ws 7 deterministic trend

*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 16:58:34 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531434cvydnijgponfw8d.htm/, Retrieved Tue, 23 Nov 2010 17:57:24 +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/t1290531434cvydnijgponfw8d.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 «

9 13 13 14 13 3 9 12 12 8 13 5 9 15 10 12 16 6 9 12 9 7 12 6 9 10 10 10 11 5 9 12 12 7 12 3 9 15 13 16 18 8 9 9 12 11 11 4 9 12 12 14 14 4 9 11 6 6 9 4 9 11 5 16 14 6 9 11 12 11 12 6 9 15 11 16 11 5 9 7 14 12 12 4 9 11 14 7 13 6 9 11 12 13 11 4 9 10 12 11 12 6 9 14 11 15 16 6 9 10 11 7 9 4 9 6 7 9 11 4 9 11 9 7 13 2 9 15 11 14 15 7 9 11 11 15 10 5 9 12 12 7 11 4 9 14 12 15 13 6 9 15 11 17 16 6 9 9 11 15 15 7 9 13 8 14 14 5 9 13 9 14 14 6 9 16 12 8 14 4 9 13 10 8 8 4 9 12 10 14 13 7 9 14 12 14 15 7 9 11 8 8 13 4 9 9 12 11 11 4 9 16 11 16 15 6 9 12 12 10 15 6 9 10 7 8 9 5 9 13 11 14 13 6 9 16 11 16 16 7 9 14 12 13 13 6 9 15 9 5 11 3 9 5 15 8 12 3 9 8 11 10 12 4 9 11 11 8 12 6 9 16 11 13 14 7 9 17 11 15 14 5 9 9 15 6 8 4 9 9 11 12 13 5 9 13 12 16 16 6 9 10 12 5 13 6 10 6 9 15 11 6 10 12 12 12 14 5 10 8 12 8 13 4 10 14 13 13 13 5 10 12 11 14 13 5 10 11 9 12 12 4 10 16 9 16 16 6 10 8 11 10 15 2 10 15 11 15 15 8 10 7 12 8 12 3 10 16 12 16 14 6 10 14 9 19 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 5.48495180027817 -0.566537820428668Tijd[t] + 0.0888510006565018FindingFriends[t] + 0.246617500855063KnowingPeople[t] + 0.354441237808493Liked[t] + 0.614549687191414Celebrity[t] + 0.00409598796722313t + 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) 5.48495180027817 5.872612 0.934 0.351821 0.17591 Tijd -0.566537820428668 0.62376 -0.9083 0.365206 0.182603 FindingFriends 0.0888510006565018 0.09708 0.9152 0.361547 0.180774 KnowingPeople 0.246617500855063 0.061755 3.9935 0.000102 5.1e-05 Liked 0.354441237808493 0.097772 3.6252 0.000396 0.000198 Celebrity 0.614549687191414 0.157303 3.9068 0.000141 7.1e-05 t 0.00409598796722313 0.006547 0.6256 0.532503 0.266251 Multiple Linear Regression - Regression Statistics Multiple R 0.708574818609038 R-squared 0.502078273566831 Adjusted R-squared 0.482027734247374 F-TEST (value) 25.0406368411062 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.11349919739364 Sum Squared Residuals 665.564949750152 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.4493005779774 1.55069942202258 2 12 11.1139399345406 0.886060065459391 3 15 13.6046773252320 1.39532267476802 4 12 10.8690698570334 1.13093014296659 5 10 10.7328784232224 -0.732878423222412 6 12 9.30016577336313 2.69983422663687 7 15 16.8120661324904 -1.81206613249044 8 9 10.5549362021007 -1.55493620210074 9 12 12.3622084060586 -0.362208406058635 10 11 8.08805219420388 2.91194780579612 11 11 13.4707777534905 -2.47077775349052 12 11 12.1548607661610 -1.15486076616096 13 15 12.3342023327471 2.66579766725292 14 7 11.3582728698806 -4.35827286988064 15 11 11.7128219657639 -0.712821965763871 16 11 11.0809391075487 -0.080939107548653 17 10 12.1753407059971 -2.17534070599707 18 14 14.4948206479620 -0.494820647962019 19 10 8.81578859004646 1.18421140995354 20 6 9.66659805271479 -3.66659805271479 21 11 8.83494414151905 2.16505585848095 22 15 14.5246955483588 0.475304451641231 23 11 11.7741034737558 -0.774103473755758 24 12 9.63400200615606 2.36599799384394 25 14 13.5490198509636 0.450980149036398 26 15 15.0208235534099 -0.0208235534099302 27 9 14.7917929890499 -5.79179298904995 28 13 12.6991778620013 0.300822137998718 29 13 13.4066745378164 -0.40667453781642 30 16 10.9685191482399 5.03148085176006 31 13 8.6682657080432 4.3317342919568 32 12 13.7679219517575 -1.76792195175751 33 14 14.6586024166547 -0.658602416654726 34 11 10.2750578596743 0.724942140325664 35 9 10.6655278772158 -1.66552787721577 36 16 14.4607246944186 1.53927530558140 37 12 13.0739666779120 -1.07396667791195 38 10 9.39937554684417 0.600624453155834 39 13 13.2708951809932 -0.270895180993161 40 16 15.4460995712874 0.553900428712596 41 14 13.1213206567290 0.878679343270954 42 15 8.33339209869503 6.66660790130497 43 5 9.96488783097495 -4.96488783097495 44 8 10.7213645052177 -2.72136450521770 45 11 11.4613248658576 -0.46132486585763 46 16 14.0219405209086 1.97805947909143 47 17 13.2901721362031 3.70982786379691 48 9 8.68891750505838 0.311082494941622 49 9 12.2040703717639 -3.20407037176385 50 13 14.9613607644247 -1.96136076442472 51 10 11.1893405295608 -1.18934052956077 52 6 12.1176382280635 -6.11763822806347 53 12 12.0972087416691 -0.097208741669074 54 8 10.1458438012161 -2.14584380121614 55 14 12.0864279813066 1.91357201869341 56 12 12.1594394688159 -0.159439468815874 57 11 10.5236075287601 0.47639247123994 58 16 14.1610378457643 1.83896215423566 59 8 10.0504908433400 -2.05049084334004 60 15 14.9749724587311 0.0250275412689427 61 7 9.2055247919868 -2.20552479198679 62 16 13.7350923239857 2.26490767601425 63 14 13.5036053369317 0.496394663068334 64 16 13.5156395353621 2.48436046463794 65 9 9.69122011455888 -0.691220114558882 66 14 12.0426328482895 1.95736715171046 67 11 12.8000722873498 -1.80007228734981 68 13 10.2166785812851 2.78332141871488 69 15 12.6694704993826 2.33052950061737 70 5 5.33798232973368 -0.337982329733683 71 15 12.2208792883242 2.77912071167578 72 13 12.0672087760929 0.932791223907117 73 11 11.8436599995020 -0.843659999501972 74 11 13.8212268873688 -2.82122688736877 75 12 12.2697269250179 -0.2697269250179 76 12 13.1913774168633 -1.19137741686331 77 12 12.0687159796321 -0.0687159796320693 78 12 11.7363807012702 0.263619298729785 79 14 10.6026847382052 3.39731526179479 80 6 7.821122636654 -1.821122636654 81 7 9.6553767376676 -2.65537673766761 82 14 11.8351711012090 2.16482889879098 83 14 13.7012870436927 0.298712956307269 84 10 11.0909823908679 -1.09098239086794 85 13 8.56397600063496 4.43602399936504 86 12 12.2268945568184 -0.226894556818366 87 9 9.12883669005252 -0.128836690052520 88 12 11.9041370541928 0.0958629458071936 89 16 14.8471386089255 1.15286139107453 90 10 10.0966246304262 -0.096624630426239 91 14 12.9942024448653 1.00579755513467 92 10 13.3837096975892 -3.38370969758925 93 16 15.1855001137781 0.814499886221934 94 15 13.3340206998154 1.66597930018461 95 12 11.2248892591639 0.775110740836106 96 10 9.60899282022252 0.391007179777477 97 8 10.1203456514868 -2.1203456514868 98 8 8.4904273709585 -0.4904273709585 99 11 12.7778964250540 -1.77789642505395 100 13 12.3032111246564 0.696788875343581 101 16 15.3760345177144 0.623965482285588 102 16 14.6213052668195 1.37869473318048 103 14 15.7451122840439 -1.74511228404394 104 11 8.81853900850769 2.18146099149231 105 4 6.89814409500296 -2.89814409500296 106 14 14.4624436400695 -0.462443640069505 107 9 10.3105319775397 -1.31053197753974 108 14 15.1715798811578 -1.17157988115777 109 8 10.4265476904276 -2.42654769042761 110 8 10.8864641005702 -2.88646410057018 111 11 12.1570740424550 -1.15707404245501 112 12 13.5979786682488 -1.59797866824875 113 11 11.3699889648101 -0.369988964810069 114 14 13.5626724335247 0.437327566475344 115 15 14.2891418456367 0.710858154363276 116 16 13.3741896718492 2.62581032815083 117 16 13.4671366604729 2.53286333952711 118 11 12.7004101189267 -1.70041011892673 119 14 13.7219461372624 0.278053862737596 120 14 10.9593567720081 3.04064322799188 121 12 11.4067449984403 0.59325500155966 122 14 12.5685684385542 1.43143156144577 123 8 10.2317922333446 -2.2317922333446 124 13 13.8312770777550 -0.831277077755021 125 16 13.7465220650657 2.25347793493426 126 12 10.9165108581460 1.08348914185401 127 16 15.4460783901449 0.553921609855059 128 12 13.4043687911589 -1.40436879115892 129 11 11.5598648228419 -0.5598648228419 130 4 6.41852874211252 -2.41852874211252 131 16 15.4624623420138 0.537537657986166 132 15 12.5920492398061 2.40795076019388 133 10 11.5327505640522 -1.53275056405225 134 13 13.2402081918155 -0.240208191815495 135 15 13.2942469430278 1.70575305697215 136 12 10.7283323153835 1.2716676846165 137 14 13.7068229200159 0.293177079984082 138 7 10.7540033697383 -3.75400336973829 139 19 14.1583071344154 4.84169286558464 140 12 12.7690926952146 -0.76909269521461 141 12 12.3862837605486 -0.386283760548553 142 13 13.5695363596535 -0.569536359653473 143 15 13.0534154488549 1.94658455114514 144 8 8.34892705400389 -0.348927054003887 145 12 11.0118137079436 0.98818629205643 146 10 10.8541550658197 -0.854155065819745 147 8 11.4957616071678 -3.4957616071678 148 10 14.4617240280899 -4.46172402808988 149 15 14.0025922764777 0.997407723522341 150 16 14.6926098738725 1.30739012612755 151 13 13.2844226983748 -0.284422698374774 152 16 15.1805459029892 0.819454097010831 153 9 10.3546718723613 -1.35467187236130 154 14 13.3021924500455 0.697807549954485 155 14 12.8250507269539 1.17494927304612 156 12 10.3399779392073 1.66002206079275 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0741712171667625 0.148342434333525 0.925828782833238 11 0.112202301095871 0.224404602191742 0.887797698904129 12 0.0741244480892257 0.148248896178451 0.925875551910774 13 0.551140337566569 0.897719324866862 0.448859662433431 14 0.721848220248342 0.556303559503315 0.278151779751658 15 0.655715183066684 0.688569633866633 0.344284816933316 16 0.580082450484022 0.839835099031956 0.419917549515978 17 0.494046717222321 0.988093434444641 0.505953282777679 18 0.457164118630552 0.914328237261104 0.542835881369448 19 0.398702691806448 0.797405383612896 0.601297308193552 20 0.527646011800372 0.944707976399257 0.472353988199628 21 0.527310648948094 0.945378702103813 0.472689351051906 22 0.566379806582869 0.867240386834263 0.433620193417131 23 0.503524519147538 0.992950961704923 0.496475480852462 24 0.517815059112432 0.964369881775137 0.482184940887568 25 0.491173905781173 0.982347811562347 0.508826094218827 26 0.434174203378595 0.86834840675719 0.565825796621405 27 0.665506774401732 0.668986451196536 0.334493225598268 28 0.617299688975276 0.765400622049447 0.382700311024724 29 0.562210370549315 0.875579258901371 0.437789629450685 30 0.724856060399248 0.550287879201505 0.275143939600752 31 0.815272135970578 0.369455728058845 0.184727864029422 32 0.781849336375504 0.436301327248993 0.218150663624496 33 0.73713017621658 0.52573964756684 0.26286982378342 34 0.700991496824609 0.598017006350782 0.299008503175391 35 0.70754766997187 0.58490466005626 0.29245233002813 36 0.711411276126 0.577177447747999 0.288588723873999 37 0.680668306625127 0.638663386749746 0.319331693374873 38 0.629960901945593 0.740078196108814 0.370039098054407 39 0.576764139013112 0.846471721973775 0.423235860986888 40 0.546327939559265 0.90734412088147 0.453672060440735 41 0.503426595810007 0.993146808379986 0.496573404189993 42 0.760193257406362 0.479613485187277 0.239806742593638 43 0.955199677249064 0.0896006455018713 0.0448003227509357 44 0.966171914935365 0.0676561701292693 0.0338280850646347 45 0.955673579790998 0.0886528404180045 0.0443264202090022 46 0.960283165639154 0.0794336687216919 0.0397168343608460 47 0.98249463097523 0.0350107380495389 0.0175053690247694 48 0.978626268770566 0.0427474624588676 0.0213737312294338 49 0.9830455852271 0.033908829545799 0.0169544147728995 50 0.978879152705956 0.0422416945880871 0.0211208472940435 51 0.97430177395400 0.0513964520919977 0.0256982260459989 52 0.989925402143615 0.0201491957127703 0.0100745978563851 53 0.992519880838565 0.0149602383228694 0.00748011916143468 54 0.991164592609655 0.0176708147806899 0.00883540739034496 55 0.994908677893344 0.0101826442133122 0.00509132210665612 56 0.993470720982195 0.0130585580356100 0.00652927901780498 57 0.991211645067473 0.0175767098650537 0.00878835493252685 58 0.991508942778104 0.0169821144437913 0.00849105722189564 59 0.992613299721703 0.0147734005565943 0.00738670027829715 60 0.99122780368389 0.0175443926322215 0.00877219631611077 61 0.991493443936462 0.0170131121270769 0.00850655606353845 62 0.99331276136589 0.0133744772682205 0.00668723863411024 63 0.991397378134413 0.0172052437311733 0.00860262186558665 64 0.992450240136325 0.0150995197273493 0.00754975986367465 65 0.990096362028706 0.0198072759425878 0.0099036379712939 66 0.989566390431926 0.0208672191361473 0.0104336095680737 67 0.989265419238058 0.0214691615238844 0.0107345807619422 68 0.991261034079185 0.0174779318416295 0.00873896592081476 69 0.99158391175856 0.0168321764828785 0.00841608824143925 70 0.988635618904562 0.0227287621908753 0.0113643810954376 71 0.99045338502367 0.0190932299526586 0.0095466149763293 72 0.98748207428565 0.0250358514286988 0.0125179257143494 73 0.984225920503106 0.0315481589937888 0.0157740794968944 74 0.988480271248361 0.0230394575032776 0.0115197287516388 75 0.98446794834342 0.031064103313159 0.0155320516565795 76 0.981763138190198 0.0364737236196037 0.0182368618098018 77 0.976039476331006 0.0479210473379888 0.0239605236689944 78 0.968474997917452 0.0630500041650965 0.0315250020825482 79 0.979911528836039 0.0401769423279225 0.0200884711639613 80 0.979051045490935 0.0418979090181291 0.0209489545090645 81 0.982441884988268 0.0351162300234634 0.0175581150117317 82 0.983310438131075 0.0333791237378504 0.0166895618689252 83 0.977691230126222 0.0446175397475563 0.0223087698737782 84 0.972682221381389 0.0546355572372218 0.0273177786186109 85 0.992596794742124 0.0148064105157528 0.0074032052578764 86 0.989797392071149 0.0204052158577029 0.0102026079288514 87 0.98628477793078 0.0274304441384386 0.0137152220692193 88 0.98218367226876 0.0356326554624804 0.0178163277312402 89 0.977885466648729 0.0442290667025428 0.0221145333512714 90 0.971191399152196 0.0576172016956074 0.0288086008478037 91 0.966093146569196 0.0678137068616084 0.0339068534308042 92 0.979256530494548 0.0414869390109042 0.0207434695054521 93 0.973176766043085 0.0536464679138295 0.0268232339569148 94 0.96963095479708 0.0607380904058385 0.0303690452029192 95 0.962474782729718 0.0750504345405634 0.0375252172702817 96 0.953952927856277 0.0920941442874463 0.0460470721437232 97 0.949820090992317 0.100359818015365 0.0501799090076827 98 0.937088820835008 0.125822358329984 0.0629111791649919 99 0.931970141655347 0.136059716689306 0.0680298583446528 100 0.918071441069307 0.163857117861385 0.0819285589306927 101 0.898329928577223 0.203340142845555 0.101670071422777 102 0.884123545874621 0.231752908250757 0.115876454125379 103 0.88616665796714 0.22766668406572 0.11383334203286 104 0.924474543313484 0.151050913373033 0.0755254566865163 105 0.921545875976543 0.156908248046914 0.0784541240234568 106 0.900678625503464 0.198642748993072 0.0993213744965358 107 0.879656537389574 0.240686925220852 0.120343462610426 108 0.870054808590735 0.259890382818530 0.129945191409265 109 0.865998093532728 0.268003812934544 0.134001906467272 110 0.889364476303296 0.221271047393409 0.110635523696704 111 0.878953946591296 0.242092106817408 0.121046053408704 112 0.916753704637318 0.166492590725365 0.0832462953626823 113 0.89301023524797 0.213979529504059 0.106989764752029 114 0.867185372220987 0.265629255558026 0.132814627779013 115 0.836867795364546 0.326264409270908 0.163132204635454 116 0.830879687750082 0.338240624499836 0.169120312249918 117 0.834685476689381 0.330629046621238 0.165314523310619 118 0.827651400084535 0.34469719983093 0.172348599915465 119 0.789342118736039 0.421315762527923 0.210657881263961 120 0.838035114338567 0.323929771322866 0.161964885661433 121 0.807463655315766 0.385072689368469 0.192536344684234 122 0.781633839476693 0.436732321046615 0.218366160523307 123 0.767836747529315 0.46432650494137 0.232163252470685 124 0.723150216700639 0.553699566598723 0.276849783299361 125 0.722966162521897 0.554067674956206 0.277033837478103 126 0.711175056042909 0.577649887914182 0.288824943957091 127 0.65220729612298 0.69558540775404 0.34779270387702 128 0.613090521765875 0.77381895646825 0.386909478234125 129 0.627141908039979 0.745716183920041 0.372858091960021 130 0.628583444228252 0.742833111543497 0.371416555771748 131 0.572747829282612 0.854504341434777 0.427252170717388 132 0.540323234254351 0.919353531491297 0.459676765745649 133 0.525914513137671 0.948170973724657 0.474085486862329 134 0.449145895515348 0.898291791030697 0.550854104484652 135 0.404058068115826 0.808116136231651 0.595941931884174 136 0.390644611089812 0.781289222179624 0.609355388910188 137 0.316892689001983 0.633785378003967 0.683107310998017 138 0.3827700494465 0.765540098893 0.6172299505535 139 0.752204540523978 0.495590918952044 0.247795459476022 140 0.755926579817525 0.48814684036495 0.244073420182475 141 0.707273400881692 0.585453198236616 0.292726599118308 142 0.621385605239751 0.757228789520498 0.378614394760249 143 0.544097586276402 0.911804827447195 0.455902413723598 144 0.417459848433508 0.834919696867016 0.582540151566492 145 0.477376684850801 0.954753369701602 0.522623315149199 146 0.617289921074538 0.765420157850924 0.382710078925462 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 41 0.299270072992701 NOK 10% type I error level 54 0.394160583941606 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = 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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