*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: Tue, 23 Nov 2010 16:03:13 +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/23/t12905281704xs6mljx4oehdz6.htm/, Retrieved Tue, 23 Nov 2010 17:02:50 +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/23/t12905281704xs6mljx4oehdz6.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 «

26 24 14 11 12 24 23 25 11 7 8 25 25 17 6 17 8 30 23 18 12 10 8 19 19 18 8 12 9 22 29 16 10 12 7 22 25 20 10 11 4 25 21 16 11 11 11 23 22 18 16 12 7 17 25 17 11 13 7 21 24 23 13 14 12 19 18 30 12 16 10 19 22 23 8 11 10 15 15 18 12 10 8 16 22 15 11 11 8 23 28 12 4 15 4 27 20 21 9 9 9 22 12 15 8 11 8 14 24 20 8 17 7 22 20 31 14 17 11 23 21 27 15 11 9 23 20 34 16 18 11 21 21 21 9 14 13 19 23 31 14 10 8 18 28 19 11 11 8 20 24 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 23 22 9 16 9 24 23 17 9 13 6 22 29 24 10 9 6 25 24 25 16 18 16 26 18 26 11 18 5 29 25 25 8 12 7 32 21 17 9 17 9 25 26 32 16 9 6 29 22 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 23 25 12 12 7 29 30 29 14 18 10 26 23 22 9 14 9 25 17 18 10 15 8 14 23 17 9 16 5 25 23 20 10 10 8 26 25 15 12 11 8 20 24 20 14 14 10 18 24 33 14 9 6 32 23 29 10 12 8 25 21 23 14 17 7 25 24 26 16 5 4 23 24 18 9 12 8 21 28 20 10 12 8 20 16 11 6 6 4 15 20 28 8 24 20 30 29 26 13 12 8 24 27 22 10 12 8 26 22 17 8 14 6 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 19 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation YT[t] = + 17.4684655763519 -0.0593663461768209X1[t] + 0.216789584253540X2[t] -0.133176572068144X3[t] -0.253140065700683X4[t] + 0.395987020465247X5[t] -0.0148718920049206t + 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) 17.4684655763519 2.042261 8.5535 0 0 X1 -0.0593663461768209 0.062074 -0.9564 0.340397 0.170199 X2 0.216789584253540 0.110801 1.9566 0.052231 0.026115 X3 -0.133176572068144 0.102779 -1.2958 0.197025 0.098512 X4 -0.253140065700683 0.128304 -1.973 0.050313 0.025157 X5 0.395987020465247 0.075181 5.2671 0 0 t -0.0148718920049206 0.006034 -2.4646 0.014829 0.007414 Multiple Linear Regression - Regression Statistics Multiple R 0.502249529664989 R-squared 0.252254590048702 Adjusted R-squared 0.222738323866414 F-TEST (value) 8.5462906619291 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 5.24699078630064e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.44273447491298 Sum Squared Residuals 1801.56794104266 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 24.064920965661 1.93507903433902 2 23 25.2815675462592 -2.28156754625918 3 25 25.3058478840459 -0.305847884045926 4 23 23.1087259307447 -0.108725930744719 5 19 22.8951635532844 -3.89516355328441 6 29 23.9388836535416 5.06111634645843 7 25 25.7671042073953 -0.767104207395301 8 21 23.6425327835159 -2.64253278351593 9 22 23.0963376883682 -1.09633768836818 10 25 23.5076557310652 1.49234426893478 11 24 21.3793139890044 2.6206860109956 12 18 20.9720150767733 -2.97201507677327 13 22 19.5874840494717 2.41251595052833 14 15 21.7720459492998 -6.77204594929977 15 22 24.3572160827604 -2.35721608276036 16 28 25.0667181959023 2.93328180409774 17 20 23.1549211111529 -3.15492111115287 18 12 20.0983484697977 -8.09834846979775 19 24 22.4086216439225 1.59137835607748 20 20 22.4248842071563 -2.42488420715633 21 21 24.1696068479225 -3.16960684792246 22 20 21.7254699401245 -1.72546994012447 23 21 20.1992855745841 0.80071442541585 24 23 22.0771177383895 0.922882261610534 25 28 22.7830707166081 5.21692928339187 26 24 22.6980438177955 1.30195618220447 27 24 24.2138903633694 -0.213890363369409 28 24 21.2706629494304 2.72933705056958 29 23 22.7768300973705 0.223169902629514 30 23 23.4257658086257 -0.425765808625657 31 29 24.9327864273048 4.06721357269516 32 24 22.8252829094895 1.17471709051053 33 18 25.6395985341433 -7.63959853414328 34 25 26.5144645979578 -1.51446459795780 35 21 23.2472409246222 -2.24724092462217 36 26 27.2681817852479 -1.26818178524791 37 22 25.7140086053332 -3.71400860533322 38 22 23.4681646825109 -1.46816468251095 39 22 23.2429912089363 -1.24299120893634 40 23 26.1044305215467 -3.10443052154670 41 30 23.5392317224349 6.46076827756508 42 23 23.2458356659081 -0.245835665908053 43 17 19.4493250113788 -2.44932501137878 44 23 24.2591307314488 -1.25913073144876 45 23 24.718575640939 -1.71857564093898 46 25 22.9250159534656 2.07498404653438 47 24 21.3491076105474 2.65089238945262 48 24 27.7847346279007 -3.7847346279007 49 23 23.4624507927264 -0.462450792726373 50 21 24.2581925201565 -3.25819252015650 51 24 26.0643657791175 -2.06436577911748 52 24 22.2701272585421 1.72987274145789 53 28 21.9573252379718 6.04267476202816 54 16 21.4412767174295 -5.44127671742951 55 20 20.3431420674669 -0.343142067466901 56 29 23.7908283195178 5.20917168048223 57 27 24.15502710039 2.84497289961 58 22 23.4513607170967 -1.45136071709669 59 28 24.1630730666702 3.83692693332979 60 16 20.7842692974064 -4.7842692974064 61 25 23.1304675723697 1.86953242763029 62 24 23.7211635049449 0.278836495055051 63 28 23.8722868360319 4.12771316396808 64 24 24.4263501754649 -0.426350175464861 65 23 22.8691357443860 0.130864255614047 66 30 26.9612902489942 3.03870975100577 67 24 21.5876603864495 2.41233961355052 68 21 24.2155561910099 -3.2155561910099 69 25 23.3994197816712 1.60058021832883 70 25 24.0344043325361 0.965595667463887 71 22 21.0342613096623 0.965738690337692 72 23 22.565992854172 0.434007145828005 73 26 22.9686737132033 3.03132628679670 74 23 21.8241477434297 1.17585225657035 75 25 23.1438414700723 1.85615852992771 76 21 21.4371726833282 -0.437172683328207 77 25 23.6522131699041 1.34778683009587 78 24 22.2322215912726 1.76777840872739 79 29 23.5179157660598 5.48208423394016 80 22 23.6506816303374 -1.65068163033742 81 27 23.5704499591745 3.42955004082551 82 26 19.7228302358410 6.27716976415897 83 22 21.3562177076211 0.643782292378905 84 24 22.0036660999645 1.99633390003548 85 27 23.0666234572075 3.93337654279254 86 24 21.3444098173143 2.65559018268571 87 24 24.6608334555894 -0.660833455589399 88 29 24.1882898632981 4.81171013670194 89 22 22.1009479856673 -0.100947985667271 90 21 20.5316105842715 0.468389415728455 91 24 20.4488393962061 3.55116060379393 92 24 21.5300363894891 2.46996361051086 93 23 21.7876933786466 1.21230662135342 94 20 22.1275694295439 -2.12756942954389 95 27 21.1981659968205 5.80183400317952 96 26 23.2054989079822 2.79450109201783 97 25 21.8271634979598 3.17283650204017 98 21 19.9885290601733 1.0114709398267 99 21 20.5769609924390 0.423039007561034 100 19 20.2144630083883 -1.21446300838830 101 21 21.3475265969951 -0.347526596995136 102 21 20.9853586187903 0.0146413812096625 103 16 19.5584249175939 -3.5584249175939 104 22 20.3741894424269 1.62581055757310 105 29 21.4999425928665 7.50005740713355 106 15 21.4440772756156 -6.44407727561556 107 17 20.3888167239287 -3.38881672392871 108 15 19.6496724848056 -4.64967248480563 109 21 21.3278500194504 -0.327850019450360 110 21 20.6812297983111 0.318770201688875 111 19 18.9539586993263 0.0460413006736844 112 24 17.8341330797541 6.16586692024592 113 20 21.7961238039561 -1.79612380395608 114 17 24.4842650194948 -7.48426501949475 115 23 24.1583086799554 -1.15830867995539 116 24 21.8465129033612 2.1534870966388 117 14 21.5117844008051 -7.5117844008051 118 19 22.2913507280418 -3.29135072804180 119 24 21.6854112308025 2.31458876919748 120 13 19.9510554657143 -6.95105546571428 121 22 24.6828942962343 -2.68289429623433 122 16 20.5693313552517 -4.56933135525173 123 19 22.6188802033758 -3.61888020337582 124 25 22.0700130318097 2.92998696819027 125 25 23.5036705358378 1.49632946416220 126 23 20.8185708659907 2.18142913400929 127 24 22.7909452398543 1.20905476014574 128 26 22.7758475757855 3.22415242421453 129 26 20.8222879485798 5.1777120514202 130 25 23.4166840851681 1.58331591483193 131 18 21.5867258661787 -3.58672586617873 132 21 19.2191734881759 1.78082651182413 133 26 22.8094411624211 3.19055883757895 134 23 21.1767041398501 1.82329586014985 135 23 19.0945156655305 3.90548433446945 136 22 21.8213582921081 0.178641707891905 137 20 21.5874808656089 -1.58748086560890 138 13 21.2551966611107 -8.25519666111074 139 24 20.5657093503366 3.43429064966338 140 15 20.7213804063778 -5.72138040637781 141 14 22.2564443286843 -8.25644432868427 142 22 23.1317158928542 -1.13171589285421 143 10 17.0087352770752 -7.00873527707519 144 24 23.4498547185230 0.550145281477034 145 22 20.9427715840559 1.05722841594408 146 24 24.7520455181703 -0.752045518170322 147 19 20.7504601735956 -1.75046017359557 148 20 21.1100095714849 -1.11000957148492 149 13 16.3372891356001 -3.33728913560006 150 20 19.1898065770962 0.810193422903831 151 22 22.1054696978879 -0.105469697887947 152 24 22.3620564591798 1.63794354082021 153 29 22.2367654918252 6.76323450817484 154 12 19.9636818356675 -7.96368183566751 155 20 19.9100170145359 0.0899829854640947 156 21 20.3639463546099 0.63605364539008 157 24 22.5200006909888 1.47999930901117 158 22 20.8135768311869 1.18642316881314 159 20 16.8832947915483 3.11670520845174 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.680450223902582 0.639099552194837 0.319549776097418 11 0.635984546996439 0.728030906007123 0.364015453003561 12 0.577322827957608 0.845354344084783 0.422677172042392 13 0.581068405323667 0.837863189352666 0.418931594676333 14 0.73390627518273 0.532187449634541 0.266093724817270 15 0.653079843776733 0.693840312446535 0.346920156223267 16 0.652192143607114 0.695615712785772 0.347807856392886 17 0.566207033561846 0.867585932876309 0.433792966438154 18 0.710150490897466 0.579699018205069 0.289849509102534 19 0.648191463167074 0.703617073665853 0.351808536832926 20 0.594530476217182 0.810939047565636 0.405469523782818 21 0.525089666204278 0.949820667591445 0.474910333795722 22 0.451523569787596 0.903047139575193 0.548476430212404 23 0.440215606759447 0.880431213518894 0.559784393240553 24 0.490098652726698 0.980197305453397 0.509901347273302 25 0.660631160282357 0.678737679435286 0.339368839717643 26 0.596398043077134 0.807203913845732 0.403601956922866 27 0.532967872116531 0.934064255766937 0.467032127883469 28 0.512652082650983 0.974695834698034 0.487347917349017 29 0.448314460200061 0.896628920400123 0.551685539799939 30 0.38722174869975 0.7744434973995 0.61277825130025 31 0.387811489547507 0.775622979095015 0.612188510452493 32 0.327885532975003 0.655771065950006 0.672114467024997 33 0.597865908094353 0.804268183811294 0.402134091905647 34 0.556715814545882 0.886568370908236 0.443284185454118 35 0.52690067555812 0.94619864888376 0.47309932444188 36 0.471589141540206 0.943178283080413 0.528410858459794 37 0.457660319302905 0.91532063860581 0.542339680697095 38 0.406076584096374 0.812153168192748 0.593923415903626 39 0.357738344937554 0.715476689875108 0.642261655062446 40 0.33524549362302 0.67049098724604 0.66475450637698 41 0.499536270408898 0.999072540817795 0.500463729591102 42 0.44576727214139 0.89153454428278 0.55423272785861 43 0.418199228089768 0.836398456179535 0.581800771910232 44 0.371840279816575 0.74368055963315 0.628159720183425 45 0.333037345135403 0.666074690270805 0.666962654864597 46 0.306540999150889 0.613081998301779 0.69345900084911 47 0.282763625550193 0.565527251100386 0.717236374449807 48 0.279287011927953 0.558574023855906 0.720712988072047 49 0.242666884893964 0.485333769787928 0.757333115106036 50 0.243302621148881 0.486605242297762 0.756697378851119 51 0.223717998676663 0.447435997353327 0.776282001323337 52 0.194148224271929 0.388296448543858 0.80585177572807 53 0.261284270094502 0.522568540189004 0.738715729905498 54 0.341299150350042 0.682598300700083 0.658700849649958 55 0.325844433704422 0.651688867408844 0.674155566295578 56 0.385933681890316 0.771867363780631 0.614066318109684 57 0.362759712377965 0.72551942475593 0.637240287622035 58 0.332672250738428 0.665344501476856 0.667327749261572 59 0.332673707087912 0.665347414175825 0.667326292912088 60 0.41394208319198 0.82788416638396 0.58605791680802 61 0.370202178994205 0.74040435798841 0.629797821005795 62 0.328403442065222 0.656806884130444 0.671596557934778 63 0.329885821769878 0.659771643539756 0.670114178230122 64 0.296427536519409 0.592855073038818 0.703572463480591 65 0.258087037189134 0.516174074378267 0.741912962810866 66 0.241939008092637 0.483878016185274 0.758060991907363 67 0.214043776263457 0.428087552526915 0.785956223736543 68 0.236880230056861 0.473760460113723 0.763119769943138 69 0.204071914709640 0.408143829419280 0.79592808529036 70 0.172207106592652 0.344414213185303 0.827792893407348 71 0.144173729847397 0.288347459694794 0.855826270152603 72 0.119834347787419 0.239668695574838 0.88016565221258 73 0.104200550249152 0.208401100498304 0.895799449750848 74 0.0846771706516799 0.169354341303360 0.91532282934832 75 0.0688722752200003 0.137744550440001 0.93112772478 76 0.0576025525859477 0.115205105171895 0.942397447414052 77 0.0456198367978948 0.0912396735957896 0.954380163202105 78 0.0355472037893019 0.0710944075786038 0.964452796210698 79 0.0405978269243494 0.0811956538486989 0.95940217307565 80 0.0373198682695846 0.0746397365391692 0.962680131730415 81 0.0312864294062717 0.0625728588125435 0.968713570593728 82 0.0415270526715279 0.0830541053430559 0.958472947328472 83 0.0324367301794561 0.0648734603589123 0.967563269820544 84 0.0253926836340081 0.0507853672680161 0.974607316365992 85 0.0233181897516908 0.0466363795033817 0.97668181024831 86 0.0184557083726284 0.0369114167452568 0.981544291627372 87 0.0150337845441561 0.0300675690883122 0.984966215455844 88 0.0154610710606837 0.0309221421213675 0.984538928939316 89 0.0130056647435021 0.0260113294870042 0.986994335256498 90 0.00983515067279134 0.0196703013455827 0.990164849327209 91 0.0084021433954155 0.016804286790831 0.991597856604585 92 0.0068644923105666 0.0137289846211332 0.993135507689433 93 0.00505838765009745 0.0101167753001949 0.994941612349903 94 0.00482075544927397 0.00964151089854794 0.995179244550726 95 0.00719271638049006 0.0143854327609801 0.99280728361951 96 0.00587184626345418 0.0117436925269084 0.994128153736546 97 0.00502376309309223 0.0100475261861845 0.994976236906908 98 0.00385119678426691 0.00770239356853381 0.996148803215733 99 0.00291177044409987 0.00582354088819973 0.9970882295559 100 0.00242558168742070 0.00485116337484139 0.99757441831258 101 0.00191256833383417 0.00382513666766835 0.998087431666166 102 0.00140812827315077 0.00281625654630154 0.99859187172685 103 0.00173541208573882 0.00347082417147763 0.998264587914261 104 0.00135770159401232 0.00271540318802464 0.998642298405988 105 0.00596291985149438 0.0119258397029888 0.994037080148506 106 0.0144736692877781 0.0289473385755562 0.985526330712222 107 0.0153006489935963 0.0306012979871925 0.984699351006404 108 0.0208411750588295 0.0416823501176591 0.97915882494117 109 0.0163117021657954 0.0326234043315907 0.983688297834205 110 0.0118968127947449 0.0237936255894899 0.988103187205255 111 0.00864692791493286 0.0172938558298657 0.991353072085067 112 0.0249343415991939 0.0498686831983878 0.975065658400806 113 0.0250773923575804 0.0501547847151607 0.97492260764242 114 0.061951222052911 0.123902444105822 0.93804877794709 115 0.0533024591081406 0.106604918216281 0.94669754089186 116 0.0450105889253199 0.0900211778506398 0.95498941107468 117 0.116099901786624 0.232199803573249 0.883900098213376 118 0.110022546252399 0.220045092504799 0.8899774537476 119 0.0988238873190695 0.197647774638139 0.90117611268093 120 0.170298309360065 0.340596618720131 0.829701690639935 121 0.167887378513134 0.335774757026268 0.832112621486866 122 0.212322430705873 0.424644861411746 0.787677569294127 123 0.212549501662186 0.425099003324371 0.787450498337814 124 0.202595743644363 0.405191487288725 0.797404256355637 125 0.177262688528817 0.354525377057635 0.822737311471183 126 0.143970194470238 0.287940388940475 0.856029805529762 127 0.114308395403422 0.228616790806844 0.885691604596578 128 0.112120160648500 0.224240321297000 0.8878798393515 129 0.156046937750750 0.312093875501499 0.84395306224925 130 0.136643414082242 0.273286828164485 0.863356585917758 131 0.116172198322327 0.232344396644654 0.883827801677673 132 0.104425661178245 0.208851322356489 0.895574338821755 133 0.103083906385061 0.206167812770122 0.896916093614939 134 0.0930289220764472 0.186057844152894 0.906971077923553 135 0.210219174148618 0.420438348297235 0.789780825851382 136 0.171437696748182 0.342875393496363 0.828562303251818 137 0.146613959230718 0.293227918461436 0.853386040769282 138 0.204602597777390 0.409205195554779 0.79539740222261 139 0.464282877494266 0.928565754988532 0.535717122505734 140 0.410398047063312 0.820796094126624 0.589601952936688 141 0.565461332019034 0.869077335961933 0.434538667980966 142 0.476837148829576 0.953674297659152 0.523162851170424 143 0.648440828701084 0.703118342597833 0.351559171298916 144 0.603518416498861 0.792963167002278 0.396481583501139 145 0.513747415406566 0.972505169186867 0.486252584593434 146 0.409838013852135 0.81967602770427 0.590161986147865 147 0.415303853624173 0.830607707248346 0.584696146375827 148 0.285548084201274 0.571096168402547 0.714451915798726 149 0.198960259016768 0.397920518033536 0.801039740983232 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.0571428571428571 NOK 5% type I error level 28 0.2 NOK 10% type I error level 38 0.271428571428571 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/10zpxa1290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/10zpxa1290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/1t6ih1290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/1t6ih1290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/280781290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/280781290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/380781290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/380781290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/480781290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/480781290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/5w6hn1290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/5w6hn1290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/6w6hn1290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/6w6hn1290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/77gz81290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/77gz81290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/87gz81290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/87gz81290528170.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/9zpxa1290528170.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905281704xs6mljx4oehdz6/9zpxa1290528170.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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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