ws7

*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 18:48:03 +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/t1290538406q1w1e77gq345j98.htm/, Retrieved Tue, 23 Nov 2010 19:53:27 +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/Nov/23/t1290538406q1w1e77gq345j98.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 «

7 7 1 7 7 1 7 7 5 6 1 5 5 1 5 5 6 6 2 5 6 1 4 5 4 5 2 5 6 2 5 6 5 6 2 5 6 2 5 6 6 7 1 7 5 1 6 7 7 7 1 7 7 1 7 6 6 7 1 5 6 1 5 7 6 7 1 3 7 2 7 7 6 6 1 6 6 1 5 6 5 4 1 7 7 1 4 7 5 6 1 6 7 1 6 7 4 6 1 5 6 1 4 5 6 7 1 3 6 1 6 6 6 6 1 7 7 1 7 7 5 6 2 5 6 3 6 6 3 4 1 7 7 1 4 7 7 7 1 7 7 1 6 7 3 7 1 7 7 1 6 7 5 6 2 6 7 2 6 6 3 3 1 5 5 1 4 4 5 7 1 7 7 NA 5 7 2 5 1 4 5 1 2 6 6 7 1 7 6 1 6 7 3 6 1 7 7 2 5 7 6 5 1 7 6 1 6 5 6 5 1 7 6 1 6 5 5 6 1 3 6 1 5 7 5 5 1 7 6 1 5 6 7 6 1 5 6 1 5 6 6 6 1 7 6 1 6 6 5 5 1 5 5 1 6 6 5 4 4 5 3 6 5 1 4 5 3 4 3 3 4 5 4 4 1 5 5 1 6 7 6 6 2 6 6 2 5 5 5 6 1 7 7 1 5 7 5 7 1 5 7 1 5 5 7 7 1 7 7 1 7 7 5 7 1 7 6 1 5 6 5 7 1 6 7 1 5 7 6 5 1 6 7 1 7 6 5 6 2 7 6 2 5 6 6 6 1 7 6 2 7 5 7 3 1 6 5 1 6 6 5 6 4 6 6 4 3 6 5 5 1 4 6 2 4 5 5 4 3 7 7 3 6 7 6 6 2 5 6 2 5 6 2 6 3 6 7 2 4 7 4 6 2 5 6 2 4 5 4 5 1 3 5 1 6 5 6 6 2 7 7 1 5 7 3 5 1 6 4 1 4 3 6 7 1 6 7 1 6 6 6 6 1 5 5 2 5 6 5 6 1 5 6 1 5 5 6 7 1 7 7 1 6 6 1 4 1 7 7 1 6 6 5 3 2 7 7 1 6 7 7 4 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 16 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Q1_2[t] = + 1.40959032447186 + 0.214052726496256Q1_3[t] -0.221309515615679Q1_5[t] + 0.139321285447932Q1_7[t] -0.170063333558011Q1_8[t] + 0.0973404013927267Q1_12[t] + 0.533060442743739Q1_16[t] + 0.000288089514899795Q1_22[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 1.40959032447186 0.743998 1.8946 0.060018 0.030009 Q1_3 0.214052726496256 0.080117 2.6718 0.008357 0.004179 Q1_5 -0.221309515615679 0.116417 -1.901 0.059169 0.029584 Q1_7 0.139321285447932 0.073452 1.8968 0.05973 0.029865 Q1_8 -0.170063333558011 0.114261 -1.4884 0.138695 0.069348 Q1_12 0.0973404013927267 0.097946 0.9938 0.321873 0.160937 Q1_16 0.533060442743739 0.086151 6.1875 0 0 Q1_22 0.000288089514899795 0.099806 0.0029 0.997701 0.49885 Multiple Linear Regression - Regression Statistics Multiple R 0.589668535792311 R-squared 0.347708982103448 Adjusted R-squared 0.318059390380877 F-TEST (value) 11.7272772373036 F-TEST (DF numerator) 7 F-TEST (DF denominator) 154 p-value 6.46072084720117e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.987559040203053 Sum Squared Residuals 150.192020114564 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7 6.30223568476263 0.69776431523737 2 5 5.08296998996925 -0.0829699899692469 3 6 4.15853669805182 1.84146330194818 4 4 4.57517290520693 -0.575172905206927 5 5 4.78922563170318 0.210774368296816 6 6 6.1093019091349 -0.109301909134906 7 7 6.30194759524773 0.698052404752275 8 6 5.12753556193729 0.872464438062708 9 6 5.84229094436362 0.157709055636378 10 6 5.05251603137407 0.947483968625932 11 5 4.06089617704264 0.939103822957362 12 5 5.4158012300747 -0.415801230074696 13 4 4.3798462136675 -0.379846213667498 14 6 5.38166534427027 0.618334655729733 15 6 6.08818295826637 -0.0881829582663672 16 5 5.41962647583965 -0.419626475839649 17 3 4.06089617704264 -1.06089617704264 18 7 5.76917524201888 1.23082475798112 19 3 5.76917524201888 -2.76917524201888 20 5 5.29154402633684 -0.291544026336844 21 3 3.90746327822184 -0.90746327822184 22 5 6.13070273930874 -1.13070273930874 23 2 1.93923857557690 0.060761424423105 24 6 8.11940247417162 -2.11940247417162 25 3 2.51055694355458 0.489443056445417 26 6 5.51055694355458 0.489443056445417 27 6 5.63484026454517 0.365159735454828 28 5 4.97778459032574 0.0222154096742560 29 5 2.91319474592614 2.08680525407386 30 7 6.72489775956574 0.275102240434261 31 6 6.40226579573163 -0.402265795731630 32 5 4.81661230614975 0.183387693850248 33 5 5.28872397395144 -0.288723973951436 34 4 5.18850115875027 -1.18850115875027 35 4 2.92825882763622 1.07174117236378 36 6 6.02206207277889 -0.0220620727788895 37 5 4.95689604934948 0.0431039506505178 38 5 4.30223568476262 0.697764315237376 39 7 7.40589004331826 -0.405890043318256 40 5 5.09679351382721 -0.0967935138272135 41 5 4.73452085680728 0.265479143192721 42 6 6.06786820259905 -0.0678682025990474 43 5 5.3550105141873 -0.355010514187305 44 6 4.11348162818705 1.88651837181295 45 7 5.61448780321773 1.38551219678227 46 5 4.12381260311604 0.876187396883964 47 5 4.87907883408421 0.120921165915790 48 5 3.78922563170318 1.21077436829682 49 6 8.00440171474859 -2.00440171474859 50 2 2.25587709944454 -0.255877099444545 51 4 5.12333513532087 -1.12333513532087 52 4 2.80075255716321 1.19924744283679 53 6 7.6446652607054 -1.64466526070540 54 3 2.62956586705605 0.370434132943947 55 6 5.18059848087687 0.819401519123126 56 6 5.91290665641124 0.0870933435887634 57 5 4.76888715250398 0.231112847496015 58 6 10.1267289730152 -4.12672897301521 59 1 0.69165482041818 0.30834517958182 60 5 2.45463533433845 2.54536466566155 61 7 7.1817915471502 -0.181791547150197 62 4 3.97749650081084 0.0225034991891557 63 5 3.76315568479969 1.23684431520031 64 6 6.34806553811466 -0.348065538114661 65 4 3.40589004331826 0.594109956681744 66 6 5.68291687551053 0.317083124489466 67 6 6.27647994462676 -0.276479944626764 68 5 4.88245269781606 0.117547302183942 69 5 6.84075990327575 -1.84075990327575 70 3 2.95747222837928 0.0425277716207182 71 5 4.4158012300747 0.584198769925304 72 6 6.68291687551053 -0.682916875510534 73 5 4.95003252094637 0.0499674790536287 74 6 5.86651564341161 0.133484356588389 75 6 6.35120899195423 -0.351208991954231 76 4 3.99783498001004 0.00216501998995678 77 4 3.33316711115297 0.666832888847027 78 6 4.76917524201888 1.23082475798112 79 7 7.66578421157393 -0.665784211573933 80 4 5.47143474977593 -1.47143474977593 81 5 4.05222794185917 0.947772058140831 82 6 5.37152374762155 0.628476252378449 83 6 6.938950486062 -0.938950486061995 84 5 7.09861025070913 -2.09861025070913 85 3 1.51084503306948 1.48915496693052 86 7 6.65246291691536 0.347537083084645 87 6 5.86718525569747 0.132814744302533 88 4 4.86661147038852 -0.866611470388524 89 4 3.92883500666602 0.0711649933339847 90 5 5.83215565814372 -0.832155658143717 91 3 1.76497481540246 1.23502518459754 92 7 6.8242466698415 0.175753330158494 93 6 5.62956586705605 0.370434132943947 94 6 6.5121987995109 -0.512198799510906 95 4 4.23611479927515 -0.236114799275146 96 5 4.58528838460291 0.414711615397093 97 6 5.78692903330524 0.213070966694757 98 5 3.68951892218834 1.31048107781166 99 6 5.91267957247085 0.0873204275291543 100 6 7.37181183713645 -1.37181183713645 101 4 4.12667129339259 -0.126671293392593 102 5 4.10823334795067 0.891766652049334 103 6 6.58557647411781 -0.585576474117807 104 5 5.00823854892092 -0.00823854892092293 105 5 5.9816098360907 -0.981609836090697 106 4 4.74494814925004 -0.744948149250038 107 4 2.76574037271253 1.23425962728747 108 6 6.88427182841883 -0.884271828418827 109 5 4.58557647411781 0.414423525882193 110 6 7.30223568476262 -1.30223568476262 111 5 4.65246291691536 0.347537083084645 112 6 6.038980597031 -0.0389805970310015 113 5 5.2121757960212 -0.212175796021199 114 4 3.76917524201888 0.230824757981116 115 6 6.02905688963615 -0.0290568896361497 116 4 2.6179193465722 1.38208065342780 117 5 5.19824725049979 -0.198247250499793 118 5 4.03084750926533 0.969152490734675 119 6 6.87995180677858 -0.879951806778578 120 3 3.71449419065486 -0.71449419065486 121 5 4.69159714079556 0.308402859204443 122 4 2.32030128909576 1.67969871090424 123 5 4.30223568476262 0.697764315237376 124 5 5.57860777451328 -0.578607774513283 125 7 5.34078169951147 1.65921830048853 126 5 4.27356357472758 0.726436425272415 127 7 6.90803945725164 0.0919605427483604 128 5 4.58557647411781 0.414423525882193 129 4 3.96012423229544 0.0398757677045588 130 6 7.07749129984059 -1.07749129984059 131 4 3.47980388019258 0.520196119807415 132 4 4.6683999713198 -0.668399971319801 133 4 3.28946580772963 0.710534192270373 134 4 3.28030519039172 0.719694809608282 135 6 5.54555753959788 0.454442460402119 136 6 7.56697010771707 -1.56697010771707 137 5 4.62956586705605 0.370434132943947 138 3 3.29154402633684 -0.291544026336844 139 6 6.59285938048997 -0.592859380489967 140 5 5.11156950602239 -0.111569506022393 141 4 5.73369769340686 -1.73369769340686 142 5 5.23220246217362 -0.232202462173619 143 2 0.879894276693928 1.12010572330607 144 5 5.83817521536291 -0.838175215362912 145 7 8.24985123179654 -1.24985123179654 146 4 3.42974195523563 0.570258044764371 147 4 3.22257936493208 0.777420635067921 148 7 7.15167316964871 -0.151673169648707 149 6 5.84075990327575 0.159240096724248 150 5 5.72719435796368 -0.727194357963679 151 5 4.42773344635259 0.572266553647411 152 5 5.30223568476262 -0.302235684762623 153 7 6.79962920061406 0.200370799385937 154 6 6.0012698493164 -0.00126984931639935 155 6 9.46160735989486 -3.46160735989486 156 5 4.68898883437378 0.31101116562622 157 2 1.82424666984151 0.175753330158494 158 4 4.44596709915498 -0.445967099154975 159 6 5.121804094233 0.878195905767004 160 5 4.69885392991498 0.301146070085020 161 5 5.94422488355112 -0.944224883551115 162 5 4.96689196521231 0.0331080347876898 163 4 NA NA 164 4 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.0396478784904319 0.0792957569808637 0.960352121509568 12 0.0962910106905559 0.192582021381112 0.903708989309444 13 0.311465784700262 0.622931569400525 0.688534215299738 14 0.200615315331795 0.401230630663589 0.799384684668205 15 0.132027095428362 0.264054190856724 0.867972904571638 16 0.0896774961384443 0.179354992276889 0.910322503861556 17 0.120800283147769 0.241600566295539 0.87919971685223 18 0.0813541184464132 0.162708236892826 0.918645881553587 19 0.82715554764775 0.345688904704499 0.172844452352249 20 0.776101474717416 0.447797050565167 0.223898525282584 21 0.73046901970177 0.53906196059646 0.26953098029823 22 0.720722080805013 0.558555838389973 0.279277919194987 23 0.651733569912669 0.696532860174662 0.348266430087331 24 0.638725609883142 0.722548780233716 0.361274390116858 25 0.595864142767584 0.808271714464832 0.404135857232416 26 0.540585499137858 0.918829001724285 0.459414500862142 27 0.470876834464128 0.941753668928257 0.529123165535872 28 0.407131433209109 0.814262866418217 0.592868566790891 29 0.60308850262733 0.793822994745339 0.396911497372669 30 0.539745074116958 0.920509851766084 0.460254925883042 31 0.504230767435402 0.991538465129196 0.495769232564598 32 0.512306784248484 0.975386431503032 0.487693215751516 33 0.46502189154861 0.93004378309722 0.53497810845139 34 0.438965410044033 0.877930820088065 0.561034589955967 35 0.405317894252058 0.810635788504116 0.594682105747942 36 0.349377098280012 0.698754196560023 0.650622901719988 37 0.333791801770453 0.667583603540906 0.666208198229547 38 0.293609683930772 0.587219367861544 0.706390316069228 39 0.258752655135572 0.517505310271143 0.741247344864428 40 0.214230930219794 0.428461860439588 0.785769069780206 41 0.175429762540815 0.350859525081631 0.824570237459185 42 0.141757674798527 0.283515349597055 0.858242325201472 43 0.112443431114408 0.224886862228817 0.887556568885592 44 0.232691907382714 0.465383814765428 0.767308092617286 45 0.251470831386039 0.502941662772079 0.74852916861396 46 0.309383670672473 0.618767341344947 0.690616329327527 47 0.267510461504391 0.535020923008781 0.73248953849561 48 0.264886816721733 0.529773633443465 0.735113183278267 49 0.542738797118694 0.914522405762612 0.457261202881306 50 0.501967396585043 0.996065206829914 0.498032603414957 51 0.563340311785777 0.873319376428445 0.436659688214223 52 0.557459093077988 0.885081813844024 0.442540906922012 53 0.649262063331203 0.701475873337594 0.350737936668797 54 0.605441643128089 0.789116713743822 0.394558356871911 55 0.614217192167306 0.771565615665389 0.385782807832694 56 0.566124142509879 0.867751714980241 0.433875857490121 57 0.518580866640026 0.962838266719947 0.481419133359973 58 0.969183959089182 0.0616320818216357 0.0308160409108179 59 0.961594537908143 0.0768109241837136 0.0384054620918568 60 0.993035549429039 0.0139289011419221 0.00696445057096103 61 0.99093524304124 0.0181295139175214 0.00906475695876071 62 0.987672845333294 0.0246543093334116 0.0123271546667058 63 0.989873848488257 0.0202523030234859 0.0101261515117430 64 0.986859801115851 0.0262803977682979 0.0131401988841490 65 0.984038745691762 0.0319225086164766 0.0159612543082383 66 0.979323801556637 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0.138124433924957 101 0.833375428150405 0.33324914369919 0.166624571849595 102 0.829092334384926 0.341815331230148 0.170907665615074 103 0.805862724326039 0.388274551347923 0.194137275673961 104 0.77004084589673 0.45991830820654 0.22995915410327 105 0.782709473485619 0.434581053028762 0.217290526514381 106 0.776043699243548 0.447912601512904 0.223956300756452 107 0.806090176972925 0.387819646054149 0.193909823027075 108 0.787584399459635 0.42483120108073 0.212415600540365 109 0.756978174783088 0.486043650433825 0.243021825216912 110 0.77204717344146 0.455905653117081 0.227952826558540 111 0.740082154168036 0.519835691663927 0.259917845831964 112 0.702254088368739 0.595491823262522 0.297745911631261 113 0.662104873627186 0.675790252745628 0.337895126372814 114 0.621777492916527 0.756445014166946 0.378222507083473 115 0.574712472546641 0.850575054906718 0.425287527453359 116 0.68098069569435 0.638038608611301 0.319019304305651 117 0.634650915955812 0.730698168088377 0.365349084044188 118 0.615763730282597 0.768472539434806 0.384236269717403 119 0.578216400296009 0.843567199407983 0.421783599703991 120 0.54889762465404 0.902204750691919 0.451102375345960 121 0.497898468121106 0.995796936242212 0.502101531878894 122 0.539596784208966 0.920806431582069 0.460403215791034 123 0.523926746730295 0.95214650653941 0.476073253269705 124 0.47670476194534 0.95340952389068 0.52329523805466 125 0.65181574402686 0.696368511946281 0.348184255973141 126 0.626951613176919 0.746096773646162 0.373048386823081 127 0.578473793957425 0.84305241208515 0.421526206042575 128 0.539279758109049 0.921440483781902 0.460720241890951 129 0.485556689502507 0.971113379005013 0.514443310497493 130 0.463218723574411 0.926437447148822 0.536781276425589 131 0.409438995836741 0.818877991673482 0.590561004163259 132 0.353708440660384 0.707416881320768 0.646291559339616 133 0.360570509875693 0.721141019751387 0.639429490124306 134 0.318578558993168 0.637157117986337 0.681421441006832 135 0.298258700185722 0.596517400371444 0.701741299814278 136 0.35782481766581 0.71564963533162 0.64217518233419 137 0.344802702126051 0.689605404252103 0.655197297873949 138 0.281402089553381 0.562804179106761 0.71859791044662 139 0.225465942111032 0.450931884222063 0.774534057888968 140 0.199872665475725 0.39974533095145 0.800127334524275 141 0.233117538574713 0.466235077149425 0.766882461425287 142 0.183940301623975 0.367880603247951 0.816059698376025 143 0.172149153961965 0.344298307923929 0.827850846038035 144 0.178707468487789 0.357414936975578 0.821292531512211 145 0.137893315951069 0.275786631902139 0.86210668404893 146 0.119840872995435 0.23968174599087 0.880159127004565 147 0.0922040252606787 0.184408050521357 0.907795974739321 148 0.0562660561547363 0.112532112309473 0.943733943845264 149 0.0335863749326929 0.0671727498653858 0.966413625067307 150 0.0168366775093965 0.0336733550187930 0.983163322490604 151 0.120474803612656 0.240949607225312 0.879525196387344 152 0.558551316157083 0.882897367685834 0.441448683842917 153 0.433642625948752 0.867285251897505 0.566357374051248 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 10 0.06993006993007 NOK 10% type I error level 25 0.174825174825175 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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