*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 03 Dec 2010 11:23:31 +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/03/t12913754826l3plk68k3javsb.htm/, Retrieved Fri, 03 Dec 2010 12:24:53 +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/03/t12913754826l3plk68k3javsb.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 «

4 4 5 4 4 4 4 4 4 4 3 4 5 5 4 4 5 5 3 3 2 3 4 4 2 3 2 3 2 4 5 4 3 3 4 5 4 3 3 3 3 4 2 3 4 4 2 4 4 4 3 4 4 5 4 3 2 3 2 2 4 3 2 4 4 4 2 3 2 4 2 3 5 4 2 5 5 5 3 4 2 3 3 4 4 3 4 4 4 4 4 3 3 4 4 5 3 2 3 3 3 3 4 4 4 4 4 4 2 3 2 2 2 4 4 2 4 4 3 4 3 3 2 4 4 4 3 2 4 4 2 3 4 4 2 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 3 4 5 4 4 4 4 4 4 1 4 4 4 4 4 4 2 4 4 4 4 4 2 4 4 4 4 3 4 3 2 4 4 3 2 4 4 4 4 4 5 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 5 3 2 3 3 5 4 4 2 4 4 4 4 3 3 3 3 4 4 4 3 4 3 4 3 3 4 4 3 3 4 4 4 4 3 4 2 3 2 3 2 3 2 2 4 2 2 5 4 3 4 4 4 5 4 4 4 4 2 4 5 4 4 4 4 5 4 3 2 4 4 4 4 3 3 4 3 4 4 4 2 4 4 4 5 4 2 4 4 4 3 3 4 3 3 4 2 2 4 2 1 4 4 4 4 4 4 4 4 4 3 4 4 4 2 3 4 4 2 4 2 2 5 2 2 4 4 4 4 4 4 4 4 3 4 4 4 4 4 3 4 4 3 4 3 4 4 4 3 4 2 3 2 3 1 4 4 4 4 4 4 4 5 3 4 4 2 4 4 4 3 4 4 4 5 4 4 5 5 5 4 4 2 4 3 4 3 3 2 3 3 4 3 3 2 3 2 3 4 3 4 4 4 4 3 4 4 3 2 4 2 3 3 3 2 2 4 2 2 2 2 4 3 4 2 4 4 5 5 4 2 4 5 4 5 4 5 4 4 5 4 3 4 2 2 3 5 5 4 4 5 4 4 3 2 4 2 4 3 2 2 3 3 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 18 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = -0.377574463704221 + 0.134562581071375x1[t] + 0.0510098609463206x2[t] + 0.336315636002047x3[t] + 0.272305484877694x4[t] + 0.330922737595275x5[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) -0.377574463704221 0.431842 -0.8743 0.383382 0.191691 x1 0.134562581071375 0.091901 1.4642 0.145301 0.072651 x2 0.0510098609463206 0.061331 0.8317 0.406935 0.203467 x3 0.336315636002047 0.089729 3.7481 0.000257 0.000128 x4 0.272305484877694 0.0705 3.8625 0.000169 8.4e-05 x5 0.330922737595275 0.096183 3.4405 0.000759 0.000379 Multiple Linear Regression - Regression Statistics Multiple R 0.66880462193062 R-squared 0.447299622315759 Adjusted R-squared 0.428240988602509 F-TEST (value) 23.4696583735062 F-TEST (DF numerator) 5 F-TEST (DF denominator) 145 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.674861643367005 Sum Squared Residuals 66.0385444647621 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.17390059921299 -0.173900599212986 2 4 3.85058525338894 0.149414746611058 3 5 4.86068154181098 0.139318458189023 4 3 3.54999279930057 -0.549992799300572 5 2 3.00538182954518 -1.00538182954518 6 5 4.06648797891354 0.933512021086462 7 4 3.32869717536919 0.671302824630807 8 2 3.44371718743986 -1.44371718743986 9 4 4.40280361491558 -0.402803614915584 10 4 2.34353635435463 1.65646364564537 11 4 3.88630843530261 0.113691564697388 12 2 3.01077472795195 -1.01077472795195 13 5 4.960414874849 0.0395851251509964 14 3 3.41224989549425 -0.412249895494248 15 4 3.98832815719525 0.0116718428047465 16 4 4.26824103384421 -0.268241033844208 17 3 2.86321185670254 0.136788143297459 18 4 4.12289073826663 -0.122890738266630 19 2 2.66906619354313 -0.669066193543132 20 4 3.58146009124618 0.418539908753817 21 3 3.88630843530261 -0.886308435302612 22 3 2.97823186877321 0.0217681312267863 23 4 4.02087101637399 -0.0208710163739883 24 4 4.07188087732031 -0.071880877320309 25 4 4.12289073826663 -0.122890738266630 26 4 3.66501281137124 0.334987188628761 27 5 4.12289073826663 0.87710926173337 28 4 3.7192029950525 0.280797004947499 29 4 4.02087101637399 -0.0208710163739883 30 4 4.02087101637399 -0.0208710163739883 31 4 3.10740155143782 0.892598448562181 32 4 3.88630843530261 0.113691564697388 33 4 4.50482333680823 -0.504823336808225 34 4 4.12289073826663 -0.122890738266630 35 4 4.12289073826663 -0.122890738266630 36 5 3.60861005201815 1.39138994798185 37 4 4.02087101637399 -0.0208710163739883 38 4 3.32869717536919 0.671302824630807 39 4 3.79957539244261 0.200424607557385 40 3 3.38509993472228 -0.385099934722284 41 4 3.85058525338894 0.149414746611064 42 2 2.6744590919499 -0.674459091949903 43 2 2.96744607195967 -0.967446071959672 44 4 4.31925089479053 -0.319250894790529 45 4 3.57827976851124 0.421720231488759 46 5 4.45381347586190 0.546186524138095 47 4 3.88630843530261 0.113691564697388 48 4 3.66501281137124 0.334987188628761 49 4 4.02087101637399 -0.0208710163739883 50 5 4.02087101637399 0.979128983626011 51 3 3.37970703631551 -0.379707036315513 52 2 2.36421784948670 -0.364217849486703 53 4 4.12289073826663 -0.122890738266630 54 4 4.07188087732031 -0.071880877320309 55 2 3.44371718743986 -1.44371718743986 56 2 2.68753319531072 -0.687533195310717 57 4 4.12289073826663 -0.122890738266630 58 4 3.98832815719525 0.0116718428047465 59 4 3.71602267231756 0.283977327682441 60 3 3.85058525338894 -0.850585253388936 61 2 2.73307634466748 -0.733076344667483 62 4 4.12289073826663 -0.122890738266630 63 5 3.44371718743986 1.55628281256014 64 4 4.07188087732031 -0.071880877320309 65 5 5.06243459674165 -0.062434596741645 66 4 3.74856553149629 0.251434468503706 67 3 3.27768731442287 -0.277687314422872 68 3 2.6744590919499 0.325540908050097 69 4 3.98832815719525 0.0116718428047465 70 3 3.24196413250920 -0.241964132509195 71 2 2.39454621530095 -0.394546215300948 72 4 2.53450361247176 1.46549638752824 73 3 4.35179375396926 -1.35179375396926 74 5 4.29317650125168 0.706823498748317 75 5 4.50482333680823 0.495176663191774 76 4 2.4401631778405 1.55983682215950 77 5 4.5297588042157 0.4702411957843 78 4 3.34169746554722 0.658302534452776 79 3 2.81220199575622 0.187798004243779 80 3 3.65201252119321 -0.652012521193208 81 4 3.37970703631551 0.620292963684487 82 4 3.57827976851124 0.421720231488759 83 3 3.51426961738689 -0.51426961738689 84 4 3.54999279930057 0.450007200699434 85 3 2.26219812759406 0.737801872405939 86 3 3.90920250610652 -0.909202506106516 87 3 3.52726990756492 -0.52726990756492 88 2 2.94137167842083 -0.941371678420826 89 5 3.74856553149629 1.25143446850371 90 3 3.10740155143782 -0.107401551437819 91 4 2.96744607195967 1.03255392804033 92 4 3.93731829624893 0.0626817037510672 93 3 3.37970703631551 -0.379707036315513 94 3 2.99777443777392 0.00222556222608242 95 4 3.73556524131826 0.264434758681737 96 4 4.45920637426868 -0.459206374268676 97 3 3.57827976851124 -0.578279768511241 98 3 3.10200865303105 -0.102008653031048 99 4 4.45381347586190 -0.453813475861905 100 2 3.46325975644057 -1.46325975644057 101 4 2.77108591543577 1.22891408456423 102 4 4.35179375396926 -0.351793753969263 103 4 3.99593554896651 0.00406445103348649 104 5 3.51426961738689 1.48573038261311 105 5 4.40280361491558 0.597196385084416 106 5 3.66501281137124 1.33498718862876 107 4 3.88630843530261 0.113691564697388 108 4 3.61400295042492 0.385997049575082 109 3 3.61400295042492 -0.614002950424918 110 2 2.95215747523437 -0.952157475234368 111 2 2.6365233343644 -0.636523334364397 112 4 3.80718278421387 0.192817215786125 113 2 2.64952362454243 -0.649523624542428 114 3 3.10740155143782 -0.107401551437819 115 4 3.66501281137124 0.334987188628761 116 4 3.32869717536919 0.671302824630807 117 4 3.85058525338894 0.149414746611064 118 4 3.13233701884529 0.867662981154706 119 3 3.00538182954518 -0.00538182954517756 120 4 4.07188087732031 -0.071880877320309 121 3 2.6744590919499 0.325540908050097 122 4 3.66501281137124 0.334987188628761 123 4 3.71062977391079 0.289370226089212 124 4 4.40280361491558 -0.402803614915584 125 2 2.52689622070050 -0.526896220700495 126 5 3.84519235498216 1.15480764501784 127 5 3.61400295042492 1.38599704957508 128 3 3.54999279930057 -0.549992799300566 129 3 3.74095813972503 -0.740958139725034 130 3 3.13233701884529 -0.132337018845294 131 4 4.07188087732031 -0.071880877320309 132 3 3.63361933260841 -0.633619332608406 133 2 1.97467785917385 0.0253221408261531 134 5 4.12289073826663 0.87710926173337 135 4 3.85376557612388 0.146234423876123 136 2 3.32869717536919 -1.32869717536919 137 4 4.18150799098421 -0.181507990984211 138 3 3.93731829624893 -0.937318296248933 139 2 2.94137167842083 -0.941371678420826 140 3 3.44371718743986 -0.443717187439865 141 3 3.98832815719525 -0.988328157195254 142 4 4.12289073826663 -0.122890738266630 143 4 3.88630843530261 0.113691564697388 144 4 4.04694540991283 -0.0469454099128343 145 2 2.74819184463187 -0.748191844631869 146 5 3.85376557612388 1.14623442387612 147 4 3.60100266024689 0.398997339753113 148 4 4.02087101637399 -0.0208710163739883 149 3 3.32869717536919 -0.328697175369193 150 3 3.74856553149629 -0.748565531496294 151 5 4.97888187661659 0.0211181233834108 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.622871122561292 0.754257754877417 0.377128877438709 10 0.699257298745655 0.601485402508691 0.300742701254345 11 0.773975133948668 0.452049732102663 0.226024866051332 12 0.746136225078931 0.507727549842138 0.253863774921069 13 0.754504423376951 0.490991153246098 0.245495576623049 14 0.780690095347543 0.438619809304914 0.219309904652457 15 0.700318025846144 0.599363948307711 0.299681974153856 16 0.64846550975354 0.70306898049292 0.35153449024646 17 0.570291694093831 0.859416611812338 0.429708305906169 18 0.507160164017797 0.985679671964406 0.492839835982203 19 0.460518594956866 0.921037189913732 0.539481405043134 20 0.542462212656561 0.915075574686878 0.457537787343439 21 0.59883817603314 0.80232364793372 0.40116182396686 22 0.536048620252424 0.927902759495152 0.463951379747576 23 0.460627140547107 0.921254281094213 0.539372859452893 24 0.392304264909782 0.784608529819563 0.607695735090218 25 0.340008019925463 0.680016039850925 0.659991980074537 26 0.346959450856732 0.693918901713465 0.653040549143268 27 0.351204144541816 0.702408289083633 0.648795855458184 28 0.291585606919879 0.583171213839757 0.708414393080121 29 0.236359056556522 0.472718113113044 0.763640943443478 30 0.188012972936943 0.376025945873887 0.811987027063057 31 0.275366254673022 0.550732509346044 0.724633745326978 32 0.22967498209126 0.45934996418252 0.77032501790874 33 0.208712900413570 0.417425800827141 0.79128709958643 34 0.177498277754374 0.354996555508748 0.822501722245626 35 0.148054125880101 0.296108251760201 0.8519458741199 36 0.394959869234456 0.789919738468912 0.605040130765544 37 0.339675498579513 0.679350997159026 0.660324501420487 38 0.316933966114869 0.633867932229738 0.683066033885131 39 0.286314548923521 0.572629097847042 0.713685451076479 40 0.259241190737361 0.518482381474721 0.740758809262639 41 0.223036088562334 0.446072177124669 0.776963911437666 42 0.227714369228471 0.455428738456942 0.77228563077153 43 0.291005218896122 0.582010437792244 0.708994781103878 44 0.25090818395845 0.5018163679169 0.74909181604155 45 0.255703334735448 0.511406669470896 0.744296665264552 46 0.246176370630193 0.492352741260386 0.753823629369807 47 0.207072210664389 0.414144421328778 0.79292778933561 48 0.185958919319355 0.371917838638709 0.814041080680645 49 0.152522846235174 0.305045692470347 0.847477153764826 50 0.185558746873597 0.371117493747195 0.814441253126403 51 0.166284139267588 0.332568278535176 0.833715860732412 52 0.140619156221054 0.281238312442108 0.859380843778946 53 0.116617830867788 0.233235661735575 0.883382169132212 54 0.0944173912779607 0.188834782555921 0.90558260872204 55 0.160807975485153 0.321615950970307 0.839192024514847 56 0.163305809984068 0.326611619968136 0.836694190015932 57 0.136389754894473 0.272779509788945 0.863610245105527 58 0.110625949184111 0.221251898368221 0.88937405081589 59 0.0962885000160055 0.192577000032011 0.903711499983994 60 0.104739422171841 0.209478844343683 0.895260577828159 61 0.097743947367106 0.195487894734212 0.902256052632894 62 0.0793058663109155 0.158611732621831 0.920694133689084 63 0.245756631549167 0.491513263098335 0.754243368450833 64 0.209897950455607 0.419795900911214 0.790102049544393 65 0.176642283877388 0.353284567754777 0.823357716122612 66 0.152145551010056 0.304291102020112 0.847854448989944 67 0.128907288744385 0.25781457748877 0.871092711255615 68 0.11021045054715 0.2204209010943 0.88978954945285 69 0.0889237504413444 0.177847500882689 0.911076249558656 70 0.0725725969719455 0.145145193943891 0.927427403028054 71 0.0642921802372247 0.128584360474449 0.935707819762775 72 0.144730570273127 0.289461140546254 0.855269429726873 73 0.230543094207136 0.461086188414272 0.769456905792864 74 0.230119189204843 0.460238378409686 0.769880810795157 75 0.216374099399639 0.432748198799277 0.783625900600361 76 0.357059826347454 0.714119652694907 0.642940173652546 77 0.335787395004985 0.67157479000997 0.664212604995015 78 0.352199493930447 0.704398987860895 0.647800506069553 79 0.312387849360779 0.624775698721558 0.687612150639221 80 0.32017391239418 0.64034782478836 0.67982608760582 81 0.309766993290319 0.619533986580639 0.69023300670968 82 0.289794966815046 0.579589933630092 0.710205033184954 83 0.273128958210655 0.54625791642131 0.726871041789345 84 0.251461186188479 0.502922372376958 0.748538813811521 85 0.258694583201476 0.517389166402953 0.741305416798524 86 0.291635449020187 0.583270898040375 0.708364550979813 87 0.276545413108937 0.553090826217873 0.723454586891063 88 0.317836359485684 0.635672718971367 0.682163640514317 89 0.436235594329587 0.872471188659174 0.563764405670413 90 0.391725574969366 0.783451149938733 0.608274425030634 91 0.447669993704599 0.895339987409197 0.552330006295401 92 0.400694005562742 0.801388011125485 0.599305994437258 93 0.370126357517414 0.740252715034828 0.629873642482586 94 0.327030332087733 0.654060664175465 0.672969667912267 95 0.293423456024596 0.586846912049192 0.706576543975404 96 0.275647721584822 0.551295443169645 0.724352278415178 97 0.283395717350284 0.566791434700569 0.716604282649716 98 0.244364066522229 0.488728133044458 0.755635933477771 99 0.230792353352420 0.461584706704839 0.76920764664758 100 0.406862075422453 0.813724150844906 0.593137924577547 101 0.505924454010173 0.988151091979655 0.494075545989827 102 0.46716016386319 0.93432032772638 0.53283983613681 103 0.417584726688242 0.835169453376484 0.582415273311758 104 0.595057059461622 0.809885881076755 0.404942940538378 105 0.578429378339288 0.843141243321425 0.421570621660712 106 0.724383829931213 0.551232340137575 0.275616170068787 107 0.68336704394789 0.633265912104221 0.316632956052111 108 0.659326785907293 0.681346428185415 0.340673214092707 109 0.639855310195112 0.720289379609775 0.360144689804888 110 0.681436620554469 0.637126758891062 0.318563379445531 111 0.663338668885203 0.673322662229594 0.336661331114797 112 0.614786971284004 0.770426057431991 0.385213028715996 113 0.624436536921387 0.751126926157226 0.375563463078613 114 0.577426301329159 0.845147397341681 0.422573698670841 115 0.528560778059842 0.942878443880316 0.471439221940158 116 0.537568526155266 0.924862947689467 0.462431473844734 117 0.478974028036779 0.957948056073558 0.521025971963221 118 0.553704618856142 0.892590762287716 0.446295381143858 119 0.492298755550039 0.984597511100077 0.507701244449961 120 0.431800599400765 0.86360119880153 0.568199400599235 121 0.401592822365193 0.803185644730385 0.598407177634807 122 0.354547936252085 0.70909587250417 0.645452063747915 123 0.306197777160525 0.61239555432105 0.693802222839475 124 0.263308522532820 0.526617045065641 0.73669147746718 125 0.224076638152746 0.448153276305491 0.775923361847255 126 0.406503574197925 0.813007148395849 0.593496425802075 127 0.744223702062177 0.511552595875646 0.255776297937823 128 0.688420812151832 0.623158375696336 0.311579187848168 129 0.720008229149283 0.559983541701435 0.279991770850717 130 0.651749150180826 0.696501699638349 0.348250849819174 131 0.574426780156198 0.851146439687605 0.425573219843802 132 0.508373046918126 0.983253906163748 0.491626953081874 133 0.444038709736349 0.888077419472698 0.555961290263651 134 0.588082812532794 0.823834374934412 0.411917187467206 135 0.49476124883644 0.98952249767288 0.50523875116356 136 0.559695188101687 0.880609623796625 0.440304811898313 137 0.4628541900963 0.9257083801926 0.5371458099037 138 0.540675740447357 0.918648519105287 0.459324259552643 139 0.460642210174210 0.921284420348419 0.53935778982579 140 0.338860717194898 0.677721434389797 0.661139282805102 141 0.496850782298951 0.993701564597903 0.503149217701049 142 0.335624696102007 0.671249392204014 0.664375303897993 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/Dec/03/t12913754826l3plk68k3javsb/10anlm1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/10anlm1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/1lmoa1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/1lmoa1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/2wvnd1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/2wvnd1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/3wvnd1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/3wvnd1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/4wvnd1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/4wvnd1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/564mg1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/564mg1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/664mg1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/664mg1291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/7hw411291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/7hw411291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/8hw411291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/8hw411291375391.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/9anlm1291375391.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913754826l3plk68k3javsb/9anlm1291375391.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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