Paper: Multiple Linear Regression + tijd

*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: Sun, 05 Dec 2010 12:22:18 +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/Dec/05/t1291551706x1dj1frkfqw96ae.htm/, Retrieved Sun, 05 Dec 2010 13:21:56 +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/Dec/05/t1291551706x1dj1frkfqw96ae.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 «

9 13 14 13 3 9 12 8 13 5 9 15 12 16 6 9 12 7 12 6 9 10 10 11 5 9 12 7 12 3 9 15 16 18 8 9 9 11 11 4 9 12 14 14 4 9 11 6 9 4 9 11 16 14 6 9 11 11 12 6 9 15 16 11 5 9 7 12 12 4 9 11 7 13 6 9 11 13 11 4 9 10 11 12 6 9 14 15 16 6 9 10 7 9 4 9 6 9 11 4 9 11 7 13 2 9 15 14 15 7 9 11 15 10 5 9 12 7 11 4 9 14 15 13 6 9 15 17 16 6 9 9 15 15 7 9 13 14 14 5 9 13 14 14 6 9 16 8 14 4 9 13 8 8 4 9 12 14 13 7 9 14 14 15 7 9 11 8 13 4 9 9 11 11 4 9 16 16 15 6 9 12 10 15 6 9 10 8 9 5 9 13 14 13 6 9 16 16 16 7 9 14 13 13 6 9 15 5 11 3 9 5 8 12 3 9 8 10 12 4 9 11 8 12 6 9 16 13 14 7 9 17 15 14 5 9 9 6 8 4 9 9 12 13 5 9 13 16 16 6 9 10 5 13 6 10 6 15 11 6 10 12 12 14 5 10 8 8 13 4 10 14 13 13 5 10 12 14 13 5 10 11 12 12 4 10 16 16 16 6 10 8 10 15 2 10 15 15 15 8 10 7 8 12 3 10 16 16 14 6 10 14 19 12 6 10 16 14 15 6 10 9 6 12 5 10 14 13 13 5 10 11 15 12 6 10 13 7 12 5 10 15 13 13 6 10 5 4 5 2 10 15 14 13 5 10 13 13 13 5 10 11 11 14 5 10 11 14 17 6 10 12 12 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 Popularity[t] = + 3.49514166391521 -0.240396339657892Tijd[t] + 0.242393786561951KnowingPeople[t] + 0.365785984054008Liked[t] + 0.62160080454706Celebrity[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) 3.49514166391521 3.53926 0.9875 0.32496 0.16248 Tijd -0.240396339657892 0.363679 -0.661 0.509611 0.254806 KnowingPeople 0.242393786561951 0.061463 3.9438 0.000122 6.1e-05 Liked 0.365785984054008 0.0971 3.7671 0.000236 0.000118 Celebrity 0.62160080454706 0.156427 3.9738 0.000109 5.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.705290485738547 R-squared 0.497434669273315 Adjusted R-squared 0.484121680379893 F-TEST (value) 37.3646123538115 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10922287268072 Sum Squared Residuals 671.771990122567 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.3451078252048 1.65489217479524 2 12 11.1339467149272 0.866053285072809 3 15 13.8224806178841 1.17751938211590 4 12 11.1473677488583 0.852632251141696 5 10 10.8871623199431 -0.88716231994308 6 12 9.28256533521712 2.71743466478288 7 15 16.7668293413340 -1.76682934133403 8 9 10.5079553019580 -1.50795530195797 9 12 12.3324946138059 -0.332494613805853 10 11 8.5644144010402 2.4355855989598 11 11 14.0604837960239 -3.06048379602387 12 11 12.1169428951061 -1.11694289510610 13 15 12.3415250393148 2.65847496068521 14 7 11.1161350725739 -4.11613507257393 15 11 11.5131537329123 -0.513153732912306 16 11 10.9927428750819 0.00725712491812329 17 10 12.1169428951061 -2.11694289510610 18 14 14.5496619775699 -0.549661977569941 19 10 8.80680818760215 1.19319181239785 20 6 10.0231677288341 -4.02316772883407 21 11 9.02675051472407 1.97324948527593 22 15 14.5630830115010 0.436916988498959 23 11 11.7333452686988 -0.73334526869883 24 12 9.53838015571017 2.46161984428983 25 14 13.4523040254079 0.547695974592085 26 15 15.0344495506938 -0.034449550693843 27 9 14.805476798063 -5.80547679806299 28 13 12.9540954183529 0.0459045816470873 29 13 13.5756962229000 -0.575696222899973 30 16 10.8781318944341 5.12186810556585 31 13 8.6834159901101 4.31658400988990 32 12 13.8315110433930 -1.83151104339302 33 14 14.5630830115010 -0.563083011501041 34 11 10.5123459103801 0.487654089619862 35 9 10.5079553019580 -1.50795530195797 36 16 14.4262697800779 1.57373021992212 37 12 12.9719070607062 -0.971907060706176 38 10 9.67080277871116 0.329197221288836 39 13 13.2099102388460 -0.209910238845964 40 16 15.4136565686790 0.586343431321049 41 14 12.967516452284 1.03248354771599 42 15 8.4319917780392 6.56800822196079 43 5 9.52495912177907 -4.52495912177907 44 8 10.6313474994500 -2.63134749945003 45 11 11.3897615354202 -0.389761535420249 46 16 13.9549032408851 2.04509675911492 47 17 13.1964892049149 3.80351079508514 48 9 8.1986284169862 0.801371583013807 49 9 12.103521861175 -3.103521861175 50 13 14.7920557641319 -1.79205576413189 51 10 11.0283661597884 -1.02836615978840 52 6 12.480335717642 -6.48033571764201 53 12 12.2289115055711 -0.228911505571119 54 8 10.2719495707222 -2.27194957072225 55 14 12.1055193080791 1.89448069192094 56 12 12.3479130946410 -0.347913094641013 57 11 10.8757387329160 0.124261267083957 58 16 14.551659424474 1.448340575526 59 8 10.2451075028600 -2.24510750286005 60 15 15.1866812629522 -0.186681262952160 61 7 9.28456278212118 -2.28456278212118 62 16 13.820087456366 2.17991254363402 63 14 13.8156968479438 0.18430315205618 64 16 13.7010858672961 2.29891413270391 65 9 10.0429768180914 -1.04297681809140 66 14 12.1055193080791 1.89448069192094 67 11 12.8461217016960 -1.84612170169602 68 13 10.2853706046533 2.71462939534665 69 15 12.7271201126261 2.27287988737388 70 5 5.13288494294826 -0.132884942948255 71 15 12.3479130946410 2.65208690535899 72 13 12.1055193080791 0.894480691920938 73 11 11.9865177190092 -0.986517719009168 74 11 14.4326578354041 -3.43265783540411 75 12 12.4847263260642 -0.484726326064171 76 12 13.2119076857500 -1.21190768575002 77 12 11.982127110587 0.0178728894129951 78 12 12.1055193080791 -0.105519308079062 79 14 10.6377355547763 3.36226444522374 80 6 7.81238842039621 -1.81238842039621 81 7 9.66376980010629 -2.66376980010629 82 14 12.3613341285721 1.63866587142789 83 14 13.8244780647881 0.175521935211853 84 10 11.2549457509012 -1.25494575090115 85 13 8.55738142243533 4.44261857756467 86 12 12.1189403420102 -0.118940342010162 87 9 9.17459161856022 -0.174591618560221 88 12 12.3523037030632 -0.352303703063177 89 16 14.9442874763902 1.05571252360979 90 10 10.1485573732302 -0.148557373230189 91 14 13.0972967051023 0.902703294897706 92 10 13.4586920807341 -3.45869208073414 93 16 15.1732602290211 0.82673977097894 94 15 13.4543014723120 1.54569852768802 95 12 11.2549457509012 0.745054249098849 96 10 9.54037760261423 0.45962239738577 97 8 10.5455760335686 -2.54557603356856 98 8 8.31059702745121 -0.310597027451210 99 11 13.0794850627490 -2.07948506274903 100 13 12.2423325395022 0.75766746049778 101 16 15.415654015583 0.584345984416989 102 16 14.5650804584051 1.4349195415949 103 14 15.5256251791440 -1.52562517914397 104 11 8.92316740648933 2.07683259351067 105 4 6.9618148632183 -2.96181486321830 106 14 14.3404983141964 -0.340498314196413 107 9 10.3775301258610 -1.37753012586104 108 14 15.1866812629522 -1.18668126295216 109 8 10.5009223233531 -2.5009223233531 110 8 11.2459153253922 -3.24591532539222 111 11 12.2289115055711 -1.22891150557112 112 12 13.8335084902971 -1.83350849029708 113 11 11.2727573932544 -0.272757393254415 114 14 13.4586920807341 0.541307919265861 115 15 14.2036850827733 0.796314917226744 116 16 13.3352998832421 2.66470011675792 117 16 13.3352998832421 2.66470011675792 118 11 12.6125091319784 -1.61250913197839 119 14 13.5776936698040 0.422306330195967 120 14 10.8757387329160 3.12426126708396 121 12 11.2415247169701 0.758475283029949 122 14 12.4669146837109 1.53308531628909 123 8 10.1485573732302 -2.14855737323019 124 13 13.5776936698040 -0.577693669804033 125 16 13.5776936698040 2.42230633019597 126 12 10.7745487861994 1.22545121380059 127 16 15.3100734604442 0.689926539555782 128 12 13.2119076857500 -1.21190768575002 129 11 11.7441239324472 -0.744123932447217 130 4 6.49508814111227 -2.49508814111227 131 16 15.3100734604442 0.689926539555782 132 15 12.4847263260642 2.51527367393583 133 10 11.3693075228843 -1.36930752288427 134 13 12.9739045076102 0.0260954923897635 135 15 13.0929060966801 1.90709390331987 136 12 10.5143433572842 1.48565664271580 137 14 13.5776936698040 0.422306330195967 138 7 10.4965317149309 -3.49653171493093 139 19 13.9434796538580 5.05652034614196 140 12 12.7136990786950 -0.713699078695022 141 12 12.2110998632179 -0.211099863217856 142 13 13.3352998832421 -0.335299883242082 143 15 12.8236702422560 2.17632975774402 144 8 8.1962352554681 -0.196235255468090 145 12 10.7567371438461 1.24326285615385 146 10 10.5455760335686 -0.545576033568562 147 8 11.2593363593233 -3.25933635932331 148 10 13.9434796538580 -3.94347965385804 149 15 13.820087456366 1.17991254363402 150 16 14.4594999032663 1.54050009673369 151 13 13.1063271306112 -0.106327130611230 152 16 14.9308664424591 1.06913355754089 153 9 10.1485573732302 -1.14855737323019 154 14 13.2162982941722 0.783701705827813 155 14 12.6037279151341 1.39627208486594 156 12 10.1217153053680 1.87828469463201 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.127514957262765 0.255029914525530 0.872485042737235 9 0.0635313000659471 0.127062600131894 0.936468699934053 10 0.0847751220823577 0.169550244164715 0.915224877917642 11 0.0433853298095546 0.0867706596191093 0.956614670190445 12 0.0196112708280225 0.039222541656045 0.980388729171978 13 0.346571630621525 0.69314326124305 0.653428369378475 14 0.696739602581205 0.606520794837589 0.303260397418795 15 0.621500725383042 0.756998549233916 0.378499274616958 16 0.530986057313098 0.938027885373805 0.469013942686902 17 0.487925986037719 0.975851972075437 0.512074013962281 18 0.406683686924412 0.813367373848825 0.593316313075588 19 0.332468526230137 0.664937052460273 0.667531473769863 20 0.59979977150374 0.80040045699252 0.40020022849626 21 0.531636574289975 0.93672685142005 0.468363425710025 22 0.498966590680976 0.997933181361951 0.501033409319024 23 0.429768269352671 0.859536538705343 0.570231730647329 24 0.416451148700541 0.832902297401083 0.583548851299459 25 0.383300093023595 0.76660018604719 0.616699906976405 26 0.327995456298815 0.65599091259763 0.672004543701185 27 0.598933898808472 0.802132202383057 0.401066101191528 28 0.538237336626264 0.923525326747471 0.461762663373736 29 0.478615444546823 0.957230889093645 0.521384555453177 30 0.648766198353575 0.70246760329285 0.351233801646425 31 0.773077836349461 0.453844327301079 0.226922163650539 32 0.736123722411629 0.527752555176742 0.263876277588371 33 0.69420877756902 0.61158244486196 0.30579122243098 34 0.649221804905754 0.701556390188493 0.350778195094246 35 0.63871822750469 0.72256354499062 0.36128177249531 36 0.657303729395 0.68539254121 0.342696270605 37 0.616163625580746 0.767672748838509 0.383836374419254 38 0.561773939453182 0.876452121093637 0.438226060546818 39 0.511722773396646 0.976554453206708 0.488277226603354 40 0.493674700182179 0.987349400364358 0.506325299817821 41 0.466213791791783 0.932427583583565 0.533786208208217 42 0.753477446875755 0.493045106248489 0.246522553124245 43 0.929115161530606 0.141769676938788 0.0708848384693939 44 0.943523597097611 0.112952805804777 0.0564764029023886 45 0.928463589076474 0.143072821847052 0.0715364109235262 46 0.934605231571096 0.130789536857808 0.065394768428904 47 0.969734025086922 0.0605319498261568 0.0302659749130784 48 0.96700997644179 0.0659800471164207 0.0329900235582103 49 0.97097436446139 0.0580512710772196 0.0290256355386098 50 0.96414648588855 0.0717070282228996 0.0358535141114498 51 0.957311057493635 0.0853778850127303 0.0426889425063651 52 0.984679798943632 0.0306404021127369 0.0153202010563684 53 0.987727911814627 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0.0333125022563462 0.0166562511281731 71 0.985894884806572 0.0282102303868554 0.0141051151934277 72 0.98194757604818 0.0361048479036409 0.0180524239518204 73 0.977584521953422 0.0448309560931568 0.0224154780465784 74 0.986884147637398 0.0262317047252046 0.0131158523626023 75 0.982613605666612 0.0347727886667765 0.0173863943333883 76 0.979350378079672 0.0412992438406559 0.0206496219203280 77 0.972830817223086 0.0543383655538287 0.0271691827769143 78 0.964643581992183 0.070712836015633 0.0353564180078165 79 0.978433634725952 0.0431327305480958 0.0215663652740479 80 0.97694291731598 0.0461141653680395 0.0230570826840197 81 0.979717148056942 0.0405657038861164 0.0202828519430582 82 0.977449898054504 0.0451002038909926 0.0225501019454963 83 0.970418781515412 0.0591624369691754 0.0295812184845877 84 0.964729758704368 0.0705404825912636 0.0352702412956318 85 0.99112269684952 0.0177546063009617 0.00887730315048086 86 0.987842174579449 0.0243156508411029 0.0121578254205514 87 0.983718378002019 0.0325632439959624 0.0162816219979812 88 0.978274473297597 0.0434510534048054 0.0217255267024027 89 0.972923364811018 0.0541532703779631 0.0270766351889815 90 0.96475448192464 0.0704910361507215 0.0352455180753608 91 0.957065297745902 0.085869404508196 0.042934702254098 92 0.975831050007902 0.0483378999841951 0.0241689499920975 93 0.96920579020948 0.0615884195810413 0.0307942097905206 94 0.963939016715154 0.0721219665696915 0.0360609832848457 95 0.954982518197891 0.090034963604217 0.0450174818021086 96 0.945075036472616 0.109849927054767 0.0549249635273837 97 0.946072682890616 0.107854634218769 0.0539273171093843 98 0.93265195346162 0.134696093076761 0.0673480465383807 99 0.935925548281581 0.128148903436838 0.0640744517184188 100 0.921476855227734 0.157046289544533 0.0785231447722663 101 0.90370584138813 0.192588317223740 0.0962941586118698 102 0.888096787549133 0.223806424901734 0.111903212450867 103 0.893902365293411 0.212195269413177 0.106097634706589 104 0.921301947231 0.157396105538000 0.0786980527689998 105 0.920507876708337 0.158984246583325 0.0794921232916627 106 0.900521600571826 0.198956798856349 0.0994783994281743 107 0.883589442658997 0.232821114682007 0.116410557341003 108 0.882534610109942 0.234930779780115 0.117465389890058 109 0.886036146040042 0.227927707919916 0.113963853959958 110 0.916446589682532 0.167106820634935 0.0835534103174675 111 0.906060678089456 0.187878643821088 0.0939393219105441 112 0.91673274941309 0.166534501173820 0.0832672505869099 113 0.893831387320111 0.212337225359778 0.106168612679889 114 0.867545852904492 0.264908294191017 0.132454147095508 115 0.837536278829772 0.324927442340456 0.162463721170228 116 0.84319490888362 0.313610182232762 0.156805091116381 117 0.849763058830443 0.300473882339113 0.150236941169556 118 0.836667664596908 0.326664670806185 0.163332335403092 119 0.800000724658608 0.399998550682785 0.199999275341392 120 0.854803327722928 0.290393344554144 0.145196672277072 121 0.823976274679679 0.352047450640642 0.176023725320321 122 0.79928108298358 0.401437834032842 0.200718917016421 123 0.788373598192652 0.423252803614696 0.211626401807348 124 0.755906450122305 0.488187099755389 0.244093549877695 125 0.750807158949071 0.498385682101858 0.249192841050929 126 0.728737454402369 0.542525091195262 0.271262545597631 127 0.675550849494946 0.648898301010108 0.324449150505054 128 0.657244110423703 0.685511779152594 0.342755889576297 129 0.601329681796972 0.797340636406055 0.398670318203028 130 0.561866495788193 0.876267008423613 0.438133504211807 131 0.49779025060864 0.99558050121728 0.50220974939136 132 0.505926457895498 0.988147084209005 0.494073542104502 133 0.459710424868903 0.919420849737805 0.540289575131097 134 0.390644325090296 0.781288650180593 0.609355674909704 135 0.3549824839198 0.7099649678396 0.6450175160802 136 0.331670677023814 0.663341354047628 0.668329322976186 137 0.264956720477079 0.529913440954157 0.735043279522921 138 0.381306222063638 0.762612444127276 0.618693777936362 139 0.67663021674644 0.64673956650712 0.32336978325356 140 0.613069329603474 0.773861340793051 0.386930670396526 141 0.543317412468145 0.91336517506371 0.456682587531855 142 0.456154993704211 0.912309987408423 0.543845006295789 143 0.405471703876934 0.810943407753868 0.594528296123066 144 0.312551990742469 0.625103981484937 0.687448009257531 145 0.248839834498755 0.49767966899751 0.751160165501245 146 0.176123282327660 0.352246564655319 0.82387671767234 147 0.209021068295575 0.418042136591151 0.790978931704425 148 0.848122652962786 0.303754694074427 0.151877347037214 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 35 0.24822695035461 NOK 10% type I error level 51 0.361702127659574 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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