Tutorial WS7

*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: Tue, 23 Nov 2010 19:46:06 +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/23/t1290541492yxt5q9y8yvk8lsn.htm/, Retrieved Tue, 23 Nov 2010 20:45:02 +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/23/t1290541492yxt5q9y8yvk8lsn.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 «

11 12 24 7 8 25 17 8 30 10 8 19 12 9 22 12 7 22 11 4 25 11 11 23 12 7 17 13 7 21 14 12 19 16 10 19 11 10 15 10 8 16 11 8 23 15 4 27 9 9 22 11 8 14 17 7 22 17 11 23 11 9 23 18 11 21 14 13 19 10 8 18 11 8 20 15 9 23 15 6 25 13 9 19 16 9 24 13 6 22 9 6 25 18 16 26 18 5 29 12 7 32 17 9 25 9 6 29 9 6 28 12 5 17 18 12 28 12 7 29 18 10 26 14 9 25 15 8 14 16 5 25 10 8 26 11 8 20 14 10 18 9 6 32 12 8 25 17 7 25 5 4 23 12 8 21 12 8 20 6 4 15 24 20 30 12 8 24 12 8 26 14 6 24 7 4 22 13 8 14 12 9 24 13 6 24 14 7 24 8 9 24 11 5 19 9 5 31 11 8 22 13 8 27 10 6 19 11 8 25 12 7 20 9 7 21 15 9 27 18 11 23 15 6 25 12 8 20 13 6 21 14 9 22 10 8 23 13 6 25 13 10 25 11 8 17 13 8 19 16 10 25 8 5 19 16 7 20 11 5 26 9 8 23 16 14 27 12 7 17 14 8 17 8 6 19 9 5 17 15 6 22 11 10 21 21 12 32 14 9 21 18 12 21 12 7 18 13 8 18 15 10 23 12 6 19 19 10 20 15 10 21 11 10 20 11 5 17 10 7 18 13 10 19 15 11 22 12 6 15 12 7 14 16 12 18 9 11 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation PerStandards[t] = + 18.3823499874315 + 0.313043159644399ParExpectations[t] -0.0318454635433938ParCriticism[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) 18.3823499874315 1.308238 14.0512 0 0 ParExpectations 0.313043159644399 0.118036 2.6521 0.008826 0.004413 ParCriticism -0.0318454635433938 0.150234 -0.212 0.832405 0.416202 Multiple Linear Regression - Regression Statistics Multiple R 0.244201249146055 R-squared 0.0596342500844937 Adjusted R-squared 0.0475782789317307 F-TEST (value) 4.94644930125161 F-TEST (DF numerator) 2 F-TEST (DF denominator) 156 p-value 0.00826324483165364 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.11541833268082 Sum Squared Residuals 2642.1202162626 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 21.4436791809991 2.55632081900086 2 25 20.3188883965951 4.68111160340486 3 30 23.4493199930391 6.55068000696088 4 19 21.2580178755283 -2.25801787552833 5 22 21.8522587312737 0.147741268726262 6 22 21.9159496583605 0.0840503416394744 7 25 21.6984428893463 3.30155711065369 8 23 21.4755246445426 1.52447535545745 9 17 21.9159496583605 -4.91594965836053 10 21 22.2289928180049 -1.22899281800492 11 19 22.3828086599324 -3.38280865993235 12 19 23.0725859063079 -4.07258590630794 13 15 21.5073701080859 -6.50737010808595 14 16 21.2580178755283 -5.25801787552833 15 23 21.5710610351727 1.42893896482727 16 27 22.9506155279239 4.0493844720761 17 22 20.9131292523405 1.08687074765946 18 14 21.5710610351727 -7.57106103517273 19 22 23.4811654565825 -1.48116545658252 20 23 23.3537836024089 -0.353783602408943 21 23 21.5392155716293 1.46078442837066 22 21 23.6668267620533 -2.66682676205334 23 19 22.3509631963890 -3.35096319638896 24 18 21.2580178755283 -3.25801787552833 25 20 21.5710610351727 -1.57106103517273 26 23 22.7913882102069 0.208611789793066 27 25 22.8869246008371 2.11307539916289 28 19 22.1653018909181 -3.16530189091814 29 24 23.1044313698513 0.895568630148668 30 22 22.2608382815483 -0.260838281548318 31 25 21.0086656429707 3.99133435702928 32 26 23.5075994443364 2.49240055566363 33 29 23.8578995433137 5.1421004566863 34 32 21.9159496583605 10.0840503416395 35 25 23.4174745294957 1.58252547050427 36 29 21.0086656429707 7.99133435702928 37 28 21.0086656429707 6.99133435702928 38 17 21.9796405854473 -4.97964058544731 39 28 23.6349812985099 4.36501870149005 40 29 21.9159496583605 7.08405034163947 41 26 23.6986722255967 2.30132777440326 42 25 22.4783450505625 2.52165494943746 43 14 22.8232336737503 -8.82323367375033 44 25 23.2318132240249 1.76818677597509 45 26 21.2580178755283 4.74198212447167 46 20 21.5710610351727 -1.57106103517273 47 18 22.4464995870191 -4.44649958701914 48 32 21.0086656429707 10.9913343570293 49 25 21.8841041948171 3.11589580518287 50 25 23.4811654565825 1.51883454341748 51 23 19.8201839314799 3.17981606852008 52 21 21.8841041948171 -0.884104194817132 53 20 21.8841041948171 -1.88410419481713 54 15 20.1332270911243 -5.13322709112431 55 30 25.2584765480292 4.74152345197081 56 24 21.8841041948171 2.11589580518287 57 26 21.8841041948171 4.11589580518287 58 24 22.5738814411927 1.42611855880728 59 22 20.4462702507687 1.55372974923129 60 14 22.1971473544615 -8.19714735446153 61 24 21.8522587312737 2.14774126872626 62 24 22.2608382815483 1.73916171845168 63 24 22.5420359776493 1.45796402235068 64 24 20.6000860926961 3.39991390730386 65 19 21.6665974258029 -2.66659742580291 66 31 21.0405111065141 9.95948889348588 67 22 21.5710610351727 0.428938964827266 68 27 22.1971473544615 4.80285264553847 69 19 21.3217088026151 -2.32170880261512 70 25 21.5710610351727 3.42893896482727 71 20 21.9159496583605 -1.91594965836053 72 21 20.9768201794273 0.0231798205726697 73 27 22.7913882102069 4.20861178979307 74 23 23.6668267620533 -0.666826762053342 75 25 22.8869246008371 2.11307539916289 76 20 21.8841041948171 -1.88410419481713 77 21 22.2608382815483 -1.26083828154832 78 22 22.4783450505625 -0.478345050562535 79 23 21.2580178755283 1.74198212447166 80 25 22.2608382815483 2.73916171845168 81 25 22.1334564273747 2.86654357262526 82 17 21.5710610351727 -4.57106103517273 83 19 22.1971473544615 -3.19714735446153 84 25 23.0725859063079 1.92741409369206 85 19 20.7274679468697 -1.72746794686972 86 20 23.1681222969381 -3.16812229693812 87 26 21.6665974258029 4.33340257419709 88 23 20.9449747158839 2.05502528411606 89 27 22.9452040521344 4.05479594786564 90 17 21.9159496583605 -4.91594965836053 91 17 22.5101905141059 -5.51019051410593 92 19 20.6956224833263 -1.69562248332633 93 17 21.0405111065141 -4.04051110651412 94 22 22.8869246008371 -0.886924600837115 95 21 21.5073701080859 -0.507370108085946 96 32 24.5741107774431 7.42588922255686 97 21 22.4783450505625 -1.47834505056254 98 21 23.6349812985099 -2.63498129850995 99 18 21.9159496583605 -3.91594965836053 100 18 22.1971473544615 -4.19714735446153 101 23 22.7595427466635 0.24045725333646 102 19 21.9477951219039 -2.94779512190392 103 20 24.0117153852411 -4.01171538524113 104 21 22.7595427466635 -1.75954274666354 105 20 21.5073701080859 -1.50737010808595 106 17 21.6665974258029 -4.66659742580291 107 18 21.2898633390717 -3.28986333907173 108 19 22.1334564273747 -3.13345642737474 109 22 22.7276972831201 -0.727697283120146 110 15 21.9477951219039 -6.94779512190392 111 14 21.9159496583605 -7.91594965836053 112 18 23.0088949792212 -5.00889497922115 113 24 20.8494383252538 3.15056167474624 114 35 23.6668267620533 11.3331732379467 115 29 20.5363951656094 8.46360483439064 116 21 22.2926837450917 -1.29268374509171 117 25 23.4493199930391 1.55068000696088 118 20 21.0086656429707 -1.00866564297072 119 22 22.7913882102069 -0.791388210206934 120 13 20.7593134104131 -7.75931341041311 121 26 20.4462702507687 5.55372974923129 122 17 21.9159496583605 -4.91594965836053 123 25 22.4146541234757 2.58534587652425 124 20 20.0695361640375 -0.0695361640375286 125 19 20.6637770197829 -1.66377701978293 126 21 23.4493199930391 -2.44931999303912 127 22 21.3853997297019 0.614600270298090 128 24 21.5710610351727 2.42893896482727 129 21 22.4783450505625 -1.47834505056254 130 26 21.5710610351727 4.42893896482727 131 24 22.1016109638313 1.89838903616865 132 16 21.8841041948171 -5.88410419481713 133 23 21.6665974258029 1.33340257419709 134 18 21.0723565700575 -3.07235657005751 135 16 21.8841041948171 -5.88410419481713 136 26 24.3247585448855 1.67524145511447 137 19 21.9477951219039 -2.94779512190392 138 21 22.1653018909181 -1.16530189091814 139 21 21.8522587312737 -0.852258731273738 140 22 21.7248768771002 0.275123122899836 141 23 20.9131292523405 2.08687074765946 142 29 22.7595427466635 6.24045725333646 143 21 25.2584765480292 -4.25847654802919 144 21 20.4144247872253 0.585575212774679 145 23 23.3537836024089 -0.353783602408943 146 27 21.6347519622595 5.36524803774048 147 25 23.4174745294957 1.58252547050427 148 21 21.6029064987161 -0.602906498716127 149 10 21.8522587312737 -11.8522587312737 150 20 22.4464995870191 -2.44649958701914 151 26 21.5392155716293 4.46078442837066 152 24 23.1362768333947 0.863723166605274 153 29 24.7333380951601 4.26666190483989 154 19 22.5738814411927 -3.57388144119272 155 24 24.2292221542553 -0.229222154255351 156 19 22.2608382815483 -3.26083828154832 157 24 21.5710610351727 2.42893896482727 158 22 22.7595427466635 -0.75954274666354 159 17 23.8206426039808 -6.82064260398077 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.568082632496341 0.863834735007317 0.431917367503659 7 0.422739807802873 0.845479615605746 0.577260192197127 8 0.281603840275079 0.563207680550158 0.718396159724921 9 0.519552112519362 0.960895774961276 0.480447887480638 10 0.443882303786013 0.887764607572026 0.556117696213987 11 0.457936095586342 0.915872191172683 0.542063904413658 12 0.444318094168748 0.888636188337495 0.555681905831252 13 0.567626805199936 0.864746389600129 0.432373194800064 14 0.608361982856247 0.783276034287507 0.391638017143753 15 0.536539701895451 0.926920596209098 0.463460298104549 16 0.481901985374483 0.963803970748965 0.518098014625517 17 0.414148896848305 0.82829779369661 0.585851103151695 18 0.58435147316892 0.831297053662161 0.415648526831081 19 0.521699767862112 0.956600464275776 0.478300232137888 20 0.451528553832058 0.903057107664116 0.548471446167942 21 0.400140952005603 0.800281904011206 0.599859047994397 22 0.340948787612127 0.681897575224254 0.659051212387873 23 0.286384002097254 0.572768004194508 0.713615997902746 24 0.258424736764597 0.516849473529195 0.741575263235403 25 0.209871953209755 0.419743906419509 0.790128046790245 26 0.166982378041719 0.333964756083438 0.833017621958281 27 0.134694392296594 0.269388784593188 0.865305607703406 28 0.114356614721688 0.228713229443377 0.885643385278312 29 0.0897490514681926 0.179498102936385 0.910250948531807 30 0.0671496179226434 0.134299235845287 0.932850382077357 31 0.0662134157256436 0.132426831451287 0.933786584274356 32 0.0844705568949069 0.168941113789814 0.915529443105093 33 0.0850618323429993 0.170123664685999 0.914938167657001 34 0.278502681376176 0.557005362752352 0.721497318623824 35 0.235887804108605 0.471775608217209 0.764112195891395 36 0.352876355594525 0.705752711189049 0.647123644405476 37 0.41634074847129 0.83268149694258 0.58365925152871 38 0.500699235165476 0.998601529669049 0.499300764834524 39 0.523669075615241 0.952661848769519 0.476330924384759 40 0.598992885008578 0.802014229982843 0.401007114991422 41 0.559632092076371 0.880735815847259 0.440367907923629 42 0.522016528133628 0.955966943732745 0.477983471866373 43 0.72344744342745 0.553105113145099 0.276552556572550 44 0.684661015940293 0.630677968119414 0.315338984059707 45 0.689645973763787 0.620708052472427 0.310354026236213 46 0.653955338012237 0.692089323975526 0.346044661987763 47 0.65884943589286 0.682301128214281 0.341150564107141 48 0.846888357928127 0.306223284143746 0.153111642071873 49 0.829393107571988 0.341213784856023 0.170606892428012 50 0.800398513303248 0.399202973393504 0.199601486696752 51 0.77591586330607 0.448168273387859 0.224084136693929 52 0.742462443635048 0.515075112729904 0.257537556364952 53 0.715284908792707 0.569430182414586 0.284715091207293 54 0.772737597105928 0.454524805788144 0.227262402894072 55 0.805182754602659 0.389634490794682 0.194817245397341 56 0.777924303386032 0.444151393227936 0.222075696613968 57 0.773005966956846 0.453988066086309 0.226994033043154 58 0.740152344991332 0.519695310017336 0.259847655008668 59 0.705085412815207 0.589829174369586 0.294914587184793 60 0.819342028887506 0.361315942224989 0.180657971112494 61 0.794722910955069 0.410554178089863 0.205277089044931 62 0.765908915037357 0.468182169925287 0.234091084962643 63 0.733379690527624 0.533240618944751 0.266620309472376 64 0.718992886221646 0.562014227556707 0.281007113778354 65 0.701296340808272 0.597407318383455 0.298703659191728 66 0.85685941774316 0.286281164513681 0.143140582256840 67 0.829925180683721 0.340149638632557 0.170074819316279 68 0.839539225516872 0.320921548966256 0.160460774483128 69 0.822689940952232 0.354620118095535 0.177310059047768 70 0.813369061420971 0.373261877158058 0.186630938579029 71 0.790567562203299 0.418864875593403 0.209432437796701 72 0.75734416423269 0.485311671534619 0.242655835767309 73 0.759446315430448 0.481107369139105 0.240553684569552 74 0.723927291741798 0.552145416516405 0.276072708258202 75 0.698999502683221 0.602000994633557 0.301000497316779 76 0.668474413721243 0.663051172557514 0.331525586278757 77 0.633464857845939 0.733070284308123 0.366535142154061 78 0.591162108552893 0.817675782894213 0.408837891447107 79 0.55563587983916 0.888728240321679 0.444364120160839 80 0.536300404059519 0.927399191880962 0.463699595940481 81 0.514220062008005 0.97155987598399 0.485779937991995 82 0.526327074663736 0.947345850672528 0.473672925336264 83 0.508803033696616 0.982393932606768 0.491196966303384 84 0.47503776613913 0.95007553227826 0.52496223386087 85 0.439192845846707 0.878385691693414 0.560807154153293 86 0.421096789197413 0.842193578394827 0.578903210802587 87 0.437866093785685 0.87573218757137 0.562133906214315 88 0.40702944308029 0.81405888616058 0.59297055691971 89 0.405283481158034 0.810566962316067 0.594716518841966 90 0.421115735118791 0.842231470237583 0.578884264881209 91 0.452664381534432 0.905328763068864 0.547335618465568 92 0.414238907732286 0.828477815464572 0.585761092267714 93 0.407112439469518 0.814224878939037 0.592887560530482 94 0.365546819650987 0.731093639301975 0.634453180349013 95 0.323288218796277 0.646576437592553 0.676711781203723 96 0.43320062072873 0.86640124145746 0.56679937927127 97 0.392669719620115 0.78533943924023 0.607330280379885 98 0.364324783534999 0.728649567069998 0.635675216465001 99 0.354124488524328 0.708248977048656 0.645875511475672 100 0.349603825848876 0.699207651697751 0.650396174151124 101 0.308075120690106 0.616150241380211 0.691924879309894 102 0.283329898169749 0.566659796339498 0.716670101830251 103 0.274385333351448 0.548770666702897 0.725614666648552 104 0.241023415565303 0.482046831130606 0.758976584434697 105 0.208913460838459 0.417826921676917 0.791086539161541 106 0.21081215272795 0.4216243054559 0.78918784727205 107 0.194938984364458 0.389877968728915 0.805061015635542 108 0.178660589518679 0.357321179037358 0.821339410481321 109 0.149052844903037 0.298105689806073 0.850947155096963 110 0.195885600730539 0.391771201461077 0.804114399269461 111 0.287967139071611 0.575934278143222 0.712032860928389 112 0.304358710522082 0.608717421044164 0.695641289477918 113 0.283113788390937 0.566227576781874 0.716886211609063 114 0.614941078896998 0.770117842206004 0.385058921103002 115 0.780549146092631 0.438901707814737 0.219450853907369 116 0.744017341886415 0.51196531622717 0.255982658113585 117 0.707542021545096 0.584915956909808 0.292457978454904 118 0.661469345587212 0.677061308825576 0.338530654412788 119 0.61162349557787 0.77675300884426 0.38837650442213 120 0.747375537466007 0.505248925067985 0.252624462533993 121 0.780148191234682 0.439703617530637 0.219851808765318 122 0.797063883627058 0.405872232745884 0.202936116372942 123 0.785676361663044 0.428647276673912 0.214323638336956 124 0.741510414177551 0.516979171644898 0.258489585822449 125 0.6978741208908 0.6042517582184 0.3021258791092 126 0.665048026532812 0.669903946934376 0.334951973467188 127 0.610053648135407 0.779892703729185 0.389946351864593 128 0.580253536484337 0.839492927031325 0.419746463515663 129 0.524749835323543 0.950500329352913 0.475250164676457 130 0.553972968352212 0.892054063295576 0.446027031647788 131 0.532051052901096 0.935897894197807 0.467948947098904 132 0.574360895648656 0.851278208702687 0.425639104351344 133 0.515037818179726 0.969924363640549 0.484962181820274 134 0.496210455492136 0.992420910984271 0.503789544507864 135 0.556247817867334 0.887504364265331 0.443752182132666 136 0.499639023775985 0.99927804755197 0.500360976224015 137 0.484993643367619 0.969987286735237 0.515006356632381 138 0.418761686864493 0.837523373728986 0.581238313135507 139 0.351403447529655 0.702806895059309 0.648596552470345 140 0.307135387326262 0.614270774652524 0.692864612673738 141 0.281832428696636 0.563664857393272 0.718167571303364 142 0.412394077151242 0.824788154302483 0.587605922848758 143 0.355163501873182 0.710327003746364 0.644836498126818 144 0.282555401955409 0.565110803910818 0.717444598044591 145 0.219433217334386 0.438866434668773 0.780566782665614 146 0.260863895377465 0.52172779075493 0.739136104622535 147 0.203859953314122 0.407719906628244 0.796140046685878 148 0.144568146216794 0.289136292433588 0.855431853783206 149 0.572057814427482 0.855884371145036 0.427942185572518 150 0.471420557511283 0.942841115022566 0.528579442488717 151 0.611878490666338 0.776243018667323 0.388121509333662 152 0.474840870643746 0.949681741287492 0.525159129356254 153 0.484601821935582 0.969203643871164 0.515398178064418 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:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/10bf5l1290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/10bf5l1290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/14e7s1290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/14e7s1290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/24e7s1290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/24e7s1290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/3kqw11290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/3kqw11290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/4kqw11290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/4kqw11290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/5kqw11290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/5kqw11290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/6pe6f1290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/6pe6f1290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/7ion11290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/7ion11290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/8ion11290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/8ion11290541556.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/9bf5l1290541556.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541492yxt5q9y8yvk8lsn/9bf5l1290541556.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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