| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 569.211538461539 -41.4337606837607X[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) | 569.211538461539 | 4.992182 | 114.0206 | 0 | 0 |
| X | -41.4337606837607 | 9.844716 | -4.2087 | 7.7e-05 | 3.9e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.454597189459123 |
| R-squared | 0.206658604664134 |
| Adjusted R-squared | 0.194991819438606 |
| F-TEST (value) | 17.7134146784459 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 68 |
| p-value | 7.70627714348215e-05 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 35.9991389169965 |
| Sum Squared Residuals | 88123.7841880342 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 555 | 569.211538461537 | -14.2115384615372 |
| 2 | 562 | 569.211538461538 | -7.21153846153839 |
| 3 | 561 | 569.211538461538 | -8.21153846153849 |
| 4 | 555 | 569.211538461538 | -14.2115384615385 |
| 5 | 544 | 569.211538461538 | -25.2115384615385 |
| 6 | 537 | 569.211538461538 | -32.2115384615385 |
| 7 | 543 | 569.211538461538 | -26.2115384615385 |
| 8 | 594 | 569.211538461538 | 24.7884615384615 |
| 9 | 611 | 569.211538461538 | 41.7884615384615 |
| 10 | 613 | 569.211538461538 | 43.7884615384615 |
| 11 | 611 | 569.211538461538 | 41.7884615384615 |
| 12 | 594 | 569.211538461538 | 24.7884615384615 |
| 13 | 595 | 569.211538461538 | 25.7884615384615 |
| 14 | 591 | 569.211538461538 | 21.7884615384615 |
| 15 | 589 | 569.211538461538 | 19.7884615384615 |
| 16 | 584 | 569.211538461538 | 14.7884615384615 |
| 17 | 573 | 569.211538461538 | 3.78846153846151 |
| 18 | 567 | 569.211538461538 | -2.21153846153849 |
| 19 | 569 | 569.211538461538 | -0.211538461538488 |
| 20 | 621 | 569.211538461538 | 51.7884615384615 |
| 21 | 629 | 569.211538461538 | 59.7884615384615 |
| 22 | 628 | 569.211538461538 | 58.7884615384615 |
| 23 | 612 | 569.211538461538 | 42.7884615384615 |
| 24 | 595 | 569.211538461538 | 25.7884615384615 |
| 25 | 597 | 569.211538461538 | 27.7884615384615 |
| 26 | 593 | 569.211538461538 | 23.7884615384615 |
| 27 | 590 | 569.211538461538 | 20.7884615384615 |
| 28 | 580 | 569.211538461538 | 10.7884615384615 |
| 29 | 574 | 569.211538461538 | 4.78846153846151 |
| 30 | 573 | 569.211538461538 | 3.78846153846151 |
| 31 | 573 | 569.211538461538 | 3.78846153846151 |
| 32 | 620 | 569.211538461538 | 50.7884615384615 |
| 33 | 626 | 569.211538461538 | 56.7884615384615 |
| 34 | 620 | 569.211538461538 | 50.7884615384615 |
| 35 | 588 | 569.211538461538 | 18.7884615384615 |
| 36 | 566 | 569.211538461538 | -3.21153846153849 |
| 37 | 557 | 569.211538461538 | -12.2115384615385 |
| 38 | 561 | 569.211538461538 | -8.21153846153849 |
| 39 | 549 | 569.211538461538 | -20.2115384615385 |
| 40 | 532 | 569.211538461538 | -37.2115384615385 |
| 41 | 526 | 569.211538461538 | -43.2115384615385 |
| 42 | 511 | 569.211538461538 | -58.2115384615385 |
| 43 | 499 | 569.211538461538 | -70.2115384615385 |
| 44 | 555 | 569.211538461538 | -14.2115384615385 |
| 45 | 565 | 569.211538461538 | -4.21153846153849 |
| 46 | 542 | 569.211538461538 | -27.2115384615385 |
| 47 | 527 | 569.211538461538 | -42.2115384615385 |
| 48 | 510 | 569.211538461538 | -59.2115384615385 |
| 49 | 514 | 569.211538461538 | -55.2115384615385 |
| 50 | 517 | 569.211538461538 | -52.2115384615385 |
| 51 | 508 | 569.211538461538 | -61.2115384615385 |
| 52 | 493 | 569.211538461538 | -76.2115384615385 |
| 53 | 490 | 527.777777777778 | -37.7777777777778 |
| 54 | 469 | 527.777777777778 | -58.7777777777778 |
| 55 | 478 | 527.777777777778 | -49.7777777777778 |
| 56 | 528 | 527.777777777778 | 0.222222222222217 |
| 57 | 534 | 527.777777777778 | 6.22222222222222 |
| 58 | 518 | 527.777777777778 | -9.77777777777778 |
| 59 | 506 | 527.777777777778 | -21.7777777777778 |
| 60 | 502 | 527.777777777778 | -25.7777777777778 |
| 61 | 516 | 527.777777777778 | -11.7777777777778 |
| 62 | 528 | 527.777777777778 | 0.222222222222217 |
| 63 | 533 | 527.777777777778 | 5.22222222222222 |
| 64 | 536 | 527.777777777778 | 8.22222222222222 |
| 65 | 537 | 527.777777777778 | 9.22222222222222 |
| 66 | 524 | 527.777777777778 | -3.77777777777778 |
| 67 | 536 | 527.777777777778 | 8.22222222222222 |
| 68 | 587 | 527.777777777778 | 59.2222222222222 |
| 69 | 597 | 527.777777777778 | 69.2222222222222 |
| 70 | 581 | 527.777777777778 | 53.2222222222222 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0147486041367335 | 0.0294972082734670 | 0.985251395863266 |
| 6 | 0.0141690604894559 | 0.0283381209789117 | 0.985830939510544 |
| 7 | 0.00501776261053816 | 0.0100355252210763 | 0.994982237389462 |
| 8 | 0.0460381383695722 | 0.0920762767391444 | 0.953961861630428 |
| 9 | 0.163315300309978 | 0.326630600619956 | 0.836684699690022 |
| 10 | 0.258073857391292 | 0.516147714782585 | 0.741926142608708 |
| 11 | 0.300850214313933 | 0.601700428627866 | 0.699149785686067 |
| 12 | 0.248006787274869 | 0.496013574549738 | 0.751993212725131 |
| 13 | 0.201912270025968 | 0.403824540051937 | 0.798087729974032 |
| 14 | 0.153146120328596 | 0.306292240657192 | 0.846853879671404 |
| 15 | 0.110889394693894 | 0.221778789387788 | 0.889110605306106 |
| 16 | 0.0749015602041112 | 0.149803120408222 | 0.925098439795889 |
| 17 | 0.0478498260605723 | 0.0956996521211447 | 0.952150173939428 |
| 18 | 0.0305385315496295 | 0.0610770630992591 | 0.96946146845037 |
| 19 | 0.0185856974214338 | 0.0371713948428677 | 0.981414302578566 |
| 20 | 0.0324116074519563 | 0.0648232149039126 | 0.967588392548044 |
| 21 | 0.0661886549785211 | 0.132377309957042 | 0.933811345021479 |
| 22 | 0.110710532054162 | 0.221421064108325 | 0.889289467945838 |
| 23 | 0.116507512054175 | 0.233015024108350 | 0.883492487945825 |
| 24 | 0.0949055517137583 | 0.189811103427517 | 0.905094448286242 |
| 25 | 0.0795241213472794 | 0.159048242694559 | 0.92047587865272 |
| 26 | 0.0640536775595692 | 0.128107355119138 | 0.93594632244043 |
| 27 | 0.050341389607052 | 0.100682779214104 | 0.949658610392948 |
| 28 | 0.0372224469156677 | 0.0744448938313354 | 0.962777553084332 |
| 29 | 0.0272541024801680 | 0.0545082049603359 | 0.972745897519832 |
| 30 | 0.0198045479372334 | 0.0396090958744669 | 0.980195452062767 |
| 31 | 0.0142738059090299 | 0.0285476118180598 | 0.98572619409097 |
| 32 | 0.0291131062493444 | 0.0582262124986887 | 0.970886893750656 |
| 33 | 0.080854788189021 | 0.161709576378042 | 0.91914521181098 |
| 34 | 0.184878677890877 | 0.369757355781753 | 0.815121322109123 |
| 35 | 0.212890286095576 | 0.425780572191152 | 0.787109713904424 |
| 36 | 0.214874747133914 | 0.429749494267829 | 0.785125252866086 |
| 37 | 0.219599924815442 | 0.439199849630884 | 0.780400075184558 |
| 38 | 0.227625147643424 | 0.455250295286848 | 0.772374852356576 |
| 39 | 0.240274266282091 | 0.480548532564182 | 0.759725733717909 |
| 40 | 0.278451111616761 | 0.556902223233521 | 0.72154888838324 |
| 41 | 0.322874663701468 | 0.645749327402937 | 0.677125336298532 |
| 42 | 0.414174479130677 | 0.828348958261353 | 0.585825520869323 |
| 43 | 0.550080591320278 | 0.899838817359445 | 0.449919408679722 |
| 44 | 0.534398057690549 | 0.931203884618902 | 0.465601942309451 |
| 45 | 0.565400071289678 | 0.869199857420644 | 0.434599928710322 |
| 46 | 0.560932834419994 | 0.878134331160012 | 0.439067165580006 |
| 47 | 0.555875363686228 | 0.888249272627543 | 0.444124636313772 |
| 48 | 0.568604032761834 | 0.862791934476331 | 0.431395967238166 |
| 49 | 0.562015134642845 | 0.87596973071431 | 0.437984865357155 |
| 50 | 0.547156430104993 | 0.905687139790013 | 0.452843569895007 |
| 51 | 0.538546653244873 | 0.922906693510254 | 0.461453346755127 |
| 52 | 0.544967482950957 | 0.910065034098086 | 0.455032517049043 |
| 53 | 0.534985057305791 | 0.930029885388418 | 0.465014942694209 |
| 54 | 0.664037927564132 | 0.671924144871736 | 0.335962072435868 |
| 55 | 0.773002144401241 | 0.453995711197519 | 0.226997855598759 |
| 56 | 0.720484892143126 | 0.559030215713748 | 0.279515107856874 |
| 57 | 0.650577457379548 | 0.698845085240903 | 0.349422542620452 |
| 58 | 0.589489008667258 | 0.821021982665483 | 0.410510991332742 |
| 59 | 0.581903254227667 | 0.836193491544666 | 0.418096745772333 |
| 60 | 0.628292236339869 | 0.743415527320261 | 0.371707763660131 |
| 61 | 0.617155336361437 | 0.765689327277125 | 0.382844663638563 |
| 62 | 0.557764408579505 | 0.884471182840991 | 0.442235591420495 |
| 63 | 0.48035025133726 | 0.96070050267452 | 0.51964974866274 |
| 64 | 0.394119843283193 | 0.788239686566386 | 0.605880156716807 |
| 65 | 0.312625123032388 | 0.625250246064777 | 0.687374876967612 |
| 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 | 6 | 0.098360655737705 | NOK |
| 10% type I error level | 13 | 0.213114754098361 | NOK |
