Workshop 7 DMA

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 24 Nov 2010 10:44:23 +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/24/t129059541509outp55uv9cse8.htm/, Retrieved Wed, 24 Nov 2010 11:43:35 +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/24/t129059541509outp55uv9cse8.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:

DMA

Dataseries X:

» Textbox « » Textfile « » CSV «

12 24 14 8 25 11 8 17 6 8 18 12 9 18 8 7 16 10 4 20 10 11 16 11 7 18 16 7 17 11 12 23 13 10 30 12 10 23 8 8 18 12 8 15 11 4 12 4 9 21 9 8 15 8 7 20 8 11 31 14 9 27 15 11 34 16 13 21 9 8 31 14 8 19 11 9 16 8 6 20 9 9 21 9 9 22 9 6 17 9 6 24 10 16 25 16 5 26 11 7 25 8 9 17 9 6 32 16 6 33 11 5 13 16 12 32 12 7 25 12 10 29 14 9 22 9 8 18 10 5 17 9 8 20 10 8 15 12 10 20 14 6 33 14 8 29 10 7 23 14 4 26 16 8 18 9 8 20 10 4 11 6 20 28 8 8 26 13 8 22 10 6 17 8 4 12 7 8 14 15 9 17 9 6 21 10 7 19 12 9 18 13 5 10 10 5 29 11 8 31 8 8 19 9 6 9 13 8 20 11 7 28 8 7 19 9 9 30 9 11 29 15 6 26 9 8 23 10 6 13 14 9 21 12 8 19 12 6 28 11 10 23 14 8 18 6 8 21 12 10 20 8 5 23 14 7 21 11 5 21 10 8 15 14 14 28 12 7 19 10 8 26 14 6 10 5 5 16 11 6 22 10 10 19 9 12 31 10 9 31 16 12 29 13 7 19 9 8 22 10 10 23 10 6 15 7 10 20 9 10 18 8 10 23 14 5 25 14 7 21 8 10 24 9 11 25 14 6 17 14 7 13 8 12 28 8 11 21 8 11 25 7 11 9 6 5 16 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation ParDoubt[t] = + 6.5359359075337 + 0.0360025588876879ParCritism[t] + 0.188139523215922ParConcern[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 6.5359359075337 0.898961 7.2705 0 0 ParCritism 0.0360025588876879 0.079997 0.45 0.653302 0.326651 ParConcern 0.188139523215922 0.037841 4.9718 2e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.396660143948058 R-squared 0.157339269796894 Adjusted R-squared 0.146535927101983 F-TEST (value) 14.5639432386979 F-TEST (DF numerator) 2 F-TEST (DF denominator) 156 p-value 1.58823556339893e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.58721008230779 Sum Squared Residuals 1044.21033755923 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 11.4833151713681 2.51668482863190 2 11 11.5274444590333 -0.527444459033265 3 6 10.0223282733059 -4.02232827330589 4 12 10.2104677965218 1.78953220347819 5 8 10.2464703554095 -2.24647035540950 6 10 9.79818619120228 0.201813808797724 7 10 10.4427366074029 -0.442736607402901 8 11 9.94219642675303 1.05780357324697 9 16 10.1744652376341 5.82553476236588 10 11 9.9863257144182 1.01367428558180 11 13 11.2951756481522 1.70482435184783 12 12 12.5401471928883 -0.540147192888252 13 8 11.2231705303768 -3.22317053037680 14 12 10.2104677965218 1.78953220347819 15 11 9.64604922687404 1.35395077312596 16 4 8.93762042167553 -4.93762042167552 17 9 10.8108889250573 -1.81088892505726 18 8 9.64604922687404 -1.64604922687404 19 8 10.5507442840660 -2.55074428406596 20 14 12.7642892749919 1.23571072500814 21 15 11.9397260643528 3.06027393564720 22 16 13.3287078446396 2.67129215536037 23 9 10.9548991606080 -1.95489916060801 24 14 12.6562815983288 1.34371840167120 25 11 10.3986073197377 0.601392680262269 26 8 9.87019130897765 -1.87019130897765 27 9 10.5147417251783 -1.51474172517828 28 9 10.8108889250573 -1.81088892505726 29 9 10.9990284482732 -1.99902844827319 30 9 9.95032315553051 -0.95032315553051 31 10 11.2672998180420 -1.26729981804197 32 16 11.8154649301348 4.18453506986523 33 11 11.6075763055861 -0.607576305586123 34 8 11.4914419001456 -3.49144190014558 35 9 10.0583308321936 -1.05833083219357 36 16 12.7724160037693 3.22758399623065 37 11 12.9605555269853 -1.96055552698527 38 16 9.16176250377913 6.83823749622087 39 12 12.9884313570955 -0.988431357095472 40 12 11.4914419001456 0.508558099854423 41 14 12.3520076696723 1.64799233032767 42 9 10.9990284482732 -1.99902844827319 43 10 10.2104677965218 -0.210467796521808 44 9 9.91432059664282 -0.914320596642822 45 10 10.5867468429537 -0.586746842953653 46 12 9.64604922687404 2.35395077312596 47 14 10.6587519607290 3.34124803927097 48 14 12.9605555269853 1.03944447301473 49 10 12.2800025518970 -2.28000255189695 50 14 11.1151628537137 2.88483714628627 51 16 11.5715737466984 4.42842625330156 52 9 10.2104677965218 -1.21046779652181 53 10 10.5867468429537 -0.586746842953653 54 6 8.7494808984596 -2.7494808984596 55 8 12.5238937353333 -4.52389373533329 56 13 11.7155839822492 1.28441601775081 57 10 10.9630258893855 -0.963025889385498 58 8 9.95032315553051 -1.95032315553051 59 7 8.93762042167552 -1.93762042167552 60 15 9.45790970365812 5.54209029634188 61 9 10.0583308321936 -1.05833083219357 62 10 10.7028812483942 -0.7028812483942 63 12 10.3626047608500 1.63739523914996 64 13 10.2464703554095 2.75352964459050 65 10 8.59734393413137 1.40265606586863 66 11 12.1719948752339 -1.17199487523389 67 8 12.6562815983288 -4.6562815983288 68 9 10.3986073197377 -1.39860731973773 69 13 8.44520696980313 4.55479303019687 70 11 10.5867468429537 0.413253157046347 71 8 12.0558604697933 -4.05586046979334 72 9 10.3626047608500 -1.36260476085004 73 9 12.5041446340006 -3.50414463400056 74 15 12.3880102285600 2.61198977143998 75 9 11.6435788644738 -2.64357886447381 76 10 11.1511654126014 -1.15116541260142 77 14 9.19776506266682 4.80223493733318 78 12 10.8108889250573 1.18911107494274 79 12 10.3986073197377 1.60139268026227 80 11 12.0198579109057 -1.01985791090566 81 14 11.2231705303768 2.77682946962320 82 6 10.2104677965218 -4.21046779652181 83 12 10.7748863661696 1.22511363383042 84 8 10.6587519607290 -2.65875196072903 85 14 11.0431577359384 2.95684226406164 86 11 10.7388838072819 0.261116192718113 87 10 10.6668786895065 -0.666878689506512 88 14 9.64604922687404 4.35395077312596 89 12 12.3078783820072 -0.307878382007158 90 10 10.3626047608500 -0.362604760850043 91 14 11.7155839822492 2.28441601775081 92 5 8.63334649301905 -3.63334649301905 93 11 9.7261810734269 1.2738189265731 94 10 10.8910207716101 -0.891020771610122 95 9 10.4706124375131 -1.47061243751311 96 10 12.8002918338795 -2.80029183387955 97 16 12.6922841572165 3.30771584278351 98 13 12.4240127874477 0.575987212552295 99 9 10.3626047608500 -1.36260476085004 100 10 10.9630258893855 -0.963025889385498 101 10 11.2231705303768 -1.22317053037680 102 7 9.57404410909867 -2.57404410909867 103 9 10.6587519607290 -1.65875196072903 104 8 10.2824729142972 -2.28247291429718 105 14 11.2231705303768 2.77682946962320 106 14 11.4194367823702 2.5805632176298 107 8 10.7388838072819 -2.73888380728189 108 9 11.4113100535927 -2.41131005359272 109 14 11.6354521356963 2.36454786430367 110 14 9.95032315553051 4.04967684446949 111 8 9.23376762155451 -1.23376762155451 112 8 12.2358732642318 -4.23587326423178 113 8 10.8828940428326 -2.88289404283264 114 7 11.6354521356963 -4.63545213569633 115 6 8.62521976424157 -2.62521976424157 116 8 9.7261810734269 -1.7261810734269 117 6 10.3986073197377 -4.39860731973773 118 11 9.95032315553051 1.04967684446949 119 14 11.5634470179210 2.43655298207905 120 11 10.4427366074029 0.557263392597099 121 11 12.1359923163462 -1.13599231634620 122 11 9.42190714477043 1.57809285522957 123 14 11.0710335660486 2.92896643395144 124 8 9.57404410909866 -1.57404410909867 125 20 10.3626047608500 9.63739523914996 126 11 10.5867468429537 0.413253157046347 127 8 9.50203899132329 -1.50203899132329 128 11 10.5867468429537 0.413253157046347 129 10 10.2464703554095 -0.246470355409496 130 14 13.0325606447606 0.967439355239358 131 11 11.0710335660486 -0.071033566048561 132 9 9.83418875008996 -0.834188750089964 133 9 9.91432059664282 -0.914320596642822 134 8 9.69017851453921 -1.69017851453921 135 10 10.7748863661696 -0.774886366169575 136 13 11.7875891000246 1.21241089997544 137 13 10.1384626787464 2.86153732125357 138 12 10.2464703554095 1.75352964459050 139 8 10.0583308321936 -2.05833083219357 140 13 11.1430386838239 1.85696131617606 141 14 12.5041446340006 1.49585536599944 142 12 12.5401471928883 -0.540147192888252 143 14 11.7713356424696 2.22866435753040 144 15 10.6668786895065 4.33312131049349 145 13 10.8828940428326 2.11710595716736 146 16 12.2079974341216 3.79200256587842 147 9 12.6922841572165 -3.69228415721649 148 9 10.5507442840660 -1.55074428406596 149 9 9.87019130897765 -0.870191308977652 150 8 11.0350310071609 -3.03503100716087 151 7 10.6227494018413 -3.62274940184134 152 16 12.0918630286810 3.90813697131897 153 11 13.9372557019526 -2.93725570195257 154 9 10.8910207716101 -1.89102077161012 155 11 10.7667596373921 0.233240362607908 156 9 9.95032315553051 -0.95032315553051 157 14 12.0918630286810 1.90813697131897 158 13 11.0350310071609 1.96496899283913 159 16 12.9443020694303 3.0556979305697 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.676015735405692 0.647968529188615 0.323984264594308 7 0.537490783073278 0.925018433853444 0.462509216926722 8 0.427046314707035 0.85409262941407 0.572953685292965 9 0.844236157587574 0.311527684824853 0.155763842412426 10 0.774585478992766 0.450829042014468 0.225414521007234 11 0.692147496418243 0.615705007163515 0.307852503581757 12 0.622993756952284 0.754012486095432 0.377006243047716 13 0.688460262148796 0.623079475702409 0.311539737851204 14 0.627675250139888 0.744649499720224 0.372324749860112 15 0.547592206540966 0.904815586918068 0.452407793459034 16 0.706971386993174 0.586057226013651 0.293028613006826 17 0.673786634421644 0.652426731156711 0.326213365578356 18 0.624905839568564 0.750188320862873 0.375094160431436 19 0.594631138338985 0.81073772332203 0.405368861661015 20 0.526838960576166 0.946322078847668 0.473161039423834 21 0.537647116404694 0.924705767190612 0.462352883595306 22 0.486654117596912 0.973308235193824 0.513345882403088 23 0.49331763998202 0.98663527996404 0.50668236001798 24 0.428731601355173 0.857463202710346 0.571268398644827 25 0.370230162287577 0.740460324575155 0.629769837712423 26 0.328041586936697 0.656083173873395 0.671958413063303 27 0.283761244625065 0.567522489250131 0.716238755374935 28 0.257701942726294 0.515403885452587 0.742298057273706 29 0.240536644228678 0.481073288457356 0.759463355771322 30 0.195675832169894 0.391351664339788 0.804324167830106 31 0.164093206613762 0.328186413227524 0.835906793386238 32 0.177419134364971 0.354838268729941 0.82258086563503 33 0.141288972869599 0.282577945739197 0.858711027130401 34 0.170214862840018 0.340429725680036 0.829785137159982 35 0.138445360948742 0.276890721897485 0.861554639051258 36 0.155325988861342 0.310651977722683 0.844674011138658 37 0.152251850268897 0.304503700537793 0.847748149731103 38 0.578219652348954 0.843560695302092 0.421780347651046 39 0.548481060531679 0.903037878936641 0.451518939468321 40 0.497560850915116 0.995121701830233 0.502439149084884 41 0.458263044799677 0.916526089599353 0.541736955200323 42 0.438571069056212 0.877142138112424 0.561428930943788 43 0.387216801138181 0.774433602276362 0.612783198861819 44 0.340338844072026 0.680677688144052 0.659661155927974 45 0.295315574104753 0.590631148209506 0.704684425895247 46 0.295414941639474 0.590829883278949 0.704585058360526 47 0.319048026775260 0.638096053550521 0.68095197322474 48 0.282406566576989 0.564813133153978 0.717593433423011 49 0.27684055908191 0.55368111816382 0.72315944091809 50 0.291562782631425 0.583125565262851 0.708437217368575 51 0.391031284994783 0.782062569989566 0.608968715005217 52 0.354029399762305 0.70805879952461 0.645970600237695 53 0.311542066955464 0.623084133910928 0.688457933044536 54 0.304222306265936 0.608444612531872 0.695777693734064 55 0.417576602152673 0.835153204305346 0.582423397847327 56 0.380295687751616 0.760591375503232 0.619704312248384 57 0.341368514731663 0.682737029463327 0.658631485268337 58 0.320262870163843 0.640525740327685 0.679737129836157 59 0.297240119335628 0.594480238671256 0.702759880664372 60 0.473149245182983 0.946298490365966 0.526850754817017 61 0.432844258564787 0.865688517129574 0.567155741435213 62 0.390334480374396 0.780668960748793 0.609665519625604 63 0.363647480390274 0.727294960780547 0.636352519609726 64 0.370518121678395 0.74103624335679 0.629481878321605 65 0.341049815725505 0.682099631451011 0.658950184274495 66 0.309914197553446 0.619828395106892 0.690085802446554 67 0.407929242234361 0.815858484468721 0.59207075776564 68 0.375875112127071 0.751750224254142 0.624124887872929 69 0.466724714320231 0.933449428640462 0.533275285679769 70 0.422017921647918 0.844035843295836 0.577982078352082 71 0.485340189865329 0.970680379730657 0.514659810134671 72 0.451868582187262 0.903737164374524 0.548131417812738 73 0.487560917131662 0.975121834263324 0.512439082868338 74 0.488544992218469 0.977089984436938 0.511455007781531 75 0.489850582208347 0.979701164416694 0.510149417791653 76 0.453104993849791 0.906209987699583 0.546895006150209 77 0.564188815293619 0.871622369412762 0.435811184706381 78 0.52813450847177 0.94373098305646 0.47186549152823 79 0.500023272471764 0.999953455056471 0.499976727528236 80 0.463395382948863 0.926790765897726 0.536604617051137 81 0.469165255435197 0.938330510870395 0.530834744564803 82 0.542427292747093 0.915145414505813 0.457572707252907 83 0.506716559803358 0.986566880393285 0.493283440196643 84 0.508196495717925 0.98360700856415 0.491803504282075 85 0.520114492833342 0.959771014333317 0.479885507166658 86 0.474595449638849 0.949190899277699 0.525404550361151 87 0.431994796712319 0.863989593424639 0.56800520328768 88 0.520919518040927 0.958160963918146 0.479080481959073 89 0.475994826538085 0.95198965307617 0.524005173461915 90 0.430985483865875 0.86197096773175 0.569014516134125 91 0.418969088301951 0.837938176603901 0.581030911698049 92 0.454854724688636 0.909709449377272 0.545145275311364 93 0.421905902043774 0.843811804087548 0.578094097956226 94 0.381894513815368 0.763789027630736 0.618105486184632 95 0.350705529006161 0.701411058012321 0.649294470993839 96 0.364441814123083 0.728883628246166 0.635558185876917 97 0.383831119000707 0.767662238001413 0.616168880999293 98 0.341274882567344 0.682549765134687 0.658725117432656 99 0.309207984244069 0.618415968488138 0.690792015755931 100 0.274057282927075 0.548114565854149 0.725942717072925 101 0.244382194637986 0.488764389275972 0.755617805362014 102 0.239700055309996 0.479400110619991 0.760299944690004 103 0.217735518543598 0.435471037087195 0.782264481456402 104 0.208404672967955 0.41680934593591 0.791595327032045 105 0.209971208425607 0.419942416851213 0.790028791574393 106 0.206544551296912 0.413089102593825 0.793455448703087 107 0.2089797150264 0.4179594300528 0.7910202849736 108 0.205183741105969 0.410367482211939 0.79481625889403 109 0.195420063624530 0.390840127249059 0.80457993637547 110 0.246413280781385 0.492826561562769 0.753586719218615 111 0.214929506438218 0.429859012876436 0.785070493561782 112 0.289416388348718 0.578832776697436 0.710583611651282 113 0.303816936683459 0.607633873366918 0.696183063316541 114 0.431225873955935 0.86245174791187 0.568774126044065 115 0.434918374806555 0.86983674961311 0.565081625193445 116 0.404392654980714 0.808785309961428 0.595607345019286 117 0.519438178853705 0.96112364229259 0.480561821146295 118 0.473141337592759 0.946282675185518 0.526858662407241 119 0.453981833089306 0.907963666178611 0.546018166910694 120 0.404147601538977 0.808295203077954 0.595852398461023 121 0.362418450306584 0.724836900613167 0.637581549693417 122 0.327945016806353 0.655890033612705 0.672054983193647 123 0.322867857372479 0.645735714744958 0.677132142627521 124 0.291599575768998 0.583199151537997 0.708400424231002 125 0.912630390084778 0.174739219830444 0.0873696099152222 126 0.887101075141603 0.225797849716794 0.112898924858397 127 0.860582517653812 0.278834964692377 0.139417482346188 128 0.824728096361451 0.350543807277098 0.175271903638549 129 0.782452145856885 0.43509570828623 0.217547854143115 130 0.736534849967485 0.52693030006503 0.263465150032515 131 0.684753949857786 0.630492100284428 0.315246050142214 132 0.631406660239183 0.737186679521633 0.368593339760817 133 0.572667099273734 0.854665801452533 0.427332900726266 134 0.526784425827209 0.946431148345582 0.473215574172791 135 0.470244852550434 0.940489705100869 0.529755147449566 136 0.409673093934802 0.819346187869603 0.590326906065198 137 0.426693676153266 0.853387352306533 0.573306323846734 138 0.388310253255828 0.776620506511655 0.611689746744172 139 0.360405318173725 0.72081063634745 0.639594681826275 140 0.308539953870221 0.617079907740441 0.69146004612978 141 0.257525556519420 0.515051113038839 0.74247444348058 142 0.205842067838117 0.411684135676235 0.794157932161883 143 0.16301230499771 0.32602460999542 0.83698769500229 144 0.294201302018439 0.588402604036878 0.705798697981561 145 0.262809853478983 0.525619706957966 0.737190146521017 146 0.432975959894018 0.865951919788036 0.567024040105982 147 0.513484136514788 0.973031726970423 0.486515863485212 148 0.414214882617909 0.828429765235818 0.585785117382091 149 0.313478802853661 0.626957605707322 0.686521197146339 150 0.343871622866245 0.68774324573249 0.656128377133755 151 0.47922912840088 0.95845825680176 0.52077087159912 152 0.72940887490719 0.54118225018562 0.27059112509281 153 0.844870750084626 0.310258499830747 0.155129249915374 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 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/10fvur1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/10fvur1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/1qcxx1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/1qcxx1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/2qcxx1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/2qcxx1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/3qcxx1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/3qcxx1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/413xi1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/413xi1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/513xi1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/513xi1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/613xi1290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/613xi1290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/7uue31290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/7uue31290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/84lv61290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/84lv61290595452.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/94lv61290595452.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t129059541509outp55uv9cse8/94lv61290595452.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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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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