*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, 16 Nov 2010 08:50:28 +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/16/t1289897347jwqkkjji97euqer.htm/, Retrieved Tue, 16 Nov 2010 09:49:07 +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/16/t1289897347jwqkkjji97euqer.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 «

18 15 15 0 17 3 21 2 22 3 24 12 17 3 25 0 16 12 18 15 21 0 19 10 18 20 20 20 25 2 28 3 19 16 20 4 25 2 20 4 21 0 21 0 23 15 19 9 23 1 20 15 19 5 17 4 19 15 21 4 18 12 18 2 24 4 22 2 20 4 17 8 25 30 24 6 18 6 21 7 13 4 21 17 21 5 16 0 18 3 19 4 22 15 18 0 18 8 20 10 19 4 18 0 20 6 20 11 23 10 17 0 17 0 18 0 22 0 16 0 18 0 14 0 13 7 21 4 25 12 16 6 17 12 22 10 24 9 18 0 18 16 18 2 19 0 15 0 25 1 22 10 15 14 21 12 16 12 23 12 20 5 19 0 20 4 18 3 18 0 20 3 20 0 16 12 18 12 18 15 16 0 23 8 14 6 21 14 13 5 27 10 20 16 22 4 21 0 19 8 22 12 12 6 28 4 21 20 18 0 21 13 19 0 23 0 21 0 21 0 22 10 18 6 15 16 23 6 24 0 18 4 15 9 19 17 17 12 14 3 16 8 22 3 15 0 23 10 24 3 24 0 20 8 9 0 23 4 18 13 20 12 25 16 17 20 21 20 26 14 20 12 21 15 15 9 20 4 20 8 16 0 19 13 22 0 17 21 25 0 19 1 17 16 21 12 12 2

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Perf[t] = + 19.7340138067534 + 0.0412068018674213`Sport `[t] -0.00609760335969976t + 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) 19.7340138067534 0.616293 32.0205 0 0 `Sport ` 0.0412068018674213 0.044138 0.9336 0.352061 0.17603 t -0.00609760335969976 0.006422 -0.9495 0.343921 0.171961 Multiple Linear Regression - Regression Statistics Multiple R 0.105641315003316 R-squared 0.0111600874356298 Adjusted R-squared -0.00238566479127944 F-TEST (value) 0.823880966422807 F-TEST (DF numerator) 2 F-TEST (DF denominator) 146 p-value 0.440754840001858 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.36177350359944 Sum Squared Residuals 1650.02207906748 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 18 20.346018231405 -2.34601823140502 2 15 19.7218186000340 -4.72181860003403 3 17 19.8393414022766 -2.8393414022766 4 21 19.7920369970495 1.20796300295052 5 22 19.8271461955572 2.1728538044428 6 24 20.1919098090043 3.80809019099571 7 17 19.8149509888378 -2.8149509888378 8 25 19.6852329798758 5.31476702012417 9 16 20.1736169989252 -4.17361699892519 10 18 20.2911398011678 -2.29113980116776 11 21 19.6669401697967 1.33305983020326 12 19 20.0729105851112 -1.07291058511125 13 18 20.4788810004258 -2.47888100042576 14 20 20.4727833970661 -0.472783397066062 15 25 19.7249633600928 5.27503663990722 16 28 19.7600725586005 8.2399274413995 17 19 20.2896633795173 -1.28966337951728 18 20 19.7890841537485 0.210915846251477 19 25 19.700572946654 5.29942705334602 20 20 19.7768889470291 0.223111052970877 21 21 19.6059641361997 1.39403586380026 22 21 19.5998665328400 1.40013346715996 23 23 20.2118709574917 2.78812904250834 24 19 19.9585325429274 -0.95853254292743 25 23 19.6227805246284 3.37721947537164 26 20 20.1935781474126 -0.193578147412559 27 19 19.7754125253786 -0.775412525378647 28 17 19.7281081201515 -2.72810812015153 29 19 20.1752853373335 -1.17528533733346 30 21 19.7159129134321 1.28408708656787 31 18 20.0394697250118 -2.03946972501180 32 18 19.6213041029779 -1.62130410297788 33 24 19.6976201033530 4.30237989664697 34 22 19.6091088962585 2.39089110374152 35 20 19.6854248966336 0.314575103366373 36 17 19.8441545007436 -2.84415450074361 37 25 20.7446065384672 4.25539346153282 38 24 19.7495456902894 4.25045430971063 39 18 19.7434480869297 -1.74344808692967 40 21 19.7785572854374 1.22144271456261 41 13 19.6488392764754 -6.64883927647543 42 21 20.1784300973922 0.821569902607795 43 21 19.6778508716234 1.32214912837655 44 16 19.4657192589266 -3.46571925892664 45 18 19.5832420611692 -1.58324206116921 46 19 19.6183512596769 -0.61835125967693 47 22 20.0655284768589 1.93447152314114 48 18 19.4413288454878 -1.44132884548785 49 18 19.7648856570675 -1.76488565706752 50 20 19.8412016574427 0.158798342557342 51 19 19.5878632428784 -0.587863242878431 52 18 19.4169384320490 -1.41693843204905 53 20 19.6580816398939 0.341918360106126 54 20 19.8580180458713 0.141981954128720 55 23 19.8107136406442 3.18928635935584 56 17 19.3925480186102 -2.39254801861025 57 17 19.3864504152505 -2.38645041525055 58 18 19.3803528118908 -1.38035281189085 59 22 19.3742552085311 2.62574479146885 60 16 19.3681576051714 -3.36815760517145 61 18 19.3620600018117 -1.36206000181175 62 14 19.3559623984520 -5.35596239845205 63 13 19.6383124081643 -6.6383124081643 64 21 19.5085943992023 1.49140560079767 65 25 19.832151210782 5.167848789218 66 16 19.5788127962178 -3.57881279621778 67 17 19.8199560040626 -2.81995600406260 68 22 19.7314447969681 2.26855520303194 69 24 19.6841403917409 4.31585960825906 70 18 19.3071815715744 -1.30718157157445 71 18 19.9603927980935 -1.96039279809349 72 18 19.3773999685899 -1.37739996858989 73 19 19.2888887614954 -0.288888761495351 74 15 19.2827911581357 -4.28279115813565 75 25 19.3179003566434 5.68209964335663 76 22 19.6826639700905 2.31733602990953 77 15 19.8413935742004 -4.84139357420045 78 21 19.7528823671059 1.24711763289409 79 16 19.7467847637462 -3.74678476374621 80 23 19.7406871603865 3.25931283961349 81 20 19.4461419439549 0.553858056045141 82 19 19.2340103312581 -0.234010331258053 83 20 19.3927399353680 0.607260064631961 84 18 19.3454355301409 -1.34543553014092 85 18 19.2157175211790 -1.21571752117895 86 20 19.3332403234215 0.666759676578482 87 20 19.2035223144596 0.796477685540446 88 16 19.6919063335089 -3.69190633350891 89 18 19.6858087301492 -1.68580873014921 90 18 19.8033315323918 -1.80333153239177 91 16 19.1791319010208 -3.17913190102076 92 23 19.5026887126004 3.49731128739957 93 14 19.4141775055059 -5.41417750550588 94 21 19.7377343170856 1.26226568291445 95 13 19.3607754969191 -6.36077549691906 96 27 19.5607119028965 7.43928809710353 97 20 19.8018551107413 0.198144889258703 98 22 19.3012758849725 2.69872411502746 99 21 19.1303510741432 1.86964892585684 100 19 19.4539078857228 -0.453907885722828 101 22 19.6126374898328 2.38736251016719 102 12 19.3592990752686 -7.35929907526859 103 28 19.2707878681740 8.72921213182596 104 21 19.9239990946931 1.07600090530692 105 18 19.0937654539850 -1.09376545398496 106 21 19.6233562749017 1.37664372509826 107 19 19.0815702472656 -0.0815702472655591 108 23 19.0754726439059 3.92452735609414 109 21 19.0693750405462 1.93062495945384 110 21 19.0632774371865 1.93672256281354 111 22 19.4692478525010 2.53075214749903 112 18 19.2983230416716 -1.29832304167159 113 15 19.7042934569861 -4.7042934569861 114 23 19.2861278349522 3.71387216504781 115 24 19.0327894203880 4.96721057961204 116 18 19.1915190244979 -1.19151902449795 117 15 19.3914554304754 -4.39145543047535 118 19 19.7150122420550 -0.715012242055023 119 17 19.5028806293582 -2.50288062935822 120 14 19.1259218091917 -5.12592180919173 121 16 19.3258582151691 -3.32585821516913 122 22 19.1137266024723 2.88627339752767 123 15 18.9840085935104 -3.98400859351036 124 23 19.3899790088249 3.61002099117512 125 24 19.0954337923932 4.90456620760677 126 24 18.9657157834313 5.03428421656874 127 20 19.2892725950109 0.710727404989066 128 9 18.9535205767119 -9.95352057671186 129 23 19.1122501808218 3.88774981917815 130 18 19.4770137942689 -1.47701379426894 131 20 19.4297093890418 0.57029061095818 132 25 19.5884389931518 5.4115610068482 133 17 19.7471685972618 -2.74716859726179 134 21 19.7410709939021 1.25892900609791 135 26 19.4877325793379 6.51226742066214 136 20 19.3992213722433 0.600778627756679 137 21 19.5167441744859 1.48325582551411 138 15 19.2634057599217 -4.26340575992166 139 20 19.0512741472249 0.948725852775148 140 20 19.2100037513348 0.789996248665163 141 16 18.8742517330358 -2.87425173303577 142 19 19.4038425539525 -0.403842553952544 143 22 18.8620565263164 3.13794347368363 144 17 19.7213017621725 -2.72130176217252 145 25 18.8498613195970 6.15013868040303 146 19 18.8849705181047 0.115029481895310 147 17 19.4969749427563 -2.49697494275631 148 21 19.3260501319269 1.67394986807308 149 12 18.907884509893 -6.90788450989301 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0813066678291239 0.162613335658248 0.918693332170876 7 0.46289216076227 0.92578432152454 0.53710783923773 8 0.441397105408172 0.882794210816345 0.558602894591828 9 0.786501758806131 0.426996482387737 0.213498241193869 10 0.732192662516796 0.535614674966407 0.267807337483203 11 0.638864551562263 0.722270896875475 0.361135448437737 12 0.553673687142199 0.892652625715602 0.446326312857801 13 0.466892541503844 0.933785083007688 0.533107458496156 14 0.381382242408945 0.76276448481789 0.618617757591055 15 0.367221843615464 0.734443687230928 0.632778156384536 16 0.455763521159295 0.91152704231859 0.544236478840705 17 0.426499005718631 0.852998011437262 0.573500994281369 18 0.448277328150979 0.896554656301958 0.551722671849021 19 0.397752789090803 0.795505578181605 0.602247210909197 20 0.411073175930091 0.822146351860182 0.588926824069909 21 0.392278747678633 0.784557495357266 0.607721252321367 22 0.360911684863858 0.721823369727716 0.639088315136142 23 0.315419895518714 0.630839791037427 0.684580104481286 24 0.310264346969122 0.620528693938244 0.689735653030878 25 0.263544938303234 0.527089876606468 0.736455061696766 26 0.218803418037217 0.437606836074434 0.781196581962783 27 0.221415383046412 0.442830766092825 0.778584616953588 28 0.283831079311864 0.567662158623727 0.716168920688136 29 0.239653087467033 0.479306174934065 0.760346912532967 30 0.196696718946281 0.393393437892561 0.80330328105372 31 0.177312056990772 0.354624113981545 0.822687943009228 32 0.175947505554879 0.351895011109758 0.824052494445121 33 0.177928244848057 0.355856489696114 0.822071755151943 34 0.147378207043746 0.294756414087492 0.852621792956254 35 0.120591083920708 0.241182167841417 0.879408916079292 36 0.125019098294020 0.250038196588039 0.87498090170598 37 0.203509940733750 0.407019881467499 0.79649005926625 38 0.203571029506917 0.407142059013834 0.796428970493083 39 0.198903009318534 0.397806018637068 0.801096990681466 40 0.165150821497453 0.330301642994906 0.834849178502547 41 0.346964314816660 0.693928629633319 0.65303568518334 42 0.302059135977352 0.604118271954705 0.697940864022648 43 0.261417346468203 0.522834692936407 0.738582653531797 44 0.284001347472095 0.56800269494419 0.715998652527905 45 0.25333626316953 0.50667252633906 0.74666373683047 46 0.215003756843434 0.430007513686867 0.784996243156566 47 0.193879804829477 0.387759609658954 0.806120195170523 48 0.167914069959944 0.335828139919888 0.832085930040056 49 0.144359579025985 0.288719158051970 0.855640420974015 50 0.117422202088749 0.234844404177499 0.88257779791125 51 0.094480204024032 0.188960408048064 0.905519795975968 52 0.0775482616842252 0.155096523368450 0.922451738315775 53 0.0612297720224212 0.122459544044842 0.938770227977579 54 0.0475873413826082 0.0951746827652165 0.952412658617392 55 0.0493989202252736 0.0987978404505472 0.950601079774726 56 0.0431515600420855 0.086303120084171 0.956848439957914 57 0.0369036006352965 0.073807201270593 0.963096399364703 58 0.0286550421019723 0.0573100842039445 0.971344957898028 59 0.0273587144632939 0.0547174289265879 0.972641285536706 60 0.0262464631276883 0.0524929262553766 0.973753536872312 61 0.0200243638207713 0.0400487276415426 0.979975636179229 62 0.0281429024562453 0.0562858049124906 0.971857097543755 63 0.0514392932661093 0.102878586532219 0.94856070673389 64 0.0452354423506916 0.0904708847013832 0.954764557649308 65 0.0750976165110857 0.150195233022171 0.924902383488914 66 0.0720652623629047 0.144130524725809 0.927934737637095 67 0.0632542038322498 0.126508407664500 0.93674579616775 68 0.0598660402716328 0.119732080543266 0.940133959728367 69 0.0775545504411773 0.155109100882355 0.922445449558823 70 0.0625400349165219 0.125080069833044 0.937459965083478 71 0.0515073203203703 0.103014640640741 0.94849267967963 72 0.0408657402006225 0.081731480401245 0.959134259799377 73 0.031639793979056 0.063279587958112 0.968360206020944 74 0.0344073886215028 0.0688147772430056 0.965592611378497 75 0.0625956641472831 0.125191328294566 0.937404335852717 76 0.0578082094842742 0.115616418968548 0.942191790515726 77 0.0681760637580035 0.136352127516007 0.931823936241996 78 0.0572851083667474 0.114570216733495 0.942714891633253 79 0.0568688236800573 0.113737647360115 0.943131176319943 80 0.0595569375324891 0.119113875064978 0.94044306246751 81 0.0477066246281427 0.0954132492562853 0.952293375371857 82 0.0371307665640784 0.0742615331281569 0.962869233435922 83 0.0291248456595014 0.0582496913190028 0.970875154340499 84 0.0226771704302866 0.0453543408605733 0.977322829569713 85 0.0174386774946584 0.0348773549893168 0.982561322505342 86 0.0132775689242244 0.0265551378484487 0.986722431075776 87 0.0100566116516288 0.0201132233032576 0.989943388348371 88 0.0100334654062911 0.0200669308125822 0.989966534593709 89 0.00770503761784719 0.0154100752356944 0.992294962382153 90 0.00595094391513559 0.0119018878302712 0.994049056084864 91 0.005660624050025 0.01132124810005 0.994339375949975 92 0.00604493938334572 0.0120898787666914 0.993955060616654 93 0.00995779636927458 0.0199155927385492 0.990042203630725 94 0.00767826650655112 0.0153565330131022 0.992321733493449 95 0.0181063512359237 0.0362127024718474 0.981893648764076 96 0.0491500918537131 0.0983001837074262 0.950849908146287 97 0.0381616505899197 0.0763233011798393 0.96183834941008 98 0.0341188557422727 0.0682377114845453 0.965881144257727 99 0.0279240956191711 0.0558481912383422 0.972075904380829 100 0.0212458343524731 0.0424916687049463 0.978754165647527 101 0.0179548502724370 0.0359097005448739 0.982045149727563 102 0.053950248902692 0.107900497805384 0.946049751097308 103 0.158815198445543 0.317630396891086 0.841184801554457 104 0.132282727842871 0.264565455685743 0.867717272157129 105 0.111632355349783 0.223264710699567 0.888367644650217 106 0.0917543507227724 0.183508701445545 0.908245649277228 107 0.0730588225323481 0.146117645064696 0.926941177467652 108 0.0739673198193451 0.147934639638690 0.926032680180655 109 0.0609503499999745 0.121900699999949 0.939049650000025 110 0.05005239415528 0.10010478831056 0.94994760584472 111 0.0444545553553284 0.0889091107106568 0.955545444644672 112 0.0342832573296709 0.0685665146593418 0.96571674267033 113 0.0416858504375666 0.0833717008751331 0.958314149562433 114 0.0423074372237839 0.0846148744475678 0.957692562776216 115 0.059188907405616 0.118377814811232 0.940811092594384 116 0.0450925471098958 0.0901850942197916 0.954907452890104 117 0.0495959194817582 0.0991918389635165 0.950404080518242 118 0.0371713812180882 0.0743427624361765 0.962828618781912 119 0.0322061731332867 0.0644123462665735 0.967793826866713 120 0.0482843279871672 0.0965686559743344 0.951715672012833 121 0.0549748653031905 0.109949730606381 0.94502513469681 122 0.0445337125827382 0.0890674251654763 0.955466287417262 123 0.0618704116033677 0.123740823206735 0.938129588396632 124 0.0519099564389943 0.103819912877989 0.948090043561006 125 0.054451736612561 0.108903473225122 0.945548263387439 126 0.0681819738521 0.1363639477042 0.9318180261479 127 0.0496362458125791 0.0992724916251583 0.95036375418742 128 0.431921033602399 0.863842067204797 0.568078966397601 129 0.379785112281208 0.759570224562416 0.620214887718792 130 0.37717878379637 0.75435756759274 0.62282121620363 131 0.328155949354323 0.656311898708647 0.671844050645677 132 0.345407148156583 0.690814296313165 0.654592851843417 133 0.361782784716562 0.723565569433123 0.638217215283438 134 0.287992734192361 0.575985468384722 0.712007265807639 135 0.410456396075344 0.820912792150687 0.589543603924656 136 0.325556826645612 0.651113653291225 0.674443173354388 137 0.274934258083797 0.549868516167594 0.725065741916203 138 0.319242978727259 0.638485957454518 0.680757021272741 139 0.232438664446921 0.464877328893842 0.767561335553079 140 0.156246339329539 0.312492678659077 0.843753660670461 141 0.263824019985469 0.527648039970939 0.73617598001453 142 0.207174397351003 0.414348794702005 0.792825602648997 143 0.131563968469549 0.263127936939098 0.868436031530451 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 15 0.108695652173913 NOK 10% type I error level 45 0.326086956521739 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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