multiple regression - model 1

*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: Wed, 01 Dec 2010 17:31:46 +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/01/t1291224596nni4yngi7iif5la.htm/, Retrieved Wed, 01 Dec 2010 18:30:06 +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/01/t1291224596nni4yngi7iif5la.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 13 13 14 13 3 1 12 12 8 13 5 0 15 10 12 16 6 3 12 9 7 12 6 3 10 10 10 11 5 1 12 12 7 12 3 3 15 13 16 18 8 1 9 12 11 11 4 4 12 12 14 14 4 0 11 6 6 9 4 3 11 5 16 14 6 2 11 12 11 12 6 4 15 11 16 11 5 3 7 14 12 12 4 1 11 14 7 13 6 1 11 12 13 11 4 2 10 12 11 12 6 3 14 11 15 16 6 1 10 11 7 9 4 1 6 7 9 11 4 2 11 9 7 13 2 3 15 11 14 15 7 4 11 11 15 10 5 2 12 12 7 11 4 1 14 12 15 13 6 2 15 11 17 16 6 2 9 11 15 15 7 4 13 8 14 14 5 2 13 9 14 14 6 3 16 12 8 14 4 3 13 10 8 8 4 3 12 10 14 13 7 4 14 12 14 15 7 2 11 8 8 13 4 2 9 12 11 11 4 4 16 11 16 15 6 3 12 12 10 15 6 4 10 7 8 9 5 2 13 11 14 13 6 5 16 11 16 16 7 3 14 12 13 13 6 1 15 9 5 11 3 1 5 15 8 12 3 1 8 11 10 12 4 2 11 11 8 12 6 3 16 11 13 14 7 9 17 11 15 14 5 0 9 15 6 8 4 0 9 11 12 13 5 2 13 12 16 16 6 2 10 12 5 13 6 3 6 9 15 11 6 1 12 12 12 14 5 2 8 12 8 13 4 0 14 13 13 13 5 5 12 11 14 13 5 2 11 9 12 12 4 4 16 9 16 16 6 3 8 11 10 15 2 0 15 11 15 15 8 0 7 12 8 12 3 4 16 12 16 14 6 1 14 9 19 12 6 1 16 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation aantalVrienden[t] = + 1.23744674639409 + 0.0963613878771712Popularity[t] -0.0644187764141667FindingFriends[t] + 0.128803686232339KnowingPeople[t] -0.0747737175493632Liked[t] + 0.0387444743481176`Celebrity `[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) 1.23744674639409 0.952871 1.2987 0.196056 0.098028 Popularity 0.0963613878771712 0.054404 1.7712 0.078554 0.039277 FindingFriends -0.0644187764141667 0.064356 -1.001 0.318451 0.159225 KnowingPeople 0.128803686232339 0.043121 2.987 0.003291 0.001646 Liked -0.0747737175493632 0.067234 -1.1121 0.267856 0.133928 `Celebrity ` 0.0387444743481176 0.109749 0.353 0.724563 0.362281 Multiple Linear Regression - Regression Statistics Multiple R 0.404565543716048 R-squared 0.163673279162262 Adjusted R-squared 0.135795721801004 F-TEST (value) 5.8711485027638 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 5.51936533799147e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.40758944238227 Sum Squared Residuals 297.196205745903 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.60012739756854 -0.600127397568545 2 1 1.87285161740772 -0.872851617407716 3 0 2.62041140049695 -2.62041140049695 4 3 2.05082245231536 0.94917754768464 5 3 2.21612120204511 0.783878797954886 6 1 1.74133270002851 -0.741332700028511 7 3 2.87031132978131 0.129688670218689 8 1 2.08098147322383 -1.08098147322383 9 4 2.53215554290427 1.46784445709573 10 0 2.16574591140021 -2.16574591140021 11 3 3.22182191108718 -0.221821911087177 12 2 2.27641948012504 -0.276419480125044 13 4 3.40633148241083 0.593668517589166 14 3 1.81345111332413 1.18654888667587 15 1 1.55759346481799 -0.557593464817993 16 1 2.53131162144285 -1.53131162144285 17 2 2.18005809224787 -0.180058092247873 18 3 2.84604229490263 0.153957705097374 19 1 1.87609432768454 -0.87609432768454 20 1 1.85638381919847 -0.856383819198472 21 2 1.72470944949636 0.275290550503643 22 3 2.92711818844494 0.0728818115550605 23 4 2.96685596221917 1.03314403778083 24 2 1.85485089192599 0.145149108074011 25 1 3.00594467113655 -2.00594467113655 26 2 3.20001105524447 -1.20001105524447 27 2 2.47775354741425 -0.47775354741425 28 4 2.92493651078623 1.07506348921377 29 2 2.89926220872018 -0.899262208720176 30 3 2.14477897701892 0.855221022981077 31 3 2.43317467151192 0.566825328488078 32 3 2.85200023632632 0.147999763673682 33 4 2.7663380241536 1.23366197584640 34 2 1.99542086083910 0.00457913916090297 35 2 2.08098147322383 -0.0809814732238296 36 4 3.24234247443867 0.75765752556133 37 3 2.01965602912179 0.980343970878213 38 4 2.30131759392166 1.69868240607834 39 2 2.84519837344121 -0.845198373441206 40 5 3.20631323123742 1.79368676876258 41 3 2.74833729867187 0.251662701328128 42 1 2.04083953798721 -1.04083953798721 43 1 1.00235034187815 -0.00235034187814842 44 1 1.84546145797912 -0.845461457979123 45 2 1.95442719784219 0.0455728021578049 46 3 2.96944960763914 0.0305503923608648 47 9 3.24592941928475 5.75407058071525 48 0 1.46802786546773 -1.46802786546773 49 0 2.16340097511973 -2.16340097511973 50 2 2.81406581684363 -0.814065816843627 51 2 1.33246225730448 0.667537742695522 52 3 2.57785733246040 0.422142667539595 53 1 2.31329264478771 -1.31329264478771 54 2 1.44866159155092 0.551338408449084 55 0 2.64517404790959 -2.64517404790959 56 5 2.71009251121592 2.28990748878408 57 2 2.52099054690365 -0.520990546903648 58 4 3.29640630971764 0.70359369028236 59 3 1.54365135663480 1.45634864336520 60 0 3.09466634902540 -3.09466634902540 61 0 1.38832944687499 -1.38832944687499 62 4 3.25269741557387 0.747302584426133 63 1 3.78918946285777 -2.78918946285777 64 1 2.98473510197399 -1.98473510197399 65 4 1.59419012810339 2.40580987189661 66 2 2.70959282432375 -0.709592824323754 67 4 2.7916342250544 1.20836577494560 68 1 1.91518303660192 -0.915183036601915 69 4 2.84469868654904 1.15530131345096 70 2 1.03622592186039 0.963774078139615 71 5 2.99917667484743 2.00082332515257 72 4 2.61323143644658 1.38676856355342 73 4 2.15254634709237 1.84745365290763 74 4 2.67547460956024 1.32452539043976 75 4 2.55564838951352 1.44435161048648 76 3 2.81322189538221 0.186778104617794 77 3 2.65602867593695 0.343971324063053 78 3 2.77454515422608 0.225454845773921 79 2 1.95205620126458 0.0479437987354192 80 1 1.07038992973439 -0.0703899297343883 81 1 1.29827023499077 -0.29827023499077 82 5 3.20962367470624 1.79037632529376 83 4 2.58843492243795 1.41156507756205 84 2 2.27015117072809 -0.270151170728089 85 3 1.58008671544100 1.41991328455900 86 2 2.43716577782039 -0.437165777820387 87 2 1.83376290849034 0.166237091509656 88 2 2.43180912307684 -0.431809123076842 89 2 3.06222405067023 -1.06222405067023 90 3 1.90938054750113 1.09061945249887 91 2 2.20202386374093 -0.202023863740933 92 3 2.27776308847863 0.722236911521373 93 4 3.14189445482326 0.858105545176742 94 3 3.35994729807439 -0.359947298074392 95 3 2.39845517006826 0.601544829931735 96 0 1.79093180240399 -1.79093180240399 97 1 1.33302967738863 -0.333029677388631 98 2 1.44101580720438 0.558984192795617 99 2 2.65744001748252 -0.65744001748252 100 3 2.39436853833002 0.605631461669977 101 4 3.33511691746976 0.664883082530237 102 4 3.08786448614028 0.912135513859718 103 1 2.76084590302608 -1.76084590302608 104 2 1.44142777496563 0.558572225034369 105 2 0.823671051893065 1.17632894810694 106 3 2.15067525960883 0.849324740391165 107 3 2.02152711660532 0.97847288339468 108 3 2.99830496114822 0.00169503885177585 109 1 1.72158832494645 -0.721588324946446 110 1 1.75001172475536 -0.750011724755362 111 1 2.34576880973887 -1.34576880973887 112 1 3.10964147538699 -2.10964147538699 113 0 1.68643101764633 -1.68643101764633 114 1 2.59878986357315 -1.59878986357315 115 3 2.53031832201673 0.469681677983268 116 3 3.05950881952336 -0.0595088195233563 117 0 2.99509004310919 -2.99509004310919 118 2 1.59091355123058 0.409086448769424 119 5 2.93117095358719 2.06882904641281 120 2 2.68123715770683 -0.681237157706828 121 3 2.34932188798896 0.650678112011044 122 3 3.2351963769843 -0.235196376984300 123 5 1.71665777174678 3.28334222825322 124 4 2.77039078929585 1.22960921070415 125 4 3.12389372934153 0.876106270658472 126 0 1.54047052739368 -1.54047052739368 127 3 2.9230315567067 0.0769684432933017 128 0 2.81322189538221 -2.81322189538221 129 2 2.21699899010253 -0.216998990102528 130 0 1.73624723117849 -1.73624723117849 131 6 2.9230315567067 3.0769684432933 132 3 2.78031377673087 0.219686223269129 133 1 1.41706321465717 -0.41706321465717 134 6 2.18040232681713 3.81959767318287 135 2 2.76992496899968 -0.76992496899968 136 1 1.96291082929194 -0.96291082929194 137 3 2.99558973000135 0.00441026999864769 138 1 2.03234787803668 -1.03234787803668 139 2 3.33820417542368 -1.33820417542368 140 4 2.69973757008072 1.30026242991928 141 1 2.92895540933248 -1.92895540933248 142 2 2.70600587947768 -0.706005879477676 143 0 2.67169227143706 -2.67169227143706 144 5 2.35852253968947 2.64147746031053 145 2 2.09171451552428 -0.0917145155242786 146 1 1.13923979465797 -0.139239794657973 147 1 1.41263234834967 -0.412632348349671 148 4 2.27769535528664 1.72230464471336 149 3 3.22075480411086 -0.220754804110862 150 0 2.74019790179138 -2.74019790179138 151 3 2.62633547532465 0.373664524675354 152 3 3.01309076859092 -0.0130907685909193 153 0 1.81301915962396 -1.81301915962396 154 2 2.59882373016914 -0.598823730169140 155 5 3.01633347886774 1.98366652113226 156 2 2.13267431192519 -0.132674311925186 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.823424077388543 0.353151845222913 0.176575922611457 10 0.779558805018398 0.440882389963204 0.220441194981602 11 0.669069552909064 0.661860894181873 0.330930447090936 12 0.567046412813674 0.865907174372652 0.432953587186326 13 0.479019865716255 0.95803973143251 0.520980134283745 14 0.374756154570611 0.749512309141222 0.625243845429389 15 0.287705019789696 0.575410039579392 0.712294980210304 16 0.346736042703464 0.693472085406929 0.653263957296536 17 0.27095320817101 0.54190641634202 0.72904679182899 18 0.206173982555963 0.412347965111926 0.793826017444037 19 0.151127594575210 0.302255189150421 0.84887240542479 20 0.111174452398303 0.222348904796607 0.888825547601697 21 0.120511046024351 0.241022092048702 0.87948895397565 22 0.086682972595214 0.173365945190428 0.913317027404786 23 0.0721858795610002 0.144371759122000 0.927814120439 24 0.0566115656029318 0.113223131205864 0.943388434397068 25 0.0922420831151372 0.184484166230274 0.907757916884863 26 0.0790147212447404 0.158029442489481 0.92098527875526 27 0.0608405245197584 0.121681049039517 0.939159475480242 28 0.070161026251631 0.140322052503262 0.929838973748369 29 0.0530431082628118 0.106086216525624 0.946956891737188 30 0.0566770340867932 0.113354068173586 0.943322965913207 31 0.0482350841547162 0.0964701683094325 0.951764915845284 32 0.0354339088985067 0.0708678177970135 0.964566091101493 33 0.0383616078256309 0.0767232156512617 0.961638392174369 34 0.0279949412641024 0.0559898825282048 0.972005058735898 35 0.0191843314270802 0.0383686628541603 0.98081566857292 36 0.0151572131955214 0.0303144263910428 0.984842786804479 37 0.0139171902508264 0.0278343805016528 0.986082809749174 38 0.0226754715010825 0.0453509430021651 0.977324528498917 39 0.018269702396486 0.036539404792972 0.981730297603514 40 0.0249505061453837 0.0499010122907675 0.975049493854616 41 0.0176349038050622 0.0352698076101244 0.982365096194938 42 0.0143428749163864 0.0286857498327729 0.985657125083613 43 0.00989061470398532 0.0197812294079706 0.990109385296015 44 0.00750662762500499 0.01501325525001 0.992493372374995 45 0.00503272134329713 0.0100654426865943 0.994967278656703 46 0.00331425660317317 0.00662851320634633 0.996685743396827 47 0.280093398649187 0.560186797298373 0.719906601350813 48 0.273114327912538 0.546228655825076 0.726885672087462 49 0.319013743287547 0.638027486575095 0.680986256712453 50 0.294867926711249 0.589735853422498 0.705132073288751 51 0.279753925315252 0.559507850630504 0.720246074684748 52 0.250741173073287 0.501482346146573 0.749258826926713 53 0.244573689296539 0.489147378593079 0.75542631070346 54 0.224077669703087 0.448155339406175 0.775922330296913 55 0.343198277551388 0.686396555102776 0.656801722448612 56 0.416253738484122 0.832507476968243 0.583746261515878 57 0.374167660864889 0.748335321729778 0.625832339135111 58 0.336326506580966 0.672653013161932 0.663673493419034 59 0.347413974149647 0.694827948299293 0.652586025850353 60 0.529018510972793 0.941962978054415 0.470981489027207 61 0.522215471612316 0.955569056775368 0.477784528387684 62 0.484477390212855 0.96895478042571 0.515522609787145 63 0.627223491327932 0.745553017344137 0.372776508672069 64 0.670699094655675 0.658601810688651 0.329300905344325 65 0.749808671404105 0.50038265719179 0.250191328595895 66 0.719285445424593 0.561429109150813 0.280714554575407 67 0.711884075423549 0.576231849152901 0.288115924576451 68 0.68582266017054 0.62835467965892 0.31417733982946 69 0.672605347562828 0.654789304874344 0.327394652437172 70 0.652446805704855 0.69510638859029 0.347553194295145 71 0.692800845612182 0.614398308775636 0.307199154387818 72 0.689479521064806 0.621040957870388 0.310520478935194 73 0.715517903080208 0.568964193839583 0.284482096919792 74 0.710891207035444 0.578217585929111 0.289108792964556 75 0.712123738296976 0.575752523406049 0.287876261703024 76 0.671119268069892 0.657761463860216 0.328880731930108 77 0.62938014031476 0.74123971937048 0.37061985968524 78 0.586462835193943 0.827074329612115 0.413537164806057 79 0.540412461109037 0.919175077781926 0.459587538890963 80 0.493609007191321 0.987218014382643 0.506390992808679 81 0.449623048546083 0.899246097092166 0.550376951453917 82 0.496750877399050 0.993501754798101 0.503249122600950 83 0.499881960301622 0.999763920603244 0.500118039698378 84 0.454013042751727 0.908026085503454 0.545986957248273 85 0.458831424595288 0.917662849190577 0.541168575404712 86 0.42048946558042 0.84097893116084 0.57951053441958 87 0.375106016383693 0.750212032767387 0.624893983616307 88 0.339815312583316 0.679630625166632 0.660184687416684 89 0.317605270795698 0.635210541591395 0.682394729204302 90 0.301375532035861 0.602751064071723 0.698624467964139 91 0.262190976640837 0.524381953281673 0.737809023359163 92 0.231925335330222 0.463850670660444 0.768074664669778 93 0.210134637498360 0.420269274996721 0.78986536250164 94 0.178699460247986 0.357398920495971 0.821300539752014 95 0.154962215358259 0.309924430716517 0.845037784641741 96 0.174949130576766 0.349898261153532 0.825050869423234 97 0.145879452836730 0.291758905673460 0.85412054716327 98 0.121770155316752 0.243540310633503 0.878229844683248 99 0.102914811691459 0.205829623382919 0.89708518830854 100 0.085618208759545 0.17123641751909 0.914381791240455 101 0.0739969623266601 0.147993924653320 0.92600303767334 102 0.0653874844420825 0.130774968884165 0.934612515557917 103 0.0784162067591467 0.156832413518293 0.921583793240853 104 0.0711355937313735 0.142271187462747 0.928864406268627 105 0.0672666472245792 0.134533294449158 0.93273335277542 106 0.0562074949918657 0.112414989983731 0.943792505008134 107 0.05300553960122 0.10601107920244 0.94699446039878 108 0.0407642727190769 0.0815285454381539 0.959235727280923 109 0.0323700866819935 0.0647401733639869 0.967629913318007 110 0.0263692788287341 0.0527385576574681 0.973630721171266 111 0.0230768076688220 0.0461536153376441 0.976923192331178 112 0.0300107363081931 0.0600214726163862 0.969989263691807 113 0.0325355142536972 0.0650710285073944 0.967464485746303 114 0.0344331900406653 0.0688663800813306 0.965566809959335 115 0.0261456833140087 0.0522913666280173 0.97385431668599 116 0.0193072405001016 0.0386144810002033 0.980692759499898 117 0.0454427284426175 0.0908854568852351 0.954557271557382 118 0.0345139106609013 0.0690278213218026 0.965486089339099 119 0.0417655369171298 0.0835310738342597 0.95823446308287 120 0.0317078346309632 0.0634156692619263 0.968292165369037 121 0.0253882623695584 0.0507765247391168 0.974611737630442 122 0.0181572412929428 0.0363144825858856 0.981842758707057 123 0.0688480718455644 0.137696143691129 0.931151928154436 124 0.058103616706906 0.116207233413812 0.941896383293094 125 0.048101331393813 0.096202662787626 0.951898668606187 126 0.0433184624238062 0.0866369248476124 0.956681537576194 127 0.0314250609684691 0.0628501219369382 0.96857493903153 128 0.0871117733525593 0.174223546705119 0.91288822664744 129 0.071738838786184 0.143477677572368 0.928261161213816 130 0.100757277121648 0.201514554243295 0.899242722878352 131 0.220658046981573 0.441316093963146 0.779341953018427 132 0.176006552745457 0.352013105490913 0.823993447254543 133 0.144433056744624 0.288866113489247 0.855566943255377 134 0.648128139348192 0.703743721303616 0.351871860651808 135 0.578449798343733 0.843100403312533 0.421550201656267 136 0.504323713130948 0.991352573738104 0.495676286869052 137 0.423922180417731 0.847844360835462 0.576077819582269 138 0.454673154362546 0.909346308725093 0.545326845637454 139 0.377477668616922 0.754955337233844 0.622522331383078 140 0.438541786088808 0.877083572177616 0.561458213911192 141 0.582436238778361 0.835127522443278 0.417563761221639 142 0.522075426310623 0.955849147378754 0.477924573689377 143 0.605257612551543 0.789484774896915 0.394742387448458 144 0.504689182743459 0.990621634513082 0.495310817256541 145 0.378941510294071 0.757883020588142 0.621058489705929 146 0.43291719183645 0.8658343836729 0.56708280816355 147 0.339734261822437 0.679468523644874 0.660265738177563 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00719424460431655 OK 5% type I error level 15 0.107913669064748 NOK 10% type I error level 34 0.244604316546763 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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') }

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Software written by Ed van Stee & Patrick Wessa

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