workshop 10c

*The author of this computation has been verified*

R Software Module: Patrick.Wessa/rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 12 Dec 2010 13:04:15 +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/12/t1292159150fwui6aku241avp7.htm/, Retrieved Sun, 12 Dec 2010 14:06:00 +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/12/t1292159150fwui6aku241avp7.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 «

11 6 6 4 15 16 2 40 37 15 10 77 26 16 5 4 23 24 1 29 31 9 20 63 26 13 20 10 26 22 1 37 35 12 16 73 15 7 12 6 19 21 1 32 36 15 10 76 10 10 11 5 19 23 1 39 32 17 8 90 21 10 12 8 16 23 1 32 30 14 14 67 27 15 11 9 23 21 2 35 34 9 19 69 21 9 9 9 22 20 2 35 34 12 15 70 21 12 13 8 19 22 1 28 22 11 23 54 21 8 9 11 24 20 1 37 27 13 9 54 22 9 14 6 19 12 2 32 27 16 12 76 29 10 12 8 25 23 2 34 33 16 14 75 29 15 18 11 23 23 2 37 38 15 13 76 29 11 9 5 31 30 1 35 37 10 11 80 30 12 15 10 29 22 2 40 31 16 11 89 19 9 12 7 18 21 1 37 36 12 10 73 19 10 12 7 17 21 1 37 38 15 12 74 22 13 12 13 22 15 2 33 31 13 18 78 18 8 15 10 21 22 2 37 34 18 12 76 28 14 11 8 24 24 1 35 33 13 10 69 17 9 13 6 22 23 2 36 38 17 15 74 18 12 10 8 16 15 2 32 28 14 15 82 20 8 17 7 22 24 1 38 34 13 12 77 16 8 13 5 21 24 2 34 32 13 9 84 17 9 17 9 25 21 2 33 34 15 11 75 25 14 15 11 22 21 2 33 39 15 16 79 22 11 13 11 24 18 2 42 37 13 17 79 34 16 18 11 21 20 2 33 34 14 12 69 31 9 17 9 25 19 2 32 41 13 11 88 38 11 21 7 29 29 2 32 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Person-Standards[t] = + 3.84738057444685 + 0.328446319879134Mistakes[t] -0.354503027876362Doubts[t] + 0.163700499059318`P-Expectations`[t] + 0.0505586668721037`P-Criticism`[t] + 0.440539729096576Organization[t] + 0.969401241072715Gender[t] + 0.162183660907544connected[t] -0.0530528042838888separate[t] -0.0554072382256775hapiness[t] + 0.0229805470290063depression[t] -0.0305734635206916sport[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) 3.84738057444685 5.905611 0.6515 0.515821 0.25791 Mistakes 0.328446319879134 0.057985 5.6643 0 0 Doubts -0.354503027876362 0.12082 -2.9342 0.003918 0.001959 `P-Expectations` 0.163700499059318 0.108013 1.5156 0.131916 0.065958 `P-Criticism` 0.0505586668721037 0.136007 0.3717 0.71066 0.35533 Organization 0.440539729096576 0.081199 5.4255 0 0 Gender 0.969401241072715 0.681577 1.4223 0.157198 0.078599 connected 0.162183660907544 0.093628 1.7322 0.085471 0.042736 separate -0.0530528042838888 0.088316 -0.6007 0.549016 0.274508 hapiness -0.0554072382256775 0.155465 -0.3564 0.722087 0.361043 depression 0.0229805470290063 0.116297 0.1976 0.843647 0.421824 sport -0.0305734635206916 0.029014 -1.0537 0.293847 0.146923 Multiple Linear Regression - Regression Statistics Multiple R 0.63489725645034 R-squared 0.403094526248169 Adjusted R-squared 0.355515104427371 F-TEST (value) 8.47203498534248 F-TEST (DF numerator) 11 F-TEST (DF denominator) 138 p-value 2.73046030230262e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.4320284582129 Sum Squared Residuals 1625.47706864169 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 17.0740806190035 -2.07408061900347 2 23 20.3715351757218 2.62846482427823 3 26 23.8342038204049 2.16579617959509 4 19 19.1361375836983 -0.136137583698324 5 19 17.8599099766246 1.14009002337539 6 16 21.7663106350127 -5.76631063501266 7 23 22.5447851304171 0.45521486958288 8 22 21.6444672848715 0.355532715128475 9 19 21.3266548035707 -2.32665480357069 10 24 22.1223082531530 1.87769174684696 11 19 18.5262295388090 0.473770461190965 12 25 25.173089159465 -0.173089159464980 13 23 24.7575932040346 -1.75759320403456 14 31 26.3507924108332 4.64920758916675 15 29 25.5264459690533 3.47355403094668 16 18 20.8603358841111 -2.86033588411107 17 17 20.2488931635272 -3.24889316352721 18 22 18.6492767981611 3.35072320183892 19 21 22.6670139427815 -1.6670139427815 20 24 23.1539926856376 0.846007314362358 21 22 21.7060695868265 0.29393041317349 22 16 16.8601322325904 -0.860132232590415 23 22 23.8199561856778 -1.81995618567777 24 21 21.8940678964582 -0.89406789645821 25 25 21.3454471847145 3.6545528152855 26 22 21.7015637996342 0.298436200365845 27 24 21.8302673184335 2.16973268156649 28 21 24.533620097611 -3.53362009761103 29 25 24.2424223646168 0.757577635383178 30 29 32.0966144885543 -3.09661448855428 31 19 18.9849972890866 0.0150027109133627 32 29 23.2173401910371 5.78265980896294 33 25 23.7500060935151 1.24999390648491 34 19 21.6515247674234 -2.65152476742336 35 27 24.4446310225521 2.55536897744787 36 25 23.8829977707982 1.11700222920184 37 23 20.8247811777539 2.17521882224607 38 24 22.219675981378 1.780324018622 39 23 22.0031827554594 0.996817244540579 40 25 23.0810358701340 1.91896412986595 41 23 20.4586980093626 2.54130199063740 42 22 21.8314665555461 0.168533444453873 43 32 25.1635104081427 6.83648959185733 44 22 22.1651352309697 -0.165135230969673 45 18 22.5166334929058 -4.51663349290582 46 19 19.5390899878252 -0.539089987825227 47 23 18.3888232815704 4.61117671842957 48 19 22.3964936132109 -3.39649361321093 49 16 19.697831673144 -3.69783167314402 50 23 22.9263214138546 0.0736785861454138 51 17 19.1138547918179 -2.1138547918179 52 17 23.2533948546980 -6.25339485469803 53 28 23.2344950172915 4.7655049827085 54 24 19.0236089659178 4.97639103408225 55 21 16.6028763865689 4.39712361343114 56 14 18.1512862601056 -4.15128626010555 57 21 21.3879960128425 -0.387996012842517 58 20 23.0278722594801 -3.02787225948007 59 25 22.2889892026020 2.71101079739803 60 20 22.2586736671871 -2.25867366718711 61 17 19.6152562545267 -2.61525625452672 62 26 27.3560883694443 -1.35608836944427 63 17 17.1699587552859 -0.169958755285926 64 17 22.2473931186814 -5.24739311868136 65 24 23.4526619727744 0.547338027225605 66 30 26.7345931283344 3.26540687166560 67 25 25.4206022933960 -0.420602293395971 68 15 22.381999432999 -7.38199943299899 69 25 20.3830706580772 4.61692934192279 70 18 27.0793329461060 -9.07933294610603 71 20 25.8280089161154 -5.82800891611541 72 32 28.6888068626643 3.31119313733570 73 14 16.2529313064501 -2.25293130645009 74 20 20.3604589824629 -0.360458982462942 75 25 25.1125461880958 -0.112546188095794 76 25 23.8187478400558 1.18125215994420 77 25 22.5193132774083 2.48068672259173 78 35 22.9243965699186 12.0756034300814 79 29 24.6692755730122 4.33072442698776 80 25 24.1651958351268 0.834804164873185 81 21 22.0832609370322 -1.08326093703216 82 21 20.9245518809838 0.0754481190161932 83 24 24.1246397385776 -0.124639738577637 84 26 21.9869535922507 4.01304640774934 85 24 22.7442343495376 1.25576565046242 86 20 22.4187044772761 -2.41870447727607 87 24 22.0153542481331 1.98464575186689 88 18 20.1514057651612 -2.15140576516123 89 17 17.0438853055198 -0.0438853055197641 90 22 25.9721343619424 -3.97213436194241 91 22 22.7662670233775 -0.766267023377484 92 22 20.6834843640047 1.31651563599531 93 24 25.2559147275626 -1.25591472756256 94 32 25.6201782731591 6.37982172684093 95 19 17.8458114318772 1.15418856812280 96 21 21.6633869624894 -0.663386962489435 97 23 22.4324530082683 0.567546991731743 98 26 23.1149859583319 2.8850140416681 99 18 23.0488720328140 -5.04887203281405 100 19 21.1443370556301 -2.14433705563008 101 22 23.5597892702048 -1.55978927020481 102 27 20.9678214080211 6.03217859197892 103 21 21.2005620328168 -0.200562032816824 104 20 22.8546394220854 -2.85463942208538 105 21 24.3554460231998 -3.35544602319977 106 20 24.8628848564903 -4.86288485649034 107 29 24.3453744834521 4.65462551654795 108 30 23.4053142810518 6.59468571894822 109 10 17.1394165818265 -7.13941658182648 110 23 22.8129346642132 0.187065335786822 111 29 20.7277139995063 8.27228600049367 112 19 17.8561092704091 1.14389072959089 113 26 24.3659709416066 1.63402905839344 114 22 22.3815146209505 -0.381514620950453 115 26 24.5302566879347 1.46974331206527 116 27 27.3931475092359 -0.393147509235885 117 19 23.7776546605799 -4.77765466057991 118 24 23.6462382828210 0.353761717179024 119 26 21.7193375628655 4.2806624371345 120 22 21.2368090873668 0.763190912633181 121 23 23.4706958555525 -0.470695855552488 122 25 23.9388487562216 1.06115124377836 123 19 21.8886884837636 -2.88868848376364 124 20 22.8889528010285 -2.88895280102850 125 25 27.4208080341128 -2.42080803411276 126 14 15.4670098941009 -1.4670098941009 127 19 20.0104786659160 -1.01047866591595 128 27 25.9033778101959 1.0966221898041 129 21 24.4784741301668 -3.47847413016677 130 21 20.144250216385 0.855749783615 131 14 20.1815639394191 -6.18156393941906 132 21 24.9376480249430 -3.93764802494304 133 23 20.2649322711384 2.73506772886163 134 18 22.114907220133 -4.114907220133 135 20 19.1566420127622 0.843357987237819 136 19 23.0840626345285 -4.08406263452846 137 15 18.3728049300077 -3.37280493000771 138 23 21.734451295496 1.26554870450399 139 26 26.6250982146054 -0.625098214605373 140 21 22.7029277856591 -1.70292778565911 141 13 16.1324708726183 -3.13247087261825 142 24 21.7372936959061 2.26270630409391 143 17 18.8318118401506 -1.83181184015059 144 21 23.2303674431162 -2.23036744311617 145 28 26.0373592150529 1.96264078494714 146 22 21.0819354421218 0.91806455787817 147 25 19.7682000445561 5.23179995544386 148 27 23.4410968079910 3.55890319200903 149 25 20.9409358161876 4.05906418381244 150 21 22.5400752264709 -1.54007522647091 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.50570433995483 0.98859132009034 0.49429566004517 16 0.56674172620239 0.86651654759522 0.43325827379761 17 0.452298813533519 0.904597627067038 0.547701186466481 18 0.332110814992127 0.664221629984254 0.667889185007873 19 0.267303909781978 0.534607819563956 0.732696090218022 20 0.180389473673302 0.360778947346605 0.819610526326698 21 0.243689732385566 0.487379464771132 0.756310267614434 22 0.201381783604653 0.402763567209307 0.798618216395347 23 0.151383518668402 0.302767037336803 0.848616481331598 24 0.101774536644420 0.203549073288840 0.89822546335558 25 0.178392699563939 0.356785399127879 0.82160730043606 26 0.127536616213236 0.255073232426471 0.872463383786764 27 0.0963459576229729 0.192691915245946 0.903654042377027 28 0.101773135977076 0.203546271954151 0.898226864022924 29 0.0708732161108077 0.141746432221615 0.929126783889192 30 0.0503888980557616 0.100777796111523 0.949611101944238 31 0.0371984558010342 0.0743969116020683 0.962801544198966 32 0.139957830049939 0.279915660099878 0.860042169950061 33 0.11020783320975 0.2204156664195 0.88979216679025 34 0.102568420982843 0.205136841965686 0.897431579017157 35 0.104132466527874 0.208264933055747 0.895867533472126 36 0.0785148637307427 0.157029727461485 0.921485136269257 37 0.0592968961664551 0.118593792332910 0.940703103833545 38 0.0436712748608008 0.0873425497216015 0.9563287251392 39 0.0308847513990878 0.0617695027981755 0.969115248600912 40 0.0247597715392034 0.0495195430784068 0.975240228460797 41 0.020825046104566 0.041650092209132 0.979174953895434 42 0.0140122926574750 0.0280245853149499 0.985987707342525 43 0.0262648031561995 0.052529606312399 0.9737351968438 44 0.0181581206699040 0.0363162413398079 0.981841879330096 45 0.0343676962722497 0.0687353925444993 0.96563230372775 46 0.0248017101182232 0.0496034202364465 0.975198289881777 47 0.0330221320535262 0.0660442641070524 0.966977867946474 48 0.0274650716435383 0.0549301432870766 0.972534928356462 49 0.0242033527697656 0.0484067055395312 0.975796647230234 50 0.0170747227485034 0.0341494454970068 0.982925277251497 51 0.0141249377000597 0.0282498754001195 0.98587506229994 52 0.0225905808629525 0.0451811617259049 0.977409419137047 53 0.0260422450595502 0.0520844901191005 0.97395775494045 54 0.0319035416421234 0.0638070832842469 0.968096458357877 55 0.0459365948531474 0.0918731897062949 0.954063405146853 56 0.0474004647938451 0.0948009295876902 0.952599535206155 57 0.0354790922841108 0.0709581845682216 0.96452090771589 58 0.0311187359873525 0.0622374719747051 0.968881264012647 59 0.0282562234707771 0.0565124469415543 0.971743776529223 60 0.0229621466571950 0.0459242933143901 0.977037853342805 61 0.0179580316593750 0.0359160633187499 0.982041968340625 62 0.0175086427764834 0.0350172855529669 0.982491357223517 63 0.0127062228689386 0.0254124457378773 0.987293777131061 64 0.0294327249642981 0.0588654499285961 0.970567275035702 65 0.0217859231999235 0.0435718463998471 0.978214076800076 66 0.0232569615561086 0.0465139231122173 0.976743038443891 67 0.0180492766859583 0.0360985533719165 0.981950723314042 68 0.0481481725352638 0.0962963450705275 0.951851827464736 69 0.0769206895131697 0.153841379026339 0.92307931048683 70 0.254396786046152 0.508793572092304 0.745603213953848 71 0.35713622578779 0.71427245157558 0.64286377421221 72 0.374981726767687 0.749963453535374 0.625018273232313 73 0.360148136171089 0.720296272342178 0.639851863828911 74 0.318918895280034 0.637837790560069 0.681081104719966 75 0.276870100245021 0.553740200490042 0.723129899754979 76 0.246145712454039 0.492291424908078 0.753854287545961 77 0.230566989347688 0.461133978695377 0.769433010652312 78 0.801891704609365 0.396216590781270 0.198108295390635 79 0.849722924681618 0.300554150636765 0.150277075318382 80 0.823498465089975 0.35300306982005 0.176501534910025 81 0.791968672453814 0.416062655092372 0.208031327546186 82 0.759887183668997 0.480225632662007 0.240112816331003 83 0.727155970032122 0.545688059935756 0.272844029967878 84 0.739344589554657 0.521310820890686 0.260655410445343 85 0.705830574191575 0.58833885161685 0.294169425808425 86 0.687834717588444 0.624330564823111 0.312165282411555 87 0.66035959281959 0.67928081436082 0.33964040718041 88 0.655934711249567 0.688130577500865 0.344065288750433 89 0.606905685581063 0.786188628837873 0.393094314418937 90 0.617471269104713 0.765057461790574 0.382528730895287 91 0.567045531160929 0.865908937678142 0.432954468839071 92 0.519186476644015 0.96162704671197 0.480813523355985 93 0.481632037862927 0.963264075725854 0.518367962137073 94 0.571964556235816 0.856070887528369 0.428035443764184 95 0.525916196207305 0.94816760758539 0.474083803792695 96 0.474646757473258 0.949293514946515 0.525353242526742 97 0.423535623689969 0.847071247379938 0.576464376310031 98 0.400514037291615 0.80102807458323 0.599485962708385 99 0.430630208242826 0.861260416485652 0.569369791757174 100 0.389904921214165 0.77980984242833 0.610095078785835 101 0.366467133175697 0.732934266351393 0.633532866824303 102 0.472992575788364 0.945985151576728 0.527007424211636 103 0.42110495783457 0.84220991566914 0.57889504216543 104 0.398243740269089 0.796487480538178 0.601756259730911 105 0.372189956512127 0.744379913024254 0.627810043487873 106 0.503155134490523 0.993689731018955 0.496844865509477 107 0.680833084565609 0.638333830868783 0.319166915434391 108 0.769586899217357 0.460826201565285 0.230413100782643 109 0.925777693690912 0.148444612618175 0.0742223063090876 110 0.901973873934944 0.196052252130111 0.0980261260650557 111 0.95741069029651 0.0851786194069823 0.0425893097034911 112 0.9417369550456 0.116526089908801 0.0582630449544005 113 0.923375258518779 0.153249482962442 0.0766247414812212 114 0.897374512352715 0.205250975294570 0.102625487647285 115 0.87818708424883 0.243625831502339 0.121812915751169 116 0.843947118202328 0.312105763595345 0.156052881797672 117 0.855798477597275 0.288403044805450 0.144201522402725 118 0.81782491081764 0.364350178364719 0.182175089182360 119 0.890948429857229 0.218103140285542 0.109051570142771 120 0.853662754272916 0.292674491454167 0.146337245727083 121 0.821453642151388 0.357092715697224 0.178546357848612 122 0.773250107104297 0.453499785791406 0.226749892895703 123 0.787732364398066 0.424535271203867 0.212267635601933 124 0.770894576792114 0.458210846415771 0.229105423207885 125 0.714298073395843 0.571403853208315 0.285701926604157 126 0.682926254829113 0.634147490341774 0.317073745170887 127 0.598221540539809 0.803556918920382 0.401778459460191 128 0.701534819377031 0.596930361245939 0.298465180622970 129 0.654642622028861 0.690714755942277 0.345357377971139 130 0.780203156252218 0.439593687495565 0.219796843747782 131 0.705299451597922 0.589401096804156 0.294700548402078 132 0.732830995100679 0.534338009798642 0.267169004899321 133 0.74239496538005 0.515210069239901 0.257605034619950 134 0.632528259468402 0.734943481063196 0.367471740531598 135 0.499343199243652 0.998686398487304 0.500656800756348 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 16 0.132231404958678 NOK 10% type I error level 33 0.272727272727273 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/101vs81292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/101vs81292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/153uz1292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/153uz1292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/253uz1292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/253uz1292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/353uz1292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/353uz1292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/4yub21292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/4yub21292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/5yub21292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/5yub21292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/6yub21292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/6yub21292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/7qmt51292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/7qmt51292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/81vs81292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/81vs81292159043.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/91vs81292159043.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292159150fwui6aku241avp7/91vs81292159043.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 0 ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 0 ;

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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