workshop 7

*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: Sun, 21 Nov 2010 17:50:24 +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/21/t1290362653dl98v8ep6tt1mv2.htm/, Retrieved Sun, 21 Nov 2010 19:04:24 +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/21/t1290362653dl98v8ep6tt1mv2.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 13 14 13 3 12 12 8 13 5 10 15 12 16 6 9 12 7 12 6 10 10 10 11 5 12 12 7 12 3 13 15 16 18 8 12 9 11 11 4 12 12 14 14 4 6 11 6 9 4 5 11 16 14 6 12 11 11 12 6 11 15 16 11 5 14 7 12 12 4 14 11 7 13 6 12 11 13 11 4 12 10 11 12 6 11 14 15 16 6 11 10 7 9 4 7 6 9 11 4 9 11 7 13 2 11 15 14 15 7 11 11 15 10 5 12 12 7 11 4 12 14 15 13 6 11 15 17 16 6 11 9 15 15 7 8 13 14 14 5 9 13 14 14 6 12 16 8 14 4 10 13 8 8 4 10 12 14 13 7 12 14 14 15 7 8 11 8 13 4 12 9 11 11 4 11 16 16 15 6 12 12 10 15 6 7 10 8 9 5 11 13 14 13 6 11 16 16 16 7 12 14 13 13 6 9 15 5 11 3 15 5 8 12 3 11 8 10 12 4 11 11 8 12 6 11 16 13 14 7 11 17 15 14 5 15 9 6 8 4 11 9 12 13 5 12 13 16 16 6 12 10 5 13 6 9 6 15 11 6 12 12 12 14 5 12 8 8 13 4 13 14 13 13 5 11 12 14 13 5 9 11 12 12 4 9 16 16 16 6 11 8 10 15 2 11 15 15 15 8 12 7 8 12 3 12 16 16 14 6 9 14 19 12 6 11 16 14 15 6 9 9 6 12 5 12 14 13 13 5 12 11 15 12 6 12 13 7 12 5 12 15 13 13 6 14 5 4 5 2 11 15 14 13 5 12 13 13 13 5 11 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 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 KnowingPeople[t] = + 0.725680871464287 -0.0675593352860248FindingFriends[t] + 0.387096838191507Popularity[t] + 0.27399933524668Liked[t] + 0.670538732124844`Celebrity `[t] -0.00187723512719696t + 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) 0.725680871464287 1.803242 0.4024 0.68794 0.34397 FindingFriends -0.0675593352860248 0.122209 -0.5528 0.581212 0.290606 Popularity 0.387096838191507 0.098004 3.9498 0.00012 6e-05 Liked 0.27399933524668 0.126403 2.1677 0.031762 0.015881 `Celebrity ` 0.670538732124844 0.200407 3.3459 0.001037 0.000518 t -0.00187723512719696 0.004821 -0.3894 0.697525 0.348762 Multiple Linear Regression - Regression Statistics Multiple R 0.653361596228413 R-squared 0.426881375426139 Adjusted R-squared 0.407777421273677 F-TEST (value) 22.3451842492579 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.66394071596264 Sum Squared Residuals 1064.48702072453 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 10.4513987286897 3.54860127131033 2 8 11.4710614549067 -3.47106145490674 3 12 14.2581301427910 -2.25813014279098 4 7 12.0665243873886 -5.06652438738857 5 10 10.2783560732208 -0.278356073220814 6 7 9.84847571490158 -2.84847571490158 7 16 15.9370193311672 0.0629806688328206 8 11 9.07997012695083 1.92002987304917 9 14 11.0613814121382 2.93861858786181 10 6 9.70776667430223 -3.70776667430223 11 16 12.4845229149442 3.51547708505585 12 11 11.4617316623214 -0.461731662321422 13 16 12.1312630478748 3.86873695212525 14 12 8.43339370447926 3.56660629552074 15 7 11.5949806216145 -4.59498062161446 16 13 9.83914592231627 3.16085407768373 17 11 11.0652486484939 -0.0652486484939305 18 15 13.7753154424055 1.22468455759449 19 7 8.96597804353583 -1.96597804353583 20 9 8.23394946728007 0.766050532719934 21 7 9.23935895878203 -2.23935895878203 22 14 14.5514427369664 -0.551442736966389 23 15 10.2901040085901 4.70989599140993 24 7 10.2112248794902 -3.2112248794902 25 15 12.8726174554891 2.12738254451094 26 17 14.1473943995794 2.85260560042056 27 15 12.2194755321814 2.78052446781864 28 14 12.3535868561819 1.6464131438181 29 14 12.9546890178935 1.04531098210648 30 8 12.5703468272331 -4.57034682723309 31 8 9.89830173662333 -1.89830173662333 32 14 12.8909405359126 1.10905946408744 33 14 14.0761369770897 -0.0761369770896918 34 8 10.6235917016642 -2.62359170166418 35 11 9.0292847785165 1.97071522148349 36 16 14.2417195512523 1.75828044874770 37 10 12.6238956280730 -2.62389562807305 38 8 9.87108664938803 -1.87108664938803 39 14 12.5267986608028 1.47320133919718 40 16 15.1787486781150 0.821251321884969 41 13 12.8425816934539 0.157418306546089 42 5 10.8708644355084 -5.8708644355084 43 8 6.86666214199667 1.13333785800333 44 10 8.96685149471294 1.03314850528706 45 8 11.4673422384099 -3.46734223840995 46 13 14.6194865968585 -1.61948659685849 47 15 13.6636287356731 1.33637126432689 48 6 7.98020471026484 -1.98020471026484 49 12 10.2891002246400 1.71089977536002 50 16 13.2605877448577 2.73941225514233 51 5 11.2754219894159 -6.27542198941592 52 15 9.3798367368874 5.6201632631126 53 12 11.6493217986664 0.350678201333629 54 8 9.15451914340162 -1.15451914340162 55 13 12.0782023342623 0.921797665737714 56 14 11.4372500933241 2.56274990667588 57 12 10.2388566232059 1.76114337679405 58 16 14.6095383842727 1.39046161572731 59 10 8.41961350929533 1.58038649070466 60 15 15.1506465342577 -0.150646534257749 61 8 7.80974359194821 0.190256408051787 62 16 13.8513527674125 2.14864723258753 63 19 12.7299611912670 6.27003880873303 64 14 14.1891569676908 -0.189156967690781 65 6 10.1201837979302 -4.1201837979302 66 13 12.1251120831491 0.874887916850856 67 15 11.3584837303256 3.64151626967441 68 7 11.4602614394566 -4.46026143945656 69 13 13.1771159480839 -0.177115948083903 70 4 4.29500204999677 -0.295002049996772 71 14 12.5703820809907 1.42961791900931 72 13 11.7267518341945 1.27324816580554 73 11 11.2922395932169 -0.292239593216950 74 14 13.1206957723848 0.87930422761524 75 12 12.1396806933183 -0.139680693318250 76 15 12.002684787619 2.99731521238100 77 14 10.9887101498343 3.01128985016574 78 13 11.5986289263839 1.40137107361614 79 8 11.7041686296174 -3.70416862961742 80 6 6.44244121896844 -0.44244121896844 81 7 8.44273762152912 -1.44273762152912 82 13 12.8969717297083 0.103028270291697 83 13 13.6532951591377 -0.653295159137705 84 11 10.4040538334189 0.59594616658106 85 5 10.0872709780445 -5.08727097804453 86 12 11.6423537658143 0.35764623418567 87 8 8.72522855194161 -0.725228551941614 88 11 12.1954145808913 -1.19541458089128 89 14 15.4833035537605 -1.48330355376054 90 9 9.65469235524489 -0.65469235524489 91 10 13.6382772781201 -3.63827727812013 92 13 11.8140133549802 1.18598664501978 93 16 15.0116958810876 0.988304118912432 94 16 13.2653037404760 2.73469625952397 95 11 11.0900385881168 -0.0900385881167627 96 8 9.301870273949 -1.30187027394900 97 4 10.7526721736120 -6.75267217361196 98 7 7.51182472465405 -0.511824724654047 99 14 11.7201088210146 2.27989117898542 100 11 12.3447279827578 -1.34472798275778 101 17 15.0642373353560 1.93576266464398 102 15 14.7208014296961 0.279198570303885 103 17 13.9610711212291 3.03892887877095 104 5 9.6865278400635 -4.6865278400635 105 4 5.48243599973087 -1.48243599973087 106 10 14.8160775448898 -4.81607754488981 107 11 8.90670245829889 2.09329754170110 108 15 14.6734424099608 0.326557590039212 109 10 8.78985048509968 1.21014951490032 110 9 9.93518932320208 -0.935189323202077 111 12 11.2884639936695 0.71153600633051 112 15 12.8758803963089 2.12411960369114 113 7 11.5461302497212 -4.54613024972121 114 13 13.2535421996619 -0.253542199661895 115 12 14.5832998700977 -2.58329987009773 116 14 13.8175414058299 0.182458594170141 117 14 13.7481048354166 0.251895164583363 118 8 12.3587420798253 -4.35874207982527 119 15 12.9701566887792 2.02984331122077 120 12 11.146762654195 0.85323734580499 121 12 10.5771317426455 1.42286825735455 122 16 11.8135469160655 4.18645308393454 123 9 8.81854991966438 0.181450080335623 124 15 12.5061143396657 2.49388566033429 125 15 13.7330869543991 1.26691304560094 126 6 11.512283634381 -5.512283634381 127 14 15.6184086188877 -1.61840861888772 128 15 11.9050685610048 3.09493143899524 129 10 11.389792431952 -1.38979243195199 130 6 5.2677052448926 0.732294755107398 131 14 15.6108996783789 -1.61089967837893 132 12 13.1264094703565 -1.12640947035652 133 8 10.6024092504761 -2.60240925047612 134 11 12.7613413236404 -1.76134132364042 135 13 13.3272177649356 -0.327217764935585 136 9 10.5489732157375 -1.5489732157375 137 15 13.0039257917757 1.99607420822429 138 13 7.66519648715405 5.33480351284595 139 15 15.1420955124395 -0.142095512439505 140 14 11.6211210131723 2.37887898682771 141 16 10.6071463753875 5.39285362461246 142 14 12.5398834426622 1.46011655733781 143 14 12.5191210901617 1.48087890983832 144 10 7.20269130579918 2.79730869420082 145 10 10.5320780995927 -0.532078099592727 146 4 11.0295253170462 -7.02952531704618 147 8 9.92447434394383 -1.92447434394383 148 15 11.4386508467131 3.5613491532869 149 16 13.3684958084409 2.63150419155915 150 12 15.3012328757155 -3.30123287571551 151 12 12.9870870586816 -0.987087058681607 152 15 14.9009390085829 0.099060991417052 153 9 9.14932970403997 -0.149329704039975 154 12 13.3135714651461 -1.31357146514607 155 14 12.4221368889928 1.57786311100720 156 11 9.51190971947658 1.48809028052342 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.672993749575081 0.654012500849837 0.327006250424919 10 0.642495655047936 0.715008689904129 0.357504344952064 11 0.50849608424266 0.98300783151468 0.49150391575734 12 0.428900278991959 0.857800557983918 0.571099721008041 13 0.77539832153592 0.449203356928159 0.224601678464079 14 0.711597944838265 0.576804110323469 0.288402055161735 15 0.90906323987734 0.181873520245319 0.0909367601226594 16 0.873843565201118 0.252312869597764 0.126156434798882 17 0.824057662731802 0.351884674536397 0.175942337268198 18 0.810564421013917 0.378871157972165 0.189435578986083 19 0.807924998670845 0.38415000265831 0.192075001329155 20 0.77275070121581 0.454498597568381 0.227249298784190 21 0.892691966214902 0.214616067570196 0.107308033785098 22 0.856085109932638 0.287829780134723 0.143914890067362 23 0.903959419399131 0.192081161201738 0.096040580600869 24 0.927599754361027 0.144800491277945 0.0724002456389724 25 0.911549014314716 0.176901971370567 0.0884509856852835 26 0.894505825454754 0.210988349090492 0.105494174545246 27 0.871248731251911 0.257502537496177 0.128751268748088 28 0.837229887187749 0.325540225624502 0.162770112812251 29 0.797503809742895 0.40499238051421 0.202496190257105 30 0.886354914746792 0.227290170506416 0.113645085253208 31 0.86197821969575 0.276043560608501 0.138021780304251 32 0.827902386787547 0.344195226424905 0.172097613212453 33 0.792334896330018 0.415330207339963 0.207665103669982 34 0.803796913801174 0.392406172397653 0.196203086198826 35 0.770603245923423 0.458793508153154 0.229396754076577 36 0.741652032180247 0.516695935639505 0.258347967819753 37 0.772171400000452 0.455657199999096 0.227828599999548 38 0.744809590131499 0.510380819737002 0.255190409868501 39 0.708681963079524 0.582636073840952 0.291318036920476 40 0.661948674442302 0.676102651115397 0.338051325557699 41 0.610228142274341 0.779543715451319 0.389771857725659 42 0.733843490546386 0.532313018907227 0.266156509453614 43 0.699309009587014 0.601381980825972 0.300690990412986 44 0.654760551812696 0.690478896374608 0.345239448187304 45 0.692726885268272 0.614546229463456 0.307273114731728 46 0.656776111549387 0.686447776901226 0.343223888450613 47 0.643608755817373 0.712782488365253 0.356391244182627 48 0.613670855754704 0.772658288490592 0.386329144245296 49 0.577893877320781 0.844212245358439 0.422106122679219 50 0.567314268655629 0.865371462688742 0.432685731344371 51 0.782361523665034 0.435276952669933 0.217638476334966 52 0.880797870101772 0.238404259796456 0.119202129898228 53 0.854438619948492 0.291122760103017 0.145561380051508 54 0.834714512104977 0.330570975790046 0.165285487895023 55 0.810990383923116 0.378019232153767 0.189009616076884 56 0.808470648005543 0.383058703988914 0.191529351994457 57 0.787485109128471 0.425029781743058 0.212514890871529 58 0.756917348986921 0.486165302026157 0.243082651013079 59 0.72865260634877 0.54269478730246 0.27134739365123 60 0.688717555037758 0.622564889924484 0.311282444962242 61 0.648896562962073 0.702206874075855 0.351103437037927 62 0.635645828242656 0.728708343514688 0.364354171757344 63 0.807019411778625 0.385961176442749 0.192980588221375 64 0.77429120912167 0.45141758175666 0.22570879087833 65 0.83142835004005 0.3371432999199 0.16857164995995 66 0.802602745147945 0.39479450970411 0.197397254852055 67 0.832467716634208 0.335064566731584 0.167532283365792 68 0.881461440553534 0.237077118892932 0.118538559446466 69 0.856327874692653 0.287344250614694 0.143672125307347 70 0.829731777690764 0.340536444618472 0.170268222309236 71 0.80551860922803 0.388962781543939 0.194481390771970 72 0.77834317473687 0.443313650526261 0.221656825263130 73 0.746657499136332 0.506685001727337 0.253342500863668 74 0.726840351819517 0.546319296360967 0.273159648180483 75 0.688999098470906 0.622001803058187 0.311000901529093 76 0.708006039775724 0.583987920448552 0.291993960224276 77 0.725968085269886 0.548063829460229 0.274031914730114 78 0.699615374432004 0.600769251135992 0.300384625567996 79 0.741491067741814 0.517017864516372 0.258508932258186 80 0.70383488791249 0.592330224175021 0.296165112087511 81 0.677106288900781 0.645787422198438 0.322893711099219 82 0.633469313628138 0.733061372743724 0.366530686371862 83 0.595925027095157 0.808149945809686 0.404074972904843 84 0.55811060828776 0.88377878342448 0.44188939171224 85 0.707407220228597 0.585185559542806 0.292592779771403 86 0.668550156753092 0.662899686493816 0.331449843246908 87 0.627609439072175 0.74478112185565 0.372390560927825 88 0.589728601791803 0.820542796416395 0.410271398208197 89 0.557797133917057 0.884405732165886 0.442202866082943 90 0.512986333074871 0.974027333850258 0.487013666925129 91 0.5474242256197 0.9051515487606 0.4525757743803 92 0.539024509195157 0.921950981609687 0.460975490804843 93 0.503953008816759 0.992093982366482 0.496046991183241 94 0.507070088792487 0.985859822415027 0.492929911207513 95 0.458586737129305 0.91717347425861 0.541413262870695 96 0.423766588937372 0.847533177874744 0.576233411062628 97 0.623543846758856 0.752912306482288 0.376456153241144 98 0.580905840150339 0.838188319699323 0.419094159849661 99 0.581886770602418 0.836226458795164 0.418113229397582 100 0.54394524172895 0.9121095165421 0.45605475827105 101 0.534712900278224 0.930574199443553 0.465287099721776 102 0.488075491649375 0.97615098329875 0.511924508350625 103 0.571582589804618 0.856834820390764 0.428417410195382 104 0.717860395548497 0.564279208903007 0.282139604451503 105 0.705068588575037 0.589862822849926 0.294931411424963 106 0.74815371180075 0.503692576398502 0.251846288199251 107 0.724414659105042 0.551170681789917 0.275585340894958 108 0.703810904231639 0.592378191536722 0.296189095768361 109 0.666982575410507 0.666034849178986 0.333017424589493 110 0.618665995520391 0.762668008959217 0.381334004479608 111 0.576997070154409 0.846005859691181 0.423002929845591 112 0.633792687241786 0.732414625516428 0.366207312758214 113 0.692135460221124 0.615729079557753 0.307864539778876 114 0.643066896926194 0.713866206147612 0.356933103073806 115 0.60840603904613 0.78318792190774 0.39159396095387 116 0.555508204360359 0.888983591279283 0.444491795639641 117 0.50256329651968 0.99487340696064 0.49743670348032 118 0.522255846950964 0.955488306098071 0.477744153049036 119 0.498384865533384 0.996769731066767 0.501615134466616 120 0.461054472542074 0.922108945084147 0.538945527457926 121 0.411035987309852 0.822071974619704 0.588964012690148 122 0.438868748859365 0.877737497718731 0.561131251140635 123 0.380838949698585 0.761677899397169 0.619161050301415 124 0.384235931715124 0.768471863430249 0.615764068284876 125 0.33971331208871 0.67942662417742 0.66028668791129 126 0.534992216772501 0.930015566454998 0.465007783227499 127 0.475054605949401 0.950109211898802 0.524945394050599 128 0.516695581249197 0.966608837501607 0.483304418750803 129 0.455380064948302 0.910760129896604 0.544619935051698 130 0.399688426840368 0.799376853680735 0.600311573159632 131 0.340360904117779 0.680721808235558 0.659639095882221 132 0.295324989533931 0.590649979067862 0.704675010466069 133 0.313772846352729 0.627545692705457 0.686227153647271 134 0.278241525863858 0.556483051727717 0.721758474136142 135 0.228278951461775 0.45655790292355 0.771721048538225 136 0.298717716279923 0.597435432559847 0.701282283720077 137 0.23970907140185 0.4794181428037 0.76029092859815 138 0.257050882020855 0.51410176404171 0.742949117979145 139 0.254786331982826 0.509572663965652 0.745213668017174 140 0.211234043900898 0.422468087801796 0.788765956099102 141 0.295277023795257 0.590554047590514 0.704722976204743 142 0.264237938911651 0.528475877823301 0.73576206108835 143 0.200750198663441 0.401500397326883 0.799249801336559 144 0.216733051559074 0.433466103118148 0.783266948440926 145 0.141498546457949 0.282997092915898 0.858501453542051 146 0.66001393117389 0.67997213765222 0.33998606882611 147 0.545294136072753 0.909411727854493 0.454705863927247 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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Software written by Ed van Stee & Patrick Wessa

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