Workshop 4

*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, 30 Nov 2010 13:44:41 +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/30/t1291124610yd9xvvgxhpy4ox5.htm/, Retrieved Tue, 30 Nov 2010 14:43:42 +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/30/t1291124610yd9xvvgxhpy4ox5.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 «

13 14 13 3 25 55 147 12 8 13 5 158 7 71 10 12 16 6 0 0 0 9 7 12 6 143 10 0 10 10 11 5 67 74 43 12 7 12 3 0 0 0 13 16 18 8 148 138 8 12 11 11 4 28 0 0 12 14 14 4 114 113 34 6 6 9 4 0 0 0 5 16 14 6 123 115 103 12 11 12 6 145 9 0 11 16 11 5 113 114 73 14 12 12 4 152 59 159 14 7 13 6 0 0 0 12 13 11 4 36 114 113 12 11 12 6 0 0 0 11 15 16 6 8 102 44 11 7 9 4 108 0 0 7 9 11 4 112 86 0 9 7 13 2 51 17 41 11 14 15 7 43 45 74 11 15 10 5 120 123 0 12 7 11 4 13 24 0 12 15 13 6 55 5 0 11 17 16 6 103 123 32 11 15 15 7 127 136 126 8 14 14 5 14 4 154 9 14 14 6 135 76 129 12 8 14 4 38 99 98 10 8 8 4 11 98 82 10 14 13 7 43 67 45 12 14 15 7 141 92 8 8 8 13 4 62 13 0 12 11 11 4 62 24 129 11 16 15 6 135 129 31 12 10 15 6 117 117 117 7 8 9 5 82 11 99 11 14 13 6 145 20 55 11 16 16 7 87 91 132 12 13 13 6 76 111 58 9 5 11 3 124 0 0 15 8 12 3 151 58 0 11 10 12 4 131 0 0 11 8 12 6 127 146 101 11 13 14 7 76 129 31 11 15 14 5 25 48 147 15 6 8 4 0 0 0 11 12 13 5 58 111 132 12 16 16 6 115 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 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 Liked[t] = + 6.68487647585357 + 0.0804780908515764FindingFriends[t] + 0.171089311176096KnowingPeople[t] + 0.554952662162989Celebrity[t] + 0.00330749834696466friendone[t] -0.00236012166624288friendtwo[t] + 0.00334213262966336`friendthree `[t] + 0.00590218756718485t + 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) 6.68487647585357 1.062645 6.2908 0 0 FindingFriends 0.0804780908515764 0.081404 0.9886 0.32446 0.16223 KnowingPeople 0.171089311176096 0.051901 3.2965 0.001226 0.000613 Celebrity 0.554952662162989 0.122991 4.5121 1.3e-05 6e-06 friendone 0.00330749834696466 0.003029 1.092 0.276588 0.138294 friendtwo -0.00236012166624288 0.003057 -0.7719 0.441389 0.220695 `friendthree ` 0.00334213262966336 0.002762 1.21 0.228211 0.114105 t 0.00590218756718485 0.003247 1.8178 0.071113 0.035557 Multiple Linear Regression - Regression Statistics Multiple R 0.610957784065894 R-squared 0.373269413910707 Adjusted R-squared 0.343626751055132 F-TEST (value) 12.5923037255241 F-TEST (DF numerator) 7 F-TEST (DF denominator) 148 p-value 1.30406796472471e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.76255186325910 Sum Squared Residuals 459.775182460365 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.2412764510371 0.758723548962934 2 13 12.5492510452934 0.450748954706606 3 16 12.8901516541620 3.10984834583802 4 12 12.4095002419506 -0.409500241950638 5 11 12.1954898338014 -1.19548983380136 6 12 10.5485098561972 1.45149014380275 7 18 15.1400072724624 2.85999272753762 8 11 11.892234091914 -0.892234091914003 9 14 12.5427878319715 1.45721216802846 10 9 10.4731134123434 -1.47311341234342 11 14 13.6989839110600 0.301016088939982 12 12 13.3914843781074 -1.39148437810740 13 11 13.5077253284476 -2.50772532844755 14 12 13.0619744150281 -1.06197441502812 15 13 12.4274437124940 0.57255628750597 16 11 12.4166973187797 -1.41669731877966 17 12 12.9626491506296 -0.962649150629632 18 16 13.5052119045738 2.49478809542624 19 9 11.4569226873542 -2.45692268735425 20 11 11.2933506639583 -0.293350663958290 21 13 10.1062435201726 2.89375647982743 22 15 14.2632373618389 0.736762638161104 23 10 13.1535936044104 -3.15359360441045 24 11 11.1960564530903 -0.196056453090276 25 13 13.8643356966233 -0.864335696623336 26 16 14.119152223878 1.88084777612199 27 15 14.7006872971103 0.299312702889659 28 14 13.2155290369884 0.78447096301165 29 14 14.0035872018418 -0.00358720184175349 30 14 11.6357662210824 2.36423377891761 31 8 11.34029577117 -3.34029577117001 32 13 14.0929366237416 -1.09293662374159 33 15 14.4012678820608 0.598732117939154 34 13 11.2922840338619 1.70771596613814 35 11 12.5385402892615 -1.53854028926154 36 15 14.0954218728495 0.90457812715049 37 15 13.4114761801123 1.58852381988771 38 9 12.1921086960505 -3.19210869605046 39 13 14.1414892414009 -1.14148924140091 40 16 14.9424633835402 1.05753661645984 41 13 13.6297203365311 -0.62972033653109 42 11 10.5875055087326 0.4124944912674 43 12 11.5419595736635 0.458040426336511 44 12 12.1938177720423 -0.193817772042343 45 12 12.94719430052 -0.947194300519995 46 14 14.0009860746851 -0.000986074685144223 47 14 13.6493363845900 0.350663615410032 48 8 11.4216993575606 -3.42169935756063 49 13 13.0582006172276 -0.0582006172276327 50 16 14.7287886262570 1.27121137374303 51 13 12.4327719919004 0.567228008099584 52 11 14.0025399921850 -3.00253999218499 53 14 13.4747836359235 0.52521636407655 54 13 11.3181383597696 1.68186164023035 55 13 13.0546363292234 -0.0546363292234351 56 13 13.3887952814912 -0.388795281491164 57 12 12.5265099394571 -0.52650993945706 58 16 14.7118736660021 1.28812633399790 59 15 10.9098399872551 4.09016001274485 60 15 15.3544473216950 -0.354447321695035 61 12 11.0442194835685 0.95578051643149 62 14 14.2495576324261 -0.249557632426077 63 12 14.3956537173204 -2.39565371732038 64 15 14.1270905466143 0.872909453385653 65 12 11.8191166745717 0.180883325428266 66 13 13.1905657649825 -0.190565764982453 67 12 14.0285792972029 -2.02857929720291 68 12 12.2856431790989 -0.285643179098895 69 13 14.0578624192014 -1.05786241920144 70 5 10.1742054615072 -5.17420546150722 71 13 13.3634865890547 -0.363486589054693 72 13 13.2811376779636 -0.281137677963601 73 14 13.1770608532435 0.822939146756533 74 17 13.7576458299441 3.24235417005586 75 13 13.8884682145868 -0.888468214586758 76 13 14.5393126769409 -1.5393126769409 77 12 13.73108124722 -1.73108124722001 78 13 12.8078283904091 0.192171609590942 79 14 12.3862499975458 1.61375000245418 80 11 10.4543721653008 0.545627834699243 81 12 11.6639169019733 0.336083098026707 82 12 13.3317410554062 -1.33174105540617 83 16 13.9750870526317 2.02491294736828 84 12 13.1091272321134 -1.10912723211341 85 12 10.5463045392097 1.45369546079026 86 12 13.8069869235033 -1.80698692350330 87 10 11.6616138613276 -1.66161386132758 88 15 12.5853516984990 2.41464830150104 89 15 15.2872147832097 -0.287214783209686 90 12 12.0979694998763 -0.0979694998763433 91 16 13.2794291467672 2.72057085323277 92 15 13.9408797936226 1.05912020637738 93 16 15.2636191786083 0.73638082139174 94 13 14.9482687822939 -1.94826878229385 95 12 12.6663420064809 -0.666342006480869 96 11 12.1232685518916 -1.12326855189158 97 13 11.8348085235139 1.16519147648613 98 10 11.2414466685161 -1.24144666851609 99 15 13.3183250160991 1.68167498390088 100 13 13.9733775621092 -0.973377562109227 101 16 15.4806887212472 0.519311278752849 102 15 15.0685137262809 -0.0685137262809203 103 18 14.6990371527316 3.30096284726836 104 13 10.7240782413135 2.27592175868646 105 10 10.4210863327862 -0.421086332786162 106 16 15.0793533677046 0.920646632295382 107 13 11.5548791440735 1.44512085592652 108 15 15.4605022774142 -0.460502277414208 109 14 11.9458435343159 2.05415646568413 110 15 11.6638998049924 3.33610019500760 111 14 13.3191355817355 0.680864418264513 112 13 14.764795042679 -1.76479504267901 113 13 13.3016576607498 -0.301657660749802 114 15 14.3561188776616 0.643881122338433 115 16 14.7803841209011 1.21961587909889 116 14 14.5997422003543 -0.599742200354303 117 14 14.2562178902544 -0.256217890254429 118 16 13.3053910537611 2.69460894623890 119 14 14.7100053530057 -0.710005353005711 120 12 12.9242922224764 -0.9242922224764 121 13 12.8091147825838 0.190885217416204 122 12 14.0030273251826 -2.00302732518263 123 12 12.2735552407858 -0.273555240785795 124 14 14.6227499100675 -0.622749910067525 125 14 14.5826488947704 -0.582648894770411 126 14 12.1955883774093 1.80441162259069 127 16 15.5201963586449 0.479803641355146 128 13 14.5858352055783 -1.58583520557829 129 14 13.3054114132075 0.694588586792506 130 4 11.3423321021088 -7.34233210210876 131 16 15.3978494898521 0.602150510147868 132 13 13.5934505145228 -0.593450514522837 133 16 12.0869721191611 3.91302788083886 134 15 13.7336831868418 1.26631681315817 135 14 13.9975315233723 0.00246847662768872 136 13 12.1170819570579 0.882918042942112 137 14 14.5911438736323 -0.591143873632276 138 12 12.3541344821222 -0.354134482122223 139 15 14.4759550365291 0.524044963470921 140 14 13.7577560818821 0.242243918117944 141 13 13.3727877505990 -0.372787750598957 142 14 14.3148335968670 -0.314833596866979 143 16 13.7165697344689 2.28343026553106 144 6 12.3421935818361 -6.34219358183612 145 13 12.9479737161740 0.0520262838259557 146 13 13.1810783373908 -0.181078337390845 147 14 12.9163903113887 1.08360968861134 148 15 14.8777635333202 0.122236466679822 149 14 14.4494877870511 -0.449487787051067 150 15 15.2846955848154 -0.284695584815386 151 13 14.2434534268062 -1.24345342680624 152 16 15.062457124864 0.93754287513601 153 12 12.0024567156971 -0.00245671569706828 154 15 14.2068656799723 0.79313432002769 155 12 14.5793882744699 -2.57938827446993 156 14 12.0809652568081 1.91903474319191 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.614183251547004 0.771633496905992 0.385816748452996 12 0.457004356795727 0.914008713591454 0.542995643204273 13 0.423487303203681 0.846974606407362 0.576512696796319 14 0.518839327700192 0.962321344599616 0.481160672299808 15 0.408997650337011 0.817995300674023 0.591002349662989 16 0.312380412120605 0.624760824241209 0.687619587879395 17 0.231212437541904 0.462424875083808 0.768787562458096 18 0.312357243297686 0.624714486595372 0.687642756702314 19 0.252483372581924 0.504966745163848 0.747516627418076 20 0.276824932888765 0.55364986577753 0.723175067111235 21 0.737028280539688 0.525943438920624 0.262971719460312 22 0.689393732298444 0.621212535403111 0.310606267701556 23 0.75943098865341 0.481138022693179 0.240569011346590 24 0.698155808438477 0.603688383123046 0.301844191561523 25 0.632257905215796 0.735484189568408 0.367742094784204 26 0.67556684137588 0.64886631724824 0.32443315862412 27 0.614276576169619 0.771446847660761 0.385723423830381 28 0.563799888417966 0.872400223164068 0.436200111582034 29 0.501138558576353 0.997722882847294 0.498861441423647 30 0.521191951726215 0.95761609654757 0.478808048273785 31 0.701839794095751 0.596320411808497 0.298160205904249 32 0.665012059003457 0.669975881993085 0.334987940996543 33 0.632665535022916 0.734668929954167 0.367334464977083 34 0.677499959830684 0.645000080338631 0.322500040169316 35 0.641879201811494 0.716241596377011 0.358120798188506 36 0.607649647537517 0.784700704924966 0.392350352462483 37 0.602129748988718 0.795740502022563 0.397870251011282 38 0.661267635283085 0.67746472943383 0.338732364716915 39 0.613158769937377 0.773682460125245 0.386841230062623 40 0.577193041853473 0.845613916293054 0.422806958146527 41 0.528373732389966 0.943252535220069 0.471626267610034 42 0.51867836921461 0.96264326157078 0.48132163078539 43 0.475525896604225 0.95105179320845 0.524474103395775 44 0.424205051963235 0.84841010392647 0.575794948036765 45 0.381884302402740 0.763768604805481 0.61811569759726 46 0.331471297647056 0.662942595294112 0.668528702352944 47 0.287496774834937 0.574993549669874 0.712503225165063 48 0.390877900479821 0.781755800959642 0.609122099520179 49 0.341986307604583 0.683972615209165 0.658013692395417 50 0.328636372419606 0.657272744839212 0.671363627580394 51 0.298990946490515 0.59798189298103 0.701009053509485 52 0.364461527091621 0.728923054183243 0.635538472908379 53 0.331278010359398 0.662556020718796 0.668721989640602 54 0.332067148306613 0.664134296613227 0.667932851693387 55 0.287461438525094 0.574922877050188 0.712538561474906 56 0.246238663686031 0.492477327372062 0.753761336313969 57 0.209732743895579 0.419465487791159 0.79026725610442 58 0.206324929283367 0.412649858566733 0.793675070716633 59 0.381049200011986 0.762098400023972 0.618950799988014 60 0.335170618204117 0.670341236408235 0.664829381795883 61 0.302112272343655 0.604224544687311 0.697887727656345 62 0.263969812211942 0.527939624423884 0.736030187788058 63 0.314302389624287 0.628604779248574 0.685697610375713 64 0.287036858674757 0.574073717349515 0.712963141325243 65 0.249827130785926 0.499654261571853 0.750172869214074 66 0.214417744569918 0.428835489139835 0.785582255430082 67 0.220307346768124 0.440614693536248 0.779692653231876 68 0.186467072710080 0.372934145420159 0.81353292728992 69 0.164031220643572 0.328062441287143 0.835968779356429 70 0.454932838727764 0.909865677455529 0.545067161272236 71 0.409812775317801 0.819625550635603 0.590187224682199 72 0.36639894805875 0.7327978961175 0.63360105194125 73 0.337584577940799 0.675169155881597 0.662415422059201 74 0.457991320705653 0.915982641411306 0.542008679294347 75 0.419977311007081 0.839954622014162 0.580022688992919 76 0.407903753309977 0.815807506619955 0.592096246690023 77 0.413785803975965 0.82757160795193 0.586214196024035 78 0.368424788697396 0.736849577394792 0.631575211302604 79 0.367035237739052 0.734070475478104 0.632964762260948 80 0.331861000674946 0.663722001349893 0.668138999325054 81 0.295336120486016 0.590672240972032 0.704663879513984 82 0.272097884900502 0.544195769801003 0.727902115099498 83 0.281398798744628 0.562797597489256 0.718601201255372 84 0.259392943494830 0.518785886989660 0.74060705650517 85 0.242219490767259 0.484438981534517 0.757780509232741 86 0.257697519815525 0.51539503963105 0.742302480184475 87 0.275922905341536 0.551845810683073 0.724077094658464 88 0.305551735700861 0.611103471401723 0.694448264299139 89 0.267357535021409 0.534715070042818 0.732642464978591 90 0.234571133084293 0.469142266168587 0.765428866915707 91 0.270146250926026 0.540292501852051 0.729853749073974 92 0.240633529899204 0.481267059798409 0.759366470100796 93 0.208060289400303 0.416120578800606 0.791939710599697 94 0.218902808932398 0.437805617864796 0.781097191067602 95 0.194339437185819 0.388678874371639 0.80566056281418 96 0.199074517383941 0.398149034767882 0.800925482616059 97 0.183268095915686 0.366536191831371 0.816731904084314 98 0.217515388165898 0.435030776331796 0.782484611834102 99 0.228412157091936 0.456824314183872 0.771587842908064 100 0.248770574210544 0.497541148421088 0.751229425789456 101 0.212932283141011 0.425864566282021 0.78706771685899 102 0.185098109330496 0.370196218660992 0.814901890669504 103 0.210122691609742 0.420245383219484 0.789877308390258 104 0.204251649476032 0.408503298952065 0.795748350523968 105 0.182476204697326 0.364952409394653 0.817523795302674 106 0.154547609643945 0.30909521928789 0.845452390356055 107 0.134546527078346 0.269093054156691 0.865453472921655 108 0.110116738341792 0.220233476683584 0.889883261658208 109 0.111958448277658 0.223916896555317 0.888041551722342 110 0.340131954969683 0.680263909939367 0.659868045030317 111 0.318159515191705 0.63631903038341 0.681840484808295 112 0.310535262972548 0.621070525945096 0.689464737027452 113 0.277659468026099 0.555318936052198 0.722340531973901 114 0.235438326244052 0.470876652488105 0.764561673755948 115 0.204146615117632 0.408293230235265 0.795853384882368 116 0.170974072692954 0.341948145385909 0.829025927307046 117 0.139273778367050 0.278547556734099 0.86072622163295 118 0.171380838770516 0.342761677541031 0.828619161229484 119 0.150019750296178 0.300039500592357 0.849980249703822 120 0.124217470941768 0.248434941883536 0.875782529058232 121 0.097909927372255 0.19581985474451 0.902090072627745 122 0.0919249210132654 0.183849842026531 0.908075078986735 123 0.0705726563710108 0.141145312742022 0.92942734362899 124 0.0633689080904404 0.126737816180881 0.93663109190956 125 0.0530501968955802 0.106100393791160 0.94694980310442 126 0.0526621157411015 0.105324231482203 0.947337884258898 127 0.0377844618074192 0.0755689236148384 0.962215538192581 128 0.046259995195456 0.092519990390912 0.953740004804544 129 0.0602030153845756 0.120406030769151 0.939796984615424 130 0.322348276296455 0.644696552592911 0.677651723703545 131 0.264270569673596 0.528541139347192 0.735729430326404 132 0.209553802727002 0.419107605454003 0.790446197272998 133 0.388494368269311 0.776988736538621 0.611505631730689 134 0.362987501582569 0.725975003165138 0.637012498417431 135 0.303624538910124 0.607249077820249 0.696375461089876 136 0.282805992019736 0.565611984039472 0.717194007980264 137 0.215645392194042 0.431290784388085 0.784354607805958 138 0.158051546998318 0.316103093996637 0.841948453001682 139 0.130211236414436 0.260422472828871 0.869788763585564 140 0.100507098063979 0.201014196127958 0.899492901936021 141 0.072707013649217 0.145414027298434 0.927292986350783 142 0.0486336146706985 0.097267229341397 0.951366385329302 143 0.147018009191066 0.294036018382132 0.852981990808934 144 0.591898819402207 0.816202361195586 0.408101180597793 145 0.428247259168519 0.856494518337038 0.571752740831481 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 0 0 OK 10% type I error level 3 0.0222222222222222 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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