Ws 10 - Multiple Regression

*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 22:21:38 +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/t1292365452uxmsdu44lkp2av4.htm/, Retrieved Tue, 14 Dec 2010 23:24:12 +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/t1292365452uxmsdu44lkp2av4.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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PC[t] = + 2.18714234745475 + 0.271235107786437G[t] + 0.0434255996311821CM[t] + 0.103582456740995DA[t] + 0.424577505469688PE[t] + 0.00930133630698519PS[t] -0.0953227133970645O[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) 2.18714234745475 1.557532 1.4042 0.162289 0.081144 G 0.271235107786437 0.354958 0.7641 0.445973 0.222986 CM 0.0434255996311821 0.038583 1.1255 0.262141 0.13107 DA 0.103582456740995 0.069828 1.4834 0.140041 0.070021 PE 0.424577505469688 0.054873 7.7375 0 0 PS 0.00930133630698519 0.050874 0.1828 0.855175 0.427587 O -0.0953227133970645 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 699.751709535157 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 7.63717543176045 4.36282456823955 2 8 5.96681311578808 2.03318688421192 3 8 9.20313234447132 -1.20313234447132 4 8 6.71310576589152 1.28689423410849 5 9 7.82836092016256 1.17163907983744 6 7 6.99544750041154 0.00455249958845706 7 4 7.1537672559758 -3.15376725597579 8 11 7.44633549516635 3.55366450483365 9 7 8.3245457523644 -1.32454575236440 10 7 7.93902257953468 -0.93902257953468 11 12 8.6368035292701 3.36319647072989 12 10 10.5295266690556 -0.529526669055586 13 10 6.99859881072226 3.00140118927774 14 8 7.71901857193351 0.280981428066488 15 8 7.3075871821381 0.692412817861896 16 4 7.34457716499546 -3.34457716499546 17 9 6.42192983820454 2.57807016179546 18 8 7.8663549191229 0.133645080877104 19 7 9.2902509720016 -2.29025097200160 20 11 11.0512546060723 -0.0512546060722577 21 9 8.0671118102869 0.932888189713104 22 11 11.7946711513035 -0.794671151303512 23 13 8.6928257510214 4.30717424897861 24 8 7.74673724605832 0.253262753941677 25 8 6.61021418357305 1.38978581642695 26 9 8.54793000663092 0.452069993369077 27 6 8.57258242672418 -2.57258242672418 28 9 7.98228010536051 1.01771989463949 29 9 9.44126761633275 -0.441267616332748 30 6 7.66056932136737 -1.66056932136737 31 6 6.09702378997289 -0.0970237899728906 32 16 10.7978214747831 5.2021785252169 33 5 11.1944101877991 -6.19441018779909 34 7 7.6534172002683 -0.6534172002683 35 9 9.5774287789612 -0.577428778961202 36 6 7.11786170510101 -1.11786170510101 37 6 7.0153645383085 -1.01536453830849 38 5 7.83618264642205 -2.83618264642205 39 12 11.1679540524319 0.832045947568065 40 7 7.95925333731902 -0.959253337319017 41 10 10.1924226794435 -0.192422679443455 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 0.90270251023305 47 10 8.872042958597 1.12795704140299 48 6 7.44390693475173 -1.44390693475173 49 8 8.15982058492025 -0.159820584920251 50 7 10.3558946604533 -3.35589466045327 51 4 5.56507060217383 -1.56507060217383 52 8 7.17479336582481 0.825206634175189 53 8 6.97463483193293 1.02536516806707 54 4 4.99061056248646 -0.990610562486465 55 20 13.0653998513830 6.93460014861699 56 8 7.75905353956032 0.240946460439682 57 8 7.4838518702207 0.516148129779296 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 8.29596960973749 -1.29596960973749 64 9 6.18995228761743 2.81004771238257 65 5 6.85434866861619 -1.85434866861619 66 5 6.1069844415282 -1.10698444152821 67 8 7.49170264291292 0.508297357087083 68 8 7.98457262895879 0.0154273710412143 69 6 6.50644750694418 -0.506447506944179 70 8 6.98611460493035 1.01388539506965 71 7 7.68681099588278 -0.686810995882781 72 7 6.31104427023043 0.688955729769569 73 9 9.10603077664228 -0.106030776642279 74 11 10.9353601210429 0.0646398789570543 75 6 8.7378133111142 -2.73781331111421 76 8 8.04340573239236 -0.0434057323923618 77 6 8.07606755123294 -2.07606755123294 78 9 8.74550898997414 0.254491010025860 79 8 6.22180043036825 1.77819956963175 80 6 8.46864255311038 -2.46864255311038 81 10 8.08564835819213 1.91435164180787 82 8 6.21161771811007 1.78838228188993 83 8 8.48367290237763 -0.483672902377626 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 6.10192054764226 1.89807945235774 89 14 10.1357953066608 3.86420469333916 90 7 7.84179932494668 -0.841799324946678 91 8 9.12329522007711 -1.12329522007711 92 6 4.96738115510509 1.03261884489491 93 5 6.35072703959093 -1.35072703959093 94 6 9.38763803518128 -3.38763803518128 95 10 6.77890842758155 3.22109157241845 96 12 11.8470105473675 0.152989452632491 97 9 9.4894707635459 -0.489470763545892 98 12 11.1714730695276 0.828526930472448 99 7 7.47628309672623 -0.476283096726231 100 8 8.32536528462459 -0.325365284624589 101 10 9.34504225772238 0.65495774227762 102 6 7.1047171210265 -1.10471712102650 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 7.26292278968292 -0.262922789682919 108 10 8.6992262170412 1.3007737829588 109 11 9.5656868398553 1.43431316014470 110 6 8.15067528003432 -2.15067528003432 111 7 7.53682223155077 -0.536822231550769 112 12 9.44710802613987 2.55289197386013 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 -0.80334750173133 119 9 9.55095380745055 -0.550953807450546 120 4 7.01587372138868 -3.01587372138868 121 4 6.24513956401686 -2.24513956401686 122 7 8.20486735051709 -1.20486735051709 123 11 9.50061707899359 1.49938292100641 124 6 4.56008013545453 1.43991986454547 125 7 6.81662568950359 0.18337431049641 126 8 9.9582548271011 -1.95825482710111 127 4 6.10108043555788 -2.10108043555788 128 8 7.15272566301274 0.847274336987259 129 9 8.20812051449749 0.79187948550251 130 8 8.14193121445213 -0.141931214452128 131 11 8.58007847260456 2.41992152739544 132 8 7.32740362521871 0.672596374781286 133 5 6.80598261433022 -1.80598261433022 134 4 5.7780458978885 -1.77804589788850 135 8 7.45746865332149 0.542531346678509 136 10 11.8415352497112 -1.84153524971124 137 6 7.95181137376308 -1.95181137376308 138 9 8.9586680888852 0.0413319111148067 139 9 7.29902041723907 1.70097958276093 140 13 8.90126645598052 4.09873354401948 141 9 7.91191013527952 1.08808986472048 142 10 9.8166716730675 0.183328326932508 143 20 14.3827073005120 5.61729269948797 144 5 6.07491248560233 -1.07491248560233 145 11 10.0515356184389 0.948464381561124 146 6 8.28001777911344 -2.28001777911344 147 9 10.6472677083783 -1.64726770837832 148 7 7.21835791320574 -0.218357913205745 149 9 8.03417731455332 0.965822685446681 150 10 8.4660578358292 1.53394216417081 151 9 7.13828936225099 1.86171063774901 152 8 10.3315756979097 -2.33157569790974 153 7 11.6694649446282 -4.66946494462819 154 6 9.59415577122616 -3.59415577122616 155 13 11.5458594926223 1.45414050737768 156 6 8.09454584702698 -2.09454584702698 157 8 8.00152325707931 -0.00152325707931182 158 10 9.50773997861013 0.492260021389866 159 16 12.0517665126517 3.94823348734829 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.94250431304707 0.114991373905859 0.0574956869529295 11 0.919793803402653 0.160412393194695 0.0802061965973474 12 0.870468796957182 0.259062406085635 0.129531203042818 13 0.841412234225302 0.317175531549396 0.158587765774698 14 0.766337449290304 0.467325101419393 0.233662550709696 15 0.679101653624742 0.641796692750517 0.320898346375258 16 0.736923128163878 0.526153743672243 0.263076871836122 17 0.665971797196865 0.66805640560627 0.334028202803135 18 0.582330828795302 0.835338342409396 0.417669171204698 19 0.550038127918413 0.899923744163173 0.449961872081587 20 0.47086670828232 0.94173341656464 0.52913329171768 21 0.455708802781006 0.911417605562012 0.544291197218994 22 0.386166237965586 0.772332475931172 0.613833762034414 23 0.610268526327807 0.779462947344387 0.389731473672193 24 0.627403777157403 0.745192445685194 0.372596222842597 25 0.562291485262485 0.87541702947503 0.437708514737515 26 0.511345033630785 0.977309932738431 0.488654966369216 27 0.513507748190595 0.97298450361881 0.486492251809405 28 0.448709328195628 0.897418656391256 0.551290671804372 29 0.384107980469322 0.768215960938645 0.615892019530678 30 0.357004414983788 0.714008829967577 0.642995585016212 31 0.330228078213231 0.660456156426462 0.669771921786769 32 0.645461557161976 0.709076885676049 0.354538442838024 33 0.863988049381961 0.272023901236078 0.136011950618039 34 0.834504033632202 0.330991932735595 0.165495966367798 35 0.798676231383103 0.402647537233794 0.201323768616897 36 0.802440190768912 0.395119618462176 0.197559809231088 37 0.765940025101545 0.468119949796910 0.234059974898455 38 0.857247537950656 0.285504924098688 0.142752462049344 39 0.840136538984043 0.319726922031915 0.159863461015957 40 0.807019124736379 0.385961750527242 0.192980875263621 41 0.767351918572327 0.465296162855346 0.232648081427673 42 0.727386158443687 0.545227683112626 0.272613841556313 43 0.69984444364294 0.60031111271412 0.30015555635706 44 0.758202530445951 0.483594939108098 0.241797469554049 45 0.724380670391428 0.551238659217145 0.275619329608572 46 0.680847103105917 0.638305793788166 0.319152896894083 47 0.638836900674042 0.722326198651916 0.361163099325958 48 0.616030480919363 0.767939038161275 0.383969519080637 49 0.567966181448081 0.864067637103838 0.432033818551919 50 0.598311732470671 0.803376535058659 0.401688267529329 51 0.624431210871907 0.751137578256185 0.375568789128093 52 0.580632285757079 0.838735428485843 0.419367714242921 53 0.535967246965058 0.928065506069884 0.464032753034942 54 0.510686459369264 0.978627081261471 0.489313540630736 55 0.921643430722807 0.156713138554386 0.0783565692771929 56 0.90281122137944 0.194377557241120 0.0971887786205599 57 0.88113067601975 0.237738647960501 0.118869323980251 58 0.883422535611672 0.233154928776655 0.116577464388327 59 0.858212434552163 0.283575130895673 0.141787565447837 60 0.833507728739669 0.332984542520663 0.166492271260331 61 0.829215694914195 0.34156861017161 0.170784305085805 62 0.821697147727493 0.356605704545014 0.178302852272507 63 0.801059662984535 0.39788067403093 0.198940337015465 64 0.833321623733413 0.333356752533173 0.166678376266587 65 0.824119442114691 0.351761115770618 0.175880557885309 66 0.801507035971956 0.396985928056089 0.198492964028044 67 0.775048145945518 0.449903708108964 0.224951854054482 68 0.74213543521809 0.51572912956382 0.25786456478191 69 0.707961008176996 0.584077983646008 0.292038991823004 70 0.675576139357315 0.64884772128537 0.324423860642685 71 0.647033336035569 0.705933327928863 0.352966663964431 72 0.606321606832618 0.787356786334763 0.393678393167382 73 0.561712453943829 0.876575092112342 0.438287546056171 74 0.515690249081336 0.968619501837329 0.484309750918664 75 0.547998260602549 0.904003478794902 0.452001739397451 76 0.502024628587543 0.995950742824913 0.497975371412457 77 0.510424297238602 0.979151405522797 0.489575702761398 78 0.463680838318077 0.927361676636154 0.536319161681923 79 0.442537018466689 0.885074036933378 0.557462981533311 80 0.454187710396243 0.908375420792486 0.545812289603757 81 0.439152535796631 0.878305071593263 0.560847464203369 82 0.426663764039338 0.853327528078677 0.573336235960662 83 0.384294961926496 0.768589923852992 0.615705038073504 84 0.351551683004133 0.703103366008267 0.648448316995867 85 0.325638389520498 0.651276779040996 0.674361610479502 86 0.343304233596702 0.686608467193405 0.656695766403298 87 0.339798956176606 0.679597912353212 0.660201043823394 88 0.323061186534121 0.646122373068241 0.67693881346588 89 0.42156727131185 0.8431345426237 0.57843272868815 90 0.382645918075545 0.76529183615109 0.617354081924455 91 0.352420963680625 0.704841927361251 0.647579036319375 92 0.317415991749283 0.634831983498566 0.682584008250717 93 0.292231833017604 0.584463666035209 0.707768166982396 94 0.353649385739753 0.707298771479506 0.646350614260247 95 0.407580264280146 0.815160528560293 0.592419735719854 96 0.361909602360508 0.723819204721016 0.638090397639492 97 0.321402914571942 0.642805829143884 0.678597085428058 98 0.287837853135205 0.57567570627041 0.712162146864795 99 0.249132393673607 0.498264787347214 0.750867606326393 100 0.212467248374169 0.424934496748338 0.787532751625831 101 0.181937830719570 0.363875661439141 0.81806216928043 102 0.159104568687957 0.318209137375914 0.840895431312043 103 0.142926916208303 0.285853832416605 0.857073083791697 104 0.127164569405627 0.254329138811254 0.872835430594373 105 0.153254335468514 0.306508670937028 0.846745664531486 106 0.187316966969162 0.374633933938325 0.812683033030838 107 0.155449611890654 0.310899223781309 0.844550388109346 108 0.139328372531309 0.278656745062618 0.860671627468691 109 0.125569187098132 0.251138374196263 0.874430812901869 110 0.124354425479007 0.248708850958015 0.875645574520993 111 0.102231379877337 0.204462759754674 0.897768620122663 112 0.149324132505508 0.298648265011016 0.850675867494492 113 0.290647395841172 0.581294791682344 0.709352604158828 114 0.257657935502597 0.515315871005194 0.742342064497403 115 0.539585953228561 0.920828093542878 0.460414046771439 116 0.539442886570389 0.921114226859221 0.460557113429611 117 0.555769789412674 0.888460421174652 0.444230210587326 118 0.507547130473243 0.984905739053514 0.492452869526757 119 0.453032806352504 0.906065612705008 0.546967193647496 120 0.52832615776241 0.94334768447518 0.47167384223759 121 0.502246978997532 0.995506042004937 0.497753021002468 122 0.520168984184323 0.959662031631354 0.479831015815677 123 0.476507214368858 0.953014428737716 0.523492785631142 124 0.482298436150573 0.964596872301145 0.517701563849427 125 0.424734046375015 0.84946809275003 0.575265953624985 126 0.423568958912516 0.847137917825033 0.576431041087484 127 0.393731357914712 0.787462715829424 0.606268642085288 128 0.365007535613997 0.730015071227995 0.634992464386003 129 0.329367117619033 0.658734235238067 0.670632882380967 130 0.297122637602707 0.594245275205415 0.702877362397293 131 0.303402992492924 0.606805984985848 0.696597007507076 132 0.253215034778046 0.506430069556093 0.746784965221954 133 0.211895819957315 0.42379163991463 0.788104180042685 134 0.175925925497721 0.351851850995442 0.824074074502279 135 0.144652959979243 0.289305919958486 0.855347040020757 136 0.146106006551988 0.292212013103975 0.853893993448013 137 0.158309441393098 0.316618882786196 0.841690558606902 138 0.165587829998990 0.331175659997981 0.83441217000101 139 0.179119239092396 0.358238478184793 0.820880760907604 140 0.220368422606797 0.440736845213595 0.779631577393203 141 0.171419997725983 0.342839995451966 0.828580002274017 142 0.143497579791547 0.286995159583094 0.856502420208453 143 0.202894708259673 0.405789416519345 0.797105291740327 144 0.155702291166403 0.311404582332807 0.844297708833597 145 0.109847889127326 0.219695778254651 0.890152110872674 146 0.0724177103321861 0.144835420664372 0.927582289667814 147 0.04330852216312 0.08661704432624 0.95669147783688 148 0.0220190729102943 0.0440381458205887 0.977980927089706 149 0.0100333620186114 0.0200667240372228 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:

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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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