| Multiple Linear Regression - Estimated Regression Equation |
| yt[t] = + 169.803669378881 + 0.982878385352796xt[t] + 53.0505660825984M1[t] -0.269148200396778M2[t] + 11.6519447450388M3[t] + 65.945969813359M4[t] -11.0060367652886M5[t] + 7.85788440982509M6[t] + 30.8704282258714M7[t] -12.3135781387198M8[t] + 44.8369121538511M9[t] + 68.197242675119M10[t] -10.0188622503012M11[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) | 169.803669378881 | 52.293214 | 3.2471 | 0.001557 | 0.000779 |
| xt | 0.982878385352796 | 0.057437 | 17.1122 | 0 | 0 |
| M1 | 53.0505660825984 | 54.201379 | 0.9788 | 0.329903 | 0.164951 |
| M2 | -0.269148200396778 | 54.063772 | -0.005 | 0.996037 | 0.498019 |
| M3 | 11.6519447450388 | 53.698271 | 0.217 | 0.82863 | 0.414315 |
| M4 | 65.945969813359 | 53.631333 | 1.2296 | 0.221538 | 0.110769 |
| M5 | -11.0060367652886 | 53.445423 | -0.2059 | 0.837237 | 0.418618 |
| M6 | 7.85788440982509 | 53.938598 | 0.1457 | 0.884446 | 0.442223 |
| M7 | 30.8704282258714 | 53.811682 | 0.5737 | 0.567391 | 0.283696 |
| M8 | -12.3135781387198 | 53.529792 | -0.23 | 0.818506 | 0.409253 |
| M9 | 44.8369121538511 | 53.309205 | 0.8411 | 0.402183 | 0.201091 |
| M10 | 68.197242675119 | 53.65466 | 1.271 | 0.206471 | 0.103235 |
| M11 | -10.0188622503012 | 53.32958 | -0.1879 | 0.851337 | 0.425668 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.863673532333926 |
| R-squared | 0.745931970454162 |
| Adjusted R-squared | 0.717438359663974 |
| F-TEST (value) | 26.1789204585837 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 107 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 119.105356593924 |
| Sum Squared Residuals | 1517911.19872213 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 384 | 476.338571043963 | -92.3385710439632 |
| 2 | 367.6 | 440.612379858785 | -73.0123798587849 |
| 3 | 457.1 | 495.386970405603 | -38.2869704056027 |
| 4 | 429.4 | 530.416579121008 | -101.016579121008 |
| 5 | 442.2 | 484.228666003903 | -42.0286660039031 |
| 6 | 507.5 | 511.15218993891 | -3.6521899389097 |
| 7 | 348.5 | 406.685407174698 | -58.1854071746983 |
| 8 | 393.2 | 433.580629685761 | -40.3806296857615 |
| 9 | 426.8 | 495.252360550955 | -68.4523605509554 |
| 10 | 403 | 481.361600267352 | -78.3616002673522 |
| 11 | 454.8 | 430.174650939134 | 24.6253490608661 |
| 12 | 413 | 427.612669856919 | -14.6126698569194 |
| 13 | 388.9 | 486.069067058958 | -97.1690670589582 |
| 14 | 406.5 | 610.060613493607 | -203.560613493607 |
| 15 | 447.4 | 735.209296431685 | -287.809296431685 |
| 16 | 474.4 | 576.415287555519 | -102.015287555519 |
| 17 | 428.5 | 606.10558578765 | -177.605585787650 |
| 18 | 472.8 | 594.795140532433 | -121.995140532433 |
| 19 | 411 | 575.347338101238 | -164.347338101238 |
| 20 | 463.9 | 533.834224991747 | -69.9342249917467 |
| 21 | 497.3 | 673.251636138347 | -175.951636138347 |
| 22 | 474 | 631.348841872189 | -157.348841872189 |
| 23 | 518.1 | 644.93357813872 | -126.83357813872 |
| 24 | 566 | 531.011475996033 | 34.9885240039665 |
| 25 | 509.4 | 524.696187603323 | -15.2961876033231 |
| 26 | 445.1 | 480.812105819715 | -35.7121058197146 |
| 27 | 466.6 | 490.276002801768 | -23.6760028017682 |
| 28 | 600.5 | 632.537643359164 | -32.0376433591637 |
| 29 | 538.7 | 523.052362225339 | 15.6476377746615 |
| 30 | 548 | 515.476854834462 | 32.5231451655380 |
| 31 | 591.9 | 577.116519194873 | 14.7834808051268 |
| 32 | 547.3 | 516.633853248073 | 30.6661467519272 |
| 33 | 610.2 | 624.697443901919 | -14.4974439019185 |
| 34 | 621.6 | 641.963928433999 | -20.3639284339991 |
| 35 | 582.4 | 573.380031685036 | 9.01996831496368 |
| 36 | 635.8 | 654.36271335781 | -18.5627133578095 |
| 37 | 663.9 | 686.576257670929 | -22.6762576709286 |
| 38 | 624.2 | 614.188702712089 | 10.0112972879109 |
| 39 | 654.1 | 638.2974876359 | 15.8025123641007 |
| 40 | 723.5 | 767.978284860779 | -44.4782848607790 |
| 41 | 641.2 | 634.510771124346 | 6.68922887565443 |
| 42 | 565.5 | 619.367100166253 | -53.8671001662526 |
| 43 | 698.6 | 629.995376326854 | 68.6046236731464 |
| 44 | 651 | 639.100500063031 | 11.8994999369688 |
| 45 | 721.6 | 681.900965929451 | 39.6990340705487 |
| 46 | 643.5 | 624.86184452886 | 18.6381554711394 |
| 47 | 604 | 638.250005118321 | -34.2500051183209 |
| 48 | 618.2 | 697.314498797727 | -79.1144987977266 |
| 49 | 783.5 | 681.858441421235 | 101.641558578765 |
| 50 | 672.9 | 636.893193413739 | 36.0068065862613 |
| 51 | 726.7 | 705.13321783989 | 21.5667821601106 |
| 52 | 738.6 | 780.362552516224 | -41.7625525162243 |
| 53 | 692.2 | 657.411837503066 | 34.7881624969343 |
| 54 | 669.5 | 625.067794801299 | 44.4322051987012 |
| 55 | 546.2 | 658.007410309408 | -111.807410309408 |
| 56 | 715 | 711.047197870856 | 3.95280212914403 |
| 57 | 789.8 | 883.096171411169 | -93.2961714111688 |
| 58 | 684 | 747.328491343819 | -63.328491343819 |
| 59 | 639 | 579.080726320082 | 59.9192736799175 |
| 60 | 768.5 | 771.718392568933 | -3.21839256893334 |
| 61 | 643.8 | 732.083526912763 | -88.2835269127631 |
| 62 | 623 | 700.288849268994 | -77.288849268994 |
| 63 | 692.8 | 713.88083546953 | -21.0808354695295 |
| 64 | 936.5 | 852.604113839655 | 83.8958861603452 |
| 65 | 795.9 | 784.891164083323 | 11.0088359166765 |
| 66 | 695.7 | 732.201538804754 | -36.5015388047536 |
| 67 | 648.3 | 854.288223864362 | -205.988223864362 |
| 68 | 675.2 | 848.650171820247 | -173.450171820247 |
| 69 | 826.5 | 1024.92552241758 | -198.425522417577 |
| 70 | 742.4 | 926.310645316563 | -183.910645316563 |
| 71 | 793.9 | 1358.50328590485 | -564.60328590485 |
| 72 | 685.3 | 921.410770658164 | -236.110770658164 |
| 73 | 756.1 | 694.537572592286 | 61.5624274077138 |
| 74 | 704 | 703.630635779194 | 0.36936422080643 |
| 75 | 860.6 | 764.597360153734 | 96.0026398462664 |
| 76 | 795.9 | 810.045479753879 | -14.1454797538787 |
| 77 | 816.7 | 793.638781712963 | 23.0612182870367 |
| 78 | 777.9 | 717.163499508856 | 60.7365004911442 |
| 79 | 746.4 | 615.252200546562 | 131.147799453438 |
| 80 | 694.7 | 609.909012018053 | 84.7909879819469 |
| 81 | 909.2 | 758.565479986969 | 150.634520013031 |
| 82 | 783.6 | 655.134498797727 | 128.465501202273 |
| 83 | 730.4 | 621.934223921464 | 108.465776078536 |
| 84 | 847.7 | 707.634721843931 | 140.065278156069 |
| 85 | 758.7 | 660.038541266403 | 98.661458733597 |
| 86 | 839.2 | 687.216566743802 | 151.983433256198 |
| 87 | 784.8 | 769.511752080498 | 15.2882479195023 |
| 88 | 906.1 | 769.944041631485 | 136.155958368515 |
| 89 | 838.2 | 789.019253301805 | 49.1807466981948 |
| 90 | 729 | 693.672706098924 | 35.327293901076 |
| 91 | 768.1 | 713.245175566236 | 54.8548244337645 |
| 92 | 710.5 | 699.842384277834 | 10.657615722166 |
| 93 | 863 | 749.031559649047 | 113.968440350953 |
| 94 | 778.3 | 702.017797779055 | 76.2822022209449 |
| 95 | 827.7 | 639.429459180744 | 188.270540819256 |
| 96 | 853.1 | 801.597895483658 | 51.5021045163417 |
| 97 | 859.3 | 814.252159928257 | 45.0478400717431 |
| 98 | 779.2 | 713.950858825398 | 65.2491411746021 |
| 99 | 724.6 | 695.009570470756 | 29.5904295292443 |
| 100 | 829.2 | 794.41771342677 | 34.7822865732308 |
| 101 | 862.9 | 822.63369408087 | 40.2663059191292 |
| 102 | 601.6 | 668.216155918287 | -66.6161559182866 |
| 103 | 964.9 | 740.667482517578 | 224.232517482422 |
| 104 | 766.3 | 679.595089539567 | 86.7049104604335 |
| 105 | 847.8 | 787.953543709018 | 59.846456290982 |
| 106 | 992.7 | 755.486381942247 | 237.213618057753 |
| 107 | 865.3 | 664.197994491635 | 201.102005508365 |
| 108 | 1054.1 | 886.420300139605 | 167.679699860395 |
| 109 | 972.5 | 963.649674501882 | 8.8503254981181 |
| 110 | 857.4 | 731.446094084678 | 125.953905915322 |
| 111 | 1043.3 | 850.697506710639 | 192.602493289361 |
| 112 | 1061 | 980.378303935518 | 80.6216960644816 |
| 113 | 989.4 | 950.407884176734 | 38.9921158232656 |
| 114 | 963.2 | 853.587019395824 | 109.612980604176 |
| 115 | 1181.9 | 1135.19486639819 | 46.7051336018092 |
| 116 | 1256.4 | 1201.30693648483 | 55.0930635151694 |
| 117 | 1492.7 | 1306.22531630555 | 186.474683694453 |
| 118 | 1360.8 | 1318.08596971819 | 42.7140302818122 |
| 119 | 1342.8 | 1208.51604430001 | 134.283955699987 |
| 120 | 1464 | 1506.61656129722 | -42.616561297219 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0098860822815344 | 0.0197721645630688 | 0.990113917718466 |
| 17 | 0.00211227907396922 | 0.00422455814793844 | 0.99788772092603 |
| 18 | 0.000737482989050658 | 0.00147496597810132 | 0.99926251701095 |
| 19 | 0.00049123652548627 | 0.00098247305097254 | 0.999508763474514 |
| 20 | 0.000343221421122599 | 0.000686442842245198 | 0.999656778578877 |
| 21 | 0.000154019584361669 | 0.000308039168723339 | 0.999845980415638 |
| 22 | 6.83904242630176e-05 | 0.000136780848526035 | 0.999931609575737 |
| 23 | 1.89754909607471e-05 | 3.79509819214942e-05 | 0.99998102450904 |
| 24 | 0.000167366770440008 | 0.000334733540880016 | 0.99983263322956 |
| 25 | 0.000475434028639092 | 0.000950868057278185 | 0.999524565971361 |
| 26 | 0.000376972553655711 | 0.000753945107311421 | 0.999623027446344 |
| 27 | 0.000205714982051149 | 0.000411429964102297 | 0.999794285017949 |
| 28 | 0.000564666484900926 | 0.00112933296980185 | 0.999435333515099 |
| 29 | 0.000777601424771632 | 0.00155520284954326 | 0.999222398575228 |
| 30 | 0.000523865105022342 | 0.00104773021004468 | 0.999476134894978 |
| 31 | 0.00281462249363718 | 0.00562924498727436 | 0.997185377506363 |
| 32 | 0.00277099959469696 | 0.00554199918939392 | 0.997229000405303 |
| 33 | 0.00378755538086966 | 0.00757511076173932 | 0.99621244461913 |
| 34 | 0.00573274088172983 | 0.0114654817634597 | 0.99426725911827 |
| 35 | 0.0042891077820156 | 0.0085782155640312 | 0.995710892217984 |
| 36 | 0.00291400848530788 | 0.00582801697061577 | 0.997085991514692 |
| 37 | 0.00376055267165271 | 0.00752110534330543 | 0.996239447328347 |
| 38 | 0.00575745143559892 | 0.0115149028711978 | 0.9942425485644 |
| 39 | 0.00819124510378489 | 0.0163824902075698 | 0.991808754896215 |
| 40 | 0.00694063560977714 | 0.0138812712195543 | 0.993059364390223 |
| 41 | 0.00597598545748317 | 0.0119519709149663 | 0.994024014542517 |
| 42 | 0.00386454708514244 | 0.00772909417028488 | 0.996135452914858 |
| 43 | 0.00545925502974195 | 0.0109185100594839 | 0.994540744970258 |
| 44 | 0.00380911480998602 | 0.00761822961997204 | 0.996190885190014 |
| 45 | 0.00422817451301952 | 0.00845634902603905 | 0.99577182548698 |
| 46 | 0.00380219302826786 | 0.00760438605653571 | 0.996197806971732 |
| 47 | 0.0024985931843985 | 0.004997186368797 | 0.997501406815602 |
| 48 | 0.00197664023615277 | 0.00395328047230554 | 0.998023359763847 |
| 49 | 0.0031508630015224 | 0.0063017260030448 | 0.996849136998478 |
| 50 | 0.00293385572762185 | 0.00586771145524369 | 0.997066144272378 |
| 51 | 0.00259277913863388 | 0.00518555827726775 | 0.997407220861366 |
| 52 | 0.00183992436574145 | 0.0036798487314829 | 0.998160075634259 |
| 53 | 0.00138575413822938 | 0.00277150827645876 | 0.99861424586177 |
| 54 | 0.00100427916375323 | 0.00200855832750645 | 0.998995720836247 |
| 55 | 0.00103643902055473 | 0.00207287804110945 | 0.998963560979445 |
| 56 | 0.000627925728889727 | 0.00125585145777945 | 0.99937207427111 |
| 57 | 0.000510048837177101 | 0.00102009767435420 | 0.999489951162823 |
| 58 | 0.000382477423432174 | 0.000764954846864347 | 0.999617522576568 |
| 59 | 0.000291955252886069 | 0.000583910505772139 | 0.999708044747114 |
| 60 | 0.000176832261105487 | 0.000353664522210975 | 0.999823167738894 |
| 61 | 0.00014927029289483 | 0.00029854058578966 | 0.999850729707105 |
| 62 | 0.000117781509677019 | 0.000235563019354038 | 0.999882218490323 |
| 63 | 8.34090482877503e-05 | 0.000166818096575501 | 0.999916590951712 |
| 64 | 9.98152092942444e-05 | 0.000199630418588489 | 0.999900184790706 |
| 65 | 5.88863083112e-05 | 0.0001177726166224 | 0.999941113691689 |
| 66 | 3.45783451538429e-05 | 6.91566903076857e-05 | 0.999965421654846 |
| 67 | 0.000159621445188868 | 0.000319242890377736 | 0.999840378554811 |
| 68 | 0.000346469106507081 | 0.000692938213014162 | 0.999653530893493 |
| 69 | 0.000981588723303047 | 0.00196317744660609 | 0.999018411276697 |
| 70 | 0.00257745992033896 | 0.00515491984067792 | 0.99742254007966 |
| 71 | 0.812135472941199 | 0.375729054117602 | 0.187864527058801 |
| 72 | 0.98615078845511 | 0.0276984230897796 | 0.0138492115448898 |
| 73 | 0.983455819095542 | 0.0330883618089158 | 0.0165441809044579 |
| 74 | 0.98711502377197 | 0.0257699524560583 | 0.0128849762280291 |
| 75 | 0.987871308089168 | 0.0242573838216642 | 0.0121286919108321 |
| 76 | 0.988572475092564 | 0.0228550498148723 | 0.0114275249074362 |
| 77 | 0.9849126608295 | 0.0301746783410004 | 0.0150873391705002 |
| 78 | 0.98123012469851 | 0.0375397506029803 | 0.0187698753014901 |
| 79 | 0.981413144893563 | 0.0371737102128746 | 0.0185868551064373 |
| 80 | 0.975821855428242 | 0.0483562891435153 | 0.0241781445717577 |
| 81 | 0.978254485387048 | 0.0434910292259039 | 0.0217455146129520 |
| 82 | 0.976190706655359 | 0.047618586689283 | 0.0238092933446415 |
| 83 | 0.978464460240908 | 0.043071079518184 | 0.021535539759092 |
| 84 | 0.977601085786282 | 0.0447978284274351 | 0.0223989142137175 |
| 85 | 0.972291015144632 | 0.0554179697107368 | 0.0277089848553684 |
| 86 | 0.971595534459586 | 0.0568089310808274 | 0.0284044655404137 |
| 87 | 0.968755298087912 | 0.0624894038241762 | 0.0312447019120881 |
| 88 | 0.96606651304195 | 0.0678669739161024 | 0.0339334869580512 |
| 89 | 0.950713277257794 | 0.0985734454844128 | 0.0492867227422064 |
| 90 | 0.927671718600997 | 0.144656562798007 | 0.0723282813990033 |
| 91 | 0.922286251586765 | 0.155427496826469 | 0.0777137484132347 |
| 92 | 0.904496314235518 | 0.191007371528965 | 0.0955036857644824 |
| 93 | 0.877914899949807 | 0.244170200100386 | 0.122085100050193 |
| 94 | 0.868315138225212 | 0.263369723549576 | 0.131684861774788 |
| 95 | 0.84110037427498 | 0.317799251450041 | 0.158899625725021 |
| 96 | 0.796535896614686 | 0.406928206770629 | 0.203464103385314 |
| 97 | 0.725329036522073 | 0.549341926955854 | 0.274670963477927 |
| 98 | 0.657000770636565 | 0.68599845872687 | 0.342999229363435 |
| 99 | 0.70675659864255 | 0.5864868027149 | 0.29324340135745 |
| 100 | 0.628375761336833 | 0.743248477326334 | 0.371624238663167 |
| 101 | 0.513175464543044 | 0.973649070913913 | 0.486824535456956 |
| 102 | 0.622417625967872 | 0.755164748064256 | 0.377582374032128 |
| 103 | 0.59195735239169 | 0.816085295216621 | 0.408042647608310 |
| 104 | 0.442395365607659 | 0.884790731215318 | 0.557604634392341 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 48 | 0.539325842696629 | NOK |
| 5% type I error level | 68 | 0.764044943820225 | NOK |
| 10% type I error level | 73 | 0.820224719101124 | NOK |
