Mini tutorial

*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: Thu, 02 Dec 2010 13:53:30 +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/02/t1291299973rxf2r96dt0pjved.htm/, Retrieved Thu, 02 Dec 2010 15:26:24 +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/02/t1291299973rxf2r96dt0pjved.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:

Extra variable Gender

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 13 13 14 13 3 5 1 3 12 12 8 13 5 6 1 3 15 10 12 16 6 4 1 3 12 9 7 12 6 6 2 3 10 10 10 11 5 3 1 3 12 12 7 12 3 10 1 2 15 13 16 18 8 8 2 3 9 12 11 11 4 3 1 3 12 12 14 14 4 4 1 4 11 6 6 9 4 3 1 3 11 5 16 14 6 5 2 3 11 12 11 12 6 5 2 2 15 11 16 11 5 6 1 3 7 14 12 12 4 5 1 3 11 14 7 13 6 3 1 3 11 12 13 11 4 4 2 3 10 12 11 12 6 8 1 3 14 11 15 16 6 8 2 2 10 11 7 9 4 8 2 4 6 7 9 11 4 5 1 3 11 9 7 13 2 8 2 2 15 11 14 15 7 2 1 3 11 11 15 10 5 0 1 3 12 12 7 11 4 5 2 2 14 12 15 13 6 2 1 2 15 11 17 16 6 7 1 4 9 11 15 15 7 5 1 2 13 8 14 14 5 2 1 3 13 9 14 14 6 12 2 2 16 12 8 14 4 7 1 4 13 10 8 8 4 0 2 3 12 10 14 13 7 2 1 2 14 12 14 15 7 3 1 3 11 8 8 13 4 0 2 3 9 12 11 11 4 9 2 1 16 11 16 15 6 2 2 3 12 12 10 15 6 3 1 3 10 7 8 9 5 1 2 3 13 11 14 13 6 10 2 2 16 11 16 16 7 1 1 3 14 12 13 13 6 4 1 15 9 5 11 3 6 1 5 5 15 8 12 3 6 1 4 8 11 10 12 4 4 2 3 11 11 8 12 6 4 2 2 16 11 13 14 7 7 1 2 17 11 15 14 5 7 2 3 9 15 6 8 4 7 2 4 9 11 12 13 5 0 1 2 13 12 16 16 6 3 2 3 10 12 5 13 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation NotPopular[t] = + 0.410809067919239 -0.0103714850389617Popularity[t] + 0.54902968172845FindingFriends[t] + 0.434073395267413KnowingPeople[t] -0.606370476015817Liked[t] -0.0301007884568122Celebrity[t] -0.267226482953949WeightedSum[t] + 1.05529571126129Gender[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) 0.410809067919239 1.799578 0.2283 0.819743 0.409872 Popularity -0.0103714850389617 0.113987 -0.091 0.927625 0.463812 FindingFriends 0.54902968172845 0.070241 7.8164 0 0 KnowingPeople 0.434073395267413 0.089109 4.8713 3e-06 1e-06 Liked -0.606370476015817 0.084094 -7.2106 0 0 Celebrity -0.0301007884568122 0.073612 -0.4089 0.683194 0.341597 WeightedSum -0.267226482953949 0.129772 -2.0592 0.041227 0.020614 Gender 1.05529571126129 0.25144 4.197 4.6e-05 2.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.86112661610235 R-squared 0.741539048959883 Adjusted R-squared 0.729314544518797 F-TEST (value) 60.6600498640721 F-TEST (DF numerator) 7 F-TEST (DF denominator) 148 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.54591980271415 Sum Squared Residuals 959.292730994106 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 5.23643790154167 -3.23643790154167 2 3 1.76591127338030 1.23408872661970 3 3 1.05827178527982 1.94172821472018 4 3 1.31631423174784 1.68368576825216 5 3 3.57116207142968 -0.571162071429684 6 3 0.929503999226545 2.07049600077346 7 2 3.15510166203506 -1.15510166203506 8 3 5.14376710364973 -2.14376710364973 9 3 4.32853492333369 -1.32853492333369 10 4 0.87122001889567 3.12877998110433 11 3 2.09171307820204 0.90828692179796 12 3 4.97729482599576 -1.97729482599576 13 2 5.87109525070591 -3.87109525070591 14 3 5.55581939052826 -2.55581939052826 15 3 3.2118473870138 -0.211847387013796 16 3 6.77924015241397 -3.77924015241397 17 3 3.13069115091159 -0.130691150911585 18 3 2.90628291729496 0.0937170827050397 19 2 3.77997660433584 -1.77997660433584 20 4 1.02713339368164 2.97286660631836 21 3 0.30626542869034 2.69373457130966 22 2 3.58617091101000 -1.58617091101000 23 3 7.68823716933386 -4.68823716933386 24 3 3.89720181281658 -0.89720181281658 25 2 5.82248721353326 -3.82248721353326 26 2 2.97598899448349 -0.975988994483487 27 4 3.28079376764934 0.719206232350662 28 2 2.62639688883201 -0.62639688883201 29 3 1.52835666382545 1.47164333617455 30 2 0.88092916271151 1.11907083728849 31 4 6.37808820240532 -2.37808820240532 32 3 4.28099663643006 -1.28099663643006 33 2 3.87834559482346 -1.87834559482346 34 3 2.26891942894727 0.731080571052733 35 3 4.59570391718733 -1.59570391718733 36 1 5.52934271622395 -4.52934271622395 37 3 2.19289577228854 0.807104227711458 38 3 3.85841586491028 -0.858415864910283 39 3 3.76723946920606 -0.76723946920606 40 2 4.10480222344399 -2.10480222344399 41 3 4.41988745709054 -1.41988745709054 42 15 10.8469573737165 4.15304262628347 43 5 11.8105951926742 -6.81059519267423 44 8 11.0814494029696 -3.08144940296955 45 11 7.71535337621973 3.28464662378027 46 16 10.8992022169645 5.10079778303549 47 17 13.9980717607604 3.00192823923962 48 9 8.0725445007211 0.927455499278898 49 9 11.3395456111980 -2.33954561119796 50 13 14.9189094257961 -1.91890942579612 51 10 8.7493809929121 1.25061900708789 52 6 12.3473497635174 -6.34734976351738 53 12 13.5728310593809 -1.57283105938086 54 8 10.4636129134974 -2.46361291349737 55 14 12.4752968204150 1.52470317958505 56 12 14.4879948202638 -2.48799482026381 57 11 11.3519809312834 -0.351980931283416 58 16 16.3327476520419 -0.332747652041872 59 8 12.5110140410853 -4.51101404108533 60 15 13.7586318046121 1.24136819538793 61 7 9.73111822526854 -2.73111822526854 62 16 14.2276867528448 1.77231324715519 63 14 14.0426493282646 -0.0426493282645574 64 16 13.4573497290244 2.54265027097560 65 9 8.50672807615819 0.493271923841813 66 14 12.4555675169971 1.5444324830029 67 11 12.5131830091708 -1.51318300917077 68 13 7.82252426238176 5.17747573761824 69 15 13.1717192351965 1.82828076480348 70 5 5.02191166050712 -0.0219116605071172 71 15 13.3423967436321 1.65760325636791 72 13 13.6011655936288 -0.601165593628824 73 11 10.8971612648694 0.102838735130649 74 11 14.6746812161648 -3.6746812161648 75 12 11.5881368122847 0.411863187715291 76 12 13.4251884065898 -1.42518840658982 77 12 12.8875803782867 -0.88758037828675 78 12 11.5621608997189 0.437839100281086 79 14 11.9265618447266 2.07343815527338 80 6 10.7390232474991 -4.73902324749911 81 7 8.39879394994077 -1.39879394994077 82 14 10.6892833276403 3.31071667235969 83 14 14.5144116944945 -0.514411694494536 84 10 11.3318073651319 -1.33180736513191 85 13 9.0527031391314 3.94729686086859 86 12 11.0062264212305 0.99377357876948 87 9 9.50287288575902 -0.502872885759023 88 12 11.4292415640489 0.570758435951121 89 16 13.2962238750967 2.70377612490331 90 10 10.8297469926519 -0.829746992651864 91 14 12.8372218608524 1.16277813914763 92 10 11.7928227591210 -1.79282275912104 93 16 13.4341673561025 2.56583264389747 94 15 13.8444571161121 1.15554288388787 95 12 11.4117382454634 0.588261754536615 96 10 9.92657479598748 0.0734252040125248 97 8 8.10538540725177 -0.105385407251773 98 8 8.48417499870718 -0.484174998707177 99 11 14.1249354486139 -3.12493544861391 100 13 9.6958419662631 3.3041580337369 101 16 14.0838708882404 1.91612911175962 102 16 13.1488311420436 2.85116885795643 103 14 16.5524686224786 -2.55246862247861 104 11 11.7649342561260 -0.764934256126018 105 4 6.7558325748484 -2.7558325748484 106 14 11.6037379387428 2.39626206125718 107 9 12.5608912871929 -3.56089128719295 108 14 14.0860598644796 -0.0860598644796395 109 8 13.7684571949471 -5.76845719494714 110 8 12.0530499647827 -4.05304996478271 111 11 12.7489838373952 -1.74898383739519 112 12 12.7700015053594 -0.770001505359418 113 11 8.85234622202135 2.14765377797865 114 14 11.8991738147520 2.10082618524804 115 15 11.2681494176455 3.73185058235445 116 16 11.8174766802116 4.18252331978836 117 16 11.9539285242994 4.04607147570063 118 11 8.77360939777034 2.22639060222966 119 14 12.3862356653579 1.61376433464206 120 14 12.5671384032077 1.43286159679235 121 12 12.9908403134361 -0.9908403134361 122 14 15.0616784230829 -1.06167842308286 123 8 10.6190414734542 -2.61904147345418 124 13 12.7935946055570 0.206405394443017 125 16 13.7087578595732 2.29124214042683 126 12 8.02123821736089 3.97876178263911 127 16 12.9355371701752 3.06446282982483 128 12 13.2746844643058 -1.27468446430576 129 11 13.5150323835848 -2.51503238358484 130 4 4.41866304622886 -0.418663046228862 131 16 11.7297375166298 4.27026248337018 132 15 11.4610427865759 3.53895721342414 133 10 9.56861992456396 0.431380075436043 134 13 11.6390137714771 1.36098622852294 135 15 12.4337743785328 2.56622562146724 136 12 11.2534489028803 0.746551097119685 137 14 14.7142234789598 -0.714223478959797 138 7 11.1537444396956 -4.15374443969556 139 19 12.8805106375390 6.11948936246103 140 12 14.8120365467429 -2.81203654674294 141 12 13.8711277180163 -1.87112771801627 142 13 12.1947348319539 0.80526516804613 143 15 16.2959116316725 -1.29591163167247 144 8 8.30677578566316 -0.306775785663164 145 12 11.6218738538679 0.378126146132109 146 10 8.1899798261447 1.81002017385530 147 8 8.00380029264288 -0.00380029264287846 148 10 12.7891946055085 -2.78919460550846 149 15 12.8252336782981 2.1747663217019 150 16 10.8953716208424 5.1046283791576 151 13 9.70539362077096 3.29460637922904 152 16 13.9705341740922 2.02946582590782 153 9 10.5588398965406 -1.55883989654055 154 14 12.2191579083224 1.7808420916776 155 14 12.0046256009381 1.99537439906190 156 12 12.5356679621759 -0.535667962175926 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.00204030870922384 0.00408061741844768 0.997959691290776 12 0.000704123212388132 0.00140824642477626 0.999295876787612 13 9.11470877084195e-05 0.000182294175416839 0.999908852912292 14 1.04901895837160e-05 2.09803791674320e-05 0.999989509810416 15 1.26701420902535e-06 2.53402841805071e-06 0.99999873298579 16 2.76734651127936e-07 5.53469302255872e-07 0.999999723265349 17 4.71627724089860e-08 9.43255448179719e-08 0.999999952837228 18 2.48213438723599e-08 4.96426877447197e-08 0.999999975178656 19 6.74172140833907e-08 1.34834428166781e-07 0.999999932582786 20 1.05513699378691e-08 2.11027398757383e-08 0.99999998944863 21 1.82898147117726e-09 3.65796294235451e-09 0.999999998171019 22 1.33154717811144e-09 2.66309435622289e-09 0.999999998668453 23 3.23967597570423e-10 6.47935195140846e-10 0.999999999676032 24 5.97155256761306e-11 1.19431051352261e-10 0.999999999940284 25 1.89803094409970e-11 3.79606188819941e-11 0.99999999998102 26 3.59250774835323e-12 7.18501549670646e-12 0.999999999996408 27 2.90803398368766e-12 5.81606796737532e-12 0.999999999997092 28 4.65818297966566e-12 9.31636595933131e-12 0.999999999995342 29 1.10617596213715e-12 2.21235192427430e-12 0.999999999998894 30 2.14680073418647e-13 4.29360146837294e-13 0.999999999999785 31 1.03079158423742e-12 2.06158316847484e-12 0.99999999999897 32 2.15887551578811e-13 4.31775103157622e-13 0.999999999999784 33 7.70242086991453e-14 1.54048417398291e-13 0.999999999999923 34 2.13433849214609e-14 4.26867698429217e-14 0.999999999999979 35 4.06818996302778e-15 8.13637992605556e-15 0.999999999999996 36 1.49029312026209e-14 2.98058624052418e-14 0.999999999999985 37 3.42727782299467e-15 6.85455564598934e-15 0.999999999999997 38 1.33602555057221e-15 2.67205110114441e-15 0.999999999999999 39 4.87772594681312e-16 9.75545189362624e-16 1 40 1.07842513679661e-15 2.15685027359323e-15 0.999999999999999 41 2.02513063197858e-14 4.05026126395715e-14 0.99999999999998 42 0.00103911949720972 0.00207823899441944 0.99896088050279 43 0.00595200714916037 0.0119040142983207 0.99404799285084 44 0.00663585071722644 0.0132717014344529 0.993364149282774 45 0.0892208966784639 0.178441793356928 0.910779103321536 46 0.7980231326372 0.403953734725599 0.201976867362800 47 0.935404702583758 0.129190594832484 0.064595297416242 48 0.918274146110174 0.163451707779652 0.0817258538898261 49 0.928053171816412 0.143893656367176 0.0719468281835878 50 0.93500416694074 0.129991666118519 0.0649958330592597 51 0.918123722422 0.163752555155999 0.0818762775779993 52 0.990528103315161 0.0189437933696771 0.00947189668483856 53 0.9870930270078 0.0258139459844016 0.0129069729922008 54 0.988165275054302 0.0236694498913962 0.0118347249456981 55 0.99162048781189 0.0167590243762206 0.00837951218811032 56 0.988935231122986 0.0221295377540283 0.0110647688770142 57 0.985750503313012 0.0284989933739769 0.0142494966869885 58 0.985610933963421 0.028778132073158 0.014389066036579 59 0.985882638269684 0.0282347234606328 0.0141173617303164 60 0.986561561059778 0.0268768778804438 0.0134384389402219 61 0.98409744784753 0.0318051043049387 0.0159025521524694 62 0.989029341390541 0.0219413172189176 0.0109706586094588 63 0.986898589918422 0.0262028201631563 0.0131014100815782 64 0.990957610512994 0.0180847789740129 0.00904238948700645 65 0.987579405579117 0.0248411888417652 0.0124205944208826 66 0.987749991528443 0.0245000169431143 0.0122500084715571 67 0.987594840042452 0.0248103199150965 0.0124051599575483 68 0.996206853611693 0.00758629277661465 0.00379314638830732 69 0.995877030654123 0.0082459386917548 0.0041229693458774 70 0.994158272235093 0.0116834555298145 0.00584172776490724 71 0.994880108005052 0.0102397839898951 0.00511989199494755 72 0.992861371117637 0.0142772577647264 0.0071386288823632 73 0.990531385802415 0.0189372283951701 0.00946861419758507 74 0.993129794101194 0.0137404117976121 0.00687020589880606 75 0.990759039645798 0.0184819207084042 0.00924096035420208 76 0.989473730048021 0.0210525399039573 0.0105262699519787 77 0.985928432754604 0.0281431344907914 0.0140715672453957 78 0.981797259091213 0.0364054818175741 0.0182027409087870 79 0.985060845963064 0.0298783080738712 0.0149391540369356 80 0.991820024184826 0.0163599516303482 0.00817997581517408 81 0.991180392446333 0.0176392151073332 0.0088196075536666 82 0.994517235096338 0.0109655298073234 0.0054827649036617 83 0.992337425960907 0.0153251480781864 0.0076625740390932 84 0.990187398654597 0.0196252026908059 0.00981260134540294 85 0.997344879421548 0.00531024115690357 0.00265512057845179 86 0.996607264083644 0.00678547183271216 0.00339273591635608 87 0.995206372015426 0.00958725596914853 0.00479362798457426 88 0.99437071664833 0.0112585667033406 0.00562928335167032 89 0.993599861707294 0.0128002765854124 0.00640013829270622 90 0.99106789107628 0.0178642178474414 0.00893210892372069 91 0.988431104811917 0.0231377903761662 0.0115688951880831 92 0.991743382287153 0.0165132354256937 0.00825661771284684 93 0.992447982213685 0.0151040355726295 0.00755201778631473 94 0.990840935971168 0.0183181280576639 0.00915906402883193 95 0.987729215324424 0.0245415693511528 0.0122707846755764 96 0.983282480691511 0.0334350386169774 0.0167175193084887 97 0.979932936855762 0.0401341262884761 0.0200670631442380 98 0.972849217739267 0.0543015645214664 0.0271507822607332 99 0.974836326568887 0.0503273468622258 0.0251636734311129 100 0.974349155925344 0.0513016881493123 0.0256508440746561 101 0.971213196445838 0.057573607108324 0.028786803554162 102 0.967198844374806 0.0656023112503881 0.0328011556251941 103 0.973086965466296 0.0538260690674081 0.0269130345337041 104 0.975759019160432 0.0484819616791363 0.0242409808395681 105 0.973144185923617 0.0537116281527654 0.0268558140763827 106 0.969118869359974 0.061762261280051 0.0308811306400255 107 0.966999809775915 0.0660003804481705 0.0330001902240852 108 0.968475758788268 0.0630484824234644 0.0315242412117322 109 0.979221287157658 0.0415574256846845 0.0207787128423422 110 0.982311357016816 0.0353772859663685 0.0176886429831842 111 0.979118053991036 0.0417638920179285 0.0208819460089643 112 0.983699847055142 0.0326003058897163 0.0163001529448582 113 0.978708236764146 0.0425835264717074 0.0212917632358537 114 0.973686929865117 0.0526261402697668 0.0263130701348834 115 0.971797607405585 0.056404785188829 0.0282023925944145 116 0.976456339980549 0.0470873200389021 0.0235436600194510 117 0.984592626546172 0.0308147469076555 0.0154073734538278 118 0.981511083411302 0.0369778331773968 0.0184889165886984 119 0.974059865501467 0.0518802689970668 0.0259401344985334 120 0.977795174753013 0.0444096504939737 0.0222048252469868 121 0.968636192127628 0.0627276157447445 0.0313638078723723 122 0.95675693600277 0.0864861279944581 0.0432430639972291 123 0.950093832653847 0.0998123346923058 0.0499061673461529 124 0.932124017683433 0.135751964633133 0.0678759823165665 125 0.927176256119342 0.145647487761316 0.072823743880658 126 0.927971707632583 0.144056584734834 0.0720282923674172 127 0.908118031918131 0.183763936163738 0.0918819680818689 128 0.89532063519619 0.209358729607621 0.104679364803810 129 0.94916644257013 0.101667114859742 0.0508335574298711 130 0.94429810208315 0.1114037958337 0.05570189791685 131 0.928369344172011 0.143261311655978 0.071630655827989 132 0.905524974411916 0.188950051176169 0.0944750255880843 133 0.872306296019067 0.255387407961866 0.127693703980933 134 0.824657094742417 0.350685810515167 0.175342905257583 135 0.771855830476231 0.456288339047538 0.228144169523769 136 0.73507697145772 0.529846057084559 0.264923028542280 137 0.677916738995388 0.644166522009224 0.322083261004612 138 0.678717501789195 0.642564996421609 0.321282498210805 139 0.918234114860024 0.163531770279952 0.0817658851399762 140 0.979559200584246 0.0408815988315087 0.0204407994157543 141 0.96201142755507 0.0759771448898617 0.0379885724449309 142 0.934605514808501 0.130788970382999 0.0653944851914993 143 0.880137878129648 0.239724243740705 0.119862121870352 144 0.777020072564249 0.445959854871502 0.222979927435751 145 0.677829731944075 0.64434053611185 0.322170268055925 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 37 0.274074074074074 NOK 5% type I error level 91 0.674074074074074 NOK 10% type I error level 108 0.8 NOK

Charts produced by software:

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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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Software written by Ed van Stee & Patrick Wessa

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