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: Tue, 23 Nov 2010 15:17:38 +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/Nov/23/t1290525397oskzt0o6hfmkfrr.htm/, Retrieved Tue, 23 Nov 2010 16:16:52 +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/Nov/23/t1290525397oskzt0o6hfmkfrr.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 «

4 2 5 4 3 4 2 4 3 2 5 4 4 2 2 3 2 4 2 2 4 3 2 2 2 3 4 5 2 2 4 3 5 3 2 3 3 4 2 1 2 3 3 1 2 4 2 4 2 2 2 4 4 2 2 2 3 3 2 2 1 3 3 2 2 4 4 4 2 2 4 4 5 1 1 2 3 4 2 2 2 3 2 2 1 3 3 4 3 2 3 4 4 4 2 3 2 4 4 2 4 5 4 4 4 3 4 4 4 2 2 2 4 4 4 2 3 5 2 2 4 4 4 2 2 4 4 4 4 2 3 3 4 2 2 4 4 4 3 2 2 4 4 2 2 4 1 4 4 2 4 4 4 3 3 5 5 2 4 2 5 2 4 2 2 4 4 4 2 2 4 3 5 4 3 4 2 5 5 4 2 4 4 2 1 4 5 3 4 2 4 4 4 4 3 4 4 5 5 3 3 4 4 3 2 2 3 4 2 2 3 4 5 3 2 4 2 4 2 2 3 2 5 1 2 2 4 4 2 2 4 2 4 4 4 4 4 4 4 4 3 4 3 4 2 4 1 4 4 3 3 4 4 2 2 4 2 4 2 2 2 1 2 1 1 4 4 3 4 3 4 3 5 2 4 4 2 4 4 2 4 4 4 2 2 3 3 5 2 1 1 2 3 1 2 3 2 5 2 2 3 3 4 2 2 4 2 5 2 2 2 1 4 2 2 3 3 4 1 1 5 2 5 5 2 4 3 4 3 3 4 3 4 2 2 3 3 5 1 1 4 2 4 2 2 2 3 3 4 4 3 2 4 2 2 4 4 5 5 3 3 4 5 4 4 4 4 5 3 2 4 2 4 2 4 3 3 4 2 1 3 4 5 2 2 2 3 5 2 2 4 4 4 4 4 3 2 5 2 3 2 3 3 2 2 2 3 4 4 2 3 4 4 4 2 2 2 4 2 3 2 4 4 2 2 4 2 4 3 2 4 2 5 2 1 4 4 4 4 2 2 3 4 2 2 2 4 4 4 4 4 2 5 1 1 2 2 3 2 2 3 3 3 3 2 3 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 24 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation YT[t] = + 1.29605226452594 + 0.0689248642585393X1[t] + 0.252916716305925X2[t] + 0.363828375948588X3[t] -0.118420136069921X4[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) 1.29605226452594 0.431979 3.0003 0.003153 0.001577 X1 0.0689248642585393 0.073619 0.9362 0.350634 0.175317 X2 0.252916716305925 0.0826 3.0619 0.002601 0.001301 X3 0.363828375948588 0.072444 5.0222 1e-06 1e-06 X4 -0.118420136069921 0.089782 -1.319 0.189163 0.094582 Multiple Linear Regression - Regression Statistics Multiple R 0.456901675014126 R-squared 0.208759140630714 Adjusted R-squared 0.187937012752575 F-TEST (value) 10.0258312624181 F-TEST (DF numerator) 4 F-TEST (DF denominator) 152 p-value 3.15112685944641e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.866596311038476 Sum Squared Residuals 114.150353278435 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 3.79853867015723 0.201461329842773 2 4 3.30021371397264 0.699786286027362 3 5 3.07423506654113 1.92576493345887 4 3 2.93638533802405 0.0636146619759458 5 4 2.49947676967074 1.50052323032926 6 3 3.32715178284706 -0.327151782847056 7 4 3.6220552945371 0.377944705462896 8 3 3.12373033835251 -0.123730338352512 9 2 2.38856511002808 -0.388565110028079 10 4 2.93638533802405 1.06361466197595 11 2 3.07423506654113 -1.07423506654113 12 2 2.75239348597667 -0.752393485976667 13 1 2.75239348597667 -1.75239348597667 14 4 3.07423506654113 0.925764933458869 15 4 3.08174354296839 0.918256457031611 16 2 3.00531020228259 -1.00531020228259 17 2 2.61789690574066 -0.617896905740663 18 3 3.36913857823118 -0.369138578231179 19 3 3.80189181843831 -0.801891818438307 20 3 3.66404208992123 -0.664042089921228 21 4 3.63397641055700 0.366023589442996 22 3 3.80189181843831 -0.801891818438307 23 2 3.42720181778139 -1.42720181778139 24 2 3.25822691858852 -1.25822691858852 25 4 3.07423506654113 0.925764933458869 26 4 3.80189181843831 0.198108181561693 27 3 3.00531020228259 -0.00531020228259128 28 4 3.43806344248972 0.561936557510281 29 2 3.07423506654113 -1.07423506654113 30 4 3.59511722566269 0.404882774337312 31 4 3.3196433064198 0.680356693580202 32 5 3.364983250085 1.63501674991500 33 5 2.93638533802405 2.06361466197595 34 4 3.07423506654113 0.925764933458869 35 4 3.86746353441577 0.132536465584229 36 4 4.0439469100359 -0.0439469100358984 37 2 3.19265520261105 -1.19265520261105 38 4 3.61789996639092 0.382100033609078 39 4 3.68347168236839 0.316528317631614 40 4 4.3002167746229 -0.300216774622899 41 3 3.43806344248972 -0.438063442489719 42 2 3.00531020228259 -1.00531020228259 43 3 3.69098015879564 -0.690980158795644 44 4 2.93638533802405 1.06361466197595 45 3 2.82547367838139 0.174526321618612 46 2 3.07423506654113 -1.07423506654113 47 4 3.42720181778139 0.572798182218614 48 4 3.56505154629846 0.434948453701535 49 3 3.54897510213238 -0.548975102132382 50 4 3.47669708959277 0.523302910407233 51 3 3.07423506654113 -0.0742350665411309 52 4 2.93638533802405 1.06361466197595 53 2 2.11621880127500 -0.116218801274996 54 4 3.43055496606246 0.569445033937539 55 4 3.02138664644867 0.978613353551326 56 4 3.66404208992123 0.335957910078772 57 4 3.07423506654113 0.925764933458869 58 3 3.37664705465844 -0.376647054658437 59 1 2.31964024576954 -1.31964024576954 60 3 3.18930205432998 -0.189302054329976 61 3 3.00531020228259 -0.00531020228259128 62 4 3.18930205432998 0.810697945670024 63 2 2.86746047376551 -0.867460473765512 64 3 2.75990196240392 0.240098037596076 65 5 4.28078718217574 0.719212817824259 66 4 3.25071844216126 0.749281557838742 67 4 3.00531020228259 0.99468979771741 68 3 3.01281867870985 -0.0128186787098493 69 4 2.93638533802405 1.06361466197595 70 2 3.243209965734 -1.243209965734 71 3 2.93638533802405 0.0636146619759482 72 4 4.3002167746229 -0.300216774622899 73 3 3.81796826260439 -0.81796826260439 74 4 3.69098015879564 0.309019841204356 75 4 2.69954506588421 1.30045493411579 76 3 3.12373033835251 -0.123730338352512 77 3 3.32715178284706 -0.327151782847056 78 2 3.25822691858852 -1.25822691858852 79 4 3.56505154629846 0.434948453701535 80 3 3.07088191826006 -0.0708819182600554 81 2 2.75239348597667 -0.752393485976667 82 2 3.73296695417977 -1.73296695417977 83 3 3.80189181843831 -0.801891818438307 84 2 2.81796520195413 -0.81796520195413 85 2 3.07423506654113 -1.07423506654113 86 4 3.30021371397264 0.69978628602736 87 4 3.3077221903999 0.692277809600103 88 4 3.80189181843831 0.198108181561693 89 2 3.00531020228259 -1.00531020228259 90 2 3.56505154629846 -1.56505154629846 91 4 2.94389381445131 1.05610618554869 92 2 2.68346862171813 -0.683468621718127 93 3 3.11622186192525 -0.116221861925255 94 3 3.25822691858852 -0.258226918588516 95 5 3.88689312686293 1.11310687313707 96 3 2.69954506588421 0.300454934115790 97 4 3.25071844216126 0.749281557838742 98 3 3.07423506654113 -0.0742350665411309 99 2 2.88689006621267 -0.88689006621267 100 4 3.07423506654113 0.925764933458869 101 3 3.12373033835251 -0.123730338352512 102 3 3.00531020228259 -0.00531020228259128 103 3 2.93638533802405 0.0636146619759482 104 4 3.6220552945371 0.377944705462896 105 1 2.19371163327236 -1.19371163327236 106 3 3.00531020228259 -0.00531020228259128 107 2 3.03978852123946 -1.03978852123946 108 3 3.3196433064198 -0.319643306419798 109 2 3.18930205432998 -1.18930205432998 110 2 2.57591011035654 -0.575910110356539 111 2 2.83739479440129 -0.837394794401289 112 4 2.61454375745959 1.38545624254041 113 5 4.23464505864543 0.765354941354565 114 5 2.69097709814538 2.30902290185462 115 3 3.00531020228259 -0.00531020228259128 116 4 2.56840163392928 1.43159836607072 117 4 2.10871032484774 1.89128967515226 118 3 3.02473979472975 -0.0247397947297494 119 2 2.87081362204659 -0.870813622046588 120 4 3.97837519405843 0.0216248059415657 121 2 2.75239348597667 -0.752393485976667 122 3 2.63397334990675 0.366026650093254 123 2 3.3077221903999 -1.30772219039990 124 2 2.93638533802405 -0.936385338024052 125 2 2.70289821416528 -0.702898214165285 126 4 3.19265520261105 0.807344797388948 127 4 3.36913857823118 0.630861421768821 128 4 3.00531020228259 0.99468979771741 129 4 3.61454681810985 0.385453181890154 130 3 3.54897510213238 -0.548975102132382 131 2 3.00531020228259 -1.00531020228259 132 4 3.80189181843831 0.198108181561693 133 3 3.80189181843831 -0.801891818438307 134 2 2.93638533802405 -0.936385338024052 135 4 3.80189181843831 0.198108181561693 136 3 2.92887686159679 0.0711231384032061 137 3 3.07423506654113 -0.0742350665411309 138 3 3.00531020228259 -0.00531020228259128 139 3 2.74488500954941 0.255114990450591 140 3 3.15820865730938 -0.158208657309378 141 4 3.66404208992123 0.335957910078772 142 5 3.84723176210351 1.15276823789649 143 2 3.05480547409397 -1.05480547409397 144 4 3.13229830609134 0.867701693908663 145 3 3.72545847775251 -0.72545847775251 146 3 2.38105663360082 0.61894336639918 147 1 2.49947676967074 -1.49947676967074 148 2 3.07423506654113 -1.07423506654113 149 4 2.82131835023521 1.17868164976479 150 4 2.83739479440129 1.16260520559871 151 5 4.04730005831697 0.952699941683026 152 2 2.81380987380795 -0.813809873807948 153 4 3.39607664710560 0.603923352894405 154 3 3.00531020228259 -0.00531020228259128 155 2 3.36913857823118 -1.36913857823118 156 4 3.3196433064198 0.680356693580202 157 2 2.46605794202544 -0.466057942025443 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.472229617660685 0.94445923532137 0.527770382339315 9 0.417243607614547 0.834487215229093 0.582756392385453 10 0.581513620444951 0.836972759110097 0.418486379555049 11 0.773498499251351 0.453003001497298 0.226501500748649 12 0.839907386007692 0.320185227984615 0.160092613992308 13 0.958567373770467 0.0828652524590654 0.0414326262295327 14 0.95367933502914 0.0926413299417217 0.0463206649708608 15 0.944736877159966 0.110526245680067 0.0552631228400336 16 0.950054109948924 0.0998917801021516 0.0499458900510758 17 0.93764045957818 0.124719080843638 0.0623595404218189 18 0.916592744509712 0.166814510980577 0.0834072554902883 19 0.8967140702546 0.206571859490798 0.103285929745399 20 0.868059672172746 0.263880655654509 0.131940327827254 21 0.832705912575118 0.334588174849764 0.167294087424882 22 0.795358060813185 0.409283878373630 0.204641939186815 23 0.839660680348203 0.320678639303594 0.160339319651797 24 0.886869022248661 0.226261955502678 0.113130977751339 25 0.880999036365217 0.238001927269565 0.119000963634783 26 0.853051723651679 0.293896552696643 0.146948276348321 27 0.81269123652185 0.374617526956301 0.187308763478151 28 0.784927419159922 0.430145161680156 0.215072580840078 29 0.81379556419361 0.372408871612780 0.186204435806390 30 0.799003740513366 0.401992518973268 0.200996259486634 31 0.786268021932328 0.427463956135345 0.213731978067672 32 0.847840709388467 0.304318581223065 0.152159290611533 33 0.953237238800319 0.0935255223993624 0.0467627611996812 34 0.950223607719392 0.0995527845612164 0.0497763922806082 35 0.935028002050801 0.129943995898398 0.0649719979491991 36 0.916662742587525 0.166674514824951 0.0833372574124753 37 0.934852722701419 0.130294554597162 0.065147277298581 38 0.917711409081531 0.164577181836938 0.0822885909184688 39 0.896871468016046 0.206257063967908 0.103128531983954 40 0.873389069959593 0.253221860080814 0.126610930040407 41 0.852176397269945 0.295647205460109 0.147823602730055 42 0.859852108439239 0.280295783121523 0.140147891560762 43 0.844315718471663 0.311368563056674 0.155684281528337 44 0.856577886873351 0.286844226253298 0.143422113126649 45 0.82673474469639 0.346530510607219 0.173265255303610 46 0.842192167908972 0.315615664182055 0.157807832091028 47 0.818831451895815 0.36233709620837 0.181168548104185 48 0.788326526763531 0.423346946472937 0.211673473236469 49 0.765999427414306 0.468001145171387 0.234000572585693 50 0.736666344684264 0.526667310631471 0.263333655315736 51 0.694385415700725 0.611229168598551 0.305614584299276 52 0.706325001418897 0.587349997162206 0.293674998581103 53 0.669164775003665 0.661670449992669 0.330835224996335 54 0.636485429109733 0.727029141780533 0.363514570890266 55 0.627315138766855 0.745369722466289 0.372684861233145 56 0.589655106853709 0.820689786292582 0.410344893146291 57 0.590247620938251 0.819504758123498 0.409752379061749 58 0.54665065565443 0.90669868869114 0.45334934434557 59 0.630615303125799 0.738769393748402 0.369384696874201 60 0.585656769231592 0.828686461536816 0.414343230768408 61 0.538118583182334 0.923762833635332 0.461881416817666 62 0.532827337165651 0.934345325668698 0.467172662834349 63 0.532345631541649 0.935308736916703 0.467654368458351 64 0.489559581201966 0.979119162403932 0.510440418798034 65 0.482348949898236 0.964697899796471 0.517651050101764 66 0.464751986816671 0.929503973633341 0.535248013183329 67 0.47547825139185 0.9509565027837 0.52452174860815 68 0.428658797783253 0.857317595566505 0.571341202216747 69 0.449108218469997 0.898216436939995 0.550891781530003 70 0.512417235725819 0.975165528548361 0.487582764274181 71 0.466086199724719 0.932172399449439 0.533913800275281 72 0.425135270148557 0.850270540297115 0.574864729851443 73 0.421354985797159 0.842709971594318 0.578645014202841 74 0.382035179059019 0.764070358118037 0.617964820940981 75 0.431099941899274 0.862199883798548 0.568900058100726 76 0.386194662790985 0.77238932558197 0.613805337209015 77 0.348338181156095 0.69667636231219 0.651661818843905 78 0.392849216610069 0.785698433220138 0.607150783389931 79 0.359282093106964 0.718564186213927 0.640717906893036 80 0.318627588443937 0.637255176887874 0.681372411556063 81 0.311096470401163 0.622192940802325 0.688903529598837 82 0.429723702009406 0.859447404018812 0.570276297990594 83 0.420712624977346 0.841425249954692 0.579287375022654 84 0.417434877220091 0.834869754440182 0.582565122779909 85 0.443155021463674 0.886310042927347 0.556844978536326 86 0.428706742356588 0.857413484713176 0.571293257643412 87 0.414969065036804 0.829938130073607 0.585030934963196 88 0.372598995908807 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0.780846301346419 106 0.184309419261686 0.368618838523371 0.815690580738314 107 0.203692599681598 0.407385199363196 0.796307400318402 108 0.173235725146631 0.346471450293263 0.826764274853369 109 0.187516905197643 0.375033810395286 0.812483094802357 110 0.170465448874449 0.340930897748899 0.82953455112555 111 0.166005322209869 0.332010644419738 0.833994677790131 112 0.222208057889540 0.444416115779081 0.77779194211046 113 0.207683680499927 0.415367360999855 0.792316319500073 114 0.566859173561306 0.866281652877388 0.433140826438694 115 0.516318069751983 0.967363860496035 0.483681930248017 116 0.587318581075517 0.825362837848966 0.412681418924483 117 0.87908804795162 0.241823904096761 0.120911952048381 118 0.857706390559669 0.284587218880662 0.142293609440331 119 0.836553393509502 0.326893212980997 0.163446606490498 120 0.800542086119869 0.398915827760263 0.199457913880131 121 0.772374914463799 0.455250171072402 0.227625085536201 122 0.745423930048809 0.509152139902383 0.254576069951191 123 0.749959339338505 0.50008132132299 0.250040660661495 124 0.724689775634267 0.550620448731466 0.275310224365733 125 0.715895904801093 0.568208190397813 0.284104095198907 126 0.722272399995635 0.555455200008731 0.277727600004365 127 0.710527200675484 0.578945598649032 0.289472799324516 128 0.780718141983957 0.438563716032086 0.219281858016043 129 0.734716139690558 0.530567720618883 0.265283860309442 130 0.715874259806147 0.568251480387707 0.284125740193853 131 0.697981123721364 0.604037752557272 0.302018876278636 132 0.635372477163432 0.729255045673135 0.364627522836568 133 0.67846002434435 0.6430799513113 0.32153997565565 134 0.630875170292535 0.73824965941493 0.369124829707465 135 0.563849109525387 0.872301780949227 0.436150890474613 136 0.506010842922659 0.987978314154681 0.493989157077341 137 0.431152514684984 0.862305029369968 0.568847485315016 138 0.361846104788853 0.723692209577706 0.638153895211147 139 0.307912055508669 0.615824111017337 0.692087944491331 140 0.258239923707795 0.51647984741559 0.741760076292205 141 0.250993082784963 0.501986165569925 0.749006917215037 142 0.260772806539506 0.521545613079013 0.739227193460494 143 0.199184763047546 0.398369526095091 0.800815236952454 144 0.173159443295815 0.346318886591629 0.826840556704185 145 0.125738879765476 0.251477759530952 0.874261120234524 146 0.202731199659177 0.405462399318353 0.797268800340823 147 0.141861585929578 0.283723171859155 0.858138414070422 148 0.186646559806457 0.373293119612915 0.813353440193542 149 0.367052722357574 0.734105444715149 0.632947277642426 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 5 0.0352112676056338 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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