WS10 multiple regression

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 14 Dec 2010 00:46:57 +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/Dec/14/t1292287549zbmg5iyitv3s9p3.htm/, Retrieved Tue, 14 Dec 2010 01:45:59 +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/Dec/14/t1292287549zbmg5iyitv3s9p3.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 «

2 3 3 1 2 4 3 4 4 4 2 1 2 2 2 2 3 2 3 2 4 3 2 2 3 2 1 1 3 3 3 3 3 3 2 4 2 3 2 2 4 3 3 2 4 4 2 4 3 2 2 4 3 2 2 2 4 1 3 3 4 1 1 2 3 3 3 1 3 2 2 2 3 2 3 2 4 3 4 4 2 4 2 3 5 4 3 4 4 3 5 1 2 2 2 4 3 3 2 2 4 4 3 2 4 3 2 2 3 2 2 3 4 1 2 3 4 3 2 2 1 2 3 3 4 4 4 3 5 4 1 2 2 5 3 2 4 2 3 1 3 4 2 4 2 4 1 4 4 2 1 1 5 4 2 5 4 4 2 3 4 2 2 2 4 3 1 2 3 2 2 2 4 4 1 3 2 3 2 1 2 1 2 2 4 2 4 4 2 5 2 5 4 2 2 2 4 4 2 3 1 4 1 2 4 2 2 4 2 2 2 2 1 2 1 1 4 4 5 3 3 3 2 4 2 4 2 2 4 2 2 3 3 3 1 2 2 2 3 1 2 2 1 1 3 3 1 2 2 2 2 1 1 3 3 2 3 2 2 1 2 4 2 4 3 2 2 4 3 5 4 3 3 1 1 1 2 3 2 3 3 2 2 2 2 2 2 2 4 3 2 3 4 4 2 3 4 4 1 4 2 2 2 2 3 3 2 1 4 4 2 2 3 2 2 2 4 2 1 4 2 4 4 1 3 2 2 2 3 4 3 2 4 2 2 1 2 3 1 4 4 4 2 2 2 3 2 2 2 1 1 1 4 3 2 4 3 2 1 2 4 2 2 4 2 1 1 1 2 3 2 2 3 2 2 4 3 3 3 3 5 5 4 4 2 3 1 4 3 3 4 4 2 1 2 3 2 1 2 4 3 2 2 3 2 1 2 3 2 3 2 2 2 2 3 3 3 2 2 2 5 1 4 3 2 2 4 2 3 2 2 4 3 1 2 2 1 2 2 4 1 2 1 4 3 4 4 1 4 3 1 5 5 2 4 etc...

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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation verw/ouders[t] = + 2.40851027893910 + 0.0835274578394345`verw/student`[t] + 0.0488147689783496`begrip/ouders`[t] + 0.05902448979797`begrip/student`[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) 2.40851027893910 0.312492 7.7074 0 0 `verw/student` 0.0835274578394345 0.075392 1.1079 0.269617 0.134808 `begrip/ouders` 0.0488147689783496 0.077347 0.6311 0.528896 0.264448 `begrip/student` 0.05902448979797 0.071975 0.8201 0.413433 0.206717 Multiple Linear Regression - Regression Statistics Multiple R 0.131423474756780 R-squared 0.0172721297171459 Adjusted R-squared -0.00174840970768342 F-TEST (value) 0.908077806384337 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 0.438658378154772 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.989373519883344 Sum Squared Residuals 151.723294086186 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.86456144919041 -0.86456144919041 2 2 3.12516237642376 -1.12516237642376 3 4 2.89927413805150 1.10072586194850 4 2 2.79124371217060 -0.791243712170603 5 3 2.84005848114895 0.159941518851047 6 4 2.87477117001004 1.12522882998996 7 3 2.68340445339428 0.316595546605716 8 3 2.98261042878636 0.0173895712136420 9 3 2.99282014960598 0.00717985039402151 10 2 2.87477117001004 -0.874771170010038 11 4 2.92358593898839 1.07641406101161 12 4 3.07634760744541 0.923652392554587 13 3 2.90929269176654 0.0907073082334561 14 3 2.79124371217060 0.208756287829396 15 4 2.81555551310749 1.18444448689251 16 4 2.65890148535282 1.34109851464718 17 3 2.86456144919042 0.135438550809582 18 3 2.79124371217060 0.208756287829396 19 3 2.84005848114895 0.159941518851047 20 4 3.09044968756268 0.909550312437322 21 2 3.01732311764744 -1.01732311764744 22 5 3.12516237642376 1.87483762357624 23 4 2.96219098714712 1.03780901285288 24 2 2.90929269176654 -0.909292691766544 25 3 2.87477117001004 0.125228829989962 26 4 3.00711339682782 0.992886603172177 27 4 2.87477117001004 1.12522882998996 28 3 2.85026820196857 0.149731798031426 29 4 2.76674074412914 1.23325925587086 30 4 2.87477117001004 1.12522882998996 31 1 2.89908297094692 -1.89908297094692 32 4 3.11495265560414 0.885047344395858 33 5 2.90948385887112 2.09051614112888 34 2 3.09064085466726 -1.09064085466726 35 4 2.78103399135098 1.21896600864902 36 3 3.07634760744541 -0.0763476074454131 37 2 3.02753283846706 -1.02753283846706 38 4 2.68340445339428 1.31659554660572 39 5 3.13537209724338 1.86462790275662 40 4 3.01732311764744 0.982676882352557 41 4 2.79124371217060 1.20875628782940 42 4 2.82595640103169 1.17404359896831 43 3 2.79124371217060 0.208756287829396 44 4 2.96850834866909 1.03149165133091 45 2 2.81574668021207 -0.815746680212068 46 2 2.70771625433117 -0.707716254331169 47 4 3.00692222972324 0.993077770276757 48 2 3.21889955508282 -1.21889955508282 49 4 2.79124371217060 1.20875628782940 50 4 3.01732311764744 0.982676882352557 51 1 2.90948385887112 -1.90948385887112 52 4 2.90929269176654 1.09070730823346 53 2 2.79124371217060 -0.791243712170604 54 1 2.68340445339428 -1.68340445339428 55 4 3.16376742458249 0.836232575417508 56 3 2.99282014960598 0.00717985039402151 57 2 2.95829862784947 -0.958298627849473 58 4 2.85026820196857 1.14973179803143 59 3 2.82595640103169 0.174043598968311 60 2 2.78103399135098 -0.781033991350983 61 2 2.68340445339428 -0.683404453394284 62 3 2.82595640103169 0.174043598968311 63 2 2.73221922237263 -0.732219222372634 64 1 2.92358593898839 -1.92358593898839 65 3 2.73221922237263 0.267780777627366 66 2 3.07634760744541 -1.07634760744541 67 3 2.90929269176654 0.0907073082334561 68 3 3.19848011344358 -0.198480113443577 69 3 2.59987699555485 0.400123004445150 70 2 2.93379565980801 -0.933795659808008 71 3 2.79124371217060 0.208756287829396 72 2 2.79124371217060 -0.791243712170604 73 4 2.93379565980801 1.06620434019199 74 4 3.01732311764744 0.982676882352557 75 4 3.02753283846706 0.972467161532936 76 2 2.79124371217060 -0.791243712170604 77 3 2.81574668021207 0.184253319787932 78 4 2.95829862784947 1.04170137215053 79 3 2.79124371217060 0.208756287829396 80 4 2.86047792278819 1.13952207721181 81 2 2.9969036760082 -0.996903676008202 82 3 2.79124371217060 0.208756287829396 83 3 3.00711339682782 -0.00711339682782257 84 4 2.73221922237263 1.26778077762737 85 2 2.94400538062763 -0.94400538062763 86 4 2.95829862784947 1.04170137215053 87 2 2.87477117001004 -0.874771170010038 88 2 2.59987699555485 -0.59987699555485 89 4 2.99282014960598 1.00717985039402 90 3 2.74242894319225 0.257571056807746 91 4 2.90929269176654 1.09070730823346 92 2 2.59987699555485 -0.59987699555485 93 2 2.87477117001004 -0.874771170010038 94 3 2.90929269176654 0.0907073082334561 95 3 2.98261042878636 0.0173895712136420 96 5 3.25750460324155 1.74249539675845 97 2 2.94400538062763 -0.94400538062763 98 3 3.09044968756268 -0.0904496875626777 99 2 2.76674074412914 -0.766740744129139 100 2 2.82576523392711 -0.82576523392711 101 3 2.85026820196857 0.149731798031426 102 2 2.76674074412914 -0.766740744129139 103 2 2.87477117001004 -0.874771170010038 104 2 2.89908297094692 -0.899082970946924 105 3 2.79124371217060 0.208756287829396 106 5 2.86437028208584 2.13562971791416 107 2 2.88887325012730 -0.888873250127303 108 3 2.90929269176654 0.0907073082334561 109 3 2.70771625433117 0.292283745668831 110 1 2.90929269176654 -1.90929269176654 111 1 2.86047792278819 -1.86047792278819 112 3 2.9969036760082 0.00309632399179798 113 4 3.0030298704256 0.9969701295744 114 5 2.8888732501273 2.11112674987270 115 3 3.05203580650853 -0.052035806508528 116 3 2.82576523392711 0.174234766072891 117 3 2.68340445339428 0.316595546605716 118 2 2.83597495474673 -0.83597495474673 119 3 2.94789773992527 0.0521022600747269 120 2 2.86437028208584 -0.864370282085839 121 3 2.71792597515079 0.282074024849210 122 2 2.80145343299022 -0.801453432990224 123 4 2.79124371217060 1.20875628782940 124 2 2.74242894319225 -0.742428943192254 125 2 2.99282014960598 -0.992820149605979 126 4 2.90929269176654 1.09070730823346 127 4 2.76674074412914 1.23325925587086 128 3 2.85026820196857 0.149731798031426 129 3 2.85026820196857 0.149731798031426 130 3 3.09044968756268 -0.0904496875626777 131 4 2.94789773992527 1.05210226007473 132 2 2.86047792278819 -0.860477922788194 133 1 2.86047792278819 -1.86047792278819 134 3 2.65890148535282 0.34109851464718 135 2 3.00692222972324 -1.00692222972324 136 3 2.79124371217060 0.208756287829396 137 2 2.95810746074489 -0.958107460744894 138 2 2.88498089082966 -0.884980890829659 139 3 2.76674074412914 0.233259255870861 140 2 2.82595640103169 -0.825956401031689 141 4 3.05592816580617 0.944071834193828 142 4 3.06594671952121 0.934053280478787 143 2 3.09064085466726 -1.09064085466726 144 2 2.87458000290546 -0.87458000290546 145 3 2.85026820196857 0.149731798031426 146 4 3.04163491858433 0.958365081415672 147 2 3.04163491858433 -1.04163491858433 148 2 2.86456144919042 -0.864561449190418 149 3 3.00692222972324 -0.00692222972324315 150 2 3.00692222972324 -1.00692222972324 151 1 3.03142519776471 -2.03142519776471 152 2 2.9969036760082 -0.996903676008202 153 1 3.13945562364561 -2.13945562364561 154 2 2.93768801910565 -0.937688019105653 155 3 2.84005848114895 0.159941518851047 156 2 2.89908297094692 -0.899082970946924 157 2 3.11495265560414 -1.11495265560414 158 2 2.94789773992527 -0.947897739925273 159 4 3.01732311764744 0.982676882352557 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.629994252203463 0.740011495593074 0.370005747796537 8 0.523266341523834 0.953467316952332 0.476733658476166 9 0.382847934231229 0.765695868462458 0.617152065768771 10 0.404421151560345 0.80884230312069 0.595578848439655 11 0.478388908815499 0.956777817630998 0.521611091184501 12 0.441331105973331 0.882662211946661 0.55866889402667 13 0.353422307012912 0.706844614025823 0.646577692987088 14 0.267673393917914 0.535346787835828 0.732326606082086 15 0.355455455874641 0.710910911749282 0.64454454412536 16 0.322754526552858 0.645509053105716 0.677245473447142 17 0.248261987609189 0.496523975218378 0.751738012390811 18 0.187529608963812 0.375059217927624 0.812470391036188 19 0.136078191686208 0.272156383372415 0.863921808313792 20 0.140947657709226 0.281895315418453 0.859052342290774 21 0.150911877487697 0.301823754975395 0.849088122512303 22 0.30004220527716 0.60008441055432 0.69995779472284 23 0.270956870982706 0.541913741965412 0.729043129017294 24 0.302721514323400 0.605443028646801 0.6972784856766 25 0.244758620842355 0.48951724168471 0.755241379157645 26 0.224379782220663 0.448759564441327 0.775620217779337 27 0.222803982872065 0.44560796574413 0.777196017127935 28 0.176834099557222 0.353668199114444 0.823165900442778 29 0.179374815406076 0.358749630812151 0.820625184593924 30 0.175673399255911 0.351346798511823 0.824326600744089 31 0.394737092076302 0.789474184152604 0.605262907923698 32 0.359930441567716 0.719860883135432 0.640069558432284 33 0.481769433620548 0.963538867241096 0.518230566379452 34 0.559956463340395 0.88008707331921 0.440043536659605 35 0.55343987109346 0.89312025781308 0.44656012890654 36 0.499404534067437 0.998809068134873 0.500595465932563 37 0.510487920003536 0.979024159992928 0.489512079996464 38 0.506808333640786 0.986383332718427 0.493191666359214 39 0.648151628493944 0.703696743012111 0.351848371506056 40 0.630006182525232 0.739987634949536 0.369993817474768 41 0.625804090493992 0.748391819012017 0.374195909506008 42 0.61713645270153 0.765727094596939 0.382863547298470 43 0.571398389108666 0.857203221782669 0.428601610891334 44 0.555071746785177 0.889856506429645 0.444928253214823 45 0.582858542917917 0.834282914164166 0.417141457082083 46 0.583605345931352 0.832789308137296 0.416394654068648 47 0.573561337310924 0.852877325378152 0.426438662689076 48 0.619311759227656 0.761376481544689 0.380688240772344 49 0.622342279559494 0.755315440881013 0.377657720440506 50 0.612439433402951 0.775121133194099 0.387560566597049 51 0.762258245444482 0.475483509111036 0.237741754555518 52 0.756703022149004 0.486593955701992 0.243296977850996 53 0.761072385423206 0.477855229153588 0.238927614576794 54 0.839133305342406 0.321733389315188 0.160866694657594 55 0.824199579304088 0.351600841391824 0.175800420695912 56 0.793168155473195 0.413663689053610 0.206831844526805 57 0.793453640038813 0.413092719922374 0.206546359961187 58 0.795959390562455 0.40808121887509 0.204040609437545 59 0.762157923387139 0.475684153225721 0.237842076612861 60 0.76050312866968 0.478993742660641 0.239496871330320 61 0.741630567692522 0.516738864614955 0.258369432307478 62 0.703869742484321 0.592260515031358 0.296130257515679 63 0.688998255872981 0.622003488254037 0.311001744127019 64 0.804373972982033 0.391252054035935 0.195626027017968 65 0.772955210024824 0.454089579950352 0.227044789975176 66 0.784073412195244 0.431853175609512 0.215926587804756 67 0.750770981326448 0.498458037347104 0.249229018673552 68 0.715207828046931 0.569584343906138 0.284792171953069 69 0.68068066569197 0.63863866861606 0.31931933430803 70 0.680110598567611 0.639778802864777 0.319889401432389 71 0.639925645080036 0.720148709839928 0.360074354919964 72 0.62836962115416 0.74326075769168 0.37163037884584 73 0.633446498298931 0.733107003402137 0.366553501701069 74 0.636294533393668 0.727410933212664 0.363705466606332 75 0.640233037150197 0.719533925699607 0.359766962849803 76 0.62801313855306 0.74397372289388 0.37198686144694 77 0.5868250485756 0.826349902848801 0.413174951424401 78 0.604103355014347 0.791793289971306 0.395896644985653 79 0.562167038605838 0.875665922788325 0.437832961394162 80 0.577270858716402 0.845458282567196 0.422729141283598 81 0.570245366594695 0.85950926681061 0.429754633405305 82 0.527851930857229 0.944296138285541 0.472148069142771 83 0.483281272423296 0.966562544846591 0.516718727576704 84 0.52234914167875 0.9553017166425 0.47765085832125 85 0.520685064331496 0.958629871337007 0.479314935668504 86 0.549106125746662 0.901787748506676 0.450893874253338 87 0.532735350777987 0.934529298444025 0.467264649222013 88 0.501694589520079 0.996610820959843 0.498305410479921 89 0.513379419743506 0.973241160512987 0.486620580256494 90 0.475738667788956 0.951477335577912 0.524261332211044 91 0.490799605271387 0.981599210542775 0.509200394728613 92 0.459294000544018 0.918588001088037 0.540705999455982 93 0.441226811529234 0.882453623058467 0.558773188470767 94 0.401447316411709 0.802894632823418 0.598552683588291 95 0.360357342209309 0.720714684418617 0.639642657790691 96 0.526036264257111 0.947927471485778 0.473963735742889 97 0.510874930010175 0.97825013997965 0.489125069989825 98 0.474761532325133 0.949523064650266 0.525238467674867 99 0.464849727960311 0.929699455920622 0.535150272039689 100 0.456664827556196 0.913329655112393 0.543335172443804 101 0.413374788855650 0.826749577711301 0.58662521114435 102 0.4016180492267 0.8032360984534 0.5983819507733 103 0.381611624834017 0.763223249668035 0.618388375165983 104 0.373123188740556 0.746246377481113 0.626876811259444 105 0.330205964387332 0.660411928774665 0.669794035612668 106 0.485037726934332 0.970075453868663 0.514962273065668 107 0.479447131157162 0.958894262314324 0.520552868842838 108 0.436596574863002 0.873193149726003 0.563403425136998 109 0.389731906583542 0.779463813167084 0.610268093416458 110 0.502855092735044 0.994289814529913 0.497144907264956 111 0.609765361260819 0.780469277478361 0.390234638739181 112 0.569991423022048 0.860017153955904 0.430008576977952 113 0.620040274092426 0.759919451815148 0.379959725907574 114 0.8037337019508 0.392532596098401 0.196266298049201 115 0.785507854032995 0.428984291934009 0.214492145967005 116 0.74620587069146 0.507588258617079 0.253794129308540 117 0.70828566575394 0.583428668492121 0.291714334246060 118 0.69601639706864 0.60796720586272 0.30398360293136 119 0.653291215433693 0.693417569132613 0.346708784566307 120 0.649116617949412 0.701766764101176 0.350883382050588 121 0.598987539524842 0.802024920950316 0.401012460475158 122 0.571585231501371 0.856829536997257 0.428414768498629 123 0.624744484773731 0.750511030452537 0.375255515226269 124 0.590853519699369 0.818292960601262 0.409146480300631 125 0.564127866356887 0.871744267286227 0.435872133643113 126 0.60296981052492 0.794060378950161 0.397030189475081 127 0.646240629493862 0.707518741012276 0.353759370506138 128 0.600392586727766 0.799214826544469 0.399607413272234 129 0.554071392278227 0.891857215443546 0.445928607721773 130 0.507612987835873 0.984774024328253 0.492387012164127 131 0.584847304709383 0.830305390581233 0.415152695290617 132 0.548232622833912 0.903534754332176 0.451767377166088 133 0.720854474348063 0.558291051303874 0.279145525651937 134 0.66916009956992 0.661679800860161 0.330839900430080 135 0.639189288787035 0.72162142242593 0.360810711212965 136 0.597258112105521 0.805483775788958 0.402741887894479 137 0.576791069038788 0.846417861922424 0.423208930961212 138 0.568332964706594 0.863334070586811 0.431667035293406 139 0.499811000633938 0.999622001267877 0.500188999366062 140 0.484744192492254 0.969488384984509 0.515255807507746 141 0.751444510709444 0.497110978581113 0.248555489290556 142 0.840408137773881 0.319183724452237 0.159591862226119 143 0.79672998331016 0.406540033379681 0.203270016689840 144 0.802041657620082 0.395916684759836 0.197958342379918 145 0.749224255668291 0.501551488663418 0.250775744331709 146 0.83276291217207 0.334474175655860 0.167237087827930 147 0.809055810650894 0.381888378698212 0.190944189349106 148 0.761672082690242 0.476655834619517 0.238327917309758 149 0.798630029016145 0.402739941967710 0.201369970983855 150 0.705623077741266 0.588753844517468 0.294376922258734 151 0.69499042769393 0.610019144612141 0.305009572306070 152 0.531370957957678 0.937258084084645 0.468629042042322 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

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 0 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 0 ;

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') }

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Software written by Ed van Stee & Patrick Wessa

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