| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 166.003349213917 -0.186646203096086X[t] -0.489517076251396M1[t] + 2.20866906927609M2[t] + 5.42220860381535M3[t] + 3.5820772390031M4[t] + 2.75521474069136M5[t] + 4.29262827771532M6[t] + 8.38857622241007M7[t] + 7.53675875273427M8[t] + 6.99725709994741M9[t] + 5.83788602922274M10[t] + 3.84606317907899M11[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) | 166.003349213917 | 12.458667 | 13.3243 | 0 | 0 |
| X | -0.186646203096086 | 0.043866 | -4.255 | 3.9e-05 | 2e-05 |
| M1 | -0.489517076251396 | 12.296727 | -0.0398 | 0.968306 | 0.484153 |
| M2 | 2.20866906927609 | 12.550217 | 0.176 | 0.860574 | 0.430287 |
| M3 | 5.42220860381535 | 12.541467 | 0.4323 | 0.666198 | 0.333099 |
| M4 | 3.5820772390031 | 12.542338 | 0.2856 | 0.775633 | 0.387817 |
| M5 | 2.75521474069136 | 12.543435 | 0.2197 | 0.82648 | 0.41324 |
| M6 | 4.29262827771532 | 12.540624 | 0.3423 | 0.732671 | 0.366336 |
| M7 | 8.38857622241007 | 12.538506 | 0.669 | 0.504648 | 0.252324 |
| M8 | 7.53675875273427 | 12.537392 | 0.6011 | 0.548776 | 0.274388 |
| M9 | 6.99725709994741 | 12.535855 | 0.5582 | 0.577667 | 0.288834 |
| M10 | 5.83788602922274 | 12.536008 | 0.4657 | 0.642205 | 0.321103 |
| M11 | 3.84606317907899 | 12.537174 | 0.3068 | 0.7595 | 0.37975 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.356108948662137 |
| R-squared | 0.126813583317253 |
| Adjusted R-squared | 0.0474329999824576 |
| F-TEST (value) | 1.59753907051054 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 132 |
| p-value | 0.0995913824155088 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 30.7064059990919 |
| Sum Squared Residuals | 124460.604758301 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 100 | 146.849211828057 | -46.8492118280574 |
| 2 | 103.53 | 149.058384921473 | -45.5283849214725 |
| 3 | 108.36 | 151.338693440531 | -42.9786934405314 |
| 4 | 115.2 | 150.275010280599 | -35.0750102805989 |
| 5 | 123.51 | 149.420150851823 | -25.9101508518227 |
| 6 | 132.87 | 150.492815343137 | -17.6228153431374 |
| 7 | 130.55 | 154.396517698643 | -23.8465176986432 |
| 8 | 136.68 | 153.229268145735 | -16.5492681457350 |
| 9 | 140.63 | 151.922650598223 | -11.2926505982233 |
| 10 | 143.47 | 151.431472934583 | -7.96147293458257 |
| 11 | 124.1 | 149.551637806296 | -25.4516378062965 |
| 12 | 111.49 | 145.317350524778 | -33.8273505247776 |
| 13 | 119.93 | 144.805435904155 | -24.8754359041547 |
| 14 | 131.79 | 146.755170775267 | -14.9651707752669 |
| 15 | 136.61 | 148.944022654809 | -12.3340226548086 |
| 16 | 141.79 | 146.648474554442 | -4.85847455444195 |
| 17 | 142.23 | 146.280761715747 | -4.05076171574658 |
| 18 | 146.74 | 147.569935802653 | -0.829935802652725 |
| 19 | 154.85 | 151.475504620189 | 3.37449537981052 |
| 20 | 148.44 | 150.149605794650 | -1.70960579464963 |
| 21 | 154.18 | 148.98297289946 | 5.19702710054009 |
| 22 | 149.1 | 147.967319405119 | 1.13268059488078 |
| 23 | 152.22 | 146.421580980375 | 5.79841901962488 |
| 24 | 149.34 | 142.19475954698 | 7.14524045301989 |
| 25 | 160.94 | 141.641782761676 | 19.2982172383240 |
| 26 | 176.16 | 143.808027228380 | 32.3519727716203 |
| 27 | 195.12 | 146.495224470188 | 48.624775529812 |
| 28 | 186.07 | 144.233272686379 | 41.8367273136214 |
| 29 | 200.78 | 143.512798523832 | 57.2672014761684 |
| 30 | 208.15 | 144.913960332595 | 63.2360396674045 |
| 31 | 209.56 | 148.425705661599 | 61.1342943384005 |
| 32 | 203.33 | 147.850124572506 | 55.4798754274942 |
| 33 | 198.84 | 147.133309026778 | 51.7066909732223 |
| 34 | 200.63 | 146.024332430889 | 54.605667569111 |
| 35 | 206.47 | 144.467395233959 | 62.0026047660409 |
| 36 | 196.68 | 140.440285237877 | 56.2397147621231 |
| 37 | 203.81 | 139.919038307099 | 63.8909616929008 |
| 38 | 190.18 | 142.329789299859 | 47.8502107001413 |
| 39 | 187.5 | 144.727684926868 | 42.7723150731319 |
| 40 | 187.62 | 142.712106131146 | 44.9078938688545 |
| 41 | 168.92 | 141.864712550493 | 27.0552874495068 |
| 42 | 164.78 | 143.237877428793 | 21.5421225712074 |
| 43 | 175.98 | 146.811216004818 | 29.1687839951817 |
| 44 | 174.7 | 145.593571977074 | 29.1064280229258 |
| 45 | 166.95 | 144.423206157823 | 22.5267938421775 |
| 46 | 161.76 | 143.549403777835 | 18.2105962221651 |
| 47 | 149.65 | 142.031662283555 | 7.61833771644482 |
| 48 | 137.42 | 137.129181594952 | 0.290818405047642 |
| 49 | 142.6 | 136.600468816051 | 5.99953118394922 |
| 50 | 146.94 | 138.520340294668 | 8.41965970533243 |
| 51 | 152.52 | 140.067129235559 | 12.4528707644412 |
| 52 | 147.47 | 138.943719290635 | 8.52628070936449 |
| 53 | 146.15 | 138.191515273562 | 7.9584847264378 |
| 54 | 152.04 | 139.781189747453 | 12.2588102525469 |
| 55 | 144.42 | 143.384391715974 | 1.03560828402583 |
| 56 | 138.15 | 142.528841322236 | -4.37884132223643 |
| 57 | 125.94 | 141.261419477375 | -15.3214194773748 |
| 58 | 112.61 | 140.602260230948 | -27.9922602309477 |
| 59 | 111.48 | 139.090118122761 | -27.6101181227609 |
| 60 | 95.25 | 134.361218403037 | -39.1112184030374 |
| 61 | 105.38 | 134.125540162997 | -28.7455401629967 |
| 62 | 109.59 | 136.024880559273 | -26.4348805592729 |
| 63 | 99.07 | 138.237996445217 | -39.1679964452172 |
| 64 | 92.07 | 136.851415353928 | -44.7814153539284 |
| 65 | 89.1 | 135.976024842812 | -46.8760248428117 |
| 66 | 86.36 | 136.923636378052 | -50.563636378052 |
| 67 | 95.39 | 140.704152239514 | -45.3141522395143 |
| 68 | 95.27 | 139.437980198965 | -44.1679801989653 |
| 69 | 98.56 | 138.334807012828 | -39.7748070128282 |
| 70 | 101.79 | 137.653250222029 | -35.8632502220295 |
| 71 | 102.02 | 135.859272347168 | -33.8392723471676 |
| 72 | 98.21 | 131.393543773810 | -33.1835437738096 |
| 73 | 104.42 | 130.930157165992 | -26.5101571659917 |
| 74 | 105.62 | 133.019876689426 | -27.3998766894259 |
| 75 | 109.46 | 135.610017905624 | -26.1500179056243 |
| 76 | 110.94 | 134.006927218744 | -23.0669272187440 |
| 77 | 113.09 | 133.241657967454 | -20.151657967454 |
| 78 | 109.58 | 134.222865819252 | -24.6428658192516 |
| 79 | 111.41 | 138.081773086014 | -26.6717730860144 |
| 80 | 109.83 | 137.065706957614 | -27.235706957614 |
| 81 | 110.58 | 135.936403303044 | -25.3564033030435 |
| 82 | 109.04 | 134.959945511353 | -25.919945511353 |
| 83 | 107.8 | 133.524328346436 | -25.7243283464356 |
| 84 | 109.79 | 128.804760936867 | -19.0147609368669 |
| 85 | 110.76 | 128.276048157965 | -17.5160481579653 |
| 86 | 112.64 | 130.307907358440 | -17.6679073584398 |
| 87 | 114.17 | 133.282539753016 | -19.1125397530161 |
| 88 | 115.99 | 131.048584899671 | -15.0585848996711 |
| 89 | 119.01 | 130.214256553235 | -11.2042565532355 |
| 90 | 117.92 | 131.456769089368 | -13.5367690893676 |
| 91 | 115.92 | 135.181291089901 | -19.2612910899012 |
| 92 | 120.75 | 133.892721504981 | -13.1427215049805 |
| 93 | 124.94 | 129.825606613678 | -4.88560661367766 |
| 94 | 129.17 | 128.550514897033 | 0.619485102966584 |
| 95 | 128.14 | 127.290345163026 | 0.849654836973676 |
| 96 | 134.18 | 122.710762405780 | 11.4692375942203 |
| 97 | 131.74 | 121.861018157553 | 9.87898184244714 |
| 98 | 134.32 | 124.172846662671 | 10.1471533373285 |
| 99 | 137.8 | 126.085462161631 | 11.7145378383690 |
| 100 | 141.79 | 124.641020747382 | 17.1489792526175 |
| 101 | 142.75 | 123.900015502495 | 18.8499844975051 |
| 102 | 144.3 | 125.136928652534 | 19.1630713474658 |
| 103 | 145.49 | 128.363105290801 | 17.1268947091989 |
| 104 | 138.21 | 127.289178839441 | 10.920821160559 |
| 105 | 139.02 | 126.158008722840 | 12.8619912771605 |
| 106 | 141.91 | 125.532445792970 | 16.3775542070303 |
| 107 | 144.95 | 124.354400388325 | 20.5955996116751 |
| 108 | 146.11 | 119.567640345642 | 26.5423596543584 |
| 109 | 150.96 | 119.406620586839 | 31.5533794131607 |
| 110 | 148.2 | 121.459010869654 | 26.7409891303456 |
| 111 | 152.12 | 122.74262866418 | 29.3773713358199 |
| 112 | 154.74 | 121.762936295641 | 32.9770637043592 |
| 113 | 150.8 | 121.102188918085 | 29.6978110819154 |
| 114 | 152.6 | 121.853821940074 | 30.746178059926 |
| 115 | 158.74 | 125.744459061363 | 32.9955409386369 |
| 116 | 161.83 | 124.601473514857 | 37.2285264851426 |
| 117 | 162.4 | 123.111942688311 | 39.2880573116886 |
| 118 | 156.11 | 122.277336010974 | 33.8326639890261 |
| 119 | 154.93 | 121.509912253141 | 33.4200877468595 |
| 120 | 157.18 | 116.534639545330 | 40.6453604546698 |
| 121 | 159.85 | 116.578930609934 | 43.2710693900664 |
| 122 | 154.4 | 118.741442152575 | 35.6585578474247 |
| 123 | 151.57 | 121.258791349566 | 30.3112086504338 |
| 124 | 133.34 | 119.950601663578 | 13.3893983364222 |
| 125 | 131.2 | 119.987911085601 | 11.2120889143990 |
| 126 | 124.17 | 120.797404430550 | 3.37259556944983 |
| 127 | 133.19 | 125.255446009251 | 7.93455399074867 |
| 128 | 130.94 | 124.002339202919 | 6.93766079708106 |
| 129 | 119.58 | 122.839439231791 | -3.25943923179116 |
| 130 | 118.55 | 122.94926234212 | -4.39926234211986 |
| 131 | 119.96 | 121.664828601710 | -1.70482860171029 |
| 132 | 108.42 | 116.501043228773 | -8.08104322877292 |
| 133 | 95.93 | 115.615836201958 | -19.6858362019578 |
| 134 | 88.83 | 118.002323188315 | -29.1723231883148 |
| 135 | 84.98 | 120.489808992810 | -35.5098089928103 |
| 136 | 81.61 | 117.555930877855 | -35.945930877855 |
| 137 | 72.84 | 116.688006214862 | -43.8480062148621 |
| 138 | 74.72 | 117.842795035539 | -43.1227950355391 |
| 139 | 83.4 | 121.07643752193 | -37.6764375219299 |
| 140 | 87.42 | 119.909187969022 | -32.4891879690218 |
| 141 | 86.33 | 118.020234267850 | -31.6902342678502 |
| 142 | 94.28 | 116.922456444147 | -22.6424564441472 |
| 143 | 98.81 | 114.764518473248 | -15.954518473248 |
| 144 | 100.96 | 110.074814456175 | -9.1148144561747 |
| 145 | 99.14 | 108.849911339725 | -9.70991133972471 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.00509233305648633 | 0.0101846661129727 | 0.994907666943514 |
| 17 | 0.00180620093478409 | 0.00361240186956817 | 0.998193799065216 |
| 18 | 0.000672342666635313 | 0.00134468533327063 | 0.999327657333365 |
| 19 | 0.000110962808286424 | 0.000221925616572848 | 0.999889037191714 |
| 20 | 5.5992035685428e-05 | 0.000111984071370856 | 0.999944007964315 |
| 21 | 1.48336367168753e-05 | 2.96672734337505e-05 | 0.999985166363283 |
| 22 | 1.79599706575509e-05 | 3.59199413151018e-05 | 0.999982040029342 |
| 23 | 5.16463509976646e-06 | 1.03292701995329e-05 | 0.9999948353649 |
| 24 | 4.19030120846973e-06 | 8.38060241693947e-06 | 0.999995809698792 |
| 25 | 6.8028838130413e-06 | 1.36057676260826e-05 | 0.999993197116187 |
| 26 | 1.60565182806383e-05 | 3.21130365612766e-05 | 0.99998394348172 |
| 27 | 0.000186050844015828 | 0.000372101688031656 | 0.999813949155984 |
| 28 | 0.000106358134884494 | 0.000212716269768988 | 0.999893641865115 |
| 29 | 0.000104497615522017 | 0.000208995231044035 | 0.999895502384478 |
| 30 | 0.000113548016393769 | 0.000227096032787537 | 0.999886451983606 |
| 31 | 7.9917878385504e-05 | 0.000159835756771008 | 0.999920082121615 |
| 32 | 5.73890498504845e-05 | 0.000114778099700969 | 0.99994261095015 |
| 33 | 3.57107760842477e-05 | 7.14215521684954e-05 | 0.999964289223916 |
| 34 | 2.22683153444217e-05 | 4.45366306888435e-05 | 0.999977731684656 |
| 35 | 3.57784326221804e-05 | 7.15568652443608e-05 | 0.999964221567378 |
| 36 | 5.18181378728402e-05 | 0.000103636275745680 | 0.999948181862127 |
| 37 | 6.20528874441142e-05 | 0.000124105774888228 | 0.999937947112556 |
| 38 | 4.13713099282516e-05 | 8.27426198565031e-05 | 0.999958628690072 |
| 39 | 3.96969139579014e-05 | 7.93938279158028e-05 | 0.999960303086042 |
| 40 | 4.63053587485512e-05 | 9.26107174971023e-05 | 0.999953694641252 |
| 41 | 0.000409243119115279 | 0.000818486238230558 | 0.999590756880885 |
| 42 | 0.00329068043419809 | 0.00658136086839618 | 0.996709319565802 |
| 43 | 0.00924280164649974 | 0.0184856032929995 | 0.9907571983535 |
| 44 | 0.0207402360159420 | 0.0414804720318841 | 0.979259763984058 |
| 45 | 0.052366849786809 | 0.104733699573618 | 0.94763315021319 |
| 46 | 0.111067131906831 | 0.222134263813661 | 0.88893286809317 |
| 47 | 0.203206447600369 | 0.406412895200738 | 0.796793552399631 |
| 48 | 0.34356415310688 | 0.68712830621376 | 0.65643584689312 |
| 49 | 0.465311445898213 | 0.930622891796425 | 0.534688554101787 |
| 50 | 0.56446264280424 | 0.87107471439152 | 0.43553735719576 |
| 51 | 0.66744494976783 | 0.665110100464339 | 0.332555050232170 |
| 52 | 0.738978439792263 | 0.522043120415474 | 0.261021560207737 |
| 53 | 0.797406315863923 | 0.405187368272154 | 0.202593684136077 |
| 54 | 0.843717017812928 | 0.312565964374144 | 0.156282982187072 |
| 55 | 0.886384166201414 | 0.227231667597172 | 0.113615833798586 |
| 56 | 0.915238134620782 | 0.169523730758436 | 0.0847618653792182 |
| 57 | 0.942324769482455 | 0.115350461035090 | 0.0576752305175452 |
| 58 | 0.964642371080253 | 0.0707152578394944 | 0.0353576289197472 |
| 59 | 0.973874440200112 | 0.0522511195997756 | 0.0261255597998878 |
| 60 | 0.982755174086857 | 0.0344896518262863 | 0.0172448259131431 |
| 61 | 0.984433087256214 | 0.0311338254875715 | 0.0155669127437857 |
| 62 | 0.985120606954826 | 0.0297587860903491 | 0.0148793930451746 |
| 63 | 0.989022911818257 | 0.0219541763634867 | 0.0109770881817434 |
| 64 | 0.99250627505099 | 0.01498744989802 | 0.00749372494901 |
| 65 | 0.994950208659743 | 0.0100995826805138 | 0.0050497913402569 |
| 66 | 0.996873070555122 | 0.00625385888975652 | 0.00312692944487826 |
| 67 | 0.997516636606454 | 0.00496672678709285 | 0.00248336339354643 |
| 68 | 0.997843025883327 | 0.00431394823334543 | 0.00215697411667272 |
| 69 | 0.997789797026545 | 0.00442040594690991 | 0.00221020297345495 |
| 70 | 0.997471666049222 | 0.00505666790155573 | 0.00252833395077786 |
| 71 | 0.99699121791874 | 0.00601756416252166 | 0.00300878208126083 |
| 72 | 0.996462899371485 | 0.00707420125702954 | 0.00353710062851477 |
| 73 | 0.995381966077317 | 0.0092360678453651 | 0.00461803392268255 |
| 74 | 0.994198770810085 | 0.0116024583798298 | 0.0058012291899149 |
| 75 | 0.992573870321305 | 0.0148522593573901 | 0.00742612967869505 |
| 76 | 0.990205311968094 | 0.0195893760638125 | 0.00979468803190626 |
| 77 | 0.986811624918182 | 0.0263767501636366 | 0.0131883750818183 |
| 78 | 0.983074661383093 | 0.0338506772338142 | 0.0169253386169071 |
| 79 | 0.979149196815788 | 0.0417016063684234 | 0.0208508031842117 |
| 80 | 0.975144390535447 | 0.0497112189291053 | 0.0248556094645527 |
| 81 | 0.970289243968973 | 0.0594215120620549 | 0.0297107560310274 |
| 82 | 0.96625815504318 | 0.0674836899136405 | 0.0337418449568202 |
| 83 | 0.963913700518457 | 0.0721725989630858 | 0.0360862994815429 |
| 84 | 0.961985280835943 | 0.0760294383281144 | 0.0380147191640572 |
| 85 | 0.960538005097326 | 0.0789239898053483 | 0.0394619949026742 |
| 86 | 0.95951701947137 | 0.0809659610572602 | 0.0404829805286301 |
| 87 | 0.96090215556564 | 0.078195688868721 | 0.0390978444343605 |
| 88 | 0.960462654941324 | 0.0790746901173524 | 0.0395373450586762 |
| 89 | 0.95782016424137 | 0.0843596715172603 | 0.0421798357586301 |
| 90 | 0.958207563245096 | 0.0835848735098076 | 0.0417924367549038 |
| 91 | 0.968775828888697 | 0.0624483422226069 | 0.0312241711113035 |
| 92 | 0.978093680649422 | 0.0438126387011558 | 0.0219063193505779 |
| 93 | 0.979503223158982 | 0.0409935536820365 | 0.0204967768410182 |
| 94 | 0.979800486099535 | 0.0403990278009299 | 0.0201995139004649 |
| 95 | 0.982644338148 | 0.0347113237040007 | 0.0173556618520004 |
| 96 | 0.985330121962633 | 0.0293397560747345 | 0.0146698780373672 |
| 97 | 0.988172354054467 | 0.0236552918910658 | 0.0118276459455329 |
| 98 | 0.987737835658438 | 0.0245243286831238 | 0.0122621643415619 |
| 99 | 0.986140171958277 | 0.0277196560834455 | 0.0138598280417227 |
| 100 | 0.982872330742905 | 0.0342553385141899 | 0.0171276692570949 |
| 101 | 0.977446353101748 | 0.0451072937965043 | 0.0225536468982522 |
| 102 | 0.970300673905117 | 0.0593986521897652 | 0.0296993260948826 |
| 103 | 0.961563921732473 | 0.0768721565350547 | 0.0384360782675274 |
| 104 | 0.954508796436477 | 0.0909824071270458 | 0.0454912035635229 |
| 105 | 0.945924273343235 | 0.108151453313529 | 0.0540757266567647 |
| 106 | 0.935329882853474 | 0.129340234293052 | 0.0646701171465258 |
| 107 | 0.925579219883836 | 0.148841560232328 | 0.074420780116164 |
| 108 | 0.91583714637401 | 0.168325707251981 | 0.0841628536259903 |
| 109 | 0.903714799765374 | 0.192570400469252 | 0.0962852002346258 |
| 110 | 0.875809071849942 | 0.248381856300117 | 0.124190928150058 |
| 111 | 0.850008965606489 | 0.299982068787022 | 0.149991034393511 |
| 112 | 0.824124888114799 | 0.351750223770402 | 0.175875111885201 |
| 113 | 0.799144197229694 | 0.401711605540612 | 0.200855802770306 |
| 114 | 0.78639536328644 | 0.427209273427122 | 0.213604636713561 |
| 115 | 0.76801609634142 | 0.463967807317159 | 0.231983903658580 |
| 116 | 0.756258887414767 | 0.487482225170465 | 0.243741112585233 |
| 117 | 0.767731898374282 | 0.464536203251435 | 0.232268101625718 |
| 118 | 0.756879732482047 | 0.486240535035905 | 0.243120267517953 |
| 119 | 0.716468435839013 | 0.567063128321973 | 0.283531564160987 |
| 120 | 0.699722736538758 | 0.600554526922485 | 0.300277263461242 |
| 121 | 0.702175103036127 | 0.595649793927747 | 0.297824896963873 |
| 122 | 0.795434946886522 | 0.409130106226956 | 0.204565053113478 |
| 123 | 0.893543315567906 | 0.212913368864188 | 0.106456684432094 |
| 124 | 0.901759076810299 | 0.196481846379402 | 0.098240923189701 |
| 125 | 0.926946365746793 | 0.146107268506414 | 0.0730536342532068 |
| 126 | 0.939939957259897 | 0.120120085480206 | 0.0600600427401028 |
| 127 | 0.953542053838166 | 0.0929158923236677 | 0.0464579461618338 |
| 128 | 0.967765304147628 | 0.0644693917047434 | 0.0322346958523717 |
| 129 | 0.964360944112966 | 0.071278111774068 | 0.035639055887034 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 34 | 0.298245614035088 | NOK |
| 5% type I error level | 60 | 0.526315789473684 | NOK |
| 10% type I error level | 79 | 0.692982456140351 | NOK |
