workshop 7 multiple regressions

*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 13:53:50 +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/t12905203865djx88g8che4o6h.htm/, Retrieved Tue, 23 Nov 2010 14:53:09 +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/t12905203865djx88g8che4o6h.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 24 14 11 12 24 23 25 11 7 8 25 25 17 6 17 8 30 23 18 12 10 8 19 19 18 8 12 9 22 29 16 10 12 7 22 25 20 10 11 4 25 21 16 11 11 11 23 22 18 16 12 7 17 25 17 11 13 7 21 24 23 13 14 12 19 18 30 12 16 10 19 22 23 8 11 10 15 15 18 12 10 8 16 22 15 11 11 8 23 28 12 4 15 4 27 20 21 9 9 9 22 12 15 8 11 8 14 24 20 8 17 7 22 20 31 14 17 11 23 21 27 15 11 9 23 20 34 16 18 11 21 21 21 9 14 13 19 23 31 14 10 8 18 28 19 11 11 8 20 24 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 23 22 9 16 9 24 23 17 9 13 6 22 29 24 10 9 6 25 24 25 16 18 16 26 18 26 11 18 5 29 25 25 8 12 7 32 21 17 9 17 9 25 26 32 16 9 6 29 22 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 23 25 12 12 7 29 30 29 14 18 10 26 23 22 9 14 9 25 17 18 10 15 8 14 23 17 9 16 5 25 23 20 10 10 8 26 25 15 12 11 8 20 24 20 14 14 10 18 24 33 14 9 6 32 23 29 10 12 8 25 21 23 14 17 7 25 24 26 16 5 4 23 24 18 9 12 8 21 28 20 10 12 8 20 16 11 6 6 4 15 20 28 8 24 20 30 29 26 13 12 8 24 27 22 10 12 8 26 22 17 8 14 6 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation O[t] = + 16.134380517971 -0.0706755178434466CM[t] + 0.21817366617141D[t] -0.14895346558074PE[t] -0.255161534021278PC[t] + 0.422756959732833PS[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) 16.134380517971 2.001611 8.0607 0 0 CM -0.0706755178434466 0.062922 -1.1232 0.263103 0.131551 D 0.21817366617141 0.112622 1.9372 0.05456 0.02728 PE -0.14895346558074 0.104267 -1.4286 0.155164 0.077582 PC -0.255161534021278 0.130412 -1.9566 0.052218 0.026109 PS 0.422756959732833 0.075616 5.5908 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.47156352837492 R-squared 0.222372161293404 Adjusted R-squared 0.196959486825868 F-TEST (value) 8.7504430742809 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 2.54750247341562e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.4993600467452 Sum Squared Residuals 1873.56467272376 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 22.9383399200725 3.06166007992749 2 23 24.2523603618557 -1.25236036185575 3 25 24.351146316603 0.648853683396967 4 23 21.9818604977921 1.01813950220793 5 19 21.8243682471222 -2.82436824712216 6 29 22.9123896831944 6.08761031680556 7 25 24.8123965586637 0.18760344133628 8 21 22.6816276385943 -1.68162763859431 9 22 21.9662958458718 0.0337041541281645 10 25 22.4881774062088 2.51182259379118 11 24 20.2301965763382 3.76980342366183 12 18 19.7297104221437 -1.72971042214371 13 22 18.4054838713346 3.59451612866544 14 15 20.7135896185936 -5.71358961859357 15 22 23.5177877585016 -1.51778775850159 16 28 24.3184587615255 3.68154123847446 17 20 22.2773757565055 -2.27737575650546 18 12 19.0584541223919 -7.05845412239186 19 24 21.4485729515741 2.55142704842587 20 20 21.3822950759724 -1.3822950759724 21 21 23.2872146750446 -2.28721467504459 22 20 20.6121484697385 -0.612148469738471 23 21 19.2436914133181 1.75630858668185 24 23 21.0766691384372 1.92333086156275 25 28 21.9668148079293 6.0331851920707 26 24 21.9416158457997 2.05838415420033 27 24 23.4880859621268 0.511914037873207 28 24 20.413291014984 3.586708985016 29 23 22.0095398990625 0.990460100937506 30 23 22.7297485676201 0.270251432379885 31 29 24.3172783504089 4.68272164959114 32 24 22.0862052588873 1.91379474111273 33 18 24.9997091636193 -6.99970916361933 34 25 26.0675322875889 -1.06753228758893 35 21 22.6367209824318 -1.63672098243182 36 26 26.7519440436211 -0.751944043621079 37 22 25.1676432351877 -3.16764323518775 38 22 22.8299965031316 -0.829996503131624 39 22 22.5849420248483 -0.584942024848278 40 23 25.6719560730761 -2.67195607307607 41 30 22.8981250592983 7.10187494070167 42 23 22.7302037899568 0.269796210043192 43 17 18.6869610388814 -1.68696103888138 44 23 23.8063205840977 -0.806320584097671 45 23 24.3634608478922 -1.36346084789218 46 25 22.4676905454745 2.5323094545255 47 24 20.7479629043496 3.25203709565036 48 24 27.5131920726333 -3.51319207263331 49 23 23.0067172964069 -0.00671729640684957 50 21 23.8138592742707 -2.81385927427075 51 24 25.7455923226503 -1.74559232265028 52 24 21.874946487582 2.12505351241798 53 28 21.5290121583337 6.4709878416663 54 16 21.0929792851445 -5.09297928514447 55 20 19.9054502853474 0.0945497146525729 56 29 23.4505078887186 5.54949211128141 57 27 23.9242028810438 3.07579711895619 58 22 23.2081353553336 -1.20813535533363 59 28 24.0508226860215 3.94917731397847 60 16 20.3584383722737 -4.3584383722737 61 25 22.9587313506027 2.04126864939731 62 24 23.5107340818834 0.489265918116595 63 28 23.6843174503111 4.3156825496889 64 24 24.3565643597678 -0.356564359767843 65 23 22.7274484446799 0.27255155532009 66 30 26.9737777197813 3.02622228021869 67 24 21.3097015147594 2.69029848524062 68 21 24.1918592625548 -3.19185926255483 69 25 23.3464368925971 1.65356310740295 70 25 24.00992408875 0.99007591124998 71 22 20.7824222172646 1.21757778273541 72 23 22.5062929005021 0.493707099497928 73 26 22.8613601010942 3.13863989890584 74 23 21.59286631225 1.40713368775004 75 25 23.0640328550661 1.93596714493389 76 21 21.3169856048034 -0.316985604803363 77 25 23.6805620101181 1.31943798988188 78 24 22.187129427116 1.81287057288401 79 29 23.60221281888 5.39778718112005 80 22 23.6569360828835 -1.65693608288352 81 27 23.6441885345299 3.35581146547012 82 26 19.6783511157172 6.3216488842828 83 22 21.3229735475195 0.677026452480496 84 24 22.1003126942895 1.89968730571047 85 27 23.128221774143 3.87177822585703 86 24 21.33585797836 2.66414202164002 87 24 24.9093164665318 -0.90931646653183 88 29 24.4702156881773 4.5297843118227 89 22 22.2324709996082 -0.232470999608157 90 21 20.5865783309999 0.413421669000071 91 24 20.4114759055987 3.58852409440132 92 24 21.8282789765438 2.1717210234562 93 23 21.9739620154865 1.02603798451355 94 20 22.2966377134128 -2.29663771341281 95 27 21.4429013672768 5.55709863272324 96 26 23.463437652538 2.53656234746198 97 25 21.9303119536343 3.06968804636567 98 21 20.0558435264202 0.944156473579805 99 21 20.7911616245614 0.208838375438649 100 19 20.3931937376004 -1.3931937376004 101 21 21.6280730192171 -0.628073019217087 102 21 21.3154348573464 -0.315434857346428 103 16 19.7578411650546 -3.75784116505456 104 22 20.6995893566258 1.30041064337417 105 29 21.8283106670272 7.17168933297281 106 15 21.6944964222482 -6.69449642224818 107 17 20.7295438538645 -3.72954385386453 108 15 19.9461029274324 -4.94610292743238 109 21 21.6814981544617 -0.681498154461724 110 21 21.0102716459281 -0.0102716459280732 111 19 19.3060132265193 -0.306013226519288 112 24 18.0652867653696 5.93471323463043 113 20 22.3943929417572 -2.39439294175716 114 17 25.2032625710465 -8.20326257104646 115 23 25.0688900877806 -2.0688900877806 116 24 22.4146549935806 1.5853450064194 117 14 22.096010482252 -8.09601048225197 118 19 22.9163958428202 -3.91639584282023 119 24 22.1918212225043 1.80817877749572 120 13 20.4043471047834 -7.40434710478335 121 22 25.4130613862999 -3.4130613862999 122 16 21.1581295863886 -5.15812958638857 123 19 23.3107490527713 -4.31074905277131 124 25 22.8500862767351 2.14991372326489 125 25 24.2096427745027 0.790357225497343 126 23 21.4251754563342 1.57482454366575 127 24 23.6101094019204 0.389890598079626 128 26 23.5871671290172 2.41283287098281 129 26 21.5400516885707 4.45994831142933 130 25 24.1684203150323 0.831579684967723 131 18 22.382424560105 -4.38242456010498 132 21 19.9025127246047 1.09748727539525 133 26 23.7055739925357 2.29442600746429 134 23 21.9973595107263 1.00264048927367 135 23 19.7673088015589 3.23269119844108 136 22 22.5940710154958 -0.594071015495776 137 20 22.4124503008445 -2.41245030084455 138 13 22.1253524864942 -9.12535248649423 139 24 21.4722868052328 2.52771319476722 140 15 21.6118883705203 -6.61188837052032 141 14 23.1549213865043 -9.15492138650432 142 22 24.1062334850528 -2.10623348505278 143 10 17.6923817161542 -7.69238171615418 144 24 24.4822138610477 -0.482213861047675 145 22 21.8708765882355 0.129123411764547 146 24 25.8205497465243 -1.82054974652427 147 19 21.6472637326236 -2.64726373262357 148 20 22.1377104514971 -2.13771045149714 149 13 17.1108094321865 -4.11080943218647 150 20 20.1430837911 -0.143083791099954 151 22 23.3048248497759 -1.30482484977593 152 24 23.367863989223 0.632136010777037 153 29 23.1944194847132 5.80558051528681 154 12 20.9591466336236 -8.95914663362364 155 20 20.9707782686841 -0.970778268684136 156 21 21.4614776884216 -0.461477688421615 157 24 23.6762839847838 0.323716015216156 158 22 21.9305125758419 0.0694874241580689 159 20 17.7083860486504 2.29161395134965 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.725321323051689 0.549357353896623 0.274678676948311 10 0.598646410990628 0.802707178018743 0.401353589009372 11 0.489326081512457 0.978652163024914 0.510673918487543 12 0.444855893125708 0.889711786251417 0.555144106874292 13 0.452954235062625 0.90590847012525 0.547045764937375 14 0.693424168960564 0.613151662078872 0.306575831039436 15 0.62489742460661 0.750205150786779 0.37510257539339 16 0.572942457733762 0.854115084532476 0.427057542266238 17 0.506926763076946 0.986146473846108 0.493073236923054 18 0.637026244645205 0.72594751070959 0.362973755354795 19 0.562011259448265 0.87597748110347 0.437988740551735 20 0.567128159613713 0.865743680772574 0.432871840386287 21 0.519310434734046 0.961379130531908 0.480689565265954 22 0.450175128547052 0.900350257094104 0.549824871452948 23 0.391153994468666 0.782307988937332 0.608846005531334 24 0.391798132523954 0.783596265047908 0.608201867476046 25 0.535610016044239 0.928779967911521 0.464389983955761 26 0.473009181805933 0.946018363611866 0.526990818194067 27 0.409442266741783 0.818884533483566 0.590557733258217 28 0.402731633034033 0.805463266068066 0.597268366965967 29 0.341805978531842 0.683611957063684 0.658194021468158 30 0.285095563615993 0.570191127231987 0.714904436384007 31 0.309301996906045 0.618603993812089 0.690698003093955 32 0.260709369595044 0.521418739190087 0.739290630404956 33 0.485169644374519 0.970339288749038 0.514830355625481 34 0.438774416156108 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52 0.08290365208951 0.16580730417902 0.91709634791049 53 0.138931975617041 0.277863951234081 0.86106802438296 54 0.170471402156214 0.340942804312429 0.829528597843786 55 0.16269887329643 0.325397746592861 0.83730112670357 56 0.218070247848134 0.436140495696269 0.781929752151866 57 0.208985548633658 0.417971097267317 0.791014451366342 58 0.179227056893827 0.358454113787653 0.820772943106174 59 0.189699479837792 0.379398959675584 0.810300520162208 60 0.218014963152691 0.436029926305382 0.781985036847309 61 0.19196761488896 0.38393522977792 0.80803238511104 62 0.161100317479318 0.322200634958636 0.838899682520682 63 0.17585070006338 0.35170140012676 0.82414929993662 64 0.148204637335997 0.296409274671994 0.851795362664003 65 0.122207971208563 0.244415942417125 0.877792028791437 66 0.118450250350765 0.23690050070153 0.881549749649235 67 0.108257660319206 0.216515320638411 0.891742339680794 68 0.108501928849591 0.217003857699181 0.89149807115041 69 0.0921121725832256 0.184224345166451 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0.980527550833356 87 0.0148403973007964 0.0296807946015928 0.985159602699204 88 0.0194335033176889 0.0388670066353778 0.980566496682311 89 0.0153314797194656 0.0306629594389312 0.984668520280534 90 0.0115000866139575 0.0230001732279149 0.988499913386042 91 0.0116204889655518 0.0232409779311037 0.988379511034448 92 0.0101887227732266 0.0203774455464532 0.989811277226773 93 0.00783804546403496 0.0156760909280699 0.992161954535965 94 0.00650194667191566 0.0130038933438313 0.993498053328084 95 0.0119822817990193 0.0239645635980385 0.98801771820098 96 0.0108962189414889 0.0217924378829778 0.989103781058511 97 0.0104096581526117 0.0208193163052235 0.989590341847388 98 0.00799734060893606 0.0159946812178721 0.992002659391064 99 0.00592545375701772 0.0118509075140354 0.994074546242982 100 0.00455676916767527 0.00911353833535055 0.995443230832325 101 0.00338316985638741 0.00676633971277481 0.996616830143613 102 0.00241919471052093 0.00483838942104186 0.99758080528948 103 0.00260122539917081 0.00520245079834162 0.997398774600829 104 0.00204888840023197 0.00409777680046394 0.997951111599768 105 0.00872519341726219 0.0174503868345244 0.991274806582738 106 0.0196000146925631 0.0392000293851261 0.980399985307437 107 0.0195357245502724 0.0390714491005447 0.980464275449728 108 0.0246994942341648 0.0493989884683297 0.975300505765835 109 0.0191755329092125 0.038351065818425 0.980824467090788 110 0.0141016823939225 0.028203364787845 0.985898317606077 111 0.0102827520878318 0.0205655041756637 0.989717247912168 112 0.0251917225426449 0.0503834450852898 0.974808277457355 113 0.0229861661181929 0.0459723322363858 0.977013833881807 114 0.0636468323383209 0.127293664676642 0.936353167661679 115 0.0546299437080108 0.109259887416022 0.94537005629199 116 0.0446244976845885 0.089248995369177 0.955375502315411 117 0.129387032773897 0.258774065547793 0.870612967226103 118 0.124835816508556 0.249671633017111 0.875164183491444 119 0.111484017313207 0.222968034626413 0.888515982686793 120 0.19231221466335 0.3846244293267 0.80768778533665 121 0.184371447512484 0.368742895024967 0.815628552487516 122 0.219367208755992 0.438734417511984 0.780632791244008 123 0.213118891955399 0.426237783910798 0.7868811080446 124 0.212845029310844 0.425690058621688 0.787154970689156 125 0.194886458924387 0.389772917848774 0.805113541075613 126 0.160685224709238 0.321370449418476 0.839314775290762 127 0.127496803875606 0.254993607751211 0.872503196124394 128 0.132029071784119 0.264058143568238 0.867970928215881 129 0.187366426008174 0.374732852016347 0.812633573991826 130 0.163448624687226 0.326897249374452 0.836551375312774 131 0.144802100426718 0.289604200853435 0.855197899573282 132 0.127110095870616 0.254220191741232 0.872889904129384 133 0.117873102837016 0.235746205674032 0.882126897162984 134 0.097915893536309 0.195831787072618 0.902084106463691 135 0.13278938351908 0.265578767038159 0.86721061648092 136 0.100909489540108 0.201818979080215 0.899090510459892 137 0.0755583554656438 0.151116710931288 0.924441644534356 138 0.18521161974934 0.370423239498681 0.81478838025066 139 0.258473502321093 0.516947004642185 0.741526497678908 140 0.239168503437986 0.478337006875972 0.760831496562014 141 0.483356133716307 0.966712267432614 0.516643866283693 142 0.435364617171764 0.870729234343527 0.564635382828236 143 0.747117313723112 0.505765372553777 0.252882686276888 144 0.696970796153235 0.606058407693531 0.303029203846765 145 0.597987981334714 0.804024037330571 0.402012018665286 146 0.535180865336135 0.92963826932773 0.464819134663865 147 0.55807827732984 0.88384344534032 0.44192172267016 148 0.430789275280491 0.861578550560983 0.569210724719509 149 0.337911226975226 0.675822453950453 0.662088773024774 150 0.241861644608907 0.483723289217813 0.758138355391093 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0352112676056338 NOK 5% type I error level 36 0.253521126760563 NOK 10% type I error level 43 0.302816901408451 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/10g7zw1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/10g7zw1290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/197kk1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/197kk1290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/297kk1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/297kk1290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/3jg151290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/3jg151290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/4jg151290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/4jg151290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/5jg151290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/5jg151290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/6cpiq1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/6cpiq1290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/7ng0t1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/7ng0t1290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/8ng0t1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/8ng0t1290520417.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/9ng0t1290520417.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905203865djx88g8che4o6h/9ng0t1290520417.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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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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