WS 10 Multiple Regression

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 10 Dec 2010 16:40:54 +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/10/t12919992718in0u94hflxlyyb.htm/, Retrieved Fri, 10 Dec 2010 17:41:11 +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/10/t12919992718in0u94hflxlyyb.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 «

1 26 21 21 23 17 23 4 1 20 16 15 24 17 20 4 1 19 19 18 22 18 20 6 2 19 18 11 20 21 21 8 1 20 16 8 24 20 24 8 1 25 23 19 27 28 22 4 2 25 17 4 28 19 23 4 1 22 12 20 27 22 20 8 1 26 19 16 24 16 25 5 1 22 16 14 23 18 23 4 2 17 19 10 24 25 27 4 2 22 20 13 27 17 27 4 1 19 13 14 27 14 22 4 1 24 20 8 28 11 24 4 1 26 27 23 27 27 25 4 2 21 17 11 23 20 22 8 1 13 8 9 24 22 28 4 2 26 25 24 28 22 28 4 2 20 26 5 27 21 27 4 1 22 13 15 25 23 25 8 2 14 19 5 19 17 16 4 1 21 15 19 24 24 28 7 1 7 5 6 20 14 21 4 2 23 16 13 28 17 24 4 1 17 14 11 26 23 27 5 1 25 24 17 23 24 14 4 1 25 24 17 23 24 14 4 1 19 9 5 20 8 27 4 2 20 19 9 11 22 20 4 1 23 19 15 24 23 21 4 2 22 25 17 25 25 22 4 1 22 19 17 23 21 21 4 1 21 18 20 18 24 12 15 2 15 15 12 20 15 20 10 2 20 12 7 20 22 24 4 2 22 21 16 24 21 19 8 1 18 12 7 23 25 28 4 2 20 15 14 25 16 23 4 2 28 28 24 28 28 27 4 1 22 25 15 26 23 22 4 1 18 19 15 26 21 27 7 1 23 20 10 23 21 26 4 1 20 24 14 22 26 22 6 2 25 26 18 24 22 21 5 2 26 25 12 21 21 19 4 1 1 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 15 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation AM[t] = + 12.4988741565566 -0.441931117230605G[t] -0.185414422148506IM1[t] -0.138080158199122IM2[t] + 0.195649644221861IM3[t] -0.182548514840863EM1[t] + 0.083052060156604EM2[t] + 0.000807027024654495EM3[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) 12.4988741565566 1.755983 7.1179 0 0 G -0.441931117230605 0.400716 -1.1029 0.271811 0.135905 IM1 -0.185414422148506 0.073716 -2.5153 0.01292 0.00646 IM2 -0.138080158199122 0.066287 -2.0831 0.038898 0.019449 IM3 0.195649644221861 0.048662 4.0206 9.1e-05 4.5e-05 EM1 -0.182548514840863 0.071556 -2.5511 0.011713 0.005856 EM2 0.083052060156604 0.055628 1.493 0.137487 0.068744 EM3 0.000807027024654495 0.05736 0.0141 0.988793 0.494396 Multiple Linear Regression - Regression Statistics Multiple R 0.489720104489983 R-squared 0.23982578074168 Adjusted R-squared 0.205272407139029 F-TEST (value) 6.94073416678714 F-TEST (DF numerator) 7 F-TEST (DF denominator) 154 p-value 3.49570361768414e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.34105723547157 Sum Squared Residuals 844.004542882085 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 5.67695807283194 -1.67695807283193 2 4 6.12097793547255 -2.12097793547255 3 6 6.9272499055276 -0.927249905527603 4 8 5.86891167411928 2.13108832588072 5 8 5.00381471448795 2.99618528551205 6 4 5.37748446547298 -1.37748446547298 7 4 1.90007960488354 2.09992039511646 8 8 7.14833270134176 0.851667298658239 9 5 4.71088364717268 0.289116352827322 10 4 5.8225211030251 -1.82252110302510 11 4 5.5128670594062 -1.5128670594062 12 4 3.82260169735471 0.177398302645285 13 4 5.72979551705347 -1.72979551705347 14 4 2.23217379232455 1.76782620767545 15 4 5.34171700833279 -1.34171700833279 16 8 5.00627241036685 2.99372758963315 17 4 7.77133880775415 -3.77133880775415 18 4 4.77620811717237 -0.776208117172371 19 4 2.13196067930852 1.86803932069148 20 8 6.48418854699493 1.51581145300507 21 4 5.33031090042269 -1.33031090042269 22 7 7.44406288570407 -0.444062885704072 23 4 8.771245271515 -4.771245271515 24 4 4.00453831208787 -0.00453831208786888 25 5 6.30964746185934 -1.30964746185934 26 4 5.23963462136993 -1.23963462136993 27 4 5.23963462136993 -1.23963462136993 28 4 5.30483172992289 -1.30483172992289 29 4 6.87929947202764 -2.87929947202764 30 4 5.64961358239394 -1.64961358239394 31 4 4.94027785905784 -0.940277859057837 32 4 6.24277168751383 -2.24277168751383 33 15 8.30785071197927 6.69214928802073 34 10 6.72134009356825 3.27865990643175 35 4 5.81485276550862 -1.81485276550862 36 8 5.14486804077295 2.85513195922705 37 4 6.33235147108208 -2.33235147108208 38 4 5.3582978382957 -1.3582978382957 39 4 4.48864413219296 -0.488644132192964 40 4 4.64225705269065 -0.642257052690649 41 7 6.05032670528947 0.949673294710535 42 4 4.55376473273644 -0.553764732736442 43 6 5.93486665079818 0.065133349201817 44 5 4.37418938598146 0.625810614018543 45 4 3.61593668701758 0.384063312982421 46 16 7.24294704129907 8.75705295870093 47 5 5.56274255402683 -0.562742554026828 48 12 5.29078890320673 6.70921109679327 49 6 6.20349782699895 -0.20349782699895 50 9 7.59287456522733 1.40712543477267 51 9 7.08290600460645 1.91709399539355 52 4 6.65390485968321 -2.65390485968321 53 5 5.96485434536672 -0.96485434536672 54 4 6.66621437839058 -2.66621437839058 55 4 5.65864780137634 -1.65864780137634 56 5 5.65935022319656 -0.65935022319656 57 4 5.76105102414779 -1.76105102414779 58 4 3.83451528035804 0.165484719641961 59 4 5.16427660757093 -1.16427660757093 60 5 7.98328923790498 -2.98328923790498 61 4 5.46029298462823 -1.46029298462824 62 6 6.91465313012529 -0.914653130125286 63 4 5.04484313969089 -1.04484313969089 64 4 4.02427249926857 -0.0242724992685656 65 18 7.66075469843238 10.3392453015676 66 4 3.38623982440560 0.613760175594404 67 6 6.17818719124655 -0.178187191246545 68 4 5.33503213281464 -1.33503213281464 69 4 6.50825710546325 -2.50825710546325 70 5 6.63071581127478 -1.63071581127478 71 4 5.33204741816375 -1.33204741816375 72 4 4.95272136304416 -0.952721363044156 73 5 5.10442451953804 -0.104424519538036 74 10 6.70715358693103 3.29284641306897 75 5 6.21398867955508 -1.21398867955508 76 8 8.1759233156236 -0.175923315623595 77 8 8.19236771015125 -0.192367710151250 78 5 5.08110361765834 -0.0811036176583432 79 4 5.05003984475139 -1.05003984475139 80 4 5.91431934416135 -1.91431934416135 81 4 2.36758054780674 1.63241945219326 82 5 6.62895445417955 -1.62895445417955 83 4 5.0866077514322 -1.0866077514322 84 4 5.21603421000194 -1.21603421000194 85 8 6.9384851579807 1.0615148420193 86 4 5.50634011730237 -1.50634011730237 87 5 5.07846171857777 -0.0784617185777747 88 14 7.61045606655054 6.38954393344946 89 8 6.12571901862589 1.87428098137411 90 8 5.92397380333015 2.07602619666985 91 4 7.84711143795842 -3.84711143795842 92 4 4.14134820762883 -0.141348207628825 93 6 5.67622770287988 0.323772297120118 94 4 5.95603910732897 -1.95603910732897 95 7 6.32105971718034 0.678940282819657 96 7 5.59951935744627 1.40048064255373 97 4 4.64454724179112 -0.644547241791122 98 6 6.60336015987926 -0.603360159879262 99 4 5.7930760902168 -1.79307609021680 100 7 4.8742981671101 2.1257018328899 101 4 5.7917785366493 -1.79177853664930 102 4 3.27399679698867 0.72600320301133 103 8 6.71127091459261 1.28872908540739 104 4 5.96823057502311 -1.96823057502311 105 4 5.65559874662117 -1.65559874662117 106 10 7.13996860516206 2.86003139483794 107 8 6.79987529221217 1.20012470778783 108 6 6.45554336087752 -0.455543360877523 109 4 4.70878364854452 -0.708783648544517 110 4 5.63703701072413 -1.63703701072413 111 4 4.02419554742627 -0.0241955474262719 112 5 4.88641779959654 0.113582200403463 113 4 6.70995107093478 -2.70995107093478 114 6 6.3326944811654 -0.332694481165405 115 4 5.19887859350065 -1.19887859350065 116 5 5.98394956717018 -0.98394956717018 117 7 7.6595020266622 -0.659502026662194 118 8 5.94013596693574 2.05986403306426 119 5 4.52008430802969 0.479915691970305 120 8 7.80611479627662 0.193885203723384 121 10 7.55185005791891 2.44814994208109 122 8 6.87646974176936 1.12353025823064 123 5 5.85158595629847 -0.851585956298474 124 12 8.5158352943592 3.48416470564079 125 4 1.99421653204634 2.00578346795366 126 5 4.68377237304181 0.316227626958187 127 4 6.5285233371888 -2.52852333718880 128 6 5.39075091159936 0.609249088400642 129 4 6.85623497499053 -2.85623497499053 130 4 5.32951311736035 -1.32951311736035 131 7 7.26406235006322 -0.264062350063223 132 7 6.291316943942 0.708683056057996 133 10 6.92519229441233 3.07480770558767 134 4 5.7440495153258 -1.7440495153258 135 5 5.88312843473695 -0.883128434736946 136 8 5.6525312492186 2.3474687507814 137 11 5.29541848568447 5.70458151431553 138 7 6.07638714836269 0.923612851637312 139 4 4.90458522192834 -0.904585221928338 140 8 6.67313718716965 1.32686281283035 141 6 6.33550975171926 -0.335509751719256 142 7 6.42758844491706 0.57241155508294 143 5 7.64453058875027 -2.64453058875027 144 4 6.12701170487861 -2.12701170487861 145 8 5.30324502498435 2.69675497501565 146 4 6.00125121754969 -2.00125121754969 147 8 5.5669039272224 2.4330960727776 148 6 3.65870021033187 2.34129978966813 149 4 5.69311296301741 -1.69311296301741 150 9 6.13928579801545 2.86071420198455 151 5 5.47041741820395 -0.470417418203952 152 6 5.2092599044077 0.790740095592295 153 4 5.37004610455364 -1.37004610455364 154 4 3.7363771211985 0.263622878801498 155 4 3.90899308701198 0.0910069129880203 156 5 6.47633105093158 -1.47633105093158 157 6 7.3945195585339 -1.39451955853390 158 16 8.80558357918206 7.19441642081794 159 6 5.67622770287988 0.323772297120118 160 6 6.96123334077925 -0.961233340779253 161 4 6.52950713668606 -2.52950713668606 162 4 6.88164485267556 -2.88164485267556 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.498687554551351 0.997375109102703 0.501312445448649 12 0.455390300737347 0.910780601474695 0.544609699262653 13 0.327031869241258 0.654063738482516 0.672968130758742 14 0.274588869680124 0.549177739360248 0.725411130319876 15 0.194035241733146 0.388070483466292 0.805964758266854 16 0.176128523241123 0.352257046482246 0.823871476758877 17 0.143067555844848 0.286135111689696 0.856932444155152 18 0.0985622039596027 0.197124407919205 0.901437796040397 19 0.0653853701775192 0.130770740355038 0.93461462982248 20 0.0751991224189996 0.150398244837999 0.924800877581 21 0.0750915276830287 0.150183055366057 0.924908472316971 22 0.0528296762396117 0.105659352479223 0.947170323760388 23 0.0436091486483387 0.0872182972966774 0.956390851351661 24 0.0305106965168846 0.0610213930337691 0.969489303483115 25 0.0191522784227065 0.0383045568454131 0.980847721577293 26 0.0168523853111591 0.0337047706223183 0.98314761468884 27 0.0117576239566517 0.0235152479133034 0.988242376043348 28 0.0115402895358822 0.0230805790717643 0.988459710464118 29 0.0163863674260406 0.0327727348520811 0.98361363257396 30 0.0124690376675227 0.0249380753350455 0.987530962332477 31 0.00800900924386825 0.0160180184877365 0.991990990756132 32 0.00564498922330598 0.0112899784466120 0.994355010776694 33 0.336376942684789 0.672753885369578 0.663623057315211 34 0.441751831825725 0.88350366365145 0.558248168174275 35 0.450103847079262 0.900207694158525 0.549896152920738 36 0.432130258713836 0.864260517427671 0.567869741286164 37 0.392880883934186 0.785761767868372 0.607119116065814 38 0.380837704675897 0.761675409351793 0.619162295324103 39 0.330228313669584 0.660456627339169 0.669771686330416 40 0.280064719369198 0.560129438738396 0.719935280630802 41 0.298855073133486 0.597710146266972 0.701144926866514 42 0.254041451844722 0.508082903689443 0.745958548155278 43 0.220070446978522 0.440140893957043 0.779929553021478 44 0.18290322187961 0.36580644375922 0.81709677812039 45 0.153682569596395 0.307365139192789 0.846317430403605 46 0.854369627685249 0.291260744629502 0.145630372314751 47 0.828803627529145 0.34239274494171 0.171196372470855 48 0.95495864355592 0.0900827128881617 0.0450413564440808 49 0.942131343660999 0.115737312678003 0.0578686563390014 50 0.93328177700657 0.133436445986861 0.0667182229934304 51 0.931190052681234 0.137619894637532 0.068809947318766 52 0.932667176835077 0.134665646329845 0.0673328231649226 53 0.916755809704247 0.166488380591507 0.0832441902957535 54 0.92249570389863 0.155008592202742 0.0775042961013708 55 0.91578127174165 0.168437456516699 0.0842187282583493 56 0.896221715094715 0.207556569810570 0.103778284905285 57 0.884287856627407 0.231424286745187 0.115712143372593 58 0.858734083345894 0.282531833308212 0.141265916654106 59 0.836111174967901 0.327777650064198 0.163888825032099 60 0.848355101410388 0.303289797179225 0.151644898589613 61 0.827090165454867 0.345819669090265 0.172909834545133 62 0.797638454009023 0.404723091981955 0.202361545990977 63 0.768827298431429 0.462345403137142 0.231172701568571 64 0.734848312614132 0.530303374771737 0.265151687385868 65 0.997333754795949 0.00533249040810236 0.00266624520405118 66 0.99626105501942 0.00747788996116173 0.00373894498058087 67 0.994729808536967 0.0105403829260651 0.00527019146303254 68 0.993433432706767 0.013133134586466 0.006566567293233 69 0.993677738635938 0.0126445227281234 0.00632226136406172 70 0.992617150375486 0.0147656992490272 0.00738284962451362 71 0.991046537177873 0.0179069256442537 0.00895346282212685 72 0.988470820868234 0.0230583582635314 0.0115291791317657 73 0.984497374266556 0.0310052514668886 0.0155026257334443 74 0.988888115834422 0.0222237683311555 0.0111118841655777 75 0.986302460120414 0.0273950797591727 0.0136975398795864 76 0.981623467899118 0.0367530642017631 0.0183765321008816 77 0.975648829426102 0.048702341147796 0.024351170573898 78 0.968196154020754 0.0636076919584911 0.0318038459792455 79 0.961674385094862 0.0766512298102765 0.0383256149051382 80 0.95856036361396 0.0828792727720814 0.0414396363860407 81 0.958455639960752 0.0830887200784966 0.0415443600392483 82 0.953133706522191 0.093732586955618 0.046866293477809 83 0.943520223544581 0.112959552910837 0.0564797764554187 84 0.9324892595311 0.1350214809378 0.0675107404689 85 0.919436934003095 0.161126131993809 0.0805630659969045 86 0.909507718314517 0.180984563370965 0.0904922816854827 87 0.891070777260945 0.21785844547811 0.108929222739055 88 0.97783263407612 0.0443347318477616 0.0221673659238808 89 0.973733242668547 0.0525335146629058 0.0262667573314529 90 0.970756331786636 0.058487336426729 0.0292436682133645 91 0.97839787382405 0.0432042523519005 0.0216021261759502 92 0.971566220117373 0.0568675597652534 0.0284337798826267 93 0.963051862359168 0.0738962752816638 0.0369481376408319 94 0.960141191821383 0.0797176163572344 0.0398588081786172 95 0.949733270066544 0.100533459866912 0.0502667299334558 96 0.939966184420147 0.120067631159706 0.0600338155798528 97 0.924893161128027 0.150213677743947 0.0751068388719734 98 0.907466755605333 0.185066488789333 0.0925332443946666 99 0.897392300767586 0.205215398464827 0.102607699232414 100 0.892374053403603 0.215251893192795 0.107625946596397 101 0.884920340730855 0.23015931853829 0.115079659269145 102 0.865178219281012 0.269643561437976 0.134821780718988 103 0.843505879429406 0.312988241141187 0.156494120570594 104 0.840714451436981 0.318571097126037 0.159285548563019 105 0.823128908841688 0.353742182316623 0.176871091158312 106 0.835616867448312 0.328766265103377 0.164383132551688 107 0.81493230041765 0.370135399164701 0.185067699582351 108 0.780210484295874 0.439579031408251 0.219789515704126 109 0.75069348356653 0.498613032866941 0.249306516433471 110 0.73734020314393 0.52531959371214 0.26265979685607 111 0.69558618982998 0.60882762034004 0.30441381017002 112 0.64897884455718 0.702042310885639 0.351021155442819 113 0.657597545485912 0.684804909028177 0.342402454514088 114 0.611684134999651 0.776631730000698 0.388315865000349 115 0.592188000896986 0.815623998206028 0.407811999103014 116 0.547187449318071 0.905625101363858 0.452812550681929 117 0.508465682993669 0.983068634012663 0.491534317006331 118 0.478597973264511 0.957195946529021 0.521402026735489 119 0.432770166333389 0.865540332666778 0.567229833666611 120 0.381967167849036 0.763934335698072 0.618032832150964 121 0.370052913403992 0.740105826807985 0.629947086596008 122 0.322979423110878 0.645958846221755 0.677020576889122 123 0.287464820476694 0.574929640953387 0.712535179523306 124 0.410067792692096 0.820135585384193 0.589932207307904 125 0.375093120357439 0.750186240714878 0.624906879642561 126 0.320705554065589 0.641411108131178 0.679294445934411 127 0.339468655196605 0.678937310393211 0.660531344803395 128 0.287868997721044 0.575737995442088 0.712131002278956 129 0.288005095748025 0.57601019149605 0.711994904251975 130 0.247951731944991 0.495903463889982 0.752048268055009 131 0.201297872286941 0.402595744573881 0.79870212771306 132 0.161074223154737 0.322148446309474 0.838925776845263 133 0.246527232950304 0.493054465900607 0.753472767049696 134 0.206728097436080 0.413456194872161 0.79327190256392 135 0.213047584792386 0.426095169584772 0.786952415207614 136 0.28662813064593 0.57325626129186 0.71337186935407 137 0.530895046656135 0.93820990668773 0.469104953343865 138 0.46785669961841 0.93571339923682 0.53214330038159 139 0.506323151589663 0.987353696820674 0.493676848410337 140 0.43026615222492 0.86053230444984 0.56973384777508 141 0.434367577077824 0.868735154155648 0.565632422922176 142 0.361154555966991 0.722309111933982 0.638845444033009 143 0.490782335607136 0.981564671214273 0.509217664392864 144 0.425384438217963 0.850768876435927 0.574615561782037 145 0.357084493875762 0.714168987751524 0.642915506124238 146 0.282901708557562 0.565803417115123 0.717098291442438 147 0.239112062987440 0.478224125974879 0.76088793701256 148 0.570410751932644 0.859178496134712 0.429589248067356 149 0.453088800840644 0.906177601681289 0.546911199159356 150 0.687968762797718 0.624062474404565 0.312031237202282 151 0.570847465359901 0.858305069280199 0.429152534640099 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0141843971631206 NOK 5% type I error level 23 0.163120567375887 NOK 10% type I error level 36 0.25531914893617 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/109rd91291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/109rd91291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/1k8gx1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/1k8gx1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/2k8gx1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/2k8gx1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/3uzxi1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/3uzxi1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/4uzxi1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/4uzxi1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/5uzxi1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/5uzxi1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/658ek1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/658ek1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/758ek1291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/758ek1291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/8gid51291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/8gid51291999235.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/9gid51291999235.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919992718in0u94hflxlyyb/9gid51291999235.ps (open in new window)

Parameters (Session):

par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 8 ; 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