Mini-Tutorial Multiple regression + trend

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 00:53:22 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8.htm/, Retrieved Tue, 23 Nov 2010 02:06:41 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8.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:

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13 26 9 6 25 25 16 20 9 6 25 24 19 21 9 13 19 21 15 31 14 8 18 23 14 21 8 7 18 17 13 18 8 9 22 19 19 26 11 5 29 18 15 22 10 8 26 27 14 22 9 9 25 23 15 29 15 11 23 23 16 15 14 8 23 29 16 16 11 11 23 21 16 24 14 12 24 26 17 17 6 8 30 25 15 19 20 7 19 25 15 22 9 9 24 23 20 31 10 12 32 26 18 28 8 20 30 20 16 38 11 7 29 29 16 26 14 8 17 24 19 25 11 8 25 23 16 25 16 16 26 24 17 29 14 10 26 30 17 28 11 6 25 22 16 15 11 8 23 22 15 18 12 9 21 13 14 21 9 9 19 24 15 25 7 11 35 17 12 23 13 12 19 24 14 23 10 8 20 21 16 19 9 7 21 23 14 18 9 8 21 24 7 18 13 9 24 24 10 26 16 4 23 24 14 18 12 8 19 23 16 18 6 8 17 26 16 28 14 8 24 24 16 17 14 6 15 21 14 29 10 8 25 23 20 12 4 4 27 28 14 25 12 7 29 23 14 28 12 14 27 22 11 20 14 10 18 24 15 17 9 9 25 21 16 17 9 6 22 23 14 20 10 8 26 23 16 31 14 11 23 20 14 21 10 8 16 23 12 19 9 8 27 21 16 23 14 10 25 27 9 15 8 8 14 12 14 24 9 10 19 15 16 28 8 7 20 22 16 16 9 8 16 21 15 19 9 7 18 21 16 21 9 9 22 20 12 21 15 5 21 24 16 20 8 7 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Selfconfidence[t] = + 13.7934790500029 + 0.0180156866769969ConcernMistakes[t] -0.291927723214096DoubtsActions[t] + 0.0657465203235145ParentalCriticism[t] + 0.0287198566927615PersonalStandards[t] + 0.143702684659464Organization[t] -0.00594246494433589t + 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) 13.7934790500029 1.534575 8.9885 0 0 ConcernMistakes 0.0180156866769969 0.036983 0.4871 0.626911 0.313455 DoubtsActions -0.291927723214096 0.068806 -4.2428 3.9e-05 2e-05 ParentalCriticism 0.0657465203235145 0.06865 0.9577 0.33983 0.169915 PersonalStandards 0.0287198566927615 0.049129 0.5846 0.559754 0.279877 Organization 0.143702684659464 0.050059 2.8707 0.004718 0.002359 t -0.00594246494433589 0.003996 -1.487 0.139229 0.069615 Multiple Linear Regression - Regression Statistics Multiple R 0.452228504829141 R-squared 0.204510620580000 Adjusted R-squared 0.171133443821119 F-TEST (value) 6.1272594161393 F-TEST (DF numerator) 6 F-TEST (DF denominator) 143 p-value 9.7470573310332e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.06931613429479 Sum Squared Residuals 612.335904702341 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.3336375854807 -3.33363758548074 2 16 16.0758983158146 -0.0758983158146235 3 19 15.9447699856769 3.05523001432306 4 15 14.5892986824407 0.410701317559324 5 14 15.2268030617307 -1.22680306173065 6 13 15.7005913734923 -2.70059137349233 7 19 14.7573414632175 4.24265853678253 8 15 16.3756681276067 -1.37566812760669 9 14 16.1238693108693 -2.12386931086935 10 15 14.5665236406409 0.433476359359081 11 16 15.2652658324190 0.734734167581041 12 16 15.2007403074887 0.799259692511256 13 16 15.2761199666317 0.723880033368312 14 17 17.2451198548642 -0.245119854864192 15 15 12.8065556943326 2.19344430566739 16 15 16.0535521995662 -1.05355219956623 17 20 16.7759296599918 3.2240703400082 18 18 16.9061119226905 1.09388807730952 19 16 16.6144426959105 -0.614442695910548 20 16 14.5191236379130 1.48087636208698 21 19 15.4570048248166 3.5429951751834 22 16 14.6898184477421 1.31018155225788 23 17 15.8075311619497 1.19246883805034 24 17 15.2180287647081 1.78197123529191 25 16 15.0519357002243 0.9480642997757 26 15 13.5230952170997 1.47690478290032 27 14 15.9702727996972 -1.9702727996972 28 15 16.205340483004 -1.20534048300401 29 12 15.0239479112767 -3.02394791127668 30 14 15.2284143373949 -1.22841433739495 31 16 15.6927155546449 0.307284445355108 32 14 15.8782066080065 -1.87820660800654 33 7 14.8564593406076 -7.85645934060762 34 10 13.7614067411266 -3.76140674112663 35 14 14.7834536454863 -0.783453645486254 36 16 16.9027458604194 -0.902745860419365 37 16 14.6551721040626 1.34482789593737 38 16 13.6299772808111 2.37002271918895 39 14 15.7140309257406 -1.71403092574064 40 20 17.6663551819607 2.33364481803928 41 14 15.0953607091633 -1.09536070916332 42 14 15.4025485484696 -1.40254854846959 43 11 14.4345657214711 -3.4345657214711 44 15 15.5383992351137 -0.53839923511368 45 16 15.5364630084394 0.463536991560557 46 14 15.5390123477301 -1.53901234773008 47 16 14.2435034802902 1.75649651970981 48 14 15.2579445375908 -1.25794453759079 49 12 15.536411476808 -3.536411476808 50 16 15.0791625777195 0.92083742228054 51 9 14.0777092244844 -5.07770922448437 52 14 14.6481805945081 -0.648180594508136 53 16 15.8436276878243 0.156372312175652 54 16 15.1367336684350 0.863266331565044 55 15 15.1765314565836 -0.17653145658362 56 16 15.3092901477519 0.690709852248111 57 12 13.834886144174 -1.83488614417401 58 16 16.0146349523911 -0.0146349523911425 59 16 16.0712877176079 -0.0712877176079438 60 14 16.5237297074745 -2.52372970747453 61 16 13.1485841357887 2.85141586421132 62 17 16.2664248806091 0.733575119390911 63 18 14.6694522248504 3.33054777514959 64 18 15.6062333835053 2.39376661649466 65 12 14.7800039170512 -2.7800039170512 66 16 15.9537558882834 0.0462441117166169 67 10 14.2951381926323 -4.29513819263234 68 14 12.4899883098928 1.51001169010716 69 18 15.8797058555689 2.12029414443111 70 18 16.4686987805245 1.53130121947546 71 16 15.3632363414256 0.636763658574411 72 16 15.3802076905095 0.619792309490548 73 16 14.4969052331950 1.50309476680498 74 13 15.0971435209546 -2.09714352095457 75 16 15.6772437910562 0.322756208943845 76 16 14.8018907487492 1.19810925125082 77 20 16.1914124668138 3.80858753318616 78 16 15.1608286307921 0.839171369207863 79 15 12.9776122164583 2.02238778354170 80 15 15.4187091570014 -0.418709157001429 81 16 15.6482499921624 0.351750007837575 82 14 13.9812424300750 0.018757569924991 83 15 13.0636155169332 1.93638448306675 84 12 14.7857487802600 -2.78574878026002 85 17 16.5601936853592 0.439806314640777 86 16 15.2680715393687 0.731928460631289 87 15 13.2386644210268 1.76133557897321 88 13 13.7938932409074 -0.793893240907372 89 16 15.2954076006434 0.704592399356566 90 16 15.0096286724658 0.990371327534184 91 16 15.9066837598599 0.0933162401401393 92 16 16.0765102180542 -0.0765102180542046 93 14 15.4254838247883 -1.42548382478831 94 16 13.7325961558073 2.26740384419271 95 16 14.4679328718649 1.53206712813512 96 20 16.0722204155552 3.92777958444479 97 15 15.4721975088186 -0.472197508818603 98 16 13.9473264760338 2.05267352396622 99 13 13.9811759440564 -0.981175944056362 100 17 15.7643135238767 1.23568647612331 101 16 14.4631985939052 1.53680140609482 102 12 12.8878102245442 -0.887810224544209 103 16 14.5588426978605 1.44115730213954 104 16 15.0034052846745 0.996594715325516 105 17 15.1407231176682 1.85927688233178 106 13 12.7053673491815 0.294632650818494 107 12 15.5685371317235 -3.56853713172354 108 18 15.5561691072939 2.44383089270608 109 14 13.6161413977505 0.383858602249492 110 14 14.1918537242208 -0.191853724220805 111 13 13.4772974918772 -0.477297491877212 112 16 15.2947623276982 0.705237672301835 113 13 12.4578949885071 0.542105011492933 114 16 14.6831818425548 1.31681815744520 115 13 14.7804561320193 -1.78045613201928 116 16 15.7186981095429 0.281301890457062 117 15 14.2267071599497 0.773292840050268 118 16 15.1482422167288 0.851757783271154 119 15 14.5267769822037 0.473223017796286 120 17 15.3588841314868 1.64111586851321 121 15 15.8911544822112 -0.891154482211226 122 12 13.3572191455099 -1.35721914550986 123 16 14.2617338058887 1.73826619411127 124 10 14.1383684300645 -4.13836843006447 125 16 14.4903040323603 1.50969596763972 126 14 14.4339688656289 -0.433968865628915 127 15 16.0553317082176 -1.05533170821760 128 13 14.1411487810345 -1.14114878103455 129 15 14.6102607506723 0.389739249327705 130 11 13.5018747385434 -2.5018747385434 131 12 13.8421448683037 -1.84214486830369 132 8 14.0448976812577 -6.04489768125772 133 16 15.9269287498285 0.0730712501715455 134 15 14.7238016082504 0.276198391749633 135 17 15.3199074065106 1.68009259348944 136 16 14.6359154903821 1.36408450961787 137 10 14.6684993842031 -4.66849938420314 138 18 13.4070031006688 4.59299689933119 139 13 13.8367595921559 -0.836759592155873 140 15 14.1458107173901 0.854189282609896 141 16 14.3626097666813 1.63739023331866 142 16 14.4972657315346 1.50273426846543 143 14 13.3212460197243 0.678753980275703 144 10 13.1811306844677 -3.18113068446768 145 17 16.2036457886991 0.79635421130093 146 13 14.4082905442218 -1.40829054422184 147 15 15.7366503936585 -0.736650393658493 148 16 15.2475374633531 0.752462536646864 149 12 14.9459862233475 -2.94598622334754 150 13 13.3100629366699 -0.310062936669949 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.827091293900709 0.345817412198582 0.172908706099291 11 0.725385299224928 0.549229401550144 0.274614700775072 12 0.606683993293618 0.786632013412764 0.393316006706382 13 0.48559842765586 0.97119685531172 0.51440157234414 14 0.614504352121669 0.770991295756662 0.385495647878331 15 0.515025517458358 0.969948965083284 0.484974482541642 16 0.430193165425165 0.86038633085033 0.569806834574835 17 0.439016037124501 0.878032074249003 0.560983962875499 18 0.444819309403298 0.889638618806596 0.555180690596702 19 0.360166783415760 0.720333566831521 0.63983321658424 20 0.34842473675592 0.69684947351184 0.65157526324408 21 0.395605769587558 0.791211539175116 0.604394230412442 22 0.396689743024656 0.793379486049312 0.603310256975344 23 0.330531555750073 0.661063111500146 0.669468444249927 24 0.270768006840235 0.54153601368047 0.729231993159765 25 0.218442695591133 0.436885391182266 0.781557304408867 26 0.206790072195208 0.413580144390416 0.793209927804792 27 0.177031469438127 0.354062938876254 0.822968530561873 28 0.242395175136233 0.484790350272467 0.757604824863767 29 0.327751091633548 0.655502183267097 0.672248908366452 30 0.273095204730198 0.546190409460396 0.726904795269802 31 0.249113501842175 0.498227003684351 0.750886498157825 32 0.208275652107526 0.416551304215052 0.791724347892474 33 0.880944884564803 0.238110230870394 0.119055115435197 34 0.923928485837444 0.152143028325111 0.0760715141625556 35 0.907475413234787 0.185049173530426 0.0925245867652132 36 0.908395224270264 0.183209551459473 0.0916047757297365 37 0.899215358059591 0.201569283880818 0.100784641940409 38 0.922879682532272 0.154240634935456 0.0771203174677282 39 0.908848753608601 0.182302492782798 0.091151246391399 40 0.953292583033759 0.0934148339324823 0.0467074169662412 41 0.94141131869993 0.117177362600142 0.0585886813000709 42 0.929343425625805 0.141313148748389 0.0706565743741946 43 0.94277519941444 0.114449601171118 0.0572248005855591 44 0.926847686013958 0.146304627972083 0.0731523139860417 45 0.914629388185357 0.170741223629285 0.0853706118146425 46 0.89925700624662 0.201485987506761 0.100742993753380 47 0.896207094118658 0.207585811762683 0.103792905881342 48 0.877182134643325 0.245635730713349 0.122817865356675 49 0.905614307405667 0.188771385188665 0.0943856925943326 50 0.893343926120146 0.213312147759707 0.106656073879854 51 0.954872342504312 0.0902553149913752 0.0451276574956876 52 0.947471869314372 0.105056261371257 0.0525281306856285 53 0.939301377954695 0.121397244090609 0.0606986220453047 54 0.938205239938245 0.123589520123510 0.0617947600617552 55 0.927723412214833 0.144553175570334 0.0722765877851668 56 0.917199788323613 0.165600423352773 0.0828002116763867 57 0.911941039467378 0.176117921065244 0.0880589605326222 58 0.89707379713854 0.20585240572292 0.10292620286146 59 0.878397665066692 0.243204669866617 0.121602334933308 60 0.895558831348727 0.208882337302547 0.104441168651273 61 0.909300953949514 0.181398092100972 0.0906990460504862 62 0.890930654983611 0.218138690032777 0.109069345016389 63 0.92272189055416 0.154556218891679 0.0772781094458394 64 0.9294585109494 0.141082978101200 0.0705414890505998 65 0.948568840121186 0.102862319757627 0.0514311598788136 66 0.936795525600347 0.126408948799305 0.0632044743996527 67 0.975963901971986 0.0480721960560288 0.0240360980280144 68 0.97273718470749 0.0545256305850203 0.0272628152925101 69 0.973709830864236 0.0525803382715288 0.0262901691357644 70 0.970954335393692 0.0580913292126158 0.0290456646063079 71 0.9630326584046 0.073934683190799 0.0369673415953995 72 0.953550675438493 0.092898649123014 0.046449324561507 73 0.944470397893326 0.111059204213347 0.0555296021066737 74 0.954573624849172 0.0908527503016568 0.0454263751508284 75 0.943395790424638 0.113208419150723 0.0566042095753616 76 0.931533487178836 0.136933025642329 0.0684665128211644 77 0.954331443581546 0.0913371128369085 0.0456685564184543 78 0.94178229643533 0.116435407129340 0.0582177035646701 79 0.935018694715064 0.129962610569873 0.0649813052849365 80 0.9221476909498 0.155704618100400 0.0778523090501999 81 0.902873309719445 0.194253380561109 0.0971266902805546 82 0.881014015886997 0.237971968226006 0.118985984113003 83 0.871531546347529 0.256936907304942 0.128468453652471 84 0.912192468615548 0.175615062768904 0.087807531384452 85 0.895301714154344 0.209396571691313 0.104698285845657 86 0.871657749087028 0.256684501825945 0.128342250912972 87 0.853221620041344 0.293556759917312 0.146778379958656 88 0.838449174601623 0.323101650796754 0.161550825398377 89 0.811355565215008 0.377288869569984 0.188644434784992 90 0.777309404817157 0.445381190365687 0.222690595182843 91 0.746203265911503 0.507593468176994 0.253796734088497 92 0.712658609936485 0.574682780127029 0.287341390063515 93 0.746418495237452 0.507163009525095 0.253581504762548 94 0.740308372695965 0.519383254608071 0.259691627304036 95 0.705653726379441 0.588692547241118 0.294346273620559 96 0.755174916074084 0.489650167851833 0.244825083925916 97 0.722118414611942 0.555763170776115 0.277881585388058 98 0.717122836346446 0.565754327307109 0.282877163653554 99 0.703183363345878 0.593633273308244 0.296816636654122 100 0.66265565187706 0.674688696245879 0.337344348122940 101 0.631484914812465 0.73703017037507 0.368515085187535 102 0.597910999604216 0.804178000791567 0.402089000395784 103 0.552645515844247 0.894708968311506 0.447354484155753 104 0.521105530978228 0.957788938043544 0.478894469021772 105 0.507317206360101 0.985365587279798 0.492682793639899 106 0.453180141084502 0.906360282169005 0.546819858915498 107 0.61683165951022 0.76633668097956 0.38316834048978 108 0.604106688074341 0.791786623851319 0.395893311925659 109 0.581041793296397 0.837916413407205 0.418958206703603 110 0.528617794812957 0.942764410374085 0.471382205187043 111 0.475801055524423 0.951602111048846 0.524198944475577 112 0.419711958205983 0.839423916411965 0.580288041794017 113 0.377590518351442 0.755181036702884 0.622409481648558 114 0.35569669931187 0.71139339862374 0.64430330068813 115 0.349784235604928 0.699568471209857 0.650215764395072 116 0.296331885032686 0.592663770065373 0.703668114967314 117 0.274289057580411 0.548578115160822 0.725710942419589 118 0.275749986390063 0.551499972780127 0.724250013609937 119 0.226365723948334 0.452731447896668 0.773634276051666 120 0.198408852007482 0.396817704014965 0.801591147992518 121 0.163396309283653 0.326792618567307 0.836603690716347 122 0.145892462569705 0.291784925139409 0.854107537430295 123 0.134024493984568 0.268048987969136 0.865975506015432 124 0.193097807740508 0.386195615481016 0.806902192259492 125 0.157773538797603 0.315547077595207 0.842226461202397 126 0.128830158729859 0.257660317459717 0.871169841270142 127 0.0982270166897536 0.196454033379507 0.901772983310246 128 0.0809824100265978 0.161964820053196 0.919017589973402 129 0.0565412833237916 0.113082566647583 0.943458716676208 130 0.057307325754968 0.114614651509936 0.942692674245032 131 0.0489389141419211 0.0978778282838423 0.951061085858079 132 0.574500370664337 0.850999258671326 0.425499629335663 133 0.489665480400657 0.979330960801315 0.510334519599343 134 0.397061975881217 0.794123951762434 0.602938024118783 135 0.341844185201137 0.683688370402273 0.658155814798863 136 0.2530323036374 0.5060646072748 0.7469676963626 137 0.70175145570172 0.596497088596561 0.298248544298281 138 0.638857641880724 0.722284716238552 0.361142358119276 139 0.538890064080239 0.922219871839521 0.461109935919761 140 0.378239687632652 0.756479375265304 0.621760312367348 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 1 0.00763358778625954 OK 10% type I error level 11 0.083969465648855 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/10kts11290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/10kts11290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/161va1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/161va1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/261va1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/261va1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/361va1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/361va1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/4haud1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/4haud1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/5haud1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/5haud1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/6haud1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/6haud1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/791tg1290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/791tg1290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/8kts11290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/8kts11290473590.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/9kts11290473590.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290474391r9zo53yn8td0xk8/9kts11290473590.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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