| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 4.05218005035397 + 5.57247979453095X[t] -9.08018148401166M1[t] -17.4122026084505M2[t] -87.6026002969237M3[t] -51.9540472089442M4[t] -56.6728845833714M5[t] -99.4931816097101M6[t] + 91.5516560161159M7[t] + 47.0075301255981M8[t] -37.6725414556083M9[t] -56.6356025629257M10[t] -40.4908145377453M11[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) | 4.05218005035397 | 155.550381 | 0.0261 | 0.979305 | 0.489652 |
| X | 5.57247979453095 | 1.580513 | 3.5257 | 0.000824 | 0.000412 |
| M1 | -9.08018148401166 | 28.606605 | -0.3174 | 0.752049 | 0.376024 |
| M2 | -17.4122026084505 | 28.586623 | -0.6091 | 0.544794 | 0.272397 |
| M3 | -87.6026002969237 | 33.900969 | -2.5841 | 0.012259 | 0.00613 |
| M4 | -51.9540472089442 | 29.223644 | -1.7778 | 0.080589 | 0.040294 |
| M5 | -56.6728845833714 | 29.159464 | -1.9436 | 0.056724 | 0.028362 |
| M6 | -99.4931816097101 | 33.986215 | -2.9275 | 0.004848 | 0.002424 |
| M7 | 91.5516560161159 | 35.109688 | 2.6076 | 0.011531 | 0.005765 |
| M8 | 47.0075301255981 | 28.884544 | 1.6274 | 0.108975 | 0.054488 |
| M9 | -37.6725414556083 | 34.641859 | -1.0875 | 0.281245 | 0.140622 |
| M10 | -56.6356025629257 | 35.652986 | -1.5885 | 0.117513 | 0.058757 |
| M11 | -40.4908145377453 | 30.716634 | -1.3182 | 0.19253 | 0.096265 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.576906910484904 |
| R-squared | 0.332821583365237 |
| Adjusted R-squared | 0.197124278286980 |
| F-TEST (value) | 2.45267644168245 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 59 |
| p-value | 0.0114715642009897 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 49.5074076690988 |
| Sum Squared Residuals | 144608.021432746 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 467 | 545.533002266007 | -78.5330022660068 |
| 2 | 460 | 546.674196792265 | -86.6741967922649 |
| 3 | 448 | 531.651349069648 | -83.651349069648 |
| 4 | 443 | 489.285185034194 | -46.2851850341943 |
| 5 | 436 | 515.214986529687 | -79.2149865296873 |
| 6 | 431 | 496.356352619832 | -65.3563526198317 |
| 7 | 484 | 546.974699423478 | -62.9746994234775 |
| 8 | 510 | 578.773546718034 | -68.773546718034 |
| 9 | 513 | 529.200097842372 | -16.2000978423725 |
| 10 | 503 | 557.045867009115 | -54.0458670091151 |
| 11 | 471 | 533.626048493126 | -62.6260484931257 |
| 12 | 471 | 509.476097414312 | -38.4760974143121 |
| 13 | 476 | 531.044554800221 | -55.0445548002206 |
| 14 | 475 | 522.155285696329 | -47.1552856963286 |
| 15 | 470 | 507.132437973712 | -37.1324379737118 |
| 16 | 461 | 526.620799657552 | -65.6207996575516 |
| 17 | 455 | 515.77223450914 | -60.7722345091404 |
| 18 | 456 | 487.997632928035 | -31.9976329280352 |
| 19 | 517 | 574.837098396132 | -57.8370983961324 |
| 20 | 525 | 564.285099252253 | -39.2850992522534 |
| 21 | 523 | 562.077728630105 | -39.0777286301051 |
| 22 | 519 | 574.877802351614 | -55.8778023516141 |
| 23 | 509 | 530.282560616407 | -21.2825606164072 |
| 24 | 512 | 516.720321147202 | -4.72032114720225 |
| 25 | 519 | 537.731530553658 | -18.7315305536578 |
| 26 | 517 | 527.170517511407 | -10.1705175114065 |
| 27 | 510 | 503.788950096993 | 6.21104990300668 |
| 28 | 509 | 524.391807739739 | -15.3918077397392 |
| 29 | 501 | 494.03956331047 | 6.96043668953036 |
| 30 | 507 | 486.883136969129 | 20.116863030871 |
| 31 | 569 | 582.638570108476 | -13.6385701084758 |
| 32 | 580 | 552.025643704285 | 27.9743562957146 |
| 33 | 578 | 578.237920034245 | -0.237920034244812 |
| 34 | 565 | 569.862570536536 | -4.86257053653626 |
| 35 | 547 | 513.007873253361 | 33.9921267466388 |
| 36 | 555 | 544.025472140404 | 10.9745278595961 |
| 37 | 562 | 524.914827026236 | 37.0851729737635 |
| 38 | 561 | 527.170517511407 | 33.8294824885935 |
| 39 | 555 | 544.468052597069 | 10.5319474029308 |
| 40 | 544 | 525.506303698645 | 18.4936963013546 |
| 41 | 537 | 490.138827454298 | 46.8611725457020 |
| 42 | 543 | 525.333247551393 | 17.6667524486074 |
| 43 | 594 | 582.638570108476 | 11.3614298915242 |
| 44 | 611 | 590.475754286549 | 20.5242457134511 |
| 45 | 613 | 602.199583150728 | 10.8004168492721 |
| 46 | 611 | 562.061098824193 | 48.9389011758071 |
| 47 | 594 | 542.542016164375 | 51.4579838356247 |
| 48 | 595 | 570.216127174699 | 24.7838728253006 |
| 49 | 591 | 522.128587128971 | 68.871412871029 |
| 50 | 589 | 521.040789737423 | 67.9592102625775 |
| 51 | 584 | 499.888214240822 | 84.1117857591784 |
| 52 | 573 | 524.949055719192 | 48.0509442808077 |
| 53 | 567 | 494.03956331047 | 72.9604366895303 |
| 54 | 569 | 539.26444703772 | 29.7355529622800 |
| 55 | 621 | 546.417451444025 | 74.5825485559754 |
| 56 | 629 | 584.346026512565 | 44.6539734874351 |
| 57 | 628 | 597.18435133565 | 30.8156486643499 |
| 58 | 612 | 537.542187728257 | 74.4578122717432 |
| 59 | 595 | 569.847167157577 | 25.1528328424231 |
| 60 | 597 | 574.116863030871 | 22.8831369691290 |
| 61 | 593 | 546.647498224907 | 46.3525017750927 |
| 62 | 590 | 547.788692751171 | 42.2113072488290 |
| 63 | 580 | 560.070996021756 | 19.9290039782441 |
| 64 | 574 | 513.246848150677 | 60.7531518493227 |
| 65 | 573 | 559.794824885935 | 13.2051751140651 |
| 66 | 573 | 543.165182893892 | 29.8348171061084 |
| 67 | 620 | 571.493610519414 | 48.5063894805862 |
| 68 | 626 | 611.093929526313 | 14.9060704736866 |
| 69 | 620 | 606.1003190069 | 13.8996809931004 |
| 70 | 588 | 596.610473550285 | -8.6104735502848 |
| 71 | 566 | 592.694334315154 | -26.6943343151538 |
| 72 | 557 | 572.445119092512 | -15.4451190925118 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0569342615136426 | 0.113868523027285 | 0.943065738486357 |
| 17 | 0.0346614726223942 | 0.0693229452447884 | 0.965338527377606 |
| 18 | 0.0264580663791672 | 0.0529161327583345 | 0.973541933620833 |
| 19 | 0.0411693298481614 | 0.0823386596963229 | 0.958830670151839 |
| 20 | 0.0293289545694815 | 0.0586579091389629 | 0.970671045430519 |
| 21 | 0.0184169995391228 | 0.0368339990782456 | 0.981583000460877 |
| 22 | 0.0165099816106934 | 0.0330199632213868 | 0.983490018389307 |
| 23 | 0.034640907403994 | 0.069281814807988 | 0.965359092596006 |
| 24 | 0.0580653379073016 | 0.116130675814603 | 0.941934662092698 |
| 25 | 0.175983794857455 | 0.35196758971491 | 0.824016205142545 |
| 26 | 0.371993296082033 | 0.743986592164066 | 0.628006703917967 |
| 27 | 0.561949424290689 | 0.876101151418623 | 0.438050575709311 |
| 28 | 0.77680012196335 | 0.446399756073299 | 0.223199878036650 |
| 29 | 0.896303401415752 | 0.207393197168495 | 0.103696598584248 |
| 30 | 0.958729914902964 | 0.0825401701940721 | 0.0412700850970360 |
| 31 | 0.989425659453904 | 0.0211486810921925 | 0.0105743405460962 |
| 32 | 0.995121498854478 | 0.0097570022910443 | 0.00487850114552215 |
| 33 | 0.998110823031489 | 0.00377835393702244 | 0.00188917696851122 |
| 34 | 0.99923066312496 | 0.00153867375008027 | 0.000769336875040134 |
| 35 | 0.999685574280316 | 0.000628851439367929 | 0.000314425719683965 |
| 36 | 0.999824452838195 | 0.000351094323610872 | 0.000175547161805436 |
| 37 | 0.999942057065093 | 0.000115885869814312 | 5.79429349071562e-05 |
| 38 | 0.999977118704606 | 4.57625907873837e-05 | 2.28812953936918e-05 |
| 39 | 0.99998626916426 | 2.74616714800909e-05 | 1.37308357400455e-05 |
| 40 | 0.999992521672983 | 1.49566540343420e-05 | 7.47832701717102e-06 |
| 41 | 0.99999861372127 | 2.77255746140348e-06 | 1.38627873070174e-06 |
| 42 | 0.999999482156504 | 1.03568699207632e-06 | 5.17843496038158e-07 |
| 43 | 0.999999549779121 | 9.00441757919387e-07 | 4.50220878959693e-07 |
| 44 | 0.9999993459582 | 1.30808359924549e-06 | 6.54041799622746e-07 |
| 45 | 0.999998213196842 | 3.57360631575212e-06 | 1.78680315787606e-06 |
| 46 | 0.999996701002714 | 6.59799457287187e-06 | 3.29899728643594e-06 |
| 47 | 0.999991327648296 | 1.73447034075732e-05 | 8.67235170378658e-06 |
| 48 | 0.999983579453233 | 3.28410935345649e-05 | 1.64205467672825e-05 |
| 49 | 0.999960629350277 | 7.874129944706e-05 | 3.937064972353e-05 |
| 50 | 0.999893830246037 | 0.000212339507926434 | 0.000106169753963217 |
| 51 | 0.99972266762987 | 0.000554664740260523 | 0.000277332370130261 |
| 52 | 0.99907240532355 | 0.00185518935290029 | 0.000927594676450144 |
| 53 | 0.99848304858233 | 0.00303390283534185 | 0.00151695141767092 |
| 54 | 0.994419327177858 | 0.0111613456442834 | 0.00558067282214171 |
| 55 | 0.98333069523584 | 0.0333386095283207 | 0.0166693047641604 |
| 56 | 0.947107758468507 | 0.105784483062987 | 0.0528922415314934 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 22 | 0.536585365853659 | NOK |
| 5% type I error level | 27 | 0.658536585365854 | NOK |
| 10% type I error level | 33 | 0.804878048780488 | NOK |
