*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: Fri, 24 Dec 2010 15:52:22 +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/24/t129320582016wxbxld7gwm1lt.htm/, Retrieved Fri, 24 Dec 2010 16:50:32 +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/24/t129320582016wxbxld7gwm1lt.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 «

15 10 12 16 6 1 1 3 12 9 7 12 6 1 0 0 9 12 11 11 4 1 0 3 10 12 11 12 6 1 3 0 13 9 14 14 6 1 1 3 16 11 16 16 7 1 1 0 14 12 13 13 6 1 2 0 16 11 13 14 7 2 0 1 10 12 5 13 6 1 1 1 8 12 8 13 4 0 0 0 12 11 14 13 5 2 1 0 15 11 15 15 8 1 0 2 14 12 8 14 4 1 0 0 14 6 13 12 6 1 0 0 12 13 12 12 6 1 0 1 12 11 11 12 5 0 2 1 10 12 8 11 4 0 3 1 4 10 4 10 2 0 2 0 14 11 15 15 8 0 2 1 15 12 12 16 7 0 0 0 16 12 14 14 6 1 0 0 12 12 9 13 4 2 0 0 12 11 16 13 4 0 0 0 12 12 10 13 4 0 1 0 12 12 8 13 5 0 2 0 12 12 14 14 4 1 0 0 11 6 6 9 4 1 1 0 11 5 16 14 6 3 0 0 11 12 11 12 6 0 1 3 11 14 7 13 6 0 1 2 11 12 13 11 4 1 0 0 11 9 7 13 2 2 0 1 15 11 14 15 7 1 0 0 15 11 17 16 6 1 0 1 9 11 15 15 7 0 2 2 16 12 8 14 4 0 2 1 13 10 8 8 4 0 0 1 9 12 11 11 4 2 2 0 16 11 16 15 6 1 2 0 12 12 10 15 6 1 0 0 15 9 5 11 3 2 1 0 5 15 8 12 3 0 3 0 11 11 8 12 6 1 2 0 17 11 15 14 5 2 0 0 9 15 6 8 4 0 2 1 13 12 16 16 6 2 0 0 16 9 16 16 6 0 1 1 16 12 16 14 6 0 1 0 14 9 19 12 6 1 1 0 16 11 14 15 6 0 1 1 11 12 15 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = -0.230262856605763 + 0.124421759330556FindingFriends[t] + 0.242447469145869KnowingPeople[t] + 0.352480645391408Liked[t] + 0.633321617244387Celebrity[t] + 0.320786045997284B[t] -0.112460065107071`2B`[t] -0.0264621349487461`3B`[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) -0.230262856605763 1.496946 -0.1538 0.87796 0.43898 FindingFriends 0.124421759330556 0.098238 1.2665 0.207313 0.103657 KnowingPeople 0.242447469145869 0.061613 3.935 0.000128 6.4e-05 Liked 0.352480645391408 0.097361 3.6203 0.000403 0.000202 Celebrity 0.633321617244387 0.157559 4.0196 9.3e-05 4.6e-05 B 0.320786045997284 0.227708 1.4088 0.161003 0.080501 `2B` -0.112460065107071 0.211909 -0.5307 0.596422 0.298211 `3B` -0.0264621349487461 0.197252 -0.1342 0.893463 0.446732 Multiple Linear Regression - Regression Statistics Multiple R 0.712454731757267 R-squared 0.507591744803319 Adjusted R-squared 0.484302165165638 F-TEST (value) 21.7948006232827 F-TEST (DF numerator) 7 F-TEST (DF denominator) 148 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10885387487063 Sum Squared Residuals 658.19517050242 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 13.4918839722230 1.50811602777697 2 12 10.9371487555508 1.06285124444918 3 9 10.5816936253995 -1.58169362539954 4 10 11.9428237148048 -1.94282371480475 5 13 13.1473958604014 -0.147395860401419 6 16 15.2988036302277 0.70119636977229 7 14 12.8926593635950 1.10734063640503 8 16 14.2732839081629 1.72671609183711 9 10 11.0390775405863 -1.03907754058634 10 8 10.3179128675937 -2.31791286759371 11 12 12.8106095672703 -0.810609567270254 12 15 15.3967329281444 -0.396732928144398 13 14 10.9911795589824 3.0088204410176 14 14 12.0185682924344 1.98143170756563 15 12 12.6206110036536 -0.620611003653647 16 12 10.9502922223909 1.04970777760915 17 10 9.24910924654094 0.750890753459065 18 4 6.55027417147198 -2.55027417147198 19 14 14.8774888868817 -0.877488886881718 20 15 14.2451095320846 0.754890467915425 21 16 13.7125076083464 2.28749239165361 22 12 11.2019324287341 0.798067571265853 23 12 12.1330708614301 -0.133070861430109 24 12 10.6903477407784 1.30965225922162 25 12 10.7263143546240 1.27368564537604 26 12 12.4458643738576 -0.445864373857618 27 11 7.88489077264322 3.11510922735678 28 11 13.9680223233188 -2.96802232331881 29 11 11.7675713941754 -0.767571394175375 30 11 11.4255678165932 -0.425567816593164 31 11 11.1459749685375 -0.145974968537524 32 11 9.05066684301322 1.94933315698678 33 15 14.5738881116516 0.426111888348367 34 15 14.9939274122875 0.00607258771248438 35 9 14.2177051346886 -5.21770513468858 36 16 10.4190112478222 5.58098875217777 37 13 8.28020398702681 4.71979601297319 38 9 10.7569459460289 -1.75694594602893 39 16 14.2005413024848 1.79945869751516 40 12 13.0951983771543 -1.09519837715432 41 15 8.40813430102473 6.59186569897527 42 5 9.36799568762837 -4.36799568762837 43 11 11.2035196131437 -0.203519613143663 44 17 13.5179977469146 3.4820022530854 45 9 8.1924977151737 0.807502284826292 46 13 15.2231498834182 -2.22314988341823 47 16 14.0693903133762 1.93060968662382 48 16 13.7641564355338 2.23584356446622 49 14 13.7340583201942 0.265941679805815 50 16 13.4808582483541 2.51914175164585 51 11 13.2499937867094 -2.24999378670945 52 11 11.741251443332 -0.741251443331995 53 11 13.7720367233744 -2.77203672337440 54 12 12.6262885060021 -0.626288506002135 55 12 13.4635522320450 -1.46355223204504 56 12 12.3861863945427 -0.386186394542673 57 14 13.9116774705970 0.0883225294030321 58 10 11.3451145043230 -1.34511450432298 59 9 9.02358910698186 -0.023589106981859 60 12 11.6489693212987 0.351030678701326 61 10 10.4042439780149 -0.4042439780149 62 14 13.4191231789983 0.580876821001681 63 8 10.3134434748435 -2.31344347484351 64 16 14.3685890289679 1.63141097103211 65 14 15.5859836000602 -1.58598360006015 66 14 10.7843382045065 3.21566179549352 67 12 11.1752426790701 0.824757320929884 68 14 13.3972872070574 0.602712792942648 69 7 10.4318878855802 -3.43188788558019 70 19 14.5157617037739 4.48423829622612 71 15 12.7771153487457 2.22288465125434 72 8 11.3037151302295 -3.30371513022950 73 10 14.6807010008753 -4.68070100087534 74 13 13.2715718174700 -0.271571817470007 75 13 11.5050974657061 1.49490253429386 76 10 10.7766485247344 -0.776648524734446 77 12 9.41044918180933 2.58955081819067 78 15 16.6511419410771 -1.65114194107706 79 7 11.1576034824981 -4.15760348249814 80 14 14.1882464279985 -0.188246427998494 81 10 8.72298490349312 1.27701509650688 82 6 9.87486234129855 -3.87486234129855 83 11 11.6748290542446 -0.674829054244615 84 12 9.78715606944545 2.21284393055455 85 14 14.1315864589883 -0.131586458988350 86 12 13.5195849313241 -1.51958493132412 87 14 14.2121394899803 -0.212139489980342 88 11 10.3228757222102 0.677124277789761 89 10 9.23998915261697 0.76001084738303 90 13 12.7494348226226 0.250565177377418 91 8 10.2994432662147 -2.29944326621474 92 9 12.3323261542906 -3.3323261542906 93 6 12.4117877982193 -6.4117877982193 94 12 12.5942910528103 -0.594291052810267 95 14 12.287893589898 1.712106410102 96 11 10.9786087825745 0.0213912174254618 97 8 10.0902419679002 -2.09024196790019 98 7 9.6528966509552 -2.6528966509552 99 9 9.51567349294914 -0.515673492949142 100 14 13.0133699034522 0.986630096547776 101 13 10.3563063703008 2.64369362969918 102 15 12.6314091128073 2.36859088719273 103 5 5.66587982304402 -0.665879823044024 104 15 12.0036531402711 2.99634685972888 105 13 12.0510117654604 0.948988234539627 106 12 11.6393226582965 0.360677341703524 107 6 8.18219945002766 -2.18219945002766 108 7 10.0437707990537 -3.04377079905372 109 13 9.56712633551216 3.43287366448784 110 16 15.5279957748933 0.472004225106696 111 10 13.2648729141570 -3.26487291415702 112 16 15.5356854546653 0.464314545334665 113 15 13.5960783825856 1.40392161741439 114 8 8.80344751540832 -0.803447515408322 115 11 12.9339795991712 -1.93397959917119 116 13 12.4673002205128 0.532699779487187 117 16 15.0815428533205 0.918457146679522 118 11 8.5165588542973 2.48344114570270 119 14 14.3790357703120 -0.379035770311962 120 9 10.1101658692283 -1.11016586922833 121 8 10.1606632502643 -2.16066325026429 122 8 11.2847849228642 -3.28478492286419 123 11 12.0080673388279 -1.00806733882794 124 12 13.1924028358116 -1.19240283581159 125 11 11.8712206598241 -0.871220659824113 126 14 13.8225407845919 0.177459215408068 127 11 12.962784084254 -1.96278408425399 128 14 12.6222378141733 1.3777621858267 129 13 13.7321286558768 -0.732128655876788 130 12 11.0271461728280 0.97285382717202 131 4 6.48379112945436 -2.48379112945436 132 15 12.4299242193354 2.57007578066459 133 10 11.3488926688192 -1.34889266881919 134 13 13.1412815596335 -0.141281559633465 135 15 13.0963498233057 1.90365017669425 136 12 12.5095564264436 -0.509556426443611 137 13 13.7125076083464 -0.712507608346393 138 8 8.08659976948448 -0.0865997694844794 139 10 10.7127258498808 -0.712725849880818 140 15 14.0729807873076 0.927019212692424 141 16 14.4134904388305 1.58650956116952 142 16 15.2932379855195 0.706762014480534 143 14 13.0104637507877 0.989536249212332 144 14 12.8831245582330 1.11687544176698 145 12 10.0066709266034 1.99332907339660 146 15 12.0614311878917 2.93856881210832 147 13 12.2342507728338 0.765749227166247 148 16 13.5880858490158 2.41191415098416 149 14 13.6077068965462 0.392293103453768 150 8 10.0834579320176 -2.08345793201762 151 16 13.6341690314950 2.36583096850502 152 16 15.6576499986692 0.342350001330762 153 12 13.1692283209965 -1.16922832099650 154 11 11.2909230311990 -0.290923031199022 155 16 15.3633260876207 0.636673912379299 156 9 10.0834579320176 -1.08345793201762 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.278421260652546 0.556842521305093 0.721578739347454 12 0.243165025991498 0.486330051982996 0.756834974008502 13 0.340402699310737 0.680805398621474 0.659597300689263 14 0.242319030216541 0.484638060433083 0.757680969783459 15 0.172023412594869 0.344046825189738 0.827976587405131 16 0.225399465298308 0.450798930596617 0.774600534701692 17 0.200202027696511 0.400404055393021 0.79979797230349 18 0.238353042709908 0.476706085419816 0.761646957290092 19 0.188746560137054 0.377493120274108 0.811253439862946 20 0.132423261546035 0.26484652309207 0.867576738453965 21 0.128196861409589 0.256393722819178 0.871803138590411 22 0.0875986554203562 0.175197310840712 0.912401344579644 23 0.0588579555908383 0.117715911181677 0.941142044409162 24 0.048989313562998 0.097978627125996 0.951010686437002 25 0.0406557334935991 0.0813114669871982 0.9593442665064 26 0.0312871709448228 0.0625743418896455 0.968712829055177 27 0.0377271357966173 0.0754542715932346 0.962272864203383 28 0.150414273741896 0.300828547483792 0.849585726258104 29 0.115897549100540 0.231795098201080 0.88410245089946 30 0.0879928018067442 0.175985603613488 0.912007198193256 31 0.0632808887263187 0.126561777452637 0.936719111273681 32 0.0566723790201147 0.113344758040229 0.943327620979885 33 0.0400338942403277 0.0800677884806554 0.959966105759672 34 0.0276826605678982 0.0553653211357963 0.972317339432102 35 0.122371121515857 0.244742243031715 0.877628878484143 36 0.3737568948493 0.7475137896986 0.6262431051507 37 0.560487171914822 0.879025656170357 0.439512828085178 38 0.520428689016783 0.959142621966434 0.479571310983217 39 0.534904408973813 0.930191182052373 0.465095591026187 40 0.51703001723141 0.96593996553718 0.48296998276859 41 0.813644298127953 0.372711403744094 0.186355701872047 42 0.898223173542939 0.203553652914122 0.101776826457061 43 0.873255315019678 0.253489369960644 0.126744684980322 44 0.912918538609392 0.174162922781216 0.0870814613906079 45 0.896279156826332 0.207441686347336 0.103720843173668 46 0.894286834534033 0.211426330931934 0.105713165465967 47 0.88770733908206 0.224585321835881 0.112292660917941 48 0.89262677014108 0.214746459717838 0.107373229858919 49 0.867200459684645 0.265599080630711 0.132799540315355 50 0.872120263685182 0.255759472629636 0.127879736314818 51 0.874670232969106 0.250659534061787 0.125329767030894 52 0.854896503257863 0.290206993484273 0.145103496742136 53 0.88461301242717 0.23077397514566 0.11538698757283 54 0.867745099959383 0.264509800081234 0.132254900040617 55 0.849756665007717 0.300486669984567 0.150243334992283 56 0.819837792562263 0.360324414875474 0.180162207437737 57 0.78549466497233 0.429010670055341 0.214505335027670 58 0.771072702225105 0.457854595549789 0.228927297774895 59 0.740060088652611 0.519879822694778 0.259939911347389 60 0.709634905609525 0.580730188780949 0.290365094390475 61 0.680576514681774 0.638846970636451 0.319423485318226 62 0.640613845532358 0.718772308935285 0.359386154467642 63 0.694965523440861 0.610068953118277 0.305034476559139 64 0.68558346471922 0.628833070561559 0.314416535280780 65 0.671367525481204 0.657264949037592 0.328632474518796 66 0.70862711562021 0.582745768759581 0.291372884379790 67 0.670197310717298 0.659605378565404 0.329802689282702 68 0.627572647575878 0.744854704848243 0.372427352424121 69 0.72111057440158 0.55777885119684 0.27888942559842 70 0.844328161008698 0.311343677982603 0.155671838991302 71 0.841665787871414 0.316668424257171 0.158334212128586 72 0.886143556797144 0.227712886405713 0.113856443202856 73 0.956040114776127 0.087919770447745 0.0439598852238725 74 0.943824604985614 0.112350790028772 0.0561753950143861 75 0.934451786926458 0.131096426147083 0.0655482130735416 76 0.92094312841886 0.158113743162279 0.0790568715811395 77 0.929745646561178 0.140508706877643 0.0702543534388217 78 0.926266008015846 0.147467983968307 0.0737339919841536 79 0.970700153256484 0.0585996934870317 0.0292998467435159 80 0.961853374818918 0.0762932503621632 0.0381466251810816 81 0.95595008611046 0.0880998277790801 0.0440499138895401 82 0.974520694231625 0.0509586115367501 0.0254793057683751 83 0.967651559843673 0.0646968803126541 0.0323484401563271 84 0.970220602559887 0.0595587948802267 0.0297793974401134 85 0.961050752214448 0.0778984955711035 0.0389492477855517 86 0.95549300354478 0.089013992910441 0.0445069964552205 87 0.944724543140143 0.110550913719714 0.0552754568598569 88 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0.00282064909131019 105 0.99614043922677 0.00771912154645812 0.00385956077322906 106 0.994364964157095 0.011270071685811 0.0056350358429055 107 0.994139251349308 0.0117214973013841 0.00586074865069205 108 0.996474394277624 0.00705121144475276 0.00352560572237638 109 0.999277791187466 0.00144441762506721 0.000722208812533604 110 0.998855423266196 0.00228915346760721 0.00114457673380361 111 0.999655671363472 0.000688657273055327 0.000344328636527663 112 0.999423892540623 0.00115221491875374 0.000576107459376872 113 0.99921438240574 0.00157123518851871 0.000785617594259355 114 0.998809515748649 0.00238096850270295 0.00119048425135147 115 0.99855803560656 0.00288392878688165 0.00144196439344082 116 0.997646129931326 0.00470774013734803 0.00235387006867402 117 0.99630133835073 0.00739732329854145 0.00369866164927072 118 0.999289178200081 0.00142164359983753 0.000710821799918765 119 0.998784286710906 0.00243142657818888 0.00121571328909444 120 0.998021364937406 0.00395727012518795 0.00197863506259398 121 0.997818657841193 0.00436268431761359 0.00218134215880679 122 0.998143297920036 0.00371340415992794 0.00185670207996397 123 0.996892066885061 0.0062158662298777 0.00310793311493885 124 0.997095153708944 0.00580969258211286 0.00290484629105643 125 0.995099234647272 0.0098015307054561 0.00490076535272805 126 0.991869305650795 0.0162613886984099 0.00813069434920495 127 0.991103946270788 0.0177921074584247 0.00889605372921236 128 0.985789319237864 0.0284213615242713 0.0142106807621356 129 0.985470522534924 0.0290589549301514 0.0145294774650757 130 0.991327197730366 0.0173456045392687 0.00867280226963433 131 0.986936033949424 0.0261279321011512 0.0130639660505756 132 0.989511061310252 0.0209778773794964 0.0104889386897482 133 0.984475486082136 0.031049027835728 0.015524513917864 134 0.97448738110143 0.0510252377971416 0.0255126188985708 135 0.965164484876915 0.0696710302461699 0.0348355151230849 136 0.96100292175584 0.0779941564883188 0.0389970782441594 137 0.957689713724243 0.0846205725515134 0.0423102862757567 138 0.928645075055456 0.142709849889087 0.0713549249445435 139 0.925939586285274 0.148120827429453 0.0740604137147265 140 0.902695588179466 0.194608823641067 0.0973044118205335 141 0.994764278955234 0.0104714420895325 0.00523572104476626 142 0.999627542867431 0.000744914265138172 0.000372457132569086 143 0.9986023083136 0.00279538337279912 0.00139769168639956 144 0.997075684397922 0.00584863120415693 0.00292431560207846 145 0.985514198442917 0.0289716031141653 0.0144858015570826 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 34 0.251851851851852 NOK 5% type I error level 46 0.340740740740741 NOK 10% type I error level 66 0.488888888888889 NOK

Charts produced by software:

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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') }

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Software written by Ed van Stee & Patrick Wessa

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