WS7 t1

*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: Mon, 22 Nov 2010 18:48:49 +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/22/t1290451644kfausaihvtxowrv.htm/, Retrieved Mon, 22 Nov 2010 19:47:24 +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/22/t1290451644kfausaihvtxowrv.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 27 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation ParentalExpectations[t] = + 6.16887701869768 + 0.0910412769387536ConcernoverMistakes[t] -0.124974617942723Doubtsaboutactions[t] + 0.665424927458418ParentalCriticism[t] + 0.116609399359390PersonalStandards[t] -0.0883713236862746Organization[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) 6.16887701869768 1.771341 3.4826 0.000648 0.000324 ConcernoverMistakes 0.0910412769387536 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 -0.0883713236862746 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 15.0902933123129 -4.0902933123129 2 7 13.2762821036644 -6.27628210366435 3 17 13.5791293272923 3.42087067270766 4 10 11.8143621509940 -1.81436215099402 5 12 13.6829990430466 -1.68299904304659 6 12 11.0364041615041 0.963595838495944 7 11 10.1076079797071 0.892392020292914 8 11 14.3967092422446 -3.39670924224459 9 12 10.5041912767322 1.49580872326780 10 13 11.2393467158858 1.76065328411421 11 14 14.7179223038925 -0.717922303892455 12 16 14.6795639476073 1.32043605239274 13 11 13.7222505886242 -2.72225058862422 14 10 12.1715045424060 -2.17150454240604 15 11 12.2210218592443 -1.22102185924431 16 15 10.0972302995133 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 -2.63134011595297 25 11 11.7051308268035 -0.705130826803506 26 15 13.1756692700971 1.8243307299029 27 15 11.6518037762529 3.34819622374708 28 13 13.0394634394106 -0.0394634394105844 29 16 13.8019230368326 2.19807696316744 30 13 11.1172230710448 1.88277692895524 31 9 11.4491376476338 -2.44913764763384 32 18 18.0030465092912 -0.00304650929119785 33 18 12.2793428140968 5.72065718590321 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 -0.952320155700772 41 18 14.0943833460635 3.9056166539365 42 14 13.9185324361920 0.0814675638080462 43 15 12.0114923322002 2.98850766779985 44 16 10.8016263416645 5.19837365833548 45 10 13.0626597362727 -3.06265973627270 46 11 11.4811050721646 -0.481105072164592 47 14 12.8723646008572 1.12763539914275 48 9 13.0267330822588 -4.02673308225883 49 12 13.7654218293621 -1.76542182936209 50 17 12.2305934158728 4.76940658412719 51 5 9.75916045865077 -4.75916045865077 52 12 12.3341334798547 -0.334133479854686 53 12 11.9211467216850 0.0788532783150179 54 6 9.41738287861176 -3.41738287861176 55 24 22.7575898856656 1.24241011433443 56 12 12.4705368032406 -0.470536803240622 57 12 12.8912569954051 -0.891256995405105 58 14 11.5637878113925 2.43621218860746 59 7 9.13925944888823 -2.13925944888823 60 13 11.1108254584178 1.8891745415822 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 9.33970638899418 1.66029361100583 66 9 11.7252295593965 -2.72522955939653 67 11 13.7592540973606 -2.75925409736060 68 13 13.3899451240086 -0.389945124008605 69 10 9.36242353831312 0.637576461686878 70 11 12.6443330715980 -1.64433307159803 71 12 12.7642291877397 -0.764229187739686 72 9 11.8481211530213 -2.84812115302130 73 15 14.6149674793619 0.385032520638060 74 18 14.9036047233049 3.09639527669505 75 15 12.1096801141992 2.89031988580083 76 12 12.8128698183052 -0.812869818305165 77 13 9.8348328268442 3.16516717315581 78 14 13.0143677836606 0.985632216339413 79 10 11.8416130832527 -1.84161308325268 80 13 12.3069274032501 0.693072596749949 81 13 13.6966402561304 -0.696640256130414 82 11 12.0658770888727 -1.06587708887274 83 13 12.1758573054965 0.824142694503452 84 16 14.4384781040293 1.56152189597069 85 8 9.66985922268198 -1.66985922268198 86 16 11.5752737479677 4.42472625203231 87 11 11.0690549071499 -0.0690549071499213 88 9 11.2274987396122 -2.22749873961222 89 16 17.7385710036935 -1.73857100369345 90 12 11.4334515850136 0.566548414986438 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 3.83964408246983 97 14 13.2199013582316 0.780098641768431 98 18 15.7625027353026 2.23749726469742 99 12 11.6750356023157 0.324964397684325 100 13 12.6653523900202 0.33464760997982 101 15 14.4935478713002 0.506452128699828 102 12 11.0120042023471 0.987995797652922 103 19 14.4374270787798 4.56257292122016 104 15 13.9667006000868 1.03329939991321 105 11 12.9368506119609 -1.93685061196091 106 11 10.679178862076 0.320821137923995 107 10 12.335578068881 -2.33557806888100 108 13 14.7733541108617 -1.77335411086173 109 15 14.7245474815058 0.275452518494184 110 12 9.85282683318797 2.14717316681203 111 12 10.9640676085609 1.03593239143914 112 16 15.6813923789404 0.318607621059554 113 9 15.4318202038122 -6.43182020381219 114 18 17.4687772935220 0.531222706477954 115 8 14.9072071421707 -6.90720714217072 116 13 10.2807507615446 2.71924923845535 117 17 14.1502494449219 2.84975055507809 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 0.704872799191556 123 14 14.9779944961403 -0.977994496140275 124 6 10.6501536890186 -4.65015368901865 125 8 10.0634389095600 -2.06343890956002 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 -2.56955521733305 131 13 15.3246802742953 -2.32468027429533 132 12 11.8341179002391 0.165882099760948 133 11 10.3032935718869 0.69670642811309 134 9 9.35386895969433 -0.353868959694334 135 12 11.9876070196175 0.0123929803824522 136 20 14.6532047226802 5.34679527731984 137 12 10.6236516491933 1.37634835080672 138 13 13.5967191140340 -0.596719114033957 139 12 13.0334917483171 -1.03349174831707 140 12 16.4374760656668 -4.43747606566676 141 9 14.5841126764461 -5.58411267644606 142 15 15.4921726464561 -0.492172646456068 143 24 21.4778057128825 2.52219428711755 144 7 9.86113482063936 -2.86113482063936 145 17 14.5135950673666 2.48640493263336 146 11 11.8295717418214 -0.829571741821423 147 17 15.0913892233858 1.90861077661417 148 11 12.2042764010189 -1.20427640101887 149 12 12.5068570210313 -0.506857021031325 150 14 14.3909989558550 -0.390998955854967 151 11 14.1913798412456 -3.19137984124556 152 16 12.7195521217213 3.28044787827867 153 21 13.7306034317296 7.26939656827036 154 14 12.1946858182094 1.80531418179062 155 20 16.2967049279621 3.70329507203789 156 13 10.9441375203391 2.05586247966086 157 11 12.9695013576068 -1.96950135760678 158 15 13.8226020174876 1.17739798251241 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 0.417622381927573 0.835244763855146 0.582377618072427 11 0.61551336797381 0.76897326405238 0.38448663202619 12 0.792385634609305 0.415228730781389 0.207614365390695 13 0.80349833925566 0.393003321488680 0.196501660744340 14 0.74311934674085 0.513761306518299 0.256880653259150 15 0.661325265885246 0.677349468229509 0.338674734114754 16 0.623505026072872 0.752989947854257 0.376494973927128 17 0.669203321813334 0.661593356373331 0.330796678186666 18 0.589547870867367 0.820904258265265 0.410452129132633 19 0.696933935799587 0.606132128400826 0.303066064200413 20 0.781688405780388 0.436623188439225 0.218311594219612 21 0.73923862460444 0.521522750791121 0.260761375395560 22 0.79886134078503 0.402277318429941 0.201138659214970 23 0.754037343928504 0.491925312142992 0.245962656071496 24 0.780326806735707 0.439346386528587 0.219673193264293 25 0.731266326720698 0.537467346558604 0.268733673279302 26 0.707801161068337 0.584397677863325 0.292198838931663 27 0.688859379494023 0.622281241011953 0.311140620505977 28 0.628509353892363 0.742981292215274 0.371490646107637 29 0.600710398180402 0.798579203639196 0.399289601819598 30 0.549249365765775 0.90150126846845 0.450750634234225 31 0.629092434964497 0.741815130071006 0.370907565035503 32 0.61586546474604 0.76826907050792 0.38413453525396 33 0.68127567329582 0.63744865340836 0.31872432670418 34 0.726260830030435 0.547478339939131 0.273739169969565 35 0.740119872166876 0.519760255666248 0.259880127833124 36 0.77750551748009 0.444988965039819 0.222494482519910 37 0.83049657463082 0.339006850738361 0.169503425369181 38 0.827274258587268 0.345451482825464 0.172725741412732 39 0.815157005722323 0.369685988555353 0.184842994277677 40 0.78632901356452 0.427341972870959 0.213670986435479 41 0.842437981217826 0.315124037564348 0.157562018782174 42 0.807905533583713 0.384188932832574 0.192094466416287 43 0.820335846014759 0.359328307970483 0.179664153985241 44 0.872079453344915 0.255841093310171 0.127920546655086 45 0.886216797832833 0.227566404334334 0.113783202167167 46 0.862656693675515 0.274686612648971 0.137343306324485 47 0.839613253310512 0.320773493378976 0.160386746689488 48 0.866983242360575 0.266033515278851 0.133016757639425 49 0.846650295959098 0.306699408081804 0.153349704040902 50 0.89544062323943 0.209118753521141 0.104559376760571 51 0.936384411412925 0.127231177174151 0.0636155885870754 52 0.920398198431924 0.159203603136153 0.0796018015680763 53 0.900401968694935 0.19919606261013 0.099598031305065 54 0.920837406945503 0.158325186108995 0.0791625930544975 55 0.906008130093083 0.187983739813834 0.093991869906917 56 0.884494983961559 0.231010032076882 0.115505016038441 57 0.862859147355458 0.274281705289085 0.137140852644542 58 0.855297892135244 0.289404215729512 0.144702107864756 59 0.852568647022941 0.294862705954117 0.147431352977059 60 0.834780503145584 0.330438993708831 0.165219496854416 61 0.812719104743993 0.374561790512014 0.187280895256007 62 0.79016048587672 0.419679028246561 0.209839514123280 63 0.786287722900391 0.427424554199218 0.213712277099609 64 0.861829645968663 0.276340708062674 0.138170354031337 65 0.845757302651547 0.308485394696906 0.154242697348453 66 0.842031135530718 0.315937728938563 0.157968864469282 67 0.841706124538992 0.316587750922016 0.158293875461008 68 0.814409633578083 0.371180732843833 0.185590366421917 69 0.789627796066312 0.420744407867377 0.210372203933688 70 0.76740080355609 0.465198392887821 0.232599196443910 71 0.73942000605576 0.521159987888479 0.260579993944240 72 0.742177138108445 0.515645723783109 0.257822861891555 73 0.709770786557528 0.580458426884944 0.290229213442472 74 0.728145546692956 0.543708906614088 0.271854453307044 75 0.735715888184302 0.528568223631397 0.264284111815698 76 0.700497195062969 0.599005609874062 0.299502804937031 77 0.731150657947526 0.537698684104948 0.268849342052474 78 0.697699571673996 0.604600856652009 0.302300428326004 79 0.67280403187205 0.6543919362559 0.32719596812795 80 0.633985267216993 0.732029465566013 0.366014732783007 81 0.591201825024338 0.817596349951324 0.408798174975662 82 0.555418011287605 0.88916397742479 0.444581988712395 83 0.514059273591798 0.971881452816404 0.485940726408202 84 0.482689267974837 0.965378535949675 0.517310732025163 85 0.453842936941356 0.907685873882711 0.546157063058645 86 0.536723630198914 0.926552739602172 0.463276369801086 87 0.49072089611304 0.98144179222608 0.50927910388696 88 0.469031793980476 0.938063587960953 0.530968206019524 89 0.446766260342172 0.893532520684345 0.553233739657828 90 0.402500196424304 0.805000392848607 0.597499803575696 91 0.384032748068518 0.768065496137036 0.615967251931482 92 0.375416111566465 0.75083222313293 0.624583888433535 93 0.332411345457341 0.664822690914682 0.667588654542659 94 0.352848587423913 0.705697174847825 0.647151412576087 95 0.349133332913721 0.698266665827441 0.650866667086279 96 0.38318854521471 0.76637709042942 0.61681145478529 97 0.344732846218357 0.689465692436715 0.655267153781643 98 0.323277880421803 0.646555760843606 0.676722119578197 99 0.281559473965138 0.563118947930276 0.718440526034862 100 0.242451931173832 0.484903862347665 0.757548068826168 101 0.20683405101514 0.41366810203028 0.79316594898486 102 0.179564755589086 0.359129511178173 0.820435244410914 103 0.239907732942750 0.479815465885501 0.76009226705725 104 0.209169225069567 0.418338450139134 0.790830774930433 105 0.199908051651071 0.399816103302141 0.80009194834893 106 0.167615011400069 0.335230022800137 0.832384988599931 107 0.160104685051905 0.320209370103810 0.839895314948095 108 0.146583697528313 0.293167395056626 0.853416302471687 109 0.119671533162637 0.239343066325273 0.880328466837363 110 0.111740917086331 0.223481834172662 0.888259082913669 111 0.0938149440862541 0.187629888172508 0.906185055913746 112 0.0820678921068427 0.164135784213685 0.917932107893157 113 0.222217539592551 0.444435079185102 0.777782460407449 114 0.192281116462468 0.384562232924936 0.807718883537532 115 0.403414280961798 0.806828561923595 0.596585719038202 116 0.401970546376988 0.803941092753976 0.598029453623012 117 0.428790156508028 0.857580313016056 0.571209843491972 118 0.389999075185791 0.779998150371582 0.610000924814209 119 0.353668900605938 0.707337801211877 0.646331099394062 120 0.312541993189361 0.625083986378722 0.687458006810639 121 0.363550781030553 0.727101562061105 0.636449218969447 122 0.338683347635545 0.67736669527109 0.661316652364455 123 0.291049331908194 0.582098663816387 0.708950668091806 124 0.407265600697837 0.814531201395674 0.592734399302163 125 0.365172999924424 0.730345999848848 0.634827000075576 126 0.451689054908843 0.903378109817687 0.548310945091157 127 0.396013889912453 0.792027779824906 0.603986110087547 128 0.369145345396304 0.738290690792608 0.630854654603696 129 0.314797830970583 0.629595661941166 0.685202169029417 130 0.365300748163774 0.730601496327548 0.634699251836226 131 0.350725932786963 0.701451865573926 0.649274067213037 132 0.291816654530554 0.583633309061108 0.708183345469446 133 0.23833950766976 0.47667901533952 0.76166049233024 134 0.189415379525351 0.378830759050701 0.81058462047465 135 0.152360045918678 0.304720091837356 0.847639954081322 136 0.242371823917316 0.484743647834632 0.757628176082684 137 0.230341188718384 0.460682377436768 0.769658811281616 138 0.204152873904172 0.408305747808343 0.795847126095828 139 0.18459020082502 0.36918040165004 0.81540979917498 140 0.226382729630768 0.452765459261535 0.773617270369232 141 0.430335084600332 0.860670169200665 0.569664915399668 142 0.418342015666556 0.836684031333112 0.581657984333444 143 0.339110521242647 0.678221042485294 0.660889478757353 144 0.314432144809126 0.628864289618252 0.685567855190874 145 0.281334465023908 0.562668930047816 0.718665534976092 146 0.271419059398061 0.542838118796123 0.728580940601939 147 0.195163276717108 0.390326553434215 0.804836723282892 148 0.142678154692399 0.285356309384798 0.8573218453076 149 0.082148640367979 0.164297280735958 0.91785135963202 150 0.0439466197454927 0.0878932394909854 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/22/t1290451644kfausaihvtxowrv/10kv0e1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/10kv0e1290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/16lkn1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/16lkn1290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/26lkn1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/26lkn1290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/36lkn1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/36lkn1290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/4hcj81290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/4hcj81290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/5hcj81290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/5hcj81290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/6hcj81290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/6hcj81290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/79l0t1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/79l0t1290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/8kv0e1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/8kv0e1290451698.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/9kv0e1290451698.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290451644kfausaihvtxowrv/9kv0e1290451698.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

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