| Multiple Linear Regression - Estimated Regression Equation |
| yt[t] = + 196.193390381622 + 0.97222446927995xt[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) | 196.193390381622 | 30.883563 | 6.3527 | 0 | 0 |
| xt | 0.97222446927995 | 0.054574 | 17.8148 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.853794014428263 |
| R-squared | 0.728964219073528 |
| Adjusted R-squared | 0.726667305675846 |
| F-TEST (value) | 317.366871475954 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 118 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 117.144117054869 |
| Sum Squared Residuals | 1619283.81094664 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 384 | 446.930081008918 | -62.9300810089183 |
| 2 | 367.6 | 464.332899009031 | -96.732899009031 |
| 3 | 457.1 | 506.721885869637 | -49.6218858696371 |
| 4 | 429.4 | 487.66628627175 | -58.2662862717502 |
| 5 | 442.2 | 518.096912160213 | -75.8969121602126 |
| 6 | 507.5 | 526.069152808308 | -18.5691528083082 |
| 7 | 348.5 | 399.971639142699 | -51.4716391426987 |
| 8 | 393.2 | 469.291243802359 | -76.0912438023591 |
| 9 | 426.8 | 473.763476361047 | -46.9634763610469 |
| 10 | 403 | 436.916168975337 | -33.9161689753368 |
| 11 | 454.8 | 463.652341880535 | -8.85234188053544 |
| 12 | 413 | 451.207868673752 | -38.2078686737521 |
| 13 | 388.9 | 456.555103254792 | -67.6551032547918 |
| 14 | 406.5 | 631.944397512895 | -225.444397512895 |
| 15 | 447.4 | 743.944656373945 | -296.544656373945 |
| 16 | 474.4 | 533.166391434052 | -58.7663914340519 |
| 17 | 428.5 | 638.652746350926 | -210.152746350926 |
| 18 | 472.8 | 608.805455144032 | -136.005455144032 |
| 19 | 411 | 566.805358071138 | -155.805358071138 |
| 20 | 463.9 | 568.458139668914 | -104.558139668914 |
| 21 | 497.3 | 649.833327747646 | -152.533327747646 |
| 22 | 474 | 585.277622987457 | -111.277622987457 |
| 23 | 518.1 | 676.083388418204 | -157.983388418204 |
| 24 | 566 | 553.485882842003 | 12.5141171579973 |
| 25 | 509.4 | 494.763524897494 | 14.6364751025061 |
| 26 | 445.1 | 504.096879802581 | -58.9968798025813 |
| 27 | 466.6 | 501.666318629381 | -35.0663186293814 |
| 28 | 600.5 | 588.680408629937 | 11.8195913700631 |
| 29 | 538.7 | 556.49977869677 | -17.7997786967706 |
| 30 | 548 | 530.34694047314 | 17.6530595268601 |
| 31 | 591.9 | 568.555362115842 | 23.3446378841580 |
| 32 | 547.3 | 551.444211456515 | -4.14421145651486 |
| 33 | 610.2 | 601.805438965216 | 8.39456103478386 |
| 34 | 621.6 | 595.77764725568 | 25.8223527443195 |
| 35 | 582.4 | 605.305447054624 | -22.9054470546241 |
| 36 | 635.8 | 675.500053736636 | -39.7000537366364 |
| 37 | 663.9 | 654.888894987901 | 9.01110501209853 |
| 38 | 624.2 | 636.02774028387 | -11.8277402838704 |
| 39 | 654.1 | 648.083323702942 | 6.01667629705822 |
| 40 | 723.5 | 722.652940496714 | 0.847059503286108 |
| 41 | 641.2 | 666.750033513117 | -25.5500335131168 |
| 42 | 565.5 | 633.111066876031 | -67.6110668760305 |
| 43 | 698.6 | 620.861038563103 | 77.7389614368968 |
| 44 | 651 | 672.583380328796 | -21.5833803287965 |
| 45 | 721.6 | 658.38890307731 | 63.2110969226908 |
| 46 | 643.5 | 578.86094149021 | 64.6390585097906 |
| 47 | 604 | 669.4722620271 | -65.4722620271007 |
| 48 | 618.2 | 717.98626304417 | -99.7862630441701 |
| 49 | 783.5 | 650.222217535358 | 133.277782464642 |
| 50 | 672.9 | 658.486125524237 | 14.4138744757627 |
| 51 | 726.7 | 714.194587613978 | 12.5054123860218 |
| 52 | 738.6 | 734.902968809641 | 3.69703119035875 |
| 53 | 692.2 | 689.40286364734 | 2.79713635266041 |
| 54 | 669.5 | 638.749968797854 | 30.7500312021457 |
| 55 | 546.2 | 648.569435937582 | -102.369435937582 |
| 56 | 715 | 743.750211480089 | -28.7502114800888 |
| 57 | 789.8 | 857.403251938915 | -67.6032519389149 |
| 58 | 684 | 700.000110362491 | -16.0001103624911 |
| 59 | 639 | 610.944348976448 | 28.0556510235522 |
| 60 | 768.5 | 791.583655368662 | -23.0836553686623 |
| 61 | 643.8 | 699.902887915563 | -56.1028879155631 |
| 62 | 623 | 721.194603792794 | -98.194603792794 |
| 63 | 692.8 | 722.84738539057 | -30.0473853905700 |
| 64 | 936.5 | 806.361467301718 | 130.138532698282 |
| 65 | 795.9 | 815.500377312949 | -19.6003773129491 |
| 66 | 695.7 | 744.722435949369 | -49.0224359493687 |
| 67 | 648.3 | 842.722662452788 | -194.422662452788 |
| 68 | 675.2 | 879.861637179282 | -204.661637179282 |
| 69 | 826.5 | 997.695242856011 | -171.195242856011 |
| 70 | 742.4 | 877.04218621837 | -134.642186218370 |
| 71 | 793.9 | 1381.91835311545 | -588.018353115447 |
| 72 | 685.3 | 939.653442039999 | -254.353442039999 |
| 73 | 756.1 | 662.763913189069 | 93.336086810931 |
| 74 | 704 | 724.500166988346 | -20.5001669883458 |
| 75 | 860.6 | 773.014168005415 | 87.5858319945848 |
| 76 | 795.9 | 764.264147781896 | 31.6358522181043 |
| 77 | 816.7 | 824.15317508954 | -7.4531750895405 |
| 78 | 777.9 | 729.847401569386 | 48.0525984306145 |
| 79 | 746.4 | 606.277671523904 | 140.122328476096 |
| 80 | 694.7 | 643.708313591182 | 50.991686408818 |
| 81 | 909.2 | 734.222411681145 | 174.977588318855 |
| 82 | 783.6 | 608.805455144032 | 174.794544855968 |
| 83 | 730.4 | 653.333335837053 | 77.0666641629465 |
| 84 | 847.7 | 728.19461997161 | 119.505380028390 |
| 85 | 758.7 | 628.638834317343 | 130.061165682657 |
| 86 | 839.2 | 708.26401835137 | 130.935981648629 |
| 87 | 784.8 | 777.875290351815 | 6.92470964818499 |
| 88 | 906.1 | 724.597389435274 | 181.502610564726 |
| 89 | 838.2 | 819.583720083925 | 18.6162799160752 |
| 90 | 729 | 706.611236753595 | 22.3887632464053 |
| 91 | 768.1 | 703.208451111115 | 64.8915488888851 |
| 92 | 710.5 | 732.666852530297 | -22.1668525302973 |
| 93 | 863 | 724.79183432913 | 138.208165670870 |
| 94 | 778.3 | 655.180562328685 | 123.119437671315 |
| 95 | 827.7 | 670.638931390237 | 157.061068609763 |
| 96 | 853.1 | 821.139279234773 | 31.9607207652273 |
| 97 | 859.3 | 781.180853547367 | 78.1191464526331 |
| 98 | 779.2 | 734.708523915785 | 44.4914760842148 |
| 99 | 724.6 | 704.180675580395 | 20.4193244196052 |
| 100 | 829.2 | 748.805778720345 | 80.3942212796555 |
| 101 | 862.9 | 852.833796933299 | 10.0662030667009 |
| 102 | 601.6 | 681.430622999244 | -79.830622999244 |
| 103 | 964.9 | 730.333513804025 | 234.566486195975 |
| 104 | 766.3 | 712.63902846313 | 53.6609715368695 |
| 105 | 847.8 | 763.291923312616 | 84.5080766873842 |
| 106 | 992.7 | 708.069573457515 | 284.630426542485 |
| 107 | 865.3 | 695.138988016091 | 170.161011983909 |
| 108 | 1054.1 | 905.042250933632 | 149.057749066368 |
| 109 | 972.5 | 928.958972877919 | 43.5410271220809 |
| 110 | 857.4 | 752.014119468968 | 105.385880531032 |
| 111 | 1043.3 | 858.181031514339 | 185.118968485661 |
| 112 | 1061 | 932.750648308111 | 128.249351691889 |
| 113 | 989.4 | 979.222977939692 | 10.1770220603075 |
| 114 | 963.2 | 864.792157905443 | 98.4078420945576 |
| 115 | 1181.9 | 1120.58441577300 | 61.315584227003 |
| 116 | 1256.4 | 1228.69577675693 | 27.7042232430727 |
| 117 | 1492.7 | 1275.94588596393 | 216.754114036067 |
| 118 | 1360.8 | 1264.57085967336 | 96.2291403266424 |
| 119 | 1342.8 | 1233.55689910333 | 109.243100896673 |
| 120 | 1464 | 1518.51589104928 | -54.5158910492802 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0069008378850938 | 0.0138016757701876 | 0.993099162114906 |
| 6 | 0.00332074252517141 | 0.00664148505034282 | 0.996679257474829 |
| 7 | 0.00128648483488638 | 0.00257296966977276 | 0.998713515165114 |
| 8 | 0.000292038866978543 | 0.000584077733957085 | 0.999707961133022 |
| 9 | 6.30250238829106e-05 | 0.000126050047765821 | 0.999936974976117 |
| 10 | 2.29752418172646e-05 | 4.59504836345291e-05 | 0.999977024758183 |
| 11 | 2.22934397131453e-05 | 4.45868794262906e-05 | 0.999977706560287 |
| 12 | 5.32167234897169e-06 | 1.06433446979434e-05 | 0.999994678327651 |
| 13 | 1.29627255788566e-06 | 2.59254511577132e-06 | 0.999998703727442 |
| 14 | 5.28566396782272e-05 | 0.000105713279356454 | 0.999947143360322 |
| 15 | 3.29380999791753e-05 | 6.58761999583505e-05 | 0.99996706190002 |
| 16 | 2.11362448747642e-05 | 4.22724897495284e-05 | 0.999978863755125 |
| 17 | 9.694879920924e-06 | 1.9389759841848e-05 | 0.99999030512008 |
| 18 | 4.57679316648509e-06 | 9.15358633297017e-06 | 0.999995423206834 |
| 19 | 2.09473314408442e-06 | 4.18946628816885e-06 | 0.999997905266856 |
| 20 | 9.51763227453465e-07 | 1.90352645490693e-06 | 0.999999048236773 |
| 21 | 6.26005774531525e-07 | 1.25201154906305e-06 | 0.999999373994225 |
| 22 | 3.015893181375e-07 | 6.03178636275e-07 | 0.999999698410682 |
| 23 | 2.39369811241985e-07 | 4.78739622483969e-07 | 0.999999760630189 |
| 24 | 4.37997448119579e-06 | 8.75994896239159e-06 | 0.999995620025519 |
| 25 | 6.14952583534122e-06 | 1.22990516706824e-05 | 0.999993850474165 |
| 26 | 2.76217839002568e-06 | 5.52435678005137e-06 | 0.99999723782161 |
| 27 | 1.41947041766316e-06 | 2.83894083532633e-06 | 0.999998580529582 |
| 28 | 1.4162209032819e-05 | 2.8324418065638e-05 | 0.999985837790967 |
| 29 | 1.61330242499726e-05 | 3.22660484999452e-05 | 0.99998386697575 |
| 30 | 2.39175356140545e-05 | 4.7835071228109e-05 | 0.999976082464386 |
| 31 | 6.14066360631152e-05 | 0.000122813272126230 | 0.999938593363937 |
| 32 | 6.01181968719802e-05 | 0.000120236393743960 | 0.999939881803128 |
| 33 | 0.000117586561034347 | 0.000235173122068694 | 0.999882413438966 |
| 34 | 0.000233459057525668 | 0.000466918115051336 | 0.999766540942474 |
| 35 | 0.000213479083364675 | 0.000426958166729349 | 0.999786520916635 |
| 36 | 0.00023027068568042 | 0.00046054137136084 | 0.99976972931432 |
| 37 | 0.000348571458122545 | 0.00069714291624509 | 0.999651428541877 |
| 38 | 0.000324824982034744 | 0.000649649964069488 | 0.999675175017965 |
| 39 | 0.000354855140560897 | 0.000709710281121794 | 0.99964514485944 |
| 40 | 0.000421558119079243 | 0.000843116238158486 | 0.99957844188092 |
| 41 | 0.000317392426927100 | 0.000634784853854201 | 0.999682607573073 |
| 42 | 0.000216402568524278 | 0.000432805137048555 | 0.999783597431476 |
| 43 | 0.000413399148274553 | 0.000826798296549106 | 0.999586600851725 |
| 44 | 0.000300923349061675 | 0.000601846698123351 | 0.999699076650938 |
| 45 | 0.000423276310001115 | 0.000846552620002231 | 0.99957672369 |
| 46 | 0.000478075484047462 | 0.000956150968094925 | 0.999521924515953 |
| 47 | 0.000336483672100497 | 0.000672967344200994 | 0.9996635163279 |
| 48 | 0.000266949515076312 | 0.000533899030152623 | 0.999733050484924 |
| 49 | 0.000852969186321463 | 0.00170593837264293 | 0.999147030813679 |
| 50 | 0.000654918453248795 | 0.00130983690649759 | 0.999345081546751 |
| 51 | 0.000495347790598667 | 0.000990695581197333 | 0.999504652209401 |
| 52 | 0.000351863926967962 | 0.000703727853935925 | 0.999648136073032 |
| 53 | 0.000244155113951282 | 0.000488310227902565 | 0.999755844886049 |
| 54 | 0.000186950198538119 | 0.000373900397076237 | 0.999813049801462 |
| 55 | 0.000190087549652508 | 0.000380175099305015 | 0.999809912450347 |
| 56 | 0.000124844950835703 | 0.000249689901671406 | 0.999875155049164 |
| 57 | 8.38847381307245e-05 | 0.000167769476261449 | 0.99991611526187 |
| 58 | 5.56139618157054e-05 | 0.000111227923631411 | 0.999944386038184 |
| 59 | 4.19491024582443e-05 | 8.38982049164886e-05 | 0.999958050897542 |
| 60 | 2.62535315791874e-05 | 5.25070631583747e-05 | 0.999973746468421 |
| 61 | 1.92158431404067e-05 | 3.84316862808134e-05 | 0.99998078415686 |
| 62 | 1.95525080778254e-05 | 3.91050161556507e-05 | 0.999980447491922 |
| 63 | 1.31632964088945e-05 | 2.63265928177891e-05 | 0.999986836703591 |
| 64 | 3.12088274396559e-05 | 6.24176548793118e-05 | 0.99996879117256 |
| 65 | 1.92526240074891e-05 | 3.85052480149782e-05 | 0.999980747375993 |
| 66 | 1.38864902569803e-05 | 2.77729805139607e-05 | 0.999986113509743 |
| 67 | 6.17164784883315e-05 | 0.000123432956976663 | 0.999938283521512 |
| 68 | 0.000251577050364403 | 0.000503154100728806 | 0.999748422949636 |
| 69 | 0.000391719476891106 | 0.000783438953782212 | 0.999608280523109 |
| 70 | 0.000522210361770449 | 0.00104442072354090 | 0.99947778963823 |
| 71 | 0.477312018929955 | 0.95462403785991 | 0.522687981070045 |
| 72 | 0.868049103099581 | 0.263901793800837 | 0.131950896900419 |
| 73 | 0.871902251088728 | 0.256195497822543 | 0.128097748911272 |
| 74 | 0.884449679478885 | 0.231100641042231 | 0.115550320521115 |
| 75 | 0.896398798031264 | 0.207202403937471 | 0.103601201968736 |
| 76 | 0.895727481547384 | 0.208545036905233 | 0.104272518452616 |
| 77 | 0.904471731958085 | 0.191056536083830 | 0.0955282680419152 |
| 78 | 0.900286717107315 | 0.199426565785370 | 0.0997132828926848 |
| 79 | 0.905309974101657 | 0.189380051796685 | 0.0946900258983427 |
| 80 | 0.895250208097561 | 0.209499583804878 | 0.104749791902439 |
| 81 | 0.929903184370668 | 0.140193631258665 | 0.0700968156293325 |
| 82 | 0.94287927170443 | 0.114241456591139 | 0.0571207282955696 |
| 83 | 0.932436124362724 | 0.135127751274553 | 0.0675638756372764 |
| 84 | 0.930778561436835 | 0.138442877126330 | 0.0692214385631649 |
| 85 | 0.924920103167805 | 0.150159793664389 | 0.0750798968321947 |
| 86 | 0.92297510005185 | 0.154049799896301 | 0.0770248999481506 |
| 87 | 0.91808769413211 | 0.163824611735782 | 0.0819123058678908 |
| 88 | 0.937198560349047 | 0.125602879301906 | 0.0628014396509532 |
| 89 | 0.929487361679105 | 0.141025276641791 | 0.0705126383208954 |
| 90 | 0.920268421836468 | 0.159463156327064 | 0.0797315781635319 |
| 91 | 0.902521859176762 | 0.194956281646477 | 0.0974781408232385 |
| 92 | 0.915199069618946 | 0.169601860762107 | 0.0848009303810537 |
| 93 | 0.906565542061613 | 0.186868915876774 | 0.0934344579383868 |
| 94 | 0.887492962169585 | 0.22501407566083 | 0.112507037830415 |
| 95 | 0.87999099888671 | 0.24001800222658 | 0.12000900111329 |
| 96 | 0.861012053673431 | 0.277975892653137 | 0.138987946326569 |
| 97 | 0.830210065633226 | 0.339579868733547 | 0.169789934366774 |
| 98 | 0.801815579272483 | 0.396368841455035 | 0.198184420727517 |
| 99 | 0.791075164423762 | 0.417849671152475 | 0.208924835576238 |
| 100 | 0.750071913135521 | 0.499856173728958 | 0.249928086864479 |
| 101 | 0.745138618197829 | 0.509722763604343 | 0.254861381802171 |
| 102 | 0.928659942158043 | 0.142680115683913 | 0.0713400578419567 |
| 103 | 0.942025207992126 | 0.115949584015748 | 0.0579747920078739 |
| 104 | 0.9445855388509 | 0.110828922298198 | 0.0554144611490991 |
| 105 | 0.934769173961351 | 0.130461652077297 | 0.0652308260386486 |
| 106 | 0.970458201543941 | 0.0590835969121182 | 0.0295417984560591 |
| 107 | 0.95598242432029 | 0.0880351513594212 | 0.0440175756797106 |
| 108 | 0.93877939811843 | 0.122441203763138 | 0.061220601881569 |
| 109 | 0.919519676117799 | 0.160960647764403 | 0.0804803238822014 |
| 110 | 0.87788673985379 | 0.24422652029242 | 0.12211326014621 |
| 111 | 0.851483337697007 | 0.297033324605987 | 0.148516662302993 |
| 112 | 0.780536151853306 | 0.438927696293388 | 0.219463848146694 |
| 113 | 0.756484465620842 | 0.487031068758317 | 0.243515534379158 |
| 114 | 0.677444419896127 | 0.645111160207747 | 0.322555580103873 |
| 115 | 0.623656352641125 | 0.75268729471775 | 0.376343647358875 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 65 | 0.585585585585586 | NOK |
| 5% type I error level | 66 | 0.594594594594595 | NOK |
| 10% type I error level | 68 | 0.612612612612613 | NOK |
