Workshop 10 - multiple regression

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 12 Dec 2010 09:01:46 +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/12/t12921444042wi1u6z7sqx61x1.htm/, Retrieved Sun, 12 Dec 2010 10:00:14 +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/12/t12921444042wi1u6z7sqx61x1.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 24 14 11 12 24 26 0 25 11 7 8 25 23 0 17 6 17 8 30 25 1 18 12 10 8 19 23 1 18 8 12 9 22 19 1 16 10 12 7 22 29 1 20 10 11 4 25 25 1 16 11 11 11 23 21 1 18 16 12 7 17 22 1 17 11 13 7 21 25 0 23 13 14 12 19 24 0 30 12 16 10 19 18 1 23 8 11 10 15 22 1 18 12 10 8 16 15 1 15 11 11 8 23 22 1 12 4 15 4 27 28 0 21 9 9 9 22 20 1 15 8 11 8 14 12 1 20 8 17 7 22 24 0 31 14 17 11 23 20 0 27 15 11 9 23 21 1 34 16 18 11 21 20 1 21 9 14 13 19 21 1 31 14 10 8 18 23 1 19 11 11 8 20 28 0 16 8 15 9 23 24 1 20 9 15 6 25 24 1 21 9 13 9 19 24 1 22 9 16 9 24 23 1 17 9 13 6 22 23 1 24 10 9 6 25 29 0 25 16 18 16 26 24 0 26 11 18 5 29 18 1 25 8 12 7 32 25 1 17 9 17 9 25 21 1 32 16 9 6 29 26 1 33 11 9 6 28 22 1 13 16 12 5 17 22 1 32 12 18 12 28 22 1 25 12 12 7 29 23 1 29 14 18 10 26 30 1 22 9 14 9 25 23 1 18 10 15 8 14 17 1 17 9 16 5 25 23 0 20 10 10 8 26 23 1 15 12 11 8 20 25 1 20 14 14 10 18 24 1 33 14 9 6 32 24 0 29 10 12 8 25 23 1 23 14 17 7 25 21 0 26 16 5 4 23 24 1 18 9 12 8 21 2 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 15 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Concernovermistakes[t] = -1.52488923013411 -0.599776425471935Gender[t] + 0.812146509740823Doubtsaboutactions[t] + 0.258421861231518Parentalexpectations[t] + 0.179796229544161Parentalcritism[t] + 0.563133007199381Personalstandars[t] -0.115118381547464organization[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) -1.52488923013411 3.115376 -0.4895 0.625213 0.312607 Gender -0.599776425471935 0.803715 -0.7463 0.456666 0.228333 Doubtsaboutactions 0.812146509740823 0.130552 6.2209 0 0 Parentalexpectations 0.258421861231518 0.133299 1.9387 0.054395 0.027198 Parentalcritism 0.179796229544161 0.168908 1.0645 0.288806 0.144403 Personalstandars 0.563133007199381 0.096033 5.864 0 0 organization -0.115118381547464 0.103177 -1.1157 0.266294 0.133147 Multiple Linear Regression - Regression Statistics Multiple R 0.639796340883729 R-squared 0.409339357808208 Adjusted R-squared 0.386023806142743 F-TEST (value) 17.5564946384912 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.22044604925031e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.48420824730765 Sum Squared Residuals 3056.43478799373 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 25.3674713868655 -1.36747138686548 2 25 22.0866476463817 2.91335235361827 3 17 23.1955619828947 -6.19556198289475 4 18 19.6954852711489 -1.69548527114887 5 18 19.2934117319808 -1.29341173198077 6 16 19.4069284768994 -3.40692847689944 7 20 20.7589904748235 -0.758990474823462 8 16 22.1639181031645 -6.1639181031645 9 18 22.2699711701797 -4.26997117017974 10 17 20.3748373668623 -3.37483736686228 11 23 22.7451621879169 0.254837812083117 12 30 22.7809772308356 7.21902276916444 13 23 14.9274999052554 8.07250009474464 14 18 18.9270333019304 -0.927033301930446 15 15 21.5094110329846 -6.50941103298455 16 12 17.7007097310610 -5.70070973106096 17 21 19.8149507019515 1.18504929804848 18 15 15.1559582544423 -0.155958254442304 19 20 19.6503366713127 0.349663328687277 20 31 26.8657836067955 4.13421639320452 21 27 25.6526881085114 1.34731189148859 22 34 27.0224560476379 6.97754395236206 23 21 19.4219510976682 1.57804890233179 24 31 20.7566452834311 10.2433547165689 25 19 19.1293017221016 -0.129301722101627 26 16 20.6559948406093 -4.65599484060933 27 20 21.4552422506445 -1.45524225064449 28 21 18.0989891736177 2.90101082638235 29 22 21.8050381748566 0.194961825143426 30 17 19.3641178881308 -2.36411788813078 31 24 20.1412656852589 3.85873431474111 32 25 30.8764051306377 -5.87640513063773 33 26 27.2180233678308 -1.21802336783078 34 25 23.8744390556015 1.12556094439852 35 17 22.8568298063824 -5.8568298063824 36 32 27.6120319171437 4.38796808285626 37 33 23.4486398874301 9.5513601125699 38 13 21.9103787110914 -8.91037871109142 39 32 27.6653605255195 4.33463947448045 40 25 25.6638628360616 -0.663862836061554 41 29 26.8828480191344 2.1171519808656 42 22 21.8513274595929 0.148672540407081 43 18 17.2383468111127 0.7616531888873 44 17 21.6489862638793 -4.64898626387931 45 20 22.6128997275348 -2.61289972753483 46 15 20.2868033764848 -5.28680337648484 47 20 22.0348068058981 -2.03480680589807 48 33 27.9073746823552 5.09262531764484 49 29 22.5666104427985 6.43338955720152 50 23 26.5579698959982 -3.55796989599820 51 26 23.6699671584999 2.33003284150007 52 18 18.7870370972407 -0.787037097240736 53 20 19.1753534990643 0.824646500935741 54 11 11.6230304916359 -0.623030491635949 55 28 28.7621782677923 -0.762178267792335 56 26 23.1494302500648 2.85056974993515 57 22 22.669269923808 -0.669269923808007 58 17 20.0517776355677 -3.0517776355677 59 12 15.8538857599063 -3.85388575990632 60 14 20.8973540189012 -6.89735401890124 61 17 20.5411139668356 -3.54111396683557 62 21 21.1874120307229 -0.187412030722898 63 19 22.7894496147904 -3.78944961479037 64 18 22.8711309424203 -4.87113094242026 65 10 18.3900018497382 -8.3900018497382 66 29 24.6370720525763 4.36292794742370 67 31 18.2796017334678 12.7203982665322 68 19 23.3693885717829 -4.36938857178287 69 9 19.9178025587064 -10.9178025587064 70 20 22.2903219027409 -2.29032190274092 71 28 17.4621981138513 10.5378018861487 72 19 18.5468700910214 0.453129908978576 73 30 23.4904366160527 6.50956338394726 74 29 27.5909968331254 1.40900316687457 75 26 21.9399002945690 4.06009970543103 76 23 19.9811821698965 3.01881783010349 77 13 22.6314806665406 -9.63148066654058 78 21 22.4832495856698 -1.48324958566978 79 19 21.2573070106616 -2.25730701066161 80 28 22.7929283107580 5.20707168924197 81 23 25.3729608504198 -2.37296085041982 82 18 13.6094069148943 4.3905930851057 83 21 21.1856456618628 -0.185645661862829 84 20 21.6207025203118 -1.62070252031183 85 23 19.8030723533451 3.19692764665485 86 21 20.7020883249049 0.297911675095087 87 21 21.6170380931145 -0.617038093114464 88 15 22.6231781689117 -7.62317816891174 89 28 26.9449762549455 1.05502374505455 90 19 17.5122104932823 1.48778950671773 91 26 21.1120813396104 4.88791866038963 92 10 13.0189051398643 -3.01890513986429 93 16 17.5590386226172 -1.55903862261723 94 22 21.0384632649770 0.96153673502297 95 19 18.5428525504551 0.457147449544854 96 31 28.6083915923401 2.39160840765988 97 31 25.6533606613582 5.34663933864183 98 29 24.6506943664122 4.34930563358783 99 19 17.8629734162128 1.13702658378724 100 22 18.7437983543523 3.25620164564774 101 23 22.2056628088056 0.794337191194412 102 15 16.6220171743863 -1.62201717438634 103 20 21.9131730556020 -1.91317305560195 104 18 19.3399853933777 -1.33998539337772 105 23 21.8102153288650 1.18978467113505 106 25 20.8334925012105 4.16650749878949 107 21 16.3946802847268 4.60531971527317 108 24 19.314850837089 4.68514916291101 109 25 25.0709120701137 -0.07091207011366 110 17 19.4547342883026 -2.45473428830264 111 13 14.4287552152974 -1.42875521529741 112 28 18.0383639290045 9.96163607099552 113 21 20.4886626656978 0.511337334302223 114 25 27.9423547054043 -2.94235470540426 115 9 21.0762576763391 -12.0762576763391 116 16 17.6939237600990 -1.69392376009895 117 19 21.046422718448 -2.04642271844802 118 17 19.2889309744774 -2.28893097447745 119 25 24.3659644663829 0.634035533617054 120 20 15.4196958930467 4.58030410695327 121 29 21.44593769148 7.55406230852002 122 14 18.8999489107604 -4.89994891076042 123 22 26.7321259935752 -4.73212599357521 124 15 15.3865155722756 -0.386515572275641 125 19 25.8655570594453 -6.86555705944527 126 20 21.8185578044274 -1.81855780442744 127 15 17.9017713795316 -2.90177137953155 128 20 21.6120705139941 -1.61207051399408 129 18 20.0655867958938 -2.06558679589383 130 33 25.2898944391628 7.71010556083723 131 22 23.5892499774693 -1.58924997746931 132 16 16.3167272058862 -0.316727205886227 133 17 18.8852557986806 -1.88525579868057 134 16 14.9061594455780 1.09384055442196 135 21 17.4984133780041 3.50158662199594 136 26 28.1082687097083 -2.10826870970826 137 18 21.0102381889068 -3.01023818890681 138 18 22.927996914261 -4.92799691426099 139 17 18.1546868170441 -1.15468681704407 140 22 24.5338027250514 -2.53380272505139 141 30 24.5297501216679 5.47024987833214 142 30 27.693411915408 2.30658808459201 143 24 29.7180440769175 -5.71804407691749 144 21 21.8284181608956 -0.828418160895604 145 21 25.2236239084878 -4.22362390848779 146 29 27.2328463883029 1.76715361169706 147 31 23.0870665694773 7.91293343052267 148 20 18.8092925326549 1.19070746734509 149 16 14.6384488700858 1.36155112991425 150 22 19.3484437135137 2.65155628648632 151 20 20.1300202451636 -0.130020245163564 152 28 27.1951491319507 0.804850868049288 153 38 26.4868027881196 11.5131972118804 154 22 19.7992193502582 2.2007806497418 155 20 25.5275587020833 -5.52755870208333 156 17 18.5047320550995 -1.50473205509950 157 28 24.2787468063115 3.72125319368852 158 22 23.9638509492812 -1.96385094928121 159 31 26.5271034532647 4.47289654673532 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0844420500201223 0.168884100040245 0.915557949979878 11 0.0464752780920931 0.0929505561841861 0.953524721907907 12 0.130278876290244 0.260557752580487 0.869721123709757 13 0.0844961437839682 0.168992287567936 0.915503856216032 14 0.12977175407839 0.25954350815678 0.87022824592161 15 0.0837902520070485 0.167580504014097 0.916209747992951 16 0.0616355405147509 0.123271081029502 0.93836445948525 17 0.0823406090997284 0.164681218199457 0.917659390900272 18 0.103431029533643 0.206862059067286 0.896568970466357 19 0.0989515896919389 0.197903179383878 0.901048410308061 20 0.135233178248044 0.270466356496087 0.864766821751956 21 0.0964672042442725 0.192934408488545 0.903532795755728 22 0.273774456657781 0.547548913315562 0.726225543342219 23 0.213650645233384 0.427301290466768 0.786349354766616 24 0.517651166481889 0.964697667036222 0.482348833518111 25 0.444308884692389 0.888617769384777 0.555691115307611 26 0.471727515677312 0.943455031354623 0.528272484322688 27 0.415577906259593 0.831155812519186 0.584422093740407 28 0.372566640640189 0.745133281280378 0.627433359359811 29 0.321730152490764 0.643460304981527 0.678269847509236 30 0.268755298152277 0.537510596304554 0.731244701847723 31 0.348260396122868 0.696520792245736 0.651739603877132 32 0.390621718429583 0.781243436859165 0.609378281570417 33 0.339860064439077 0.679720128878154 0.660139935560923 34 0.394515220214513 0.789030440429025 0.605484779785487 35 0.392960755307925 0.78592151061585 0.607039244692075 36 0.399333364164459 0.798666728328917 0.600666635835541 37 0.592350983294009 0.815298033411983 0.407649016705991 38 0.785550313920867 0.428899372158266 0.214449686079133 39 0.780877336142335 0.438245327715330 0.219122663857665 40 0.74129423560946 0.517411528781079 0.258705764390540 41 0.715508356100145 0.568983287799709 0.284491643899855 42 0.667162566875002 0.665674866249995 0.332837433124998 43 0.619217034978156 0.761565930043687 0.380782965021844 44 0.604204389006926 0.791591221986147 0.395795610993074 45 0.567088000813684 0.865823998372632 0.432911999186316 46 0.588424062937882 0.823151874124236 0.411575937062118 47 0.547730827594951 0.904538344810097 0.452269172405049 48 0.535401163172006 0.929197673655987 0.464598836827994 49 0.601861514362918 0.796276971274165 0.398138485637082 50 0.580082643413097 0.839834713173807 0.419917356586903 51 0.542717277929412 0.914565444141176 0.457282722070588 52 0.492846170622925 0.985692341245851 0.507153829377075 53 0.452222662546295 0.90444532509259 0.547777337453705 54 0.40451682932989 0.80903365865978 0.59548317067011 55 0.359411189714611 0.718822379429222 0.640588810285389 56 0.332533802571893 0.665067605143787 0.667466197428107 57 0.288601229177287 0.577202458354574 0.711398770822713 58 0.263304610154698 0.526609220309396 0.736695389845302 59 0.244943182346779 0.489886364693557 0.755056817653221 60 0.303065244327151 0.606130488654302 0.696934755672849 61 0.289369447181477 0.578738894362955 0.710630552818523 62 0.251115929215076 0.502231858430151 0.748884070784924 63 0.237127944220829 0.474255888441657 0.762872055779171 64 0.266326862706788 0.532653725413576 0.733673137293212 65 0.351174242752546 0.702348485505092 0.648825757247454 66 0.349383910768309 0.698767821536618 0.650616089231691 67 0.68358034050748 0.632839318985039 0.316419659492520 68 0.678779630231637 0.642440739536726 0.321220369768363 69 0.849018383732479 0.301963232535042 0.150981616267521 70 0.829029595089469 0.341940809821063 0.170970404910531 71 0.933488282012463 0.133023435975075 0.0665117179875374 72 0.917208616935737 0.165582766128527 0.0827913830642634 73 0.937387932560046 0.125224134879908 0.0626120674399539 74 0.924638154689406 0.150723690621188 0.0753618453105942 75 0.924019499881152 0.151961000237695 0.0759805001188476 76 0.91589199642776 0.168216007144480 0.0841080035722399 77 0.967098379570535 0.0658032408589309 0.0329016204294654 78 0.95904837408274 0.081903251834522 0.040951625917261 79 0.950657267973882 0.0986854640522364 0.0493427320261182 80 0.954160566639851 0.0916788667202977 0.0458394333601489 81 0.945461035479997 0.109077929040006 0.0545389645200029 82 0.945131042219938 0.109737915560123 0.0548689577800616 83 0.930773668713893 0.138452662572215 0.0692263312861075 84 0.91662897368482 0.166742052630361 0.0833710263151805 85 0.907956640746761 0.184086718506479 0.0920433592532394 86 0.891859186466488 0.216281627067024 0.108140813533512 87 0.869410974360293 0.261178051279414 0.130589025639707 88 0.914884723383783 0.170230553232434 0.0851152766162169 89 0.89716090666486 0.20567818667028 0.10283909333514 90 0.876485606412921 0.247028787174159 0.123514393587079 91 0.878605257035802 0.242789485928397 0.121394742964198 92 0.866875768263779 0.266248463472442 0.133124231736221 93 0.843596113524808 0.312807772950384 0.156403886475192 94 0.81547333487834 0.36905333024332 0.18452666512166 95 0.781491494107807 0.437017011784386 0.218508505892193 96 0.752079323785578 0.495841352428843 0.247920676214422 97 0.770068792292651 0.459862415414697 0.229931207707349 98 0.764369298000279 0.471261403999443 0.235630701999721 99 0.727740692197549 0.544518615604902 0.272259307802451 100 0.702831681335258 0.594336637329485 0.297168318664742 101 0.659377625238886 0.681244749522228 0.340622374761114 102 0.61957469148144 0.76085061703712 0.38042530851856 103 0.580960151237174 0.838079697525652 0.419039848762826 104 0.53798948378991 0.92402103242018 0.46201051621009 105 0.491796554578656 0.983593109157313 0.508203445421344 106 0.473454294885589 0.946908589771178 0.526545705114411 107 0.470712762093608 0.941425524187215 0.529287237906392 108 0.48282194808774 0.96564389617548 0.51717805191226 109 0.432307389908605 0.86461477981721 0.567692610091395 110 0.408228619747199 0.816457239494398 0.591771380252801 111 0.368641982308944 0.737283964617888 0.631358017691056 112 0.5969255547499 0.8061488905002 0.4030744452501 113 0.584118031810279 0.831763936379441 0.415881968189721 114 0.552622643035536 0.894754713928928 0.447377356964464 115 0.79288271461248 0.41423457077504 0.20711728538752 116 0.765973641984661 0.468052716030677 0.234026358015339 117 0.751625117907193 0.496749764185614 0.248374882092807 118 0.720775263703318 0.558449472593364 0.279224736296682 119 0.673303551854724 0.653392896290552 0.326696448145276 120 0.702407113800499 0.595185772399003 0.297592886199501 121 0.754183274449282 0.491633451101436 0.245816725550718 122 0.744794612473908 0.510410775052184 0.255205387526092 123 0.746704701933119 0.506590596133763 0.253295298066882 124 0.695736418514835 0.60852716297033 0.304263581485165 125 0.785352761275881 0.429294477448238 0.214647238724119 126 0.747396829293261 0.505206341413477 0.252603170706739 127 0.786170926338392 0.427658147323216 0.213829073661608 128 0.756420398622096 0.487159202755808 0.243579601377904 129 0.721057190714839 0.557885618570322 0.278942809285161 130 0.781273045377802 0.437453909244396 0.218726954622198 131 0.73060127775828 0.53879744448344 0.26939872224172 132 0.670855513792557 0.658288972414886 0.329144486207443 133 0.653577624333845 0.69284475133231 0.346422375666155 134 0.585458935116986 0.829082129766028 0.414541064883014 135 0.528290390709152 0.943419218581696 0.471709609290848 136 0.58570911619508 0.82858176760984 0.41429088380492 137 0.55016840215144 0.89966319569712 0.44983159784856 138 0.554961084126533 0.890077831746933 0.445038915873467 139 0.474402977270853 0.948805954541705 0.525597022729147 140 0.394560770488016 0.789121540976032 0.605439229511984 141 0.54014405085072 0.919711898298561 0.459855949149280 142 0.459016322924554 0.918032645849109 0.540983677075446 143 0.37658010136057 0.75316020272114 0.62341989863943 144 0.286752679566945 0.573505359133891 0.713247320433055 145 0.30398419702743 0.60796839405486 0.69601580297257 146 0.214007842756546 0.428015685513091 0.785992157243455 147 0.329429442876015 0.65885888575203 0.670570557123985 148 0.234700554394278 0.469401108788556 0.765299445605722 149 0.609356759640063 0.781286480719874 0.390643240359937 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 0 0 OK 10% type I error level 5 0.0357142857142857 OK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

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

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Software written by Ed van Stee & Patrick Wessa

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