*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, 16 Nov 2010 09:22:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g.htm/, Retrieved Tue, 16 Nov 2010 10:22:20 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g.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 15 19 0 18 3 24 2 18 3 32 12 23 3 23 0 23 12 25 15 24 0 22 10 30 20 25 20 17 2 30 3 25 16 25 4 26 2 23 4 19 0 19 0 35 15 21 9 25 1 23 15 20 5 23 4 19 15 24 4 17 12 27 2 27 4 18 2 24 4 22 8 26 30 23 6 26 6 25 7 14 4 20 17 26 5 18 0 22 3 25 4 29 15 21 0 25 8 24 10 22 4 22 0 32 6 23 11 31 10 18 0 23 0 19 0 26 0 14 0 27 0 20 0 22 7 24 4 32 12 25 6 21 12 21 10 28 9 24 0 23 16 24 2 21 0 13 0 21 1 17 10 29 14 25 12 16 12 25 12 20 5 25 0 21 4 23 3 21 0 26 3 19 0 20 12 21 12 19 15 14 0 22 8 14 6 20 14 19 5 29 10 25 16 21 4 22 0 15 8 22 12 19 6 28 4 25 20 17 0 21 13 19 0 27 0 29 0 22 0 19 10 20 6 16 16 24 6 17 0 21 4 22 9 26 17 17 12 17 3 19 8 19 3 17 0 27 10 25 3 19 0 16 8 15 0 24 4 15 13 20 12 29 16 19 20 29 20 24 14 24 12 21 15 23 9 23 4 22 8 26 0 22 13 29 0 21 21 22 0 20 1 21 16 18 12 18 2

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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk 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 Perf[t] = + 22.7825279552759 + 0.155112807490104`Sport `[t] -0.0208146540949294t + 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) 22.7825279552759 0.741305 30.733 0 0 `Sport ` 0.155112807490104 0.053092 2.9216 0.004036 0.002018 t -0.0208146540949294 0.007724 -2.6947 0.007872 0.003936 Multiple Linear Regression - Regression Statistics Multiple R 0.302294182368804 R-squared 0.0913817726940237 Adjusted R-squared 0.0789349476624349 F-TEST (value) 7.3417737022981 F-TEST (DF numerator) 2 F-TEST (DF denominator) 146 p-value 0.000915894527868333 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.04369293085108 Sum Squared Residuals 2387.31206777619 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 25.0884054135325 -0.088405413532502 2 19 22.740898647086 -3.74089864708604 3 18 23.1854224154614 -5.18542241546142 4 24 23.0094949538764 0.990505046123614 5 18 23.1437931072716 -5.14379310727156 6 32 24.5189937205876 7.48100627941244 7 23 23.1021637990817 -0.102163799081701 8 23 22.6160107225165 0.383989277483539 9 23 24.4565497583028 -1.45654975830277 10 25 24.9010735266782 0.0989264733218449 11 24 22.5535667602317 1.44643323976833 12 22 24.0838801810378 -2.08388018103778 13 30 25.6141936018439 4.38580639815612 14 25 25.593378947749 -0.593378947748955 15 17 22.7805337588322 -5.78053375883216 16 30 22.9148319122273 7.08516808777266 17 25 24.9104837555038 0.0895162444962468 18 25 23.0283154115276 1.97168458847242 19 26 22.6972751424524 3.30272485754756 20 23 22.9866861033377 0.0133138966622778 21 19 22.3454202192824 -3.34542021928238 22 19 22.3246055651875 -3.32460556518745 23 35 24.6304830234441 10.3695169765559 24 21 23.6789915244085 -2.67899152440852 25 25 22.4172744103928 2.58272558960723 26 23 24.5680390611593 -1.56803906115928 27 20 22.9960963321633 -2.99609633216332 28 23 22.8201688705783 0.179831129421713 29 19 24.5055950988745 -5.5055950988745 30 24 22.7785395623884 1.22146043761157 31 17 23.9986273682143 -6.99862736821433 32 27 22.4266846392184 4.57331536078164 33 27 22.7160956001036 4.28390439989636 34 18 22.3850553310285 -4.3850553310285 35 24 22.6744662919138 1.32553370808622 36 22 23.2741028677793 -1.27410286777927 37 26 26.6657699784666 -0.665769978466615 38 23 22.9222479446092 0.0777520553907997 39 26 22.9014332905143 3.09856670948573 40 25 23.0357314439094 1.96426855609056 41 14 22.5495783673442 -8.5495783673442 42 20 24.5452302106206 -4.54523021062062 43 26 22.6630618666445 3.33693813335555 44 18 21.866683175099 -3.866683175099 45 22 22.3112069434744 -0.311206943474384 46 25 22.4455050968696 2.55449490313044 47 29 24.1309313251658 4.86906867483423 48 21 21.7834245587193 -0.783424558719285 49 25 23.0035123645452 1.99648763545482 50 24 23.2929233254305 0.707076674569538 51 22 22.3414318263949 -0.341431826394911 52 22 21.7001659423396 0.299834057660432 53 32 22.6100281331853 9.38997186681474 54 23 23.3647775165408 -0.364777516540848 55 31 23.1888500549558 7.81114994504419 56 18 21.6169073259599 -3.61690732595985 57 23 21.5960926718649 1.40390732813508 58 19 21.57527801777 -2.57527801776999 59 26 21.5544633636751 4.44553663632494 60 14 21.5336487095801 -7.53364870958013 61 27 21.5128340554852 5.4871659445148 62 20 21.4920194013903 -1.49201940139027 63 22 22.5569943997261 -0.556994399726069 64 24 22.0708413231608 1.92915867683917 65 32 23.2909291289867 8.70907087101327 66 25 22.3394376299512 2.66056237004882 67 21 23.2492998207969 -2.24929982079687 68 21 22.9182595517217 -1.91825955172173 69 28 22.7423320901367 5.2576679098633 70 24 21.3255021686308 2.67449783136916 71 23 23.7864924343776 -0.786492434377566 72 24 21.5940984754212 2.40590152457881 73 21 21.263058206346 -0.26305820634605 74 13 21.2422435522511 -8.24224355225112 75 21 21.3765417056463 -0.376541705646295 76 17 22.7517423189623 -5.7517423189623 77 29 23.3513788948278 5.64862110517222 78 25 23.0203386257526 1.97966137424735 79 16 22.9995239716577 -6.99952397165772 80 25 22.9787093175628 2.02129068243721 81 20 21.8721050110371 -1.87210501103713 82 25 21.0757263194917 3.92427368050831 83 21 21.6753628953572 -0.67536289535717 84 23 21.4994354337721 1.50056456622786 85 21 21.0132823572069 -0.0132823572068975 86 26 21.4578061255823 4.54219387441772 87 19 20.971653049017 -1.97165304901704 88 20 22.8121920848034 -2.81219208480335 89 21 22.7913774307084 -1.79137743070842 90 19 23.2359011990838 -4.2359011990838 91 14 20.8883944326373 -6.88839443263732 92 22 22.1084822384632 -0.10848223846322 93 14 21.7774419693881 -7.77744196938808 94 20 22.997529775214 -2.99752977521398 95 19 21.5806998537081 -2.58069985370812 96 29 22.3354492370637 6.66455076293629 97 25 23.2453114279094 1.7546885720906 98 21 21.3631430839332 -0.36314308393323 99 22 20.7218771998779 1.27812280012211 100 15 21.9419650057038 -6.94196500570378 101 22 22.5416015815693 -0.54160158156927 102 19 21.5901100825337 -2.59011008253372 103 28 21.2590698134586 6.74093018654142 104 25 23.7200600792053 1.27993992079469 105 17 20.5969892753083 -3.59698927530831 106 21 22.5926411185847 -1.59264111858473 107 19 20.5553599671185 -1.55535996711845 108 27 20.5345453130235 6.46545468697648 109 29 20.5137306589286 8.48626934107141 110 22 20.4929160048337 1.50708399516634 111 19 22.0232294256398 -3.02322942563977 112 20 21.3819635415844 -1.38196354158442 113 16 22.9122769623905 -6.91227696239053 114 24 21.3403342333946 2.65966576660543 115 17 20.388842734359 -3.38884273435902 116 21 20.9884793102245 0.0115206897754997 117 22 21.7432286935801 0.256771306419911 118 26 22.963316499406 3.03668350059401 119 17 22.1669378078605 -5.16693780786054 120 17 20.7501078863547 -3.75010788635468 121 19 21.5048572697103 -2.50485726971027 122 19 20.7084785781648 -1.70847857816482 123 17 20.2223255015996 -3.22232550159958 124 27 21.7526389224057 5.24736107759431 125 25 20.64603461588 4.35396538411997 126 19 20.1598815393148 -1.15988153931479 127 16 21.3799693451407 -5.37996934514069 128 15 20.1182522311249 -5.11825223112493 129 24 20.7178888069904 3.28211119300958 130 15 22.0930894203064 -7.09308942030642 131 20 21.9171619587214 -1.91716195872139 132 29 22.5167985345869 6.48320146541313 133 19 23.1164351104524 -4.11643511045236 134 29 23.0956204563574 5.90437954364257 135 24 22.1441289573219 1.85587104267812 136 24 21.8130886882467 2.18691131175326 137 21 22.2576124566221 -1.25761245662212 138 23 21.3061209575866 1.69387904241343 139 23 20.5097422660411 2.49025773395888 140 22 21.1093788419066 0.890621158093391 141 26 19.8476617278909 6.15233827210915 142 22 21.8433135711673 0.156686428832732 143 29 19.806032419701 9.193967580299 144 21 23.0425867228982 -2.04258672289824 145 22 19.7644031115111 2.23559688848887 146 20 19.8987012649063 0.101298735093692 147 21 22.2045787231629 -1.20457872316293 148 18 21.5633128391076 -3.56331283910759 149 18 19.9913701101116 -1.99137011011162 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.582800650929598 0.834398698140803 0.417199349070402 7 0.435545111644209 0.871090223288418 0.564454888355791 8 0.292289429760681 0.584578859521361 0.70771057023932 9 0.493654642593705 0.98730928518741 0.506345357406295 10 0.434722517323475 0.86944503464695 0.565277482676525 11 0.347813149569214 0.695626299138427 0.652186850430786 12 0.332628354246124 0.665256708492247 0.667371645753876 13 0.259540213821724 0.519080427643447 0.740459786178276 14 0.243576471730367 0.487152943460734 0.756423528269633 15 0.275444807559356 0.550889615118712 0.724555192440644 16 0.503182555487424 0.993634889025152 0.496817444512576 17 0.440691486121247 0.881382972242494 0.559308513878753 18 0.369548883785815 0.73909776757163 0.630451116214185 19 0.319177953731718 0.638355907463435 0.680822046268282 20 0.263805465456964 0.527610930913927 0.736194534543036 21 0.268306545417032 0.536613090834064 0.731693454582968 22 0.252061315341955 0.50412263068391 0.747938684658045 23 0.446492639963492 0.892985279926984 0.553507360036508 24 0.471524968965059 0.943049937930118 0.528475031034941 25 0.423457851157494 0.846915702314988 0.576542148842506 26 0.433527700356305 0.86705540071261 0.566472299643695 27 0.422044140669184 0.844088281338368 0.577955859330816 28 0.360493286526759 0.720986573053519 0.639506713473241 29 0.474680000463561 0.949360000927121 0.525319999536439 30 0.421599561313652 0.843199122627305 0.578400438686348 31 0.549418726707546 0.901162546584908 0.450581273292454 32 0.584590625112495 0.830818749775009 0.415409374887505 33 0.588323322009657 0.823353355980685 0.411676677990343 34 0.593457527685261 0.813084944629478 0.406542472314739 35 0.543707020892855 0.91258595821429 0.456292979107145 36 0.493847671631311 0.987695343262622 0.506152328368689 37 0.44763987536186 0.895279750723719 0.55236012463814 38 0.393095751903737 0.786191503807473 0.606904248096263 39 0.370881917580491 0.741763835160982 0.629118082419509 40 0.329309894281172 0.658619788562344 0.670690105718828 41 0.504365711423514 0.991268577152973 0.495634288576486 42 0.51530454802614 0.96939090394772 0.48469545197386 43 0.507923562289059 0.984152875421883 0.492076437710941 44 0.492049002750244 0.984098005500488 0.507950997249756 45 0.441549175559515 0.88309835111903 0.558450824440485 46 0.417828873425481 0.835657746850962 0.582171126574519 47 0.435764965615552 0.871529931231105 0.564235034384448 48 0.387214490047403 0.774428980094806 0.612785509952597 49 0.349397330091659 0.698794660183319 0.65060266990834 50 0.303931527158761 0.607863054317522 0.696068472841239 51 0.261332609793451 0.522665219586901 0.738667390206549 52 0.222334973646272 0.444669947292544 0.777665026353728 53 0.398632015834575 0.79726403166915 0.601367984165425 54 0.354790897178209 0.709581794356418 0.645209102821791 55 0.45911308446471 0.91822616892942 0.54088691553529 56 0.458404241820977 0.916808483641953 0.541595758179024 57 0.413474613025886 0.826949226051772 0.586525386974114 58 0.390160761781752 0.780321523563504 0.609839238218248 59 0.391798478674314 0.783596957348629 0.608201521325686 60 0.521273988775641 0.957452022448717 0.478726011224359 61 0.552710437738966 0.894579124522068 0.447289562261034 62 0.513946405298536 0.972107189402928 0.486053594701464 63 0.469698853144491 0.939397706288982 0.530301146855509 64 0.429825412391562 0.859650824783124 0.570174587608438 65 0.578669041025091 0.842661917949819 0.421330958974909 66 0.549667409156033 0.900665181687934 0.450332590843967 67 0.531975407665779 0.936049184668442 0.468024592334221 68 0.504302901092716 0.991394197814568 0.495697098907284 69 0.534303120150229 0.931393759699543 0.465696879849772 70 0.507761363398959 0.984477273202082 0.492238636601041 71 0.475963118120844 0.951926236241688 0.524036881879156 72 0.448107593760381 0.896215187520762 0.551892406239619 73 0.404782204611822 0.809564409223643 0.595217795388178 74 0.555308726641486 0.889382546717027 0.444691273358514 75 0.50926528602701 0.98146942794598 0.49073471397299 76 0.558595160393434 0.882809679213132 0.441404839606566 77 0.61514671415425 0.7697065716915 0.38485328584575 78 0.591335822328223 0.817328355343553 0.408664177671777 79 0.672097426942138 0.655805146115725 0.327902573057862 80 0.64962183083088 0.70075633833824 0.35037816916912 81 0.612020713069854 0.775958573860292 0.387979286930146 82 0.616771424583022 0.766457150833956 0.383228575416978 83 0.572239609643519 0.855520780712963 0.427760390356481 84 0.537383924647147 0.925232150705706 0.462616075352853 85 0.490888574561567 0.981777149123135 0.509111425438433 86 0.522110791778125 0.95577841644375 0.477889208221875 87 0.481764955069025 0.96352991013805 0.518235044930975 88 0.452937895427056 0.905875790854112 0.547062104572944 89 0.413858026498772 0.827716052997544 0.586141973501228 90 0.403853096495924 0.807706192991847 0.596146903504077 91 0.475296520452863 0.950593040905726 0.524703479547137 92 0.428495463945716 0.856990927891433 0.571504536054284 93 0.536464374469229 0.927071251061542 0.463535625530771 94 0.50422906394473 0.99154187211054 0.49577093605527 95 0.471376372887438 0.942752745774877 0.528623627112562 96 0.575641785378096 0.848716429243809 0.424358214621904 97 0.552077330160464 0.895845339679072 0.447922669839536 98 0.502046890793035 0.99590621841393 0.497953109206965 99 0.45913600468953 0.918272009379059 0.54086399531047 100 0.532381184446461 0.935237631107078 0.467618815553539 101 0.481760915525998 0.963521831051996 0.518239084474002 102 0.447124805089283 0.894249610178565 0.552875194910717 103 0.548032484170709 0.903935031658583 0.451967515829291 104 0.525396957770364 0.949206084459272 0.474603042229636 105 0.511245807834967 0.977508384330066 0.488754192165033 106 0.460704724279425 0.92140944855885 0.539295275720575 107 0.4179132718045 0.835826543608999 0.5820867281955 108 0.49907071540775 0.998141430815501 0.50092928459225 109 0.707547785819024 0.584904428361952 0.292452214180976 110 0.679132097001469 0.641735805997062 0.320867902998531 111 0.637699451051364 0.724601097897271 0.362300548948636 112 0.5854714092593 0.8290571814814 0.4145285907407 113 0.632649071130558 0.734701857738884 0.367350928869442 114 0.62325205398005 0.7534958920399 0.37674794601995 115 0.590849845411968 0.818300309176064 0.409150154588032 116 0.535556232274923 0.928887535450154 0.464443767725077 117 0.482914398236815 0.965828796473631 0.517085601763185 118 0.505468799268897 0.989062401462206 0.494531200731103 119 0.495556878153298 0.991113756306595 0.504443121846702 120 0.471393502615334 0.942787005230667 0.528606497384666 121 0.424033280015323 0.848066560030645 0.575966719984677 122 0.374539996926254 0.749079993852507 0.625460003073746 123 0.371582302423815 0.74316460484763 0.628417697576185 124 0.412324247411587 0.824648494823173 0.587675752588414 125 0.420132344283496 0.840264688566993 0.579867655716504 126 0.361226578114273 0.722453156228545 0.638773421885727 127 0.408394501952069 0.816789003904137 0.591605498047931 128 0.603466120619809 0.793067758760383 0.396533879380191 129 0.539446201982315 0.92110759603537 0.460553798017685 130 0.850822884232981 0.298354231534038 0.149177115767019 131 0.919345669959572 0.161308660080857 0.0806543300404284 132 0.927654248152434 0.144691503695131 0.0723457518475656 133 0.968985891141818 0.0620282177163634 0.0310141088581817 134 0.98598339727929 0.0280332054414199 0.0140166027207099 135 0.973909745403927 0.0521805091921459 0.0260902545960729 136 0.953392044500688 0.0932159109986231 0.0466079554993116 137 0.942161201637988 0.115677596724025 0.0578387983620123 138 0.914957071215785 0.17008585756843 0.085042928784215 139 0.9004233350777 0.1991533298446 0.0995766649222998 140 0.923228011153624 0.153543977692751 0.0767719888463756 141 0.86680337899195 0.266393242016102 0.133196621008051 142 0.869949716382436 0.260100567235128 0.130050283617564 143 0.96917641571917 0.0616471685616589 0.0308235842808294 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 0.0072463768115942 OK 10% type I error level 5 0.036231884057971 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/10tgr01289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/10tgr01289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/15fu61289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/15fu61289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/25fu61289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/25fu61289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/3focr1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/3focr1289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/4focr1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/4focr1289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/5focr1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/5focr1289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/6qytu1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/6qytu1289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/70paf1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/70paf1289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/80paf1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/80paf1289899365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/90paf1289899365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899337826rk5ye5exeo1g/90paf1289899365.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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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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