| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.67058536444880 -0.00940480827711062X[t] + 1.4664080020596Y1[t] -0.578726593157617Y2[t] + 0.0892563503721176M1[t] + 0.0340631621848652M2[t] + 0.00541120381002455M3[t] + 0.174002531815138M4[t] + 0.646315973961958M5[t] -0.199110925542800M6[t] + 0.148855305434789M7[t] + 0.174528724554786M8[t] + 0.0891393379223372M9[t] + 0.27550884188137M10[t] + 0.244894451851841M11[t] + 0.000867678569418552t + 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) | 1.67058536444880 | 0.602183 | 2.7742 | 0.006903 | 0.003451 |
| X | -0.00940480827711062 | 0.005569 | -1.6887 | 0.09523 | 0.047615 |
| Y1 | 1.4664080020596 | 0.094486 | 15.5198 | 0 | 0 |
| Y2 | -0.578726593157617 | 0.093488 | -6.1904 | 0 | 0 |
| M1 | 0.0892563503721176 | 0.1261 | 0.7078 | 0.481139 | 0.24057 |
| M2 | 0.0340631621848652 | 0.1159 | 0.2939 | 0.769605 | 0.384802 |
| M3 | 0.00541120381002455 | 0.116226 | 0.0466 | 0.962983 | 0.481492 |
| M4 | 0.174002531815138 | 0.130926 | 1.329 | 0.187668 | 0.093834 |
| M5 | 0.646315973961958 | 0.13704 | 4.7163 | 1e-05 | 5e-06 |
| M6 | -0.199110925542800 | 0.12375 | -1.609 | 0.111612 | 0.055806 |
| M7 | 0.148855305434789 | 0.123293 | 1.2073 | 0.230907 | 0.115453 |
| M8 | 0.174528724554786 | 0.129559 | 1.3471 | 0.181801 | 0.090901 |
| M9 | 0.0891393379223372 | 0.113498 | 0.7854 | 0.434579 | 0.217289 |
| M10 | 0.27550884188137 | 0.113471 | 2.428 | 0.017455 | 0.008728 |
| M11 | 0.244894451851841 | 0.110375 | 2.2187 | 0.029374 | 0.014687 |
| t | 0.000867678569418552 | 0.001064 | 0.8156 | 0.417181 | 0.20859 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.96797577325124 |
| R-squared | 0.936977097601335 |
| Adjusted R-squared | 0.925010723728171 |
| F-TEST (value) | 78.3008376248883 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 79 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.210508612002221 |
| Sum Squared Residuals | 3.50079618244103 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 6.1 | 6.0215298352679 | 0.0784701647320955 |
| 2 | 6.3 | 6.21461696016114 | 0.0853830398388554 |
| 3 | 6.3 | 6.42838783524353 | -0.128387835243527 |
| 4 | 6 | 6.44166084759497 | -0.441660847594966 |
| 5 | 6.2 | 6.71192073627651 | -0.511920736276512 |
| 6 | 6.4 | 6.20541522030396 | 0.194584779696037 |
| 7 | 6.8 | 6.67253511948557 | 0.127464880514429 |
| 8 | 7.5 | 7.09089370983957 | 0.409106290160427 |
| 9 | 7.5 | 7.8681411047227 | -0.368141104722704 |
| 10 | 7.6 | 7.7593654480553 | -0.159365448055307 |
| 11 | 7.6 | 7.82453309127705 | -0.224533091277046 |
| 12 | 7.4 | 7.52357413950658 | -0.123574139506574 |
| 13 | 7.3 | 7.2273089660928 | 0.0726910339072044 |
| 14 | 7.1 | 7.16936191890414 | -0.0693619189041445 |
| 15 | 6.9 | 6.91651398710739 | -0.0165139871073851 |
| 16 | 6.8 | 6.88304372955332 | -0.0830437295533228 |
| 17 | 7.5 | 7.5011992834771 | -0.00119928347709286 |
| 18 | 7.6 | 7.68362899280886 | -0.0836289928088626 |
| 19 | 7.8 | 7.63480392485026 | 0.165196075149740 |
| 20 | 8 | 7.8431465564563 | 0.156853443543697 |
| 21 | 8.1 | 8.03867354039418 | 0.0613264596058233 |
| 22 | 8.2 | 8.34803284478504 | -0.148032844785038 |
| 23 | 8.3 | 8.35626830951873 | -0.056268309518726 |
| 24 | 8.2 | 8.20477160043735 | -0.00477160043735051 |
| 25 | 8 | 8.01138178032943 | -0.0113817803294315 |
| 26 | 7.9 | 7.74704031196364 | 0.152959688036361 |
| 27 | 7.6 | 7.73162266865849 | -0.13162266865849 |
| 28 | 7.6 | 7.4588411609574 | 0.141158839042606 |
| 29 | 8.3 | 8.26646248115951 | 0.0335375188404909 |
| 30 | 8.4 | 8.42487684097312 | -0.0248768409731164 |
| 31 | 8.4 | 8.32808725080125 | 0.0719127491987509 |
| 32 | 8.4 | 8.27888655344839 | 0.121113446551607 |
| 33 | 8.4 | 8.31756783381551 | 0.082432166184488 |
| 34 | 8.6 | 8.52079319041505 | 0.0792068095849475 |
| 35 | 8.9 | 8.80125673426566 | 0.0987432657343409 |
| 36 | 8.8 | 8.86353790724309 | -0.0635379072430851 |
| 37 | 8.3 | 8.48574766808074 | -0.185747668080739 |
| 38 | 7.5 | 7.84825793786455 | -0.348257937864551 |
| 39 | 7.2 | 6.98843699851436 | 0.211563001485637 |
| 40 | 7.4 | 7.04928756311756 | 0.350712436882440 |
| 41 | 8.8 | 8.21508366084366 | 0.584916339156341 |
| 42 | 9.3 | 9.2193451263554 | 0.0806548736446009 |
| 43 | 9.3 | 9.32846262331753 | -0.0284626233175294 |
| 44 | 8.7 | 9.10137869588116 | -0.401378695881158 |
| 45 | 8.2 | 8.19720295955587 | 0.00279704044412738 |
| 46 | 8.3 | 8.02010315598645 | 0.279896844013552 |
| 47 | 8.5 | 8.49219419925088 | 0.0078058007491174 |
| 48 | 8.6 | 8.47135011630437 | 0.128649883695627 |
| 49 | 8.5 | 8.50960731398177 | -0.0096073139817724 |
| 50 | 8.2 | 8.26863748056873 | -0.0686374805687286 |
| 51 | 8.1 | 7.9030060583636 | 0.196993941636394 |
| 52 | 7.9 | 7.95084627190112 | -0.0508462719011148 |
| 53 | 8.6 | 8.49897712466585 | 0.101022875334152 |
| 54 | 8.7 | 8.65745766130251 | 0.0425423386974851 |
| 55 | 8.7 | 8.58323961099571 | 0.116760389004286 |
| 56 | 8.5 | 8.62056314979227 | -0.120563149792274 |
| 57 | 8.4 | 8.2154858973137 | 0.184514102686296 |
| 58 | 8.5 | 8.43295885206894 | 0.0670411479310616 |
| 59 | 8.7 | 8.63876146744501 | 0.0612385325549858 |
| 60 | 8.7 | 8.61415546118766 | 0.085844538812338 |
| 61 | 8.6 | 8.44934300899644 | 0.150656991003563 |
| 62 | 8.5 | 8.38756786167388 | 0.112432138326119 |
| 63 | 8.3 | 8.18449120482884 | 0.115508795171158 |
| 64 | 8 | 8.0743386714048 | -0.0743386714047969 |
| 65 | 8.2 | 8.49796311182631 | -0.297963111826309 |
| 66 | 8.1 | 7.9782908642658 | 0.121709135734197 |
| 67 | 8.1 | 7.93024989661265 | 0.169750103387354 |
| 68 | 8 | 7.99867547954673 | 0.0013245204532663 |
| 69 | 7.9 | 7.80137028107534 | 0.0986297189246578 |
| 70 | 7.9 | 8.0023517329341 | -0.102351732934102 |
| 71 | 8 | 7.99285844768131 | 0.00714155231869007 |
| 72 | 8 | 7.90205584039883 | 0.097944159601175 |
| 73 | 7.9 | 7.8073422982836 | 0.0926577017163944 |
| 74 | 8 | 7.72581705357912 | 0.274182946420882 |
| 75 | 7.7 | 7.87245084680866 | -0.172450846808662 |
| 76 | 7.2 | 7.46981680806038 | -0.269816808060378 |
| 77 | 7.5 | 7.61571067013873 | -0.115710670138734 |
| 78 | 7.3 | 7.39040088955789 | -0.0904008895578896 |
| 79 | 7 | 7.19427531204567 | -0.194275312045673 |
| 80 | 7 | 6.80353172580534 | 0.196468274194664 |
| 81 | 7 | 6.9782117510113 | 0.0217882489887020 |
| 82 | 7.2 | 7.29053288362532 | -0.0905328836253206 |
| 83 | 7.3 | 7.45343632401205 | -0.153436324012047 |
| 84 | 7.1 | 7.22055493492213 | -0.120554934922129 |
| 85 | 6.8 | 6.98773912896731 | -0.187739128967314 |
| 86 | 6.4 | 6.5387004752848 | -0.138700475284793 |
| 87 | 6.1 | 6.17509040047512 | -0.0750904004751244 |
| 88 | 6.5 | 6.07216494741047 | 0.427835052589532 |
| 89 | 7.7 | 7.49268293161234 | 0.207317068387664 |
| 90 | 7.9 | 8.14058440443245 | -0.240584404432451 |
| 91 | 7.5 | 7.92834626189136 | -0.428346261891358 |
| 92 | 6.9 | 7.26292412923023 | -0.362924129230230 |
| 93 | 6.6 | 6.68334663211139 | -0.0833466321113905 |
| 94 | 6.9 | 6.8258618921298 | 0.0741381078702057 |
| 95 | 7.7 | 7.44069142654932 | 0.259308573450685 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.376152869936109 | 0.752305739872218 | 0.623847130063891 |
| 20 | 0.455051595033538 | 0.910103190067077 | 0.544948404966462 |
| 21 | 0.31413201187733 | 0.62826402375466 | 0.68586798812267 |
| 22 | 0.442399620921897 | 0.884799241843794 | 0.557600379078103 |
| 23 | 0.350929498532526 | 0.701858997065052 | 0.649070501467474 |
| 24 | 0.259905737282412 | 0.519811474564825 | 0.740094262717588 |
| 25 | 0.196804932892412 | 0.393609865784825 | 0.803195067107587 |
| 26 | 0.12967627511142 | 0.25935255022284 | 0.87032372488858 |
| 27 | 0.133473453148402 | 0.266946906296804 | 0.866526546851598 |
| 28 | 0.108057211764215 | 0.216114423528431 | 0.891942788235785 |
| 29 | 0.0832357593977387 | 0.166471518795477 | 0.916764240602261 |
| 30 | 0.0574771124577065 | 0.114954224915413 | 0.942522887542294 |
| 31 | 0.0519236401473644 | 0.103847280294729 | 0.948076359852636 |
| 32 | 0.110672925121807 | 0.221345850243615 | 0.889327074878193 |
| 33 | 0.0886705955594159 | 0.177341191118832 | 0.911329404440584 |
| 34 | 0.0864686904551533 | 0.172937380910307 | 0.913531309544847 |
| 35 | 0.0599140764097585 | 0.119828152819517 | 0.940085923590241 |
| 36 | 0.0571092761439248 | 0.114218552287850 | 0.942890723856075 |
| 37 | 0.116648974901392 | 0.233297949802784 | 0.883351025098608 |
| 38 | 0.585583539069906 | 0.828832921860188 | 0.414416460930094 |
| 39 | 0.523094628595548 | 0.953810742808904 | 0.476905371404452 |
| 40 | 0.457396164581599 | 0.914792329163198 | 0.542603835418401 |
| 41 | 0.521373269486454 | 0.957253461027092 | 0.478626730513546 |
| 42 | 0.48138039435303 | 0.96276078870606 | 0.51861960564697 |
| 43 | 0.420954223476029 | 0.841908446952058 | 0.579045776523971 |
| 44 | 0.71452023609684 | 0.570959527806321 | 0.285479763903160 |
| 45 | 0.66881214569404 | 0.66237570861192 | 0.33118785430596 |
| 46 | 0.626480712601596 | 0.747038574796807 | 0.373519287398404 |
| 47 | 0.721111327857574 | 0.557777344284851 | 0.278888672142426 |
| 48 | 0.691725826205221 | 0.616548347589558 | 0.308274173794779 |
| 49 | 0.7012320523259 | 0.597535895348199 | 0.298767947674099 |
| 50 | 0.758709080176043 | 0.482581839647913 | 0.241290919823957 |
| 51 | 0.699847393641677 | 0.600305212716647 | 0.300152606358323 |
| 52 | 0.757028922431136 | 0.485942155137728 | 0.242971077568864 |
| 53 | 0.710416811612965 | 0.57916637677407 | 0.289583188387035 |
| 54 | 0.694749819720998 | 0.610500360558004 | 0.305250180279002 |
| 55 | 0.651086305572136 | 0.697827388855728 | 0.348913694427864 |
| 56 | 0.76899301556745 | 0.462013968865099 | 0.231006984432549 |
| 57 | 0.711779937016761 | 0.576440125966478 | 0.288220062983239 |
| 58 | 0.672417614911572 | 0.655164770176855 | 0.327582385088428 |
| 59 | 0.628112936131121 | 0.743774127737759 | 0.371887063868879 |
| 60 | 0.567637877400048 | 0.864724245199903 | 0.432362122599952 |
| 61 | 0.525013060673614 | 0.949973878652771 | 0.474986939326386 |
| 62 | 0.457070932080749 | 0.914141864161498 | 0.542929067919251 |
| 63 | 0.484103501486185 | 0.96820700297237 | 0.515896498513815 |
| 64 | 0.428424281656845 | 0.85684856331369 | 0.571575718343155 |
| 65 | 0.670075801118775 | 0.65984839776245 | 0.329924198881225 |
| 66 | 0.639186410516107 | 0.721627178967786 | 0.360813589483893 |
| 67 | 0.658553822922088 | 0.682892354155823 | 0.341446177077912 |
| 68 | 0.662952323535541 | 0.674095352928919 | 0.337047676464459 |
| 69 | 0.605240169803533 | 0.789519660392935 | 0.394759830196467 |
| 70 | 0.534242021475399 | 0.931515957049201 | 0.465757978524601 |
| 71 | 0.436870608962228 | 0.873741217924455 | 0.563129391037772 |
| 72 | 0.331185947947650 | 0.662371895895299 | 0.66881405205235 |
| 73 | 0.565997077032793 | 0.868005845934414 | 0.434002922967207 |
| 74 | 0.607015214184824 | 0.785969571630351 | 0.392984785815176 |
| 75 | 0.776325894037877 | 0.447348211924246 | 0.223674105962123 |
| 76 | 0.643776035780444 | 0.712447928439113 | 0.356223964219556 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
