ws10 MP

*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 18:00:14 +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/t12923495139c3ctekecxrc6rp.htm/, Retrieved Tue, 14 Dec 2010 18:58:44 +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/t12923495139c3ctekecxrc6rp.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 24 14 11 12 24 26 2 25 11 7 8 25 23 2 17 6 17 8 30 25 1 18 12 10 8 19 23 2 18 8 12 9 22 19 2 16 10 12 7 22 29 2 20 10 11 4 25 25 2 16 11 11 11 23 21 2 18 16 12 7 17 22 2 17 11 13 7 21 25 1 23 13 14 12 19 24 2 30 12 16 10 19 18 1 23 8 11 10 15 22 2 18 12 10 8 16 15 2 15 11 11 8 23 22 1 12 4 15 4 27 28 1 21 9 9 9 22 20 2 15 8 11 8 14 12 1 20 8 17 7 22 24 2 31 14 17 11 23 20 1 27 15 11 9 23 21 2 34 16 18 11 21 20 2 21 9 14 13 19 21 2 31 14 10 8 18 23 1 19 11 11 8 20 28 2 16 8 15 9 23 24 1 20 9 15 6 25 24 2 21 9 13 9 19 24 2 22 9 16 9 24 23 1 17 9 13 6 22 23 2 24 10 9 6 25 29 1 25 16 18 16 26 24 2 26 11 18 5 29 18 2 25 8 12 7 32 25 1 17 9 17 9 25 21 1 32 16 9 6 29 26 1 33 11 9 6 28 22 1 13 16 12 5 17 22 2 32 12 18 12 28 22 1 25 12 12 7 29 23 1 29 14 18 10 26 30 2 22 9 14 9 25 23 1 18 10 15 8 14 17 1 17 9 16 5 25 23 2 20 10 10 8 26 23 2 15 12 11 8 20 25 2 20 14 14 10 18 24 2 33 14 9 6 32 24 2 29 10 12 8 25 23 1 23 14 17 7 25 21 2 26 16 5 4 23 24 1 18 9 12 8 21 2 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 29 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation PC[t] = + 2.18714234745473 + 0.271235107786439G[t] + 0.0434255996311816CM[t] + 0.103582456740996DA[t] + 0.424577505469688PE[t] + 0.00930133630698559PS[t] -0.0953227133970643O[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) 2.18714234745473 1.557532 1.4042 0.162289 0.081144 G 0.271235107786439 0.354958 0.7641 0.445973 0.222986 CM 0.0434255996311816 0.038583 1.1255 0.262141 0.13107 DA 0.103582456740996 0.069828 1.4834 0.140041 0.070021 PE 0.424577505469688 0.054873 7.7375 0 0 PS 0.00930133630698559 0.050874 0.1828 0.855175 0.427587 O -0.0953227133970643 0.048963 -1.9468 0.053398 0.026699 Multiple Linear Regression - Regression Statistics Multiple R 0.629003287475925 R-squared 0.395645135655521 Adjusted R-squared 0.371789022589291 F-TEST (value) 16.5846437161464 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.16573417585641e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.14560706281333 Sum Squared Residuals 699.751709535158 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 7.63717543176037 4.36282456823963 2 8 5.96681311578807 2.03318688421193 3 8 9.20313234447133 -1.20313234447133 4 8 6.71310576589152 1.28689423410848 5 9 7.82836092016256 1.17163907983744 6 7 6.99544750041155 0.00455249958845472 7 4 7.1537672559758 -3.15376725597579 8 11 7.44633549516635 3.55366450483365 9 7 8.3245457523644 -1.32454575236441 10 7 7.93902257953468 -0.939022579534683 11 12 8.63680352927011 3.36319647072989 12 10 10.5295266690556 -0.529526669055582 13 10 6.99859881072225 3.00140118927775 14 8 7.71901857193351 0.280981428066488 15 8 7.30758718213811 0.692412817861892 16 4 7.34457716499546 -3.34457716499546 17 9 6.42192983820453 2.57807016179547 18 8 7.8663549191229 0.133645080877108 19 7 9.2902509720016 -2.29025097200160 20 11 11.0512546060723 -0.0512546060722585 21 9 8.0671118102869 0.932888189713102 22 11 11.7946711513035 -0.794671151303512 23 13 8.6928257510214 4.30717424897861 24 8 7.74673724605832 0.253262753941680 25 8 6.61021418357305 1.38978581642695 26 9 8.54793000663092 0.452069993369076 27 6 8.57258242672418 -2.57258242672418 28 9 7.98228010536051 1.01771989463949 29 9 9.44126761633275 -0.441267616332747 30 6 7.66056932136737 -1.66056932136737 31 6 6.09702378997289 -0.0970237899728896 32 16 10.7978214747831 5.20217852521689 33 5 11.1944101877991 -6.19441018779909 34 7 7.6534172002683 -0.6534172002683 35 9 9.5774287789612 -0.577428778961205 36 6 7.11786170510102 -1.11786170510102 37 6 7.01536453830849 -1.01536453830849 38 5 7.83618264642206 -2.83618264642206 39 12 11.1679540524319 0.832045947568065 40 7 7.95925333731902 -0.95925333731902 41 10 10.1924226794435 -0.192422679443459 42 9 8.60141394170036 0.398586058299643 43 8 9.15425797860542 -1.15425797860542 44 5 8.96220584669739 -3.96220584669739 45 8 6.92913651360722 1.07086348639278 46 8 7.09729748976695 0.902702510233046 47 10 8.87204295859701 1.12795704140299 48 6 7.44390693475173 -1.44390693475173 49 8 8.15982058492025 -0.159820584920248 50 7 10.3558946604533 -3.35589466045328 51 4 5.56507060217383 -1.56507060217383 52 8 7.17479336582481 0.82520663417519 53 8 6.97463483193293 1.02536516806707 54 4 4.99061056248646 -0.990610562486462 55 20 13.0653998513830 6.93460014861699 56 8 7.75905353956032 0.24094646043968 57 8 7.4838518702207 0.516148129779295 58 6 8.36672486389353 -2.36672486389353 59 4 4.21219780992602 -0.212197809926016 60 8 9.0158706740298 -1.01587067402980 61 9 7.06394906171752 1.93605093828248 62 6 7.86113413585 -1.86113413585000 63 7 8.2959696097375 -1.29596960973749 64 9 6.18995228761744 2.81004771238256 65 5 6.8543486686162 -1.85434866861620 66 5 6.1069844415282 -1.10698444152820 67 8 7.49170264291291 0.508297357087091 68 8 7.98457262895879 0.0154273710412133 69 6 6.50644750694419 -0.506447506944187 70 8 6.98611460493036 1.01388539506964 71 7 7.68681099588277 -0.686810995882772 72 7 6.31104427023043 0.688955729769571 73 9 9.10603077664227 -0.106030776642275 74 11 10.9353601210429 0.0646398789570511 75 6 8.7378133111142 -2.73781331111420 76 8 8.04340573239236 -0.0434057323923593 77 6 8.07606755123295 -2.07606755123295 78 9 8.74550898997414 0.254491010025857 79 8 6.22180043036825 1.77819956963175 80 6 8.46864255311038 -2.46864255311038 81 10 8.08564835819214 1.91435164180786 82 8 6.21161771811006 1.78838228188994 83 8 8.48367290237763 -0.483672902377627 84 10 8.89357747545287 1.10642252454713 85 5 6.17818792078822 -1.17818792078822 86 7 9.47247887155855 -2.47247887155855 87 5 7.03058179752459 -2.03058179752459 88 8 6.10192054764227 1.89807945235773 89 14 10.1357953066608 3.86420469333915 90 7 7.84179932494668 -0.841799324946676 91 8 9.12329522007711 -1.12329522007712 92 6 4.96738115510509 1.03261884489491 93 5 6.35072703959093 -1.35072703959094 94 6 9.38763803518128 -3.38763803518128 95 10 6.77890842758155 3.22109157241845 96 12 11.8470105473675 0.152989452632491 97 9 9.4894707635459 -0.489470763545893 98 12 11.1714730695276 0.828526930472448 99 7 7.47628309672623 -0.476283096726228 100 8 8.32536528462458 -0.325365284624586 101 10 9.34504225772238 0.65495774227762 102 6 7.1047171210265 -1.10471712102649 103 10 11.2582025820310 -1.25820258203096 104 10 8.535588852287 1.46441114771299 105 10 7.27057634671014 2.72942365328986 106 5 8.39280641682401 -3.39280641682401 107 7 7.26292278968291 -0.262922789682914 108 10 8.6992262170412 1.30077378295880 109 11 9.5656868398553 1.43431316014469 110 6 8.15067528003433 -2.15067528003433 111 7 7.53682223155077 -0.536822231550766 112 12 9.44710802613986 2.55289197386014 113 11 6.60818516186395 4.39181483813605 114 11 10.6165503846565 0.383449615343534 115 11 5.21587408868182 5.78412591131818 116 5 7.40893721529114 -2.40893721529114 117 8 10.2920267095665 -2.29202670956647 118 6 6.80334750173133 -0.803347501731331 119 9 9.55095380745055 -0.55095380745055 120 4 7.01587372138867 -3.01587372138867 121 4 6.24513956401685 -2.24513956401685 122 7 8.20486735051709 -1.20486735051709 123 11 9.5006170789936 1.49938292100640 124 6 4.56008013545453 1.43991986454547 125 7 6.8166256895036 0.183374310496400 126 8 9.9582548271011 -1.95825482710111 127 4 6.10108043555788 -2.10108043555788 128 8 7.15272566301274 0.847274336987257 129 9 8.20812051449749 0.791879485502509 130 8 8.14193121445213 -0.141931214452128 131 11 8.58007847260456 2.41992152739544 132 8 7.32740362521871 0.672596374781288 133 5 6.80598261433022 -1.80598261433022 134 4 5.7780458978885 -1.77804589788849 135 8 7.45746865332149 0.542531346678513 136 10 11.8415352497112 -1.84153524971125 137 6 7.95181137376308 -1.95181137376308 138 9 8.9586680888852 0.0413319111148046 139 9 7.29902041723907 1.70097958276093 140 13 8.90126645598052 4.09873354401948 141 9 7.91191013527952 1.08808986472048 142 10 9.8166716730675 0.183328326932507 143 20 14.3827073005120 5.61729269948796 144 5 6.07491248560233 -1.07491248560233 145 11 10.0515356184389 0.94846438156112 146 6 8.28001777911344 -2.28001777911344 147 9 10.6472677083783 -1.64726770837831 148 7 7.21835791320574 -0.218357913205743 149 9 8.03417731455331 0.965822685446687 150 10 8.46605783582919 1.53394216417081 151 9 7.13828936225099 1.86171063774901 152 8 10.3315756979097 -2.33157569790975 153 7 11.6694649446282 -4.66946494462819 154 6 9.59415577122615 -3.59415577122615 155 13 11.5458594926223 1.45414050737768 156 6 8.09454584702697 -2.09454584702698 157 8 8.00152325707931 -0.00152325707931311 158 10 9.50773997861014 0.492260021389862 159 16 12.0517665126517 3.94823348734829 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.94250431304707 0.114991373905860 0.0574956869529299 11 0.919793803402653 0.160412393194694 0.0802061965973471 12 0.870468796957183 0.259062406085634 0.129531203042817 13 0.841412234225302 0.317175531549396 0.158587765774698 14 0.766337449290304 0.467325101419392 0.233662550709696 15 0.679101653624742 0.641796692750515 0.320898346375258 16 0.736923128163878 0.526153743672244 0.263076871836122 17 0.665971797196864 0.668056405606272 0.334028202803136 18 0.582330828795302 0.835338342409397 0.417669171204698 19 0.550038127918413 0.899923744163174 0.449961872081587 20 0.470866708282323 0.941733416564646 0.529133291717677 21 0.455708802781009 0.911417605562019 0.54429119721899 22 0.386166237965586 0.772332475931172 0.613833762034414 23 0.610268526327807 0.779462947344386 0.389731473672193 24 0.627403777157401 0.745192445685197 0.372596222842598 25 0.562291485262484 0.875417029475032 0.437708514737516 26 0.511345033630784 0.977309932738432 0.488654966369216 27 0.513507748190594 0.972984503618812 0.486492251809406 28 0.448709328195629 0.897418656391258 0.551290671804371 29 0.384107980469323 0.768215960938646 0.615892019530677 30 0.357004414983787 0.714008829967574 0.642995585016213 31 0.330228078213229 0.660456156426459 0.669771921786771 32 0.645461557161976 0.709076885676047 0.354538442838024 33 0.863988049381961 0.272023901236078 0.136011950618039 34 0.834504033632203 0.330991932735594 0.165495966367797 35 0.798676231383104 0.402647537233792 0.201323768616896 36 0.802440190768912 0.395119618462176 0.197559809231088 37 0.765940025101546 0.468119949796909 0.234059974898454 38 0.857247537950657 0.285504924098686 0.142752462049343 39 0.840136538984043 0.319726922031913 0.159863461015957 40 0.807019124736379 0.385961750527242 0.192980875263621 41 0.767351918572328 0.465296162855344 0.232648081427672 42 0.727386158443687 0.545227683112626 0.272613841556313 43 0.699844443642941 0.600311112714117 0.300155556357059 44 0.75820253044595 0.48359493910810 0.24179746955405 45 0.724380670391426 0.551238659217148 0.275619329608574 46 0.680847103105915 0.638305793788169 0.319152896894085 47 0.638836900674043 0.722326198651915 0.361163099325957 48 0.616030480919364 0.767939038161271 0.383969519080636 49 0.567966181448081 0.864067637103838 0.432033818551919 50 0.598311732470669 0.803376535058662 0.401688267529331 51 0.62443121087191 0.75113757825618 0.37556878912809 52 0.580632285757079 0.838735428485843 0.419367714242921 53 0.535967246965057 0.928065506069886 0.464032753034943 54 0.510686459369264 0.978627081261472 0.489313540630736 55 0.921643430722808 0.156713138554385 0.0783565692771924 56 0.90281122137944 0.194377557241119 0.0971887786205594 57 0.881130676019749 0.237738647960503 0.118869323980251 58 0.883422535611673 0.233154928776655 0.116577464388327 59 0.858212434552163 0.283575130895675 0.141787565447837 60 0.83350772873967 0.332984542520661 0.166492271260330 61 0.829215694914198 0.341568610171605 0.170784305085802 62 0.821697147727495 0.356605704545010 0.178302852272505 63 0.801059662984535 0.397880674030931 0.198940337015465 64 0.833321623733414 0.333356752533172 0.166678376266586 65 0.824119442114691 0.351761115770619 0.175880557885309 66 0.801507035971957 0.396985928056086 0.198492964028043 67 0.775048145945518 0.449903708108964 0.224951854054482 68 0.742135435218091 0.515729129563818 0.257864564781909 69 0.707961008176995 0.58407798364601 0.292038991823005 70 0.675576139357316 0.648847721285367 0.324423860642684 71 0.647033336035566 0.705933327928867 0.352966663964434 72 0.606321606832619 0.787356786334762 0.393678393167381 73 0.561712453943831 0.876575092112338 0.438287546056169 74 0.515690249081334 0.968619501837331 0.484309750918666 75 0.547998260602547 0.904003478794906 0.452001739397453 76 0.502024628587545 0.99595074282491 0.497975371412455 77 0.510424297238607 0.979151405522786 0.489575702761393 78 0.463680838318078 0.927361676636155 0.536319161681922 79 0.442537018466688 0.885074036933377 0.557462981533312 80 0.454187710396245 0.90837542079249 0.545812289603755 81 0.439152535796628 0.878305071593257 0.560847464203372 82 0.426663764039337 0.853327528078674 0.573336235960663 83 0.384294961926499 0.768589923852997 0.615705038073501 84 0.351551683004131 0.703103366008261 0.648448316995869 85 0.325638389520497 0.651276779040994 0.674361610479503 86 0.343304233596703 0.686608467193407 0.656695766403297 87 0.339798956176609 0.679597912353217 0.660201043823391 88 0.323061186534124 0.646122373068248 0.676938813465876 89 0.421567271311846 0.843134542623693 0.578432728688154 90 0.382645918075544 0.765291836151089 0.617354081924456 91 0.352420963680622 0.704841927361243 0.647579036319379 92 0.317415991749281 0.634831983498563 0.682584008250719 93 0.292231833017599 0.584463666035199 0.7077681669824 94 0.353649385739754 0.707298771479507 0.646350614260246 95 0.407580264280146 0.815160528560292 0.592419735719854 96 0.361909602360502 0.723819204721004 0.638090397639498 97 0.321402914571944 0.642805829143889 0.678597085428056 98 0.287837853135208 0.575675706270416 0.712162146864792 99 0.249132393673605 0.498264787347211 0.750867606326395 100 0.212467248374165 0.424934496748331 0.787532751625835 101 0.18193783071957 0.36387566143914 0.81806216928043 102 0.159104568687959 0.318209137375917 0.840895431312041 103 0.142926916208301 0.285853832416602 0.857073083791699 104 0.127164569405624 0.254329138811248 0.872835430594376 105 0.153254335468511 0.306508670937023 0.846745664531488 106 0.187316966969162 0.374633933938324 0.812683033030838 107 0.155449611890652 0.310899223781304 0.844550388109348 108 0.139328372531308 0.278656745062616 0.860671627468692 109 0.125569187098132 0.251138374196264 0.874430812901868 110 0.124354425479007 0.248708850958014 0.875645574520993 111 0.102231379877336 0.204462759754673 0.897768620122664 112 0.149324132505508 0.298648265011017 0.850675867494492 113 0.290647395841172 0.581294791682343 0.709352604158828 114 0.257657935502595 0.51531587100519 0.742342064497405 115 0.53958595322856 0.92082809354288 0.46041404677144 116 0.53944288657039 0.92111422685922 0.46055711342961 117 0.555769789412675 0.88846042117465 0.444230210587325 118 0.507547130473245 0.98490573905351 0.492452869526755 119 0.453032806352503 0.906065612705006 0.546967193647497 120 0.528326157762409 0.943347684475182 0.471673842237591 121 0.502246978997533 0.995506042004934 0.497753021002467 122 0.520168984184323 0.959662031631354 0.479831015815677 123 0.476507214368856 0.953014428737713 0.523492785631144 124 0.482298436150575 0.96459687230115 0.517701563849425 125 0.424734046375015 0.84946809275003 0.575265953624985 126 0.423568958912516 0.847137917825031 0.576431041087484 127 0.393731357914709 0.787462715829417 0.606268642085291 128 0.365007535613997 0.730015071227994 0.634992464386003 129 0.329367117619032 0.658734235238063 0.670632882380968 130 0.297122637602709 0.594245275205418 0.702877362397291 131 0.303402992492925 0.606805984985849 0.696597007507075 132 0.253215034778049 0.506430069556098 0.746784965221951 133 0.211895819957315 0.42379163991463 0.788104180042685 134 0.175925925497721 0.351851850995442 0.824074074502279 135 0.144652959979244 0.289305919958487 0.855347040020756 136 0.146106006551988 0.292212013103976 0.853893993448012 137 0.158309441393098 0.316618882786196 0.841690558606902 138 0.165587829998991 0.331175659997981 0.83441217000101 139 0.179119239092396 0.358238478184793 0.820880760907604 140 0.220368422606797 0.440736845213595 0.779631577393203 141 0.171419997725984 0.342839995451967 0.828580002274016 142 0.143497579791546 0.286995159583092 0.856502420208454 143 0.202894708259673 0.405789416519346 0.797105291740327 144 0.155702291166403 0.311404582332807 0.844297708833597 145 0.109847889127325 0.219695778254651 0.890152110872675 146 0.0724177103321857 0.144835420664371 0.927582289667814 147 0.0433085221631197 0.0866170443262395 0.95669147783688 148 0.0220190729102943 0.0440381458205885 0.977980927089706 149 0.0100333620186115 0.0200667240372230 0.989966637981389 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 2 0.0142857142857143 OK 10% type I error level 3 0.0214285714285714 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/10ul6p1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/10ul6p1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/1o2rd1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/1o2rd1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/2o2rd1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/2o2rd1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/3gu9y1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/3gu9y1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/4gu9y1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/4gu9y1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/5gu9y1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/5gu9y1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/6938j1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/6938j1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/7938j1292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/7938j1292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/8ju741292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/8ju741292349582.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/9ju741292349582.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923495139c3ctekecxrc6rp/9ju741292349582.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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