| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 591.50371057514 -8.29035250463811X[t] -3.07157287157266M1[t] + 0.940806019377407M2[t] -1.71348175633892M3[t] -9.03443619872196M4[t] -12.6403318903319M5[t] -22.1279529993816M6[t] -18.2822407750979M7[t] + 33.8968047825191M8[t] + 44.4091836734694M9[t] + 35.4215625644197M10[t] + 14.3876211090497M11[t] -1.01237889095032t + 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) | 591.50371057514 | 15.026986 | 39.3628 | 0 | 0 |
| X | -8.29035250463811 | 12.233982 | -0.6776 | 0.500784 | 0.250392 |
| M1 | -3.07157287157266 | 17.448855 | -0.176 | 0.860903 | 0.430452 |
| M2 | 0.940806019377407 | 17.435715 | 0.054 | 0.95716 | 0.47858 |
| M3 | -1.71348175633892 | 17.426521 | -0.0983 | 0.922024 | 0.461012 |
| M4 | -9.03443619872196 | 17.42128 | -0.5186 | 0.606093 | 0.303046 |
| M5 | -12.6403318903319 | 17.514591 | -0.7217 | 0.47348 | 0.23674 |
| M6 | -22.1279529993816 | 17.494108 | -1.2649 | 0.211153 | 0.105576 |
| M7 | -18.2822407750979 | 17.477546 | -1.046 | 0.300036 | 0.150018 |
| M8 | 33.8968047825191 | 17.464916 | 1.9409 | 0.057316 | 0.028658 |
| M9 | 44.4091836734694 | 17.456226 | 2.544 | 0.013744 | 0.006872 |
| M10 | 35.4215625644197 | 17.451482 | 2.0297 | 0.047147 | 0.023574 |
| M11 | 14.3876211090497 | 18.194291 | 0.7908 | 0.432411 | 0.216205 |
| t | -1.01237889095032 | 0.262558 | -3.8558 | 3e-04 | 0.00015 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.763457076793766 |
| R-squared | 0.582866708106483 |
| Adjusted R-squared | 0.486032193916916 |
| F-TEST (value) | 6.01920413382199 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 56 |
| p-value | 7.92639047064725e-07 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 28.7647049822638 |
| Sum Squared Residuals | 46334.8621521335 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 555 | 587.419758812615 | -32.4197588126149 |
| 2 | 562 | 590.419758812616 | -28.419758812616 |
| 3 | 561 | 586.753092145949 | -25.7530921459494 |
| 4 | 555 | 578.419758812616 | -23.419758812616 |
| 5 | 544 | 573.801484230056 | -29.8014842300557 |
| 6 | 537 | 563.301484230056 | -26.3014842300557 |
| 7 | 543 | 566.134817563389 | -23.1348175633891 |
| 8 | 594 | 617.301484230056 | -23.3014842300557 |
| 9 | 611 | 626.801484230056 | -15.8014842300557 |
| 10 | 613 | 616.801484230056 | -3.80148423005572 |
| 11 | 611 | 594.755163883735 | 16.2448361162646 |
| 12 | 594 | 579.355163883735 | 14.6448361162646 |
| 13 | 595 | 575.271212121212 | 19.7287878787876 |
| 14 | 591 | 578.271212121212 | 12.7287878787879 |
| 15 | 589 | 574.604545454545 | 14.3954545454545 |
| 16 | 584 | 566.271212121212 | 17.7287878787878 |
| 17 | 573 | 561.652937538652 | 11.3470624613481 |
| 18 | 567 | 551.152937538652 | 15.8470624613481 |
| 19 | 569 | 553.986270871985 | 15.0137291280148 |
| 20 | 621 | 605.152937538652 | 15.8470624613481 |
| 21 | 629 | 614.652937538652 | 14.3470624613481 |
| 22 | 628 | 604.652937538652 | 23.3470624613482 |
| 23 | 612 | 582.606617192331 | 29.3933828076685 |
| 24 | 595 | 567.206617192331 | 27.7933828076685 |
| 25 | 597 | 563.122665429809 | 33.8773345701915 |
| 26 | 593 | 566.122665429808 | 26.8773345701917 |
| 27 | 590 | 562.455998763142 | 27.5440012368584 |
| 28 | 580 | 554.122665429808 | 25.8773345701917 |
| 29 | 574 | 549.504390847248 | 24.495609152752 |
| 30 | 573 | 539.004390847248 | 33.995609152752 |
| 31 | 573 | 541.837724180581 | 31.1622758194187 |
| 32 | 620 | 593.004390847248 | 26.995609152752 |
| 33 | 626 | 602.504390847248 | 23.495609152752 |
| 34 | 620 | 592.504390847248 | 27.495609152752 |
| 35 | 588 | 570.458070500928 | 17.5419294990724 |
| 36 | 566 | 555.058070500928 | 10.9419294990724 |
| 37 | 557 | 550.974118738405 | 6.02588126159534 |
| 38 | 561 | 553.974118738404 | 7.02588126159559 |
| 39 | 549 | 550.307452071738 | -1.30745207173775 |
| 40 | 532 | 541.974118738404 | -9.97411873840442 |
| 41 | 526 | 537.355844155844 | -11.3558441558441 |
| 42 | 511 | 526.855844155844 | -15.8558441558441 |
| 43 | 499 | 529.689177489177 | -30.6891774891774 |
| 44 | 555 | 580.855844155844 | -25.8558441558441 |
| 45 | 565 | 590.355844155844 | -25.3558441558441 |
| 46 | 542 | 580.355844155844 | -38.3558441558441 |
| 47 | 527 | 558.309523809524 | -31.3095238095238 |
| 48 | 510 | 542.909523809524 | -32.9095238095238 |
| 49 | 514 | 538.825572047001 | -24.8255720470008 |
| 50 | 517 | 541.825572047001 | -24.8255720470006 |
| 51 | 508 | 538.158905380334 | -30.1589053803339 |
| 52 | 493 | 529.825572047 | -36.8255720470005 |
| 53 | 490 | 516.916944959802 | -26.9169449598021 |
| 54 | 469 | 506.416944959802 | -37.4169449598021 |
| 55 | 478 | 509.250278293135 | -31.2502782931355 |
| 56 | 528 | 560.416944959802 | -32.4169449598021 |
| 57 | 534 | 569.916944959802 | -35.9169449598021 |
| 58 | 518 | 559.916944959802 | -41.9169449598021 |
| 59 | 506 | 537.870624613482 | -31.8706246134818 |
| 60 | 502 | 522.470624613482 | -20.4706246134818 |
| 61 | 516 | 518.386672850959 | -2.38667285095879 |
| 62 | 528 | 521.386672850959 | 6.61332714904145 |
| 63 | 533 | 517.720006184292 | 15.2799938157081 |
| 64 | 536 | 509.386672850959 | 26.6133271490415 |
| 65 | 537 | 504.768398268398 | 32.2316017316018 |
| 66 | 524 | 494.268398268398 | 29.7316017316018 |
| 67 | 536 | 497.101731601732 | 38.8982683982684 |
| 68 | 587 | 548.268398268398 | 38.7316017316018 |
| 69 | 597 | 557.768398268398 | 39.2316017316018 |
| 70 | 581 | 547.768398268398 | 33.2316017316018 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00411903984332895 | 0.0082380796866579 | 0.995880960156671 |
| 18 | 0.000482134583191116 | 0.000964269166382232 | 0.99951786541681 |
| 19 | 7.7669714250712e-05 | 0.000155339428501424 | 0.99992233028575 |
| 20 | 9.80996717100343e-06 | 1.96199343420069e-05 | 0.99999019003283 |
| 21 | 9.41010820462715e-06 | 1.88202164092543e-05 | 0.999990589891795 |
| 22 | 8.18733064884226e-06 | 1.63746612976845e-05 | 0.999991812669351 |
| 23 | 6.58260966644286e-05 | 0.000131652193328857 | 0.999934173903336 |
| 24 | 0.000100978748918412 | 0.000201957497836824 | 0.999899021251082 |
| 25 | 4.49679249799968e-05 | 8.99358499599937e-05 | 0.99995503207502 |
| 26 | 2.54917462437811e-05 | 5.09834924875622e-05 | 0.999974508253756 |
| 27 | 1.34306990079566e-05 | 2.68613980159132e-05 | 0.999986569300992 |
| 28 | 9.02518452776325e-06 | 1.80503690555265e-05 | 0.999990974815472 |
| 29 | 3.55065168030406e-06 | 7.10130336060813e-06 | 0.99999644934832 |
| 30 | 1.35337992499143e-06 | 2.70675984998287e-06 | 0.999998646620075 |
| 31 | 6.10635342241606e-07 | 1.22127068448321e-06 | 0.999999389364658 |
| 32 | 3.60935141565962e-07 | 7.21870283131924e-07 | 0.999999639064858 |
| 33 | 4.02388039935824e-07 | 8.04776079871649e-07 | 0.99999959761196 |
| 34 | 1.71833121303689e-06 | 3.43666242607379e-06 | 0.999998281668787 |
| 35 | 0.000145791678670359 | 0.000291583357340717 | 0.99985420832133 |
| 36 | 0.00360743579909755 | 0.00721487159819509 | 0.996392564200902 |
| 37 | 0.0261494816267839 | 0.0522989632535677 | 0.973850518373216 |
| 38 | 0.100417395847193 | 0.200834791694387 | 0.899582604152807 |
| 39 | 0.340756824639401 | 0.681513649278803 | 0.659243175360599 |
| 40 | 0.751196154346844 | 0.497607691306313 | 0.248803845653156 |
| 41 | 0.830815222309392 | 0.338369555381217 | 0.169184777690608 |
| 42 | 0.925729131390937 | 0.148541737218125 | 0.0742708686090625 |
| 43 | 0.947226368277213 | 0.105547263445574 | 0.0527736317227869 |
| 44 | 0.961023503433084 | 0.077952993133833 | 0.0389764965669165 |
| 45 | 0.978875856847086 | 0.0422482863058288 | 0.0211241431529144 |
| 46 | 0.991873572145554 | 0.0162528557088912 | 0.00812642785444561 |
| 47 | 0.997845498387438 | 0.00430900322512409 | 0.00215450161256204 |
| 48 | 0.999084970693295 | 0.00183005861341076 | 0.000915029306705382 |
| 49 | 0.99943369150073 | 0.00113261699853934 | 0.00056630849926967 |
| 50 | 0.999716131640888 | 0.000567736718224272 | 0.000283868359112136 |
| 51 | 0.99970223768906 | 0.000595524621878573 | 0.000297762310939286 |
| 52 | 0.998108773532647 | 0.00378245293470584 | 0.00189122646735292 |
| 53 | 0.998385811062537 | 0.00322837787492503 | 0.00161418893746252 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.72972972972973 | NOK |
| 5% type I error level | 29 | 0.783783783783784 | NOK |
| 10% type I error level | 31 | 0.837837837837838 | NOK |
