*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: Thu, 02 Dec 2010 19:05:14 +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/02/t1291316618r0d4bpr2fmgxq17.htm/, Retrieved Thu, 02 Dec 2010 20:03:38 +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/02/t1291316618r0d4bpr2fmgxq17.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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation liked[t] = + 6.68487647585358 + 0.0804780908515778findingFriends[t] + 0.171089311176097knowingPeople[t] + 0.554952662162986celebrity[t] + 0.00330749834696463friend[t] -0.00236012166624288secondbestfriend[t] + 0.00334213262966341thirdbestfriend[t] + 0.00590218756718479t + 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) 6.68487647585358 1.062645 6.2908 0 0 findingFriends 0.0804780908515778 0.081404 0.9886 0.32446 0.16223 knowingPeople 0.171089311176097 0.051901 3.2965 0.001226 0.000613 celebrity 0.554952662162986 0.122991 4.5121 1.3e-05 6e-06 friend 0.00330749834696463 0.003029 1.092 0.276588 0.138294 secondbestfriend -0.00236012166624288 0.003057 -0.7719 0.441389 0.220695 thirdbestfriend 0.00334213262966341 0.002762 1.21 0.228211 0.114105 t 0.00590218756718479 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 12.2412764510369 0.758723548963133 2 13 12.5492510452934 0.450748954706599 3 16 12.890151654162 3.10984834583801 4 12 12.4095002419506 -0.409500241950625 5 11 12.1954898338014 -1.19548983380136 6 12 10.5485098561973 1.45149014380274 7 18 15.1400072724624 2.85999272753762 8 11 11.892234091914 -0.89223409191401 9 14 12.5427878319716 1.45721216802845 10 9 10.4731134123434 -1.47311341234342 11 14 13.6989839110600 0.301016088939985 12 12 13.3914843781074 -1.39148437810740 13 11 13.5077253284476 -2.50772532844756 14 12 13.0619744150281 -1.06197441502814 15 13 12.4274437124940 0.572556287505966 16 11 12.4166973187797 -1.41669731877967 17 12 12.9626491506296 -0.962649150629635 18 16 13.5052119045738 2.49478809542624 19 9 11.4569226873542 -2.45692268735425 20 11 11.2933506639583 -0.293350663958286 21 13 10.1062435201726 2.89375647982742 22 15 14.2632373618389 0.7367626381611 23 10 13.1535936044104 -3.15359360441045 24 11 11.1960564530903 -0.196056453090281 25 13 13.8643356966233 -0.864335696623341 26 16 14.119152223878 1.88084777612199 27 15 14.7006872971103 0.299312702889655 28 14 13.2155290369884 0.784470963011641 29 14 14.0035872018418 -0.00358720184175577 30 14 11.6357662210824 2.3642337789176 31 8 11.3402957711700 -3.34029577117001 32 13 14.0929366237416 -1.09293662374159 33 15 14.4012678820608 0.598732117939156 34 13 11.2922840338619 1.70771596613815 35 11 12.5385402892615 -1.53854028926155 36 15 14.0954218728495 0.904578127150489 37 15 13.4114761801123 1.58852381988770 38 9 12.1921086960505 -3.19210869605046 39 13 14.1414892414009 -1.14148924140091 40 16 14.9424633835402 1.05753661645983 41 13 13.6297203365311 -0.629720336531094 42 11 10.5875055087326 0.412494491267403 43 12 11.5419595736635 0.458040426336504 44 12 12.1938177720423 -0.193817772042344 45 12 12.94719430052 -0.947194300519994 46 14 14.0009860746851 -0.000986074685142166 47 14 13.6493363845900 0.35066361541002 48 8 11.4216993575606 -3.42169935756064 49 13 13.0582006172276 -0.0582006172276401 50 16 14.7287886262570 1.27121137374302 51 13 12.4327719919004 0.567228008099589 52 11 14.002539992185 -3.00253999218499 53 14 13.4747836359235 0.525216364076542 54 13 11.3181383597696 1.68186164023035 55 13 13.0546363292234 -0.0546363292234419 56 13 13.3887952814912 -0.388795281491174 57 12 12.5265099394571 -0.526509939457064 58 16 14.7118736660021 1.28812633399789 59 15 10.9098399872552 4.09016001274485 60 15 15.3544473216950 -0.354447321695036 61 12 11.0442194835685 0.955780516431483 62 14 14.2495576324261 -0.249557632426084 63 12 14.3956537173204 -2.39565371732038 64 15 14.1270905466144 0.872909453385647 65 12 11.8191166745717 0.180883325428266 66 13 13.1905657649825 -0.190565764982455 67 12 14.0285792972029 -2.02857929720291 68 12 12.2856431790989 -0.285643179098892 69 13 14.0578624192014 -1.05786241920144 70 5 10.1742054615072 -5.17420546150722 71 13 13.3634865890547 -0.363486589054699 72 13 13.2811376779636 -0.281137677963608 73 14 13.1770608532435 0.822939146756531 74 17 13.7576458299441 3.24235417005586 75 13 13.8884682145868 -0.88846821458676 76 13 14.5393126769409 -1.53931267694091 77 12 13.7310812472200 -1.73108124722002 78 13 12.8078283904091 0.192171609590942 79 14 12.3862499975458 1.61375000245418 80 11 10.4543721653008 0.545627834699239 81 12 11.6639169019733 0.336083098026708 82 12 13.3317410554062 -1.33174105540616 83 16 13.9750870526317 2.02491294736828 84 12 13.1091272321134 -1.10912723211341 85 12 10.5463045392097 1.45369546079026 86 12 13.8069869235033 -1.80698692350329 87 10 11.6616138613276 -1.66161386132757 88 15 12.5853516984989 2.41464830150105 89 15 15.2872147832097 -0.287214783209684 90 12 12.0979694998763 -0.0979694998763441 91 16 13.2794291467672 2.72057085323278 92 15 13.9408797936226 1.05912020637738 93 16 15.2636191786083 0.73638082139174 94 13 14.9482687822939 -1.94826878229385 95 12 12.6663420064809 -0.666342006480868 96 11 12.1232685518916 -1.12326855189158 97 13 11.8348085235139 1.16519147648615 98 10 11.2414466685161 -1.24144666851609 99 15 13.3183250160991 1.68167498390088 100 13 13.9733775621092 -0.973377562109222 101 16 15.4806887212472 0.519311278752845 102 15 15.0685137262809 -0.0685137262809211 103 18 14.6990371527316 3.30096284726835 104 13 10.7240782413135 2.27592175868646 105 10 10.4210863327862 -0.421086332786167 106 16 15.0793533677046 0.920646632295383 107 13 11.5548791440735 1.44512085592652 108 15 15.4605022774142 -0.460502277414206 109 14 11.9458435343159 2.05415646568412 110 15 11.6638998049924 3.33610019500761 111 14 13.3191355817355 0.680864418264514 112 13 14.764795042679 -1.764795042679 113 13 13.3016576607498 -0.301657660749798 114 15 14.3561188776616 0.643881122338437 115 16 14.7803841209011 1.21961587909889 116 14 14.5997422003543 -0.599742200354304 117 14 14.2562178902544 -0.256217890254430 118 16 13.3053910537611 2.69460894623891 119 14 14.7100053530057 -0.710005353005712 120 12 12.9242922224764 -0.924292222476409 121 13 12.8091147825838 0.190885217416195 122 12 14.0030273251826 -2.00302732518263 123 12 12.2735552407858 -0.273555240785796 124 14 14.6227499100675 -0.62274991006753 125 14 14.5826488947704 -0.582648894770409 126 14 12.1955883774093 1.80441162259069 127 16 15.5201963586448 0.479803641355155 128 13 14.5858352055783 -1.58583520557830 129 14 13.3054114132075 0.69458858679251 130 4 11.3423321021088 -7.34233210210875 131 16 15.3978494898521 0.602150510147872 132 13 13.5934505145228 -0.593450514522831 133 16 12.0869721191611 3.91302788083886 134 15 13.7336831868418 1.26631681315817 135 14 13.9975315233723 0.00246847662768986 136 13 12.1170819570579 0.882918042942115 137 14 14.5911438736323 -0.591143873632274 138 12 12.3541344821222 -0.354134482122229 139 15 14.4759550365291 0.524044963470924 140 14 13.7577560818821 0.242243918117941 141 13 13.3727877505990 -0.372787750598958 142 14 14.3148335968670 -0.31483359686698 143 16 13.7165697344689 2.28343026553106 144 6 12.3421935818361 -6.34219358183612 145 13 12.9479737161740 0.0520262838259516 146 13 13.1810783373908 -0.181078337390839 147 14 12.9163903113887 1.08360968861134 148 15 14.8777635333202 0.122236466679821 149 14 14.4494877870511 -0.449487787051066 150 15 15.2846955848154 -0.284695584815378 151 13 14.2434534268062 -1.24345342680624 152 16 15.062457124864 0.937542875136014 153 12 12.0024567156971 -0.00245671569706484 154 15 14.2068656799723 0.793134320027697 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 0.423487303203682 0.846974606407363 0.576512696796318 14 0.518839327700192 0.962321344599617 0.481160672299808 15 0.408997650337009 0.817995300674019 0.59100234966299 16 0.312380412120604 0.624760824241208 0.687619587879396 17 0.231212437541905 0.462424875083809 0.768787562458095 18 0.312357243297684 0.624714486595369 0.687642756702316 19 0.252483372581925 0.504966745163851 0.747516627418075 20 0.276824932888767 0.553649865777533 0.723175067111233 21 0.737028280539688 0.525943438920624 0.262971719460312 22 0.689393732298444 0.621212535403111 0.310606267701556 23 0.75943098865341 0.48113802269318 0.24056901134659 24 0.698155808438477 0.603688383123045 0.301844191561523 25 0.632257905215795 0.73548418956841 0.367742094784205 26 0.675566841375881 0.648866317248238 0.324433158624119 27 0.614276576169618 0.771446847660764 0.385723423830382 28 0.563799888417966 0.872400223164068 0.436200111582034 29 0.501138558576353 0.997722882847293 0.498861441423647 30 0.521191951726216 0.957616096547568 0.478808048273784 31 0.70183979409575 0.596320411808501 0.298160205904250 32 0.665012059003458 0.669975881993085 0.334987940996542 33 0.632665535022914 0.734668929954173 0.367334464977086 34 0.677499959830683 0.645000080338633 0.322500040169317 35 0.641879201811496 0.716241596377007 0.358120798188504 36 0.607649647537516 0.784700704924968 0.392350352462484 37 0.602129748988721 0.795740502022557 0.397870251011279 38 0.661267635283085 0.67746472943383 0.338732364716915 39 0.613158769937379 0.773682460125243 0.386841230062621 40 0.577193041853473 0.845613916293055 0.422806958146527 41 0.528373732389965 0.94325253522007 0.471626267610035 42 0.518678369214611 0.962643261570777 0.481321630785389 43 0.475525896604226 0.951051793208452 0.524474103395774 44 0.424205051963234 0.848410103926468 0.575794948036766 45 0.381884302402740 0.763768604805481 0.61811569759726 46 0.331471297647055 0.662942595294111 0.668528702352945 47 0.287496774834936 0.574993549669873 0.712503225165064 48 0.39087790047982 0.78175580095964 0.60912209952018 49 0.341986307604583 0.683972615209166 0.658013692395417 50 0.328636372419606 0.657272744839212 0.671363627580394 51 0.298990946490516 0.597981892981032 0.701009053509484 52 0.364461527091621 0.728923054183243 0.635538472908379 53 0.3312780103594 0.6625560207188 0.6687219896406 54 0.332067148306613 0.664134296613227 0.667932851693387 55 0.287461438525093 0.574922877050187 0.712538561474907 56 0.246238663686031 0.492477327372062 0.753761336313969 57 0.209732743895579 0.419465487791157 0.790267256104421 58 0.206324929283364 0.412649858566729 0.793675070716636 59 0.381049200011986 0.762098400023972 0.618950799988014 60 0.335170618204117 0.670341236408235 0.664829381795883 61 0.302112272343655 0.60422454468731 0.697887727656345 62 0.263969812211943 0.527939624423886 0.736030187788057 63 0.314302389624288 0.628604779248576 0.685697610375712 64 0.287036858674757 0.574073717349515 0.712963141325243 65 0.249827130785926 0.499654261571852 0.750172869214074 66 0.214417744569917 0.428835489139833 0.785582255430083 67 0.220307346768124 0.440614693536247 0.779692653231876 68 0.186467072710080 0.372934145420159 0.81353292728992 69 0.164031220643570 0.328062441287140 0.83596877935643 70 0.454932838727764 0.909865677455529 0.545067161272236 71 0.409812775317801 0.819625550635601 0.5901872246822 72 0.366398948058751 0.732797896117502 0.633601051941249 73 0.337584577940802 0.675169155881604 0.662415422059198 74 0.457991320705650 0.915982641411301 0.54200867929435 75 0.419977311007082 0.839954622014165 0.580022688992918 76 0.407903753309981 0.815807506619961 0.592096246690019 77 0.413785803975964 0.827571607951929 0.586214196024036 78 0.368424788697395 0.736849577394791 0.631575211302605 79 0.367035237739053 0.734070475478105 0.632964762260947 80 0.331861000674945 0.66372200134989 0.668138999325055 81 0.295336120486012 0.590672240972025 0.704663879513988 82 0.272097884900499 0.544195769800998 0.727902115099501 83 0.281398798744627 0.562797597489254 0.718601201255373 84 0.259392943494830 0.518785886989661 0.74060705650517 85 0.242219490767261 0.484438981534522 0.757780509232739 86 0.257697519815526 0.515395039631052 0.742302480184474 87 0.275922905341538 0.551845810683075 0.724077094658462 88 0.305551735700859 0.611103471401719 0.69444826429914 89 0.267357535021409 0.534715070042817 0.732642464978591 90 0.234571133084295 0.469142266168591 0.765428866915705 91 0.270146250926023 0.540292501852045 0.729853749073977 92 0.240633529899203 0.481267059798406 0.759366470100797 93 0.208060289400301 0.416120578800603 0.791939710599698 94 0.218902808932399 0.437805617864798 0.781097191067601 95 0.19433943718582 0.38867887437164 0.80566056281418 96 0.199074517383941 0.398149034767881 0.80092548261606 97 0.183268095915685 0.366536191831369 0.816731904084315 98 0.217515388165901 0.435030776331802 0.782484611834099 99 0.228412157091936 0.456824314183872 0.771587842908064 100 0.248770574210542 0.497541148421084 0.751229425789458 101 0.21293228314101 0.42586456628202 0.78706771685899 102 0.185098109330496 0.370196218660991 0.814901890669504 103 0.210122691609740 0.420245383219481 0.78987730839026 104 0.204251649476032 0.408503298952065 0.795748350523968 105 0.182476204697328 0.364952409394656 0.817523795302672 106 0.154547609643946 0.309095219287892 0.845452390356054 107 0.134546527078346 0.269093054156691 0.865453472921654 108 0.110116738341792 0.220233476683583 0.889883261658208 109 0.111958448277659 0.223916896555318 0.88804155172234 110 0.340131954969686 0.680263909939371 0.659868045030314 111 0.318159515191706 0.636319030383412 0.681840484808294 112 0.310535262972547 0.621070525945094 0.689464737027453 113 0.2776594680261 0.5553189360522 0.7223405319739 114 0.235438326244055 0.470876652488110 0.764561673755945 115 0.204146615117633 0.408293230235267 0.795853384882367 116 0.170974072692955 0.34194814538591 0.829025927307045 117 0.139273778367052 0.278547556734104 0.860726221632948 118 0.171380838770516 0.342761677541033 0.828619161229484 119 0.150019750296179 0.300039500592358 0.849980249703821 120 0.124217470941768 0.248434941883537 0.875782529058232 121 0.0979099273722539 0.195819854744508 0.902090072627746 122 0.0919249210132654 0.183849842026531 0.908075078986735 123 0.0705726563710113 0.141145312742023 0.929427343628989 124 0.0633689080904408 0.126737816180882 0.93663109190956 125 0.0530501968955791 0.106100393791158 0.94694980310442 126 0.0526621157411017 0.105324231482203 0.947337884258898 127 0.0377844618074189 0.0755689236148378 0.962215538192581 128 0.0462599951954562 0.0925199903909125 0.953740004804544 129 0.0602030153845773 0.120406030769155 0.939796984615423 130 0.322348276296454 0.644696552592908 0.677651723703546 131 0.264270569673596 0.528541139347193 0.735729430326404 132 0.209553802727002 0.419107605454003 0.790446197272998 133 0.388494368269312 0.776988736538624 0.611505631730688 134 0.362987501582569 0.725975003165138 0.637012498417431 135 0.303624538910124 0.607249077820248 0.696375461089876 136 0.282805992019736 0.565611984039472 0.717194007980264 137 0.215645392194044 0.431290784388088 0.784354607805956 138 0.158051546998319 0.316103093996637 0.841948453001681 139 0.130211236414436 0.260422472828873 0.869788763585564 140 0.100507098063979 0.201014196127958 0.899492901936021 141 0.0727070136492167 0.145414027298433 0.927292986350783 142 0.0486336146706975 0.097267229341395 0.951366385329303 143 0.147018009191067 0.294036018382134 0.852981990808933 144 0.591898819402207 0.816202361195586 0.408101180597793 145 0.428247259168518 0.856494518337035 0.571752740831482 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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