| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 467.571130434783 + 49.8834782608694` `[t] + 26.9059130434780M1[t] + 46.7478260869565M2[t] + 36.2130434782609M3[t] -17.5217391304347M4[t] -22.2565217391304M5[t] -13.5913043478261M6[t] -11.1260869565217M7[t] -4.86086956521739M8[t] -3.19565217391303M9[t] -7.93043478260867M10[t] -12.8652173913043M11[t] + 2.53478260869565t + 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) | 467.571130434783 | 14.050575 | 33.2777 | 0 | 0 |
| ` ` | 49.8834782608694 | 9.939399 | 5.0188 | 8e-06 | 4e-06 |
| M1 | 26.9059130434780 | 13.880686 | 1.9384 | 0.058729 | 0.029364 |
| M2 | 46.7478260869565 | 13.966667 | 3.3471 | 0.001635 | 0.000817 |
| M3 | 36.2130434782609 | 13.927725 | 2.6001 | 0.012489 | 0.006245 |
| M4 | -17.5217391304347 | 13.89279 | -1.2612 | 0.213592 | 0.106796 |
| M5 | -22.2565217391304 | 13.861892 | -1.6056 | 0.115208 | 0.057604 |
| M6 | -13.5913043478261 | 13.835058 | -0.9824 | 0.331051 | 0.165525 |
| M7 | -11.1260869565217 | 13.812311 | -0.8055 | 0.424664 | 0.212332 |
| M8 | -4.86086956521739 | 13.793673 | -0.3524 | 0.726149 | 0.363074 |
| M9 | -3.19565217391303 | 13.779158 | -0.2319 | 0.817629 | 0.408815 |
| M10 | -7.93043478260867 | 13.768782 | -0.576 | 0.567441 | 0.283721 |
| M11 | -12.8652173913043 | 13.762552 | -0.9348 | 0.354774 | 0.177387 |
| t | 2.53478260869565 | 0.239105 | 10.6011 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.888041241395152 |
| R-squared | 0.788617246418643 |
| Adjusted R-squared | 0.728878642145651 |
| F-TEST (value) | 13.2011327686003 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 1.89785964721523e-11 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21.7572209945670 |
| Sum Squared Residuals | 21775.3266086956 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 581 | 546.895304347827 | 34.104695652173 |
| 2 | 597 | 569.272 | 27.7279999999999 |
| 3 | 587 | 561.272 | 25.7280000000001 |
| 4 | 536 | 510.072 | 25.9280000000001 |
| 5 | 524 | 507.872 | 16.1280000000000 |
| 6 | 537 | 519.072 | 17.9280000000001 |
| 7 | 536 | 524.072 | 11.9280000000001 |
| 8 | 533 | 532.872 | 0.12800000000008 |
| 9 | 528 | 537.072 | -9.07199999999994 |
| 10 | 516 | 534.872 | -18.8719999999999 |
| 11 | 502 | 532.472 | -30.4720000000000 |
| 12 | 506 | 547.872 | -41.8719999999999 |
| 13 | 518 | 577.312695652174 | -59.3126956521736 |
| 14 | 534 | 549.805913043478 | -15.8059130434781 |
| 15 | 528 | 541.805913043478 | -13.8059130434783 |
| 16 | 478 | 490.605913043478 | -12.6059130434783 |
| 17 | 469 | 488.405913043478 | -19.4059130434783 |
| 18 | 490 | 499.605913043478 | -9.60591304347826 |
| 19 | 493 | 504.605913043478 | -11.6059130434783 |
| 20 | 508 | 513.405913043478 | -5.40591304347827 |
| 21 | 517 | 517.605913043478 | -0.605913043478274 |
| 22 | 514 | 515.405913043478 | -1.40591304347828 |
| 23 | 510 | 513.005913043478 | -3.00591304347828 |
| 24 | 527 | 528.405913043478 | -1.40591304347825 |
| 25 | 542 | 557.846608695652 | -15.8466086956520 |
| 26 | 565 | 580.223304347826 | -15.2233043478261 |
| 27 | 555 | 572.223304347826 | -17.2233043478261 |
| 28 | 499 | 521.023304347826 | -22.0233043478261 |
| 29 | 511 | 518.823304347826 | -7.8233043478261 |
| 30 | 526 | 530.023304347826 | -4.02330434782611 |
| 31 | 532 | 535.023304347826 | -3.02330434782609 |
| 32 | 549 | 543.823304347826 | 5.17669565217392 |
| 33 | 561 | 548.023304347826 | 12.9766956521739 |
| 34 | 557 | 545.823304347826 | 11.1766956521739 |
| 35 | 566 | 543.423304347826 | 22.5766956521739 |
| 36 | 588 | 558.823304347826 | 29.1766956521739 |
| 37 | 620 | 588.264 | 31.7360000000002 |
| 38 | 626 | 610.640695652174 | 15.3593043478261 |
| 39 | 620 | 602.640695652174 | 17.3593043478261 |
| 40 | 573 | 551.440695652174 | 21.5593043478260 |
| 41 | 573 | 549.240695652174 | 23.7593043478261 |
| 42 | 574 | 560.440695652174 | 13.5593043478261 |
| 43 | 580 | 565.440695652174 | 14.5593043478261 |
| 44 | 590 | 574.240695652174 | 15.7593043478261 |
| 45 | 593 | 578.440695652174 | 14.5593043478261 |
| 46 | 597 | 576.240695652174 | 20.7593043478261 |
| 47 | 595 | 573.840695652174 | 21.1593043478261 |
| 48 | 612 | 589.240695652174 | 22.7593043478261 |
| 49 | 628 | 618.681391304348 | 9.31860869565238 |
| 50 | 629 | 641.058086956522 | -12.0580869565217 |
| 51 | 621 | 633.058086956522 | -12.0580869565218 |
| 52 | 569 | 581.858086956522 | -12.8580869565218 |
| 53 | 567 | 579.658086956522 | -12.6580869565218 |
| 54 | 573 | 590.858086956522 | -17.8580869565218 |
| 55 | 584 | 595.858086956522 | -11.8580869565218 |
| 56 | 589 | 604.658086956522 | -15.6580869565218 |
| 57 | 591 | 608.858086956522 | -17.8580869565218 |
| 58 | 595 | 606.658086956522 | -11.6580869565218 |
| 59 | 594 | 604.258086956522 | -10.2580869565218 |
| 60 | 611 | 619.658086956522 | -8.65808695652178 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00331008180403206 | 0.00662016360806412 | 0.996689918195968 |
| 18 | 0.00633017131285227 | 0.0126603426257045 | 0.993669828687148 |
| 19 | 0.00701112779350704 | 0.0140222555870141 | 0.992988872206493 |
| 20 | 0.0482407733238209 | 0.0964815466476417 | 0.95175922667618 |
| 21 | 0.167792583927958 | 0.335585167855916 | 0.832207416072042 |
| 22 | 0.321869927099705 | 0.64373985419941 | 0.678130072900295 |
| 23 | 0.506300384414559 | 0.987399231170883 | 0.493699615585441 |
| 24 | 0.709696501695739 | 0.580606996608522 | 0.290303498304261 |
| 25 | 0.880741238367227 | 0.238517523265547 | 0.119258761632773 |
| 26 | 0.913926898734206 | 0.172146202531588 | 0.0860731012657942 |
| 27 | 0.928642971674956 | 0.142714056650089 | 0.0713570283250444 |
| 28 | 0.964858211860916 | 0.0702835762781683 | 0.0351417881390841 |
| 29 | 0.983527460906105 | 0.0329450781877901 | 0.0164725390938950 |
| 30 | 0.987220210590474 | 0.0255595788190516 | 0.0127797894095258 |
| 31 | 0.994756631848337 | 0.0104867363033254 | 0.00524336815166272 |
| 32 | 0.997434271003126 | 0.00513145799374894 | 0.00256572899687447 |
| 33 | 0.998081456416822 | 0.00383708716635532 | 0.00191854358317766 |
| 34 | 0.999795928103154 | 0.000408143793691373 | 0.000204071896845687 |
| 35 | 0.999984285615203 | 3.14287695941118e-05 | 1.57143847970559e-05 |
| 36 | 0.999999985293208 | 2.94135839225577e-08 | 1.47067919612788e-08 |
| 37 | 0.999999994954803 | 1.00903943443971e-08 | 5.04519717219855e-09 |
| 38 | 0.999999974904866 | 5.01902671981372e-08 | 2.50951335990686e-08 |
| 39 | 0.999999765794193 | 4.68411613329511e-07 | 2.34205806664756e-07 |
| 40 | 0.99999796887573 | 4.06224853845481e-06 | 2.03112426922741e-06 |
| 41 | 0.999995602505714 | 8.79498857197069e-06 | 4.39749428598535e-06 |
| 42 | 0.999931101833304 | 0.000137796333392322 | 6.88981666961608e-05 |
| 43 | 0.99998991272377 | 2.01745524593534e-05 | 1.00872762296767e-05 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 13 | 0.481481481481481 | NOK |
| 5% type I error level | 18 | 0.666666666666667 | NOK |
| 10% type I error level | 20 | 0.740740740740741 | NOK |
