workshop 7

*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 15:30:58 +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/t1291303770t4j7fpijhxvq5xi.htm/, Retrieved Thu, 02 Dec 2010 16:29:41 +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/t1291303770t4j7fpijhxvq5xi.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 «

0 5 1 1 1 2 1 21 1 4 1 4 1 4 1 21 0 7 1 5 2 4 1 24 0 7 2 2 1 4 2 21 5 5 1 1 1 3 2 21 5 1 1 1 2 2 22 4 4 1 2 1 3 2 22 4 4 2 1 1 4 1 20 0 6 2 1 1 2 1 21 0 5 2 1 1 3 0 21 0 1 2 3 2 3 2 21 5 5 1 1 1 3 1 22 0 4 2 1 1 4 1 22 2 6 1 1 1 3 1 23 3 7 1 2 1 2 1 23 0 7 1 4 2 5 2 21 0 2 2 1 1 2 2 24 0 6 2 1 1 3 1 23 0 4 2 1 1 3 2 21 4 3 1 2 1 3 1 23 0 6 1 3 1 3 2 32 8 6 1 1 1 4 1 21 0 5 2 1 2 3 2 21 0 4 2 1 1 1 2 21 0 6 1 1 2 3 1 21 3 4 2 1 1 2 2 21 0 3 2 2 4 4 1 20 24 4 2 1 1 4 1 24 15 5 1 1 1 4 1 22 0 6 1 1 1 1 2 22 12 6 2 1 1 3 2 21 0 4 2 1 1 1 2 21 0 6 1 1 1 4 1 21 0 6 2 1 1 2 2 21 4 5 2 1 1 3 1 23 1 6 2 1 1 3 1 23 0 4 1 1 1 2 2 21 16 6 2 1 1 4 1 20 9 7 1 1 1 1 2 21 0 5 2 1 1 2 1 20 8 6 2 1 1 3 2 21 10 6 1 1 1 3 1 22 0 5 2 4 1 5 2 21 6 7 2 1 1 3 1 22 0 6 2 1 1 4 1 22 0 3 1 4 3 3 2 22 15 4 1 2 2 4 1 22 0 5 1 2 1 2 1 21 0 4 1 1 1 3 1 21 0 3 2 1 1 2 2 21 0 5 1 2 2 3 1 23 0 5 1 1 1 2 2 23 0 4 2 1 1 3 2 23 0 5 2 1 1 4 1 22 10 1 2 1 1 1 1 24 7 2 2 1 1 1 1 23 2 3 2 1 1 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 meer_sport[t] = -0.312893344343957 -0.0246829759182962Fietsen[t] -0.198504165639036algemene_tevredenheid[t] + 0.284660002112055roken[t] + 0.327147951886211drugs[t] + 0.348520585269895drankgebruik[t] + 0.0154843612941977geslacht[t] + 0.00451209386384474leeftijd[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) -0.312893344343957 0.639265 -0.4895 0.625223 0.312612 Fietsen -0.0246829759182962 0.048425 -0.5097 0.610988 0.305494 algemene_tevredenheid -0.198504165639036 0.108497 -1.8296 0.069272 0.034636 roken 0.284660002112055 0.103623 2.7471 0.00674 0.00337 drugs 0.327147951886211 0.0731 4.4753 1.5e-05 7e-06 drankgebruik 0.348520585269895 0.138489 2.5166 0.012887 0.006444 geslacht 0.0154843612941977 0.017058 0.9077 0.365456 0.182728 leeftijd 0.00451209386384474 0.011487 0.3928 0.695026 0.347513 Multiple Linear Regression - Regression Statistics Multiple R 0.456956700210581 R-squared 0.208809425867343 Adjusted R-squared 0.172373017848076 F-TEST (value) 5.73079063547996 F-TEST (DF numerator) 7 F-TEST (DF denominator) 152 p-value 6.72660873723974e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.809346669646454 Sum Squared Residuals 99.5663888135065 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 0.113673284433876 0.886326715566124 2 1 1.83851565103055 -0.838515651030554 3 1 1.89303036562154 -0.893030365621545 4 2 0.713850487101831 1.28614951289817 5 1 0.35426335140647 0.64573664859353 6 1 1.35988901077752 -0.359889010777522 7 2 1.71171993858203 0.288280061417971 8 1 1.44282604151553 -0.442826041515535 9 1 0.754648547200719 0.245351452799281 10 1 0.75795888973533 0.242041110264669 11 3 1.86095243537958 1.13904756462042 12 1 1.32046800193846 -0.320468001938459 13 1 1.48281895183162 -0.48281895183162 14 1 1.32480566890589 -0.324805668905895 15 2 0.959438459509854 1.04056154049015 16 4 2.54309417996204 1.45690582003796 17 1 1.24835412002639 -0.248354120026392 18 1 1.11276522167532 -0.112765221675325 19 1 1.49773141164880 -0.497731411648796 20 2 1.38531831506925 0.614681684930751 21 3 1.83524597514279 1.16475402485721 22 1 1.60744861661218 -0.607448616612176 23 1 1.73966006238718 -0.739660062387176 24 1 0.825387132420996 0.174612867579004 25 1 1.57849694842955 -0.578496948429555 26 1 1.15253508430721 -0.152535084307207 27 2 2.42977927650227 -0.429779276502271 28 1 1.57244489465000 -0.572444894649997 29 1 1.64761595382467 -0.64761595382467 30 1 1.04415483388377 -0.0441548338837738 31 1 1.43031708435682 -0.430317084356825 32 1 0.825387132420996 0.174612867579004 33 1 1.60744861661218 -0.607448616612176 34 1 1.12121750792599 -0.121217507925993 35 1 1.14196029145747 -0.141960291457466 36 1 1.11276522167532 -0.112765221675325 37 1 1.42323275176776 -0.423232751767758 38 1 1.43406893445355 -0.434068934453545 39 1 0.949842370305143 0.0501576296948569 40 1 0.799943912735575 0.200056087264425 41 1 1.47543802299527 -0.475438022995272 42 1 1.29578502602016 -0.295785026020163 43 4 2.13636852723061 1.86363147276939 44 1 1.07259788446283 -0.072597884462831 45 1 1.42442881226734 -0.424428812267338 46 4 2.35535595122673 1.64464404877327 47 2 1.95695893185502 0.0430410681449788 48 2 0.97783568875805 1.02216431124195 49 1 1.32966661656256 -0.329666616562558 50 1 1.17721806022550 -0.177218060225503 51 2 1.62061236534471 0.379387634655288 52 1 1.35732499661634 -0.357324996616341 53 1 1.51065175878181 -0.510651758781813 54 1 1.49423272682408 -0.494232726824082 55 1 0.628953215835496 0.371046784164504 56 1 0.566225409303778 0.433774590696222 57 1 0.850070108339292 0.149929891660708 58 2 1.48281895183162 0.51718104816838 59 1 1.1927024215197 -0.192702421519701 60 1 1.09202243814385 -0.0920224381438522 61 1 1.23467352912625 -0.234673529126252 62 2 2.26862252244703 -0.268622522447034 63 1 1.54258526962154 -0.542585269621544 64 2 1.28949927935006 0.710500720649936 65 4 1.64430561129006 2.35569438870994 66 1 1.44580144565102 -0.445801445651023 67 1 1.13337761129189 -0.133377611291885 68 1 1.42442881226734 -0.424428812267338 69 2 1.63903327365909 0.360966726340911 70 3 1.92307734131263 1.07692265868737 71 1 1.51153477390603 -0.51153477390603 72 1 1.47379476410393 -0.473794764103931 73 1 1.11351724087841 -0.113517240878409 74 1 1.30498364064426 -0.304983640644262 75 1 1.12824958296952 -0.128249582969523 76 1 1.12824958296952 -0.128249582969523 77 1 2.04444565091675 -1.04444565091675 78 4 2.00533515371866 1.99466484628134 79 1 1.10630504810882 -0.106305048108817 80 1 1.91911220720419 -0.91911220720419 81 2 1.44955329574774 0.550446704252257 82 1 1.55518688054954 -0.555186880549545 83 1 1.67725253116892 -0.67725253116892 84 1 1.90759298001843 -0.907592980018429 85 1 1.52675205453453 -0.526752054534528 86 1 1.15806058721018 -0.158060587210182 87 1 1.60744861661218 -0.607448616612176 88 1 1.29578502602016 -0.295785026020163 89 1 0.850070108339292 0.149929891660708 90 2 2.17676862083629 -0.176768620836286 91 1 1.63664368639432 -0.636643686394317 92 1 1.44580144565102 -0.445801445651023 93 1 1.49516739748762 -0.495167397487615 94 1 1.57713468559761 -0.577134685597606 95 1 1.44911178818563 -0.449111788185634 96 2 0.626004760953544 1.37399523904646 97 1 1.71906312727276 -0.719063127272756 98 5 1.76121688633976 3.23878311366024 99 1 1.38426147505484 -0.384261475054844 100 1 1.40894445097314 -0.40894445097314 101 1 1.46128580694522 -0.46128580694522 102 2 1.43991317356154 0.560086826438464 103 1 1.92564135547381 -0.925641355473808 104 3 2.13893380404723 0.861066195952774 105 1 1.48870722392111 -0.488707223921107 106 1 1.47968303619342 -0.479683036193417 107 1 1.09728086038113 -0.0972808603811273 108 3 1.76077537877765 1.23922462122235 109 1 1.55076744045499 -0.550767440454991 110 1 1.28030066472597 -0.280300664725965 111 1 1.08874161119082 -0.0887416111908218 112 1 1.58276564069388 -0.58276564069388 113 1 1.55373196394831 -0.553731963948306 114 1 1.03348738726474 -0.0334873872647423 115 2 1.89636427712871 0.103635722871285 116 2 1.08377286379499 0.916227136205011 117 4 1.81218206408620 2.18781793591380 118 4 2.19225298213048 1.80774701786952 119 1 1.56728127939968 -0.567281279399682 120 1 1.21592744608524 -0.215927446085236 121 1 1.13765090949543 -0.137650909495426 122 1 1.51891570274238 -0.518915702742378 123 4 1.99374881649145 2.00625118350855 124 1 2.0609197421839 -1.0609197421839 125 1 1.33878345805954 -0.338783458059538 126 1 1.52678033953992 -0.526780339539924 127 1 1.45831040280973 -0.458310402809733 128 3 1.46128580694522 1.53871419305478 129 1 1.40563410843853 -0.405634108438529 130 1 2.07583220200108 -1.07583220200108 131 1 2.32483696076448 -1.32483696076448 132 4 1.77551341169842 2.22448658830158 133 4 1.98556174624482 2.01443825375518 134 1 1.48264452493521 -0.482644524935211 135 2 1.96906584057315 0.0309341594268482 136 1 0.825387132420996 0.174612867579004 137 2 1.74518556529015 0.254814434709849 138 1 1.40894445097314 -0.40894445097314 139 3 1.58276564069388 1.41723435930612 140 2 1.98304176506514 0.0169582349348603 141 2 1.42442881226734 0.575571187732662 142 1 1.42716725332493 -0.427167253324928 143 1 1.45500006027512 -0.455000060275121 144 2 1.45500006027512 0.544999939724879 145 1 1.42442881226734 -0.424428812267338 146 2 2.17676862083629 -0.176768620836286 147 2 2.02703815164151 -0.0270381516415052 148 1 0.9781823893332 0.0218176106668005 149 1 1.80391812012563 -0.803918120125629 150 2 1.61869343404838 0.381306565951621 151 1 1.59825000198808 -0.598250001988077 152 2 1.42442881226734 0.575571187732662 153 1 1.6534371158727 -0.653437115872701 154 1 1.13116245092352 -0.131162450923522 155 1 1.64292943306442 -0.642929433064416 156 1 1.47968303619342 -0.479683036193417 157 1 1.82487936353501 -0.824879363535007 158 1 1.61373436328228 -0.613734363282275 159 1 1.78942348880438 -0.789423488804381 160 1 1.39974583634904 -0.399745836349042 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.428963219323043 0.857926438646085 0.571036780676957 12 0.273375549200463 0.546751098400926 0.726624450799537 13 0.20563554030992 0.41127108061984 0.79436445969008 14 0.118063654936425 0.236127309872850 0.881936345063575 15 0.188817872187008 0.377635744374016 0.811182127812992 16 0.71970935967699 0.56058128064602 0.28029064032301 17 0.691997605507714 0.616004788984572 0.308002394492286 18 0.617384184832234 0.765231630335533 0.382615815167766 19 0.612148829549336 0.775702340901327 0.387851170450664 20 0.563416781974449 0.873166436051103 0.436583218025551 21 0.569239373351798 0.861521253296405 0.430760626648202 22 0.557722227586914 0.884555544826171 0.442277772413086 23 0.517864075666236 0.964271848667528 0.482135924333764 24 0.444378036190572 0.888756072381144 0.555621963809428 25 0.382417761878458 0.764835523756917 0.617582238121541 26 0.319447877101197 0.638895754202393 0.680552122898803 27 0.263898883392278 0.527797766784556 0.736101116607722 28 0.313568938139152 0.627137876278305 0.686431061860848 29 0.288981563829652 0.577963127659305 0.711018436170348 30 0.243942950624675 0.48788590124935 0.756057049375325 31 0.221424125008629 0.442848250017257 0.778575874991371 32 0.175905440337650 0.351810880675301 0.82409455966235 33 0.152113117283971 0.304226234567941 0.84788688271603 34 0.121567302047267 0.243134604094534 0.878432697952733 35 0.0929041630440892 0.185808326088178 0.907095836955911 36 0.0693261153288846 0.138652230657769 0.930673884671115 37 0.0621587800545870 0.124317560109174 0.937841219945413 38 0.0496879086160312 0.0993758172320624 0.950312091383969 39 0.0358598874676490 0.0717197749352979 0.96414011253235 40 0.0260883598875104 0.0521767197750208 0.97391164011249 41 0.0223443891103371 0.0446887782206741 0.977655610889663 42 0.0158574108084438 0.0317148216168877 0.984142589191556 43 0.0607803393752815 0.121560678750563 0.939219660624719 44 0.0453142221807071 0.0906284443614142 0.954685777819293 45 0.0370599541599356 0.0741199083198713 0.962940045840064 46 0.121834733080198 0.243669466160397 0.878165266919802 47 0.0981751656788983 0.196350331357797 0.901824834321102 48 0.123681138143085 0.247362276286170 0.876318861856915 49 0.103096545624513 0.206193091249026 0.896903454375487 50 0.0846776165561347 0.169355233112269 0.915322383443865 51 0.074696932966651 0.149393865933302 0.925303067033349 52 0.0631242608006086 0.126248521601217 0.936875739199391 53 0.0571750661235235 0.114350132247047 0.942824933876476 54 0.0500020313085003 0.100004062617001 0.9499979686915 55 0.0392009242379699 0.0784018484759399 0.96079907576203 56 0.0315051215379242 0.0630102430758485 0.968494878462076 57 0.0237337302004648 0.0474674604009297 0.976266269799535 58 0.0198629063692316 0.0397258127384633 0.980137093630768 59 0.0152843714024987 0.0305687428049974 0.984715628597501 60 0.0110131995533691 0.0220263991067382 0.98898680044663 61 0.00860315188037568 0.0172063037607514 0.991396848119624 62 0.00622215696465587 0.0124443139293117 0.993777843035344 63 0.00565367892057157 0.0113073578411431 0.994346321079428 64 0.00548313222205346 0.0109662644441069 0.994516867777947 65 0.0534253272503716 0.106850654500743 0.946574672749628 66 0.0452912807979275 0.090582561595855 0.954708719202072 67 0.0349160555745631 0.0698321111491262 0.965083944425437 68 0.0281319578135886 0.0562639156271772 0.971868042186411 69 0.0220580400531193 0.0441160801062386 0.977941959946881 70 0.0299679713333959 0.0599359426667918 0.970032028666604 71 0.0263908831732578 0.0527817663465156 0.973609116826742 72 0.0218626919700504 0.0437253839401007 0.97813730802995 73 0.0170548160456380 0.0341096320912760 0.982945183954362 74 0.0132685585600671 0.0265371171201342 0.986731441439933 75 0.00972681858538311 0.0194536371707662 0.990273181414617 76 0.0070485925080213 0.0140971850160426 0.992951407491979 77 0.00887295358864193 0.0177459071772839 0.991127046411358 78 0.0376606723925312 0.0753213447850625 0.962339327607469 79 0.0292126686375245 0.0584253372750491 0.970787331362476 80 0.0317796388197603 0.0635592776395206 0.96822036118024 81 0.0280609938849614 0.0561219877699228 0.971939006115039 82 0.0243573616561258 0.0487147233122515 0.975642638343874 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0.867333628986627 100 0.114217737446956 0.228435474893913 0.885782262553044 101 0.0970379924412504 0.194075984882501 0.90296200755875 102 0.0859788362202432 0.171957672440486 0.914021163779757 103 0.0917638672167743 0.183527734433549 0.908236132783226 104 0.096854830127242 0.193709660254484 0.903145169872758 105 0.0821016323266812 0.164203264653362 0.917898367673319 106 0.0689119331775137 0.137823866355027 0.931088066822486 107 0.0539393181040783 0.107878636208157 0.946060681895922 108 0.0708334177150814 0.141666835430163 0.929166582284919 109 0.0615546706879603 0.123109341375921 0.93844532931204 110 0.0493492915625452 0.0986985831250904 0.950650708437455 111 0.0387375341029927 0.0774750682059854 0.961262465897007 112 0.0356158350599682 0.0712316701199364 0.964384164940032 113 0.0289365856957289 0.0578731713914578 0.971063414304271 114 0.0214386464196482 0.0428772928392964 0.978561353580352 115 0.0176727480943084 0.0353454961886168 0.982327251905692 116 0.0181054014765752 0.0362108029531504 0.981894598523425 117 0.0917809119747304 0.183561823949461 0.90821908802527 118 0.186137047855713 0.372274095711426 0.813862952144287 119 0.176643139355610 0.353286278711221 0.82335686064439 120 0.144772830484592 0.289545660969183 0.855227169515408 121 0.122394506432941 0.244789012865882 0.877605493567059 122 0.0992968693460783 0.198593738692157 0.900703130653922 123 0.372898716811555 0.745797433623109 0.627101283188445 124 0.361331598269790 0.722663196539581 0.63866840173021 125 0.343799618823467 0.687599237646934 0.656200381176533 126 0.295618422442769 0.591236844885538 0.704381577557231 127 0.248828919074152 0.497657838148305 0.751171080925848 128 0.369034852448455 0.73806970489691 0.630965147551545 129 0.329182549579083 0.658365099158167 0.670817450420917 130 0.318079041474142 0.636158082948285 0.681920958525858 131 0.356820497034663 0.713640994069326 0.643179502965337 132 0.756704796830244 0.486590406339511 0.243295203169756 133 0.974474111290283 0.051051777419434 0.025525888709717 134 0.961574918201695 0.0768501635966103 0.0384250817983051 135 0.941865802522946 0.116268394954108 0.0581341974770542 136 0.914253833866633 0.171492332266735 0.0857461661333674 137 0.895338836164795 0.209322327670411 0.104661163835205 138 0.857512837508233 0.284974324983534 0.142487162491767 139 0.971752625280533 0.0564947494389339 0.0282473747194669 140 0.975764150035868 0.0484716999282636 0.0242358499641318 141 0.982715380312327 0.0345692393753450 0.0172846196876725 142 0.96810734161337 0.06378531677326 0.03189265838663 143 0.94949993513134 0.101000129737320 0.0505000648686602 144 0.967303503089556 0.0653929938208889 0.0326964969104445 145 0.938337198702177 0.123325602595645 0.0616628012978227 146 0.960350540747635 0.0792989185047294 0.0396494592523647 147 0.958396793081912 0.0832064138361766 0.0416032069180883 148 0.908431265468036 0.183137469063927 0.0915687345319636 149 0.8330134422748 0.3339731154504 0.1669865577252 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.0503597122302158 NOK 5% type I error level 38 0.273381294964029 NOK 10% type I error level 65 0.467625899280576 NOK

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 = 3 ; 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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