WS7 - Multiple regression model

*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 15:49:33 +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/t1290528230dniycisyqzngiq1.htm/, Retrieved Tue, 23 Nov 2010 17:03:53 +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/Nov/23/t1290528230dniycisyqzngiq1.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 «

13 13 14 13 3 2 12 12 8 13 5 1 15 10 12 16 6 0 12 9 7 12 6 3 10 10 10 11 5 3 12 12 7 12 3 1 15 13 16 18 8 3 9 12 11 11 4 1 12 12 14 14 4 4 11 6 6 9 4 0 11 5 16 14 6 3 11 12 11 12 6 2 15 11 16 11 5 4 7 14 12 12 4 3 11 14 7 13 6 1 11 12 13 11 4 1 10 12 11 12 6 2 14 11 15 16 6 3 10 11 7 9 4 1 6 7 9 11 4 1 11 9 7 13 2 2 15 11 14 15 7 3 11 11 15 10 5 4 12 12 7 11 4 2 14 12 15 13 6 1 15 11 17 16 6 2 9 11 15 15 7 2 13 8 14 14 5 4 13 9 14 14 6 2 16 12 8 14 4 3 13 10 8 8 4 3 12 10 14 13 7 3 14 12 14 15 7 4 11 8 8 13 4 2 9 12 11 11 4 2 16 11 16 15 6 4 12 12 10 15 6 3 10 7 8 9 5 4 13 11 14 13 6 2 16 11 16 16 7 5 14 12 13 13 6 3 15 9 5 11 3 1 5 15 8 12 3 1 8 11 10 12 4 1 11 11 8 12 6 2 16 11 13 14 7 3 17 11 15 14 5 9 9 15 6 8 4 0 9 11 12 13 5 0 13 12 16 16 6 2 10 12 5 13 6 2 6 9 15 11 6 3 12 12 12 14 5 1 8 12 8 13 4 2 14 13 13 13 5 0 12 11 14 13 5 5 11 9 12 12 4 2 16 9 16 16 6 4 8 11 10 15 2 3 15 11 15 15 8 0 7 12 8 12 3 0 16 12 16 14 6 4 14 9 19 12 6 1 16 11 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.0342768235376161 + 0.106305539542869FindingFriends[t] + 0.21144283590659KnowingPeople[t] + 0.357652188002145Liked[t] + 0.60600258577461Celebrity[t] + 0.212600241949771Sum_friends[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) 0.0342768235376161 1.423283 0.0241 0.980818 0.490409 FindingFriends 0.106305539542869 0.095517 1.113 0.267509 0.133755 KnowingPeople 0.21144283590659 0.063626 3.3232 0.001118 0.000559 Liked 0.357652188002145 0.095931 3.7282 0.000273 0.000136 Celebrity 0.60600258577461 0.155396 3.8997 0.000145 7.2e-05 Sum_friends 0.212600241949771 0.12003 1.7712 0.078554 0.039277 Multiple Linear Regression - Regression Statistics Multiple R 0.713764528070818 R-squared 0.509459801532158 Adjusted R-squared 0.49310846158323 F-TEST (value) 31.1570674405529 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09077045674136 Sum Squared Residuals 655.69816541737 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.2691352255384 1.73086477446156 2 12 10.8935776001555 1.10642239984454 3 15 12.9930967725274 2.00690322747264 4 12 11.0367690272923 0.963230972707725 5 10 10.8137483007782 -0.813748300778158 6 12 9.11247740469751 2.88752259530249 7 15 16.7228950081851 -1.72289500818515 8 9 10.2065991460963 -1.20659914609633 9 12 12.5516849436718 -0.551684943671851 10 11 7.58364711135211 3.41635288864789 11 11 13.2298367682844 -2.2298367682844 12 11 11.9888567475975 -0.98885674759747 13 15 12.4013110977103 2.59868890228966 14 7 11.4135057329903 -4.41350573299035 15 11 11.5007484291092 -0.500748429109224 16 11 10.6294848179095 0.370515182090486 17 10 11.9888567475975 -1.98885674759747 18 14 14.3715315456393 -0.37153154563931 19 10 8.53921788692282 1.46078211307718 20 6 9.25218577656881 -3.25218577656881 21 11 8.75781063024621 2.24218936975379 22 15 14.4084391075052 0.591560892494814 23 11 11.8322160738016 -0.832216073801602 24 12 9.57342804441975 2.42657195558025 25 14 12.9796800372762 1.0203199627238 26 15 14.5818169755027 0.418183024497282 27 9 14.407281701462 -5.407281701462 28 13 12.732465371275 0.267534628725015 29 13 13.0195730126929 -0.0195730126929221 30 16 11.0704276862825 4.92957231371746 31 13 8.71190347918393 4.28809652081606 32 12 13.586829191958 -1.58682919195803 33 14 14.7273448889978 -0.727344888997826 34 11 10.0749530981592 0.92504690184085 35 9 10.4191993880461 -1.41919938804611 36 16 14.4379224354935 1.56207756450647 37 12 13.0629707176471 -1.06297071764709 38 10 9.56924187628185 0.430758123718145 39 13 12.8745319037765 0.125468096223485 40 16 15.6141774512201 0.385822548779949 41 14 12.9819948493626 1.01800515063743 42 15 8.01302292625358 6.98697707374642 43 5 9.6428368592327 -4.64283685923271 44 8 10.246502958649 -2.24650295864902 45 11 11.2482227003348 -0.248222700334833 46 16 13.8393440835965 2.16065591640355 47 17 14.325826035559 2.67417396444096 48 9 8.18274477923579 0.817255220764212 49 9 11.4204431622892 -2.42044316228918 50 13 14.476679679139 -1.476679679139 51 10 11.0778519201601 -1.07785192016008 52 6 12.3706595265428 -6.37065952654285 53 12 12.097001131784 -0.0970011317839686 54 8 10.5001752563306 -2.50017525633063 55 14 11.8444970772815 2.15550292271849 56 12 12.9063300438512 -0.906330043851218 57 11 10.6693777933262 0.330622206673767 58 16 14.5829635444099 1.41703645559007 59 8 10.5326548350058 -2.53265483500578 60 15 14.5880838033371 0.411916196662927 61 7 9.11131999865433 -2.11131999865433 62 16 14.1865757870343 1.81342421296575 63 14 13.1488825742718 0.85111742572819 64 16 13.377236037831 2.62276396216897 65 9 10.4319238475608 -1.43192384756085 66 14 12.1633920216382 1.83660797836182 67 11 13.2598285751234 -2.25982857512337 68 13 10.3244825762467 2.67551742375327 69 15 13.1945950913123 1.80540490868766 70 5 5.79379231622363 -0.793792316223628 71 15 12.9063300438512 2.09366995614878 72 13 12.5885925055377 0.411407494462274 73 11 12.4170534821838 -1.41705348218382 74 11 14.1988134419703 -3.19881344197029 75 12 12.77054117632 -0.770541176320009 76 12 13.4048805211757 -1.40488052117574 77 12 12.3360884510353 -0.336088451035269 78 12 11.9507701054165 0.0492298945835205 79 14 10.8578274443328 3.14217255566723 80 6 7.93737979501417 -1.93737979501417 81 7 9.71847999047212 -2.71847999047212 82 14 12.4117099080027 1.58829009199725 83 14 14.1612461157759 -0.161246115775902 84 10 11.1702430827371 -1.17024308273712 85 13 9.11479221678387 3.88520778321613 86 12 12.3066051230469 -0.306605123046929 87 9 9.32091315278132 -0.320913152781323 88 12 11.9242830281149 0.0757169718850501 89 16 14.80184145133 1.19815854866998 90 10 10.460260606642 -0.460260606641973 91 14 13.1017171241566 0.89828287584341 92 10 13.590993685824 -3.59099368582399 93 16 15.5078827488131 0.492117251186851 94 15 13.4037122779966 1.5962877220034 95 12 11.4891488642298 0.510851135770238 96 10 9.3596703964268 0.640329603573206 97 8 10.1222811445894 -2.12228114458937 98 8 8.71607881018586 -0.71607881018586 99 11 12.6649170753776 -1.66491707537759 100 13 12.5591091775494 0.440890822450614 101 16 15.6130200451769 0.38697995482313 102 16 14.9387877249044 1.06121227509559 103 14 15.4034377281858 -1.40343772818584 104 11 9.04723308375051 1.95276691624949 105 4 7.15683109806287 -3.15683109806287 106 14 14.7389336167413 -0.73893361674132 107 9 10.5284903411398 -1.52849034113982 108 14 15.2258845291864 -1.22588452918639 109 8 10.2494992093358 -2.24949920933583 110 8 10.6827945285774 -2.68279452857739 111 11 11.8843900526982 -0.88439005269823 112 12 13.1604604648793 -1.16046046487934 113 11 11.0755371080737 -0.0755371080737151 114 14 13.2720987414673 0.727901258532687 115 15 14.449511163237 0.55048883676298 116 16 13.4447843337284 2.55521566627157 117 16 12.913289147422 3.08671085257801 118 11 12.7851369918863 -1.78513699188628 119 14 14.1877331930774 -0.187733193077431 120 14 10.881988872412 3.11801112758803 121 12 11.5585468419068 0.441453158093245 122 14 12.5463630437627 1.45363695623729 123 8 10.8854610905415 -2.88546109054151 124 13 14.0814384906705 -1.08143849067053 125 16 13.9751329511277 2.02486704887234 126 12 10.6157438743947 1.38425612560534 127 16 15.4783994208248 0.521600579175191 128 12 12.7670797953264 -0.767079795326432 129 11 11.4614935437491 -0.461493543749085 130 4 6.00799725042713 -2.00799725042713 131 16 16.1162001466741 -0.116200146674122 132 15 12.6642464739131 2.33575352608689 133 10 11.3605315783873 -1.36053157838729 134 13 14.0185198189459 -1.01851981894586 135 15 13.1270467954149 1.87295320458506 136 12 10.4990178502874 1.50098214971255 137 14 13.656227169635 0.343772830364979 138 7 10.381134420137 -3.38113442013705 139 19 13.9075846552303 5.09241534476974 140 12 12.9450764503607 -0.945076450360723 141 12 11.8728121620907 0.127187837909297 142 13 13.3384896313215 -0.338489631321529 143 15 12.4165883518771 2.58341164812294 144 8 8.84468525889237 -0.844685258892367 145 12 10.9230609281438 1.07693907185619 146 10 10.7601143818466 -0.760114381846585 147 8 11.2512297881576 -3.25122978815761 148 10 14.6517017577584 -4.65170175775841 149 15 13.8676700055416 1.13232999445839 150 16 14.0600608351602 1.93993916483983 151 13 13.2702490596877 -0.270249059687717 152 16 15.0838396709568 0.916160329043211 153 9 9.82245988079266 -0.82245988079266 154 14 13.0606450684248 0.939354931575244 155 14 13.1546804416237 0.845319558376317 156 12 10.1738452409604 1.82615475903955 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.113043399422144 0.226086798844288 0.886956600577856 10 0.0501338279117774 0.100267655823555 0.949866172088223 11 0.0726791202759012 0.145358240551802 0.927320879724099 12 0.0362939892148771 0.0725879784297541 0.963706010785123 13 0.455723219571892 0.911446439143784 0.544276780428108 14 0.76911689565418 0.461766208691641 0.23088310434582 15 0.690843322338692 0.618313355322615 0.309156677661308 16 0.602492647173724 0.795014705652551 0.397507352826276 17 0.546776085151919 0.906447829696163 0.453223914848081 18 0.460483749436223 0.920967498872446 0.539516250563777 19 0.383961884720282 0.767923769440565 0.616038115279718 20 0.68164899956003 0.636702000879942 0.318351000439971 21 0.622480475370068 0.755039049259865 0.377519524629932 22 0.591384359560493 0.817231280879015 0.408615640439507 23 0.521722083868099 0.956555832263803 0.478277916131901 24 0.50547172423208 0.98905655153584 0.49452827576792 25 0.466600374283114 0.933200748566228 0.533399625716886 26 0.405702343192012 0.811404686384024 0.594297656807988 27 0.665652538596127 0.668694922807747 0.334347461403873 28 0.609240659024031 0.781518681951937 0.390759340975969 29 0.548217805706858 0.903564388586284 0.451782194293142 30 0.696729243596923 0.606541512806154 0.303270756403077 31 0.796779695025199 0.406440609949603 0.203220304974802 32 0.759015830700384 0.481968338599232 0.240984169299616 33 0.712632486930885 0.57473502613823 0.287367513069115 34 0.67086217908285 0.658275641834299 0.329137820917149 35 0.66048546817378 0.67902906365244 0.33951453182622 36 0.662086475116606 0.675827049766787 0.337913524883394 37 0.631567039740652 0.736865920518696 0.368432960259348 38 0.581458293971187 0.837083412057626 0.418541706028813 39 0.534260918670244 0.931478162659511 0.465739081329756 40 0.493752920990991 0.987505841981982 0.506247079009009 41 0.461026226065897 0.922052452131794 0.538973773934103 42 0.786974579954075 0.42605084009185 0.213025420045925 43 0.94415076412768 0.111698471744639 0.0558492358723195 44 0.950160257918895 0.0996794841622105 0.0498397420811053 45 0.936085569397634 0.127828861204731 0.0639144306023655 46 0.942926136853231 0.114147726293538 0.0570738631467692 47 0.941015504220451 0.117968991559097 0.0589844957795486 48 0.928614456995934 0.142771086008132 0.0713855430040661 49 0.928216744769152 0.143566510461695 0.0717832552308476 50 0.917211581742263 0.165576836515474 0.0827884182577368 51 0.911008943171921 0.177982113656157 0.0889910568280787 52 0.988136800506383 0.0237263989872342 0.0118631994936171 53 0.983915640787094 0.0321687184258114 0.0160843592129057 54 0.989114188181053 0.0217716236378932 0.0108858118189466 55 0.991604992732137 0.0167900145357254 0.00839500726786271 56 0.98927481761204 0.0214503647759218 0.0107251823879609 57 0.98551004684779 0.028979906304421 0.0144899531522105 58 0.983099824833785 0.0338003503324294 0.0169001751662147 59 0.989731760158277 0.020536479683445 0.0102682398417225 60 0.987916792330477 0.0241664153390459 0.0120832076695229 61 0.988395472840583 0.023209054318833 0.0116045271594165 62 0.988181561011165 0.023636877977669 0.0118184389888345 63 0.986195084184615 0.0276098316307691 0.0138049158153845 64 0.988838717434339 0.0223225651313222 0.0111612825656611 65 0.987927903805505 0.0241441923889899 0.012072096194495 66 0.987047186436876 0.0259056271262487 0.0129528135631243 67 0.987689908526173 0.0246201829476533 0.0123100914738266 68 0.990035502882632 0.0199289942347355 0.00996449711736776 69 0.989337132793422 0.0213257344131553 0.0106628672065776 70 0.986218965835914 0.027562068328172 0.013781034164086 71 0.986490148403316 0.0270197031933688 0.0135098515966844 72 0.98204295712047 0.0359140857590597 0.0179570428795299 73 0.979098961086386 0.0418020778272283 0.0209010389136141 74 0.98622213946454 0.0275557210709193 0.0137778605354597 75 0.982088938972488 0.0358221220550232 0.0179110610275116 76 0.979375419819198 0.0412491603616041 0.0206245801808021 77 0.973063896771346 0.0538722064573072 0.0269361032286536 78 0.964812546686529 0.0703749066269421 0.0351874533134711 79 0.976797177525917 0.0464056449481659 0.023202822474083 80 0.975833657037132 0.0483326859257354 0.0241663429628677 81 0.979696646575212 0.0406067068495758 0.0203033534247879 82 0.978950843585816 0.0420983128283686 0.0210491564141843 83 0.972115647307748 0.055768705384504 0.027884352692252 84 0.966159185542055 0.0676816289158905 0.0338408144579453 85 0.988749360656196 0.0225012786876072 0.0112506393438036 86 0.985000968457257 0.0299980630854861 0.014999031542743 87 0.980084627098881 0.0398307458022372 0.0199153729011186 88 0.974186201770184 0.0516275964596329 0.0258137982298164 89 0.968542688000701 0.0629146239985974 0.0314573119992987 90 0.959702745600729 0.080594508798542 0.040297254399271 91 0.951827757817031 0.0963444843659377 0.0481722421829689 92 0.972877397905895 0.0542452041882104 0.0271226020941052 93 0.964832510425725 0.070334979148549 0.0351674895742745 94 0.960013484371968 0.0799730312560634 0.0399865156280317 95 0.94984346280624 0.100313074387521 0.0501565371937603 96 0.937707896342723 0.124584207314554 0.0622921036572768 97 0.932666328999002 0.134667342001996 0.0673336710009978 98 0.91641256679677 0.167174866406459 0.0835874332032297 99 0.911165381803443 0.177669236393115 0.0888346181965573 100 0.891111336645835 0.21777732670833 0.108888663354165 101 0.866946162597843 0.266107674804314 0.133053837402157 102 0.843851140390289 0.312297719219423 0.156148859609711 103 0.85640739909792 0.287185201804162 0.143592600902081 104 0.897096078383827 0.205807843232346 0.102903921616173 105 0.899191487777781 0.201617024444439 0.100808512222219 106 0.876914501482186 0.246170997035628 0.123085498517814 107 0.856253129727055 0.28749374054589 0.143746870272945 108 0.85173782760369 0.29652434479262 0.14826217239631 109 0.849240676022668 0.301518647954664 0.150759323977332 110 0.873884020699292 0.252231958601416 0.126115979300708 111 0.862099121874637 0.275801756250726 0.137900878125363 112 0.902424696230432 0.195150607539136 0.0975753037695679 113 0.876528722266006 0.246942555467988 0.123471277733994 114 0.848691047338282 0.302617905323436 0.151308952661718 115 0.813930187457868 0.372139625084263 0.186069812542132 116 0.812809256857318 0.374381486285364 0.187190743142682 117 0.82538322419032 0.34923355161936 0.17461677580968 118 0.814932503182843 0.370134993634313 0.185067496817156 119 0.77335508183685 0.453289836326301 0.226644918163151 120 0.834561940220552 0.330876119558896 0.165438059779448 121 0.804605728069574 0.390788543860852 0.195394271930426 122 0.777411502658301 0.445176994683398 0.222588497341699 123 0.775776866225367 0.448446267549266 0.224223133774633 124 0.734242845611248 0.531514308777504 0.265757154388752 125 0.730358805270345 0.539282389459309 0.269641194729655 126 0.713783863286045 0.572432273427911 0.286216136713955 127 0.658185458685669 0.683629082628663 0.341814541314331 128 0.627021379630042 0.745957240739915 0.372978620369957 129 0.644154788415308 0.711690423169383 0.355845211584692 130 0.638798730395771 0.722402539208458 0.361201269604229 131 0.573070752088401 0.853858495823198 0.426929247911599 132 0.560025620009999 0.879948759980003 0.439974379990001 133 0.527713477627487 0.944573044745025 0.472286522372513 134 0.460117286236231 0.920234572472463 0.539882713763769 135 0.43375822299254 0.86751644598508 0.56624177700746 136 0.428314954748377 0.856629909496754 0.571685045251623 137 0.355929452694262 0.711858905388525 0.644070547305738 138 0.440052178741231 0.880104357482463 0.559947821258769 139 0.789116061544987 0.421767876910026 0.210883938455013 140 0.811338309789578 0.377323380420843 0.188661690210422 141 0.768312391354074 0.463375217291853 0.231687608645926 142 0.68483083624476 0.63033832751048 0.31516916375524 143 0.64226336274848 0.71547327450304 0.35773663725152 144 0.527945014239736 0.944109971520528 0.472054985760264 145 0.50804576818999 0.98390846362002 0.49195423181001 146 0.672796693169096 0.654406613661809 0.327203306830904 147 0.57144807248472 0.85710385503056 0.42855192751528 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 32 0.23021582733813 NOK 10% type I error level 45 0.323741007194245 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/10ypum1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/10ypum1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/1sofa1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/1sofa1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/2sofa1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/2sofa1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/32fev1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/32fev1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/42fev1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/42fev1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/52fev1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/52fev1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/6vody1290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/6vody1290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/76xv11290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/76xv11290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/86xv11290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/86xv11290527360.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/96xv11290527360.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528230dniycisyqzngiq1/96xv11290527360.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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Software written by Ed van Stee & Patrick Wessa

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