| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 593.286943257603 -9.6360562361279X[t] -0.908505841360937t + 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) | 593.286943257603 | 9.459284 | 62.7201 | 0 | 0 |
| X | -9.6360562361279 | 14.287427 | -0.6744 | 0.50235 | 0.251175 |
| t | -0.908505841360937 | 0.309051 | -2.9397 | 0.004505 | 0.002252 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.545245856416598 |
| R-squared | 0.297293043939469 |
| Adjusted R-squared | 0.276316716892886 |
| F-TEST (value) | 14.1727883665838 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 67 |
| p-value | 7.36101093157249e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 34.1323536075516 |
| Sum Squared Residuals | 78056.1767069929 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 555 | 592.378437416241 | -37.378437416241 |
| 2 | 562 | 591.469931574881 | -29.4699315748814 |
| 3 | 561 | 590.56142573352 | -29.5614257335206 |
| 4 | 555 | 589.65291989216 | -34.6529198921596 |
| 5 | 544 | 588.744414050799 | -44.7444140507986 |
| 6 | 537 | 587.835908209438 | -50.8359082094377 |
| 7 | 543 | 586.927402368077 | -43.9274023680768 |
| 8 | 594 | 586.018896526716 | 7.98110347328416 |
| 9 | 611 | 585.110390685355 | 25.8896093146451 |
| 10 | 613 | 584.201884843994 | 28.7981151560060 |
| 11 | 611 | 583.293379002633 | 27.706620997367 |
| 12 | 594 | 582.384873161272 | 11.6151268387279 |
| 13 | 595 | 581.476367319911 | 13.5236326800889 |
| 14 | 591 | 580.56786147855 | 10.4321385214498 |
| 15 | 589 | 579.659355637189 | 9.34064436281073 |
| 16 | 584 | 578.750849795828 | 5.24915020417167 |
| 17 | 573 | 577.842343954467 | -4.84234395446740 |
| 18 | 567 | 576.933838113107 | -9.93383811310646 |
| 19 | 569 | 576.025332271745 | -7.02533227174552 |
| 20 | 621 | 575.116826430385 | 45.8831735696154 |
| 21 | 629 | 574.208320589024 | 54.7916794109764 |
| 22 | 628 | 573.299814747663 | 54.7001852523373 |
| 23 | 612 | 572.391308906302 | 39.6086910936982 |
| 24 | 595 | 571.482803064941 | 23.5171969350592 |
| 25 | 597 | 570.57429722358 | 26.4257027764201 |
| 26 | 593 | 569.665791382219 | 23.3342086177810 |
| 27 | 590 | 568.757285540858 | 21.2427144591420 |
| 28 | 580 | 567.848779699497 | 12.1512203005029 |
| 29 | 574 | 566.940273858136 | 7.05972614186386 |
| 30 | 573 | 566.031768016775 | 6.96823198322479 |
| 31 | 573 | 565.123262175414 | 7.87673782458573 |
| 32 | 620 | 564.214756334053 | 55.7852436659467 |
| 33 | 626 | 563.306250492692 | 62.6937495073076 |
| 34 | 620 | 562.397744651331 | 57.6022553486685 |
| 35 | 588 | 561.489238809971 | 26.5107611900295 |
| 36 | 566 | 560.58073296861 | 5.41926703139042 |
| 37 | 557 | 559.672227127249 | -2.67222712724864 |
| 38 | 561 | 558.763721285888 | 2.23627871411230 |
| 39 | 549 | 557.855215444527 | -8.85521544452677 |
| 40 | 532 | 556.946709603166 | -24.9467096031658 |
| 41 | 526 | 556.038203761805 | -30.0382037618049 |
| 42 | 511 | 555.129697920444 | -44.1296979204440 |
| 43 | 499 | 554.221192079083 | -55.221192079083 |
| 44 | 555 | 553.312686237722 | 1.68731376227792 |
| 45 | 565 | 552.404180396361 | 12.5958196036389 |
| 46 | 542 | 551.495674555 | -9.4956745550002 |
| 47 | 527 | 550.587168713639 | -23.5871687136393 |
| 48 | 510 | 549.678662872278 | -39.6786628722783 |
| 49 | 514 | 548.770157030917 | -34.7701570309174 |
| 50 | 517 | 547.861651189556 | -30.8616511895565 |
| 51 | 508 | 546.953145348196 | -38.9531453481955 |
| 52 | 493 | 546.044639506835 | -53.0446395068346 |
| 53 | 490 | 535.500077429346 | -45.5000774293457 |
| 54 | 469 | 534.591571587985 | -65.5915715879848 |
| 55 | 478 | 533.683065746624 | -55.6830657466239 |
| 56 | 528 | 532.774559905263 | -4.77455990526293 |
| 57 | 534 | 531.866054063902 | 2.133945936098 |
| 58 | 518 | 530.957548222541 | -12.9575482225411 |
| 59 | 506 | 530.04904238118 | -24.0490423811801 |
| 60 | 502 | 529.140536539819 | -27.1405365398192 |
| 61 | 516 | 528.232030698458 | -12.2320306984582 |
| 62 | 528 | 527.323524857097 | 0.67647514290269 |
| 63 | 533 | 526.415019015736 | 6.58498098426363 |
| 64 | 536 | 525.506513174375 | 10.4934868256246 |
| 65 | 537 | 524.598007333014 | 12.4019926669855 |
| 66 | 524 | 523.689501491654 | 0.310498508346438 |
| 67 | 536 | 522.780995650293 | 13.2190043497074 |
| 68 | 587 | 521.872489808932 | 65.1275101910683 |
| 69 | 597 | 520.963983967571 | 76.0360160324293 |
| 70 | 581 | 520.05547812621 | 60.9445218737902 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.0160919545360308 | 0.0321839090720616 | 0.98390804546397 |
| 7 | 0.00411491257883576 | 0.00822982515767152 | 0.995885087421164 |
| 8 | 0.169376886645288 | 0.338753773290575 | 0.830623113354713 |
| 9 | 0.267625555729587 | 0.535251111459174 | 0.732374444270413 |
| 10 | 0.226444627526901 | 0.452889255053802 | 0.773555372473099 |
| 11 | 0.151209105813716 | 0.302418211627433 | 0.848790894186284 |
| 12 | 0.104693231549389 | 0.209386463098777 | 0.895306768450611 |
| 13 | 0.0713069100456086 | 0.142613820091217 | 0.928693089954391 |
| 14 | 0.05297288064834 | 0.10594576129668 | 0.94702711935166 |
| 15 | 0.0406134837802216 | 0.0812269675604431 | 0.959386516219778 |
| 16 | 0.0347471786946376 | 0.0694943573892753 | 0.965252821305362 |
| 17 | 0.0403480892628224 | 0.0806961785256448 | 0.959651910737178 |
| 18 | 0.049346727218647 | 0.098693454437294 | 0.950653272781353 |
| 19 | 0.0487597526982384 | 0.097519505396477 | 0.951240247301762 |
| 20 | 0.0423320084870189 | 0.0846640169740378 | 0.95766799151298 |
| 21 | 0.0394285527388641 | 0.0788571054777283 | 0.960571447261136 |
| 22 | 0.0323019313228372 | 0.0646038626456743 | 0.967698068677163 |
| 23 | 0.0212548590048332 | 0.0425097180096664 | 0.978745140995167 |
| 24 | 0.0163400602228707 | 0.0326801204457415 | 0.98365993977713 |
| 25 | 0.0119994858015662 | 0.0239989716031325 | 0.988000514198434 |
| 26 | 0.00937800380726781 | 0.0187560076145356 | 0.990621996192732 |
| 27 | 0.00763612754115744 | 0.0152722550823149 | 0.992363872458843 |
| 28 | 0.00759880133056122 | 0.0151976026611224 | 0.99240119866944 |
| 29 | 0.00810713768811853 | 0.0162142753762371 | 0.991892862311881 |
| 30 | 0.00790431291293472 | 0.0158086258258694 | 0.992095687087065 |
| 31 | 0.0070517594599582 | 0.0141035189199164 | 0.992948240540042 |
| 32 | 0.00908017871514482 | 0.0181603574302896 | 0.990919821284855 |
| 33 | 0.019374750593415 | 0.03874950118683 | 0.980625249406585 |
| 34 | 0.0496912113104161 | 0.0993824226208322 | 0.950308788689584 |
| 35 | 0.0873866165077682 | 0.174773233015536 | 0.912613383492232 |
| 36 | 0.156630647890311 | 0.313261295780621 | 0.84336935210969 |
| 37 | 0.261107022236684 | 0.522214044473367 | 0.738892977763316 |
| 38 | 0.403962421999393 | 0.807924843998786 | 0.596037578000607 |
| 39 | 0.560584784897276 | 0.878830430205448 | 0.439415215102724 |
| 40 | 0.688395207906021 | 0.623209584187959 | 0.311604792093979 |
| 41 | 0.76946950268729 | 0.46106099462542 | 0.23053049731271 |
| 42 | 0.824446492844575 | 0.35110701431085 | 0.175553507155425 |
| 43 | 0.86713887528284 | 0.265722249434318 | 0.132861124717159 |
| 44 | 0.909662864708872 | 0.180674270582255 | 0.0903371352911276 |
| 45 | 0.976089476318352 | 0.0478210473632961 | 0.0239105236816481 |
| 46 | 0.989938982941284 | 0.0201220341174327 | 0.0100610170587163 |
| 47 | 0.99331074179871 | 0.0133785164025816 | 0.0066892582012908 |
| 48 | 0.9924701445154 | 0.0150597109692016 | 0.00752985548460082 |
| 49 | 0.991080866424564 | 0.0178382671508711 | 0.00891913357543553 |
| 50 | 0.989999116844723 | 0.0200017663105539 | 0.0100008831552770 |
| 51 | 0.987082432669886 | 0.0258351346602278 | 0.0129175673301139 |
| 52 | 0.981549240049883 | 0.0369015199002339 | 0.0184507599501169 |
| 53 | 0.969929166385356 | 0.060141667229287 | 0.0300708336146435 |
| 54 | 0.960290094377664 | 0.0794198112446729 | 0.0397099056223365 |
| 55 | 0.948303477204121 | 0.103393045591757 | 0.0516965227958785 |
| 56 | 0.956370354806724 | 0.0872592903865516 | 0.0436296451932758 |
| 57 | 0.981452169216789 | 0.0370956615664224 | 0.0185478307832112 |
| 58 | 0.981981406585232 | 0.0360371868295356 | 0.0180185934147678 |
| 59 | 0.966690987022884 | 0.0666180259542311 | 0.0333090129771155 |
| 60 | 0.933828631176138 | 0.132342737647724 | 0.0661713688238621 |
| 61 | 0.88127170061532 | 0.237456598769361 | 0.118728299384681 |
| 62 | 0.822824994789116 | 0.354350010421767 | 0.177175005210884 |
| 63 | 0.755231873861692 | 0.489536252276617 | 0.244768126138308 |
| 64 | 0.671221587746919 | 0.657556824506162 | 0.328778412253081 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0169491525423729 | NOK |
| 5% type I error level | 23 | 0.389830508474576 | NOK |
| 10% type I error level | 36 | 0.610169491525424 | NOK |
