Mini-Tutorial FMPS

*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: Mon, 22 Nov 2010 11:26:18 +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/22/t129042550883vx5i4roau69p6.htm/, Retrieved Mon, 22 Nov 2010 12:33:04 +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/22/t129042550883vx5i4roau69p6.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 «

26 9 15 6 25 25 20 9 15 6 25 24 21 9 14 13 19 21 31 14 10 8 18 23 21 8 10 7 18 17 18 8 12 9 22 19 15 14 9 8 23 29 29 15 18 11 23 23 22 9 14 9 25 23 16 11 11 11 23 21 24 14 11 12 24 26 33 14 9 6 32 24 17 6 17 8 30 25 31 10 21 12 32 26 22 9 16 9 24 23 38 11 21 7 29 29 26 14 14 8 17 24 28 8 24 20 30 20 25 11 7 8 25 23 24 10 9 6 25 29 25 16 18 16 26 24 15 11 11 8 23 22 28 11 13 6 25 22 28 11 13 6 25 22 25 7 18 11 35 17 23 13 14 12 19 24 23 10 12 8 20 21 18 9 12 8 21 24 19 9 9 7 21 23 27 15 11 9 23 21 18 13 8 9 24 24 26 16 5 4 23 24 18 12 10 8 19 23 18 6 11 8 17 26 28 14 11 8 24 24 12 4 15 4 27 28 28 12 16 14 27 22 29 10 12 8 25 23 20 14 14 10 18 24 17 9 13 6 22 23 20 10 10 8 26 23 29 14 18 10 26 30 31 14 17 11 23 20 21 10 12 8 16 23 19 9 13 8 27 21 23 14 13 10 25 27 15 8 11 8 14 12 24 9 13 10 19 15 28 8 12 7 20 22 22 10 12 8 26 27 16 9 12 8 16 21 19 9 12 7 18 21 21 9 9 9 22 20 17 9 17 9 25 21 26 11 18 5 29 18 21 15 7 5 21 24 20 8 17 7 22 24 16 10 12 7 22 29 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 6.22294541070322 + 0.329668770012704CM[t] -0.307335861753657D[t] + 0.178919946656884PE[t] + 0.0935033736509635PC[t] + 0.407206747380311O[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) 6.22294541070322 2.34676 2.6517 0.008893 0.004447 CM 0.329668770012704 0.057216 5.7619 0 0 D -0.307335861753657 0.110252 -2.7876 0.006018 0.003009 PE 0.178919946656884 0.102502 1.7455 0.082998 0.041499 PC 0.0935033736509635 0.130989 0.7138 0.476473 0.238236 O 0.407206747380311 0.074276 5.4824 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.617279978710385 R-squared 0.381034572116694 Adjusted R-squared 0.359837125956307 F-TEST (value) 17.9754942757563 F-TEST (DF numerator) 5 F-TEST (DF denominator) 146 p-value 7.23865412055602e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40954750236372 Sum Squared Residuals 1697.2520689477 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 25.4532988015174 -0.453298801517387 2 25 23.0680794340608 1.93192056593915 3 19 22.6517316308325 -3.65173163083251 4 18 24.0429568620695 -6.04295686206954 5 18 20.0535404745316 -2.05354047453161 6 22 20.4237942998698 1.57620570013019 7 23 21.0325770794913 1.96742292050875 8 23 24.7881531544984 -1.78815315449844 9 25 23.421800401002 1.57819959899801 10 23 19.6649494699891 3.3350505300109 11 24 23.5098291553823 0.49017084461772 12 32 24.7435744555164 7.25642554448355 13 30 23.9531340972797 6.04686590272026 14 32 28.8360534590547 3.16394654094532 15 24 23.7796402943158 0.220359705684247 16 29 31.5905023612761 -2.59050236127607 17 17 23.5174995460139 -6.51749954601387 18 30 27.3032652174204 2.69673478257962 19 25 22.4501919872836 2.54980801271637 20 25 25.0419327093183 -0.0419327093182908 21 26 24.0368658283291 1.96313417167091 22 23 19.4619773264038 3.53802267359619 23 25 23.9185044825808 1.08149551741919 24 25 23.9185044825808 1.08149551741919 25 35 23.484924484195 11.515075515805 26 19 23.2098425923333 -4.20984259233326 27 20 22.1783765475357 -2.17837654753568 28 21 22.0589888013667 -1.05898880136675 29 21 21.3511876103775 -0.351187610377524 30 23 21.8749557458123 1.12504425418771 31 24 20.2074689413755 3.79253105862445 32 23 20.9185348079907 2.08146519200926 33 19 20.3719345754117 -1.37193457541170 34 17 23.6164899347315 -6.61648993473145 35 24 23.6400772460686 0.359922753931377 36 27 23.4092288249468 3.59077117505316 37 27 24.8959554500055 2.10404454999448 38 25 24.9708026623725 0.0291973376274716 39 18 21.7264936732396 -3.72649367323957 40 22 21.3140264833287 0.685973516671312 41 26 21.6459438389444 4.35405616105558 42 26 27.8524328742633 -1.85243287426331 43 23 24.3542863674797 -1.35428636747969 44 16 22.3334525022709 -6.33345250227089 45 27 21.3459572758954 5.6540427241046 46 25 23.7582002787617 1.24179972123827 47 14 16.3119174378617 -2.31191743786168 48 19 20.738067388979 -1.73806738897899 49 20 24.7550954948359 -4.75509549483586 50 26 24.2919482618048 1.70805173819516 51 16 20.1780310192004 -4.1780310192004 52 18 21.0735339555876 -3.07353395558755 53 22 20.9759116555639 1.02408834443607 54 25 21.4958028961485 3.50419710385151 55 29 22.4314363126676 6.56856368733238 56 21 20.0288700866456 0.971129913354392 57 22 23.8267585627793 -1.82675856277927 58 22 23.0348457628383 -1.03484576283827 59 32 24.9877094269387 7.01229057306132 60 23 19.9630107926281 3.03698920737188 61 31 26.6966440713575 4.30335592864250 62 18 21.2132142294192 -3.21321422941924 63 23 23.1448438297063 -0.144843829706266 64 24 22.2300301523853 1.76996984761468 65 19 17.7249865310024 1.27501346899761 66 26 25.6956278435125 0.304372156487544 67 14 15.8175645184084 -1.81756451840838 68 20 20.5239986732194 -0.523998673219369 69 22 21.0558616664308 0.944138333569198 70 24 22.7325724490062 1.26742755099384 71 25 22.2652637857581 2.73473621424193 72 21 24.6819147568961 -3.68191475689609 73 21 24.6819147568961 -3.68191475689609 74 28 24.8511685460168 3.1488314539832 75 24 21.4702542646195 2.52974573538049 76 15 18.7840137331429 -3.7840137331429 77 21 23.6183646141654 -2.61836461416543 78 23 22.9021431348083 0.0978568651917416 79 24 22.7391481659886 1.26085183401142 80 21 23.0174097013384 -2.01740970133844 81 21 25.0518817936013 -4.05188179360135 82 13 16.5346871154700 -3.53468711547003 83 17 18.9997209006796 -1.99972090067956 84 29 19.1716010434584 9.82839895654158 85 25 22.3319414186083 2.66805858139173 86 16 17.1142805963692 -1.11428059636921 87 20 20.3762617067911 -0.376261706791088 88 25 21.7501294601545 3.24987053984549 89 25 21.7572829496484 3.24271705035162 90 21 21.6072716282330 -0.607271628232959 91 23 22.3372503367166 0.662749663283391 92 22 26.4730987266287 -4.47309872662868 93 19 20.2760272253931 -1.27602722539309 94 26 24.2709483402501 1.72905165974987 95 25 23.9283487370753 1.07165126292473 96 19 18.6059866791910 0.394013320808964 97 25 22.4501919872836 2.54980801271637 98 24 23.9200052558457 0.0799947441542706 99 20 23.2238928907365 -3.22389289073650 100 21 16.9301303152302 4.06986968476979 101 14 19.4379655479216 -5.43796554792157 102 22 22.42564060147 -0.425640601470004 103 14 18.5884437025044 -4.58844370250436 104 20 24.0398174691597 -4.03981746915974 105 21 20.0685074930445 0.931492506955491 106 22 21.7912541228114 0.208745877188611 107 19 19.7482955543503 -0.748295554350274 108 28 26.3854636760682 1.61453632393183 109 25 25.2967521815657 -0.296752181565735 110 17 17.1643703033141 -0.164370303314113 111 21 22.2756777556324 -1.27567775563236 112 27 23.1680675452721 3.83193245472791 113 29 22.9439524851634 6.05604751483657 114 19 19.0138116175289 -0.0138116175289485 115 22 22.0576735269149 -0.057673526914894 116 20 22.6010193942657 -2.60101939426567 117 24 22.3737040698735 1.62629593012651 118 17 18.7057000886548 -1.70570008865482 119 21 22.1301592667587 -1.13015926675866 120 22 20.6454649651647 1.35453503483533 121 26 22.4331679971329 3.56683200286707 122 19 18.2476659645214 0.752334035478633 123 17 19.5605028295302 -2.56050282953017 124 17 16.7744846451152 0.225515354884836 125 19 22.3960836772225 -3.39608367722249 126 17 20.7661980938339 -3.7661980938339 127 15 15.9681278429511 -0.96812784295114 128 27 27.4596907499014 -0.459690749901438 129 19 21.4904939780402 -2.49049397804015 130 21 22.5910476037890 -1.59104760378895 131 25 20.4433008500144 4.55669914998562 132 19 23.5524525059058 -4.55245250590583 133 18 26.7527056444788 -8.75270564447884 134 15 23.2083418190683 -8.20834181906835 135 20 23.0554998008741 -3.05549980087412 136 29 25.0023595487702 3.99764045122981 137 19 18.6620160588657 0.337983941134325 138 20 24.2147738802086 -4.21477388020858 139 29 24.6136474567571 4.38635254324295 140 24 25.5030292513553 -1.50302925135531 141 24 20.7791817412382 3.22081825876184 142 23 22.0843034585049 0.915696541495112 143 23 19.4619773264038 3.53802267359619 144 19 23.3204184317127 -4.32041843171271 145 22 22.5773307931086 -0.57733079310862 146 22 18.9509765762350 3.04902342376504 147 25 21.7501294601545 3.24987053984549 148 21 20.8170760315631 0.182923968436935 149 22 23.460254096309 -1.46025409630901 150 21 21.605396948799 -0.605396948798987 151 18 20.3890070411402 -2.38900704114018 152 10 17.0138804138089 -7.01388041380888 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.147113918133767 0.294227836267535 0.852886081866233 10 0.135204929387749 0.270409858775498 0.864795070612251 11 0.151322698005990 0.302645396011979 0.84867730199401 12 0.819711963916198 0.360576072167603 0.180288036083802 13 0.830747706692281 0.338504586615438 0.169252293307719 14 0.797727953636923 0.404544092726154 0.202272046363077 15 0.727906104178603 0.544187791642794 0.272093895821397 16 0.744451556620712 0.511096886758575 0.255548443379288 17 0.823275176139317 0.353449647721365 0.176724823860683 18 0.798485781493355 0.403028437013290 0.201514218506645 19 0.740455900164672 0.519088199670655 0.259544099835328 20 0.736798303204102 0.526403393591796 0.263201696795898 21 0.706517213583423 0.586965572833154 0.293482786416577 22 0.680585496393455 0.63882900721309 0.319414503606545 23 0.6325115063118 0.734976987376399 0.367488493688200 24 0.577850573776035 0.84429885244793 0.422149426223965 25 0.919679192576848 0.160641614846305 0.0803208074231523 26 0.931141293286804 0.137717413426392 0.0688587067131958 27 0.926219338131326 0.147561323737348 0.073780661868674 28 0.913648507857964 0.172702984284072 0.0863514921420358 29 0.891038372952032 0.217923254095936 0.108961627047968 30 0.868474416186977 0.263051167626045 0.131525583813023 31 0.870342371029732 0.259315257940536 0.129657628970268 32 0.859064040054363 0.281871919891273 0.140935959945637 33 0.835388511952966 0.329222976094067 0.164611488047034 34 0.920910662399446 0.158178675201108 0.079089337600554 35 0.897611586829606 0.204776826340789 0.102388413170395 36 0.89006733117937 0.219865337641261 0.109932668820631 37 0.869847930496138 0.260304139007724 0.130152069503862 38 0.837721483962726 0.324557032074548 0.162278516037274 39 0.850083220591615 0.299833558816771 0.149916779408385 40 0.817254558224886 0.365490883550228 0.182745441775114 41 0.825696415084154 0.348607169831691 0.174303584915846 42 0.792172170301872 0.415655659396256 0.207827829698128 43 0.763164746166377 0.473670507667245 0.236835253833623 44 0.860863789672403 0.278272420655193 0.139136210327597 45 0.886371862666966 0.227256274666068 0.113628137333034 46 0.866032150620482 0.267935698759037 0.133967849379518 47 0.876228088499946 0.247543823000108 0.123771911500054 48 0.861526297306554 0.276947405386893 0.138473702693446 49 0.885861690299387 0.228276619401225 0.114138309700613 50 0.865057761395704 0.269884477208593 0.134942238604296 51 0.88308141701592 0.233837165968159 0.116918582984080 52 0.87906021764974 0.24187956470052 0.12093978235026 53 0.853804964500572 0.292390070998856 0.146195035499428 54 0.850278707029725 0.299442585940551 0.149721292970275 55 0.904371287905732 0.191257424188537 0.0956287120942685 56 0.883282358456327 0.233435283087346 0.116717641543673 57 0.870283911696183 0.259432176607633 0.129716088303817 58 0.845076912113268 0.309846175773463 0.154923087886732 59 0.921730461188856 0.156539077622287 0.0782695388111437 60 0.914205320988204 0.171589358023592 0.085794679011796 61 0.927037970698423 0.145924058603154 0.0729620293015768 62 0.926410300514618 0.147179398970763 0.0735896994853815 63 0.907967446639198 0.184065106721604 0.0920325533608019 64 0.892262470821927 0.215475058356146 0.107737529178073 65 0.870526786504726 0.258946426990549 0.129473213495274 66 0.843722067471357 0.312555865057286 0.156277932528643 67 0.825152557478366 0.349694885043268 0.174847442521634 68 0.793877320402195 0.41224535919561 0.206122679597805 69 0.761382803574883 0.477234392850235 0.238617196425117 70 0.73037574243301 0.539248515133979 0.269624257566989 71 0.719970579052439 0.560058841895122 0.280029420947561 72 0.724630118287694 0.550739763424613 0.275369881712306 73 0.728209467445385 0.54358106510923 0.271790532554615 74 0.730759892194187 0.538480215611626 0.269240107805813 75 0.712594367724636 0.574811264550728 0.287405632275364 76 0.722949416259338 0.554101167481323 0.277050583740662 77 0.707119697299662 0.585760605400677 0.292880302700338 78 0.665637809561558 0.668724380876884 0.334362190438442 79 0.628401039922027 0.743197920155945 0.371598960077973 80 0.597497994979551 0.805004010040898 0.402502005020449 81 0.610007713865865 0.77998457226827 0.389992286134135 82 0.610191774619665 0.77961645076067 0.389808225380335 83 0.588329579156292 0.823340841687415 0.411670420843708 84 0.895353758953012 0.209292482093976 0.104646241046988 85 0.89391009971313 0.212179800573740 0.106089900286870 86 0.872964848514785 0.254070302970430 0.127035151485215 87 0.845831992317135 0.308336015365730 0.154168007682865 88 0.84269573455656 0.31460853088688 0.15730426544344 89 0.848594816129995 0.302810367740009 0.151405183870005 90 0.81867903242369 0.362641935152619 0.181320967576309 91 0.7993433846374 0.4013132307252 0.2006566153626 92 0.816281806089001 0.367436387821998 0.183718193910999 93 0.788735866258767 0.422528267482466 0.211264133741233 94 0.763505591588213 0.472988816823573 0.236494408411787 95 0.752174256241793 0.495651487516413 0.247825743758207 96 0.729933462692475 0.540133074615051 0.270066537307525 97 0.714808699178056 0.570382601643888 0.285191300821944 98 0.674953886687793 0.650092226624413 0.325046113312207 99 0.65727278251119 0.685454434977620 0.342727217488810 100 0.667301315932173 0.665397368135654 0.332698684067827 101 0.731732280741544 0.536535438516912 0.268267719258456 102 0.689556628718428 0.620886742563143 0.310443371281572 103 0.706910873967355 0.586178252065291 0.293089126032645 104 0.703711648041687 0.592576703916627 0.296288351958313 105 0.657874572048852 0.684250855902296 0.342125427951148 106 0.608807423443618 0.782385153112763 0.391192576556382 107 0.578591254625464 0.842817490749071 0.421408745374536 108 0.543076998973998 0.913846002052004 0.456923001026002 109 0.494397114162215 0.98879422832443 0.505602885837785 110 0.469936065535816 0.939872131071633 0.530063934464184 111 0.422574989445845 0.84514997889169 0.577425010554155 112 0.407576998516981 0.815153997033962 0.592423001483019 113 0.555655365602816 0.888689268794368 0.444344634397184 114 0.502362079366627 0.995275841266747 0.497637920633373 115 0.445274186667016 0.890548373334031 0.554725813332984 116 0.39963288423628 0.79926576847256 0.60036711576372 117 0.364042840594064 0.728085681188128 0.635957159405936 118 0.358037241397422 0.716074482794845 0.641962758602578 119 0.3169745189728 0.6339490379456 0.6830254810272 120 0.299089436679119 0.598178873358237 0.700910563320881 121 0.502007865878346 0.995984268243307 0.497992134121653 122 0.449640962311486 0.899281924622971 0.550359037688514 123 0.41888991813859 0.83777983627718 0.581110081861409 124 0.360158381950802 0.720316763901604 0.639841618049198 125 0.452013328835182 0.904026657670364 0.547986671164818 126 0.442513438441593 0.885026876883185 0.557486561558407 127 0.377437750691911 0.754875501383823 0.622562249308088 128 0.442771813267866 0.885543626535732 0.557228186732134 129 0.428790909169518 0.857581818339036 0.571209090830482 130 0.359890392160190 0.719780784320381 0.64010960783981 131 0.342725780942418 0.685451561884835 0.657274219057582 132 0.37090822015628 0.74181644031256 0.62909177984372 133 0.368727275553479 0.737454551106957 0.631272724446521 134 0.465466397609644 0.930932795219287 0.534533602390356 135 0.4275089755833 0.8550179511666 0.5724910244167 136 0.457543195538408 0.915086391076815 0.542456804461592 137 0.365229323053411 0.730458646106822 0.634770676946589 138 0.49131736372947 0.98263472745894 0.50868263627053 139 0.401642970020619 0.803285940041238 0.598357029979381 140 0.371278519224822 0.742557038449644 0.628721480775178 141 0.4788765290502 0.9577530581004 0.5211234709498 142 0.346946180089848 0.693892360179696 0.653053819910152 143 0.245004102295685 0.49000820459137 0.754995897704315 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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