Workshop 7 tutorial

*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 20:40:56 +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/t129132234520yawyge0skbp0s.htm/, Retrieved Thu, 02 Dec 2010 21:39:16 +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/t129132234520yawyge0skbp0s.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 «

2 2 1 4 3 3 3 3 3 2 3 4 3 3 4 3 3 4 2 3 4 4 4 3 3 3 3 2 3 3 3 3 3 3 2 3 3 2 2 2 3 1 2 4 3 3 2 2 2 4 4 5 4 4 5 4 3 2 2 4 2 2 3 2 3 2 2 4 4 3 2 3 4 2 2 2 2 2 2 2 3 4 2 2 3 2 4 4 3 3 3 4 3 2 3 3 2 3 2 4 4 4 3 3 3 2 2 5 3 4 2 3 3 3 5 3 3 4 3 3 2 2 4 3 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 3 2 2 2 4 2 2 2 2 4 2 2 2 3 2 2 3 3 1 1 4 3 3 3 2 2 4 3 4 4 4 4 3 3 3 2 4 3 3 2 3 3 2 2 4 3 3 2 2 2 3 3 4 3 4 3 3 2 3 3 4 4 4 4 3 4 4 3 4 4 2 4 4 2 3 2 3 4 3 3 3 3 3 3 3 4 3 3 3 2 2 2 4 4 4 4 2 4 2 2 3 2 4 2 2 3 4 3 4 3 3 3 4 2 4 3 4 4 3 4 4 3 2 2 4 3 2 3 3 3 2 2 4 3 2 2 3 1 3 3 4 4 4 4 4 3 3 3 4 3 3 4 3 3 3 2 3 2 2 2 2 3 3 3 4 3 3 3 3 2 4 3 4 4 4 4 4 3 3 3 4 3 4 4 3 1 2 3 2 2 3 3 5 2 1 5 2 1 4 2 4 2 2 4 3 2 3 2 3 3 3 4 3 2 3 3 2 4 3 4 4 4 3 4 2 3 2 4 4 4 3 4 3 2 2 5 2 2 2 2 4 2 3 4 3 3 4 3 2 3 3 4 4 3 4 3 3 3 3 4 3 2 4 3 4 4 2 3 3 1 2 2 3 3 2 4 4 3 3 4 4 2 2 4 3 2 3 3 3 2 3 5 3 4 3 4 3 2 3 4 3 3 3 3 4 2 2 3 3 4 2 3 2 3 3 3 4 4 4 4 4 1 1 4 3 4 4 1 2 5 3 4 4 4 4 4 4 2 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 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Y[t] = + 0.530179124767959 + 0.08203483012131X1t[t] + 0.382220352569239X2t[t] + 0.125417786702747X3t[t] -0.120826659285732X4t[t] -0.0412507968502131X5t[t] + 0.165388840699340X6t[t] + 0.139655817303533X7t[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) 0.530179124767959 0.542822 0.9767 0.330307 0.165154 X1t 0.08203483012131 0.072922 1.125 0.262422 0.131211 X2t 0.382220352569239 0.082671 4.6234 8e-06 4e-06 X3t 0.125417786702747 0.074841 1.6758 0.095892 0.047946 X4t -0.120826659285732 0.082196 -1.47 0.143687 0.071844 X5t -0.0412507968502131 0.087366 -0.4722 0.637508 0.318754 X6t 0.165388840699340 0.080641 2.0509 0.042039 0.021019 X7t 0.139655817303533 0.07695 1.8149 0.071565 0.035783 Multiple Linear Regression - Regression Statistics Multiple R 0.455185301715151 R-squared 0.207193658897513 Adjusted R-squared 0.169696061683206 F-TEST (value) 5.52551828090096 F-TEST (DF numerator) 7 F-TEST (DF denominator) 148 p-value 1.15362556940557e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.781193377548189 Sum Squared Residuals 90.3189377825218 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.00704188999157 -0.00704188999156803 2 3 2.93687143582941 0.0631285641705947 3 3 2.43122550066409 0.568774499335907 4 3 2.60268185184588 0.397318148154119 5 3 2.08208542482673 0.91791457517327 6 3 2.00218275443664 0.997817245563357 7 2 3.75154643721094 -1.75154643721094 8 3 2.41168388139324 0.588316118606763 9 3 2.10304674257575 0.896953257424245 10 4 1.99545946728840 2.00454053271160 11 3 2.64879178425104 0.351208215748962 12 3 2.89476822210159 0.105231777898412 13 2 2.30921961654619 -0.309219616546191 14 3 2.30804039171402 0.69195960828598 15 3 3.45128954683689 -0.451289546836892 16 2 3.02497377643316 -1.02497377643316 17 3 2.72809963854863 0.271900361451372 18 3 2.93400450438114 0.0659954956188643 19 2 3.03921180703395 -1.03921180703395 20 2 2.42592191199402 -0.425921911994024 21 1 2.64120567287237 -1.64120567287237 22 4 3.07366032168467 0.926339678315331 23 3 3.06953595784677 -0.06953595784677 24 2 2.7644912998439 -0.764491299843897 25 3 2.8498375145286 0.150162485471398 26 3 3.2133161389882 -0.213316138988202 27 4 3.34104666365194 0.658953336348061 28 3 2.77148259513007 0.228517404869935 29 3 2.71386160794784 0.286138392052158 30 2 2.96589246816755 -0.965892468167552 31 2 2.27568231858971 -0.275682318589713 32 4 3.13605301451367 0.863946985486327 33 4 3.35987582166974 0.64012417833026 34 2 3.14911182028229 -1.14911182028229 35 2 2.91105098252544 -0.911050982525436 36 3 3.23904916238401 -0.239049162384009 37 3 3.06906919426765 -0.0690691942676537 38 3 2.51733563716118 0.482664362838824 39 3 2.97066417381433 0.0293358261856662 40 4 3.23904916238401 0.760950837615991 41 3 2.66893090037486 0.331069099625144 42 2 2.41158336337179 -0.411583363371789 43 1 2.20527053377680 -1.20527053377680 44 2 2.72596747881740 -0.725967478817404 45 3 2.65898365857138 0.341016341428616 46 3 3.11113297039237 -0.111132970392371 47 2 3.13686599378818 -1.13686599378818 48 2 2.57234163905101 -0.572341639051014 49 3 2.52391896868487 0.476081031315134 50 3 3.07152816195345 -0.071528161953445 51 3 2.86893468068433 0.131065319315668 52 2 2.63934152127908 -0.639341521279079 53 2 3.17683704778477 -1.17683704778477 54 2 2.54506086466366 -0.545060864663658 55 3 2.83668047134025 0.163319528659751 56 3 2.83586749206574 0.164132507934255 57 2 2.80895524383777 -0.808955243837767 58 3 2.95973752777694 0.0402624722230577 59 1 3.01114998369511 -2.01114998369511 60 3 3.18142817520179 -0.181428175201785 61 1 2.43516085141532 -1.43516085141532 62 3 3.33660176595972 -0.336601765959725 63 2 2.82778440185557 -0.827784401855569 64 2 2.97525530123135 -0.97525530123135 65 3 2.47726406514313 0.522735934856866 66 2 2.89430145852247 -0.894301458522472 67 3 2.85138526552015 0.148614734479849 68 2 2.68599642482081 -0.685996424820811 69 3 2.65955200532901 0.340447994670987 70 1 2.41787944438907 -1.41787944438907 71 2 2.69143996911543 -0.69143996911543 72 2 2.81344585323333 -0.813445853233333 73 2 3.08458696772206 -1.08458696772206 74 2 2.70246485257256 -0.70246485257256 75 3 2.94979028597347 0.0502097140265289 76 2 2.81013446866994 -0.810134468669938 77 2 2.89216929879125 -0.892169298791248 78 2 2.34561127784146 -0.345611277841461 79 2 2.91635457119551 -0.916354571195506 80 1 2.24406236294123 -1.24406236294123 81 2 2.85138526552015 -0.85138526552015 82 3 2.98858211513789 0.0114178848621071 83 4 3.11277895880366 0.887221041196342 84 3 2.07059043203171 0.929409567968291 85 3 3.34624866914350 -0.346248669143496 86 3 2.46430577739597 0.535694222604032 87 3 1.83338201115246 1.16661798884754 88 4 3.49494051155626 0.505059488443742 89 4 3.08704593540785 0.912954064592148 90 3 2.72809963854863 0.271900361451372 91 4 3.21118397925698 0.788816020743022 92 4 3.45496945755967 0.545030542440335 93 4 3.57825508453119 0.421744915468811 94 3 3.11645886952643 -0.116458869526431 95 3 2.74361741200303 0.256382587996965 96 2 2.76321155699028 -0.763211556990277 97 3 3.05777295691382 -0.0577729569138207 98 3 2.6157406576145 0.384259342385504 99 4 3.16794097830009 0.83205902169991 100 3 3.32955167085692 -0.329551670856919 101 4 3.53700428768098 0.462995712319024 102 3 3.47166645584624 -0.471666455846243 103 3 3.71337857423435 -0.713378574234345 104 3 2.55259378532763 0.447406214672374 105 3 2.69781492533891 0.302185074661094 106 4 2.69996644728367 1.30003355271633 107 3 3.37411385227053 -0.374113852270527 108 4 3.04707488141126 0.952925118588741 109 3 2.79755848846248 0.202441511537515 110 3 3.23492479854611 -0.234924798546110 111 2 2.68930780938421 -0.689307809384206 112 3 3.27570883181721 -0.275708831817207 113 3 2.97552330936928 0.0244766906307223 114 4 3.25115503325357 0.748844966746429 115 4 3.47729057837063 0.522709421629372 116 4 2.85010552266653 1.14989447733347 117 4 2.98976133997006 1.01023866002994 118 2 2.72468773596378 -0.724687735963784 119 3 3.01218297880248 -0.0121829788024757 120 3 3.05556593538391 -0.0555659353839127 121 3 3.09634996865501 -0.0963499686550095 122 4 3.18098372208666 0.81901627791334 123 3 2.81391261681245 0.186087383187551 124 4 3.3719816925393 0.628018307460697 125 4 3.09634996865501 0.90365003134499 126 3 2.44546353126488 0.55453646873512 127 4 3.35774366193852 0.642256338061484 128 3 2.98858211513789 0.0114178848621071 129 3 2.61049921451984 0.38950078548016 130 1 1.81713868833171 -0.817138688331712 131 4 3.23232587523577 0.76767412476423 132 4 3.19522175268745 0.804778247312554 133 2 2.56169906313360 -0.561699063133597 134 2 2.73295877410357 -0.732958774103572 135 4 3.43778628795315 0.562213712046848 136 3 2.97552330936928 0.0244766906307223 137 4 3.68648970162742 0.313510298372578 138 2 2.31805354045546 -0.318053540455458 139 5 3.10818783138664 1.89181216861336 140 3 3.5632040746559 -0.563204074655898 141 4 2.76807069254522 1.23192930745478 142 3 3.15183879610601 -0.151838796106009 143 4 3.12336273490444 0.876637265095563 144 2 2.59131075269336 -0.591310752693364 145 3 2.89348847924797 0.106511520752032 146 1 3.13973292523645 -2.13973292523645 147 2 2.80804174654181 -0.808041746541814 148 5 3.31436070535708 1.68563929464292 149 4 3.20990423640336 0.790095763596642 150 4 2.85469665008355 1.14530334991645 151 3 2.78689985056302 0.213100149436978 152 4 3.35443227737512 0.645567722624878 153 2 2.48553510328292 -0.485535103282922 154 4 2.97552330936928 1.02447669063072 155 4 3.51650973351107 0.483490266488933 156 3 2.67121342308345 0.32878657691655 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.219061366264004 0.438122732528007 0.780938633735996 12 0.113594601725804 0.227189203451608 0.886405398274196 13 0.0566016437835751 0.113203287567150 0.943398356216425 14 0.119064967999433 0.238129935998866 0.880935032000567 15 0.085622263545484 0.171244527090968 0.914377736454516 16 0.233827267302907 0.467654534605813 0.766172732697094 17 0.160401121287444 0.320802242574889 0.839598878712556 18 0.103812198999344 0.207624397998687 0.896187801000656 19 0.0845104391564942 0.169020878312988 0.915489560843506 20 0.0937323724112021 0.187464744822404 0.906267627588798 21 0.352331579731186 0.704663159462371 0.647668420268814 22 0.551708856173536 0.896582287652927 0.448291143826464 23 0.5367320243319 0.926535951336201 0.463267975668100 24 0.54587822376117 0.908243552477661 0.454121776238830 25 0.470823027238813 0.941646054477627 0.529176972761187 26 0.427772292710612 0.855544585421223 0.572227707289388 27 0.407448449517653 0.814896899035305 0.592551550482347 28 0.369369568769656 0.738739137539312 0.630630431230344 29 0.317493893541252 0.634987787082503 0.682506106458748 30 0.275073647518494 0.550147295036988 0.724926352481506 31 0.222267217741837 0.444534435483675 0.777732782258163 32 0.233009020603464 0.466018041206927 0.766990979396536 33 0.244253254465605 0.48850650893121 0.755746745534395 34 0.267832729778613 0.535665459557226 0.732167270221387 35 0.339259192303685 0.67851838460737 0.660740807696315 36 0.287080585730714 0.574161171461429 0.712919414269286 37 0.238851185009731 0.477702370019461 0.76114881499027 38 0.215484489935692 0.430968979871384 0.784515510064308 39 0.175675008372211 0.351350016744422 0.82432499162779 40 0.212651204342366 0.425302408684732 0.787348795657634 41 0.184856064464405 0.36971212892881 0.815143935535595 42 0.212815264981890 0.425630529963781 0.78718473501811 43 0.405999414357531 0.811998828715062 0.594000585642469 44 0.386256696482876 0.772513392965752 0.613743303517124 45 0.341238535960547 0.682477071921093 0.658761464039453 46 0.311825140227965 0.62365028045593 0.688174859772035 47 0.415824219781884 0.831648439563768 0.584175780218116 48 0.396060702459234 0.792121404918469 0.603939297540766 49 0.368242104329974 0.736484208659947 0.631757895670026 50 0.328114524661846 0.656229049323693 0.671885475338154 51 0.294903926602249 0.589807853204499 0.705096073397751 52 0.270638791205819 0.541277582411638 0.729361208794181 53 0.324744643790586 0.649489287581173 0.675255356209414 54 0.303650215385106 0.607300430770212 0.696349784614894 55 0.262096897462054 0.524193794924108 0.737903102537946 56 0.226898041491313 0.453796082982627 0.773101958508687 57 0.231136329975702 0.462272659951404 0.768863670024298 58 0.194415959529781 0.388831919059562 0.805584040470219 59 0.290714546131109 0.581429092262219 0.70928545386889 60 0.250787806905219 0.501575613810437 0.749212193094781 61 0.330295542369995 0.66059108473999 0.669704457630005 62 0.304059377718023 0.608118755436047 0.695940622281977 63 0.293913179150870 0.587826358301739 0.70608682084913 64 0.309487252385291 0.618974504770583 0.690512747614709 65 0.283779173144273 0.567558346288546 0.716220826855727 66 0.302796160424538 0.605592320849076 0.697203839575462 67 0.289560855256110 0.579121710512219 0.71043914474389 68 0.269167826132222 0.538335652264444 0.730832173867778 69 0.234258457851073 0.468516915702146 0.765741542148927 70 0.310734785200184 0.621469570400367 0.689265214799816 71 0.315794556963739 0.631589113927477 0.684205443036261 72 0.328361004480882 0.656722008961764 0.671638995519118 73 0.370367332856197 0.740734665712394 0.629632667143803 74 0.363855042326008 0.727710084652017 0.636144957673991 75 0.336270409055539 0.672540818111079 0.66372959094446 76 0.344902677005711 0.689805354011423 0.655097322994289 77 0.37801923130177 0.75603846260354 0.62198076869823 78 0.356113064730377 0.712226129460754 0.643886935269623 79 0.453871400312344 0.907742800624689 0.546128599687656 80 0.61328730489843 0.77342539020314 0.38671269510157 81 0.659739745241175 0.68052050951765 0.340260254758825 82 0.618371082495634 0.763257835008732 0.381628917504366 83 0.71429815487167 0.571403690256658 0.285701845128329 84 0.733430008712301 0.533139982575398 0.266569991287699 85 0.722810125360003 0.554379749279995 0.277189874639998 86 0.703054199613637 0.593891600772727 0.296945800386363 87 0.715029877826584 0.569940244346832 0.284970122173416 88 0.708596583112666 0.582806833774668 0.291403416887334 89 0.765806629737936 0.468386740524128 0.234193370262064 90 0.730911691265942 0.538176617468116 0.269088308734058 91 0.744496413096532 0.511007173806935 0.255503586903468 92 0.737179914049654 0.525640171900692 0.262820085950346 93 0.726822472591432 0.546355054817136 0.273177527408568 94 0.690392388714387 0.619215222571226 0.309607611285613 95 0.653146767680221 0.693706464639559 0.346853232319779 96 0.721356267148736 0.557287465702528 0.278643732851264 97 0.690137614971164 0.619724770057672 0.309862385028836 98 0.657452674619465 0.68509465076107 0.342547325380535 99 0.684654940049855 0.63069011990029 0.315345059950145 100 0.646700244019385 0.70659951196123 0.353299755980615 101 0.626550436464428 0.746899127071143 0.373449563535572 102 0.590583410021479 0.818833179957042 0.409416589978521 103 0.770481622943952 0.459036754112097 0.229518377056048 104 0.755679110373303 0.488641779253393 0.244320889626696 105 0.781802002669819 0.436395994660362 0.218197997330181 106 0.792814420902784 0.414371158194432 0.207185579097216 107 0.759391568470667 0.481216863058667 0.240608431529333 108 0.744747668129819 0.510504663740362 0.255252331870181 109 0.70972270101648 0.580554597967041 0.290277298983520 110 0.671147580601953 0.657704838796094 0.328852419398047 111 0.811461712274039 0.377076575451922 0.188538287725961 112 0.800051260475284 0.399897479049432 0.199948739524716 113 0.773851572332001 0.452296855335998 0.226148427667999 114 0.762394869877905 0.47521026024419 0.237605130122095 115 0.76497352440381 0.470052951192381 0.235026475596190 116 0.784134835274588 0.431730329450824 0.215865164725412 117 0.794238979117772 0.411522041764457 0.205761020882228 118 0.889091998228402 0.221816003543197 0.110908001771598 119 0.874030415042673 0.251939169914654 0.125969584957327 120 0.839585731921186 0.320828536157629 0.160414268078814 121 0.799892130792768 0.400215738414464 0.200107869207232 122 0.878153352288745 0.24369329542251 0.121846647711255 123 0.872008832359527 0.255982335280946 0.127991167640473 124 0.842824699359343 0.314350601281315 0.157175300640657 125 0.90149025329758 0.19701949340484 0.09850974670242 126 0.875263726072645 0.249472547854710 0.124736273927355 127 0.843888324675184 0.312223350649632 0.156111675324816 128 0.819053852760545 0.36189229447891 0.180946147239455 129 0.771706618154377 0.456586763691247 0.228293381845623 130 0.744148151195922 0.511703697608157 0.255851848804078 131 0.698913733191317 0.602172533617366 0.301086266808683 132 0.937353676217425 0.125292647565149 0.0626463237825747 133 0.921878131053439 0.156243737893123 0.0781218689465615 134 0.888705137457152 0.222589725085696 0.111294862542848 135 0.899308135140525 0.201383729718950 0.100691864859475 136 0.875605681509956 0.248788636980087 0.124394318490044 137 0.826277523359027 0.347444953281947 0.173722476640973 138 0.783066374073857 0.433867251852285 0.216933625926142 139 0.761065976846048 0.477868046307903 0.238934023153952 140 0.68376168132573 0.632476637348541 0.316238318674271 141 0.769028448020252 0.461943103959496 0.230971551979748 142 0.719872519883976 0.560254960232047 0.280127480116024 143 0.618836037620859 0.762327924758282 0.381163962379141 144 0.783760743265517 0.432478513468966 0.216239256734483 145 0.77481947716183 0.45036104567634 0.22518052283817 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 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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