Workshop 8 Regression Analysis of Time Series

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 27 Nov 2010 09:22:21 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31.htm/, Retrieved Sat, 27 Nov 2010 10:22:20 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

24 25 17 18 18 16 20 16 18 17 23 30 23 18 15 12 21 15 20 31 27 34 21 31 19 16 20 21 22 17 24 25 26 25 17 32 33 13 32 25 29 22 18 17 20 15 20 33 29 23 26 18 20 11 28 26 22 17 12 14 17 21 19 18 10 29 31 19 9 20 28 19 30 29 26 23 13 21 19 28 23 18 21 20 23 21 21 15 28 19 26 10 16 22 19 31 31 29 19 22 23 15 20 18 23 25 21 24 25 17 13 28 21 25 9 16 19 17 25 20 29 14 22 15 19 20 15 20 18 33 22 16 17 16 21 26 18 18 17 22 30 30 24 21 21 29 31 20 16 22 20 28 38 22 20 17 28 22 31

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Concernovermistakes[t] = + 23.2383107088989 + 1.26328736622854M1[t] -2.74211735976439M2[t] -1.31895065718594M3[t] -3.5721468074409M4[t] -3.8083207642031M5[t] -4.42911010558068M6[t] -3.12682252388133M7[t] -2.43991955756661M8[t] -1.44532428355956M9[t] -0.989190548014066M10[t] -2.68690296631471M11[t] + 0.00540472599296133t + 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) 23.2383107088989 1.786634 13.0068 0 0 M1 1.26328736622854 2.198322 0.5747 0.566406 0.283203 M2 -2.74211735976439 2.198123 -1.2475 0.214218 0.107109 M3 -1.31895065718594 2.197968 -0.6001 0.549385 0.274692 M4 -3.5721468074409 2.23949 -1.5951 0.112859 0.056429 M5 -3.8083207642031 2.239164 -1.7008 0.091114 0.045557 M6 -4.42911010558068 2.238881 -1.9783 0.04978 0.02489 M7 -3.12682252388133 2.238642 -1.3967 0.164608 0.082304 M8 -2.43991955756661 2.238446 -1.09 0.277506 0.138753 M9 -1.44532428355956 2.238294 -0.6457 0.51947 0.259735 M10 -0.989190548014066 2.238185 -0.442 0.659171 0.329586 M11 -2.68690296631471 2.238119 -1.2005 0.231882 0.115941 t 0.00540472599296133 0.009871 0.5475 0.584849 0.292424 Multiple Linear Regression - Regression Statistics Multiple R 0.285229909227530 R-squared 0.0813561011179448 Adjusted R-squared 0.0058511231276388 F-TEST (value) 1.07749321016146 F-TEST (DF numerator) 12 F-TEST (DF denominator) 146 p-value 0.383217157247471 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.70605193364234 Sum Squared Residuals 4753.61818573583 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.5070028011206 -0.507002801120587 2 25 20.5070028011204 4.49299719887957 3 17 21.9355742296919 -4.93557422969188 4 18 19.6877828054298 -1.68778280542985 5 18 19.4570135746607 -1.45701357466066 6 16 18.841628959276 -2.84162895927602 7 20 20.1493212669683 -0.149321266968339 8 16 20.841628959276 -4.84162895927602 9 18 21.841628959276 -3.84162895927600 10 17 22.3031674208145 -5.30316742081448 11 23 20.6108597285068 2.38914027149322 12 30 23.3031674208145 6.6968325791855 13 23 24.5718595130360 -1.57185951303597 14 18 20.571859513036 -2.57185951303599 15 15 22.0004309416074 -7.00043094160741 16 12 19.7526395173454 -7.7526395173454 17 21 19.5218702865762 1.47812971342383 18 15 18.9064856711916 -3.90648567119155 19 20 20.2141779788839 -0.21417797888386 20 31 20.9064856711916 10.0935143288084 21 27 21.9064856711916 5.09351432880845 22 34 22.36802413273 11.6319758672700 23 21 20.6757164404223 0.324283559577679 24 31 23.36802413273 7.63197586727 25 19 24.6367162249515 -5.63671622495151 26 16 20.6367162249515 -4.63671622495152 27 20 22.0652876535229 -2.06528765352294 28 21 19.8174962292609 1.18250377073907 29 22 19.5867269984917 2.4132730015083 30 17 18.9713423831071 -1.97134238310709 31 24 20.2790346907994 3.72096530920060 32 25 20.9713423831071 4.02865761689292 33 26 21.9713423831071 4.02865761689291 34 25 22.4328808446455 2.56711915535445 35 17 20.7405731523379 -3.74057315233786 36 32 23.4328808446455 8.56711915535446 37 33 24.7015729368670 8.29842706313296 38 13 20.7015729368671 -7.70157293686706 39 32 22.1301443654385 9.86985563456152 40 25 19.8823529411765 5.11764705882353 41 29 19.6515837104072 9.34841628959276 42 22 19.0361990950226 2.96380090497738 43 18 20.3438914027149 -2.34389140271493 44 17 21.0361990950226 -4.03619909502262 45 20 22.0361990950226 -2.03619909502262 46 15 22.4977375565611 -7.49773755656108 47 20 20.8054298642534 -0.805429864253393 48 33 23.4977375565611 9.50226244343892 49 29 24.7664296487826 4.23357035121742 50 23 20.7664296487826 2.23357035121740 51 26 22.195001077354 3.80499892264598 52 18 19.947209653092 -1.94720965309201 53 20 19.7164404223228 0.283559577677226 54 11 19.1010558069382 -8.10105580693816 55 28 20.4087481146305 7.59125188536953 56 26 21.1010558069382 4.89894419306184 57 22 22.1010558069382 -0.101055806938159 58 17 22.5625942684766 -5.56259426847662 59 12 20.8702865761689 -8.87028657616893 60 14 23.5625942684766 -9.56259426847661 61 17 24.8312863606981 -7.83128636069812 62 21 20.8312863606981 0.168713639301869 63 19 22.2598577892695 -3.25985778926955 64 18 20.0120663650075 -2.01206636500754 65 10 19.7812971342383 -9.7812971342383 66 29 19.1659125188537 9.8340874811463 67 31 20.473604826546 10.526395173454 68 19 21.1659125188537 -2.16591251885369 69 9 22.1659125188537 -13.1659125188537 70 20 22.6274509803922 -2.62745098039216 71 28 20.9351432880845 7.06485671191554 72 19 23.6274509803921 -4.62745098039214 73 30 24.8961430726137 5.10385692738635 74 29 20.8961430726137 8.10385692738634 75 26 22.3247145011851 3.67528549881491 76 23 20.0769230769231 2.92307692307692 77 13 19.8461538461538 -6.84615384615385 78 21 19.2307692307692 1.76923076923077 79 19 20.5384615384615 -1.53846153846154 80 28 21.2307692307692 6.76923076923077 81 23 22.2307692307692 0.769230769230769 82 18 22.6923076923077 -4.69230769230769 83 21 21 -1.1518563880486e-15 84 20 23.6923076923077 -3.69230769230768 85 23 24.9609997845292 -1.96099978452919 86 21 20.9609997845292 0.0390002154707971 87 21 22.3895712131006 -1.38957121310062 88 15 20.1417797888386 -5.14177978883861 89 28 19.9110105580694 8.08898944193062 90 19 19.2956259426848 -0.295625942684766 91 26 20.6033182503771 5.39668174962293 92 10 21.2956259426848 -11.2956259426848 93 16 22.2956259426848 -6.29562594268477 94 22 22.7571644042232 -0.757164404223229 95 19 21.0648567119155 -2.06485671191554 96 31 23.7571644042232 7.24283559577678 97 31 25.0258564964447 5.97414350355528 98 29 21.0258564964447 7.97414350355526 99 19 22.4544279250162 -3.45442792501616 100 22 20.2066365007542 1.79336349924585 101 23 19.9758672699849 3.02413273001508 102 15 19.3604826546003 -4.3604826546003 103 20 20.6681749622926 -0.668174962292612 104 18 21.3604826546003 -3.3604826546003 105 23 22.3604826546003 0.639517345399697 106 25 22.8220211161388 2.17797888386124 107 21 21.1297134238311 -0.129713423831073 108 24 23.8220211161388 0.177978883861245 109 25 25.0907132083603 -0.090713208360257 110 17 21.0907132083603 -4.09071320836027 111 13 22.5192846369317 -9.5192846369317 112 28 20.2714932126697 7.72850678733031 113 21 20.0407239819005 0.959276018099546 114 25 19.4253393665158 5.57466063348416 115 9 20.7330316742081 -11.7330316742081 116 16 21.4253393665158 -5.42533936651584 117 19 22.4253393665158 -3.42533936651584 118 17 22.8868778280543 -5.8868778280543 119 25 21.1945701357466 3.80542986425339 120 20 23.8868778280543 -3.88687782805429 121 29 25.1555699202758 3.84443007972420 122 14 21.1555699202758 -7.15556992027581 123 22 22.5841413488472 -0.584141348847231 124 15 20.3363499245852 -5.33634992458522 125 19 20.105580693816 -1.10558069381599 126 20 19.4901960784314 0.509803921568626 127 15 20.7978883861237 -5.79788838612368 128 20 21.4901960784314 -1.49019607843137 129 18 22.4901960784314 -4.49019607843137 130 33 22.9517345399698 10.0482654600302 131 22 21.2594268476621 0.740573152337855 132 16 23.9517345399698 -7.95173453996983 133 17 25.2204266321913 -8.22042663219133 134 16 21.2204266321913 -5.22042663219135 135 21 22.6489980607628 -1.64899806076277 136 26 20.4012066365008 5.59879336349924 137 18 20.1704374057315 -2.17043740573152 138 18 19.5550527903469 -1.55505279034691 139 17 20.8627450980392 -3.86274509803922 140 22 21.5550527903469 0.44494720965309 141 30 22.5550527903469 7.4449472096531 142 30 23.0165912518854 6.98340874811463 143 24 21.3242835595777 2.67571644042232 144 21 24.0165912518854 -3.01659125188536 145 21 25.2852833441069 -4.28528334410686 146 29 21.2852833441069 7.71471665589312 147 31 22.7138547726783 8.2861452273217 148 20 20.4660633484163 -0.466063348416294 149 16 20.2352941176471 -4.23529411764706 150 22 19.6199095022624 2.38009049773755 151 20 20.9276018099548 -0.927601809954756 152 28 21.6199095022624 6.38009049773756 153 38 22.6199095022624 15.3800904977376 154 22 23.0814479638009 -1.08144796380091 155 20 21.3891402714932 -1.38914027149322 156 17 24.0814479638009 -7.0814479638009 157 28 25.3501400560224 2.6498599439776 158 22 21.3501400560224 0.649859943977581 159 31 22.7787114845938 8.22128851540616 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0565687891798083 0.113137578359617 0.943431210820192 17 0.0839659028663624 0.167931805732725 0.916034097133638 18 0.0367537036556018 0.0735074073112037 0.963246296344398 19 0.0166035069260113 0.0332070138520226 0.983396493073989 20 0.31258535125928 0.62517070251856 0.68741464874072 21 0.328614862613942 0.657229725227883 0.671385137386058 22 0.583569550402658 0.832860899194683 0.416430449597342 23 0.512577557448716 0.974844885102568 0.487422442551284 24 0.435076853934405 0.87015370786881 0.564923146065595 25 0.435693232606444 0.871386465212888 0.564306767393556 26 0.42543745092194 0.85087490184388 0.57456254907806 27 0.363228603103468 0.726457206206935 0.636771396896532 28 0.319845446939040 0.639690893878081 0.68015455306096 29 0.253411545645171 0.506823091290343 0.746588454354829 30 0.196227070850857 0.392454141701713 0.803772929149143 31 0.153547415235307 0.307094830470614 0.846452584764693 32 0.115456325044678 0.230912650089357 0.884543674955321 33 0.0863857570120045 0.172771514024009 0.913614242987995 34 0.0647520070783626 0.129504014156725 0.935247992921637 35 0.0655339780689108 0.131067956137822 0.934466021931089 36 0.0534670586357996 0.106934117271599 0.9465329413642 37 0.0793797507878676 0.158759501575735 0.920620249212132 38 0.115445697507034 0.230891395014069 0.884554302492966 39 0.225973925175037 0.451947850350074 0.774026074824963 40 0.207548412350879 0.415096824701757 0.792451587649121 41 0.215755276609695 0.431510553219391 0.784244723390304 42 0.178869710283796 0.357739420567593 0.821130289716204 43 0.182556945663054 0.365113891326109 0.817443054336946 44 0.233346704975982 0.466693409951964 0.766653295024018 45 0.224537952917625 0.44907590583525 0.775462047082375 46 0.332734110762307 0.665468221524614 0.667265889237693 47 0.285886216736989 0.571772433473977 0.714113783263011 48 0.298810296496208 0.597620592992415 0.701189703503792 49 0.266059945706883 0.532119891413765 0.733940054293117 50 0.22970326848285 0.4594065369657 0.77029673151715 51 0.201173352803007 0.402346705606013 0.798826647196993 52 0.173860716098747 0.347721432197493 0.826139283901253 53 0.157677134722782 0.315354269445563 0.842322865277218 54 0.192400741225735 0.38480148245147 0.807599258774265 55 0.20754962209104 0.41509924418208 0.79245037790896 56 0.189733430561107 0.379466861122213 0.810266569438893 57 0.161245958520749 0.322491917041499 0.83875404147925 58 0.170744408642889 0.341488817285779 0.82925559135711 59 0.224232022908898 0.448464045817796 0.775767977091102 60 0.46091207395646 0.92182414791292 0.53908792604354 61 0.501430525086617 0.997138949826766 0.498569474913383 62 0.4538151879924 0.9076303759848 0.5461848120076 63 0.415228804260661 0.830457608521322 0.584771195739339 64 0.369670555266206 0.739341110532411 0.630329444733794 65 0.466484551961428 0.932969103922857 0.533515448038572 66 0.595442078767857 0.809115842464287 0.404557921232143 67 0.701696464980854 0.596607070038292 0.298303535019146 68 0.668245847554227 0.663508304891546 0.331754152445773 69 0.818361916953823 0.363276166092354 0.181638083046177 70 0.789107217391002 0.421785565217997 0.210892782608998 71 0.81822726417456 0.363545471650881 0.181772735825440 72 0.8177122578938 0.364575484212398 0.182287742106199 73 0.816466604484336 0.367066791031328 0.183533395515664 74 0.854593666932024 0.290812666135951 0.145406333067976 75 0.841138396973498 0.317723206053004 0.158861603026502 76 0.820418529201479 0.359162941597042 0.179581470798521 77 0.8278918057246 0.3442163885508 0.1721081942754 78 0.799732914680829 0.400534170638342 0.200267085319171 79 0.776735951533299 0.446528096933403 0.223264048466701 80 0.809604318584409 0.380791362831182 0.190395681415591 81 0.776737766908299 0.446524466183403 0.223262233091701 82 0.759394593497527 0.481210813004947 0.240605406502473 83 0.719765970018004 0.560468059963993 0.280234029981996 84 0.699178699007767 0.601642601984466 0.300821300992233 85 0.65720917941888 0.68558164116224 0.34279082058112 86 0.612166380446944 0.775667239106111 0.387833619553056 87 0.564656826145423 0.870686347709153 0.435343173854577 88 0.549409316810711 0.901181366378577 0.450590683189288 89 0.615610673546239 0.768778652907522 0.384389326453761 90 0.567380589084137 0.865238821831726 0.432619410915863 91 0.624603686566704 0.750792626866592 0.375396313433296 92 0.717846302869109 0.564307394261782 0.282153697130891 93 0.728548220779603 0.542903558440794 0.271451779220397 94 0.688873795220087 0.622252409559826 0.311126204779913 95 0.646687012053426 0.706625975893149 0.353312987946574 96 0.743103518763444 0.513792962473111 0.256896481236556 97 0.77789152730727 0.444216945385459 0.222108472692729 98 0.858532536170661 0.282934927658677 0.141467463829339 99 0.832100571438638 0.335798857122723 0.167899428561361 100 0.803394102850334 0.393211794299332 0.196605897149666 101 0.804957325277445 0.39008534944511 0.195042674722555 102 0.781316860859402 0.437366278281197 0.218683139140598 103 0.790753304761872 0.418493390476255 0.209246695238128 104 0.754971664587716 0.490056670824568 0.245028335412284 105 0.713501113889501 0.572997772220997 0.286498886110499 106 0.67788122084635 0.6442375583073 0.32211877915365 107 0.629941156629434 0.740117686741132 0.370058843370566 108 0.663893842211742 0.672212315576517 0.336106157788258 109 0.641855196504106 0.716289606991788 0.358144803495894 110 0.599503164137837 0.800993671724326 0.400496835862163 111 0.668697455287973 0.662605089424054 0.331302544712027 112 0.760017912926561 0.479964174146879 0.239982087073439 113 0.759934984600914 0.480130030798172 0.240065015399086 114 0.80404853143598 0.391902937128039 0.195951468564020 115 0.826303859184972 0.347392281630056 0.173696140815028 116 0.801428005131353 0.397143989737294 0.198571994868647 117 0.792212355641932 0.415575288716137 0.207787644358068 118 0.816642245741585 0.36671550851683 0.183357754258415 119 0.814852602495942 0.370294795008116 0.185147397504058 120 0.808800081930461 0.382399836139077 0.191199918069539 121 0.888995987968798 0.222008024062404 0.111004012031202 122 0.873817526299002 0.252364947401996 0.126182473700998 123 0.837310408783627 0.325379182432747 0.162689591216373 124 0.820125949520516 0.359748100958969 0.179874050479484 125 0.799589858739027 0.400820282521945 0.200410141260973 126 0.760569280852472 0.478861438295056 0.239430719147528 127 0.709224136555239 0.581551726889522 0.290775863444761 128 0.646384436557423 0.707231126885154 0.353615563442577 129 0.820331020648015 0.35933795870397 0.179668979351985 130 0.897881396170347 0.204237207659306 0.102118603829653 131 0.86918115967249 0.26163768065502 0.13081884032751 132 0.829994296186691 0.340011407626618 0.170005703813309 133 0.804924521151705 0.39015095769659 0.195075478848295 134 0.820482741905018 0.359034516189964 0.179517258094982 135 0.888396403449321 0.223207193101357 0.111603596550678 136 0.880485176598369 0.239029646803262 0.119514823401631 137 0.826884324275871 0.346231351448258 0.173115675724129 138 0.769350671028098 0.461298657943804 0.230649328971902 139 0.690621719115386 0.618756561769228 0.309378280884614 140 0.67009773942681 0.65980452114638 0.32990226057319 141 0.78793192286437 0.42413615427126 0.21206807713563 142 0.761735649786674 0.476528700426651 0.238264350213326 143 0.626515308756556 0.746969382486888 0.373484691243444 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 1 0.0078125 OK 10% type I error level 2 0.015625 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/105bdw1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/105bdw1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/1gagk1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/1gagk1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/2q1fn1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/2q1fn1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/3q1fn1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/3q1fn1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/4q1fn1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/4q1fn1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/5jte81290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/5jte81290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/6jte81290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/6jte81290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/7u2va1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/7u2va1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/8u2va1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/8u2va1290849728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/95bdw1290849728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849729mi2309dns4hlm31/95bdw1290849728.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by