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: Thu, 02 Dec 2010 11:00:34 +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/02/t1291295633swtgyaazx263d78.htm/, Retrieved Thu, 02 Dec 2010 14:13:53 +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/02/t1291295633swtgyaazx263d78.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 «

5 1 1 1 2 1 21 4 1 4 1 4 1 21 7 1 5 2 4 1 24 7 2 2 1 4 2 21 5 1 1 1 3 2 21 5 1 1 1 2 2 22 4 1 2 1 3 2 22 4 2 1 1 4 1 20 6 2 1 1 2 1 21 5 2 1 1 3 0 21 1 2 3 2 3 2 21 5 1 1 1 3 1 22 4 2 1 1 4 1 22 6 1 1 1 3 1 23 7 1 2 1 2 1 23 7 1 4 2 5 2 21 2 2 1 1 2 2 24 6 2 1 1 3 1 23 4 2 1 1 3 2 21 3 1 2 1 3 1 23 6 1 3 1 3 2 32 6 1 1 1 4 1 21 5 2 1 2 3 2 21 4 2 1 1 1 2 21 6 1 1 2 3 1 21 4 2 1 1 2 2 21 3 2 2 4 4 1 20 4 2 1 1 4 1 24 5 1 1 1 4 1 22 6 1 1 1 1 2 22 6 2 1 1 3 2 21 4 2 1 1 1 2 21 6 1 1 1 4 1 21 6 2 1 1 2 2 21 5 2 1 1 3 1 23 6 2 1 1 3 1 23 4 1 1 1 2 2 21 6 2 1 1 4 1 20 7 1 1 1 1 2 21 5 2 1 1 2 1 20 6 2 1 1 3 2 21 6 1 1 1 3 1 22 5 2 4 1 5 2 21 7 2 1 1 3 1 22 6 2 1 1 4 1 22 3 1 4 3 3 2 22 4 1 2 2 4 1 22 5 1 2 1 2 1 21 4 1 1 1 3 1 21 3 2 1 1 2 2 21 5 1 2 2 3 1 23 5 1 1 1 2 2 23 4 2 1 1 3 2 23 5 2 1 1 4 1 22 1 2 1 1 1 1 24 2 2 1 1 1 1 23 3 2 1 1 1 2 21 4 2 2 1 4 1 22 3 2 1 1 2 2 22 7 2 1 1 2 2 21 2 2 1 1 3 1 21 4 1 2 2 5 1 21 2 2 1 1 3 2 21 5 1 2 1 3 1 20 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation roken[t] = -0.471846127072205 -0.0304867246153451algemene_tevredenheid[t] -0.401462556568098meer_sport[t] + 0.385195401689889drugs[t] + 0.370121634831214drankgebruik[t] + 0.351301598737133geslacht[t] + 0.0289776729828369leeftijd[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) -0.471846127072205 0.678865 -0.6951 0.488078 0.244039 algemene_tevredenheid -0.0304867246153451 0.050639 -0.602 0.548035 0.274017 meer_sport -0.401462556568098 0.144001 -2.7879 0.005978 0.002989 drugs 0.385195401689889 0.123372 3.1222 0.002147 0.001073 drankgebruik 0.370121634831214 0.076942 4.8104 4e-06 2e-06 geslacht 0.351301598737133 0.147143 2.3875 0.018185 0.009092 leeftijd 0.0289776729828369 0.020119 1.4403 0.151829 0.075915 Multiple Linear Regression - Regression Statistics Multiple R 0.503703860024925 R-squared 0.253717578604009 Adjusted R-squared 0.224451601294362 F-TEST (value) 8.66936975722927 F-TEST (DF numerator) 6 F-TEST (DF denominator) 153 p-value 3.99815324181318e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.838010449731623 Sum Squared Residuals 107.446011620488 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 1.05952909601200 -0.0595290960119978 2 4 1.83025909028977 2.16974090971023 3 5 2.21092733708213 2.78907266291787 4 2 1.68863795861277 0.311362041387232 5 1 1.78095232958034 -0.780952329580343 6 1 1.43980836773197 -0.439808367731967 7 2 1.84041672717853 0.159583272821475 8 1 1.39981886073883 -0.399818860738834 9 1 0.627579814828554 0.372420185171446 10 1 0.676886575537979 0.323113424462021 11 3 1.88663207316352 1.11336792683648 12 1 1.45862840382605 -0.458628403826047 13 1 1.45777420670451 -0.457774206704508 14 1 1.45711935219354 -0.457119352193539 15 2 1.05651099274698 0.94348900725302 16 4 2.84541755170197 1.15458244829803 17 1 1.18776133097558 -0.187761330975578 18 1 1.05565679562544 -0.0556567956254411 19 1 1.40997649762759 -0.409976497627591 20 2 1.54857952603957 0.451420473960426 21 3 2.06922000777620 0.930779992223795 22 1 1.76928564105908 -0.769285641059079 23 1 1.76468517470213 -0.764685174702135 24 1 0.669733227965164 0.330266772034837 25 1 1.78435940791775 -0.784359407917755 26 1 1.03985486279638 -0.039854862796377 27 2 2.58589179042385 -0.585891790423847 28 1 1.51572955267018 -0.515729552670182 29 1 1.82875003865726 -0.82875003865726 30 1 1.03920000828541 -0.0392000082854081 31 1 1.3490030483969 -0.349003048396901 32 1 0.669733227965164 0.330266772034837 33 1 1.76928564105908 -0.769285641059079 34 1 0.978881413565687 0.0211185864343132 35 1 1.08614352024079 -0.0861435202407862 36 1 1.05565679562544 -0.0556567956254411 37 1 1.44131741936447 -0.441317419364475 38 1 1.33884541150814 -0.338845411508144 39 1 0.979735610687226 0.0202643893127742 40 1 0.629088866461062 0.370911133538938 41 1 1.3490030483969 -0.349003048396901 42 1 1.42814167921070 -0.428141679210702 43 4 2.11973304267467 1.88026695732533 44 1 0.99619239802726 0.00380760197274099 45 1 1.39680075747382 -0.396800757473818 46 4 2.64129425517365 1.35870574482635 47 2 2.24443216496250 -0.244432164962495 48 2 1.05952909601200 0.940470903988004 49 1 1.46013745545856 -0.460137455458555 50 1 1.07034158741172 -0.070341587411722 51 2 1.87280147849877 0.127198521501227 52 1 1.46878604071480 -0.468786040714804 53 1 1.46793184359326 -0.467931843593265 54 1 1.42728748208916 -0.427287482089163 55 1 0.496824822022576 0.503175177977424 56 1 0.437360424424394 0.562639575575606 57 1 0.700219952580508 0.299780047419492 58 2 1.45777420670451 0.542225793295492 59 1 1.09931926039456 -0.099319260394559 60 1 0.948394688950342 0.0516053110496581 61 1 1.11964834812115 -0.119648348121148 62 2 2.58557612681087 -0.585576126810872 63 1 1.47094994685828 -0.470949946858281 64 2 1.40067305786037 0.599326942139627 65 4 1.77944327794783 2.22055672205217 66 1 1.37798072137974 -0.377980721379738 67 1 1.02667912264260 -0.0266791226426042 68 1 1.39680075747382 -0.396800757473818 69 2 1.76928564105908 0.230714358940921 70 3 2.21243638871464 0.787563611285358 71 1 1.3490030483969 -0.349003048396901 72 1 1.45777420670451 -0.457774206704508 73 1 1.12915113049894 -0.129151130498935 74 1 1.42965073084321 -0.42965073084321 75 1 1.08463446860828 -0.084634468608278 76 1 1.08463446860828 -0.084634468608278 77 1 2.02978192046115 -1.02978192046115 78 4 2.18156068902690 1.81843931097310 79 1 1.02667912264260 -0.0266791226426042 80 1 2.11042960290746 -1.11042960290746 81 2 1.36782308449098 0.632176915509019 82 1 1.45928325833702 -0.459283258337016 83 1 1.79977236567442 -0.799772365674424 84 1 2.18345871573181 -1.18345871573181 85 1 1.43895417061043 -0.438954170610428 86 1 1.05716584725795 -0.0571658472579492 87 1 1.76928564105908 -0.769285641059079 88 1 1.42814167921070 -0.428141679210702 89 1 0.700219952580508 0.299780047419492 90 2 2.53967644443886 -0.539676444438857 91 1 1.79977236567442 -0.799772365674424 92 1 1.37798072137974 -0.377980721379738 93 1 1.43895417061043 -0.438954170610428 94 1 1.76403032019117 -0.764030320191166 95 1 1.42728748208916 -0.427287482089163 96 2 0.658920736565438 1.34107926343456 97 1 1.750465604965 -0.750465604964999 98 5 1.70896704633936 3.29103295366064 99 1 1.33733635987564 -0.337336359875636 100 1 1.36782308449098 -0.367823084490981 101 1 1.40695839436257 -0.406958394362574 102 2 1.42577843045665 0.574221569543345 103 1 2.18345871573181 -1.18345871573181 104 3 2.37607147826349 0.623928521736513 105 1 1.40997649762759 -0.409976497627591 106 1 1.40997649762759 -0.409976497627591 107 1 1.02667912264260 -0.0266791226426042 108 3 1.76843144393754 1.23156855606246 109 1 1.39680075747382 -0.396800757473818 110 1 1.39916400622787 -0.399164006227865 111 1 1.16114690674679 -0.161146906746788 112 1 1.73879891644373 -0.738798916443734 113 1 1.50143667147363 -0.501436671473626 114 1 1.14797116659302 -0.147971166593015 115 2 1.90053597928768 0.0994640207123233 116 2 0.759291951851405 1.24070804814859 117 4 1.79590006528787 2.20409993471213 118 4 2.56865411742169 1.43134588257831 119 1 1.70982124346090 -0.709821243460897 120 1 1.11361214159111 -0.113612141591115 121 1 0.820265401082096 0.179734598917904 122 1 1.45777420670451 -0.457774206704508 123 4 2.16719156085360 1.83280843914640 124 1 2.18260451861027 -1.18260451861027 125 1 1.39765495459536 -0.397654954595357 126 1 1.17156699981923 -0.171566999819229 127 1 1.42879653372167 -0.428796533721671 128 3 1.40695839436257 1.59304160563743 129 1 1.31851632378156 -0.318516323781555 130 1 2.13480680953335 -1.13480680953335 131 1 2.46053781362506 -1.46053781362506 132 4 1.71912468322811 2.28087531677189 133 4 2.22634029483880 1.77365970516120 134 1 1.456265155072 -0.456265155072 135 2 2.13670483623825 -0.136704836238251 136 1 0.669733227965164 0.330266772034837 137 2 1.78199615916371 0.218003840836293 138 1 1.36782308449098 -0.367823084490981 139 3 1.73879891644373 1.26120108355627 140 2 2.12058723979621 -0.120587239796212 141 2 1.39680075747382 0.603199242526182 142 1 1.36933213612349 -0.369332136123489 143 1 1.37948977301225 -0.379489773012246 144 2 1.37948977301225 0.620510226987754 145 1 1.39680075747382 -0.396800757473818 146 2 2.53967644443886 -0.539676444438857 147 2 2.15060874236241 -0.150608742362413 148 1 0.727688573930837 0.272311426069163 149 1 1.80605770217663 -0.806057702176625 150 2 1.66775745120811 0.332242548791893 151 1 1.76777658942657 -0.76777658942657 152 2 1.39680075747382 0.603199242526182 153 1 1.69355408858269 -0.693554088582688 154 1 1.05867489889046 -0.0586748988904574 155 1 1.82724098702475 -0.827240987024753 156 1 1.40997649762759 -0.409976497627591 157 1 1.78009813245880 -0.780098132458804 158 1 1.79675426240941 -0.796754262409408 159 1 1.90092495436007 -0.900924954360071 160 1 1.36631403285847 -0.366314032858473 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.689300075117358 0.621399849765284 0.310699924882642 11 0.726836765063674 0.546326469872652 0.273163234936326 12 0.765418164899484 0.469163670201033 0.234581835100516 13 0.699902348742606 0.600195302514788 0.300097651257394 14 0.641611244502335 0.716777510995329 0.358388755497665 15 0.658722651250512 0.682554697498977 0.341277348749488 16 0.733248432369296 0.533503135261408 0.266751567630704 17 0.655506943256942 0.688986113486117 0.344493056743058 18 0.57624347100445 0.8475130579911 0.42375652899555 19 0.490322637890898 0.980645275781796 0.509677362109102 20 0.407737563521649 0.815475127043299 0.59226243647835 21 0.340306131553199 0.680612263106397 0.659693868446801 22 0.390750345470391 0.781500690940782 0.609249654529609 23 0.598565775164661 0.802868449670678 0.401434224835339 24 0.628814688085491 0.742370623829018 0.371185311914509 25 0.80156402268325 0.396871954633499 0.198435977316750 26 0.75749863053056 0.485002738938879 0.242501369469439 27 0.815054669474542 0.369890661050916 0.184945330525458 28 0.808423445439654 0.383153109120691 0.191576554560346 29 0.8259327327165 0.348134534567001 0.174067267283501 30 0.78233832629938 0.43532334740124 0.21766167370062 31 0.737503105718842 0.524993788562316 0.262496894281158 32 0.70690891323295 0.586182173534101 0.293091086767051 33 0.699394321068877 0.601211357862247 0.300605678931123 34 0.645667324839738 0.708665350320525 0.354332675160262 35 0.58994038692566 0.82011922614868 0.41005961307434 36 0.532538999429692 0.934922001140616 0.467461000570308 37 0.485974673003816 0.971949346007632 0.514025326996184 38 0.431058468510632 0.862116937021263 0.568941531489368 39 0.375166588993996 0.750333177987992 0.624833411006004 40 0.345680059116256 0.691360118232512 0.654319940883744 41 0.299490354532620 0.598980709065239 0.70050964546738 42 0.268805884294165 0.537611768588331 0.731194115705834 43 0.469402756350679 0.938805512701357 0.530597243649321 44 0.415634380133822 0.831268760267645 0.584365619866178 45 0.381059726422899 0.762119452845797 0.618940273577101 46 0.418645732921866 0.837291465843731 0.581354267078134 47 0.383633024156604 0.767266048313208 0.616366975843396 48 0.411143945614414 0.822287891228828 0.588856054385586 49 0.372590450788456 0.745180901576912 0.627409549211544 50 0.324300700694535 0.64860140138907 0.675699299305465 51 0.281993963089069 0.563987926178139 0.71800603691093 52 0.260462484238345 0.52092496847669 0.739537515761655 53 0.237674002563654 0.475348005127308 0.762325997436346 54 0.209750230060362 0.419500460120725 0.790249769939638 55 0.188326114823875 0.376652229647751 0.811673885176125 56 0.169787214267007 0.339574428534014 0.830212785732993 57 0.145037680645542 0.290075361291084 0.854962319354458 58 0.128944757248795 0.25788951449759 0.871055242751205 59 0.105105189003399 0.210210378006799 0.8948948109966 60 0.0844524355086748 0.168904871017350 0.915547564491325 61 0.0668651574559879 0.133730314911976 0.933134842544012 62 0.0612717118525318 0.122543423705064 0.938728288147468 63 0.0507245766291956 0.101449153258391 0.949275423370805 64 0.0479925601751948 0.0959851203503896 0.952007439824805 65 0.176226230326057 0.352452460652114 0.823773769673943 66 0.153908085106056 0.307816170212112 0.846091914893944 67 0.127122317874355 0.25424463574871 0.872877682125645 68 0.109088516648024 0.218177033296049 0.890911483351976 69 0.090279847061809 0.180559694123618 0.909720152938191 70 0.085175877911623 0.170351755823246 0.914824122088377 71 0.0704052762083863 0.140810552416773 0.929594723791614 72 0.0596196884679915 0.119239376935983 0.940380311532009 73 0.0490866814486731 0.0981733628973462 0.950913318551327 74 0.0403852090390976 0.0807704180781953 0.959614790960902 75 0.0315444929996141 0.0630889859992283 0.968455507000386 76 0.0243517089262234 0.0487034178524467 0.975648291073777 77 0.0265090941922422 0.0530181883844843 0.973490905807758 78 0.0822179629155409 0.164435925831082 0.91778203708446 79 0.0665347355291158 0.133069471058232 0.933465264470884 80 0.0731171416997174 0.146234283399435 0.926882858300282 81 0.0687009884859909 0.137401976971982 0.931299011514009 82 0.0575582900464052 0.115116580092810 0.942441709953595 83 0.053988619922747 0.107977239845494 0.946011380077253 84 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0.232681016252256 0.465362032504511 0.767318983747744 102 0.208682177468192 0.417364354936383 0.791317822531808 103 0.233624378776238 0.467248757552476 0.766375621223762 104 0.223256796926253 0.446513593852506 0.776743203073747 105 0.193688757254259 0.387377514508518 0.806311242745741 106 0.166706295830155 0.333412591660309 0.833293704169845 107 0.137686509955089 0.275373019910178 0.862313490044911 108 0.168191720470309 0.336383440940619 0.83180827952969 109 0.145693744306252 0.291387488612505 0.854306255693748 110 0.123047862225213 0.246095724450427 0.876952137774787 111 0.100504815309033 0.201009630618066 0.899495184690967 112 0.09565924645411 0.19131849290822 0.90434075354589 113 0.0782705718013113 0.156541143602623 0.921729428198689 114 0.0613937196446573 0.122787439289315 0.938606280355343 115 0.0516709057565722 0.103341811513144 0.948329094243428 116 0.0647125122398869 0.129425024479774 0.935287487760113 117 0.216778749157346 0.433557498314692 0.783221250842654 118 0.32556612404074 0.65113224808148 0.67443387595926 119 0.313215640885899 0.626431281771798 0.686784359114101 120 0.269405560719747 0.538811121439495 0.730594439280253 121 0.233649524686804 0.467299049373607 0.766350475313196 122 0.196730169551408 0.393460339102817 0.803269830448592 123 0.509502904445347 0.980994191109306 0.490497095554653 124 0.503522793894459 0.992954412211082 0.496477206105541 125 0.472582573521579 0.945165147043157 0.527417426478421 126 0.420032343465245 0.84006468693049 0.579967656534755 127 0.365400741041908 0.730801482083816 0.634599258958092 128 0.48047002158601 0.96094004317202 0.51952997841399 129 0.442656517707266 0.885313035414531 0.557343482292734 130 0.43479830678486 0.86959661356972 0.56520169321514 131 0.480693033349752 0.961386066699504 0.519306966650248 132 0.852010787339678 0.295978425320645 0.147989212660322 133 0.988577796206278 0.0228444075874448 0.0114222037937224 134 0.981860713016836 0.0362785739663286 0.0181392869831643 135 0.971189395220228 0.0576212095595451 0.0288106047797725 136 0.955625564020996 0.0887488719580082 0.0443744359790041 137 0.944507981467814 0.110984037064372 0.0554920185321859 138 0.92071573715675 0.158568525686498 0.0792842628432492 139 0.987526639766486 0.0249467204670279 0.0124733602335139 140 0.98866532037482 0.0226693592503585 0.0113346796251793 141 0.99226528512877 0.0154694297424595 0.00773471487122973 142 0.984735247440534 0.0305295051189325 0.0152647525594662 143 0.972645834365348 0.0547083312693044 0.0273541656346522 144 0.986897255667294 0.0262054886654123 0.0131027443327061 145 0.973449074958934 0.0531018500821313 0.0265509250410656 146 0.98092305236419 0.0381538952716189 0.0190769476358095 147 0.985855060212753 0.0282898795744936 0.0141449397872468 148 0.962870623897293 0.0742587522054135 0.0371293761027067 149 0.934238349318328 0.131523301363345 0.0657616506816723 150 0.851378628426063 0.297242743147874 0.148621371573937 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 18 0.127659574468085 NOK 10% type I error level 32 0.226950354609929 NOK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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