WS7

*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: Sat, 20 Nov 2010 10:28:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji.htm/, Retrieved Sat, 20 Nov 2010 11:27:25 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji.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 «

24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 14 6 24 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 13 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation ParentalExpectations[t] = + 6.16887701869769 + 0.091041276938754ConcernoverMistakes[t] -0.124974617942723Doubtsaboutactions[t] + 0.665424927458418ParentalCriticism[t] + 0.116609399359390PersonalStandards[t] -0.0883713236862745Organization[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) 6.16887701869769 1.771341 3.4826 0.000648 0.000324 ConcernoverMistakes 0.091041276938754 0.048105 1.8925 0.060307 0.030154 Doubtsaboutactions -0.124974617942723 0.087221 -1.4329 0.153941 0.07697 ParentalCriticism 0.665424927458418 0.086305 7.7102 0 0 PersonalStandards 0.116609399359390 0.063217 1.8446 0.067032 0.033516 Organization -0.0883713236862745 0.06186 -1.4286 0.155164 0.077582 Multiple Linear Regression - Regression Statistics Multiple R 0.638267527023895 R-squared 0.407385436053198 Adjusted R-squared 0.388018947035329 F-TEST (value) 21.0355855249398 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 5.55111512312578e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.69537380350115 Sum Squared Residuals 1111.55111091184 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 15.0902933123128 -4.09029331231285 2 7 13.2762821036644 -6.27628210366435 3 17 13.5791293272923 3.42087067270766 4 10 11.8143621509940 -1.81436215099401 5 12 13.6829990430466 -1.68299904304659 6 12 11.0364041615041 0.963595838495945 7 11 10.1076079797071 0.892392020292914 8 11 14.3967092422446 -3.39670924224459 9 12 10.5041912767322 1.49580872326781 10 13 11.2393467158858 1.76065328411421 11 14 14.7179223038925 -0.717922303892454 12 16 14.6795639476073 1.32043605239273 13 11 13.7222505886242 -2.72225058862423 14 10 12.1715045424060 -2.17150454240604 15 11 12.2210218592443 -1.22102185924431 16 15 10.0972302995134 4.90276970048665 17 9 13.7427769322339 -4.74277693223385 18 11 12.4301743557007 -1.43017435570071 19 17 12.0923751235759 4.90762487642411 20 17 15.475775866184 1.52422413381600 21 11 13.5674149618832 -2.56741496188315 22 18 15.2657316623960 2.73426833760396 23 14 15.9662771203031 -1.96627712030308 24 10 12.6313401159530 -2.63134011595298 25 11 11.7051308268035 -0.705130826803506 26 15 13.1756692700971 1.8243307299029 27 15 11.6518037762529 3.34819622374708 28 13 13.0394634394106 -0.0394634394105874 29 16 13.8019230368326 2.19807696316744 30 13 11.1172230710448 1.88277692895524 31 9 11.4491376476338 -2.44913764763384 32 18 18.0030465092912 -0.00304650929119143 33 18 12.2793428140968 5.72065718590322 34 12 13.6253041781773 -1.62530417817728 35 17 13.6400686988707 3.35993130112927 36 9 12.1591717239839 -3.15917172398391 37 9 13.111961986022 -4.11196198602199 38 12 8.7181350371216 3.28186496287841 39 18 16.8884956558910 1.11150434410898 40 12 12.9523201557008 -0.95232015570077 41 18 14.0943833460635 3.9056166539365 42 14 13.9185324361920 0.0814675638080454 43 15 12.0114923322002 2.98850766779984 44 16 10.8016263416645 5.19837365833549 45 10 13.0626597362727 -3.06265973627269 46 11 11.4811050721646 -0.48110507216459 47 14 12.8723646008572 1.12763539914276 48 9 13.0267330822588 -4.02673308225883 49 12 13.7654218293621 -1.76542182936209 50 17 12.2305934158728 4.7694065841272 51 5 9.75916045865076 -4.75916045865076 52 12 12.3341334798547 -0.334133479854687 53 12 11.9211467216850 0.0788532783150162 54 6 9.41738287861176 -3.41738287861177 55 24 22.7575898856656 1.24241011433443 56 12 12.4705368032406 -0.470536803240623 57 12 12.8912569954051 -0.891256995405105 58 14 11.5637878113925 2.43621218860746 59 7 9.13925944888823 -2.13925944888823 60 13 11.1108254584178 1.88917454158220 61 12 13.1699740047662 -1.16997400476625 62 13 11.5012610358896 1.49873896411044 63 14 11.3811688788399 2.61883112116007 64 8 12.8494881336204 -4.84948813362038 65 11 9.33970638899417 1.66029361100583 66 9 11.7252295593965 -2.72522955939653 67 11 13.7592540973606 -2.75925409736060 68 13 13.3899451240086 -0.389945124008603 69 10 9.36242353831312 0.637576461686884 70 11 12.6443330715980 -1.64433307159803 71 12 12.7642291877397 -0.764229187739693 72 9 11.8481211530213 -2.8481211530213 73 15 14.6149674793619 0.385032520638056 74 18 14.9036047233049 3.09639527669505 75 15 12.1096801141992 2.89031988580083 76 12 12.8128698183052 -0.812869818305168 77 13 9.8348328268442 3.16516717315581 78 14 13.0143677836606 0.985632216339414 79 10 11.8416130832527 -1.84161308325268 80 13 12.3069274032501 0.693072596749946 81 13 13.6966402561304 -0.696640256130411 82 11 12.0658770888727 -1.06587708887275 83 13 12.1758573054965 0.824142694503452 84 16 14.4384781040293 1.56152189597069 85 8 9.66985922268199 -1.66985922268198 86 16 11.5752737479677 4.42472625203230 87 11 11.0690549071499 -0.069054907149922 88 9 11.2274987396122 -2.22749873961221 89 16 17.7385710036935 -1.73857100369345 90 12 11.4334515850136 0.566548414986436 91 14 11.9711530082135 2.02884699178646 92 8 10.5416330824799 -2.54163308247993 93 9 9.5277606339652 -0.527760633965194 94 15 11.7125688088546 3.28743119114537 95 11 13.4909106406515 -2.49091064065145 96 21 17.1603559175302 3.83964408246982 97 14 13.2199013582316 0.78009864176843 98 18 15.7625027353026 2.23749726469742 99 12 11.6750356023157 0.324964397684323 100 13 12.6653523900202 0.334647609979817 101 15 14.4935478713002 0.506452128699828 102 12 11.0120042023471 0.98799579765292 103 19 14.4374270787798 4.56257292122016 104 15 13.9667006000868 1.03329939991321 105 11 12.9368506119609 -1.93685061196091 106 11 10.679178862076 0.320821137923993 107 10 12.335578068881 -2.33557806888101 108 13 14.7733541108617 -1.77335411086174 109 15 14.7245474815058 0.275452518494185 110 12 9.85282683318797 2.14717316681203 111 12 10.9640676085609 1.03593239143913 112 16 15.6813923789405 0.318607621059547 113 9 15.4318202038122 -6.43182020381219 114 18 17.4687772935220 0.531222706477957 115 8 14.9072071421707 -6.90720714217072 116 13 10.2807507615446 2.71924923845535 117 17 14.1502494449219 2.84975055507808 118 9 10.9875403311856 -1.98754033118563 119 15 13.1285836555302 1.87141634446984 120 8 9.64377645368698 -1.64377645368698 121 7 11.1837282246314 -4.18372822463136 122 12 11.2951272008084 0.704872799191557 123 14 14.9779944961403 -0.97799449614027 124 6 10.6501536890186 -4.65015368901865 125 8 10.0634389095600 -2.06343890956001 126 17 12.3546381215330 4.64536187846698 127 10 9.64089395650687 0.359106043493133 128 11 12.4393523485524 -1.43935234855237 129 14 12.6978411419978 1.30215885800217 130 11 13.5695552173331 -2.56955521733306 131 13 15.3246802742953 -2.32468027429532 132 12 11.8341179002391 0.165882099760947 133 11 10.3032935718869 0.69670642811309 134 9 9.35386895969434 -0.353868959694337 135 12 11.9876070196176 0.0123929803824485 136 20 14.6532047226802 5.34679527731984 137 12 10.6236516491933 1.37634835080672 138 13 13.5967191140340 -0.596719114033954 139 12 13.0334917483171 -1.03349174831707 140 12 16.4374760656668 -4.43747606566676 141 9 14.5841126764461 -5.58411267644606 142 15 15.4921726464561 -0.492172646456069 143 24 21.4778057128824 2.52219428711755 144 7 9.86113482063936 -2.86113482063936 145 17 14.5135950673666 2.48640493263336 146 11 11.8295717418214 -0.829571741821422 147 17 15.0913892233858 1.90861077661416 148 11 12.2042764010189 -1.20427640101888 149 12 12.5068570210313 -0.506857021031328 150 14 14.3909989558550 -0.39099895585497 151 11 14.1913798412456 -3.19137984124556 152 16 12.7195521217213 3.28044787827867 153 21 13.7306034317297 7.26939656827035 154 14 12.1946858182094 1.80531418179062 155 20 16.2967049279621 3.70329507203790 156 13 10.9441375203391 2.05586247966086 157 11 12.9695013576068 -1.96950135760678 158 15 13.8226020174876 1.17739798251242 159 19 17.8532948714343 1.14670512856569 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.558147117898382 0.883705764203236 0.441852882101618 10 0.417622381927572 0.835244763855144 0.582377618072428 11 0.61551336797381 0.76897326405238 0.38448663202619 12 0.792385634609305 0.41522873078139 0.207614365390695 13 0.80349833925566 0.393003321488679 0.196501660744340 14 0.74311934674085 0.5137613065183 0.25688065325915 15 0.661325265885246 0.677349468229508 0.338674734114754 16 0.623505026072871 0.752989947854258 0.376494973927129 17 0.669203321813334 0.661593356373333 0.330796678186666 18 0.589547870867366 0.820904258265268 0.410452129132634 19 0.696933935799586 0.606132128400827 0.303066064200414 20 0.781688405780388 0.436623188439224 0.218311594219612 21 0.73923862460444 0.521522750791121 0.260761375395560 22 0.79886134078503 0.402277318429941 0.201138659214971 23 0.754037343928504 0.491925312142993 0.245962656071497 24 0.780326806735706 0.439346386528588 0.219673193264294 25 0.731266326720699 0.537467346558602 0.268733673279301 26 0.707801161068337 0.584397677863326 0.292198838931663 27 0.688859379494022 0.622281241011956 0.311140620505978 28 0.628509353892361 0.742981292215279 0.371490646107639 29 0.600710398180403 0.798579203639195 0.399289601819597 30 0.549249365765775 0.90150126846845 0.450750634234225 31 0.629092434964497 0.741815130071006 0.370907565035503 32 0.615865464746042 0.768269070507915 0.384134535253958 33 0.68127567329582 0.63744865340836 0.31872432670418 34 0.726260830030432 0.547478339939135 0.273739169969568 35 0.740119872166876 0.519760255666248 0.259880127833124 36 0.777505517480089 0.444988965039822 0.222494482519911 37 0.83049657463082 0.339006850738361 0.169503425369180 38 0.827274258587268 0.345451482825463 0.172725741412732 39 0.815157005722322 0.369685988555356 0.184842994277678 40 0.78632901356452 0.427341972870961 0.213670986435480 41 0.842437981217825 0.315124037564349 0.157562018782175 42 0.807905533583714 0.384188932832571 0.192094466416286 43 0.82033584601476 0.359328307970481 0.179664153985240 44 0.872079453344915 0.255841093310170 0.127920546655085 45 0.886216797832833 0.227566404334334 0.113783202167167 46 0.862656693675514 0.274686612648972 0.137343306324486 47 0.839613253310513 0.320773493378973 0.160386746689487 48 0.866983242360574 0.266033515278852 0.133016757639426 49 0.846650295959097 0.306699408081805 0.153349704040903 50 0.895440623239429 0.209118753521143 0.104559376760571 51 0.936384411412925 0.12723117717415 0.063615588587075 52 0.920398198431924 0.159203603136152 0.0796018015680761 53 0.900401968694935 0.199196062610130 0.0995980313050649 54 0.920837406945503 0.158325186108993 0.0791625930544967 55 0.906008130093083 0.187983739813834 0.093991869906917 56 0.88449498396156 0.231010032076881 0.115505016038440 57 0.862859147355457 0.274281705289087 0.137140852644544 58 0.855297892135246 0.289404215729509 0.144702107864754 59 0.85256864702294 0.294862705954119 0.147431352977059 60 0.834780503145584 0.330438993708832 0.165219496854416 61 0.812719104743993 0.374561790512013 0.187280895256007 62 0.79016048587672 0.419679028246561 0.209839514123281 63 0.786287722900392 0.427424554199217 0.213712277099608 64 0.861829645968662 0.276340708062675 0.138170354031338 65 0.845757302651547 0.308485394696907 0.154242697348453 66 0.84203113553072 0.315937728938560 0.157968864469280 67 0.84170612453899 0.316587750922019 0.158293875461009 68 0.814409633578085 0.37118073284383 0.185590366421915 69 0.789627796066313 0.420744407867373 0.210372203933687 70 0.767400803556087 0.465198392887827 0.232599196443913 71 0.739420006055762 0.521159987888477 0.260579993944238 72 0.742177138108446 0.515645723783107 0.257822861891554 73 0.709770786557526 0.580458426884948 0.290229213442474 74 0.728145546692957 0.543708906614086 0.271854453307043 75 0.735715888184298 0.528568223631404 0.264284111815702 76 0.70049719506297 0.59900560987406 0.29950280493703 77 0.731150657947526 0.537698684104948 0.268849342052474 78 0.697699571673997 0.604600856652006 0.302300428326003 79 0.672804031872051 0.654391936255898 0.327195968127949 80 0.633985267216993 0.732029465566015 0.366014732783007 81 0.591201825024337 0.817596349951326 0.408798174975663 82 0.555418011287603 0.889163977424794 0.444581988712397 83 0.514059273591793 0.971881452816414 0.485940726408207 84 0.482689267974835 0.96537853594967 0.517310732025165 85 0.45384293694135 0.9076858738827 0.54615706305865 86 0.536723630198912 0.926552739602175 0.463276369801088 87 0.490720896113039 0.981441792226078 0.509279103886961 88 0.469031793980478 0.938063587960956 0.530968206019522 89 0.446766260342171 0.893532520684341 0.553233739657829 90 0.402500196424299 0.805000392848598 0.597499803575701 91 0.384032748068516 0.768065496137032 0.615967251931484 92 0.375416111566464 0.750832223132929 0.624583888433536 93 0.332411345457338 0.664822690914675 0.667588654542662 94 0.352848587423912 0.705697174847824 0.647151412576088 95 0.349133332913719 0.698266665827437 0.650866667086281 96 0.383188545214706 0.766377090429411 0.616811454785294 97 0.344732846218357 0.689465692436713 0.655267153781643 98 0.323277880421804 0.646555760843609 0.676722119578196 99 0.281559473965139 0.563118947930279 0.718440526034861 100 0.242451931173833 0.484903862347666 0.757548068826167 101 0.206834051015141 0.413668102030282 0.793165948984859 102 0.179564755589088 0.359129511178176 0.820435244410912 103 0.23990773294275 0.4798154658855 0.76009226705725 104 0.209169225069568 0.418338450139137 0.790830774930432 105 0.199908051651069 0.399816103302137 0.800091948348931 106 0.167615011400069 0.335230022800138 0.832384988599931 107 0.160104685051904 0.320209370103808 0.839895314948096 108 0.146583697528313 0.293167395056626 0.853416302471687 109 0.119671533162638 0.239343066325275 0.880328466837362 110 0.111740917086331 0.223481834172662 0.888259082913669 111 0.0938149440862537 0.187629888172507 0.906185055913746 112 0.0820678921068414 0.164135784213683 0.917932107893159 113 0.222217539592553 0.444435079185106 0.777782460407447 114 0.192281116462467 0.384562232924935 0.807718883537533 115 0.403414280961798 0.806828561923597 0.596585719038202 116 0.401970546376989 0.803941092753979 0.598029453623011 117 0.428790156508029 0.857580313016058 0.571209843491971 118 0.389999075185791 0.779998150371581 0.61000092481421 119 0.353668900605939 0.707337801211878 0.646331099394061 120 0.312541993189361 0.625083986378722 0.687458006810639 121 0.363550781030553 0.727101562061106 0.636449218969447 122 0.338683347635545 0.67736669527109 0.661316652364455 123 0.291049331908194 0.582098663816389 0.708950668091806 124 0.407265600697836 0.814531201395672 0.592734399302164 125 0.365172999924423 0.730345999848846 0.634827000075577 126 0.451689054908843 0.903378109817685 0.548310945091157 127 0.39601388991245 0.7920277798249 0.60398611008755 128 0.369145345396306 0.738290690792612 0.630854654603694 129 0.314797830970582 0.629595661941164 0.685202169029418 130 0.365300748163773 0.730601496327546 0.634699251836227 131 0.350725932786963 0.701451865573925 0.649274067213037 132 0.291816654530557 0.583633309061113 0.708183345469443 133 0.238339507669761 0.476679015339521 0.76166049233024 134 0.189415379525351 0.378830759050701 0.81058462047465 135 0.152360045918678 0.304720091837357 0.847639954081322 136 0.242371823917317 0.484743647834635 0.757628176082683 137 0.230341188718385 0.460682377436771 0.769658811281615 138 0.204152873904173 0.408305747808345 0.795847126095827 139 0.184590200825020 0.369180401650040 0.81540979917498 140 0.226382729630766 0.452765459261533 0.773617270369233 141 0.430335084600333 0.860670169200665 0.569664915399667 142 0.418342015666556 0.836684031333111 0.581657984333444 143 0.339110521242647 0.678221042485294 0.660889478757353 144 0.314432144809126 0.628864289618252 0.685567855190874 145 0.281334465023909 0.562668930047818 0.718665534976091 146 0.271419059398062 0.542838118796123 0.728580940601938 147 0.195163276717107 0.390326553434213 0.804836723282893 148 0.142678154692399 0.285356309384799 0.8573218453076 149 0.0821486403679795 0.164297280735959 0.91785135963202 150 0.0439466197454928 0.0878932394909857 0.956053380254507 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 1 0.00704225352112676 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/10uwnz1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/10uwnz1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/15v861290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/15v861290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/2gm8q1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/2gm8q1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/3gm8q1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/3gm8q1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/4gm8q1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/4gm8q1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/5gm8q1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/5gm8q1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/6rdpb1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/6rdpb1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/71mow1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/71mow1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/81mow1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/81mow1290248915.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/91mow1290248915.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t129024883305vye4xwb453hji/91mow1290248915.ps (open in new window)

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') }

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by