| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 690.68970616088 -1.2874820710457X[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) | 690.68970616088 | 55.123377 | 12.5299 | 0 | 0 |
| X | -1.2874820710457 | 0.525574 | -2.4497 | 0.016803 | 0.008402 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.280994807358491 |
| R-squared | 0.0789580817624354 |
| Adjusted R-squared | 0.0658003400733274 |
| F-TEST (value) | 6.00088401399433 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 70 |
| p-value | 0.016803462470376 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 39.5369962059785 |
| Sum Squared Residuals | 109422.184829409 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 519 | 565.288952441026 | -46.2889524410262 |
| 2 | 517 | 565.803945269447 | -48.8039452694473 |
| 3 | 510 | 554.989095872663 | -44.9890958726634 |
| 4 | 509 | 558.465297464487 | -49.4652974644868 |
| 5 | 501 | 564.387714991297 | -63.387714991297 |
| 6 | 507 | 556.147829736605 | -49.1478297366045 |
| 7 | 569 | 578.163773151486 | -9.16377315148601 |
| 8 | 580 | 574.945067973872 | 5.05493202612824 |
| 9 | 578 | 549.324174760062 | 28.6758252399377 |
| 10 | 565 | 546.877958825075 | 18.1220411749245 |
| 11 | 547 | 563.743973955774 | -16.7439739557742 |
| 12 | 555 | 565.932693476552 | -10.9326934765518 |
| 13 | 562 | 568.250161204434 | -6.25016120443413 |
| 14 | 561 | 565.803945269447 | -4.80394526944728 |
| 15 | 555 | 545.59047675403 | 9.40952324597023 |
| 16 | 544 | 558.207801050278 | -14.2078010502776 |
| 17 | 537 | 565.288952441029 | -28.288952441029 |
| 18 | 543 | 547.264203446389 | -4.26420344638918 |
| 19 | 594 | 578.163773151486 | 15.836226848514 |
| 20 | 611 | 566.061441683656 | 44.9385583163436 |
| 21 | 613 | 543.788001854566 | 69.2119981454342 |
| 22 | 611 | 548.680433724540 | 62.3195662754605 |
| 23 | 594 | 556.920318979232 | 37.0796810207681 |
| 24 | 595 | 559.881527742637 | 35.1184722573629 |
| 25 | 591 | 568.893902239957 | 22.1060977600430 |
| 26 | 589 | 567.220175547598 | 21.7798244524025 |
| 27 | 584 | 555.890333322395 | 28.1096666776046 |
| 28 | 573 | 558.336549257382 | 14.6634507426178 |
| 29 | 567 | 564.387714991297 | 2.61228500870298 |
| 30 | 569 | 544.045498268775 | 24.9545017312251 |
| 31 | 621 | 586.532406613283 | 34.4675933867169 |
| 32 | 629 | 567.477671961807 | 61.5223280381933 |
| 33 | 628 | 544.946735718507 | 83.053264281493 |
| 34 | 612 | 554.345354837141 | 57.6546451628595 |
| 35 | 595 | 550.611656831108 | 44.388343168892 |
| 36 | 597 | 558.980290292905 | 38.0197097070949 |
| 37 | 593 | 563.228981127356 | 29.7710188726441 |
| 38 | 590 | 561.040261606578 | 28.9597383934218 |
| 39 | 580 | 541.985526955102 | 38.0144730448982 |
| 40 | 574 | 561.040261606578 | 12.9597383934218 |
| 41 | 573 | 549.195426552958 | 23.8045734470423 |
| 42 | 573 | 543.144260819043 | 29.8557391809571 |
| 43 | 620 | 580.738737293577 | 39.2612627064226 |
| 44 | 626 | 561.297758020787 | 64.7022419792127 |
| 45 | 620 | 542.886764404834 | 77.1132355951662 |
| 46 | 588 | 540.698044884056 | 47.3019551159439 |
| 47 | 566 | 545.332980339821 | 20.6670196601794 |
| 48 | 557 | 559.366534914219 | -2.36653491421878 |
| 49 | 561 | 554.216606630036 | 6.78339336996403 |
| 50 | 549 | 555.117844079768 | -6.11784407976797 |
| 51 | 532 | 537.736836120651 | -5.736836120651 |
| 52 | 526 | 554.087858422931 | -28.0878584229314 |
| 53 | 511 | 549.967915795585 | -38.9679157955852 |
| 54 | 499 | 539.796807434324 | -40.7968074343241 |
| 55 | 555 | 571.597614589153 | -16.5976145891529 |
| 56 | 565 | 556.534074357918 | 8.46592564208177 |
| 57 | 542 | 545.847973168239 | -3.84797316823891 |
| 58 | 527 | 533.101900664886 | -6.10190066488647 |
| 59 | 510 | 544.817987511402 | -34.8179875114024 |
| 60 | 514 | 561.94149905631 | -47.9414990563102 |
| 61 | 517 | 548.165440896121 | -31.1654408961212 |
| 62 | 508 | 545.461728546925 | -37.4617285469252 |
| 63 | 493 | 549.324174760062 | -56.3241747600623 |
| 64 | 490 | 539.66805922722 | -49.6680592272196 |
| 65 | 469 | 550.225412209794 | -81.2254122097943 |
| 66 | 478 | 541.470534126684 | -63.4705341266835 |
| 67 | 528 | 567.091427340493 | -39.091427340493 |
| 68 | 534 | 562.198995470519 | -28.1989954705193 |
| 69 | 518 | 540.311800262742 | -22.3118002627424 |
| 70 | 506 | 541.728030540893 | -35.7280305408927 |
| 71 | 502 | 562.713988298938 | -60.7139882989376 |
| 72 | 516 | 569.280146861271 | -53.2801468612707 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.011877691833674 | 0.023755383667348 | 0.988122308166326 |
| 6 | 0.00213321583931494 | 0.00426643167862988 | 0.997866784160685 |
| 7 | 0.0121304932545001 | 0.0242609865090002 | 0.9878695067455 |
| 8 | 0.0175959214849322 | 0.0351918429698644 | 0.982404078515068 |
| 9 | 0.362739814483858 | 0.725479628967715 | 0.637260185516142 |
| 10 | 0.387681234090001 | 0.775362468180002 | 0.612318765909999 |
| 11 | 0.296583269193904 | 0.593166538387808 | 0.703416730806096 |
| 12 | 0.227118037244082 | 0.454236074488164 | 0.772881962755918 |
| 13 | 0.176185744244875 | 0.352371488489749 | 0.823814255755125 |
| 14 | 0.132446151117680 | 0.264892302235361 | 0.86755384888232 |
| 15 | 0.101174638161287 | 0.202349276322574 | 0.898825361838713 |
| 16 | 0.0667999612619813 | 0.133599922523963 | 0.933200038738019 |
| 17 | 0.0455645864576396 | 0.0911291729152792 | 0.95443541354236 |
| 18 | 0.0280801160868231 | 0.0561602321736462 | 0.971919883913177 |
| 19 | 0.0341727082746726 | 0.0683454165493451 | 0.965827291725327 |
| 20 | 0.0742676708333081 | 0.148535341666616 | 0.925732329166692 |
| 21 | 0.191543743594763 | 0.383087487189525 | 0.808456256405237 |
| 22 | 0.278690375843783 | 0.557380751687566 | 0.721309624156217 |
| 23 | 0.275064771390535 | 0.55012954278107 | 0.724935228609465 |
| 24 | 0.268381901268354 | 0.536763802536709 | 0.731618098731646 |
| 25 | 0.244068532781955 | 0.488137065563911 | 0.755931467218045 |
| 26 | 0.214206859276139 | 0.428413718552278 | 0.785793140723861 |
| 27 | 0.183570392243716 | 0.367140784487432 | 0.816429607756284 |
| 28 | 0.143129619387248 | 0.286259238774497 | 0.856870380612752 |
| 29 | 0.106589259129832 | 0.213178518259665 | 0.893410740870168 |
| 30 | 0.082302574109709 | 0.164605148219418 | 0.91769742589029 |
| 31 | 0.0964790974727624 | 0.192958194945525 | 0.903520902527238 |
| 32 | 0.149365933286106 | 0.298731866572213 | 0.850634066713894 |
| 33 | 0.288965231060441 | 0.577930462120882 | 0.711034768939559 |
| 34 | 0.343516775906376 | 0.687033551812751 | 0.656483224093624 |
| 35 | 0.348871584448182 | 0.697743168896364 | 0.651128415551818 |
| 36 | 0.344141299657668 | 0.688282599315335 | 0.655858700342332 |
| 37 | 0.323416182250834 | 0.646832364501669 | 0.676583817749166 |
| 38 | 0.303382909274226 | 0.606765818548451 | 0.696617090725774 |
| 39 | 0.299823910266792 | 0.599647820533585 | 0.700176089733208 |
| 40 | 0.256576677730916 | 0.513153355461832 | 0.743423322269084 |
| 41 | 0.232634058088175 | 0.465268116176351 | 0.767365941911825 |
| 42 | 0.22480208638241 | 0.44960417276482 | 0.77519791361759 |
| 43 | 0.292584365233931 | 0.585168730467863 | 0.707415634766069 |
| 44 | 0.549286539069867 | 0.901426921860265 | 0.450713460930133 |
| 45 | 0.860055237119841 | 0.279889525760318 | 0.139944762880159 |
| 46 | 0.949420213729171 | 0.101159572541658 | 0.0505797862708288 |
| 47 | 0.970189560937398 | 0.0596208781252029 | 0.0298104390626015 |
| 48 | 0.969960902515557 | 0.0600781949688862 | 0.0300390974844431 |
| 49 | 0.978859153072537 | 0.0422816938549252 | 0.0211408469274626 |
| 50 | 0.979921957746687 | 0.040156084506626 | 0.020078042253313 |
| 51 | 0.981390918950324 | 0.0372181620993513 | 0.0186090810496757 |
| 52 | 0.975730317500082 | 0.0485393649998353 | 0.0242696824999176 |
| 53 | 0.969994697345969 | 0.0600106053080625 | 0.0300053026540312 |
| 54 | 0.96445598072284 | 0.0710880385543191 | 0.0355440192771596 |
| 55 | 0.961427619315652 | 0.0771447613686953 | 0.0385723806843477 |
| 56 | 0.98828623685673 | 0.0234275262865393 | 0.0117137631432697 |
| 57 | 0.993391809403764 | 0.0132163811924715 | 0.00660819059623573 |
| 58 | 0.996148275459702 | 0.0077034490805959 | 0.00385172454029795 |
| 59 | 0.99368548191223 | 0.0126290361755395 | 0.00631451808776976 |
| 60 | 0.988450874050503 | 0.0230982518989937 | 0.0115491259494969 |
| 61 | 0.983065700900822 | 0.0338685981983569 | 0.0169342990991784 |
| 62 | 0.971395621260602 | 0.0572087574787964 | 0.0286043787393982 |
| 63 | 0.952277212433601 | 0.095445575132797 | 0.0477227875663985 |
| 64 | 0.914249734753584 | 0.171500530492832 | 0.0857502652464158 |
| 65 | 0.96076861383008 | 0.0784627723398388 | 0.0392313861699194 |
| 66 | 0.978167719176133 | 0.0436645616477348 | 0.0218322808238674 |
| 67 | 0.941916941683648 | 0.116166116632704 | 0.0580830583163518 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 2 | 0.0317460317460317 | NOK |
| 5% type I error level | 15 | 0.238095238095238 | NOK |
| 10% type I error level | 26 | 0.412698412698413 | NOK |
