PAPER BAEYENS (Multiple Linear Regression1)

*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 13:34:26 +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/t1292939625yuprl7itvxbmp9b.htm/, Retrieved Tue, 21 Dec 2010 14:53:55 +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/t1292939625yuprl7itvxbmp9b.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 «

13 5 14 12 3 18 15 0 11 12 7 12 10 4 16 12 1 18 15 6 14 9 3 14 12 12 15 11 0 15 11 5 17 11 6 19 15 6 10 7 6 16 11 2 18 11 1 14 10 5 14 14 7 17 10 3 14 6 3 16 11 3 18 15 7 11 11 8 14 12 6 12 14 3 17 15 5 9 9 5 16 13 10 14 13 2 15 16 6 11 13 4 16 12 6 13 14 8 17 11 4 15 9 5 14 16 10 16 12 6 9 10 7 15 13 4 17 16 10 13 14 4 15 15 3 16 5 3 16 8 3 12 11 3 12 16 7 11 17 15 15 9 0 15 9 0 17 13 4 13 10 5 16 6 5 14 12 2 11 8 3 12 14 0 12 12 9 15 11 2 16 16 7 15 8 7 12 15 0 12 7 0 8 16 10 13 14 2 11 16 1 14 9 8 15 14 6 10 11 11 11 13 3 12 15 8 15 5 6 15 15 9 14 13 9 16 11 8 15 11 8 15 12 7 13 12 6 12 12 5 17 12 4 13 14 6 15 6 3 13 7 2 15 14 12 16 14 8 15 10 5 16 13 9 15 12 6 14 9 5 15 12 2 14 16 4 13 10 7 7 14 5 17 10 6 13 16 7 15 15 8 14 12 6 13 10 0 16 8 1 12 8 5 14 11 5 17 13 5 15 16 7 17 16 7 12 14 1 16 11 3 11 4 4 15 14 8 9 9 6 16 14 6 15 8 2 10 8 2 10 11 3 15 12 3 11 11 0 13 14 2 14 15 8 18 16 8 16 1 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation IEP[t] = + 12.4178609588345 + 0.272671749159568WP[t] -0.123934071881719HS[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) 12.4178609588345 1.428251 8.6945 0 0 WP 0.272671749159568 0.072595 3.7561 0.000245 0.000122 HS -0.123934071881719 0.096627 -1.2826 0.201569 0.100784 Multiple Linear Regression - Regression Statistics Multiple R 0.307001335081348 R-squared 0.0942498197417304 Adjusted R-squared 0.0824099481043673 F-TEST (value) 7.96037513145893 F-TEST (DF numerator) 2 F-TEST (DF denominator) 153 p-value 0.000514215104067017 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.81302234661533 Sum Squared Residuals 1210.70349255125 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.0461426982883 0.953857301711705 2 12 11.0050629124423 0.994937087557735 3 15 11.0545861681356 3.9454138318644 4 12 12.8393543403708 -0.83935434037085 5 10 11.5256028053653 -1.52560280536527 6 12 10.4597194141231 1.54028058587687 7 15 12.3188144474478 2.68118555255216 8 9 11.5007991999691 -2.50079919996914 9 12 13.8309108705235 -1.83091087052353 10 11 10.5588498806087 0.441150119391281 11 11 11.6743404826431 -0.674340482643119 12 11 11.6991440880392 -0.699144088039249 13 15 12.8145507349747 2.18544926502528 14 7 12.0709463036844 -5.07094630368441 15 11 10.7323911632827 0.267608836717303 16 11 10.95545570165 0.0445442983499943 17 10 12.0461426982883 -2.04614269828828 18 14 12.2196839809623 1.78031601903775 19 10 11.5007991999691 -1.50079919996914 20 6 11.2529310562057 -5.2529310562057 21 11 11.0050629124423 -0.00506291244226453 22 15 12.9632884122526 2.03671158774743 23 11 12.864157945767 -1.86415794576698 24 12 12.5666825912113 -0.566682591211283 25 14 11.128996984324 2.87100301567602 26 15 12.6658130576969 2.33418694230313 27 9 11.7982745545248 -2.79827455452484 28 13 13.4095014440861 -0.409501444086115 29 13 11.1041933789279 1.89580662107215 30 16 12.690616663093 3.309383336907 31 13 11.5256028053653 1.47439719463473 32 12 12.4427485193296 -0.442748519329564 33 14 12.4923557301218 1.50764426987818 34 11 11.649536877247 -0.64953687724699 35 9 12.0461426982883 -3.04614269828828 36 16 13.1616333003227 2.83836669967732 37 12 12.9384848068564 -0.93848480685644 38 10 12.4675521247257 -2.46755212472569 39 13 11.4016687334836 1.59833126651645 40 16 13.5334355159678 2.46656448403217 41 14 11.649536877247 2.35046312275301 42 15 11.2529310562057 3.7470689437943 43 5 11.2529310562057 -6.2529310562057 44 8 11.7486673437326 -3.74866734373258 45 11 11.7486673437326 -0.74866734373258 46 16 12.9632884122526 3.03671158774743 47 17 14.6489261180022 2.35107388199777 48 9 10.5588498806087 -1.55884988060872 49 9 10.3109817368453 -1.31098173684528 50 13 11.8974050210104 1.10259497898957 51 10 11.7982745545248 -1.79827455452484 52 6 12.0461426982883 -6.04614269828828 53 12 11.5999296664547 0.400070333545269 54 8 11.7486673437326 -3.74866734373258 55 14 10.9306520962539 3.06934790374612 56 12 13.0128956230448 -1.01289562304483 57 11 10.9802593070461 0.0197406929538648 58 16 12.4675521247257 3.53244787527431 59 8 12.8393543403708 -4.83935434037085 60 15 10.9306520962539 4.06934790374612 61 7 11.4263883837808 -4.42638838378075 62 16 13.5334355159678 2.46656448403217 63 14 11.5999296664547 2.40007033354527 64 16 10.95545570165 5.04454429834999 65 9 12.7402238738853 -3.74022387388526 66 14 12.8145507349747 1.18544926502528 67 11 14.0539754088908 -3.05397540889084 68 13 11.7486673437326 1.25133265626742 69 15 12.7402238738853 2.25977612611474 70 5 12.1948803755661 -7.19488037556613 71 15 13.1368296949265 1.86317030507345 72 13 12.8889615511631 0.111038448836891 73 11 12.7402238738853 -1.74022387388526 74 11 12.7402238738853 -1.74022387388526 75 12 12.7154202684891 -0.715420268489131 76 12 12.5666825912113 -0.566682591211283 77 12 11.6743404826431 0.325659517356881 78 12 11.8974050210104 0.102594978989572 79 14 12.1948803755661 1.80511962443387 80 6 11.6247332718509 -5.62473327185086 81 7 11.1041933789279 -4.10419337892785 82 14 13.7069767986418 0.293023201358187 83 14 12.7402238738853 1.25977612611474 84 10 11.7982745545248 -1.79827455452484 85 13 13.0128956230448 -0.0128956230448286 86 12 12.3188144474478 -0.318814447447845 87 9 11.9222086264066 -2.92220862640656 88 12 11.2281274508096 0.771872549190426 89 16 11.8974050210104 4.10259497898957 90 10 13.4590246997794 -3.45902469977945 91 14 11.6743404826431 2.32565951735688 92 10 12.4427485193296 -2.44274851932956 93 16 12.4675521247257 3.53244787527431 94 15 12.864157945767 2.13584205423302 95 12 12.4427485193296 -0.442748519329564 96 10 10.434915808727 -0.434915808726999 97 8 11.2033238454134 -3.20332384541344 98 8 12.0461426982883 -4.04614269828828 99 11 11.6743404826431 -0.674340482643119 100 13 11.9222086264066 1.07779137359344 101 16 12.2196839809623 3.78031601903775 102 16 12.8393543403708 3.16064565962915 103 14 10.7075875578866 3.29241244211343 104 11 11.8726014156143 -0.872601415614299 105 4 11.649536877247 -7.64953687724699 106 14 13.4838283051756 0.516171694824424 107 9 12.0709463036844 -3.07094630368441 108 14 12.1948803755661 1.80511962443387 109 8 11.7238637383365 -3.72386373833645 110 8 11.7238637383365 -3.72386373833645 111 11 11.3768651280874 -0.376865128087422 112 12 11.8726014156143 0.127398584385701 113 11 10.8067180243722 0.193281975627843 114 14 11.2281274508096 2.77187254919043 115 15 12.3684216582401 2.6315783417599 116 16 12.6162898020035 3.38371019799646 117 16 10.6827839524904 5.31721604750956 118 11 12.0461426982883 -1.04614269828828 119 14 13.1368296949265 0.863170305073452 120 14 12.3188144474478 1.68118555255216 121 12 12.5666825912113 -0.566682591211283 122 14 11.5007991999691 2.49920080003086 123 8 13.0128956230448 -5.01289562304483 124 13 12.4675521247257 0.532447875274307 125 16 12.7402238738853 3.25977612611474 126 12 10.8067180243722 1.19328197562784 127 16 12.2196839809623 3.78031601903775 128 12 10.3109817368453 1.68901826315472 129 11 11.4264723388797 -0.426472338879681 130 4 10.5588498806087 -6.55884988060872 131 16 14.6241225126061 1.37587748739389 132 15 12.6658130576969 2.33418694230313 133 10 11.1041933789279 -1.10419337892785 134 13 12.7402238738853 0.259776126114739 135 15 11.649536877247 3.35046312275301 136 12 10.9802593070461 1.01974069295387 137 14 12.690616663093 1.309383336907 138 7 11.5007991999691 -4.50079919996914 139 19 12.4179449139334 6.58205508606657 140 12 13.0128956230448 -1.01289562304483 141 12 11.6247332718509 0.37526672814914 142 13 11.3768651280874 1.62313487191258 143 15 10.434915808727 4.565084191273 144 8 13.4095014440861 -5.40950144408612 145 12 11.649536877247 0.35046312275301 146 10 10.9802593070461 -0.980259307046135 147 8 11.2529310562057 -3.2529310562057 148 10 13.7813036597313 -3.78130365973127 149 15 12.8393543403708 2.16064565962915 150 16 11.302454311899 4.69754568810097 151 13 12.0709463036844 0.929053696315594 152 16 12.9880920176487 3.0119079823513 153 9 10.434915808727 -1.434915808727 154 14 12.0213390928921 1.97866090710785 155 14 14.0291718034947 -0.0291718034947114 156 12 12.17007677017 -0.170076770169996 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0856024096625658 0.171204819325132 0.914397590337434 7 0.175473232870016 0.350946465740032 0.824526767129984 8 0.345387239210576 0.690774478421151 0.654612760789424 9 0.231449339366527 0.462898678733054 0.768550660633473 10 0.16129094552241 0.322581891044819 0.83870905447759 11 0.0984436360450457 0.196887272090091 0.901556363954954 12 0.0573135521236057 0.114627104247211 0.942686447876394 13 0.0377748139340261 0.0755496278680522 0.962225186065974 14 0.137269161267901 0.274538322535802 0.862730838732099 15 0.0920543492552071 0.184108698510414 0.907945650744793 16 0.0667795163394291 0.133559032678858 0.933220483660571 17 0.0589175656805555 0.117835131361111 0.941082434319444 18 0.0732036593800357 0.146407318760071 0.926796340619964 19 0.0629289577072103 0.125857915414421 0.93707104229279 20 0.177644274726851 0.355288549453701 0.82235572527315 21 0.13513223691562 0.27026447383124 0.86486776308438 22 0.11536958105236 0.230739162104721 0.88463041894764 23 0.090906670106693 0.181813340213386 0.909093329893307 24 0.0664736198858138 0.132947239771628 0.933526380114186 25 0.0819338496548532 0.163867699309706 0.918066150345147 26 0.0650253746817432 0.130050749363486 0.934974625318257 27 0.0612181769968562 0.122436353993712 0.938781823003144 28 0.04461017002135 0.0892203400427 0.95538982997865 29 0.0359094344968719 0.0718188689937438 0.964090565503128 30 0.0378139152546709 0.0756278305093419 0.96218608474533 31 0.0311282673309669 0.0622565346619339 0.968871732669033 32 0.022073997457484 0.0441479949149679 0.977926002542516 33 0.0230083986425563 0.0460167972851125 0.976991601357444 34 0.0163355394935963 0.0326710789871925 0.983664460506404 35 0.0203758184985049 0.0407516369970098 0.979624181501495 36 0.0298987415565309 0.0597974831130619 0.97010125844347 37 0.025200926793306 0.050401853586612 0.974799073206694 38 0.0231301858716319 0.0462603717432638 0.976869814128368 39 0.0195509068892147 0.0391018137784295 0.980449093110785 40 0.0197718301959695 0.039543660391939 0.98022816980403 41 0.0182574683735652 0.0365149367471304 0.981742531626435 42 0.0252530690195617 0.0505061380391234 0.974746930980438 43 0.0939876408148374 0.187975281629675 0.906012359185163 44 0.126601217574411 0.253202435148822 0.873398782425589 45 0.104042097917823 0.208084195835647 0.895957902082177 46 0.104967068737863 0.209934137475726 0.895032931262137 47 0.0970196376971408 0.194039275394282 0.90298036230286 48 0.0813358916666705 0.162671783333341 0.918664108333329 49 0.0657731633290302 0.13154632665806 0.93422683667097 50 0.0526433057683331 0.105286611536666 0.947356694231667 51 0.0448249146637797 0.0896498293275594 0.95517508533622 52 0.117206130915129 0.234412261830258 0.882793869084871 53 0.0945236389729939 0.189047277945988 0.905476361027006 54 0.11436491840885 0.2287298368177 0.88563508159115 55 0.1226007528772 0.2452015057544 0.8773992471228 56 0.102212820863469 0.204425641726937 0.897787179136531 57 0.082435564880242 0.164871129760484 0.917564435119758 58 0.0957439599686532 0.191487919937306 0.904256040031347 59 0.150435149654537 0.300870299309075 0.849564850345463 60 0.183528706921768 0.367057413843537 0.816471293078232 61 0.24037065306141 0.480741306122819 0.75962934693859 62 0.230180311958127 0.460360623916253 0.769819688041873 63 0.221034484096735 0.44206896819347 0.778965515903265 64 0.308860317757937 0.617720635515873 0.691139682242063 65 0.340346459895125 0.68069291979025 0.659653540104875 66 0.304773471166302 0.609546942332605 0.695226528833698 67 0.312130674309918 0.624261348619836 0.687869325690082 68 0.279224106850639 0.558448213701278 0.720775893149361 69 0.266274269752073 0.532548539504146 0.733725730247927 70 0.501417585858054 0.997164828283891 0.498582414141946 71 0.475886640298565 0.95177328059713 0.524113359701435 72 0.430378491962444 0.860756983924887 0.569621508037556 73 0.401853846490552 0.803707692981104 0.598146153509448 74 0.374090734360758 0.748181468721516 0.625909265639242 75 0.333624912789429 0.667249825578859 0.666375087210571 76 0.294050199539863 0.588100399079727 0.705949800460137 77 0.256576941741265 0.51315388348253 0.743423058258735 78 0.220662164412779 0.441324328825558 0.779337835587221 79 0.201020638445058 0.402041276890115 0.798979361554942 80 0.308905449404757 0.617810898809513 0.691094550595243 81 0.355413028534974 0.710826057069949 0.644586971465026 82 0.314130614326727 0.628261228653453 0.685869385673273 83 0.281667936971669 0.563335873943339 0.718332063028331 84 0.26007728537798 0.520154570755959 0.73992271462202 85 0.224207052262116 0.448414104524232 0.775792947737884 86 0.191693236501721 0.383386473003443 0.808306763498279 87 0.195493940485528 0.390987880971055 0.804506059514472 88 0.167256503523148 0.334513007046296 0.832743496476852 89 0.199835733443172 0.399671466886343 0.800164266556828 90 0.214793732557127 0.429587465114253 0.785206267442873 91 0.202068435545907 0.404136871091814 0.797931564454093 92 0.194985362460954 0.389970724921908 0.805014637539046 93 0.209888692105857 0.419777384211715 0.790111307894143 94 0.19383362490062 0.387667249801241 0.80616637509938 95 0.164112811129606 0.328225622259213 0.835887188870394 96 0.137513126200604 0.275026252401208 0.862486873799396 97 0.146111639716819 0.292223279433638 0.853888360283181 98 0.178751160621395 0.357502321242789 0.821248839378605 99 0.151836572560545 0.303673145121089 0.848163427439455 100 0.128307887440769 0.256615774881538 0.871692112559231 101 0.144920019937287 0.289840039874574 0.855079980062713 102 0.14854681539377 0.29709363078754 0.85145318460623 103 0.154476483890222 0.308952967780445 0.845523516109777 104 0.131036377827043 0.262072755654086 0.868963622172957 105 0.367530556511481 0.735061113022962 0.632469443488519 106 0.32280484049039 0.645609680980779 0.67719515950961 107 0.337427833082728 0.674855666165456 0.662572166917272 108 0.306435400433765 0.61287080086753 0.693564599566235 109 0.358629438776954 0.717258877553909 0.641370561223046 110 0.436120066914863 0.872240133829726 0.563879933085137 111 0.391199099217689 0.782398198435379 0.608800900782311 112 0.350142036706875 0.700284073413749 0.649857963293125 113 0.310909671708196 0.621819343416392 0.689090328291804 114 0.293347108674642 0.586694217349283 0.706652891325358 115 0.299628169000467 0.599256338000933 0.700371830999533 116 0.33243495332526 0.664869906650519 0.66756504667474 117 0.41409722469223 0.82819444938446 0.58590277530777 118 0.373600777995197 0.747201555990395 0.626399222004802 119 0.32813277984964 0.65626555969928 0.67186722015036 120 0.292922011507121 0.585844023014241 0.70707798849288 121 0.255296565318066 0.510593130636131 0.744703434681934 122 0.233908993249228 0.467817986498456 0.766091006750772 123 0.319843893502366 0.639687787004732 0.680156106497634 124 0.271253248843647 0.542506497687294 0.728746751156353 125 0.287880604608277 0.575761209216554 0.712119395391723 126 0.2420175960871 0.4840351921742 0.7579824039129 127 0.317447412929327 0.634894825858653 0.682552587070673 128 0.287940071345551 0.575880142691102 0.712059928654449 129 0.253195166245098 0.506390332490195 0.746804833754902 130 0.576171934137297 0.847656131725406 0.423828065862703 131 0.60309683833002 0.79380632333996 0.39690316166998 132 0.547192819393194 0.905614361213612 0.452807180606806 133 0.510527549056783 0.978944901886435 0.489472450943217 134 0.468527623780564 0.937055247561127 0.531472376219436 135 0.505077463266293 0.989845073467414 0.494922536733707 136 0.441482459767848 0.882964919535697 0.558517540232152 137 0.371589090751499 0.743178181502999 0.628410909248501 138 0.577909183324051 0.844181633351899 0.422090816675949 139 0.763640205144796 0.472719589710409 0.236359794855204 140 0.714699690646027 0.570600618707945 0.285300309353973 141 0.647813951534382 0.704372096931235 0.352186048465618 142 0.580210812411132 0.839578375177737 0.419789187588868 143 0.668121041208729 0.663757917582542 0.331878958791271 144 0.732942312655918 0.534115374688165 0.267057687344082 145 0.646149063194372 0.707701873611256 0.353850936805628 146 0.540658245618774 0.918683508762451 0.459341754381226 147 0.566801274652941 0.866397450694118 0.433198725347059 148 0.792913264315224 0.414173471369552 0.207086735684776 149 0.6810945715424 0.6378108569152 0.3189054284576 150 0.755110080085929 0.489779839828142 0.244889919914071 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 8 0.0551724137931034 NOK 10% type I error level 17 0.117241379310345 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/104921292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/104921292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/10ixoh1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/10ixoh1292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/204921292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/204921292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/304921292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/304921292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/4m5qq1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/4m5qq1292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/5m5qq1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/5m5qq1292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/6m5qq1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/6m5qq1292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/7ew7b1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/7ew7b1292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/8p5ow1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/8p5ow1292938456.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/9p5ow1292938456.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939625yuprl7itvxbmp9b/9p5ow1292938456.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

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

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

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

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Software written by Ed van Stee & Patrick Wessa

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