verbetering WS10 Multiple regression

*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, 21 Dec 2010 08:08:54 +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/21/t1292918917bvtlrifaxfpio1f.htm/, Retrieved Tue, 21 Dec 2010 09:08:41 +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/21/t1292918917bvtlrifaxfpio1f.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 «

25 11 7 8 23 25 17 6 17 8 25 30 18 8 12 9 19 22 16 10 12 7 29 22 20 10 11 4 25 25 16 11 11 11 21 23 18 16 12 7 22 17 17 11 13 7 25 21 30 12 16 10 18 19 23 8 11 10 22 15 18 12 10 8 15 16 21 9 9 9 20 22 31 14 17 11 20 23 27 15 11 9 21 23 21 9 14 13 21 19 16 8 15 9 24 23 20 9 15 6 24 25 17 9 13 6 23 22 25 16 18 16 24 26 26 11 18 5 18 29 25 8 12 7 25 32 17 9 17 9 21 25 32 12 18 12 22 28 22 9 14 9 23 25 17 9 16 5 23 25 20 14 14 10 24 18 29 10 12 8 23 25 23 14 17 7 21 25 20 10 12 8 28 20 11 6 6 4 16 15 26 13 12 8 29 24 22 10 12 8 27 26 14 15 13 8 16 14 19 12 14 7 28 24 20 11 11 8 25 25 28 8 12 7 22 20 19 9 9 7 23 21 30 9 15 9 26 27 29 15 18 11 23 23 26 9 15 6 25 25 23 10 12 8 21 20 21 12 14 9 24 22 28 11 13 6 22 25 23 14 13 10 27 25 18 6 11 8 26 17 20 8 16 10 24 25 21 10 11 5 24 26 28 12 16 14 22 27 10 5 8 6 24 19 22 10 15 6 20 22 31 10 21 12 26 32 29 13 18 12 21 21 22 10 13 8 19 18 23 10 15 10 21 23 20 9 19 10 16 20 18 8 15 10 22 21 25 14 11 5 15 17 21 8 10 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation CM[t] = -1.97155708164813 + 0.810124516285502D[t] + 0.251253601241107PE[t] + 0.188518804715737PC[t] -0.115718741599823O[t] + 0.566064813317673PS[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) -1.97155708164813 3.052906 -0.6458 0.519378 0.259689 D 0.810124516285502 0.130335 6.2157 0 0 PE 0.251253601241107 0.13276 1.8925 0.060307 0.030154 PC 0.188518804715737 0.168259 1.1204 0.264294 0.132147 O -0.115718741599823 0.103024 -1.1232 0.263103 0.131551 PS 0.566064813317673 0.095813 5.908 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.638102890589065 R-squared 0.40717529897812 Adjusted R-squared 0.387801942735575 F-TEST (value) 21.0172823893021 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 5.55111512312578e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.47771018087769 Sum Squared Residuals 3067.63293498216 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 21.696827520052 3.30317247994805 2 17 22.7576275344242 -5.75762753442422 3 18 19.475921308563 -1.47592130856298 4 16 19.5619453157043 -3.56194531570429 5 20 20.9062047066683 -0.906204706668275 6 16 22.3667061957279 -6.36670619572789 7 18 22.4023995380277 -4.40239953802768 8 17 20.5201335863125 -3.52013358631251 9 30 22.327476885032 7.67252311496805 10 23 15.1035765940144 7.89642340598557 11 18 19.0918794530003 -1.09187945300029 12 21 19.4165662795253 1.58343372047466 13 31 26.4203200936308 4.57967990636915 14 27 25.2301666514384 1.76983334856159 15 21 19.612996323041 1.38700367695902 16 16 20.2171532176049 -4.21715321760486 17 20 21.5938509463785 -1.5938509463785 18 17 19.5088680455431 -2.50886804554309 19 25 30.4697362245754 -5.46973622457537 20 26 26.7379136808267 -0.737913680826713 21 25 24.0652193827093 0.934780617290697 22 17 23.0090707878074 -6.00907078780739 23 32 27.8387300504054 4.16126994959459 24 22 22.0238725008844 -0.0238725008844254 25 17 21.7723044845037 -4.77230448450369 26 20 22.1848414522041 -2.18484145220414 27 29 22.142971009972 6.85702899002803 28 23 26.6826557598034 -3.68265575980343 29 20 18.7340532353845 1.2659467646155 30 11 11.7902591765424 -0.790259176542405 31 26 23.3129672959119 2.68703270408813 32 22 22.2461608568904 -0.246160856890359 33 14 21.0281654373449 -7.02816543734494 34 19 22.9325499189927 -3.93254991899267 35 20 22.4704044418167 -2.47040444181673 36 28 17.6195978476967 10.3804021523033 37 19 18.1263076319767 0.873692368023276 38 30 23.0600995039614 6.93990049603859 39 29 27.134541986358 1.86545801364201 40 26 21.4781322047787 4.52186779522133 41 23 19.5440844265833 3.45591557341675 42 21 22.6403328681881 -1.64033286818809 43 28 22.9430302596669 5.05696974033307 44 23 25.5488853193873 -2.54888531938727 45 18 13.775544612248 4.22445538775199 46 20 21.7890552501971 -1.78905525019705 47 21 21.7765070663015 -0.776507066301509 48 28 27.147195644037 0.852804355963001 49 10 13.1981887926427 -3.1981887926427 50 22 21.1686559891103 0.83134401088973 51 31 28.7736261084291 2.22637389157087 52 29 24.802119615067 4.19788038493298 53 22 18.8946458843887 3.10535411561134 54 23 22.3730772796911 0.626922720308931 55 20 21.4483664364161 -1.44836643641609 56 18 19.5049798788849 -1.5049798788849 57 25 20.9638904859829 4.03610951401714 58 21 16.5635547265782 4.43644527342176 59 24 19.4904987572516 4.5095012427484 60 25 25.2360293362311 -0.23602933623114 61 13 14.5703651925901 -1.57036519259012 62 28 18.2036391664048 9.79636083359519 63 25 28.140636065485 -3.14063606548499 64 9 20.7272742072834 -11.7272742072834 65 16 17.8284411696244 -1.82844116962435 66 19 21.2002096254339 -2.20020962543391 67 29 21.6245358561065 7.37546414389351 68 14 19.0460894061991 -5.04608940619911 69 22 26.9144076581427 -4.9144076581427 70 15 15.5764012107348 -0.576401210734846 71 15 17.452226374503 -2.45222637450297 72 20 21.7886208868992 -1.78862088689923 73 18 20.2225815390998 -2.22258153909977 74 33 25.4668428039909 7.5331571960091 75 22 23.7824344363272 -1.78243443632724 76 16 16.4697006570271 -0.469700657027059 77 16 15.052432261591 0.94756773840901 78 18 21.1470742942904 -3.14707429429043 79 18 23.0959206112274 -5.09592061122735 80 22 24.7434940752527 -2.74349407525273 81 30 24.7275661238695 5.27243387613054 82 30 27.2739964505683 2.72600354943171 83 24 29.9008223341231 -5.90082233412311 84 21 25.3787580941457 -4.3787580941457 85 29 27.3918377820479 1.60816221795207 86 31 23.240508271007 7.75949172899296 87 20 18.9759710592584 1.02402894074159 88 16 14.1875805146353 1.81241948536466 89 22 18.9190989475258 3.08090105247424 90 20 20.3316462195076 -0.331646219507598 91 28 27.3269489577319 0.673051042268083 92 38 26.5958059363835 11.4041940636165 93 22 19.3348333644292 2.66516663557078 94 20 25.6868097712468 -5.68680977124681 95 17 18.0421110887897 -1.04211108878971 96 22 24.1216672736301 -2.12166727363008 97 31 26.0892814723567 4.91071852764329 98 24 24.9730696546187 -0.973069654618683 99 18 19.8643239601547 -1.86432396015473 100 23 22.3178193586678 0.682180641332218 101 15 21.6854310399808 -6.68543103998085 102 12 17.8354454157556 -5.83544541575557 103 15 15.3176615872635 -0.317661587263507 104 20 19.7765579973379 0.223442002662072 105 34 27.1596931008076 6.84030689919239 106 31 20.9185081794081 10.0814918205919 107 19 19.2929241504289 -0.292924150428892 108 21 18.2605112781375 2.73948872186254 109 22 21.960314890049 0.0396851099510343 110 24 20.3178601472182 3.68213985278175 111 32 27.7900227230014 4.20997727699858 112 33 23.6362102946555 9.36378970534448 113 13 22.0253619285962 -9.02536192859621 114 25 25.8389604910979 -0.838960491097936 115 29 27.024061914111 1.97593808588899 116 18 17.3643313167998 0.635668683200174 117 20 22.2065286208074 -2.20652862080744 118 15 20.4502048915139 -5.45020489151386 119 33 28.0994056135831 4.90059438641692 120 26 23.2430193118991 2.75698068810088 121 18 18.952868498816 -0.95286849881596 122 28 28.9774711402709 -0.977471140270934 123 17 20.1978454987339 -3.19784549873386 124 12 15.4254660880949 -3.42546608809486 125 17 20.7238630018849 -3.72386300188489 126 21 21.3354034468641 -0.335403446864113 127 18 23.0750654036623 -5.0750654036623 128 10 17.9297721146776 -7.92977211467762 129 29 24.2201359970942 4.77986400290577 130 31 18.457555194607 12.542444805393 131 19 22.9476672047626 -3.94766720476257 132 9 20.0659733838091 -11.0659733838091 133 13 22.7619883304533 -9.76198833045328 134 19 21.4342707638265 -2.43427076382648 135 21 20.7338035054779 0.266196494522131 136 23 19.953634409697 3.04636559030299 137 21 20.823548318318 0.176451681682021 138 15 22.8032661951564 -7.80326619515638 139 19 17.6573711819145 1.3426288180855 140 26 21.241739029455 4.75826097054501 141 16 17.1052598018456 -1.10525980184556 142 19 18.7314962822069 0.268503717793141 143 31 25.1990473784126 5.8009526215874 144 19 17.4133114789467 1.58668852105333 145 15 16.1706084549776 -1.1706084549776 146 23 21.984616567117 1.01538343288295 147 17 19.5772208157054 -2.57722081570542 148 21 20.1156089993067 0.884391000693341 149 17 19.4548480129136 -2.45484801291361 150 25 24.5118355020002 0.488164497999802 151 20 15.5584155586162 4.44158444138375 152 19 25.4228566000411 -6.42285660004114 153 20 21.9451042791923 -1.94510427919232 154 17 19.0367506268633 -2.03675062686334 155 21 17.0483876901129 3.95161230988708 156 26 27.6421945331063 -1.64219453310631 157 17 18.3312627872462 -1.33126278724619 158 21 21.9917911761762 -0.991791176176223 159 28 24.4504319189554 3.54956808104462 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.88674239899797 0.22651520200406 0.11325760100203 10 0.847476585570336 0.305046828859328 0.152523414429664 11 0.869006240830675 0.26198751833865 0.130993759169325 12 0.795748231243224 0.408503537513551 0.204251768756776 13 0.824722076039462 0.350555847921076 0.175277923960538 14 0.768922160387585 0.46215567922483 0.231077839612415 15 0.703040256370085 0.59391948725983 0.296959743629915 16 0.659623841955988 0.680752316088024 0.340376158044012 17 0.580825179550189 0.838349640899621 0.419174820449811 18 0.497182912291141 0.994365824582282 0.502817087708859 19 0.479872305994007 0.959744611988014 0.520127694005993 20 0.402042967789919 0.804085935579838 0.597957032210081 21 0.395844429952589 0.791688859905177 0.604155570047411 22 0.418448124115859 0.836896248231718 0.581551875884141 23 0.473653156516478 0.947306313032956 0.526346843483522 24 0.40411470430852 0.80822940861704 0.59588529569148 25 0.363944436953956 0.727888873907913 0.636055563046043 26 0.302757337995859 0.605514675991717 0.697242662004141 27 0.423560331170575 0.84712066234115 0.576439668829425 28 0.374228255017085 0.74845651003417 0.625771744982915 29 0.344948472149959 0.689896944299918 0.65505152785004 30 0.3149055601433 0.6298111202866 0.6850944398567 31 0.305472856974051 0.610945713948101 0.694527143025949 32 0.252720012202269 0.505440024404538 0.747279987797731 33 0.312874342164874 0.625748684329748 0.687125657835126 34 0.27715795825435 0.554315916508699 0.72284204174565 35 0.242575286619016 0.485150573238031 0.757424713380984 36 0.501600990205451 0.996798019589097 0.498399009794549 37 0.444532525378377 0.889065050756754 0.555467474621623 38 0.530510239896713 0.938979520206573 0.469489760103287 39 0.503053056931826 0.993893886136348 0.496946943068174 40 0.521870934531583 0.956258130936833 0.478129065468417 41 0.494517273244261 0.989034546488522 0.505482726755739 42 0.445088128676866 0.890176257353732 0.554911871323134 43 0.474070956925466 0.948141913850933 0.525929043074534 44 0.432878476846415 0.86575695369283 0.567121523153585 45 0.406900990539236 0.813801981078472 0.593099009460764 46 0.371308617366089 0.742617234732179 0.62869138263391 47 0.323269589160527 0.646539178321054 0.676730410839473 48 0.278094386627651 0.556188773255301 0.721905613372349 49 0.280889830037169 0.561779660074338 0.719110169962831 50 0.242106828404463 0.484213656808926 0.757893171595537 51 0.211848679026206 0.423697358052413 0.788151320973793 52 0.205691851289489 0.411383702578977 0.794308148710511 53 0.183964730901781 0.367929461803562 0.816035269098219 54 0.152360581072608 0.304721162145216 0.847639418927392 55 0.131285915503883 0.262571831007766 0.868714084496117 56 0.112672015087355 0.225344030174709 0.887327984912645 57 0.111907983696195 0.22381596739239 0.888092016303805 58 0.104871257107896 0.209742514215792 0.895128742892104 59 0.0970769041458973 0.194153808291795 0.902923095854103 60 0.0775858308836445 0.155171661767289 0.922414169116355 61 0.0652772772566637 0.130554554513327 0.934722722743336 62 0.135658474741993 0.271316949483985 0.864341525258007 63 0.128603704388492 0.257207408776983 0.871396295611508 64 0.332481868893956 0.664963737787911 0.667518131106044 65 0.299271870840779 0.598543741681558 0.700728129159221 66 0.272277389561176 0.544554779122353 0.727722610438824 67 0.367576798136014 0.735153596272027 0.632423201863986 68 0.388050086887236 0.776100173774471 0.611949913112764 69 0.39373447774652 0.78746895549304 0.60626552225348 70 0.350421660185773 0.700843320371546 0.649578339814227 71 0.320435434058718 0.640870868117436 0.679564565941282 72 0.284838451130802 0.569676902261603 0.715161548869198 73 0.257240766398433 0.514481532796866 0.742759233601567 74 0.334922453319789 0.669844906639578 0.665077546680211 75 0.299578191474439 0.599156382948878 0.700421808525561 76 0.262366913582606 0.524733827165211 0.737633086417394 77 0.227259442029844 0.454518884059688 0.772740557970156 78 0.210703118504108 0.421406237008216 0.789296881495892 79 0.221126115458776 0.442252230917552 0.778873884541224 80 0.199920407360797 0.399840814721595 0.800079592639203 81 0.212433907388245 0.42486781477649 0.787566092611755 82 0.191465491140587 0.382930982281174 0.808534508859413 83 0.224849021725004 0.449698043450007 0.775150978274996 84 0.22844978943166 0.456899578863321 0.77155021056834 85 0.196660286617291 0.393320573234581 0.80333971338271 86 0.257666256814711 0.515332513629421 0.742333743185289 87 0.222627384915426 0.445254769830851 0.777372615084574 88 0.194593435041257 0.389186870082513 0.805406564958743 89 0.17759149376067 0.35518298752134 0.82240850623933 90 0.148778979151357 0.297557958302714 0.851221020848643 91 0.123440041036462 0.246880082072924 0.876559958963538 92 0.303586478465122 0.607172956930244 0.696413521534878 93 0.274413532491697 0.548827064983394 0.725586467508303 94 0.305020168683013 0.610040337366026 0.694979831316987 95 0.267604840652839 0.535209681305677 0.732395159347161 96 0.240576900992972 0.481153801985945 0.759423099007028 97 0.234979861802566 0.469959723605132 0.765020138197434 98 0.204238338014135 0.40847667602827 0.795761661985865 99 0.178118315630819 0.356236631261639 0.82188168436918 100 0.148516265410345 0.29703253082069 0.851483734589655 101 0.189973117821925 0.379946235643849 0.810026882178075 102 0.197514584004801 0.395029168009602 0.802485415995199 103 0.167356038338237 0.334712076676474 0.832643961661763 104 0.140070513829302 0.280141027658603 0.859929486170698 105 0.172173518710358 0.344347037420716 0.827826481289642 106 0.326573291463565 0.65314658292713 0.673426708536435 107 0.285125555857219 0.570251111714438 0.714874444142781 108 0.263817426978216 0.527634853956432 0.736182573021784 109 0.224220227944382 0.448440455888763 0.775779772055618 110 0.212427350338538 0.424854700677075 0.787572649661462 111 0.201558817549689 0.403117635099377 0.798441182450311 112 0.318885696959492 0.637771393918984 0.681114303040508 113 0.443248751042942 0.886497502085884 0.556751248957058 114 0.393418952708781 0.786837905417561 0.606581047291219 115 0.370229296539652 0.740458593079304 0.629770703460348 116 0.321974506753488 0.643949013506976 0.678025493246512 117 0.287155434417223 0.574310868834445 0.712844565582777 118 0.295274290989087 0.590548581978175 0.704725709010913 119 0.315698958499237 0.631397916998474 0.684301041500763 120 0.311962579747457 0.623925159494913 0.688037420252543 121 0.266102838778869 0.532205677557738 0.733897161221131 122 0.245365514954415 0.49073102990883 0.754634485045585 123 0.216677486264407 0.433354972528814 0.783322513735593 124 0.189416440447017 0.378832880894034 0.810583559552983 125 0.181290125570027 0.362580251140054 0.818709874429973 126 0.145802623479987 0.291605246959974 0.854197376520013 127 0.1509275561663 0.301855112332599 0.8490724438337 128 0.211496528638068 0.422993057276136 0.788503471361932 129 0.348825427878732 0.697650855757464 0.651174572121268 130 0.786007764187513 0.427984471624973 0.213992235812487 131 0.742947574498913 0.514104851002175 0.257052425501087 132 0.918832286342411 0.162335427315178 0.0811677136575888 133 0.975559286907222 0.0488814261855555 0.0244407130927777 134 0.96301159143426 0.0739768171314799 0.03698840856574 135 0.945156868775637 0.109686262448726 0.0548431312243628 136 0.962103374716449 0.0757932505671025 0.0378966252835512 137 0.941785160568366 0.116429678863267 0.0582148394316336 138 0.96298062388259 0.0740387522348211 0.0370193761174105 139 0.94145451161154 0.11709097677692 0.0585454883884602 140 0.939146152757193 0.121707694485614 0.0608538472428072 141 0.905889921171444 0.188220157657112 0.094110078828556 142 0.859775517871819 0.280448964256363 0.140224482128181 143 0.937507459271723 0.124985081456555 0.0624925407282775 144 0.898588144227891 0.202823711544217 0.101411855772109 145 0.855156306197777 0.289687387604446 0.144843693802223 146 0.805600096783374 0.388799806433253 0.194399903216626 147 0.747496074641267 0.505007850717466 0.252503925358733 148 0.635209668107554 0.729580663784892 0.364790331892446 149 0.641557194710694 0.716885610578612 0.358442805289306 150 0.509790890383276 0.980418219233447 0.490209109616724 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 0.00704225352112676 OK 10% type I error level 4 0.028169014084507 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/1046su1292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/1046su1292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/1x5vj1292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/1x5vj1292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/2x5vj1292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/2x5vj1292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/38edm1292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/38edm1292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/48edm1292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/48edm1292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/58edm1292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/58edm1292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/6i5c61292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/6i5c61292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/7twt91292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/7twt91292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/8twt91292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/8twt91292918923.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/9twt91292918923.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918917bvtlrifaxfpio1f/9twt91292918923.ps (open in new window)

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') }

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