WS7 comp 5

*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 09:29:52 +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/23/t1290504523k1944ebujjn9elz.htm/, Retrieved Tue, 23 Nov 2010 10:28:47 +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/t1290504523k1944ebujjn9elz.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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27 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] = + 17.4557480017071 -0.0596220828042757CM[t] + 0.218935765813514D[t] -0.136852917502793PE[t] -0.247202455609299PC[t] + 0.396808017049338PS[t] -0.0151046024523753t + 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) 17.4557480017071 2.044985 8.5359 0 0 CM -0.0596220828042757 0.062157 -0.9592 0.338969 0.169485 D 0.218935765813514 0.110949 1.9733 0.050274 0.025137 PE -0.136852917502793 0.102916 -1.3297 0.185593 0.092796 PC -0.247202455609299 0.128476 -1.9241 0.056208 0.028104 PS 0.396808017049338 0.075282 5.271 0 0 t -0.0151046024523753 0.006042 -2.4999 0.013486 0.006743 Multiple Linear Regression - Regression Statistics Multiple R 0.502833009131382 R-squared 0.252841035072121 Adjusted R-squared 0.223347918035494 F-TEST (value) 8.57288277661948 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 4.9650928590772e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.44732602810375 Sum Squared Residuals 1806.37662509432 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 27 24.1263949826831 2.87360501731687 2 23 25.3278905094837 -2.32789050948365 3 25 25.3105946506167 -0.310594650616672 4 23 23.1425647952179 -0.142564795217939 5 19 22.9212328900446 -3.92123289004464 6 29 23.9576488960464 5.04235110395356 7 25 25.7729402978557 -0.772940297855665 8 21 23.6912265690701 -2.69122656907014 9 22 23.1226654327152 -1.12266543271515 10 25 23.522883234694 1.47711676530596 11 24 21.4214364373951 2.57856356260492 12 18 20.9907405657123 -2.99074056571227 13 22 19.6142799989524 2.38572000104762 14 15 21.8010947195462 -6.80109471954617 15 22 24.3867238015357 -2.38672380153568 16 28 25.0465653074249 2.95343469257509 17 20 23.1906059305252 -3.1906059305252 18 12 20.113330543294 -8.11333054329397 19 24 22.4006646138075 1.59933538619254 20 20 22.4513298900013 -2.45132989000128 21 21 24.2091718008149 -3.20917180081488 22 20 21.7496570167093 -1.74965701670926 23 21 20.2364798547118 0.763520145288229 24 23 22.1064491842925 0.89355081570746 25 28 22.8067653946468 5.19323460535319 26 24 22.7095296686943 1.29047033130573 27 24 24.2100959017649 -0.210095901764875 28 24 21.2866195823899 2.71338041761012 29 23 22.7853742298715 0.214625770128455 30 23 23.4269301266781 -0.426930126678148 31 29 24.9512424315685 4.04875756843146 32 24 22.8832375446242 1.11676245537582 33 18 25.6234830931503 -7.62348309315027 34 25 26.5283299210078 -1.5283299210078 35 21 23.2528121287252 -2.25281212872522 36 26 27.2995894199509 -1.2995894199509 37 22 25.7333758885773 -3.73337588857734 38 22 23.4771472868362 -1.47714728683625 39 22 23.2668335411094 -1.26683354110945 40 23 26.1230213183996 -3.12302131839959 41 30 23.5541509933645 6.44584900663553 42 23 23.2595282500456 -0.25952825004559 43 17 19.4473090951876 -2.44730909518762 44 23 24.2425334465938 -1.24253344659383 45 23 24.7438165167803 -1.74381651678034 46 25 22.9469928401775 2.05300715982245 47 24 21.3730696575052 2.62693034249483 48 24 27.8112646272391 -3.81126462723911 49 23 23.4762855096774 -0.476285509677433 50 21 24.2575943354001 -3.2575943354001 51 24 26.0917213589247 -2.09172135892466 52 24 22.2806467791565 1.71935322084353 53 28 21.9684257598597 6.03157424014028 54 16 21.440064081599 -5.44006408159904 55 20 20.382784054042 -0.382784054042012 56 29 23.8094188213148 5.19058117868516 57 27 24.1696112867377 2.8303887132623 58 22 23.441828608794 -1.44182860879401 59 28 24.164657954189 3.83534204581103 60 16 20.7974038487875 -4.7974038487875 61 25 23.1475490354281 1.85245096457191 62 24 23.7176463168972 0.282353683102773 63 28 23.8756020385683 4.12439796143166 64 24 24.4657678785319 -0.465767878531913 65 23 22.8650436257553 0.134956374244671 66 30 26.9714572554329 3.02854274456713 67 24 21.5937158346539 2.40628416534612 68 21 24.2233462419074 -3.22334624190743 69 25 23.4107050580841 1.58929494191586 70 25 24.0514762867323 0.94852371326766 71 22 21.028897177265 0.971102822734967 72 23 22.5766938554224 0.423306144577629 73 26 22.9710720281836 3.02892797181637 74 23 21.8370083714923 1.16299162850771 75 25 23.1273424872252 1.87265751277479 76 21 21.4421536550423 -0.442153655042264 77 25 23.6533729546518 1.34662704534815 78 24 22.2417678908569 1.75823210914312 79 29 23.5373295966829 5.46267040331713 80 22 23.6441526759874 -1.64415267598739 81 27 23.5951559625597 3.40484403744026 82 26 19.7203222574501 6.27967774254989 83 22 21.3598762005591 0.640123799440915 84 24 22.004535056226 1.99546494377402 85 27 23.0741663160147 3.92583368398533 86 24 21.3290783475387 2.6709216524613 87 24 24.6545555803014 -0.654555580301407 88 29 24.2146009549584 4.78539904504158 89 22 22.1325846564454 -0.132584656445435 90 21 20.5259559563874 0.474044043612602 91 24 20.4483315469443 3.55166845305574 92 24 21.5258968273727 2.47410317262729 93 23 21.7834078269836 1.21659217301641 94 20 22.1073550865127 -2.10735508651268 95 27 21.2139747971843 5.78602520281575 96 26 23.2042950681903 2.79570493180972 97 25 21.8374946624237 3.16250533757629 98 21 19.9958078913003 1.00419210869972 99 21 20.5678867855518 0.432113214448156 100 19 20.2087963273881 -1.20879632738806 101 21 21.3499989811539 -0.349998981153919 102 21 20.9672002504434 0.0327997495565692 103 16 19.5418845376893 -3.54188453768929 104 22 20.3713080220925 1.62869197790753 105 29 21.5223112534616 7.47768874653837 106 15 21.4335507122992 -6.43355071229919 107 17 20.3825758695164 -3.38257586951636 108 15 19.6521826821777 -4.65218268217773 109 21 21.3416505865218 -0.341650586521784 110 21 20.6724375577131 0.327562442286877 111 19 18.9381962189381 0.0618037810618711 112 24 17.8325684945613 6.1674315054387 113 20 21.8208394521637 -1.82083945216374 114 17 24.4815226826983 -7.48152268269833 115 23 24.1891167120328 -1.18911671203275 116 24 21.8190150713246 2.1809849286754 117 14 21.4853857201907 -7.48538572019065 118 19 22.2893922784086 -3.28939227840865 119 24 21.6850094732166 2.31499052678337 120 13 19.9339185344671 -6.9339185344671 121 22 24.6775723259204 -2.67757232592043 122 16 20.5596548577463 -4.55965485774628 123 19 22.6363293692522 -3.63632936925217 124 25 22.0717602843708 2.92823971562922 125 25 23.5276802327993 1.47231976720075 126 23 20.7972689761852 2.20273102381479 127 24 22.7670557523198 1.23294424768024 128 26 22.7786013274452 3.22139867255476 129 26 20.8156198655222 5.1843801344778 130 25 23.4237283776241 1.57627162237588 131 18 21.5987301526461 -3.59873015264608 132 21 19.2074826633283 1.79251733667169 133 26 22.7888723817477 3.21112761825228 134 23 21.1513223016543 1.8486776983457 135 23 19.0829942077633 3.91700579223668 136 22 21.8054384079825 0.194561592017452 137 20 21.5732875110786 -1.57328751107855 138 13 21.2544028925807 -8.25440289258065 139 24 20.5600302271813 3.43996977281871 140 15 20.7494922343872 -5.74949223438724 141 14 22.2725233273091 -8.2725233273091 142 22 23.1320753348997 -1.13207533489966 143 10 17.0344098108871 -7.03440981088713 144 24 23.4516436543481 0.548356345651932 145 22 20.9405396456836 1.05946035431638 146 24 24.7496275294982 -0.749627529498184 147 19 20.7263874947993 -1.72638749479933 148 20 21.095416151232 -1.09541615123199 149 13 16.3226538637326 -3.32265386373261 150 20 19.1780528785196 0.821947121480443 151 22 22.1018659862759 -0.101865986275926 152 24 22.3495284477076 1.65047155229237 153 29 22.190502141487 6.80949785851305 154 12 19.9285720399114 -7.92857203991143 155 20 19.9030885256595 0.0969114743405294 156 21 20.3333261665308 0.66667383346915 157 24 22.5203984913327 1.47960150866731 158 22 20.808658004564 1.19134199543599 159 20 16.8990954654 3.10090453459997 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.718619910827995 0.56276017834401 0.281380089172005 11 0.660019415013352 0.679961169973296 0.339980584986648 12 0.599606851160085 0.80078629767983 0.400393148839915 13 0.625577621390001 0.748844757219998 0.374422378609999 14 0.751302983454027 0.497394033091946 0.248697016545973 15 0.675144334194206 0.649711331611587 0.324855665805794 16 0.68909519210956 0.62180961578088 0.31090480789044 17 0.606750202385519 0.786499595228963 0.393249797614481 18 0.729059055475175 0.541881889049651 0.270940944524825 19 0.670703293768016 0.658593412463968 0.329296706231984 20 0.621144151670995 0.75771169665801 0.378855848329005 21 0.552779097294516 0.894441805410968 0.447220902705484 22 0.479721518011931 0.959443036023862 0.520278481988069 23 0.465868328576882 0.931736657153765 0.534131671423118 24 0.518990053870113 0.962019892259774 0.481009946129887 25 0.687995955473741 0.624008089052518 0.312004044526259 26 0.626121860460543 0.747756279078914 0.373878139539457 27 0.562712863819326 0.874574272361348 0.437287136180674 28 0.544286621835185 0.911426756329631 0.455713378164815 29 0.479832448785696 0.959664897571392 0.520167551214304 30 0.417262422599592 0.834524845199184 0.582737577400408 31 0.417851728241744 0.835703456483489 0.582148271758256 32 0.356829399950581 0.713658799901163 0.643170600049419 33 0.61850244104459 0.76299511791082 0.38149755895541 34 0.57821175140232 0.84357649719536 0.42178824859768 35 0.547302485769862 0.905395028460276 0.452697514230138 36 0.492119004847573 0.984238009695146 0.507880995152427 37 0.477748299775668 0.955496599551335 0.522251700224332 38 0.425770258513273 0.851540517026547 0.574229741486727 39 0.376887143687802 0.753774287375605 0.623112856312198 40 0.353918178342644 0.707836356685288 0.646081821657356 41 0.518675894946084 0.962648210107833 0.481324105053916 42 0.464795096191745 0.92959019238349 0.535204903808255 43 0.435117744975545 0.87023548995109 0.564882255024455 44 0.38798383970683 0.77596767941366 0.61201616029317 45 0.348608914550764 0.697217829101528 0.651391085449236 46 0.32178670768439 0.643573415368781 0.67821329231561 47 0.297634822789812 0.595269645579623 0.702365177210188 48 0.294230050937283 0.588460101874566 0.705769949062717 49 0.25685315230142 0.513706304602839 0.74314684769858 50 0.25675717790153 0.513514355803059 0.74324282209847 51 0.236669075283749 0.473338150567497 0.763330924716251 52 0.206553415084297 0.413106830168594 0.793446584915703 53 0.276840059857889 0.553680119715778 0.723159940142111 54 0.355039081000439 0.710078162000878 0.644960918999561 55 0.340031715260209 0.680063430520417 0.659968284739791 56 0.400755758516633 0.801511517033265 0.599244241483367 57 0.377443000341463 0.754886000682926 0.622556999658537 58 0.34634808944617 0.692696178892341 0.65365191055383 59 0.346841083601947 0.693682167203893 0.653158916398053 60 0.427876281034803 0.855752562069605 0.572123718965197 61 0.383740556430613 0.767481112861226 0.616259443569387 62 0.341548990066272 0.683097980132545 0.658451009933728 63 0.343301629878487 0.686603259756973 0.656698370121513 64 0.309632765636288 0.619265531272576 0.690367234363712 65 0.270414689892304 0.540829379784608 0.729585310107696 66 0.253991767182507 0.507983534365015 0.746008232817493 67 0.225833266643305 0.45166653328661 0.774166733356695 68 0.24878208490663 0.497564169813259 0.75121791509337 69 0.215016517732511 0.430033035465021 0.78498348226749 70 0.182093734175895 0.36418746835179 0.817906265824105 71 0.153139382320502 0.306278764641003 0.846860617679498 72 0.127726526678127 0.255453053356253 0.872273473321873 73 0.111530232310314 0.223060464620627 0.888469767689686 74 0.0910035075155011 0.182007015031002 0.908996492484499 75 0.0744439055650719 0.148887811130144 0.925556094434928 76 0.062375537878791 0.124751075757582 0.937624462121209 77 0.0496172420823974 0.099234484164795 0.950382757917603 78 0.0388297314084408 0.0776594628168816 0.961170268591559 79 0.0441176816221311 0.0882353632442622 0.955882318377869 80 0.0404637587549321 0.0809275175098643 0.959536241245068 81 0.0339647228068069 0.0679294456136138 0.966035277193193 82 0.0450489697540823 0.0900979395081645 0.954951030245918 83 0.0352958942866428 0.0705917885732856 0.964704105713357 84 0.0277237433105275 0.0554474866210551 0.972276256689472 85 0.0255062920070667 0.0510125840141335 0.974493707992933 86 0.0202934553553548 0.0405869107107096 0.979706544644645 87 0.0165361958513585 0.0330723917027171 0.983463804148641 88 0.0169484961460945 0.0338969922921889 0.983051503853905 89 0.0143108540470869 0.0286217080941738 0.985689145952913 90 0.0108381932828605 0.021676386565721 0.98916180671714 91 0.00929207129362206 0.0185841425872441 0.990707928706378 92 0.0076087117383732 0.0152174234767464 0.992391288261627 93 0.00562298169761736 0.0112459633952347 0.994377018302383 94 0.00531671331578649 0.010633426631573 0.994683286684213 95 0.00788637753022928 0.0157727550604586 0.99211362246977 96 0.00645436215487841 0.0129087243097568 0.993545637845122 97 0.00553167083282757 0.0110633416656551 0.994468329167172 98 0.00424857572689945 0.0084971514537989 0.9957514242731 99 0.00321260062833887 0.00642520125667774 0.996787399371661 100 0.00266784736454883 0.00533569472909766 0.997332152635451 101 0.00210340698781701 0.00420681397563403 0.997896593012183 102 0.00154717895435629 0.00309435790871259 0.998452821045644 103 0.00188375661540967 0.00376751323081934 0.99811624338459 104 0.00147576801674001 0.00295153603348001 0.99852423198326 105 0.00637487618927063 0.0127497523785413 0.99362512381073 106 0.0152124243878229 0.0304248487756459 0.984787575612177 107 0.0160073312015397 0.0320146624030794 0.98399266879846 108 0.0216884207074323 0.0433768414148646 0.978311579292568 109 0.0170016586041711 0.0340033172083421 0.982998341395829 110 0.0124189406353634 0.0248378812707268 0.987581059364637 111 0.00903457181675685 0.0180691436335137 0.990965428183243 112 0.0258934825133509 0.0517869650267017 0.974106517486649 113 0.0260772616690735 0.0521545233381469 0.973922738330927 114 0.0637183027563107 0.127436605512621 0.93628169724369 115 0.0549499654608643 0.109899930921729 0.945050034539136 116 0.0464972176509136 0.0929944353018273 0.953502782349086 117 0.118464157663075 0.236928315326151 0.881535842336925 118 0.112186205148525 0.224372410297051 0.887813794851475 119 0.10082608740145 0.2016521748029 0.89917391259855 120 0.172653978102336 0.345307956204671 0.827346021897664 121 0.170125417998484 0.340250835996968 0.829874582001516 122 0.21465812262451 0.429316245249021 0.78534187737549 123 0.214943641166404 0.429887282332807 0.785056358833596 124 0.204906198517687 0.409812397035373 0.795093801482313 125 0.179355065700305 0.358710131400609 0.820644934299695 126 0.145873182400785 0.29174636480157 0.854126817599215 127 0.115976365787524 0.231952731575048 0.884023634212476 128 0.113743066435253 0.227486132870506 0.886256933564747 129 0.158069707399953 0.316139414799906 0.841930292600047 130 0.138474615326792 0.276949230653583 0.861525384673208 131 0.117805781692786 0.235611563385572 0.882194218307214 132 0.10593626999299 0.21187253998598 0.89406373000701 133 0.104621513951703 0.209243027903406 0.895378486048297 134 0.0944734743075463 0.188946948615093 0.905526525692454 135 0.212612478056431 0.425224956112862 0.78738752194357 136 0.173516743792745 0.34703348758549 0.826483256207255 137 0.14841459297574 0.29682918595148 0.85158540702426 138 0.206579074250537 0.413158148501074 0.793420925749463 139 0.466771229755011 0.933542459510023 0.533228770244988 140 0.412967829577562 0.825935659155123 0.587032170422438 141 0.567839663240623 0.864320673518754 0.432160336759377 142 0.479197081870673 0.958394163741347 0.520802918129327 143 0.650488588465145 0.699022823069709 0.349511411534855 144 0.60555508107025 0.7888898378595 0.39444491892975 145 0.515794452967679 0.968411094064642 0.484205547032321 146 0.411769174934562 0.823538349869125 0.588230825065438 147 0.417030687996547 0.834061375993094 0.582969312003453 148 0.286984021129887 0.573968042259773 0.713015978870113 149 0.200020944492256 0.400041888984513 0.799979055507744 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.05 NOK 5% type I error level 26 0.185714285714286 NOK 10% type I error level 38 0.271428571428571 NOK

Charts produced by software:

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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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Software written by Ed van Stee & Patrick Wessa

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