WS 10 - MR: Personal Standards

*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, 14 Dec 2010 15:59:53 +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/14/t1292342521csutnnt9hhdcueo.htm/, Retrieved Tue, 14 Dec 2010 17:02:13 +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/14/t1292342521csutnnt9hhdcueo.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 «

0 25 11 7 8 25 23 0 17 6 17 8 30 25 0 18 8 12 9 22 19 0 16 10 12 7 22 29 0 20 10 11 4 25 25 0 16 11 11 11 23 21 0 18 16 12 7 17 22 0 17 11 13 7 21 25 0 30 12 16 10 19 18 0 23 8 11 10 15 22 0 18 12 10 8 16 15 0 21 9 9 9 22 20 0 31 14 17 11 23 20 0 27 15 11 9 23 21 0 21 9 14 13 19 21 0 16 8 15 9 23 24 0 20 9 15 6 25 24 0 17 9 13 6 22 23 0 25 16 18 16 26 24 0 26 11 18 5 29 18 0 25 8 12 7 32 25 0 17 9 17 9 25 21 0 32 12 18 12 28 22 0 22 9 14 9 25 23 0 17 9 16 5 25 23 0 20 14 14 10 18 24 0 29 10 12 8 25 23 0 23 14 17 7 25 21 0 20 10 12 8 20 28 0 11 6 6 4 15 16 0 26 13 12 8 24 29 0 22 10 12 8 26 27 0 14 15 13 8 14 16 0 19 12 14 7 24 28 0 20 11 11 8 25 25 0 28 8 12 7 20 22 0 19 9 9 7 21 23 0 30 9 15 9 27 26 0 29 15 18 11 23 23 0 26 9 15 6 25 25 0 23 10 12 8 20 21 0 21 12 14 9 22 24 0 28 11 13 6 25 22 0 23 14 13 10 25 27 0 18 6 11 8 17 26 0 20 8 16 10 25 24 0 21 10 11 5 26 24 0 28 12 16 14 27 22 0 10 5 8 6 19 24 0 22 10 15 6 22 20 0 31 10 21 12 32 26 0 29 13 18 12 21 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 12 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 7.38188475102131 -0.694832870949954Gender[t] + 0.321027523643909CM[t] -0.338195452736301D[t] + 0.173368519441836PE[t] + 0.0172607039353986PC[t] + 0.421685657869128O[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) 7.38188475102131 2.24661 3.2858 0.001263 0.000631 Gender -0.694832870949954 0.599422 -1.1592 0.248204 0.124102 CM 0.321027523643909 0.055821 5.751 0 0 D -0.338195452736301 0.109073 -3.1006 0.002302 0.001151 PE 0.173368519441836 0.101665 1.7053 0.090183 0.045092 PC 0.0172607039353986 0.128585 0.1342 0.893394 0.446697 O 0.421685657869128 0.073824 5.712 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.610418712666873 R-squared 0.372611004773883 Adjusted R-squared 0.347845649699168 F-TEST (value) 15.0456556608918 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.78523862359725e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40545024919715 Sum Squared Residuals 1762.75789276305 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 22.7378582605858 2.26214173941422 2 30 24.4376718452725 5.56232815472746 3 22 20.7026126229553 1.29738737704470 4 22 23.5665018410154 -1.56650184101536 5 25 22.9387186728665 2.06128132713354 6 23 19.7504954216258 3.24950457837419 7 17 19.2275845668015 -2.22758456680150 8 21 22.0359597998883 -1.03595979988830 9 19 23.4912102195706 -4.49121021957063 10 15 23.4166993992758 -8.4166993992758 11 16 17.2990904377145 -1.29909043771453 12 22 21.2290798406944 0.770920159305645 13 23 24.1698473768574 -1.16984737685742 14 23 21.8944949628928 1.10550503710720 15 19 22.5866509115143 -3.58665091151426 16 23 22.6890914233386 0.310908576661364 17 25 23.5832239533718 1.41677604662823 18 22 21.8517186856872 0.148281314312751 19 26 23.5137060001167 2.48629399988329 20 29 22.8057290969380 6.19427090306203 21 32 25.4453978278066 6.55460217219336 22 25 21.7536035595225 3.24639644047747 23 28 26.2012663450894 1.79873365491058 24 25 23.6820069351548 1.31799306484518 25 25 22.3545635400774 2.64543645992264 26 18 21.7879209859900 -3.78792098599003 27 25 25.2270064051068 -0.227006405106815 28 25 21.9542700298337 3.04572997016631 29 20 24.4461869816573 -4.44618698165727 30 15 16.7402392529852 -1.74023925298516 31 24 25.7794514231810 -1.77945142318095 32 26 24.6665563710760 1.33344362892404 33 14 15.9421852011246 -1.94218520112462 34 24 23.7782448874890 0.221755112510964 35 25 22.6695660358718 2.33043396412825 36 20 25.143423425131 -5.14342342513098 37 21 21.8175603591431 -0.817560359143123 38 27 27.6886526173553 -0.688652617355312 39 23 24.6280223698825 -1.62802236988252 40 25 25.9310747531044 -0.931074753104354 41 20 22.4574699475051 -2.45746994750511 42 22 22.7680787111711 -0.768078711171141 43 25 24.2849448824285 0.715055117571483 44 25 23.8426920110873 1.15730798891270 45 17 24.1401739101346 -7.14017391013457 46 25 24.1638307412915 0.836169258708496 47 26 22.8553212425766 3.14467875742336 48 27 24.6049406195009 2.39505938049909 49 19 20.5121508917850 -1.51215089178504 50 22 22.2003409164468 -0.200340916446782 51 32 28.7634779167201 3.23652208327987 52 21 24.4783026635523 -3.47830266355227 53 18 21.4664396275648 -3.46643962756478 54 23 23.0120969137014 -0.0120969137014117 55 20 20.9722555839277 -0.972255583927692 56 21 22.5050358588236 -1.50503585882360 57 17 18.9914786053849 -1.99147860538493 58 18 20.4410654313943 -2.44106543139431 59 19 20.7944689039832 -1.79446890398319 60 22 22.3186308539794 -0.318630853979425 61 14 19.0629535968650 -5.06295359686497 62 18 26.7665723383136 -8.76657233831357 63 35 23.5193619499825 11.4806380500175 64 29 19.5175457772127 9.4824542227873 65 21 22.2733115687134 -1.27331156871337 66 25 20.4411846560000 4.55881534400004 67 26 23.5312398815506 2.46876011844939 68 17 17.1043377886926 -0.104337788692593 69 25 20.3388084478676 4.66119155213239 70 20 21.1776507707811 -1.17765077078114 71 22 21.4149177828086 0.585082217191444 72 24 23.0912516937409 0.908748306259118 73 21 23.3247583614503 -2.32475836145027 74 26 25.8283374850337 0.171662514966333 75 24 20.7583406287655 3.24165937123445 76 16 20.5484727347340 -4.54847273473405 77 18 21.1408911291415 -3.1408911291415 78 19 19.3815389053367 -0.381538905336737 79 21 16.9930853842372 4.00691461576282 80 22 18.6780456381145 3.32195436188548 81 23 19.8972363425933 3.10276365740674 82 29 25.0045843316053 3.9954156683947 83 21 19.0747241041702 1.92527589582978 84 23 22.1411389088929 0.85886109110711 85 27 23.4116294192455 3.58837058075449 86 25 25.404617574799 -0.404617574799 87 21 21.2202679480633 -0.220267948063321 88 10 17.1922481757164 -7.19224817571643 89 20 22.7724061182191 -2.77240611821914 90 26 22.7745515771450 3.22544842285503 91 24 23.9919659006816 0.00803409931842777 92 29 31.8512285834216 -2.85122858342158 93 19 18.9916825867882 0.00831741321177223 94 24 22.2077579411796 1.79224205882037 95 19 21.008347369949 -2.00834736994899 96 22 22.0981686897177 -0.0981686897177283 97 17 23.9264970299455 -6.92649702994548 98 24 22.7349853748993 1.26501462510074 99 19 19.9777428297176 -0.977742829717594 100 19 22.4288875465789 -3.4288875465789 101 23 19.1045385730949 3.89546142690512 102 27 23.6633693805578 3.33663061944223 103 14 15.9022683526125 -1.90226835261250 104 22 23.5905842779772 -1.59058427797719 105 21 23.9350746908084 -2.93507469080843 106 18 23.4747097316158 -5.4747097316158 107 20 22.9187626148853 -2.91876261488528 108 19 22.9144636789883 -3.91446367898825 109 24 23.3339111030885 0.666088896911457 110 25 24.9025228969558 0.0974771030442204 111 29 24.1765133960819 4.82348660391814 112 28 24.5017755519308 3.49822444806924 113 17 16.8930926697612 0.106907330238805 114 29 22.5544118301732 6.44558816982677 115 26 27.2059238528174 -1.20592385281736 116 14 18.9908623851846 -4.99086238518461 117 26 21.296188782478 4.70381121752199 118 20 20.0314000939660 -0.0314000939659581 119 32 24.3305605094601 7.66943949053988 120 23 20.678981452842 2.32101854715798 121 21 21.7607518846793 -0.760751884679295 122 30 25.9100306229050 4.08996937709502 123 24 21.2467641290463 2.75323587095369 124 22 21.2618348668142 0.738165133185819 125 24 21.8786707228399 2.12132927716009 126 24 22.5244861144458 1.47551388555424 127 24 19.7317566999021 4.26824330009785 128 19 18.2074999536746 0.792500046325435 129 31 26.5738900163728 4.42610998362725 130 22 26.0989366253446 -4.09893662534457 131 27 20.9900909541577 6.00990904584234 132 19 17.5591495720536 1.44085042794643 133 21 19.0251697722184 1.97483022778159 134 23 22.8288843005763 0.171115699423733 135 19 21.0392453011057 -2.0392453011057 136 19 22.1947130232512 -3.19471302325118 137 20 22.7236569239704 -2.72365692397036 138 23 20.6950147810862 2.30498521891381 139 17 20.4612662780441 -3.46126627804412 140 17 22.9847318490327 -5.98473184903273 141 17 19.4487326039180 -2.44873260391805 142 21 23.2079892703595 -2.20798927035955 143 21 24.3524249235842 -3.3524249235842 144 18 20.7994617307804 -2.79946173078042 145 19 20.174481837742 -1.17448183774199 146 20 23.6444934169919 -3.64449341699193 147 15 18.4491687158757 -3.4491687158757 148 24 20.9069638303515 3.0930361696485 149 20 18.1002782000208 1.89972179997916 150 22 22.8543335487661 -0.854333548766058 151 13 16.3253568964252 -3.32535689642517 152 19 18.0725803043903 0.927419695609718 153 21 22.1715729658346 -1.17157296583456 154 23 22.0579450455256 0.94205495447439 155 16 21.9639533450056 -5.96395334500559 156 26 23.5542885105526 2.44571148944741 157 21 21.7951805177071 -0.795180517707085 158 21 19.7760370301778 1.22396296982216 159 24 23.1066813379950 0.893318662004957 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.96918116290349 0.0616376741930187 0.0308188370965094 11 0.94960498325604 0.100790033487919 0.0503950167439597 12 0.910199177603614 0.179601644792771 0.0898008223963856 13 0.897680475380423 0.204639049239154 0.102319524619577 14 0.883161313316011 0.233677373367978 0.116838686683989 15 0.846684915490134 0.306630169019731 0.153315084509866 16 0.781669637964087 0.436660724071826 0.218330362035913 17 0.707839980305813 0.584320039388374 0.292160019694187 18 0.633692682254575 0.732614635490851 0.366307317745426 19 0.643188863218717 0.713622273562565 0.356811136781282 20 0.726301671724044 0.547396656551912 0.273698328275956 21 0.829662075037792 0.340675849924416 0.170337924962208 22 0.796230309988827 0.407539380022346 0.203769690011173 23 0.744859432708105 0.510281134583791 0.255140567291895 24 0.684607342947542 0.630785314104915 0.315392657052458 25 0.628256505226388 0.743486989547225 0.371743494773612 26 0.63606996715192 0.72786006569616 0.36393003284808 27 0.574538850013241 0.850922299973519 0.425461149986759 28 0.527025027840594 0.945949944318812 0.472974972159406 29 0.577454716983629 0.84509056603274 0.42254528301637 30 0.527226871665651 0.945546256668698 0.472773128334349 31 0.473147974556078 0.946295949112157 0.526852025443922 32 0.421896572653231 0.843793145306461 0.57810342734677 33 0.372353305666047 0.744706611332094 0.627646694333953 34 0.316183568240440 0.632367136480879 0.68381643175956 35 0.300866293917917 0.601732587835834 0.699133706082083 36 0.406096808839719 0.812193617679438 0.593903191160281 37 0.350582297054213 0.701164594108426 0.649417702945787 38 0.304031116272859 0.608062232545717 0.695968883727141 39 0.271542731878073 0.543085463756146 0.728457268121927 40 0.242939987548019 0.485879975096039 0.75706001245198 41 0.217921775518445 0.43584355103689 0.782078224481555 42 0.180375505036233 0.360751010072467 0.819624494963767 43 0.146996612635592 0.293993225271185 0.853003387364408 44 0.125740507179212 0.251481014358424 0.874259492820788 45 0.240300948018433 0.480601896036867 0.759699051981567 46 0.201145836146923 0.402291672293845 0.798854163853078 47 0.194690273076082 0.389380546152165 0.805309726923918 48 0.190916858604239 0.381833717208479 0.80908314139576 49 0.160136028518349 0.320272057036699 0.839863971481651 50 0.134814052201527 0.269628104403054 0.865185947798473 51 0.121638231323247 0.243276462646494 0.878361768676753 52 0.131152121001433 0.262304242002866 0.868847878998567 53 0.131148502365931 0.262297004731862 0.868851497634069 54 0.105623772384876 0.211247544769751 0.894376227615124 55 0.0896494308284256 0.179298861656851 0.910350569171574 56 0.0739278401299039 0.147855680259808 0.926072159870096 57 0.0612797545511144 0.122559509102229 0.938720245448886 58 0.0513345488718286 0.102669097743657 0.948665451128171 59 0.0413556893311087 0.0827113786622174 0.95864431066889 60 0.0314507019044157 0.0629014038088314 0.968549298095584 61 0.0430552512168914 0.0861105024337828 0.956944748783109 62 0.156797820407946 0.313595640815892 0.843202179592054 63 0.616405781382718 0.767188437234565 0.383594218617282 64 0.879027035131405 0.241945929737190 0.120972964868595 65 0.859362542657901 0.281274914684198 0.140637457342099 66 0.870857207019945 0.258285585960110 0.129142792980055 67 0.873062937309524 0.253874125380952 0.126937062690476 68 0.846714823197337 0.306570353605326 0.153285176802663 69 0.870811100743039 0.258377798513923 0.129188899256961 70 0.848825201075586 0.302349597848828 0.151174798924414 71 0.820330144476768 0.359339711046464 0.179669855523232 72 0.791115562366637 0.417768875266726 0.208884437633363 73 0.773838496639695 0.452323006720609 0.226161503360305 74 0.741475029102052 0.517049941795896 0.258524970897948 75 0.73592191912013 0.528156161759742 0.264078080879871 76 0.767326543278044 0.465346913443912 0.232673456721956 77 0.765284588489038 0.469430823021924 0.234715411510962 78 0.728347088493338 0.543305823013324 0.271652911506662 79 0.738912408624129 0.522175182751743 0.261087591375871 80 0.73201340729353 0.53597318541294 0.26798659270647 81 0.727578188809033 0.544843622381934 0.272421811190967 82 0.742919877011291 0.514160245977418 0.257080122988709 83 0.754532738768978 0.490934522462045 0.245467261231022 84 0.725455816556315 0.54908836688737 0.274544183443685 85 0.74260217521899 0.51479564956202 0.25739782478101 86 0.708456349202984 0.583087301594033 0.291543650797016 87 0.667345811199287 0.665308377601425 0.332654188800713 88 0.776505219724246 0.446989560551508 0.223494780275754 89 0.762200906445263 0.475598187109474 0.237799093554737 90 0.756998662264193 0.486002675471614 0.243001337735807 91 0.724676091654013 0.550647816691975 0.275323908345987 92 0.705525639929823 0.588948720140354 0.294474360070177 93 0.670637255478854 0.658725489042292 0.329362744521146 94 0.678775561514647 0.642448876970706 0.321224438485353 95 0.640595220939651 0.718809558120698 0.359404779060349 96 0.63996149262651 0.720077014746981 0.360038507373491 97 0.674437257519553 0.651125484960894 0.325562742480447 98 0.631066291884679 0.737867416230642 0.368933708115321 99 0.591654287997917 0.816691424004167 0.408345712002083 100 0.586947452379846 0.826105095240307 0.413052547620154 101 0.602735262742666 0.794529474514668 0.397264737257334 102 0.59751019605166 0.804979607896679 0.402489803948340 103 0.564618655935961 0.870762688128078 0.435381344064039 104 0.522889341787177 0.954221316425646 0.477110658212823 105 0.498279128147544 0.996558256295089 0.501720871852456 106 0.594605013519398 0.810789972961204 0.405394986480602 107 0.582188615340352 0.835622769319296 0.417811384659648 108 0.596230577851336 0.807538844297327 0.403769422148664 109 0.551895470308002 0.896209059383995 0.448104529691998 110 0.508755627603701 0.982488744792598 0.491244372396299 111 0.548998016398215 0.90200396720357 0.451001983601785 112 0.543093230756007 0.913813538487986 0.456906769243993 113 0.495477427802088 0.990954855604177 0.504522572197912 114 0.637551502428044 0.724896995143913 0.362448497571956 115 0.589414813146293 0.821170373707414 0.410585186853707 116 0.620811555338378 0.758376889323245 0.379188444661622 117 0.652458317297974 0.695083365404053 0.347541682702026 118 0.599897859561427 0.800204280877146 0.400102140438573 119 0.84201995112359 0.315960097752819 0.157980048876410 120 0.854564612105552 0.290870775788895 0.145435387894448 121 0.822737344467218 0.354525311065565 0.177262655532782 122 0.820727483876218 0.358545032247563 0.179272516123782 123 0.818915182653166 0.362169634693667 0.181084817346834 124 0.776602326580686 0.446795346838628 0.223397673419314 125 0.740703622361863 0.518592755276274 0.259296377638137 126 0.71805738816185 0.563885223676300 0.281942611838150 127 0.733814717826463 0.532370564347075 0.266185282173537 128 0.679052619314716 0.641894761370568 0.320947380685284 129 0.865829557561462 0.268340884877077 0.134170442438538 130 0.837946355518949 0.324107288962101 0.162053644481051 131 0.95015791611886 0.0996841677622797 0.0498420838811398 132 0.92835437746594 0.143291245068121 0.0716456225340606 133 0.909991695269687 0.180016609460627 0.0900083047303134 134 0.8799091857213 0.2401816285574 0.1200908142787 135 0.843587577313524 0.312824845372952 0.156412422686476 136 0.799907402702713 0.400185194594574 0.200092597297287 137 0.7455328950476 0.508934209904801 0.254467104952400 138 0.710196746734597 0.579606506530806 0.289803253265403 139 0.673372435874161 0.653255128251678 0.326627564125839 140 0.742323680855041 0.515352638289917 0.257676319144959 141 0.673917746273234 0.652164507453533 0.326082253726766 142 0.606493184266809 0.787013631466381 0.393506815733191 143 0.571241608169959 0.857516783660082 0.428758391830041 144 0.499260552955808 0.998521105911615 0.500739447044192 145 0.391865342497849 0.783730684995698 0.608134657502151 146 0.462198532953014 0.924397065906029 0.537801467046986 147 0.399827591208458 0.799655182416916 0.600172408791542 148 0.421355883832998 0.842711767665996 0.578644116167002 149 0.455234100265891 0.910468200531782 0.544765899734109 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 5 0.0357142857142857 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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