test

*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 21:34:59 +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/t1290461892p6cywpt7vic7c4f.htm/, Retrieved Mon, 22 Nov 2010 22:38:15 +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/t1290461892p6cywpt7vic7c4f.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 «

5,6 5,5 6 4,8 4,4 3,5 4 4,4 2,4 8,5 4 5,6 4,8 5 4 4,8 3,2 6 4,5 8,4 4 6 3,5 4,8 4 5,5 2 8,8 4,4 5,5 5,5 4,4 6,4 6 3,5 4 4,4 6,5 3,5 5,2 5,2 7 6 4 4,8 8 5 3,2 3,2 5,5 5 6 4,8 5 4 5,6 4,4 5,5 4 4 1,6 7,5 2 5,6 3,6 4,5 4,5 5,6 3,2 5,5 4 4,4 3,2 8,5 3,5 4 5,6 8,5 5,5 5,2 6 5,5 4,5 2,8 6,4 9 5,5 5,6 3,6 7 6,5 4,8 5,6 5 4 5,6 4,4 5,5 4 4,4 3,2 7,5 4,5 3,6 3,6 7,5 3 4,4 3,6 6,5 4,5 6 3,6 8 4,5 5,6 3,6 6,5 3 5,2 4 4,5 3 3,6 6,4 9 8 6 4,4 9 2,5 4 3,2 6 3,5 4,4 3,6 8,5 4,5 5,2 6,4 4,5 3 3,2 4,4 4,5 3 8 6,4 6 2,5 4,8 4,8 9 6 4 4,8 6 3,5 4 5,6 9 5 3,6 3,6 7 4,5 5,6 4 7,5 4 3,2 3,6 8 2,5 5,6 4 5 4 4,4 4,8 5,5 4 5,2 5,6 7 5 3,6 5,6 4,5 3 4,4 4 6 4 6 5,6 8,5 3,5 4,4 6,4 2,5 2 4 3,6 6 4 5,6 4 6 4 7,2 2,4 3 2 5,6 3,2 12 10 4,4 5,2 6 4 4,8 4 6 4 5,2 3,2 7 3 3,6 2,8 3,5 2 4 6 6,5 4 6 3,6 6 4,5 8 4 6,5 3 4,8 4,8 7 3,5 4,8 5,2 4 4,5 5,6 4 5,5 2,5 5,2 4,4 4,5 2,5 4,4 3,2 5,5 4 6,8 3,6 6,5 4 4,8 5,2 5 3 5,2 4,4 5,5 4 5,6 3,2 6 3,5 5,2 3,6 4,5 3,5 6 3,6 7,5 4,5 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 5.70984648766359 -0.0799607227294421Doubts[t] -0.021800622364926Expectat[t] -0.0155788482792036Criticism[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) 5.70984648766359 0.546122 10.4553 0 0 Doubts -0.0799607227294421 0.091271 -0.8761 0.382343 0.191172 Expectat -0.021800622364926 0.072838 -0.2993 0.76511 0.382555 Criticism -0.0155788482792036 0.093796 -0.1661 0.8683 0.43415 Multiple Linear Regression - Regression Statistics Multiple R 0.0855457044326433 R-squared 0.00731806754687717 Adjusted R-squared -0.0118951311457638 F-TEST (value) 0.380887517167045 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 0.766914280365275 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.26562203627464 Sum Squared Residuals 248.278866499113 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.8 5.0486899276964 -0.248689927696399 2 4.4 5.21940173625999 -0.81940173625999 3 5.6 5.27032006989424 0.329679930105755 4 4.8 5.15471651362082 -0.354716513620825 5 8.4 5.2530636234834 3.1469363765166 6 4.8 5.20467389357905 -0.404673893579054 7 8.8 5.23894247718032 3.56105752281968 8 4.4 5.15243221911133 -0.752432219111333 9 4 5.01276815902839 -1.01276815902839 10 5.2 5.16178929330481 0.0382107066951858 11 4 5.04797328324079 -1.04797328324079 12 3.2 5.07373579824684 -1.87373579824684 13 6 5.25617451052627 0.743825489473734 14 5.6 5.15471651362082 0.445283486379175 15 4 5.17580049153014 -1.17580049153014 16 5.6 5.38724696700113 0.212753032998868 17 5.6 5.25378026793902 0.346219732060983 18 4.4 5.27175335880547 -0.87175335880547 19 4 5.21414091585029 -1.21414091585029 20 5.2 4.99107748474122 0.208922515258775 21 2.8 5.04007391102343 -2.24007391102343 22 5.6 4.91620859537521 0.683791404624792 23 4.8 5.16812101546829 -0.368121015468295 24 5.6 5.09074793543727 0.509252064562729 25 4.4 5.17580049153014 -0.775800491530138 26 3.6 5.22036268993602 -1.62036268993602 27 4.4 5.21174667326304 -0.811746673263044 28 6 5.21017902320916 0.789820976790835 29 5.6 5.17747808966178 0.422521910338224 30 5.2 5.23354729562797 -0.0335472956279698 31 3.6 5.24516425126605 -1.64516425126604 32 6 4.8772614746772 1.1227385253228 33 4 5.1228665856717 -1.1228665856717 34 4.4 5.26864247176261 -0.868642471762608 35 5.2 5.16657777847931 0.0334222215206876 36 3.2 5.05325851671538 -1.85325851671538 37 8 5.21317996217427 2.78682003782573 38 4.8 5.0283470073076 -0.228347007307597 39 4 5.03635632760271 -1.03635632760271 40 4 5.1407053153955 -1.1407053153955 41 3.6 4.98796659769836 -1.38796659769836 42 5.6 5.1992787120267 0.400721287973298 43 3.2 5.16418353589206 -1.96418353589206 44 5.6 5.20863578622018 0.391364213779817 45 4.4 5.21868509180438 -0.818685091804378 46 5.2 5.14381620243836 0.0561837975616383 47 3.6 5.03156784242822 -1.43156784242822 48 4.4 5.11722709489894 -0.717227094898937 49 6 5.19688446943945 0.803115530560548 50 4.4 5.02223518129963 -0.622235181299632 51 4 5.11243860972444 -1.11243860972444 52 5.6 5.22886875853123 0.37113124146877 53 7.2 5.19688446943945 2.00311553056055 54 5.6 5.42138118945975 0.178618810540255 55 4.4 5.03657622375823 -0.636576223758228 56 4.8 5.10093160216412 -0.300931602164122 57 5.2 5.19688446943945 0.00311553056054765 58 3.6 5.25463127353728 -1.65463127353728 59 4 5.37849658918551 -1.37849658918551 60 6 5.0260627127981 0.973937287201895 61 8 5.22107933439163 2.77892066560837 62 4.8 5.20156300653619 -0.401563006536193 63 4.8 5.11890469303057 -0.318904693030575 64 5.6 5.13674342275437 0.463256577245627 65 5.2 5.23115305304072 -0.0311530530407207 66 4.4 5.22096938631387 -0.82096938631387 67 6.8 5.27175335880547 1.52824664119453 68 4.8 5.21796844734877 -0.417968447348766 69 5.2 5.13831107280825 0.0616889271917487 70 5.6 5.17580049153014 0.424199508469861 71 5.2 5.26864247176261 -0.0686424717626078 72 6 5.26935911621822 0.73064088378178 73 5.2 5.18837840084424 0.0116215991557616 74 4 4.94819288446698 -0.948192884466985 75 4.4 5.21174667326304 -0.811746673263044 76 7.6 5.19688446943945 2.40311553056055 77 5.2 5.07362585016909 0.126374149830914 78 6.8 5.10332584475137 1.69667415524863 79 5.2 5.15471651362082 0.0452834863791753 80 3.6 5.16957871744442 -1.56957871744442 81 4.4 5.04246815361068 -0.642468153610678 82 4 5.33572193698902 -1.33572193698902 83 3.6 5.12201558007344 -1.52201558007344 84 4.8 5.20167295461395 -0.401672954613951 85 4.8 5.135916830221 -0.335916830221003 86 5.2 5.12908835975743 0.0709116402425748 87 5.2 5.23115305304072 -0.0311530530407207 88 4.8 5.10164824661973 -0.301648246619734 89 6 5.04257810168844 0.957421898311564 90 8.8 5.20467389357905 3.59532610642095 91 5.2 5.04714669070742 0.152853309292581 92 6 5.41598600790739 0.584013992092608 93 5.2 5.22096938631387 -0.0209693863138698 94 6 5.17976238417127 0.820237615828733 95 4 5.22419022143449 -1.22419022143449 96 4.4 5.06762397223888 -0.667623972238878 97 6.4 4.97538868838426 1.42461131161574 98 4.4 5.00437203851094 -0.604372038510936 99 4.4 5.23665818267083 -0.83665818267083 100 4 5.18598415825699 -1.18598415825699 101 4 5.14860468761286 -1.14860468761286 102 6.4 5.30841618499399 1.09158381500601 103 4.8 5.13698773197478 -0.336987731974785 104 4.4 5.21257326579641 -0.812573265796413 105 6.4 5.0642687759756 1.3357312240244 106 7.6 5.10321589667361 2.49678410332639 107 4.4 5.29044309412753 -0.890443094127534 108 6.4 5.20238959906956 1.19761040093044 109 6 5.01287810710615 0.98712189289385 110 9.6 5.08452616135155 4.51547383864845 111 5.6 5.26864247176261 0.331357528237392 112 6 5.18609410633475 0.813905893665253 113 4.4 5.27018570875159 -0.87018570875159 114 6 5.2040671972012 0.7959328027988 115 4.8 5.34505459811761 -0.545054598117607 116 4 5.27332100885935 -1.27332100885935 117 5.6 5.27032006989424 0.329679930105755 118 5.2 5.21317996217427 -0.013179962174268 119 3.6 5.02845695538536 -1.42845695538535 120 6 5.23965912163593 0.760340878364065 121 6 5.2505594328184 0.749440567181602 122 5.6 5.17268960448728 0.427310395512722 123 4.4 5.02377841828861 -0.623778418288613 124 3.2 5.34183376299699 -2.14183376299699 125 4.4 4.92843224739114 -0.528432247391138 126 4.4 5.11039862443536 -0.71039862443536 127 3.2 5.31381136654634 -2.11381136654634 128 4 5.17580049153014 -1.17580049153014 129 4.4 5.16729442293492 -0.767294422934924 130 5.2 5.07984762425481 0.120152375745192 131 4.4 5.13063159674641 -0.730631596746407 132 8 5.22886875853123 2.77113124146877 133 4 5.2631373421325 -1.2631373421325 134 6 5.3247116777288 0.675288322271198 135 4.8 5.19688446943945 -0.396884469439453 136 5.6 4.99815026442521 0.601849735574785 137 9.2 5.11651045044333 4.08348954955667 138 5.6 5.11422615593383 0.485773844066166 139 6.4 5.2530636234834 1.1469363765166 140 4.4 5.06198448146611 -0.661984481466113 141 4.8 5.09385882248013 -0.293858822480133 142 4 5.08463610942931 -1.08463610942931 143 5.6 4.84467048920757 0.755329510792432 144 4.8 5.11483285231169 -0.314832852311689 145 4.8 5.023061773833 -0.223061773833002 146 4.4 5.03145789435046 -0.631457894350458 147 4.8 5.16657777847931 -0.366577778479313 148 5.2 5.24755849385329 -0.047558493853294 149 4.4 5.22107933439163 -0.821079334391627 150 7.6 5.22347357697888 2.37652642302112 151 4.8 5.29594822375764 -0.495948223757644 152 6.8 4.96137749015894 1.83862250984106 153 3.6 5.07458680384511 -1.47458680384511 154 4.8 5.22264698444551 -0.422646984445507 155 7.6 5.03875057018996 2.56124942981004 156 7.2 5.23354729562797 1.96645270437203 157 6 5.07984762425481 0.920152375745192 158 5.6 5.05265182033753 0.54734817966247 159 4.4 4.86636116349474 -0.466361163494736 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.976394534322343 0.0472109313553138 0.0236054656776569 8 0.951903386473852 0.0961932270522955 0.0480966135261478 9 0.91986285096968 0.160274298060641 0.0801371490303205 10 0.873498134910829 0.253003730178342 0.126501865089171 11 0.8120660700241 0.375867859951801 0.1879339299759 12 0.787588045557719 0.424823908884562 0.212411954442281 13 0.710785546943447 0.578428906113106 0.289214453056553 14 0.627513994637114 0.744972010725773 0.372486005362886 15 0.655004303657231 0.689991392685538 0.344995696342769 16 0.723185586279466 0.553628827441067 0.276814413720534 17 0.654820272702685 0.69035945459463 0.345179727297315 18 0.67176192849256 0.656476143014881 0.328238071507441 19 0.648164279953096 0.703671440093808 0.351835720046904 20 0.680104363237949 0.639791273524101 0.319895636762051 21 0.723983109251041 0.552033781497918 0.276016890748959 22 0.775713522373843 0.448572955252315 0.224286477626157 23 0.721378411229249 0.557243177541503 0.278621588770751 24 0.680923814105871 0.638152371788258 0.319076185894129 25 0.640954701922062 0.718090596155875 0.359045298077938 26 0.670988404431302 0.658023191137396 0.329011595568698 27 0.639738613068443 0.720522773863114 0.360261386931557 28 0.607490711163809 0.785018577672382 0.392509288836191 29 0.559087494711719 0.881825010576563 0.440912505288281 30 0.4988272051629 0.9976544103258 0.5011727948371 31 0.552115623552737 0.895768752894526 0.447884376447263 32 0.587547937127836 0.824904125744329 0.412452062872164 33 0.55927066804935 0.8814586639013 0.44072933195065 34 0.524836877078318 0.950326245843365 0.475163122921682 35 0.467408388198833 0.934816776397666 0.532591611801167 36 0.471386567142905 0.94277313428581 0.528613432857095 37 0.711000334430101 0.577999331139797 0.288999665569899 38 0.667104736426315 0.66579052714737 0.332895263573685 39 0.638064769765422 0.723870460469156 0.361935230234578 40 0.615647898320574 0.768704203358852 0.384352101679426 41 0.59806912289671 0.80386175420658 0.40193087710329 42 0.552087478340427 0.895825043319146 0.447912521659573 43 0.604185923977924 0.791628152044152 0.395814076022076 44 0.564921584085117 0.870156831829767 0.435078415914883 45 0.533138973517079 0.933722052965842 0.466861026482921 46 0.483940215940761 0.967880431881523 0.516059784059239 47 0.475629581972337 0.951259163944675 0.524370418027663 48 0.434205389575812 0.868410779151623 0.565794610424188 49 0.409280129116146 0.818560258232291 0.590719870883854 50 0.368709532449743 0.737419064899487 0.631290467550257 51 0.346114995324536 0.692229990649073 0.653885004675464 52 0.305191302860987 0.610382605721974 0.694808697139013 53 0.384515857804275 0.76903171560855 0.615484142195725 54 0.340871069985913 0.681742139971825 0.659128930014087 55 0.306438385786579 0.612876771573158 0.693561614213421 56 0.267161098788423 0.534322197576846 0.732838901211577 57 0.228588099283012 0.457176198566023 0.771411900716988 58 0.256883181049085 0.513766362098169 0.743116818950916 59 0.274588059569755 0.54917611913951 0.725411940430245 60 0.27915632647311 0.55831265294622 0.72084367352689 61 0.455411491901356 0.910822983802713 0.544588508098644 62 0.412293207540601 0.824586415081201 0.587706792459399 63 0.370127462888606 0.740254925777212 0.629872537111394 64 0.333428561573203 0.666857123146406 0.666571438426797 65 0.292119828075272 0.584239656150543 0.707880171924728 66 0.268115914455726 0.536231828911452 0.731884085544274 67 0.283486402870827 0.566972805741655 0.716513597129173 68 0.249055649246785 0.498111298493571 0.750944350753215 69 0.215710535492542 0.431421070985083 0.784289464507458 70 0.187214212040947 0.374428424081894 0.812785787959053 71 0.157548154261003 0.315096308522007 0.842451845738997 72 0.138407129598372 0.276814259196745 0.861592870401628 73 0.114303309002813 0.228606618005626 0.885696690997187 74 0.103947477666358 0.207894955332717 0.896052522333642 75 0.0918498770574002 0.1836997541148 0.9081501229426 76 0.156789477427883 0.313578954855766 0.843210522572117 77 0.135658713798872 0.271317427597744 0.864341286201128 78 0.162484131249669 0.324968262499339 0.83751586875033 79 0.135691384304701 0.271382768609402 0.864308615695299 80 0.150486361071601 0.300972722143202 0.849513638928399 81 0.131515605976591 0.263031211953181 0.86848439402341 82 0.139842719963209 0.279685439926417 0.860157280036791 83 0.152712261058874 0.305424522117749 0.847287738941126 84 0.129523428728074 0.259046857456148 0.870476571271926 85 0.109827746320157 0.219655492640313 0.890172253679843 86 0.0919694246949325 0.183938849389865 0.908030575305067 87 0.0748478211911325 0.149695642382265 0.925152178808867 88 0.0611017633601321 0.122203526720264 0.938898236639868 89 0.0561871396774589 0.112374279354918 0.94381286032254 90 0.220619282243405 0.441238564486811 0.779380717756595 91 0.191734645334903 0.383469290669806 0.808265354665097 92 0.171533977666561 0.343067955333122 0.828466022333439 93 0.143821097134715 0.287642194269429 0.856178902865285 94 0.12887709352904 0.25775418705808 0.87112290647096 95 0.126834837357409 0.253669674714819 0.87316516264259 96 0.111394400062505 0.22278880012501 0.888605599937495 97 0.116623847047129 0.233247694094258 0.883376152952871 98 0.102268085583787 0.204536171167574 0.897731914416213 99 0.0913589435060663 0.182717887012133 0.908641056493934 100 0.090281230377882 0.180562460755764 0.909718769622118 101 0.0882223469861224 0.176444693972245 0.911777653013878 102 0.082434530907999 0.164869061815998 0.917565469092001 103 0.0683992185733134 0.136798437146627 0.931600781426687 104 0.0599471534027872 0.119894306805574 0.940052846597213 105 0.0602354306592327 0.120470861318465 0.939764569340767 106 0.103229356050118 0.206458712100236 0.896770643949882 107 0.092013262235437 0.184026524470874 0.907986737764563 108 0.0887288354770998 0.1774576709542 0.9112711645229 109 0.0791138836175982 0.158227767235196 0.920886116382402 110 0.469495517498111 0.938991034996222 0.530504482501889 111 0.422601212941636 0.845202425883273 0.577398787058363 112 0.390118575475749 0.780237150951498 0.609881424524251 113 0.358204890458748 0.716409780917497 0.641795109541252 114 0.324430903406468 0.648861806812936 0.675569096593532 115 0.284101187740825 0.56820237548165 0.715898812259175 116 0.286555843389545 0.57311168677909 0.713444156610455 117 0.244894626674676 0.489789253349351 0.755105373325324 118 0.205392778984916 0.410785557969831 0.794607221015084 119 0.222061136792561 0.444122273585123 0.777938863207439 120 0.198184961737776 0.396369923475552 0.801815038262224 121 0.179147871348369 0.358295742696739 0.82085212865163 122 0.148882284826899 0.297764569653798 0.8511177151731 123 0.127405813631578 0.254811627263155 0.872594186368422 124 0.165855250402199 0.331710500804398 0.8341447495978 125 0.137990332677587 0.275980665355174 0.862009667322413 126 0.122720030492509 0.245440060985019 0.87727996950749 127 0.185498757440324 0.370997514880647 0.814501242559676 128 0.187085528829706 0.374171057659411 0.812914471170294 129 0.173231281788721 0.346462563577442 0.826768718211279 130 0.137811807341951 0.275623614683903 0.862188192658049 131 0.123452485953459 0.246904971906918 0.876547514046541 132 0.221672627715068 0.443345255430137 0.778327372284932 133 0.241648622422645 0.483297244845291 0.758351377577354 134 0.19733568754618 0.39467137509236 0.80266431245382 135 0.166414078240956 0.332828156481912 0.833585921759044 136 0.130123211166474 0.260246422332948 0.869876788833526 137 0.59495868211983 0.81008263576034 0.40504131788017 138 0.527551394236182 0.944897211527636 0.472448605763818 139 0.488535085834114 0.977070171668227 0.511464914165886 140 0.447976322558 0.895952645115999 0.552023677442 141 0.379257995471569 0.758515990943138 0.620742004528431 142 0.387257939715211 0.774515879430422 0.612742060284789 143 0.316592306749894 0.633184613499787 0.683407693250106 144 0.248631282647623 0.497262565295246 0.751368717352377 145 0.198210025648444 0.396420051296888 0.801789974351556 146 0.16885831478444 0.337716629568881 0.83114168521556 147 0.125888632990713 0.251777265981425 0.874111367009287 148 0.0864737044462057 0.172947408892411 0.913526295553794 149 0.0938770751296553 0.187754150259311 0.906122924870345 150 0.115922567769026 0.231845135538052 0.884077432230974 151 0.112701268950409 0.225402537900817 0.887298731049591 152 0.354598120010482 0.709196240020964 0.645401879989518 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 1 0.00684931506849315 OK 10% type I error level 2 0.0136986301369863 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/10ev1z1290461687.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/10ev1z1290461687.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/1f11s1290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/1f11s1290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/2qb0w1290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/2qb0w1290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/3qb0w1290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/3qb0w1290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/4qb0w1290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/4qb0w1290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/5qb0w1290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/5qb0w1290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/6i2hh1290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/6i2hh1290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/7btz11290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/7btz11290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/8btz11290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/8btz11290461686.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/9btz11290461686.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290461892p6cywpt7vic7c4f/9btz11290461686.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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