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: Wed, 01 Dec 2010 18:58:39 +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/01/t1291229801xm3s8j2nblo12kj.htm/, Retrieved Wed, 01 Dec 2010 19:56:52 +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/01/t1291229801xm3s8j2nblo12kj.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 1 0 2 0 5 0 2 0 3 0 3 0 4 0 4 0 2 0 2 0 4 0 2 0 4 0 3 0 4 0 4 1 3 3 4 4 4 4 2 2 4 4 2 2 5 5 4 0 4 0 2 0 4 0 2 0 2 0 2 0 2 0 4 1 5 5 3 3 2 2 2 2 2 2 3 3 2 2 4 1 6 6 4 4 5 5 1 1 3 3 2 2 4 4 5 0 7 0 3 0 5 0 1 0 2 0 1 0 4 0 4 1 8 8 3 3 4 4 3 3 3 3 3 3 4 4 3 0 9 0 3 0 3 0 2 0 3 0 2 0 4 0 4 0 10 0 2 0 4 0 1 0 3 0 2 0 2 0 4 1 11 11 4 4 4 4 4 4 3 3 3 3 3 3 4 0 12 0 4 0 2 0 2 0 4 0 2 0 4 0 4 1 13 13 3 3 3 3 3 3 2 2 2 2 3 3 4 1 14 14 3 3 3 3 2 2 2 2 2 2 4 4 2 0 15 0 4 0 4 0 1 0 1 0 3 0 4 0 3 1 16 16 4 4 5 5 1 1 1 1 1 1 4 4 4 0 17 0 3 0 4 0 2 0 3 0 3 0 4 0 3 0 18 0 3 0 2 0 2 0 2 0 2 0 2 0 2 1 19 19 3 3 4 4 2 2 2 2 3 3 4 4 4 0 20 0 4 0 4 0 2 0 3 0 4 0 4 0 3 1 21 21 2 2 4 4 1 1 4 4 2 2 4 4 3 1 22 22 5 5 4 4 2 2 4 4 3 3 3 3 4 0 23 0 4 0 4 0 4 0 3 0 5 0 2 0 3 1 24 24 2 2 4 4 2 2 2 2 2 2 4 4 3 0 25 0 3 0 5 0 2 0 3 0 2 0 2 0 4 0 26 0 4 0 4 0 2 0 4 0 3 0 3 0 4 1 27 27 4 4 4 4 2 2 3 3 2 2 4 4 4 0 28 0 3 0 4 0 2 0 2 0 2 0 3 0 4 1 29 29 4 4 4 4 3 3 1 1 2 2 4 4 4 1 30 30 4 4 4 4 2 2 3 3 2 2 4 4 4 0 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation neat[t] = + 3.11496151267242 -0.356877549090112pop[t] -0.00119421517556334t -0.00179540754477216pop_t[t] -0.00219470236971560standards[t] -0.0349340132681785standards_t[t] + 0.304511079436017organization[t] -0.00263513485222916organization_t[t] -0.0975529079437357punished[t] -0.091053686996288punished_t[t] -0.0044969276903347secondrate[t] + 0.00189629269507838secondrate_t[t] -0.145120416918951mistakes[t] + 0.186359455031473mistakes_t[t] + 0.026158675364112competent[t] + 0.0520976377859456competent_t[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) 3.11496151267242 0.707599 4.4022 2.1e-05 1e-05 pop -0.356877549090112 0.94367 -0.3782 0.705857 0.352929 t -0.00119421517556334 0.002018 -0.5916 0.555026 0.277513 pop_t -0.00179540754477216 0.00278 -0.6458 0.519433 0.259716 standards -0.00219470236971560 0.091643 -0.0239 0.980927 0.490464 standards_t -0.0349340132681785 0.136461 -0.256 0.798318 0.399159 organization 0.304511079436017 0.102162 2.9807 0.003381 0.001691 organization_t -0.00263513485222916 0.15028 -0.0175 0.986034 0.493017 punished -0.0975529079437357 0.100025 -0.9753 0.331066 0.165533 punished_t -0.091053686996288 0.16336 -0.5574 0.578139 0.28907 secondrate -0.0044969276903347 0.085287 -0.0527 0.958023 0.479012 secondrate_t 0.00189629269507838 0.131187 0.0145 0.988487 0.494244 mistakes -0.145120416918951 0.101501 -1.4297 0.154972 0.077486 mistakes_t 0.186359455031473 0.147917 1.2599 0.209761 0.10488 competent 0.026158675364112 0.103439 0.2529 0.800716 0.400358 competent_t 0.0520976377859456 0.163981 0.3177 0.751171 0.375586 Multiple Linear Regression - Regression Statistics Multiple R 0.457606458303133 R-squared 0.209403670680737 Adjusted R-squared 0.126473985787108 F-TEST (value) 2.52507495897678 F-TEST (DF numerator) 15 F-TEST (DF denominator) 143 p-value 0.00239273837122178 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.743455096513655 Sum Squared Residuals 79.0397437160943 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.09261014167856 -0.0926101416785626 2 4 3.78240791937670 0.217592080623296 3 4 3.89424792331913 0.105752076680872 4 4 3.88181641059698 0.118183589403024 5 4 3.13331687300164 0.86668312699836 6 5 4.30010591652713 0.69989408347287 7 4 4.4755408177275 -0.475540817727498 8 3 3.69340529037304 -0.693405290373043 9 4 3.61695997595132 0.383040024048684 10 4 3.967707099797 0.0322929002030034 11 4 3.38044479848406 0.619555201515939 12 4 3.30217462092856 0.69782537907144 13 4 3.25968651592025 0.740313484079746 14 2 3.52355980129 -1.52355980129000 15 3 3.87353740836969 -0.873537408369691 16 4 4.23417192120177 -0.234171921201766 17 3 3.76679691706388 -0.766796917063876 18 2 3.25388053689734 -1.25388053689734 19 4 3.85172667038463 0.148273329615367 20 3 3.61589915224852 -0.61589915224852 21 3 4.02504242741884 -1.02504242741884 22 4 3.68504278780727 0.314957212192732 23 3 3.21977292318718 -0.219772923187184 24 3 3.83266823430833 -0.832668234308326 25 4 4.15455734128611 -0.154557341286112 26 4 3.72319867505964 0.276801324940356 27 4 3.74684129987627 0.253158700123725 28 4 3.87711921937785 0.122880780622148 29 4 3.55745672948609 0.442543270513907 30 4 3.73787243171527 0.262127568284731 31 5 3.85651714497949 1.14348285502051 32 4 3.43455743762434 0.56544256237566 33 4 3.5175747247347 0.4824252752653 34 4 3.73969610606835 0.260303893931655 35 3 3.76676399122137 -0.76676399122137 36 4 4.21540007275692 -0.215400072756917 37 3 4.04923877542472 -1.04923877542472 38 4 3.5188044205352 0.481195579464797 39 4 3.57224718825465 0.427752811745349 40 3 3.70537556951666 -0.705375569516657 41 5 4.21622814989005 0.783771850109946 42 4 4.02498766914298 -0.0249876691429781 43 3 3.58222406068394 -0.582224060683942 44 3 4.32261339053753 -1.32261339053753 45 3 3.76728552218602 -0.767285522186025 46 4 4.25997970898001 -0.259979708980013 47 4 3.53583491947042 0.464165080529580 48 4 4.01997829212459 -0.0199782921245865 49 4 3.87600467368542 0.123995326314581 50 4 3.65885843163690 0.341141568363095 51 4 3.93124342333415 0.0687565766658501 52 4 3.87242202815873 0.127577971841271 53 5 3.7459691754186 1.25403082458140 54 3 3.24546762284602 -0.245467622846023 55 3 2.85347314859141 0.146526851408595 56 5 3.99914690120823 1.00085309879177 57 5 3.86184650163967 1.13815349836033 58 4 3.96280964504908 0.0371903549509157 59 4 4.13754558987472 -0.137545589874721 60 3 3.36530886441046 -0.365308864410462 61 4 3.98268910012718 0.0173108998728230 62 4 3.82670077712993 0.173299222870073 63 5 4.26573905334672 0.734260946653285 64 4 3.78885044425007 0.211149555749933 65 4 3.93048616582574 0.0695138341742556 66 5 4.25316255243936 0.746837447560644 67 4 3.51047311539589 0.489526884604109 68 3 3.64933057875426 -0.649330578754261 69 4 4.11285063266188 -0.112850632661879 70 4 3.69254495417764 0.307455045822363 71 4 3.64496847070046 0.355031529299541 72 4 3.87777293867225 0.122227061327754 73 4 4.04980475327385 -0.0498047532738448 74 4 4.01795493504383 -0.0179549350438348 75 4 3.86137568077618 0.138624319223821 76 3 3.84815026868464 -0.84815026868464 77 4 3.82309547443742 0.176904525562582 78 3 3.70503925578767 -0.705039255787672 79 5 4.14688400022425 0.85311599977575 80 4 3.54975289258123 0.450247107418773 81 5 3.84745558302427 1.15254441697573 82 5 3.48196184509730 1.51803815490270 83 4 3.76553982808261 0.234460171917386 84 4 3.66526000201734 0.334739997982658 85 4 3.71681185705005 0.283188142949953 86 4 3.67820320617119 0.321796793828810 87 4 3.92806988200684 0.0719301179931565 88 5 4.0931765166134 0.906823483386601 89 4 3.62863332308508 0.371366676914921 90 3 3.97435697077599 -0.974356970775988 91 4 3.55810608077006 0.441893919229941 92 3 4.35456548250055 -1.35456548250055 93 4 3.51051428196616 0.489485718033843 94 4 3.47299657860318 0.527003421396817 95 4 3.88060630486222 0.119393695137784 96 4 3.58362449062356 0.416375509376438 97 4 3.76858942333895 0.231410576661046 98 3 3.56801565220917 -0.568015652209175 99 3 3.33643743459474 -0.336437434594737 100 3 3.93625614365624 -0.936256143656242 101 3 3.25874631048137 -0.258746310481367 102 3 3.63146019016171 -0.631460190161706 103 2 3.57103843171203 -1.57103843171203 104 3 3.59349841668149 -0.593498416681486 105 5 4.05902012724104 0.940979872758955 106 2 3.30877261302954 -1.30877261302954 107 2 3.46914451973253 -1.46914451973253 108 3 3.00131048061677 -0.00131048061677247 109 3 3.27184660375622 -0.271846603756217 110 3 3.91213122857843 -0.912131228578425 111 4 3.57334341363443 0.426656586365567 112 4 3.5752014448728 0.424798555127197 113 3 3.44508656576661 -0.44508656576661 114 2 3.71130096925346 -1.71130096925346 115 3 3.60347273295005 -0.603472732950051 116 4 3.91265177315689 0.0873482268431058 117 2 2.87402336587850 -0.874023365878504 118 4 2.75225582416076 1.24774417583924 119 4 3.66200639802809 0.337993601971913 120 2 3.19751472346182 -1.19751472346182 121 3 4.03039228058693 -1.03039228058693 122 3 3.12242423434371 -0.122424234343708 123 3 3.00388305984289 -0.00388305984289308 124 4 4.12149769505773 -0.121497695057728 125 4 3.76056197260699 0.239438027393013 126 4 3.44438649498624 0.555613505013757 127 3 3.99037668410938 -0.990376684109383 128 4 3.40376180761023 0.596238192389774 129 4 3.84955946689936 0.150440533100644 130 4 3.51727791343214 0.482722086567864 131 2 2.94283736244231 -0.942837362442315 132 4 3.75292084111926 0.247079158880735 133 5 3.46723653015113 1.53276346984887 134 4 3.98651410557077 0.0134858944292257 135 4 3.72537422259818 0.274625777401822 136 4 3.42097242335970 0.579027576640295 137 3 3.56834497148299 -0.568344971482994 138 1 3.45883285102681 -2.45883285102681 139 4 3.21928663778405 0.780713362215954 140 3 2.82027740340041 0.179722596599586 141 3 2.95640729309603 0.0435927069039693 142 3 3.59139107119343 -0.59139107119343 143 1 2.39835293598855 -1.39835293598855 144 4 3.62128106469557 0.378718935304433 145 5 3.35479910176125 1.64520089823875 146 4 3.46684331491151 0.533156685088489 147 3 3.19899502264492 -0.198995022644922 148 4 3.11579738405755 0.884202615942452 149 3 2.89401843120861 0.105981568791393 150 4 3.55128926968538 0.44871073031462 151 4 3.55965153251611 0.44034846748389 152 4 3.37313845983434 0.626861540165663 153 5 3.83002940745649 1.16997059254351 154 2 2.87635824201131 -0.876358242011314 155 3 3.2172869906969 -0.217286990696898 156 3 3.72425967690574 -0.724259676905745 157 4 3.47357537502061 0.526424624979389 158 4 3.54623247597121 0.453767524028792 159 3 2.89796899679350 0.102031003206497 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.6888102855993 0.6223794288014 0.3111897144007 20 0.536650009800769 0.926699980398461 0.463349990199231 21 0.571779371008937 0.856441257982125 0.428220628991063 22 0.500041805366777 0.999916389266447 0.499958194633223 23 0.383825777536625 0.767651555073251 0.616174222463375 24 0.296712463334225 0.59342492666845 0.703287536665775 25 0.237055919310422 0.474111838620844 0.762944080689578 26 0.165618908778513 0.331237817557026 0.834381091221487 27 0.179344098981817 0.358688197963635 0.820655901018183 28 0.259775620552965 0.51955124110593 0.740224379447035 29 0.228592402969910 0.457184805939819 0.77140759703009 30 0.182264790183306 0.364529580366612 0.817735209816694 31 0.236091967024009 0.472183934048018 0.763908032975991 32 0.197939014215330 0.395878028430659 0.80206098578467 33 0.149816160917861 0.299632321835722 0.850183839082139 34 0.181396250910028 0.362792501820056 0.818603749089972 35 0.174341143311333 0.348682286622665 0.825658856688667 36 0.157011463075869 0.314022926151738 0.842988536924131 37 0.133684753977949 0.267369507955898 0.866315246022051 38 0.105739637100126 0.211479274200252 0.894260362899874 39 0.0851512003114212 0.170302400622842 0.914848799688579 40 0.067799576326132 0.135599152652264 0.932200423673868 41 0.0772378928545593 0.154475785709119 0.92276210714544 42 0.0607748356288537 0.121549671257707 0.939225164371146 43 0.0514775017104057 0.102955003420811 0.948522498289594 44 0.124441615139296 0.248883230278591 0.875558384860704 45 0.116352989010445 0.23270597802089 0.883647010989555 46 0.120116285274519 0.240232570549038 0.879883714725481 47 0.104803317392661 0.209606634785323 0.895196682607339 48 0.157347992627089 0.314695985254177 0.842652007372911 49 0.124097620076251 0.248195240152503 0.875902379923749 50 0.0990655525791966 0.198131105158393 0.900934447420803 51 0.116669988043768 0.233339976087536 0.883330011956232 52 0.0906337493251018 0.181267498650204 0.909366250674898 53 0.197712733890751 0.395425467781502 0.802287266109249 54 0.162817448473643 0.325634896947285 0.837182551526357 55 0.135192717359471 0.270385434718941 0.86480728264053 56 0.157052979452233 0.314105958904467 0.842947020547766 57 0.156980385671720 0.313960771343439 0.84301961432828 58 0.129932650060821 0.259865300121642 0.870067349939179 59 0.105951894533687 0.211903789067374 0.894048105466313 60 0.111516943623100 0.223033887246201 0.8884830563769 61 0.0885562875228908 0.177112575045782 0.911443712477109 62 0.0695443021157688 0.139088604231538 0.930455697884231 63 0.0599284299276209 0.119856859855242 0.94007157007238 64 0.0465783714261572 0.0931567428523145 0.953421628573843 65 0.0358460229230428 0.0716920458460856 0.964153977076957 66 0.0317165175445349 0.0634330350890699 0.968283482455465 67 0.0262712363095948 0.0525424726191895 0.973728763690405 68 0.0348467162810975 0.069693432562195 0.965153283718903 69 0.0267983609755968 0.0535967219511936 0.973201639024403 70 0.0200900450281040 0.0401800900562081 0.979909954971896 71 0.0160891528564016 0.0321783057128031 0.983910847143598 72 0.0115760714881670 0.0231521429763340 0.988423928511833 73 0.00828148423986422 0.0165629684797284 0.991718515760136 74 0.00579456709094373 0.0115891341818875 0.994205432909056 75 0.00407942266744451 0.00815884533488903 0.995920577332555 76 0.00680931112227698 0.0136186222445540 0.993190688877723 77 0.00474187952338259 0.00948375904676517 0.995258120476617 78 0.00632556976807046 0.0126511395361409 0.99367443023193 79 0.00689899150184172 0.0137979830036834 0.993101008498158 80 0.00516747831162209 0.0103349566232442 0.994832521688378 81 0.0103784501437844 0.0207569002875687 0.989621549856216 82 0.0247127218030481 0.0494254436060962 0.975287278196952 83 0.0184014559254125 0.036802911850825 0.981598544074588 84 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0.984878137944794 101 0.0130623221818862 0.0261246443637724 0.986937677818114 102 0.0118083835462026 0.0236167670924052 0.988191616453797 103 0.0217678771417946 0.0435357542835892 0.978232122858205 104 0.0185774440960066 0.0371548881920131 0.981422555903993 105 0.0285728536075277 0.0571457072150555 0.971427146392472 106 0.0512573819736752 0.102514763947350 0.948742618026325 107 0.088184792250654 0.176369584501308 0.911815207749346 108 0.0737090169615706 0.147418033923141 0.92629098303843 109 0.0566484339344924 0.113296867868985 0.943351566065508 110 0.0893981677246235 0.178796335449247 0.910601832275376 111 0.0766673450836765 0.153334690167353 0.923332654916323 112 0.107501190350289 0.215002380700577 0.892498809649712 113 0.108218762091783 0.216437524183565 0.891781237908217 114 0.138453906246183 0.276907812492367 0.861546093753817 115 0.127463760686962 0.254927521373925 0.872536239313038 116 0.102651353276611 0.205302706553222 0.897348646723389 117 0.101181979160621 0.202363958321242 0.89881802083938 118 0.150694568929069 0.301389137858138 0.849305431070931 119 0.125332738868266 0.250665477736532 0.874667261131734 120 0.337302602038987 0.674605204077975 0.662697397961013 121 0.384563301757937 0.769126603515875 0.615436698242063 122 0.324315286975512 0.648630573951024 0.675684713024488 123 0.270045355763848 0.540090711527696 0.729954644236152 124 0.250653857573878 0.501307715147757 0.749346142426122 125 0.207281454132855 0.414562908265709 0.792718545867145 126 0.194903673919935 0.38980734783987 0.805096326080065 127 0.256317113257481 0.512634226514961 0.74368288674252 128 0.270960357499880 0.541920714999761 0.72903964250012 129 0.260662438648220 0.521324877296441 0.73933756135178 130 0.242091742516807 0.484183485033615 0.757908257483193 131 0.233570852418519 0.467141704837037 0.766429147581481 132 0.194969188547223 0.389938377094446 0.805030811452777 133 0.262106704526266 0.524213409052531 0.737893295473735 134 0.199013306434898 0.398026612869797 0.800986693565102 135 0.230475258378346 0.460950516756692 0.769524741621654 136 0.434114315686866 0.868228631373732 0.565885684313134 137 0.326741428980826 0.653482857961652 0.673258571019174 138 0.278394160965989 0.556788321931979 0.72160583903401 139 0.308092156331023 0.616184312662047 0.691907843668977 140 0.313951991529306 0.627903983058612 0.686048008470694 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0163934426229508 NOK 5% type I error level 35 0.286885245901639 NOK 10% type I error level 42 0.344262295081967 NOK

Charts produced by software:

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Parameters (Session):

par1 = 16 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 16 ; 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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