094 | 0.609383852628189 | 0.695308073685906 |
| 57 | 0.392469866129472 | 0.784939732258944 | 0.607530133870528 |
| 58 | 0.273537991619287 | 0.547075983238575 | 0.726462008380713 |
| 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 |
