Multiple Regression Analysis

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 15 Dec 2010 22:44:30 +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/15/t129245359239avfuql0aseud0.htm/, Retrieved Wed, 15 Dec 2010 23:53:23 +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/15/t129245359239avfuql0aseud0.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:

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13 26 9 15 25 25 16 20 9 15 25 24 19 21 9 14 19 21 15 31 14 10 18 23 14 21 8 10 18 17 13 18 8 12 22 19 19 26 11 18 29 18 15 22 10 12 26 27 14 22 9 14 25 23 15 29 15 18 23 23 16 15 14 9 23 29 16 16 11 11 23 21 16 24 14 11 24 26 17 17 6 17 30 25 15 19 20 8 19 25 15 22 9 16 24 23 20 31 10 21 32 26 18 28 8 24 30 20 16 38 11 21 29 29 16 26 14 14 17 24 19 25 11 7 25 23 16 25 16 18 26 24 17 29 14 18 26 30 17 28 11 13 25 22 16 15 11 11 23 22 15 18 12 13 21 13 14 21 9 13 19 24 15 25 7 18 35 17 12 23 13 14 19 24 14 23 10 12 20 21 16 19 9 9 21 23 14 18 9 12 21 24 10 26 16 5 23 24 14 18 12 10 19 23 16 18 6 11 17 26 16 28 14 11 24 24 16 17 14 12 15 21 14 29 10 12 25 23 20 12 4 15 27 28 14 25 12 12 29 23 14 28 12 16 27 22 11 20 14 14 18 24 15 17 9 17 25 21 16 17 9 13 22 23 14 20 10 10 26 23 16 31 14 17 23 20 14 21 10 12 16 23 12 19 9 13 27 21 16 23 14 13 25 27 9 15 8 11 14 12 14 24 9 13 19 15 16 28 8 12 20 22 16 16 9 12 16 21 15 19 9 12 18 21 16 21 9 9 22 20 12 21 15 7 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 11.9901927558636 -0.00378845716147222Concern[t] -0.237184323200024Doubts[t] + 0.0977584702116675Expectations[t] + 0.0389221932355093Standards[t] + 0.161470621403681Organization[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) 11.9901927558636 1.327814 9.03 0 0 Concern -0.00378845716147222 0.034854 -0.1087 0.913597 0.456798 Doubts -0.237184323200024 0.063738 -3.7212 0.000285 0.000142 Expectations 0.0977584702116675 0.05038 1.9404 0.054309 0.027154 Standards 0.0389221932355093 0.045058 0.8638 0.389139 0.19457 Organization 0.161470621403681 0.044937 3.5933 0.000449 0.000225 Multiple Linear Regression - Regression Statistics Multiple R 0.468251783455381 R-squared 0.219259732709145 Adjusted R-squared 0.191768878227072 F-TEST (value) 7.9757336336028 F-TEST (DF numerator) 5 F-TEST (DF denominator) 142 p-value 1.19072741711079e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.89981292365133 Sum Squared Residuals 512.519058571912 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.2332313800198 -3.23323138001978 2 16 16.094491501585 -0.0944915015849864 3 19 15.2749995505877 3.72500044941226 4 15 13.9441785316981 1.05582146830191 5 14 14.4363453140909 -0.436345314090865 6 13 15.121857641748 -2.12185764174802 7 19 15.0775325673711 3.92246743262894 8 15 16.0797889108736 -1.07978891087357 9 14 15.8276854956467 -1.82768549564669 10 15 14.6912498506919 0.308750149308103 11 16 15.0704700706696 0.929529929330389 12 16 14.6819865523021 1.31801344769790 13 16 14.7864012256642 1.21359877433584 14 17 17.3690083706740 -0.369008370674034 15 15 12.7328805740552 2.26711942594485 16 15 15.9842802428345 -0.984280242834518 17 20 16.9975815663347 3.0024184336653 18 18 16.7299228799611 1.27007712003894 19 16 17.1015233275089 -1.10152332750889 20 16 14.4767031265203 1.52329687347971 21 19 14.6576421862806 4.34235781371944 22 16 14.7474565572480 1.25254344275203 23 17 16.1754951034242 0.824504896575784 24 17 15.0713570146625 1.92864298533754 25 16 14.8472456308672 1.15275436913275 26 15 13.263132897502 1.73686710249800 27 14 15.6616529445871 -1.66165294458712 28 15 16.102120855342 -1.10212085534200 29 12 14.8030972076758 -2.80309720767575 30 14 14.8736435658770 -0.873643565876952 31 16 15.1945697431307 0.805430256869266 32 14 15.6531042323309 -1.65310423233089 33 10 13.3560414076283 -3.35604140762829 34 14 14.5067193144328 -0.506719314432785 35 16 16.4341512015846 -0.434151201584617 36 16 14.4483061542109 1.55169384578909 37 16 13.7530260498681 2.24697395013185 38 14 15.3684650318930 -1.36846503189303 39 20 18.0344476469626 1.96555235303738 40 14 15.0649389870809 -1.06493898708091 41 14 15.2052924885685 -1.20529248856846 42 11 14.5383560627246 -3.53835606272464 43 15 15.8169619492817 -0.816961949281693 44 16 15.6321027315359 0.367897268464142 45 14 15.2459663991585 -1.24596639915845 46 16 14.3386869251463 1.66131307485374 47 14 15.0484729500652 -1.04847295006522 48 12 15.4961955405831 -3.49619554058310 49 16 15.1860994378882 0.81390056211184 50 9 13.5937926473109 -4.59379264731092 51 14 14.1970519804696 -0.197051980469575 52 16 15.4905405478733 0.509459452126681 53 16 14.9816583162652 1.01834168373476 54 15 15.0481373312518 -0.0481373312518462 55 16 14.7415031578323 1.25849684216774 56 12 13.729840570588 -1.72984057058800 57 16 16.4104261855018 -0.410426185501815 58 16 16.2697721237077 -0.269772123707726 59 14 16.4533841023949 -2.45338410239489 60 16 12.5915838921923 3.40841610780769 61 17 16.2018328072968 0.798167192703174 62 18 14.5744048639717 3.42559513602829 63 18 15.6274433586354 2.37255664136456 64 12 14.6686788762782 -2.66867887627825 65 16 15.9351298906026 0.0648701093974289 66 10 14.6265723484934 -4.62657234849337 67 14 12.7786902681103 1.22130973188971 68 18 15.4376515339135 2.56234846608650 69 18 16.3462159494917 1.65378405050833 70 16 15.6190795875646 0.380920412435355 71 16 15.6277439189420 0.372256081058027 72 16 14.7648328678136 1.23516713218644 73 13 14.7781474277150 -1.77814742771496 74 16 15.0565318675033 0.943468132496703 75 16 14.9777065921717 1.02229340782826 76 20 16.0359691691688 3.9640308308312 77 16 15.2836855562185 0.716314443781517 78 15 12.6925704094367 2.30742959056334 79 15 15.5131080239101 -0.513108023910121 80 16 15.9343780923616 0.0656219076384369 81 14 14.3005515886586 -0.300551588658603 82 15 13.5141839541813 1.48581604581867 83 12 14.8294223816713 -2.82942238167130 84 17 16.1576263600179 0.842373639982065 85 16 15.3905595957419 0.60944040425805 86 15 13.0981877634968 1.90181223650319 87 13 14.6083095903127 -1.60830959031274 88 16 16.0421447218774 -0.0421447218773881 89 16 15.4417531347077 0.558246865292336 90 16 16.2689852669599 -0.268985266959879 91 16 15.7822023354556 0.217797664544384 92 14 15.5765819995333 -1.57658199953329 93 16 14.4627298588692 1.5372701411308 94 16 15.3277967673025 0.672203232697458 95 20 16.4294342949967 3.57056570500332 96 15 15.6841489509369 -0.684148950936918 97 16 14.2884491558599 1.71155084414006 98 13 14.3064456172915 -1.30644561729154 99 17 16.0153032871871 0.984696712812863 100 16 14.5452244738643 1.45477552613571 101 12 13.3569648162504 -1.35696481625041 102 16 15.0870811987408 0.912918801259235 103 16 15.4245777935814 0.575422206418584 104 17 15.4409823062137 1.55901769378628 105 13 13.5331262399887 -0.533126239988688 106 12 15.8606227233586 -3.86062272335855 107 18 15.9599198485591 2.04008015144092 108 14 14.0869156303559 -0.08691563035592 109 14 14.6984694719481 -0.698469471948057 110 13 13.9806400674451 -0.980640067445053 111 16 15.3858469884581 0.614153011541875 112 13 12.7339805804136 0.266019419586368 113 16 15.4241105273930 0.575889472606958 114 13 14.9018863621816 -1.90188636218155 115 16 15.8940770126924 0.105922987307615 116 15 14.9366970627684 0.0633029372316269 117 16 15.5981789689640 0.401821031036048 118 15 15.1091540883363 -0.109154088336277 119 17 15.7450591798275 1.25494082017250 120 15 15.8938072175665 -0.893807217566509 121 12 13.7464356704052 -1.74643567040525 122 16 14.5758776952731 1.42412230472693 123 10 14.4637739274168 -4.46377392741677 124 16 14.2793274501488 1.72067254985124 125 14 14.7720308148163 -0.772030814816313 126 15 16.4573925592486 -1.45739255924864 127 13 14.6271587321797 -1.62715873217969 128 15 15.4984804012626 -0.498480401262555 129 11 13.9958813940319 -2.99588139403185 130 12 14.2404555427467 -2.24045554274672 131 16 16.1266712850563 -0.126671285056332 132 15 15.1189127740946 -0.118912774094640 133 17 15.2171133972915 1.78288660270853 134 16 15.5194819020576 0.480518097942414 135 10 15.1778014905049 -5.17780149050487 136 18 13.8179755007931 4.18202449920686 137 13 14.2808189477265 -1.28081894772655 138 15 14.4092830787811 0.590716921218937 139 16 14.8472456308672 1.15275436913275 140 16 15.1646250249052 0.835374975094753 141 14 13.6915762307258 0.308423769274193 142 10 13.2748997114873 -3.27489971148729 143 17 16.1576263600179 0.842373639982065 144 13 14.5199399294665 -1.51993992946650 145 15 15.8938072175665 -0.893807217566509 146 16 15.9956239400655 0.00437605993447482 147 12 15.3263528581086 -3.32635285810865 148 13 13.4563601856227 -0.456360185622739 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.623477167360614 0.753045665278772 0.376522832639386 10 0.929214642749359 0.141570714501282 0.070785357250641 11 0.879828861612479 0.240342276775043 0.120171138387521 12 0.812026655998345 0.375946688003311 0.187973344001655 13 0.740190037960121 0.519619924079758 0.259809962039879 14 0.682383348662476 0.635233302675049 0.317616651337524 15 0.640603758396567 0.718792483206867 0.359396241603433 16 0.570467370601311 0.859065258797377 0.429532629398689 17 0.653164038332483 0.693671923335033 0.346835961667517 18 0.580666269055534 0.838667461888931 0.419333730944466 19 0.510075564546023 0.979848870907953 0.489924435453977 20 0.444117002597461 0.888234005194921 0.555882997402539 21 0.662336203041617 0.675327593916767 0.337663796958383 22 0.617986871517262 0.764026256965477 0.382013128482738 23 0.5626583815821 0.8746832368358 0.4373416184179 24 0.503592505319581 0.992814989360838 0.496407494680419 25 0.438474149263183 0.876948298526365 0.561525850736817 26 0.404530717574790 0.809061435149579 0.59546928242521 27 0.348701586002294 0.697403172004588 0.651298413997706 28 0.447148497566688 0.894296995133377 0.552851502433312 29 0.554529163181976 0.890941673636048 0.445470836818024 30 0.505047244582253 0.989905510835493 0.494952755417747 31 0.459969160567271 0.919938321134541 0.540030839432729 32 0.417082011700953 0.834164023401906 0.582917988299047 33 0.737114831484927 0.525770337030147 0.262885168515073 34 0.689820221676462 0.620359556647076 0.310179778323538 35 0.661343745014746 0.677312509970509 0.338656254985254 36 0.626345067506328 0.747309864987344 0.373654932493672 37 0.61516253571839 0.769674928563219 0.384837464281610 38 0.583634126525534 0.832731746948933 0.416365873474466 39 0.631464831702694 0.737070336594612 0.368535168297306 40 0.606099947526025 0.78780010494795 0.393900052473975 41 0.588499394016714 0.823001211966573 0.411500605983286 42 0.748126404971694 0.503747190056611 0.251873595028306 43 0.72058407042447 0.558831859151059 0.279415929575530 44 0.675019348671959 0.649961302656083 0.324980651328041 45 0.647281334242454 0.705437331515091 0.352718665757546 46 0.621368767896053 0.757262464207894 0.378631232103947 47 0.581016500413814 0.837966999172372 0.418983499586186 48 0.698772531636185 0.602454936727631 0.301227468363815 49 0.658761366466534 0.682477267066933 0.341238633533466 50 0.824618685927396 0.350762628145208 0.175381314072604 51 0.792619047189502 0.414761905620996 0.207380952810498 52 0.767426668886717 0.465146662226566 0.232573331113283 53 0.747865363165108 0.504269273669783 0.252134636834892 54 0.707732434716431 0.584535130567138 0.292267565283569 55 0.689941012466775 0.62011797506645 0.310058987533225 56 0.684284141021393 0.631431717957215 0.315715858978607 57 0.639679925916585 0.72064014816683 0.360320074083415 58 0.592096107760902 0.815807784478195 0.407903892239098 59 0.613300159592091 0.773399680815818 0.386699840407909 60 0.699293151440039 0.601413697119923 0.300706848559961 61 0.665777496093722 0.668445007812556 0.334222503906278 62 0.757525001391074 0.484949997217851 0.242474998608926 63 0.783825018998817 0.432349962002367 0.216174981001183 64 0.818399763271914 0.363200473456173 0.181600236728086 65 0.784726282619628 0.430547434760745 0.215273717380372 66 0.913468445839856 0.173063108320288 0.0865315541601439 67 0.900522410053234 0.198955179893531 0.0994775899467656 68 0.922407533288077 0.155184933423846 0.077592466711923 69 0.920540105382368 0.158919789235263 0.0794598946176316 70 0.90171119486147 0.196577610277059 0.0982888051385295 71 0.879852957989805 0.240294084020390 0.120147042010195 72 0.865616274372724 0.268767451254553 0.134383725627276 73 0.860863996092643 0.278272007814715 0.139136003907357 74 0.839529332847072 0.320941334305855 0.160470667152928 75 0.817503390979547 0.364993218040906 0.182496609020453 76 0.905663482029662 0.188673035940677 0.0943365179703383 77 0.886867734382889 0.226264531234223 0.113132265617111 78 0.89949489832722 0.201010203345560 0.100505101672780 79 0.87764098587946 0.244718028241078 0.122359014120539 80 0.850947281909066 0.298105436181869 0.149052718090934 81 0.82334411200977 0.353311775980461 0.176655887990231 82 0.81970509384939 0.36058981230122 0.18029490615061 83 0.85610159246857 0.287796815062858 0.143898407531429 84 0.830950186446972 0.338099627106057 0.169049813553028 85 0.802642425767383 0.394715148465233 0.197357574232617 86 0.81299880184013 0.37400239631974 0.18700119815987 87 0.802073085401555 0.39585382919689 0.197926914598445 88 0.765897331908814 0.468205336182372 0.234102668091186 89 0.730243010101881 0.539513979796238 0.269756989898119 90 0.689687667720601 0.620624664558797 0.310312332279399 91 0.644944761307188 0.710110477385625 0.355055238692812 92 0.63365675407176 0.73268649185648 0.36634324592824 93 0.637097244133781 0.725805511732438 0.362902755866219 94 0.59708621150002 0.80582757699996 0.40291378849998 95 0.7071132898985 0.585773420202999 0.292886710101500 96 0.664309328313249 0.671381343373503 0.335690671686751 97 0.680930673647064 0.638138652705873 0.319069326352936 98 0.653015611036173 0.693968777927654 0.346984388963827 99 0.623843608300317 0.752312783399365 0.376156391699683 100 0.649191787731207 0.701616424537585 0.350808212268793 101 0.621415929781938 0.757168140436124 0.378584070218062 102 0.585627566649818 0.828744866700365 0.414372433350182 103 0.558131606935706 0.883736786128587 0.441868393064294 104 0.57208770131131 0.85582459737738 0.42791229868869 105 0.520432634301212 0.959134731397576 0.479567365698788 106 0.699975136575818 0.600049726848363 0.300024863424182 107 0.716645663169539 0.566708673660922 0.283354336830461 108 0.714252785010261 0.571494429979478 0.285747214989739 109 0.666447605565707 0.667104788868587 0.333552394434293 110 0.619023052636646 0.761953894726707 0.380976947363354 111 0.568656545332075 0.86268690933585 0.431343454667925 112 0.538206276467929 0.923587447064143 0.461793723532072 113 0.488944554250216 0.977889108500432 0.511055445749784 114 0.477814161934069 0.955628323868138 0.522185838065931 115 0.417883741785552 0.835767483571104 0.582116258214448 116 0.372008393849958 0.744016787699917 0.627991606150042 117 0.362769083329396 0.725538166658793 0.637230916670604 118 0.306604576827158 0.613209153654315 0.693395423172842 119 0.273749694450066 0.547499388900133 0.726250305549934 120 0.230341086168659 0.460682172337319 0.76965891383134 121 0.226575827176011 0.453151654352022 0.773424172823989 122 0.214825903409343 0.429651806818686 0.785174096590657 123 0.336668325217437 0.673336650434875 0.663331674782563 124 0.286150872003949 0.572301744007898 0.713849127996051 125 0.237752741184000 0.475505482367999 0.762247258816 126 0.190062085592425 0.38012417118485 0.809937914407575 127 0.162377238366138 0.324754476732277 0.837622761633862 128 0.120237598511927 0.240475197023855 0.879762401488073 129 0.129032290468010 0.258064580936020 0.87096770953199 130 0.115903660331833 0.231807320663666 0.884096339668167 131 0.0801982657297328 0.160396531459466 0.919801734270267 132 0.0543571693422493 0.108714338684499 0.94564283065775 133 0.0605407502214166 0.121081500442833 0.939459249778583 134 0.0419577538500129 0.0839155077000259 0.958042246149987 135 0.319368280634640 0.638736561269279 0.68063171936536 136 0.598296835493433 0.803406329013135 0.401703164506567 137 0.479449418299052 0.958898836598103 0.520550581700948 138 0.37156629955109 0.74313259910218 0.62843370044891 139 0.25835637340333 0.51671274680666 0.74164362659667 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 0.00763358778625954 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/10foux1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/10foux1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/11ewp1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/11ewp1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/21ewp1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/21ewp1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/3t5dr1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/3t5dr1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/4t5dr1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/4t5dr1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/5t5dr1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/5t5dr1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/6t5dr1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/6t5dr1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/74wvu1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/74wvu1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/8foux1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/8foux1292453059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/9foux1292453059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129245359239avfuql0aseud0/9foux1292453059.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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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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