WS7 deterministic trend

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 22 Nov 2010 20:46:59 +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/22/t1290458780f4w2ima7qwre2v4.htm/, Retrieved Mon, 22 Nov 2010 21:46:20 +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/22/t1290458780f4w2ima7qwre2v4.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 «

41 25 15 9 3 38 25 15 9 4 37 19 14 9 4 36 18 10 14 2 42 18 10 8 4 44 23 9 14 4 40 23 18 15 3 43 25 14 9 4 40 23 11 11 4 45 24 11 14 4 47 32 9 14 4 45 30 17 6 5 45 32 21 10 4 40 24 16 9 4 49 17 14 14 4 48 30 24 8 5 44 25 7 11 4 29 25 9 10 4 42 26 18 16 4 45 23 11 11 5 32 25 13 11 5 32 25 13 11 5 41 35 18 7 4 29 19 14 13 2 38 20 12 10 4 41 21 12 9 4 38 21 9 9 4 24 23 11 15 3 34 24 8 13 2 38 23 5 16 2 37 19 10 12 3 46 17 11 6 5 48 27 15 4 5 42 27 16 12 4 46 25 12 10 4 43 18 14 14 5 38 22 13 9 4 39 26 10 10 4 34 26 18 14 4 39 23 17 14 4 35 16 12 10 2 41 27 13 9 3 40 25 13 14 3 43 14 11 8 4 37 19 13 9 2 41 20 12 8 4 46 26 12 10 4 26 16 12 9 3 41 18 12 9 3 37 22 9 9 3 39 25 17 9 4 44 29 18 11 5 39 21 7 15 2 36 22 17 8 4 38 22 12 10 2 38 32 12 8 0 38 23 9 14 4 32 31 9 11 4 33 18 13 10 3 46 23 10 12 4 42 24 12 9 4 42 19 10 13 2 43 26 11 14 4 41 14 13 15 2 49 20 6 8 4 45 22 7 7 3 39 24 13 10 4 45 25 11 10 5 31 21 18 13 3 30 21 18 13 3 45 28 9 11 4 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Career[t] = + 31.7622562372553 + 0.188776879139715PersonalStandards[t] + 0.0437388904055657ParentalExpectations[t] -0.218043009341138Doubts[t] + 1.40702742932656LeadershipPreference[t] + 0.00608276680367076t + 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) 31.7622562372553 3.493424 9.092 0 0 PersonalStandards 0.188776879139715 0.106859 1.7666 0.079475 0.039738 ParentalExpectations 0.0437388904055657 0.128329 0.3408 0.733739 0.366869 Doubts -0.218043009341138 0.155328 -1.4038 0.162605 0.081302 LeadershipPreference 1.40702742932656 0.483551 2.9098 0.004209 0.002104 t 0.00608276680367076 0.010123 0.6009 0.548887 0.274443 Multiple Linear Regression - Regression Statistics Multiple R 0.370926417662263 R-squared 0.137586407319759 Adjusted R-squared 0.106785921866894 F-TEST (value) 4.46702073999156 F-TEST (DF numerator) 5 F-TEST (DF denominator) 140 p-value 0.000831035690440629 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.99345534545331 Sum Squared Residuals 3490.84348018507 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 39.4025395425448 1.59746045745523 2 38 40.815649738675 -2.81564973867502 3 37 39.6453323402348 -2.64533234023484 4 36 35.3834127609177 0.616587239082285 5 42 39.5118084424213 2.48819155757866 6 44 39.1097786584712 4.89022134152881 7 40 37.8844410002572 2.11555899974275 8 43 40.8084074490915 2.19159255090852 9 40 39.8696337677167 0.130366232283254 10 45 39.4103643856367 5.58963561436328 11 47 40.839184404747 6.16081559525302 12 45 43.9689960405714 1.03100395942859 13 45 42.2483886605857 2.75161133941434 14 40 40.7436049515849 -0.743604951584918 15 49 38.2505567368938 10.7494432631062 16 48 43.8634133219428 4.13658667805722 17 44 40.1208940988033 3.87910590119672 18 29 40.4324976557592 -11.4324976557592 19 42 39.7127492593059 2.28725074069413 20 45 41.3435716318837 3.65642836811631 21 32 41.8146859377779 -9.81468593777792 22 32 41.8207687045816 -9.82076870458159 23 41 43.3984593228482 -2.39845932284823 24 29 36.0868435470942 -7.08684354709424 25 38 39.662409298903 -1.66240929890304 26 41 40.0753119541876 0.92468804581244 27 38 39.9501780497745 -1.95017804977453 28 24 37.7060068702954 -13.7060068702954 29 34 36.7987084343778 -2.79870843437778 30 38 35.8306686228016 2.16933137719837 31 37 37.5795377917654 -0.579537791765378 32 46 41.3741186053951 4.62588139460486 33 48 43.8790117439005 4.12098825609951 34 42 40.7774618970541 1.22253810294593 35 46 40.6671213626383 5.33287863736168 36 43 39.9740991482371 3.02590085176287 37 38 40.3747381585732 -2.37473815857322 38 39 40.7866687613779 -1.78666876137791 39 34 40.2704906140616 -6.27049061406156 40 39 39.6665038530405 -0.66650385304052 41 35 36.1905711925498 -1.19057119254978 42 41 39.9420089589636 1.05799104103642 43 40 38.4803229207821 1.51967707921786 44 43 39.0376677216112 3.9623322783888 45 37 37.0430147969303 -0.0430147969303161 46 41 40.2262334204624 0.773766579537602 47 46 40.9288914434221 5.07110855657792 48 26 37.8582209988432 -11.8582209988432 49 41 38.2418575239263 2.75814247607372 50 37 38.8718311360721 -1.87183113607211 51 39 41.201183092866 -2.20118309286602 52 44 42.9770536772784 1.0229463227216 53 39 35.8985392911589 3.10146070884111 54 36 40.871143765199 -4.87114376519902 55 38 37.4083912026395 0.591608797360536 56 38 36.9242739208694 1.07572607913057 57 38 39.4199997654584 -1.41999976545840 58 32 41.5904265934032 -9.5904265934032 59 33 38.1283810730274 -5.12838107302742 60 46 39.9180729749572 6.08192702504275 61 42 40.8545394297352 1.14546057026482 62 42 36.1430331240115 5.85696687598853 63 43 40.1103047845107 2.8896952154893 64 41 34.9064449144547 6.09355508554534 65 49 40.0793726472987 8.92062735270125 66 45 39.317763642802 5.68223635719801 67 39 40.7167319116216 -1.71673191162163 68 45 42.2311412060805 2.76885879391955 69 31 38.3201048024877 -7.32010480248768 70 30 38.3261875692914 -8.32618756929135 71 45 41.1031719244318 3.89682807556822 72 48 42.4153036320266 5.58469636797344 73 28 38.1383256724161 -10.1383256724161 74 35 37.5094910117051 -2.50949101170507 75 38 40.6640949477224 -2.66409494772242 76 39 40.4659560227024 -1.4659560227024 77 40 40.2549678326448 -0.254967832644762 78 38 38.9527925434016 -0.952792543401607 79 42 38.2764419813599 3.72355801864015 80 36 35.3083179209858 0.691682079014167 81 49 43.8062800572349 5.19371994276512 82 41 40.6912295026641 0.308770497335859 83 18 35.9224835988106 -17.9224835988106 84 36 38.1344402019052 -2.13444020190521 85 42 38.9107546881586 3.08924531184143 86 41 42.7773684699155 -1.77736846991549 87 43 40.0540136009348 2.94598639906523 88 46 39.7722295055258 6.22777049447415 89 37 40.8216072608941 -3.82160726089410 90 38 39.1161138606988 -1.11611386069877 91 43 40.8923152780047 2.10768472199529 92 41 43.0319080800787 -2.03190808007865 93 35 34.7178200487262 0.282179951273831 94 39 40.5892671426859 -1.58926714268593 95 42 39.7100079972943 2.28999200270571 96 36 39.8325038422170 -3.83250384221696 97 35 41.3038256889569 -6.3038256889569 98 33 36.2909518132963 -3.29095181329628 99 36 38.3421050051797 -2.34210500517969 100 48 39.4220415530223 8.57795844697767 101 41 40.124699575982 0.875300424017985 102 47 38.5652264401011 8.43477355989893 103 41 39.2386081097589 1.76139189024108 104 31 42.2764579116633 -11.2764579116633 105 36 41.4855930000655 -5.48559300006554 106 46 41.5357352670679 4.46426473293209 107 39 38.2866074833381 0.713392516661932 108 44 40.9233585126464 3.07664148735360 109 43 37.3287480592839 5.67125194071613 110 32 41.4423503707902 -9.44235037079021 111 40 40.7496487661822 -0.749648766182157 112 40 39.3081463809892 0.691853619010763 113 46 37.3084237831102 8.69157621688976 114 45 39.4216110129252 5.57838898707484 115 39 40.936020307384 -1.93602030738398 116 44 41.9589924904932 2.04100750950679 117 35 39.9895080752955 -4.98950807529546 118 38 37.9054888643409 0.0945111356591246 119 38 36.6357608730347 1.36423912696532 120 36 37.5973402377987 -1.59734023779867 121 42 38.2729968453097 3.72700315469028 122 39 39.9182919780917 -0.918291978091683 123 41 43.3362457095252 -2.33624570952517 124 41 39.68347920505 1.31652079494998 125 47 39.0530868717700 7.94691312823004 126 39 39.0289314558924 -0.0289314558923762 127 40 39.8329441766777 0.167055823322273 128 44 40.5224221017062 3.47757789829377 129 42 39.7434797790629 2.25652022093707 130 35 38.850984936243 -3.85098493624303 131 46 43.1083325742106 2.89166742578945 132 43 37.9903269897991 5.00967301020087 133 40 40.5788652986934 -0.57886529869339 134 44 40.4264093690386 3.57359063096141 135 37 40.9123170449301 -3.91231704493011 136 46 41.0782311704652 4.92176882953479 137 44 42.0552553479132 1.94474465208683 138 35 39.0157395389983 -4.01573953899826 139 39 37.5707353762767 1.42926462372334 140 40 38.6783247822546 1.32167521774537 141 42 39.2513896291641 2.74861037083587 142 37 39.3301465836812 -2.33014658368124 143 29 40.0167741738678 -11.0167741738678 144 33 38.2408054781143 -5.24080547811429 145 35 40.3196569045297 -5.31965690452968 146 42 35.9146434414381 6.08535655856194 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.227457998266173 0.454915996532346 0.772542001733827 10 0.120985996183421 0.241971992366841 0.87901400381658 11 0.060086004543474 0.120172009086948 0.939913995456526 12 0.0256372195817378 0.0512744391634755 0.974362780418262 13 0.0105573272206529 0.0211146544413058 0.989442672779347 14 0.00634892685450191 0.0126978537090038 0.993651073145498 15 0.0281914269115133 0.0563828538230267 0.971808573088487 16 0.0159552021939422 0.0319104043878843 0.984044797806058 17 0.00907560567686041 0.0181512113537208 0.99092439432314 18 0.322086110642595 0.644172221285189 0.677913889357405 19 0.322958305747510 0.645916611495021 0.67704169425249 20 0.257671778761508 0.515343557523016 0.742328221238492 21 0.586796054985821 0.826407890028358 0.413203945014179 22 0.7254079866881 0.549184026623801 0.274592013311901 23 0.684278422430127 0.631443155139746 0.315721577569873 24 0.635945115816869 0.728109768366261 0.364054884183131 25 0.60569406377029 0.78861187245942 0.39430593622971 26 0.626604604832169 0.746790790335662 0.373395395167831 27 0.581707180596965 0.83658563880607 0.418292819403035 28 0.78417810590012 0.431643788199761 0.215821894099881 29 0.77360024242392 0.452799515152159 0.226399757576080 30 0.789550517688911 0.420898964622178 0.210449482311089 31 0.765252096984235 0.469495806031531 0.234747903015765 32 0.819369211489672 0.361261577020657 0.180630788510328 33 0.838527388368635 0.32294522326273 0.161472611631365 34 0.810228904579387 0.379542190841226 0.189771095420613 35 0.833150977495169 0.333698045009663 0.166849022504831 36 0.803798750859097 0.392402498281806 0.196201249140903 37 0.764374814282456 0.471250371435088 0.235625185717544 38 0.719179227350202 0.561641545299597 0.280820772649798 39 0.722765242388572 0.554469515222857 0.277234757611428 40 0.674446441224222 0.651107117551555 0.325553558775778 41 0.631963676149035 0.73607264770193 0.368036323850965 42 0.603809183410784 0.792381633178432 0.396190816589216 43 0.570551004921608 0.858897990156784 0.429448995078392 44 0.556252724346702 0.887494551306597 0.443747275653298 45 0.507330078469422 0.985339843061157 0.492669921530578 46 0.456601074374852 0.913202148749703 0.543398925625148 47 0.471732618688816 0.943465237377633 0.528267381311183 48 0.660934275778857 0.678131448442285 0.339065724221143 49 0.641078061079927 0.717843877840146 0.358921938920073 50 0.593879418049488 0.812241163901025 0.406120581950513 51 0.546809073809532 0.906381852380937 0.453190926190468 52 0.499309660527937 0.998619321055873 0.500690339472063 53 0.485304274968008 0.970608549936017 0.514695725031992 54 0.467341541576426 0.934683083152852 0.532658458423574 55 0.427090339316054 0.854180678632109 0.572909660683946 56 0.394344347378861 0.788688694757722 0.605655652621139 57 0.348333156350139 0.696666312700278 0.651666843649861 58 0.458407831902688 0.916815663805377 0.541592168097311 59 0.447365036174678 0.894730072349356 0.552634963825322 60 0.489105589796132 0.978211179592264 0.510894410203868 61 0.446040113113709 0.892080226227418 0.553959886886291 62 0.473619074882744 0.947238149765489 0.526380925117256 63 0.443058458428971 0.886116916857942 0.556941541571029 64 0.468456129594169 0.936912259188339 0.531543870405831 65 0.577940500025611 0.844118999948778 0.422059499974389 66 0.59423583353098 0.81152833293804 0.40576416646902 67 0.551257390548256 0.897485218903488 0.448742609451744 68 0.520525959341149 0.958948081317702 0.479474040658851 69 0.562409287953999 0.875181424092002 0.437590712046001 70 0.630891262814233 0.738217474371534 0.369108737185767 71 0.619151319810877 0.761697360378246 0.380848680189123 72 0.646033594535094 0.707932810929812 0.353966405464906 73 0.759325214576869 0.481349570846262 0.240674785423131 74 0.725070929904225 0.549858140191551 0.274929070095776 75 0.691919493856534 0.616161012286933 0.308080506143466 76 0.648986132874778 0.702027734250444 0.351013867125222 77 0.603091129873587 0.793817740252826 0.396908870126413 78 0.557340778960982 0.885318442078036 0.442659221039018 79 0.547787660060173 0.904424679879654 0.452212339939827 80 0.50443226380856 0.99113547238288 0.49556773619144 81 0.55884829081543 0.88230341836914 0.44115170918457 82 0.518416418137797 0.963167163724406 0.481583581862203 83 0.94541618328173 0.109167633436541 0.0545838167182706 84 0.934340709097778 0.131318581804444 0.0656592909022219 85 0.926373915367213 0.147252169265573 0.0736260846327867 86 0.907944187916559 0.184111624166882 0.0920558120834412 87 0.895822493547362 0.208355012905276 0.104177506452638 88 0.91229436986366 0.175411260272679 0.0877056301363397 89 0.898536805425585 0.202926389148829 0.101463194574415 90 0.875178733492747 0.249642533014506 0.124821266507253 91 0.853281977173142 0.293436045653715 0.146718022826858 92 0.823743839885157 0.352512320229687 0.176256160114843 93 0.793692740738723 0.412614518522555 0.206307259261277 94 0.760022749478536 0.479954501042928 0.239977250521464 95 0.725279982536743 0.549440034926515 0.274720017463257 96 0.703142194498975 0.59371561100205 0.296857805501025 97 0.727846654089985 0.54430669182003 0.272153345910015 98 0.775392144210561 0.449215711578878 0.224607855789439 99 0.781926685554553 0.436146628890893 0.218073314445447 100 0.835571653412115 0.32885669317577 0.164428346587885 101 0.799982491237333 0.400035017525334 0.200017508762667 102 0.815379069425825 0.36924186114835 0.184620930574175 103 0.778230757932635 0.443538484134731 0.221769242067365 104 0.888852063505443 0.222295872989113 0.111147936494557 105 0.912330437801133 0.175339124397733 0.0876695621988667 106 0.899139163792617 0.201721672414766 0.100860836207383 107 0.878238702828778 0.243522594342445 0.121761297171222 108 0.852211117444327 0.295577765111346 0.147788882555673 109 0.842577918730061 0.314844162539878 0.157422081269939 110 0.930387955131977 0.139224089736047 0.0696120448680234 111 0.915247823216512 0.169504353566976 0.0847521767834881 112 0.894440542294716 0.211118915410568 0.105559457705284 113 0.913190679520826 0.173618640958347 0.0868093204791736 114 0.907661509910388 0.184676980179224 0.0923384900896122 115 0.88518615866528 0.229627682669440 0.114813841334720 116 0.856947096295046 0.286105807409907 0.143052903704954 117 0.88109489416703 0.237810211665940 0.118905105832970 118 0.849831489269224 0.300337021461552 0.150168510730776 119 0.812957311348095 0.37408537730381 0.187042688651905 120 0.81592862576943 0.368142748461141 0.184071374230571 121 0.767832753445104 0.464334493109793 0.232167246554896 122 0.755375687094161 0.489248625811677 0.244624312905839 123 0.719218733703758 0.561562532592484 0.280781266296242 124 0.673663176708118 0.652673646583763 0.326336823291882 125 0.692213154351581 0.615573691296837 0.307786845648419 126 0.644214929492162 0.711570141015677 0.355785070507838 127 0.580688364763756 0.838623270472487 0.419311635236244 128 0.512166539271804 0.975666921456392 0.487833460728196 129 0.429069523512879 0.858139047025757 0.570930476487121 130 0.581918238885136 0.836163522229727 0.418081761114864 131 0.517740755401431 0.964518489197138 0.482259244598569 132 0.449496241244478 0.898992482488955 0.550503758755522 133 0.398360322627083 0.796720645254167 0.601639677372917 134 0.2936210521642 0.5872421043284 0.7063789478358 135 0.270692557961984 0.541385115923969 0.729307442038016 136 0.238682070364268 0.477364140728537 0.761317929635732 137 0.322334335869288 0.644668671738575 0.677665664130712 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 4 0.0310077519379845 OK 10% type I error level 6 0.0465116279069767 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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

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

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

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

Software written by Ed van Stee & Patrick Wessa

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