multiple regression model 3

*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: Fri, 26 Nov 2010 10:20:52 +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/26/t1290766854ku88gxiwe9giqig.htm/, Retrieved Fri, 26 Nov 2010 11:20:54 +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/26/t1290766854ku88gxiwe9giqig.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 «

0 24 0 14 0 11 0 12 0 24 26 0 1 25 25 11 11 7 7 8 8 25 23 23 1 17 17 6 6 17 17 8 8 30 25 25 0 18 0 12 0 10 0 8 0 19 23 0 1 18 18 8 8 12 12 9 9 22 19 19 1 16 16 10 10 12 12 7 7 22 29 29 1 20 20 10 10 11 11 4 4 25 25 25 1 16 16 11 11 11 11 11 11 23 21 21 1 18 18 16 16 12 12 7 7 17 22 22 1 17 17 11 11 13 13 7 7 21 25 25 0 23 0 13 0 14 0 12 0 19 24 0 1 30 30 12 12 16 16 10 10 19 18 18 1 23 23 8 8 11 11 10 10 15 22 22 1 18 18 12 12 10 10 8 8 16 15 15 0 15 0 11 0 11 0 8 0 23 22 0 0 12 0 4 0 15 0 4 0 27 28 0 1 21 21 9 9 9 9 9 9 22 20 20 0 15 0 8 0 11 0 8 0 14 12 0 0 20 0 8 0 17 0 7 0 22 24 0 1 31 31 14 14 17 17 11 11 23 20 20 1 27 27 15 15 11 11 9 9 23 21 21 0 34 0 16 0 18 0 11 0 21 20 0 1 21 21 9 9 14 14 13 13 19 21 21 0 31 0 14 0 10 0 8 0 18 23 0 0 19 0 11 0 11 0 8 0 20 28 0 1 16 16 8 8 15 15 9 9 23 24 24 1 20 20 9 9 15 15 6 6 25 24 24 0 21 0 9 0 13 0 9 0 19 24 0 0 22 0 9 0 16 0 9 0 24 23 0 1 17 17 9 9 13 13 6 6 22 23 23 0 24 0 10 0 9 0 6 0 25 29 0 1 25 25 16 16 18 18 16 16 26 24 24 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 PS[t] = + 6.64886266317348 + 1.00060504318254G[t] + 0.357831221394554CM[t] -0.0605931223005844`CM*G`[t] -0.474063883689896D[t] + 0.160074708225534`D*G`[t] -0.0192549611452811PE[t] + 0.307813649819778`PE*G`[t] + 0.0940545498504233PC[t] -0.128018935601633`PC*G`[t] + 0.526291068222185O[t] -0.156397668244835`O*G`[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) 6.64886266317348 4.027199 1.651 0.10089 0.050445 G 1.00060504318254 4.892433 0.2045 0.838231 0.419116 CM 0.357831221394554 0.086665 4.1289 6.1e-05 3.1e-05 `CM*G` -0.0605931223005844 0.115787 -0.5233 0.601547 0.300774 D -0.474063883689896 0.172618 -2.7463 0.006785 0.003393 `D*G` 0.160074708225534 0.229485 0.6975 0.486575 0.243288 PE -0.0192549611452811 0.171933 -0.112 0.910984 0.455492 `PE*G` 0.307813649819778 0.217427 1.4157 0.15899 0.079495 PC 0.0940545498504233 0.228131 0.4123 0.680737 0.340368 `PC*G` -0.128018935601633 0.278779 -0.4592 0.646764 0.323382 O 0.526291068222185 0.131322 4.0076 9.7e-05 4.9e-05 `O*G` -0.156397668244835 0.159899 -0.9781 0.329641 0.164821 Multiple Linear Regression - Regression Statistics Multiple R 0.623538425311713 R-squared 0.388800167840211 Adjusted R-squared 0.342750865417213 F-TEST (value) 8.44312828604408 F-TEST (DF numerator) 11 F-TEST (DF denominator) 146 p-value 2.11740625033485e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.42879202788709 Sum Squared Residuals 1716.4657564933 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.2003354043681 0.799664595631942 2 25 21.8822831877881 3.11771681221189 3 30 24.6996979590578 5.30030204094217 4 19 20.0656394004575 -1.06563940045752 5 22 20.6728394782353 1.32716052176471 6 22 23.2172477003945 -1.21724770039454 7 25 22.7399609654402 2.26003903455985 8 23 19.5196950934320 3.48030490656796 9 17 19.3385350459549 -2.33853504595486 10 21 22.0094817127892 -1.00948171278925 11 19 22.2062210467831 -3.20622104678314 12 19 23.7341169344749 -4.7341169344749 13 15 22.9461870992115 -7.94618709921147 14 16 17.3941561848707 -1.39415618487066 15 23 18.9206635905963 4.07933640940371 16 27 23.8701254775922 3.12987452240781 17 22 20.7547819340067 1.24521806599331 18 14 15.0799445594441 -1.07994455944413 19 22 22.975009168361 -0.975009168361003 20 23 24.3977577855181 -1.39775778551813 21 23 21.6012862531107 1.39871374688932 22 21 22.4439341637333 -1.44393416373326 23 19 22.4316112343517 -3.43161123435168 24 18 23.7693175112069 -5.76931751120692 25 20 23.5097348855076 -3.50973488550761 26 23 22.7935063459576 0.206493654042416 27 25 23.7703627241227 1.22963727587727 28 19 23.1239054503476 -4.12390545034763 29 24 22.8976807200842 1.10231927991584 30 22 21.9316376495145 0.0683623504855209 31 25 26.1496467669822 -1.14964676698218 32 26 23.5846611998534 2.41533880014656 33 29 23.6060930196684 5.39390698033157 34 32 25.0407953432596 6.95920465674041 35 25 22.2441924470041 2.75580755299586 36 29 24.5890400313327 4.41095996866733 37 28 25.2120263982880 2.78797360171203 38 17 15.5332631186612 1.46673688133885 39 28 26.3173553384188 1.68264466158119 40 29 22.4378934780784 6.56210652192159 41 26 26.7717619565117 -0.771761956511709 42 25 23.6044936764052 1.39550632359481 43 14 17.7597459527778 -3.7597459527778 44 25 22.8312781012892 2.16872189871082 45 26 21.7294296106264 4.27057038937358 46 20 20.0254729115729 -0.0254729115729464 47 18 21.7760006151216 -3.77600061512159 48 32 24.8424168836627 7.15758311633735 49 25 24.8280182030008 0.171981796999167 50 25 22.5256039357486 2.47439606425143 51 23 21.2783813114013 1.72161868859874 52 21 21.9756121974588 -0.975612197458829 53 20 24.0023423110419 -4.00234231104186 54 15 16.5489407322832 -1.54894073228325 55 30 24.8204190866672 5.17958091333277 56 24 25.2136967791899 -1.21369677918994 57 26 24.2269251092524 1.77307489074756 58 24 20.8126437013184 3.18735629868161 59 22 22.6019735156847 -0.601973515684749 60 14 16.4988057281025 -2.49880572810254 61 24 22.2381265941369 1.76187340586312 62 24 22.3676779171065 1.63232208289353 63 24 23.6882076241194 0.311792375880633 64 24 20.2504310571308 3.74956894286921 65 19 17.8496987859843 1.15030121401567 66 31 27.8969755086368 3.10302449136319 67 22 27.1207369204232 -5.1207369204232 68 27 20.7353152530415 6.26468474695845 69 19 17.2355675609602 1.76443243903984 70 25 22.2901142469709 2.70988575302905 71 20 24.8228294406094 -4.82282944060944 72 21 21.3379147072532 -0.337914707253221 73 27 27.3806373577635 -0.380637357763491 74 23 24.8875313004724 -1.88753130047238 75 25 25.9236847186639 -0.923684718663894 76 20 22.3048028084823 -2.30480280848232 77 22 22.7351814508955 -0.735181450895488 78 23 23.5812170311852 -0.581217031185181 79 25 24.2033849886421 0.79661501135793 80 25 23.4888364236610 1.51116357633895 81 17 23.6354773260822 -6.63547732608216 82 19 20.5550771129832 -1.55507711298315 83 25 24.2370530452567 0.762946954743252 84 19 22.7681782856785 -3.76817828567853 85 20 21.9299036998312 -1.92990369983115 86 26 22.6333412788056 3.36665872119444 87 23 21.2210193393725 1.77898066062755 88 27 24.4833567931915 2.51664320680848 89 17 20.1864517806465 -3.18645178064651 90 17 22.4294326278752 -5.42943262787521 91 19 20.034027614319 -1.03402761431901 92 17 19.5611321529523 -2.56113215295232 93 22 22.5712761469369 -0.57127614693691 94 21 24.1196806843661 -3.11968068436606 95 32 28.9933452561864 3.00665474381355 96 21 23.8908065855408 -2.8908065855408 97 21 24.7417584656952 -3.74175846569519 98 18 20.6605156643364 -2.66051566433641 99 18 21.5563365981081 -3.55633659810815 100 23 23.1025501030034 -0.102550103003389 101 19 20.0832639962876 -1.08326399628756 102 20 21.8295927359971 -1.82959273599708 103 21 22.6142313584396 -1.61423135843962 104 20 24.2332682879392 -4.23326828793917 105 17 19.2372963735279 -2.23729637352785 106 18 20.3155783697159 -2.31557836971592 107 19 20.9172996003486 -1.91729960034863 108 22 22.4071052135827 -0.407105213582672 109 15 17.4804792532474 -2.48047925324740 110 14 19.2545777542679 -5.25457775426786 111 18 26.5470290665061 -8.54702906650608 112 24 21.7579340054308 2.24206599456924 113 35 23.9911319079473 11.0088680920527 114 29 18.8830850110273 10.1169149889727 115 21 22.3522465116134 -1.35224651161343 116 25 21.2253467574949 3.77465324250507 117 20 17.9078536513086 2.09214634869144 118 22 22.1464009951858 -0.146400995185805 119 13 15.6547467676035 -2.65474676760355 120 26 22.8371997271915 3.16280027280852 121 17 17.5001681270367 -0.500168127036697 122 25 20.4870454276716 4.51295457232843 123 20 20.3710266060241 -0.371026606024124 124 19 17.6279970612174 1.37200293878259 125 21 21.1205809989196 -0.120580998919554 126 22 21.2232967322472 0.77670326775282 127 24 22.6600076469483 1.3399923530517 128 21 23.211232304497 -2.21123230449700 129 26 25.2122420087995 0.787757991200534 130 24 20.7705608654128 3.22943913458719 131 16 20.5381252902889 -4.53812529028889 132 23 22.4074544241027 0.592545575897344 133 18 20.8620827426893 -2.86208274268930 134 16 22.0487509097304 -6.04875090973041 135 26 21.9234937079499 4.0765062920501 136 19 19.5746801581445 -0.574680158144459 137 21 17.4860810651882 3.51391893481176 138 21 22.1858994096046 -1.18589940960459 139 22 18.6764148543751 3.32358514562488 140 23 19.6406185486665 3.35938145133349 141 29 24.9251318457098 4.0748681542902 142 21 20.3323884410474 0.667611558952556 143 21 20.0188337156783 0.98116628432175 144 23 22.4791527699975 0.520847230002501 145 27 23.0933466330199 3.90665336698006 146 25 25.665739034365 -0.665739034365009 147 21 21.1025899837641 -0.102589983764136 148 10 17.5450137047189 -7.5450137047189 149 20 22.7748382661863 -2.77483826618630 150 26 22.4024263631451 3.59757363685486 151 24 24.1709732057960 -0.170973205796031 152 29 32.039524903068 -3.03952490306797 153 19 19.637559433908 -0.637559433907981 154 24 22.8678535163986 1.13214648360138 155 19 21.1918508495598 -2.19185084955978 156 24 23.2028599541002 0.797140045899833 157 22 22.2332378774937 -0.233237877493685 158 17 24.1770748831824 -7.17707488318235 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.973088949667026 0.0538221006659476 0.0269110503329738 16 0.94455559813714 0.110888803725721 0.0554444018628604 17 0.902156584036718 0.195686831926563 0.0978434159632816 18 0.84104471966543 0.31791056066914 0.15895528033457 19 0.830628482735025 0.33874303452995 0.169371517264975 20 0.818097677611522 0.363804644776956 0.181902322388478 21 0.801927021381503 0.396145957236994 0.198072978618497 22 0.766797923299243 0.466404153401514 0.233202076700757 23 0.721279605424518 0.557440789150964 0.278720394575482 24 0.685525749284692 0.628948501430616 0.314474250715308 25 0.677437751328814 0.645124497342373 0.322562248671186 26 0.601262997425155 0.79747400514969 0.398737002574845 27 0.524883878973261 0.950232242053478 0.475116121026739 28 0.467165425594442 0.934330851188883 0.532834574405558 29 0.430749536794706 0.861499073589412 0.569250463205294 30 0.366430883394089 0.732861766788177 0.633569116605911 31 0.344030905580567 0.688061811161133 0.655969094419433 32 0.35773109149087 0.71546218298174 0.64226890850913 33 0.445385199552044 0.890770399104089 0.554614800447956 34 0.590563294799148 0.818873410401705 0.409436705200852 35 0.55154870089086 0.89690259821828 0.44845129910914 36 0.603875367231965 0.79224926553607 0.396124632768035 37 0.647058662796457 0.705882674407085 0.352941337203543 38 0.611674796538519 0.776650406922963 0.388325203461481 39 0.55771213498035 0.8845757300393 0.44228786501965 40 0.673281516708229 0.653436966583543 0.326718483291771 41 0.618109622794757 0.763780754410486 0.381890377205243 42 0.564219071896227 0.871561856207547 0.435780928103774 43 0.56915673969955 0.8616865206009 0.43084326030045 44 0.527624384980633 0.944751230038734 0.472375615019367 45 0.559711007952347 0.880577984095307 0.440288992047653 46 0.503619458047092 0.992761083905816 0.496380541952908 47 0.511778323050971 0.976443353898058 0.488221676949029 48 0.615039577642598 0.769920844714803 0.384960422357402 49 0.565059515946604 0.869880968106793 0.434940484053396 50 0.533238439274767 0.933523121450466 0.466761560725233 51 0.526126199504565 0.94774760099087 0.473873800495435 52 0.476114900694779 0.952229801389559 0.523885099305221 53 0.512094326982101 0.975811346035799 0.487905673017899 54 0.47028700262356 0.94057400524712 0.52971299737644 55 0.635254901233033 0.729490197533934 0.364745098766967 56 0.592381615373818 0.815236769252364 0.407618384626182 57 0.552167282679787 0.895665434640426 0.447832717320213 58 0.53537733345995 0.929245333080101 0.464622666540050 59 0.487265014956429 0.974530029912859 0.51273498504357 60 0.45044194001358 0.90088388002716 0.54955805998642 61 0.411744970142045 0.82348994028409 0.588255029857955 62 0.375069660516152 0.750139321032304 0.624930339483848 63 0.329853050494562 0.659706100989124 0.670146949505438 64 0.338069647040874 0.676139294081748 0.661930352959126 65 0.296414375750511 0.592828751501023 0.703585624249489 66 0.335604366728279 0.671208733456558 0.664395633271721 67 0.395281433077466 0.790562866154933 0.604718566922534 68 0.506950636485358 0.986098727029284 0.493049363514642 69 0.459195543956686 0.918391087913372 0.540804456043314 70 0.443038281790675 0.88607656358135 0.556961718209325 71 0.515759291070674 0.968481417858652 0.484240708929326 72 0.467302653641881 0.934605307283763 0.532697346358118 73 0.422440630430215 0.844881260860431 0.577559369569784 74 0.388777337282568 0.777554674565137 0.611222662717432 75 0.353922907707424 0.707845815414848 0.646077092292576 76 0.328408619501094 0.656817239002188 0.671591380498906 77 0.28675667354655 0.5735133470931 0.71324332645345 78 0.251274096694671 0.502548193389342 0.748725903305329 79 0.215995566458201 0.431991132916402 0.784004433541799 80 0.189909105734587 0.379818211469173 0.810090894265413 81 0.298742963111195 0.59748592622239 0.701257036888805 82 0.269584894977688 0.539169789955375 0.730415105022312 83 0.232667143336634 0.465334286673269 0.767332856663366 84 0.229824027520288 0.459648055040576 0.770175972479712 85 0.204387917861425 0.408775835722849 0.795612082138575 86 0.203820724925977 0.407641449851955 0.796179275074023 87 0.180276452137965 0.36055290427593 0.819723547862035 88 0.166879361023855 0.333758722047711 0.833120638976145 89 0.160350709662245 0.320701419324489 0.839649290337755 90 0.194364208084727 0.388728416169453 0.805635791915273 91 0.164943518734998 0.329887037469996 0.835056481265002 92 0.147068604750052 0.294137209500104 0.852931395249948 93 0.123113993144372 0.246227986288744 0.876886006855628 94 0.113183538782221 0.226367077564442 0.88681646121778 95 0.11049532271011 0.22099064542022 0.88950467728989 96 0.100911234076297 0.201822468152595 0.899088765923703 97 0.101817210078911 0.203634420157823 0.898182789921088 98 0.0902633387872756 0.180526677574551 0.909736661212724 99 0.0885709477327893 0.177141895465579 0.91142905226721 100 0.0698674350752704 0.139734870150541 0.93013256492473 101 0.0552428680460308 0.110485736092062 0.94475713195397 102 0.0441207770846839 0.0882415541693678 0.955879222915316 103 0.0348122420432040 0.0696244840864079 0.965187757956796 104 0.039782210379665 0.07956442075933 0.960217789620335 105 0.0327543072288038 0.0655086144576077 0.967245692771196 106 0.0290744949333668 0.0581489898667335 0.970925505066633 107 0.0257265403774991 0.0514530807549982 0.9742734596225 108 0.0188772279661053 0.0377544559322106 0.981122772033895 109 0.0157886676240331 0.0315773352480661 0.984211332375967 110 0.0218758058986637 0.0437516117973274 0.978124194101336 111 0.112968174875058 0.225936349750117 0.887031825124942 112 0.110198659331325 0.220397318662650 0.889801340668675 113 0.470134746456066 0.940269492912132 0.529865253543934 114 0.797426572679204 0.405146854641592 0.202573427320796 115 0.756358370689361 0.487283258621278 0.243641629310639 116 0.81821525330709 0.363569493385819 0.181784746692910 117 0.82710984529455 0.345780309410899 0.172890154705449 118 0.791777610955696 0.416444778088607 0.208222389044304 119 0.771571589636254 0.456856820727492 0.228428410363746 120 0.742384595911409 0.515230808177182 0.257615404088591 121 0.688276411621966 0.623447176756067 0.311723588378034 122 0.709152670239552 0.581694659520896 0.290847329760448 123 0.6536540889557 0.692691822088599 0.346345911044299 124 0.691164283018335 0.617671433963329 0.308835716981665 125 0.641332709622885 0.71733458075423 0.358667290377115 126 0.595140031182743 0.809719937634513 0.404859968817257 127 0.538883780298492 0.922232439403015 0.461116219701508 128 0.474404993363325 0.94880998672665 0.525595006636675 129 0.412659241960565 0.82531848392113 0.587340758039435 130 0.392256283999552 0.784512567999103 0.607743716000448 131 0.39871739209824 0.79743478419648 0.60128260790176 132 0.32483441360426 0.64966882720852 0.67516558639574 133 0.294280632652042 0.588561265304083 0.705719367347958 134 0.246405404082550 0.492810808165099 0.75359459591745 135 0.192611400976326 0.385222801952652 0.807388599023674 136 0.141537893395174 0.283075786790347 0.858462106604826 137 0.133520115918677 0.267040231837354 0.866479884081323 138 0.088850382676402 0.177700765352804 0.911149617323598 139 0.0648716483708902 0.129743296741780 0.93512835162911 140 0.0458075186903516 0.0916150373807031 0.954192481309648 141 0.0511513121391102 0.102302624278220 0.94884868786089 142 0.0861263857412065 0.172252771482413 0.913873614258793 143 0.0424546495638446 0.0849092991276893 0.957545350436155 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 3 0.0232558139534884 OK 10% type I error level 12 0.0930232558139535 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/10pm0e1290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/10pm0e1290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/1tc251290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/1tc251290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/2tc251290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/2tc251290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/3tc251290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/3tc251290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/4llj81290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/4llj81290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/5llj81290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/5llj81290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/6llj81290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/6llj81290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/7wcib1290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/7wcib1290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/8pm0e1290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/8pm0e1290766840.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/9pm0e1290766840.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290766854ku88gxiwe9giqig/9pm0e1290766840.ps (open in new window)

Parameters (Session):

par1 = 10 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 10 ; 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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