*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 20:20:00 +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/t1293221928owcs90so0ryv4pp.htm/, Retrieved Fri, 24 Dec 2010 21:18:59 +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/t1293221928owcs90so0ryv4pp.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 «

9.1 4.5 1.0 -1.0 1989.3 9.0 4.3 1.0 3.0 2097.8 9.0 4.3 1.3 2.0 2154.9 8.9 4.2 1.1 3.0 2152.2 8.8 4.0 0.8 5.0 2250.3 8.7 3.8 0.7 5.0 2346.9 8.5 4.1 0.7 3.0 2525.6 8.3 4.2 0.9 2.0 2409.4 8.1 4.0 1.3 1.0 2394.4 7.9 4.3 1.4 -4.0 2401.3 7.8 4.7 1.6 1.0 2354.3 7.6 5.0 2.1 1.0 2450.4 7.4 5.1 0.3 6.0 2504.7 7.2 5.4 2.1 3.0 2661.4 7.0 5.4 2.5 2.0 2880.4 7.0 5.4 2.3 2.0 3064.4 6.8 5.5 2.4 2.0 3141.1 6.8 5.8 3.0 -8.0 3327.7 6.7 5.7 1.7 0.0 3565.0 6.8 5.5 3.5 -2.0 3403.1 6.7 5.6 4.0 3.0 3149.9 6.7 5.6 3.7 5.0 3006.8 6.7 5.5 3.7 8.0 3230.7 6.5 5.5 3.0 8.0 3361.1 6.3 5.7 2.7 9.0 3484.7 6.3 5.6 2.5 11.0 3411.1 6.3 5.6 2.2 13.0 3288.2 6.5 5.4 2.9 12.0 3280.4 6.6 5.2 3.1 13.0 3174.0 6.5 5.1 3.0 15.0 3165.3 6.3 5.1 2.8 13.0 3092.7 6.3 5.0 2.5 16.0 3053.1 6.5 5.3 1.9 10.0 3182.0 7.0 5.4 1.9 14.0 2999.9 7.1 5.3 1.8 14.0 3249.6 7.3 5.1 2.0 15.0 3210.5 7.3 5.0 2.6 13.0 3030.3 7.4 5.0 2.5 8.0 2803.5 7.4 4.6 2.5 7.0 2767.6 7.3 4.8 1.6 3.0 2882.6 7.4 5.1 1.4 3.0 2863.4 7.5 5.1 0.8 4.0 2897.1 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 Werkloosheid[t] = + 11.3640291504025 -0.46071028839786rente[t] -0.16307043917458inflatie[t] -0.0260912652092994consumer[t] -0.000433460991891714Bel20[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) 11.3640291504025 0.221392 51.3298 0 0 rente -0.46071028839786 0.051956 -8.8673 0 0 inflatie -0.16307043917458 0.021961 -7.4254 0 0 consumer -0.0260912652092994 0.004013 -6.5017 0 0 Bel20 -0.000433460991891714 4.2e-05 -10.3773 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.903987694364819 R-squared 0.81719375156302 Adjusted R-squared 0.811856342849532 F-TEST (value) 153.106834314159 F-TEST (DF numerator) 4 F-TEST (DF denominator) 137 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.309640357013574 Sum Squared Residuals 13.1351696447346 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.1 8.29156972747669 0.808430272523308 2 9 8.2323162066988 0.767683793301202 3 9 8.1847357175187 0.815264282481295 4 8.9 8.23849991366221 0.661500086337786 5 8.8 8.28485804937099 0.515141950629016 6 8.7 8.35143481915128 0.348565180848724 7 8.5 8.18794478379947 0.312055216200533 8 8.3 8.18571909959188 0.114280900408120 9 8.1 8.2452261616893 -0.145226161689297 10 7.9 8.21817147645493 -0.318171476454924 11 7.8 7.89118961383328 -0.0911896138332781 12 7.6 7.62978570640584 -0.0297857064058367 13 7.4 7.72324821017408 -0.323248210174077 14 7.2 7.30185879133894 -0.101858791338942 15 7 7.16779392365412 -0.167793923654124 16 7 7.12065118898096 -0.120651188980964 17 6.8 7.02502665814563 -0.225026658145626 18 6.8 6.96900013912752 -0.169000139127520 19 6.7 6.91547232384396 -0.215472323843961 20 6.8 6.83644745601516 -0.0364474560151568 21 6.7 6.68813720468857 0.0118627953114343 22 6.7 6.74690407396205 -0.0469040739620452 23 6.7 6.61764939108938 0.0823506089106217 24 6.5 6.6752753851689 -0.175275385168905 25 6.3 6.55238741543459 -0.252387415434592 26 6.3 6.61079273069392 -0.310792730693925 27 6.3 6.66080368793119 -0.360803687931192 28 6.5 6.66826869913461 -0.168268699134613 29 6.6 6.74782565330725 -0.147825653307248 30 6.5 6.76179230627535 -0.261792306275351 31 6.3 6.8780581925402 -0.578058192540205 32 6.3 6.91194161278338 -0.611941612783378 33 6.5 6.97224525916972 -0.472245259169722 34 7 6.90074241611622 0.0992575838837806 35 7.1 6.8548852791981 0.245114720801897 36 7.3 6.90527030861643 0.394729691383574 37 7.3 6.98379127510895 0.316208724891051 38 7.4 7.22886359803394 0.171136401966056 39 7.4 7.4548002282113 -0.0548002282113004 40 7.3 7.5639386125585 -0.263938612558501 41 7.4 7.46666206491838 -0.0666620649183795 42 7.5 7.52380542778708 -0.0238054277870777 43 7.7 7.42481955147121 0.275180448528789 44 7.7 7.30183412461145 0.398165875388546 45 7.7 7.51630131341317 0.183698686586826 46 7.7 7.7553152747933 -0.0553152747933061 47 7.7 7.9563915549696 -0.256391554969598 48 7.8 7.79718262723232 0.00281737276767588 49 8 7.73430620425263 0.265693795747368 50 8.1 7.75142416625248 0.34857583374752 51 8.1 7.68727786452937 0.412722135470635 52 8.2 7.81129682795078 0.388703172049223 53 8.2 8.04475449852611 0.155245501473885 54 8.2 8.0432557778197 0.156744222180293 55 8.1 8.1015128846514 -0.0015128846513974 56 8.1 8.03864879577388 0.0613512042261173 57 8.2 8.14726520971962 0.052734790280383 58 8.3 8.36430236183357 -0.0643023618335725 59 8.3 8.27124877858001 0.0287512214199862 60 8.4 8.2629405159426 0.137059484057395 61 8.5 8.30249580376754 0.197504196232463 62 8.5 8.474449379887 0.0255506201129918 63 8.4 8.50372800936636 -0.103728009366358 64 8 8.1279257812555 -0.127925781255501 65 7.9 8.05906757129454 -0.159067571294536 66 8.1 8.25619484029443 -0.156194840294435 67 8.5 8.51879893595494 -0.0187989359549430 68 8.8 8.52193493872406 0.278065061275944 69 8.8 8.32446072877406 0.475539271225939 70 8.6 8.44685161905418 0.153148380945820 71 8.3 8.2332621171633 0.0667378828366928 72 8.3 8.36476060389508 -0.0647606038950793 73 8.3 8.38338802623523 -0.0833880262352327 74 8.4 8.36069745749747 0.0393025425025287 75 8.4 8.4800968315494 -0.0800968315494098 76 8.5 8.53161867877458 -0.0316186787745790 77 8.6 8.61280278557476 -0.0128027855747601 78 8.6 8.46179944942844 0.138200550571558 79 8.6 8.46973118876634 0.130268811233660 80 8.6 8.34514285145717 0.254857148542834 81 8.6 8.40706376737956 0.192936232620444 82 8.5 8.72215040605816 -0.222150406058156 83 8.4 8.7547288009252 -0.354728800925198 84 8.4 8.59145179936802 -0.191451799368016 85 8.4 8.61697090259383 -0.216970902593832 86 8.5 8.45365793495508 0.0463420650449174 87 8.5 8.44700758901393 0.0529924109860734 88 8.6 8.38615398445276 0.213846015547241 89 8.6 8.63049120222455 -0.0304912022245511 90 8.4 8.56689760967844 -0.166897609678442 91 8.2 8.5860221500432 -0.386022150043197 92 8 8.41648183093498 -0.416481830934978 93 8 8.42986747516084 -0.429867475160841 94 8 8.2577331094416 -0.257733109441602 95 8 8.14873707230876 -0.148737072308758 96 7.9 8.0428834588785 -0.142883458878495 97 7.9 8.06966424138125 -0.169664241381253 98 7.8 8.08273689161317 -0.282736891613169 99 7.8 8.10384305700885 -0.303843057008853 100 8 8.11814448164556 -0.118144481645558 101 7.8 8.1387898826618 -0.338789882661808 102 7.4 7.92667816843694 -0.526678168436936 103 7.2 7.99090533823868 -0.790905338238682 104 7 7.9197458285907 -0.919745828590696 105 7 7.83247818427654 -0.832478184276538 106 7.2 7.4515113494287 -0.251511349428700 107 7.2 7.28760350823305 -0.0876035082330467 108 7.2 7.47944521497731 -0.27944521497731 109 7 7.1566761234435 -0.156676123443494 110 6.9 7.02485789819206 -0.124857898192058 111 6.8 6.94718504806134 -0.147185048061338 112 6.8 6.97365628534316 -0.173656285343164 113 6.8 6.75936250612359 0.0406374938764103 114 6.9 6.95571806839681 -0.0557180683968129 115 7.2 6.9345934344642 0.265406565535807 116 7.2 6.88042068018421 0.319579319815788 117 7.2 6.77131551250104 0.428684487498959 118 7.1 6.64816563716002 0.451834362839975 119 7.2 6.92693295098213 0.273067049017872 120 7.3 7.00282789989024 0.297172100109756 121 7.5 7.17867521973373 0.321324780266269 122 7.6 7.1075713517167 0.492428648283295 123 7.7 7.38267484306309 0.317325156936908 124 7.7 6.90846266118474 0.791537338815258 125 7.7 7.52230204841537 0.177697951584631 126 7.8 7.78378161000043 0.0162183899995682 127 8 8.06765631964566 -0.0676563196456628 128 8.1 8.14679243195043 -0.0467924319504271 129 8.1 8.10278570004638 -0.00278570004638115 130 8 8.09687465170858 -0.0968746517085788 131 8.1 8.3157517675018 -0.215751767501792 132 8.2 8.43226168765013 -0.232261687650134 133 8.3 8.38432925284906 -0.0843292528490561 134 8.4 8.54222674618488 -0.142226746184881 135 8.4 8.383048545315 0.0169514546850034 136 8.4 8.21884187334692 0.18115812665308 137 8.5 8.09983044809107 0.400169551908928 138 8.5 8.12366194250134 0.376338057498658 139 8.6 8.39706973385871 0.202930266141286 140 8.6 8.32642236199925 0.273577638000751 141 8.5 8.28160128842519 0.218398711574813 142 8.5 8.79074350945993 -0.290743509459930 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.206299724836443 0.412599449672887 0.793700275163557 9 0.15397082966387 0.30794165932774 0.84602917033613 10 0.074748907755762 0.149497815511524 0.925251092244238 11 0.152924255806527 0.305848511613054 0.847075744193473 12 0.111695032066961 0.223390064133923 0.888304967933039 13 0.259933486794504 0.519866973589008 0.740066513205496 14 0.308372596133874 0.616745192267747 0.691627403866126 15 0.407087860808927 0.814175721617853 0.592912139191073 16 0.6117124831754 0.7765750336492 0.3882875168246 17 0.618291901846478 0.763416196307044 0.381708098153522 18 0.807364836020524 0.385270327958953 0.192635163979476 19 0.844283774948797 0.311432450102406 0.155716225051203 20 0.821791716170507 0.356416567658986 0.178208283829493 21 0.769689700983131 0.460620598033738 0.230310299016869 22 0.715386893256016 0.569226213487968 0.284613106743984 23 0.658757299649509 0.682485400700981 0.341242700350491 24 0.597993256158218 0.804013487683565 0.402006743841782 25 0.541982917743188 0.916034164513625 0.458017082256812 26 0.495133792835533 0.990267585671065 0.504866207164467 27 0.463027964374681 0.926055928749363 0.536972035625319 28 0.406448168567006 0.812896337134012 0.593551831432994 29 0.358925602794928 0.717851205589856 0.641074397205072 30 0.339525466816758 0.679050933633516 0.660474533183242 31 0.49287007557012 0.98574015114024 0.50712992442988 32 0.625622235187438 0.748755529625124 0.374377764812562 33 0.650555487575237 0.698889024849526 0.349444512424763 34 0.661093551962847 0.677812896074306 0.338906448037153 35 0.760472752472688 0.479054495054623 0.239527247527312 36 0.853622969757051 0.292754060485898 0.146377030242949 37 0.8622666142306 0.275466771538799 0.137733385769400 38 0.833216584547098 0.333566830905804 0.166783415452902 39 0.805709016425135 0.38858196714973 0.194290983574865 40 0.803164941602782 0.393670116794435 0.196835058397218 41 0.768180676676457 0.463638646647086 0.231819323323543 42 0.72751718638424 0.544965627231521 0.272482813615761 43 0.737595954253013 0.524808091493974 0.262404045746987 44 0.793029384753403 0.413941230493194 0.206970615246597 45 0.765516417369037 0.468967165261925 0.234483582630963 46 0.733099077344775 0.53380184531045 0.266900922655225 47 0.741266114329242 0.517467771341517 0.258733885670758 48 0.701849084987227 0.596301830025546 0.298150915012773 49 0.688907665457162 0.622184669085677 0.311092334542838 50 0.702858157359652 0.594283685280696 0.297141842640348 51 0.724519230123319 0.550961539753363 0.275480769876681 52 0.737936358640286 0.524127282719429 0.262063641359714 53 0.714054570129544 0.571890859740913 0.285945429870456 54 0.689875884615262 0.620248230769477 0.310124115384738 55 0.66131241981009 0.67737516037982 0.33868758018991 56 0.622008870916448 0.755982258167104 0.377991129083552 57 0.588956473145222 0.822087053709555 0.411043526854778 58 0.573671538419383 0.852656923161234 0.426328461580617 59 0.538018830468163 0.923962339063673 0.461981169531837 60 0.498025027104956 0.996050054209911 0.501974972895044 61 0.468843679450683 0.937687358901366 0.531156320549317 62 0.425648113767575 0.85129622753515 0.574351886232425 63 0.398845613555593 0.797691227111186 0.601154386444407 64 0.368707098384441 0.737414196768882 0.631292901615559 65 0.341526080008069 0.683052160016138 0.658473919991931 66 0.325375320950031 0.650750641900062 0.674624679049969 67 0.290697705229093 0.581395410458185 0.709302294770907 68 0.273182622934880 0.546365245869759 0.72681737706512 69 0.323278600238509 0.646557200477018 0.676721399761491 70 0.284445845856291 0.568891691712582 0.715554154143709 71 0.258901397937728 0.517802795875455 0.741098602062272 72 0.252762753476857 0.505525506953713 0.747237246523143 73 0.250342869944387 0.500685739888774 0.749657130055613 74 0.244028979079119 0.488057958158238 0.755971020920881 75 0.233009986035996 0.466019972071992 0.766990013964004 76 0.218959835101623 0.437919670203246 0.781040164898377 77 0.204653623820173 0.409307247640346 0.795346376179827 78 0.216116575901818 0.432233151803636 0.783883424098182 79 0.229363093911751 0.458726187823502 0.770636906088249 80 0.301787585155961 0.603575170311922 0.698212414844039 81 0.3649739278241 0.7299478556482 0.6350260721759 82 0.366010229901706 0.732020459803412 0.633989770098294 83 0.371554013710766 0.743108027421533 0.628445986289234 84 0.339867460123989 0.679734920247977 0.660132539876011 85 0.301257598232296 0.602515196464592 0.698742401767704 86 0.305366020818400 0.610732041636799 0.6946339791816 87 0.353514949332610 0.707029898665219 0.64648505066739 88 0.489269772773155 0.97853954554631 0.510730227226845 89 0.488377974683353 0.976755949366706 0.511622025316647 90 0.46216220090611 0.92432440181222 0.53783779909389 91 0.442256164640405 0.88451232928081 0.557743835359595 92 0.42761630343995 0.8552326068799 0.57238369656005 93 0.420662441806635 0.84132488361327 0.579337558193365 94 0.38669484388335 0.7733896877667 0.61330515611665 95 0.34741920926998 0.69483841853996 0.65258079073002 96 0.318680832333019 0.637361664666037 0.681319167666981 97 0.312738152684531 0.625476305369062 0.687261847315469 98 0.281057973004084 0.562115946008167 0.718942026995916 99 0.243008062797803 0.486016125595607 0.756991937202197 100 0.236110460876849 0.472220921753698 0.763889539123151 101 0.210568756117467 0.421137512234933 0.789431243882533 102 0.207530683308612 0.415061366617224 0.792469316691388 103 0.290327867558374 0.580655735116748 0.709672132441626 104 0.524425112134835 0.95114977573033 0.475574887865165 105 0.766045712763366 0.467908574473267 0.233954287236634 106 0.73940251299933 0.521194974001341 0.260597487000671 107 0.71249698087608 0.575006038247839 0.287503019123920 108 0.802285858125689 0.395428283748622 0.197714141874311 109 0.847702547239706 0.304594905520589 0.152297452760294 110 0.886826298242437 0.226347403515126 0.113173701757563 111 0.932041063226113 0.135917873547773 0.0679589367738867 112 0.962899201586012 0.0742015968279757 0.0371007984139879 113 0.979564867136035 0.040870265727931 0.0204351328639655 114 0.992881711595183 0.0142365768096341 0.00711828840481707 115 0.992933186595665 0.0141336268086697 0.00706681340433484 116 0.993146136164568 0.0137077276708639 0.00685386383543194 117 0.992964037986908 0.0140719240261834 0.0070359620130917 118 0.994558906534332 0.0108821869313360 0.00544109346566801 119 0.998554809790192 0.00289038041961515 0.00144519020980758 120 0.999720554416605 0.000558891166789564 0.000279445583394782 121 0.999915477278738 0.000169045442523802 8.4522721261901e-05 122 0.999963733535165 7.25329296699107e-05 3.62664648349553e-05 123 0.999974004087188 5.19918256231923e-05 2.59959128115961e-05 124 0.999953366087272 9.32678254560814e-05 4.66339127280407e-05 125 0.999982644943598 3.47101128040383e-05 1.73550564020191e-05 126 0.99999449174127 1.10165174605763e-05 5.50825873028816e-06 127 0.999977487786413 4.5024427173769e-05 2.25122135868845e-05 128 0.99990733569002 0.000185328619962102 9.26643099810511e-05 129 0.999736473824752 0.000527052350496852 0.000263526175248426 130 0.999162301397546 0.00167539720490871 0.000837698602454353 131 0.999524210873404 0.00095157825319178 0.00047578912659589 132 0.998922884955962 0.00215423008807565 0.00107711504403782 133 0.998403630177478 0.0031927396450446 0.0015963698225223 134 0.991835303511718 0.0163293929765647 0.00816469648828234 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.118110236220472 NOK 5% type I error level 22 0.173228346456693 NOK 10% type I error level 23 0.181102362204724 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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