*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: Sun, 19 Dec 2010 15:06:30 +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/19/t12927710675ih6ps3ehb3t23b.htm/, Retrieved Sun, 19 Dec 2010 16:04:27 +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/19/t12927710675ih6ps3ehb3t23b.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:

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9 24 14 11 12 24 26 9 25 11 7 8 25 23 9 17 6 17 8 30 25 9 18 12 10 8 19 23 9 18 8 12 9 22 19 9 16 10 12 7 22 29 10 20 10 11 4 25 25 10 16 11 11 11 23 21 10 18 16 12 7 17 22 10 17 11 13 7 21 25 10 23 13 14 12 19 24 10 30 12 16 10 19 18 10 23 8 11 10 15 22 10 18 12 10 8 16 15 10 15 11 11 8 23 22 10 12 4 15 4 27 28 10 21 9 9 9 22 20 10 15 8 11 8 14 12 10 20 8 17 7 22 24 10 31 14 17 11 23 20 10 27 15 11 9 23 21 10 34 16 18 11 21 20 10 21 9 14 13 19 21 10 31 14 10 8 18 23 10 19 11 11 8 20 28 10 16 8 15 9 23 24 10 20 9 15 6 25 24 10 21 9 13 9 19 24 10 22 9 16 9 24 23 10 17 9 13 6 22 23 10 24 10 9 6 25 29 10 25 16 18 16 26 24 10 26 11 18 5 29 18 10 25 8 12 7 32 25 10 17 9 17 9 25 21 10 32 16 9 6 29 26 10 33 11 9 6 28 22 10 13 16 12 5 17 22 10 32 12 18 12 28 22 10 25 12 12 7 29 23 10 29 14 18 10 26 30 10 22 9 14 9 25 23 10 18 10 15 8 14 17 10 17 9 16 5 25 23 10 20 10 10 8 26 23 10 15 12 11 8 20 25 10 20 14 14 10 18 24 10 33 14 9 6 32 24 10 29 10 12 8 25 23 10 23 14 17 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 20.5443468355652 -1.34456042983868Month[t] + 0.317541932006347ConcernOverMistakes[t] -0.333075539403863DoubtsAboutActions[t] + 0.190532531457494ParentalExpectations[t] + 0.0631702202398643ParentalCriticism[t] + 0.39852922691684Organization[t] -0.00145199529513204t + 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) 20.5443468355652 15.111514 1.3595 0.17601 0.088005 Month -1.34456042983868 1.517767 -0.8859 0.377091 0.188545 ConcernOverMistakes 0.317541932006347 0.054868 5.7874 0 0 DoubtsAboutActions -0.333075539403863 0.107661 -3.0938 0.002355 0.001178 ParentalExpectations 0.190532531457494 0.10231 1.8623 0.064504 0.032252 ParentalCriticism 0.0631702202398643 0.131179 0.4816 0.630818 0.315409 Organization 0.39852922691684 0.073724 5.4057 0 0 t -0.00145199529513204 0.006409 -0.2266 0.821062 0.410531 Multiple Linear Regression - Regression Statistics Multiple R 0.607791545143314 R-squared 0.369410562347697 Adjusted R-squared 0.340177939410173 F-TEST (value) 12.6369283774912 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 1.05226938273972e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40786144542361 Sum Squared Residuals 1753.64146431191 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.6154601769689 -0.615460176968857 2 25 23.7203780443517 1.27962195564829 3 30 25.5463520584338 4.45364794156625 4 19 21.7332025846856 -2.73320258468564 5 22 21.9141711224935 0.085828877506543 6 22 24.4704360130666 -2.47043601306658 7 25 22.4204312161137 2.57956878388629 8 23 19.663810587401 3.33618941259899 9 17 18.9684456365141 -1.96844563651413 10 21 21.70094961844 -0.700949618439988 11 19 23.0464525421152 -4.04645254211519 12 19 23.4644188712026 -4.46441887120256 13 15 23.2139297598583 -8.21392975985835 14 16 17.1858883865609 -1.18588838656092 15 23 19.545123254526 3.45487674547401 16 27 23.8231988454104 3.17680115458958 17 22 20.9986686382727 1.00133136172727 18 14 16.5547016176838 -2.55470161768378 19 22 24.0033349739276 -2.00333497392757 20 23 24.1549549675712 -1.15495496757116 21 23 21.6792533025389 1.32074669746107 22 21 24.6290582256497 -3.62905822564971 23 19 22.5938294316657 -3.59382943166571 24 18 23.8214962862191 -5.8214962862191 25 20 23.1919463911011 -3.1919463911011 26 23 22.468278656401 0.531721343599004 27 25 23.2144081890078 1.78559181099220 28 19 23.3389437235236 -4.33894372352361 29 24 23.8281020276905 0.171897972309529 30 22 21.4778321172715 0.52216788272847 31 25 24.995143342288 0.00485665771197539 32 26 23.6666288935079 2.33337110649205 33 29 22.5620487430989 6.43795125690107 34 32 25.0151312741617 6.98486872583831 35 25 21.6251544735118 3.37484552648824 36 29 24.3341779046894 4.66582209531057 37 28 24.7215286307526 3.27847136924739 38 17 17.2122876724438 -0.212287672443842 39 28 26.1618212733088 1.83817872669123 40 29 22.8770586909418 6.12294130905824 41 26 27.6020337827467 -1.60203378274673 42 25 23.4281610259388 1.57183897406123 43 14 19.5596527129310 -5.55965271293097 44 25 21.9659315572723 3.0340684427277 45 26 21.6303452905670 4.36965470943303 46 20 20.3626235417236 -0.362623541723554 47 18 21.5821389355878 -3.5821389355878 48 32 24.5033885181282 7.49661148187175 49 25 24.8634797603586 0.136520239641448 50 25 21.7169079986238 3.28309200137619 51 23 20.721617363081 2.27838263691901 52 21 22.0977672887240 -1.09776728872405 53 20 23.9924405257051 -3.99244052570510 54 15 16.2871865072618 -1.2871865072618 55 30 27.0522222750069 2.94777772499308 56 24 25.2926387405630 -1.29263874056304 57 26 24.2231871816204 1.77681281837957 58 23 19.4826874568353 3.51731254316469 59 22 21.2372761778482 0.7627238221518 60 14 15.8198290780372 -1.81982907803719 61 24 22.2288568462182 1.77114315378178 62 24 22.7669896833657 1.23301031663433 63 22 23.0431118514054 -1.04311185140537 64 24 20.0490812819769 3.95091871802311 65 19 18.4269079353388 0.573092064661235 66 31 26.5343166342632 4.46568336573675 67 22 26.3465754833259 -4.34657548332594 68 27 21.3870221467152 5.61297785328475 69 19 17.7740275465564 1.22597245344365 70 25 22.248560854076 2.75143914592402 71 20 24.7184455635103 -4.71844556351032 72 21 21.3529722732986 -0.352972273298564 73 27 27.3096048400485 -0.309604840048460 74 23 24.4945080304255 -1.49450803042549 75 25 25.4484932337964 -0.448493233796377 76 20 22.1219658415182 -2.12196584151823 77 21 19.2711013671893 1.7288986328107 78 22 22.4576498720129 -0.457649872012915 79 23 22.9884598012194 0.0115401987805513 80 25 23.8335132988602 1.16648670113983 81 25 23.4904520408654 1.50954795913462 82 17 23.6599599704579 -6.65995997045786 83 19 21.3996286900062 -2.39962869000622 84 25 23.9079334090061 1.09206659099392 85 19 22.2161303011981 -3.21613030119806 86 20 23.033834071491 -3.03383407149098 87 25 22.3042715925031 2.69572840749686 88 23 20.8485405052727 2.15145949472735 89 27 24.5643291580915 2.43567084190848 90 17 20.7682999591211 -3.76829995912113 91 17 23.2971622941603 -6.29716229416034 92 19 19.9431836121737 -0.94318361217374 93 17 19.5773630567943 -2.57736305679429 94 22 21.8250159211754 0.174984078824584 95 21 23.4842690128125 -2.48426901281247 96 32 28.5933811903275 3.40661880967254 97 21 24.6717083507703 -3.67170835077026 98 21 24.3919229885562 -3.39192298855623 99 18 21.0883075408688 -3.0883075408688 100 18 21.1630501000525 -3.16305010005252 101 23 22.7836039939921 0.216396006007864 102 19 20.4167646855259 -1.41676468552588 103 19 23.3322872993455 -4.33228729934554 104 21 22.2562186537996 -1.25621865379957 105 20 23.8715975447009 -3.8715975447009 106 17 18.6099691353834 -1.60996913538337 107 18 20.0696690113420 -2.06966901134195 108 19 20.6518170739204 -1.65181707392039 109 22 22.1379399582682 -0.137939958268183 110 15 18.7087038113505 -3.70870381135047 111 14 18.7016490908593 -4.70164909085932 112 18 26.5339534372729 -8.53395343727288 113 24 21.3186930698236 2.68130693017636 114 35 23.4396894443247 11.5603105556753 115 29 19.1764921232580 9.82350787674203 116 21 21.7038531359647 -0.703853135964666 117 25 20.2875265328775 4.71247346712253 118 19 20.2231146912019 -1.22311469120191 119 22 23.1926672455877 -1.19266724558766 120 13 16.5693318909854 -3.56933189098536 121 26 22.8219877945414 3.17801220545859 122 17 16.8084047756571 0.191595224342898 123 25 20.1773952428261 4.82260475717388 124 20 20.5026669685515 -0.502666968551508 125 19 18.2187115115903 0.781288488409747 126 21 22.5133858524599 -1.51338585245987 127 22 20.7355714410995 1.26442855890048 128 24 22.5628743538752 1.43712564612484 129 21 22.8941818485835 -1.89418184858355 130 26 25.290259634239 0.709740365761025 131 24 20.5759441403023 3.42405585969768 132 16 20.1509361203503 -4.15093612035027 133 23 22.0796289994686 0.920371000531403 134 18 20.4538876476656 -2.45388764766561 135 16 22.1982727089264 -6.19827270892642 136 26 24.0373752206743 1.96262477932572 137 19 18.9215881828753 0.0784118171247219 138 21 16.8435503307432 4.15644966925678 139 21 22.0501475256849 -1.05014752568494 140 22 18.6369453321101 3.36305466788988 141 23 19.6199455512131 3.38005444878689 142 29 24.6792438590453 4.32075614095474 143 21 19.6705334554183 1.32946654458167 144 21 19.7761829631607 1.22381703683931 145 23 21.9281702288537 1.07182977114626 146 27 22.8058392352872 4.19416076471282 147 25 25.1110595947121 -0.111059594712143 148 21 20.7456399450393 0.254360054960657 149 10 17.0011886052382 -7.00118860523817 150 20 22.4720036129577 -2.47200361295771 151 26 22.3308339322751 3.66916606772492 152 24 23.5585884292772 0.441411570722758 153 29 31.2800720226967 -2.2800720226967 154 19 18.6922053960791 0.307794603920859 155 24 22.1631390037223 1.83686099627767 156 22 20.7968412922494 1.20315870775063 157 24 23.2648168743218 0.735183125678164 158 22 21.7826009388685 0.217399061131487 159 19 23.2509755628181 -4.25097556281815 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.0477993147051032 0.0955986294102064 0.952200685294897 12 0.0144490054928866 0.0288980109857732 0.985550994507113 13 0.0653354410451843 0.130670882090369 0.934664558954816 14 0.125641389605271 0.251282779210543 0.874358610394729 15 0.580729561396217 0.838540877207566 0.419270438603783 16 0.526101017347537 0.947797965304925 0.473898982652462 17 0.572861771014859 0.854276457970282 0.427138228985141 18 0.531008253791037 0.937983492417926 0.468991746208963 19 0.452039652486717 0.904079304973434 0.547960347513283 20 0.560726085383884 0.878547829232233 0.439273914616116 21 0.575345763206358 0.849308473587284 0.424654236793642 22 0.50789145334768 0.98421709330464 0.49210854665232 23 0.449515791721746 0.899031583443492 0.550484208278254 24 0.462299505166648 0.924599010333296 0.537700494833352 25 0.409154964363566 0.818309928727131 0.590845035636434 26 0.35661004783477 0.71322009566954 0.64338995216523 27 0.322917871533897 0.645835743067795 0.677082128466103 28 0.305463862767436 0.610927725534872 0.694536137232564 29 0.266902753264103 0.533805506528205 0.733097246735897 30 0.214956144676834 0.429912289353669 0.785043855323166 31 0.184011046430381 0.368022092860762 0.81598895356962 32 0.225303532244413 0.450607064488827 0.774696467755587 33 0.318032200903403 0.636064401806807 0.681967799096597 34 0.54148344644783 0.91703310710434 0.45851655355217 35 0.493510367799752 0.987020735599504 0.506489632200248 36 0.501830320278492 0.996339359443015 0.498169679721508 37 0.465811235485127 0.931622470970255 0.534188764514873 38 0.496207631543304 0.992415263086608 0.503792368456696 39 0.443241630861509 0.886483261723019 0.556758369138491 40 0.474068356951109 0.948136713902217 0.525931643048891 41 0.464853350755543 0.929706701511086 0.535146649244457 42 0.414540260180431 0.829080520360862 0.585459739819569 43 0.623522967491294 0.752954065017413 0.376477032508706 44 0.591396279468569 0.817207441062862 0.408603720531431 45 0.580299981407849 0.839400037184302 0.419700018592151 46 0.542609751407607 0.914780497184786 0.457390248592393 47 0.568845869176787 0.862308261646427 0.431154130823213 48 0.652351782864302 0.695296434271395 0.347648217135698 49 0.623937192760621 0.752125614478757 0.376062807239379 50 0.60035282781643 0.799294344367139 0.399647172183570 51 0.566319252462551 0.867361495074897 0.433680747537449 52 0.541785506006094 0.916428987987811 0.458214493993906 53 0.600811151697671 0.798377696604659 0.399188848302329 54 0.576920089366981 0.846159821266039 0.423079910633019 55 0.596672119842571 0.806655760314858 0.403327880157429 56 0.57287739692248 0.85424520615504 0.42712260307752 57 0.530351787685096 0.939296424629807 0.469648212314904 58 0.523846665264392 0.952306669471216 0.476153334735608 59 0.480109777200272 0.960219554400544 0.519890222799728 60 0.45005560431613 0.90011120863226 0.54994439568387 61 0.409181858313862 0.818363716627723 0.590818141686138 62 0.375831334443078 0.751662668886156 0.624168665556922 63 0.344368791957969 0.688737583915938 0.655631208042031 64 0.358688579553876 0.717377159107753 0.641311420446124 65 0.319396407710402 0.638792815420803 0.680603592289598 66 0.339508416496954 0.679016832993908 0.660491583503046 67 0.430658638415186 0.861317276830371 0.569341361584814 68 0.500429668450226 0.999140663099548 0.499570331549774 69 0.46147313543214 0.92294627086428 0.53852686456786 70 0.445150830589446 0.890301661178892 0.554849169410554 71 0.535581861304422 0.928836277391155 0.464418138695578 72 0.494266033277097 0.988532066554194 0.505733966722903 73 0.459165732010826 0.918331464021652 0.540834267989174 74 0.430347263221608 0.860694526443215 0.569652736778392 75 0.405886116179535 0.811772232359069 0.594113883820465 76 0.380421257472327 0.760842514944653 0.619578742527673 77 0.359785138741109 0.719570277482217 0.640214861258891 78 0.320734638669827 0.641469277339654 0.679265361330173 79 0.283329099243829 0.566658198487659 0.71667090075617 80 0.263099816785428 0.526199633570856 0.736900183214572 81 0.238882354208839 0.477764708417677 0.761117645791161 82 0.34019501537892 0.68039003075784 0.65980498462108 83 0.315252797649315 0.63050559529863 0.684747202350685 84 0.284601870375966 0.569203740751933 0.715398129624034 85 0.279980432804311 0.559960865608623 0.720019567195689 86 0.268402248548380 0.536804497096759 0.73159775145162 87 0.281620486228191 0.563240972456382 0.718379513771809 88 0.27283772159317 0.54567544318634 0.72716227840683 89 0.264680544024125 0.529361088048251 0.735319455975875 90 0.25799815668345 0.5159963133669 0.74200184331655 91 0.324235401492015 0.64847080298403 0.675764598507985 92 0.282801648409032 0.565603296818064 0.717198351590968 93 0.254385501518886 0.508771003037772 0.745614498481114 94 0.226664990896849 0.453329981793697 0.773335009103151 95 0.202270772569564 0.404541545139128 0.797729227430436 96 0.225413018665835 0.450826037331671 0.774586981334165 97 0.213363466915261 0.426726933830521 0.78663653308474 98 0.196593106180592 0.393186212361183 0.803406893819408 99 0.175959618515543 0.351919237031087 0.824040381484457 100 0.158068396790124 0.316136793580247 0.841931603209876 101 0.132671828543327 0.265343657086655 0.867328171456673 102 0.108371651134512 0.216743302269024 0.891628348865488 103 0.111238700096056 0.222477400192111 0.888761299903944 104 0.0906307256316616 0.181261451263323 0.909369274368338 105 0.0972875216812718 0.194575043362544 0.902712478318728 106 0.0787828283292672 0.157565656658534 0.921217171670733 107 0.0676119581527791 0.135223916305558 0.93238804184722 108 0.0616230586628013 0.123246117325603 0.938376941337199 109 0.0509487268905939 0.101897453781188 0.949051273109406 110 0.0507024897207455 0.101404979441491 0.949297510279254 111 0.0630306368252847 0.126061273650569 0.936969363174715 112 0.37471594195935 0.7494318839187 0.62528405804065 113 0.396065767017274 0.792131534034548 0.603934232982726 114 0.777236468589418 0.445527062821164 0.222763531410582 115 0.944703825227534 0.110592349544932 0.0552961747724658 116 0.92696163895201 0.146076722095981 0.0730383610479903 117 0.961282129391954 0.0774357412160923 0.0387178706080461 118 0.952686405316563 0.0946271893668732 0.0473135946834366 119 0.946333602324715 0.107332795350570 0.0536663976752852 120 0.955537504985884 0.088924990028232 0.044462495014116 121 0.94545858358664 0.109082832826721 0.0545414164133605 122 0.926410162352212 0.147179675295576 0.0735898376477878 123 0.930201968433878 0.139596063132244 0.0697980315661218 124 0.906593504726756 0.186812990546488 0.0934064952732442 125 0.897408804868619 0.205182390262763 0.102591195131381 126 0.869686847682626 0.260626304634748 0.130313152317374 127 0.858412016813367 0.283175966373266 0.141587983186633 128 0.822520124924674 0.354959750150653 0.177479875075326 129 0.785631510235046 0.428736979529909 0.214368489764954 130 0.756669643427386 0.486660713145227 0.243330356572614 131 0.728441878977573 0.543116242044854 0.271558121022427 132 0.742964464855606 0.514071070288788 0.257035535144394 133 0.699744922384611 0.600510155230778 0.300255077615389 134 0.641156486173096 0.717687027653807 0.358843513826904 135 0.877761802088364 0.244476395823273 0.122238197911636 136 0.834019475099343 0.331961049801315 0.165980524900657 137 0.78982252669633 0.420354946607341 0.210177473303671 138 0.79575811486991 0.40848377026018 0.20424188513009 139 0.781703414312484 0.436593171375031 0.218296585687516 140 0.71358677564883 0.572826448702339 0.286413224351170 141 0.640580769608577 0.718838460782846 0.359419230391423 142 0.597856761483372 0.804286477033256 0.402143238516628 143 0.540158227201639 0.919683545596722 0.459841772798361 144 0.470879728138157 0.941759456276313 0.529120271861843 145 0.356802453877931 0.713604907755861 0.643197546122069 146 0.343077876374913 0.686155752749826 0.656922123625087 147 0.516330738520749 0.967338522958502 0.483669261479251 148 0.352999393926963 0.705998787853926 0.647000606073037 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 1 0.0072463768115942 OK 10% type I error level 5 0.036231884057971 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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