*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 19:29:24 +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/t1291318041sgph6rmslj1stt5.htm/, Retrieved Thu, 02 Dec 2010 20:27:32 +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/t1291318041sgph6rmslj1stt5.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 24 14 11 12 24 26 9 25 11 7 8 25 23 9 17 6 17 8 30 25 9 18 12 10 8 19 23 9 18 8 12 9 22 19 9 16 10 12 7 22 29 10 20 10 11 4 25 25 10 16 11 11 11 23 21 10 18 16 12 7 17 22 10 17 11 13 7 21 25 10 23 13 14 12 19 24 10 30 12 16 10 19 18 10 23 8 11 10 15 22 10 18 12 10 8 16 15 10 15 11 11 8 23 22 10 12 4 15 4 27 28 10 21 9 9 9 22 20 10 15 8 11 8 14 12 10 20 8 17 7 22 24 10 31 14 17 11 23 20 10 27 15 11 9 23 21 10 34 16 18 11 21 20 10 21 9 14 13 19 21 10 31 14 10 8 18 23 10 19 11 11 8 20 28 10 16 8 15 9 23 24 10 20 9 15 6 25 24 10 21 9 13 9 19 24 10 22 9 16 9 24 23 10 17 9 13 6 22 23 10 24 10 9 6 25 29 10 25 16 18 16 26 24 10 26 11 18 5 29 18 10 25 8 12 7 32 25 10 17 9 17 9 25 21 10 32 16 9 6 29 26 10 33 11 9 6 28 22 10 13 16 12 5 17 22 10 32 12 18 12 28 22 10 25 12 12 7 29 23 10 29 14 18 10 26 30 10 22 9 14 9 25 23 10 18 10 15 8 14 17 10 17 9 16 5 25 23 10 20 10 10 8 26 23 10 15 12 11 8 20 25 10 20 14 14 10 18 24 10 33 14 9 6 32 24 10 29 10 12 8 25 23 10 23 14 17 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 21.0638481525474 -1.33226514613105month[t] + 0.331360289672297ConcernoverMistakes[t] -0.355719150002528Doubtsaboutactions[t] + 0.197976188475ParentalExpectations[t] + 0.00683989436930336ParentalCriticism[t] + 0.387508988376619`Organization `[t] -0.00225008961774506t + 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) 21.0638481525474 15.165043 1.389 0.166886 0.083443 month -1.33226514613105 1.523395 -0.8745 0.383215 0.191607 ConcernoverMistakes 0.331360289672297 0.055769 5.9416 0 0 Doubtsaboutactions -0.355719150002528 0.107595 -3.3061 0.001182 0.000591 ParentalExpectations 0.197976188475 0.102008 1.9408 0.054147 0.027074 ParentalCriticism 0.00683989436930336 0.130045 0.0526 0.958123 0.479062 `Organization ` 0.387508988376619 0.074104 5.2293 1e-06 0 t -0.00225008961774506 0.006424 -0.3503 0.726633 0.363316 Multiple Linear Regression - Regression Statistics Multiple R 0.609951812691802 R-squared 0.372041213806015 Adjusted R-squared 0.342930541598346 F-TEST (value) 12.7802343811220 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 7.8070883091641e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.41825913153243 Sum Squared Residuals 1764.35881903603 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.3788411032984 -0.378841103298412 2 25 23.7933174568537 1.20668254314629 3 30 25.6735606613735 4.32643933862652 4 19 21.7075046653346 -2.70750466533463 5 22 21.9808874935398 0.0191125064601897 6 22 24.4658886196 -2.4658886196 7 25 22.688282717451 2.31171728254899 8 23 19.5027156262202 3.4972843737798 9 17 18.9427159653088 -1.94271596530881 10 21 21.7482044896363 -0.748204489636267 11 19 22.8673445099921 -3.86734450999215 12 19 23.5975542560347 -4.59755425603468 13 15 23.2588137498524 -8.25881374985245 14 16 17.2526667160132 -1.25266671601317 15 23 19.5225940144924 3.47740598550761 16 27 24.1058962125580 2.89410378744205 17 22 21.0535634139618 0.946436586038194 18 14 16.7079113118806 -2.70791131188055 19 22 24.1935877676244 -2.19358776762441 20 23 24.1793095883575 -1.17930958835751 21 23 21.6818712588361 1.31812874116394 22 21 24.6554281666088 -3.65542816660885 23 19 22.4448123844842 -3.44481238448417 24 18 23.9264831925835 -5.92648319258348 25 20 23.1505882072638 -3.15058820726385 26 23 22.4701233933996 0.529876606600380 27 25 23.4170756293606 1.58292437063938 28 19 23.3707531355731 -4.37075313557309 29 24 23.906282912676 0.0937170873239819 30 22 21.6327831261639 0.367216873836121 31 25 25.1274850906094 -0.127485090609402 32 26 23.2349200887337 2.76507991126628 33 29 22.9423332704789 6.05766672952114 34 32 25.2142659177213 6.78573408227866 35 25 21.6589391383298 3.34106086167018 36 29 24.470275094754 4.52972490524597 37 28 25.0279450913147 2.97205490868526 38 17 17.2069821292941 -0.206982129294115 39 28 26.1591905348952 1.84080946510476 40 29 23.0028708032515 5.99712919674848 41 26 27.5355633049122 -1.53556330491216 42 25 23.4810793706953 1.51892062930467 43 14 19.6637513362319 -5.66375133623185 44 25 22.1883705425711 2.81162945742886 45 26 21.6571447242257 4.34285527577433 46 20 20.2596490514696 -0.259649051469628 47 18 21.4228614759953 -3.4228614759953 48 32 24.7110546322652 7.2889453677348 49 25 25.0263393497554 -0.0263393497553649 50 25 21.8210739933462 3.17892600665381 51 23 20.8677594930622 2.13224050693777 52 21 22.117854032886 -1.11785403288601 53 20 23.9726413261168 -3.97264132611681 54 15 16.5457006606119 -1.54570066061186 55 30 26.6881828513834 3.31181714861657 56 24 25.2744043336664 -1.27440433366639 57 26 24.2388525586138 1.76114744138620 58 24 21.7359669669679 2.26403303303208 59 22 21.3581754011873 0.641824598812666 60 14 15.7380015387017 -1.73800153870174 61 24 22.1605918193999 1.83940818060007 62 24 22.9180112554593 1.08198874454068 63 24 23.2964543228427 0.703545677157297 64 24 19.8829114979323 4.11708850206774 65 19 18.4759965405149 0.524003459485107 66 31 26.7304833463546 4.26951665364540 67 22 26.5495294158872 -4.54952941588722 68 27 21.4486621120195 5.55133788798047 69 19 17.6523601250116 1.34763987498842 70 25 22.2181674990078 2.78183250099224 71 20 24.9625665057518 -4.96256650575181 72 21 21.4159350820325 -0.415935082032485 73 27 27.4227120635285 -0.422712063528469 74 23 24.399868173257 -1.39986817325701 75 25 25.6847420541193 -0.684742054119261 76 20 22.2024072152892 -2.20240721528923 77 21 19.1980099821813 1.80199001781872 78 22 22.3890673931533 -0.389067393153251 79 23 22.8628970178047 0.137102982195293 80 25 24.0662945432902 0.933705456709783 81 25 23.3049900746637 1.69500992533628 82 17 23.6945505826395 -6.69455058263948 83 19 21.397982885467 -2.39798288546698 84 25 23.8698754371039 1.13012456289610 85 19 22.2719093019712 -3.27190930197122 86 20 23.1090584144252 -3.10905841442521 87 26 22.4589667436964 3.54103325630361 88 23 20.6077905640758 2.39220943592424 89 27 24.3389723071074 2.66102769289259 90 17 20.8386249075823 -3.83862490758231 91 17 23.2983394821097 -6.29833948210969 92 19 19.9942601881693 -0.994260188169338 93 17 19.6494842422993 -2.64948424229929 94 22 22.0232851008073 -0.0232851008072933 95 21 23.3306910343887 -2.33069103438874 96 32 28.554977955948 3.44502204405199 97 21 24.6245509755056 -3.62455097550557 98 21 24.2891262400522 -3.28912624005225 99 18 21.1740932510251 -3.17409325102513 100 18 21.2400029865128 -3.24000298651281 101 23 22.7537633290092 0.246236670990792 102 19 20.5465002291185 -1.54650022911846 103 20 20.9652612427763 -0.965261242776257 104 21 22.1891589001762 -1.18915890017616 105 20 23.6300535236411 -3.63005352364107 106 17 18.8311987042487 -1.83119870424873 107 18 20.2285439329738 -2.22854393297381 108 19 20.7040858341501 -1.70408583415010 109 22 21.9824464857710 0.0175535142289650 110 15 18.7011860415034 -3.7011860415034 111 14 18.7396316108277 -4.7396316108277 112 18 26.471435033924 -8.47143503392401 113 24 21.2069537493994 2.79304625060058 114 35 23.5051226996185 11.4948773003815 115 29 18.9021191707563 10.0978808292437 116 21 21.8443033733754 -0.84430337337535 117 25 20.4849070060213 4.51509299397873 118 20 18.3813962323908 1.61860376760922 119 22 23.1087927659848 -1.10879276598484 120 13 16.8342670146989 -3.83426701469886 121 26 23.1038642390464 2.89613576095364 122 17 16.8165564995674 0.183443500432643 123 25 19.9838701968775 5.01612980312253 124 20 20.503457930182 -0.503457930182017 125 19 17.9608114705424 1.03918852945757 126 21 22.5050016345108 -1.50500163451080 127 22 20.8874236381136 1.11257636188644 128 24 22.4751712895552 1.52482871044484 129 21 22.7666882303897 -1.76668823038966 130 26 25.3236884376753 0.676311562324669 131 24 20.4475417530915 3.55245824690852 132 16 20.1125993189920 -4.11259931899195 133 23 22.1607585893467 0.839241410653308 134 18 20.61754812361 -2.61754812361002 135 16 22.1819493252509 -6.18194932525092 136 26 23.9793235421491 2.02067645785094 137 19 18.9400040731225 0.0599959268775127 138 21 16.7994060864538 4.20059391354616 139 21 21.9532949908417 -0.953294990841725 140 22 18.3690292816605 3.63097071833953 141 23 19.6531452281397 3.34685477186026 142 29 24.6571023707593 4.3428976292407 143 21 19.1553290225513 1.84467097744868 144 21 19.7602111315723 1.23978886842772 145 23 21.7151826161722 1.28481738382783 146 27 22.8496187679819 4.15038123201806 147 25 25.2709551798013 -0.270955179801295 148 21 20.8097139725763 0.190286027423701 149 10 16.9811157828466 -6.98111578284664 150 20 22.4381017712208 -2.43810177122084 151 26 22.3030997692200 3.69690023078004 152 24 23.5083186717168 0.49168132828322 153 29 31.5188532187234 -2.51885321872343 154 19 18.9459507782572 0.0540492217428360 155 24 21.9053501077378 2.09464989226215 156 19 20.5742538575748 -1.57425385757476 157 24 23.2186255812581 0.781374418741888 158 22 21.6144994694945 0.38550053050552 159 17 23.5852606802824 -6.58526068028241 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.0472282915691036 0.0944565831382072 0.952771708430896 12 0.0142347569152268 0.0284695138304537 0.985765243084773 13 0.0642884291271374 0.128576858254275 0.935711570872863 14 0.123589412073294 0.247178824146588 0.876410587926706 15 0.575257265962158 0.849485468075684 0.424742734037842 16 0.519010929924004 0.961978140151993 0.480989070075996 17 0.565297800917807 0.869404398164387 0.434702199082193 18 0.523739753075165 0.95252049384967 0.476260246924835 19 0.445228556854438 0.890457113708876 0.554771443145562 20 0.553461908153067 0.893076183693865 0.446538091846933 21 0.567823026707247 0.864353946585506 0.432176973292753 22 0.500235496645313 0.999529006709373 0.499764503354687 23 0.440707102527054 0.881414205054107 0.559292897472946 24 0.453828745485484 0.907657490970968 0.546171254514516 25 0.400417821039417 0.800835642078835 0.599582178960583 26 0.348124189519325 0.69624837903865 0.651875810480675 27 0.314056394869064 0.628112789738128 0.685943605130936 28 0.296953027500917 0.593906055001835 0.703046972499083 29 0.258975082499486 0.517950164998971 0.741024917500514 30 0.207909708067084 0.415819416134167 0.792090291932916 31 0.177696269978822 0.355392539957644 0.822303730021178 32 0.218286360932852 0.436572721865705 0.781713639067148 33 0.303572864201354 0.607145728402709 0.696427135798646 34 0.519976459980546 0.960047080038907 0.480023540019454 35 0.470327384966914 0.940654769933828 0.529672615033086 36 0.477197878354428 0.954395756708857 0.522802121645572 37 0.439092817132165 0.87818563426433 0.560907182867835 38 0.46889131168129 0.93778262336258 0.53110868831871 39 0.416064234285362 0.832128468570725 0.583935765714638 40 0.442220690310919 0.884441380621838 0.557779309689081 41 0.432593978651678 0.865187957303357 0.567406021348322 42 0.382317559691076 0.764635119382151 0.617682440308924 43 0.593569903380535 0.812860193238931 0.406430096619465 44 0.555139652780362 0.889720694439276 0.444860347219638 45 0.541799462494252 0.916401075011496 0.458200537505748 46 0.503485339228549 0.993029321542902 0.496514660771451 47 0.527545036320013 0.944909927359974 0.472454963679987 48 0.60402464243179 0.79195071513642 0.39597535756821 49 0.573896690688722 0.852206618622556 0.426103309311278 50 0.544530198697438 0.910939602605124 0.455469801302562 51 0.506772835878187 0.986454328243625 0.493227164121813 52 0.482234695374461 0.964469390748923 0.517765304625539 53 0.542038359366441 0.915923281267119 0.457961640633559 54 0.51964994486688 0.96070011026624 0.48035005513312 55 0.541571718001004 0.916856563997991 0.458428281998996 56 0.51722826349151 0.96554347301698 0.48277173650849 57 0.473043887309257 0.946087774618515 0.526956112690742 58 0.437026924682028 0.874053849364055 0.562973075317972 59 0.391121375622773 0.782242751245547 0.608878624377227 60 0.358828134438247 0.717656268876494 0.641171865561753 61 0.32140907445437 0.64281814890874 0.67859092554563 62 0.287047696003948 0.574095392007896 0.712952303996052 63 0.251122554730347 0.502245109460695 0.748877445269653 64 0.266685808766533 0.533371617533067 0.733314191233467 65 0.230991341772084 0.461982683544169 0.769008658227916 66 0.239388059482966 0.478776118965933 0.760611940517034 67 0.325787745537041 0.651575491074082 0.674212254462959 68 0.383511522592426 0.767023045184852 0.616488477407574 69 0.346088853758203 0.692177707516406 0.653911146241797 70 0.328086479270663 0.656172958541326 0.671913520729337 71 0.421911096223903 0.843822192447805 0.578088903776097 72 0.380587027040322 0.761174054080645 0.619412972959678 73 0.346821416633166 0.693642833266333 0.653178583366834 74 0.31972326588666 0.63944653177332 0.68027673411334 75 0.295548688997915 0.59109737799583 0.704451311002085 76 0.274237520590348 0.548475041180696 0.725762479409652 77 0.255485900174983 0.510971800349966 0.744514099825017 78 0.222082992141231 0.444165984282462 0.777917007858769 79 0.191449790494697 0.382899580989394 0.808550209505303 80 0.169174982172543 0.338349964345085 0.830825017827457 81 0.151373914628040 0.302747829256081 0.84862608537196 82 0.237000881738235 0.47400176347647 0.762999118261765 83 0.216546064716956 0.433092129433911 0.783453935283044 84 0.190524507820138 0.381049015640276 0.809475492179862 85 0.188270714820023 0.376541429640045 0.811729285179977 86 0.180517677955146 0.361035355910293 0.819482322044854 87 0.196938458108752 0.393876916217505 0.803061541891248 88 0.192026882069032 0.384053764138064 0.807973117930968 89 0.186970016335473 0.373940032670947 0.813029983664527 90 0.184409520496719 0.368819040993437 0.815590479503281 91 0.243920107721789 0.487840215443578 0.756079892278211 92 0.208409628417874 0.416819256835747 0.791590371582126 93 0.186249858358829 0.372499716717658 0.813750141641171 94 0.159004318154898 0.318008636309797 0.840995681845102 95 0.139346450366477 0.278692900732953 0.860653549633523 96 0.154191619247150 0.308383238494299 0.84580838075285 97 0.145698330114228 0.291396660228456 0.854301669885772 98 0.132788191434042 0.265576382868084 0.867211808565958 99 0.119969940673306 0.239939881346612 0.880030059326694 100 0.109707536189959 0.219415072379919 0.89029246381004 101 0.0898547171429609 0.179709434285922 0.91014528285704 102 0.0724505645799833 0.144901129159967 0.927549435420017 103 0.0571492647100174 0.114298529420035 0.942850735289983 104 0.0450266537814175 0.090053307562835 0.954973346218583 105 0.0459545537331827 0.0919091074663654 0.954045446266817 106 0.0368570957724971 0.0737141915449942 0.963142904227503 107 0.0323609234853466 0.0647218469706932 0.967639076514653 108 0.0296258900221629 0.0592517800443258 0.970374109977837 109 0.0233345576698011 0.0466691153396022 0.976665442330199 110 0.0242205239089534 0.0484410478179068 0.975779476091047 111 0.0340420963504668 0.0680841927009337 0.965957903649533 112 0.234976770150145 0.469953540300291 0.765023229849855 113 0.247492821953589 0.494985643907178 0.752507178046411 114 0.60599894736637 0.78800210526726 0.39400105263363 115 0.865155824369819 0.269688351260363 0.134844175630181 116 0.833691444848146 0.332617110303708 0.166308555151854 117 0.863113349005083 0.273773301989834 0.136886650994917 118 0.834485996019012 0.331028007961976 0.165514003980988 119 0.812858004053467 0.374283991893065 0.187141995946533 120 0.869066892748669 0.261866214502662 0.130933107251331 121 0.84169527327878 0.316609453442439 0.158304726721219 122 0.806966057766138 0.386067884467723 0.193033942233862 123 0.815122072529896 0.369755854940207 0.184877927470104 124 0.771456209007541 0.457087581984917 0.228543790992459 125 0.736799556790731 0.526400886418537 0.263200443209269 126 0.697696746248103 0.604606507503793 0.302303253751897 127 0.648882492388105 0.70223501522379 0.351117507611895 128 0.596281405803019 0.807437188393962 0.403718594196981 129 0.540965730975205 0.91806853804959 0.459034269024795 130 0.489738838803071 0.979477677606142 0.510261161196929 131 0.461247229111773 0.922494458223546 0.538752770888227 132 0.484645975860347 0.969291951720694 0.515354024139653 133 0.419661915912352 0.839323831824704 0.580338084087648 134 0.390303674321781 0.780607348643562 0.609696325678219 135 0.691076384406584 0.617847231186832 0.308923615593416 136 0.621994720576027 0.756010558847946 0.378005279423973 137 0.607920932467513 0.784158135064974 0.392079067532487 138 0.55206301159818 0.895873976803641 0.447936988401820 139 0.575613737369328 0.848772525261345 0.424386262630673 140 0.498889616226112 0.997779232452225 0.501110383773888 141 0.43665290848957 0.87330581697914 0.56334709151043 142 0.393752184975431 0.787504369950861 0.606247815024569 143 0.412108142838477 0.824216285676954 0.587891857161523 144 0.352430242804263 0.704860485608526 0.647569757195737 145 0.252953861156967 0.505907722313934 0.747046138843033 146 0.216073128162615 0.432146256325230 0.783926871837385 147 0.174856985634632 0.349713971269263 0.825143014365368 148 0.0968604437437478 0.193720887487496 0.903139556256252 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 3 0.0217391304347826 OK 10% type I error level 10 0.072463768115942 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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