*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, 30 Nov 2010 13:20:01 +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/30/t1291123212r53wf9rjpn9g3wv.htm/, Retrieved Tue, 30 Nov 2010 14:20:24 +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/30/t1291123212r53wf9rjpn9g3wv.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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.0342768235376193 + 0.106305539542869FindingFriends[t] + 0.21144283590659KnowingPeople[t] + 0.357652188002145Liked[t] + 0.60600258577461Celebrity[t] + 0.212600241949771Sum[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) 0.0342768235376193 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 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) 31.1570674405528 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 1.73086477446163 2 12 10.8935776001555 1.10642239984454 3 15 12.9930967725273 2.00690322747266 4 12 11.0367690272923 0.963230972707738 5 10 10.8137483007782 -0.813748300778157 6 12 9.11247740469751 2.88752259530249 7 15 16.7228950081851 -1.72289500818514 8 9 10.2065991460963 -1.20659914609634 9 12 12.5516849436719 -0.551684943671851 10 11 7.58364711135212 3.41635288864788 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 -0.500748429109222 16 11 10.6294848179095 0.370515182090483 17 10 11.9888567475975 -1.98885674759747 18 14 14.3715315456393 -0.371531545639309 19 10 8.53921788692282 1.46078211307718 20 6 9.25218577656882 -3.25218577656881 21 11 8.75781063024621 2.24218936975379 22 15 14.4084391075052 0.591560892494816 23 11 11.8322160738016 -0.832216073801606 24 12 9.57342804441975 2.42657195558025 25 14 12.9796800372762 1.02031996272380 26 15 14.5818169755027 0.418183024497282 27 9 14.407281701462 -5.407281701462 28 13 12.7324653712750 0.267534628725014 29 13 13.0195730126929 -0.0195730126929230 30 16 11.0704276862825 4.92957231371746 31 13 8.71190347918394 4.28809652081606 32 12 13.5868291919580 -1.58682919195803 33 14 14.7273448889978 -0.727344888997824 34 11 10.0749530981592 0.925046901840848 35 9 10.4191993880461 -1.41919938804611 36 16 14.4379224354935 1.56207756450647 37 12 13.0629707176471 -1.06297071764708 38 10 9.56924187628186 0.430758123718142 39 13 12.8745319037765 0.125468096223484 40 16 15.6141774512200 0.385822548779951 41 14 12.9819948493626 1.01800515063743 42 15 8.01302292625358 6.98697707374642 43 5 9.64283685923271 -4.64283685923271 44 8 10.2465029586490 -2.24650295864902 45 11 11.2482227003348 -0.248222700334833 46 16 13.8393440835965 2.16065591640355 47 17 14.3258260355590 2.67417396444096 48 9 8.18274477923579 0.81725522076421 49 9 11.4204431622892 -2.42044316228919 50 13 14.476679679139 -1.47667967913900 51 10 11.0778519201601 -1.07785192016008 52 6 12.3706595265429 -6.37065952654285 53 12 12.0970011317840 -0.0970011317839686 54 8 10.5001752563306 -2.50017525633063 55 14 11.8444970772815 2.15550292271849 56 12 12.9063300438512 -0.906330043851219 57 11 10.6693777933262 0.330622206673764 58 16 14.5829635444099 1.41703645559007 59 8 10.5326548350058 -2.53265483500578 60 15 14.5880838033371 0.411916196662928 61 7 9.11131999865433 -2.11131999865433 62 16 14.1865757870343 1.81342421296575 63 14 13.1488825742718 0.851117425728186 64 16 13.3772360378310 2.62276396216897 65 9 10.4319238475608 -1.43192384756085 66 14 12.1633920216382 1.83660797836181 67 11 13.2598285751234 -2.25982857512337 68 13 10.3244825762467 2.67551742375327 69 15 13.1945950913123 1.80540490868766 70 5 5.79379231622363 -0.793792316223632 71 15 12.9063300438512 2.09366995614878 72 13 12.5885925055377 0.411407494462273 73 11 12.4170534821838 -1.41705348218382 74 11 14.1988134419703 -3.19881344197029 75 12 12.77054117632 -0.770541176320009 76 12 13.4048805211757 -1.40488052117575 77 12 12.3360884510353 -0.33608845103527 78 12 11.9507701054165 0.0492298945835183 79 14 10.8578274443328 3.14217255566723 80 6 7.93737979501417 -1.93737979501417 81 7 9.71847999047212 -2.71847999047212 82 14 12.4117099080028 1.58829009199725 83 14 14.1612461157759 -0.161246115775900 84 10 11.1702430827371 -1.17024308273712 85 13 9.11479221678387 3.88520778321613 86 12 12.3066051230469 -0.306605123046929 87 9 9.32091315278133 -0.320913152781326 88 12 11.9242830281150 0.0757169718850493 89 16 14.8018414513300 1.19815854866998 90 10 10.4602606066420 -0.460260606641974 91 14 13.1017171241566 0.898282875843412 92 10 13.5909936858240 -3.59099368582398 93 16 15.5078827488131 0.492117251186852 94 15 13.4037122779966 1.5962877220034 95 12 11.4891488642298 0.510851135770237 96 10 9.3596703964268 0.640329603573203 97 8 10.1222811445894 -2.12228114458937 98 8 8.71607881018586 -0.716078810185863 99 11 12.6649170753776 -1.66491707537759 100 13 12.5591091775494 0.440890822450614 101 16 15.6130200451769 0.386979954823131 102 16 14.9387877249044 1.06121227509559 103 14 15.4034377281858 -1.40343772818584 104 11 9.04723308375051 1.95276691624949 105 4 7.15683109806288 -3.15683109806288 106 14 14.7389336167413 -0.738933616741316 107 9 10.5284903411398 -1.52849034113982 108 14 15.2258845291864 -1.22588452918638 109 8 10.2494992093358 -2.24949920933583 110 8 10.6827945285774 -2.68279452857739 111 11 11.8843900526982 -0.884390052698232 112 12 13.1604604648793 -1.16046046487934 113 11 11.0755371080737 -0.0755371080737139 114 14 13.2720987414673 0.727901258532688 115 15 14.4495111632370 0.550488836762983 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 10.8819888724120 3.11801112758803 121 12 11.5585468419068 0.441453158093244 122 14 12.5463630437627 1.45363695623729 123 8 10.8854610905415 -2.88546109054152 124 13 14.0814384906705 -1.08143849067053 125 16 13.9751329511277 2.02486704887234 126 12 10.6157438743947 1.38425612560534 127 16 15.4783994208248 0.521600579175193 128 12 12.7670797953264 -0.767079795326434 129 11 11.4614935437491 -0.461493543749085 130 4 6.00799725042713 -2.00799725042713 131 16 16.1162001466741 -0.116200146674119 132 15 12.6642464739131 2.33575352608689 133 10 11.3605315783873 -1.36053157838729 134 13 14.0185198189459 -1.01851981894585 135 15 13.1270467954149 1.87295320458506 136 12 10.4990178502874 1.50098214971256 137 14 13.6562271696350 0.343772830364979 138 7 10.3811344201371 -3.38113442013705 139 19 13.9075846552303 5.09241534476974 140 12 12.9450764503607 -0.945076450360723 141 12 11.8728121620907 0.127187837909294 142 13 13.3384896313215 -0.338489631321529 143 15 12.4165883518771 2.58341164812294 144 8 8.84468525889237 -0.844685258892373 145 12 10.9230609281438 1.07693907185619 146 10 10.7601143818466 -0.760114381846583 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 -0.270249059687716 152 16 15.0838396709568 0.916160329043213 153 9 9.82245988079266 -0.822459880792662 154 14 13.0606450684248 0.939354931575244 155 14 13.1546804416237 0.845319558376316 156 12 10.1738452409605 1.82615475903955 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.113043399422145 0.226086798844289 0.886956600577856 10 0.0501338279117769 0.100267655823554 0.949866172088223 11 0.0726791202759016 0.145358240551803 0.927320879724098 12 0.0362939892148767 0.0725879784297535 0.963706010785123 13 0.455723219571891 0.911446439143783 0.544276780428109 14 0.76911689565418 0.461766208691640 0.230883104345820 15 0.690843322338694 0.618313355322612 0.309156677661306 16 0.602492647173724 0.795014705652552 0.397507352826276 17 0.546776085151918 0.906447829696164 0.453223914848082 18 0.460483749436226 0.920967498872452 0.539516250563774 19 0.383961884720282 0.767923769440564 0.616038115279718 20 0.681648999560028 0.636702000879943 0.318351000439972 21 0.622480475370067 0.755039049259867 0.377519524629933 22 0.591384359560492 0.817231280879017 0.408615640439508 23 0.5217220838681 0.956555832263801 0.478277916131900 24 0.505471724232079 0.989056551535841 0.494528275767921 25 0.466600374283114 0.933200748566229 0.533399625716886 26 0.405702343192011 0.811404686384022 0.594297656807989 27 0.665652538596127 0.668694922807745 0.334347461403873 28 0.609240659024031 0.781518681951937 0.390759340975969 29 0.54821780570686 0.90356438858628 0.45178219429314 30 0.696729243596925 0.60654151280615 0.303270756403075 31 0.796779695025199 0.406440609949603 0.203220304974801 32 0.759015830700385 0.481968338599230 0.240984169299615 33 0.712632486930885 0.57473502613823 0.287367513069115 34 0.670862179082851 0.658275641834298 0.329137820917149 35 0.660485468173782 0.679029063652437 0.339514531826218 36 0.662086475116607 0.675827049766786 0.337913524883393 37 0.631567039740653 0.736865920518695 0.368432960259347 38 0.581458293971188 0.837083412057624 0.418541706028812 39 0.534260918670243 0.931478162659513 0.465739081329757 40 0.493752920990991 0.987505841981983 0.506247079009009 41 0.461026226065895 0.92205245213179 0.538973773934105 42 0.786974579954076 0.426050840091848 0.213025420045924 43 0.944150764127681 0.111698471744638 0.0558492358723188 44 0.950160257918895 0.0996794841622107 0.0498397420811053 45 0.936085569397635 0.127828861204730 0.0639144306023652 46 0.94292613685323 0.114147726293540 0.0570738631467698 47 0.941015504220451 0.117968991559097 0.0589844957795486 48 0.928614456995934 0.142771086008132 0.0713855430040658 49 0.928216744769153 0.143566510461695 0.0717832552308476 50 0.917211581742264 0.165576836515471 0.0827884182577357 51 0.911008943171923 0.177982113656155 0.0889910568280774 52 0.988136800506383 0.0237263989872342 0.0118631994936171 53 0.983915640787094 0.0321687184258113 0.0160843592129057 54 0.989114188181053 0.0217716236378930 0.0108858118189465 55 0.991604992732137 0.0167900145357257 0.00839500726786285 56 0.98927481761204 0.0214503647759218 0.0107251823879609 57 0.98551004684779 0.0289799063044212 0.0144899531522106 58 0.983099824833785 0.0338003503324295 0.0169001751662147 59 0.989731760158278 0.0205364796834450 0.0102682398417225 60 0.987916792330477 0.0241664153390456 0.0120832076695228 61 0.988395472840583 0.0232090543188331 0.0116045271594166 62 0.988181561011165 0.023636877977669 0.0118184389888345 63 0.986195084184616 0.0276098316307688 0.0138049158153844 64 0.988838717434339 0.0223225651313223 0.0111612825656612 65 0.987927903805505 0.0241441923889896 0.0120720961944948 66 0.987047186436876 0.0259056271262485 0.0129528135631242 67 0.987689908526173 0.0246201829476538 0.0123100914738269 68 0.990035502882632 0.0199289942347356 0.00996449711736778 69 0.989337132793422 0.0213257344131551 0.0106628672065776 70 0.986218965835914 0.0275620683281719 0.0137810341640860 71 0.986490148403316 0.0270197031933689 0.0135098515966845 72 0.98204295712047 0.0359140857590597 0.0179570428795298 73 0.979098961086386 0.0418020778272285 0.0209010389136143 74 0.98622213946454 0.0275557210709192 0.0137778605354596 75 0.982088938972489 0.0358221220550231 0.0179110610275116 76 0.979375419819198 0.0412491603616045 0.0206245801808022 77 0.973063896771346 0.0538722064573077 0.0269361032286539 78 0.96481254668653 0.0703749066269418 0.0351874533134709 79 0.976797177525917 0.0464056449481659 0.0232028224740829 80 0.975833657037132 0.0483326859257354 0.0241663429628677 81 0.979696646575212 0.0406067068495758 0.0203033534247879 82 0.978950843585816 0.042098312828369 0.0210491564141845 83 0.972115647307748 0.0557687053845046 0.0278843526922523 84 0.966159185542055 0.0676816289158901 0.0338408144579451 85 0.988749360656196 0.0225012786876074 0.0112506393438037 86 0.985000968457257 0.0299980630854862 0.0149990315427431 87 0.980084627098881 0.0398307458022371 0.0199153729011185 88 0.974186201770184 0.0516275964596325 0.0258137982298163 89 0.968542688000701 0.0629146239985973 0.0314573119992987 90 0.959702745600729 0.0805945087985417 0.0402972543992709 91 0.951827757817031 0.096344484365938 0.048172242182969 92 0.972877397905895 0.0542452041882106 0.0271226020941053 93 0.964832510425725 0.070334979148549 0.0351674895742745 94 0.960013484371968 0.0799730312560636 0.0399865156280318 95 0.94984346280624 0.100313074387521 0.0501565371937606 96 0.937707896342723 0.124584207314553 0.0622921036572765 97 0.932666328999002 0.134667342001995 0.0673336710009975 98 0.91641256679677 0.167174866406461 0.0835874332032303 99 0.911165381803443 0.177669236393114 0.0888346181965571 100 0.891111336645835 0.217777326708331 0.108888663354165 101 0.866946162597843 0.266107674804315 0.133053837402158 102 0.843851140390287 0.312297719219425 0.156148859609713 103 0.856407399097918 0.287185201804164 0.143592600902082 104 0.897096078383827 0.205807843232346 0.102903921616173 105 0.89919148777778 0.201617024444439 0.100808512222220 106 0.876914501482186 0.246170997035629 0.123085498517814 107 0.856253129727054 0.287493740545892 0.143746870272946 108 0.85173782760369 0.296524344792621 0.148262172396310 109 0.849240676022668 0.301518647954664 0.150759323977332 110 0.873884020699292 0.252231958601417 0.126115979300708 111 0.862099121874637 0.275801756250726 0.137900878125363 112 0.902424696230432 0.195150607539136 0.097575303769568 113 0.876528722266006 0.246942555467988 0.123471277733994 114 0.848691047338282 0.302617905323436 0.151308952661718 115 0.813930187457869 0.372139625084263 0.186069812542131 116 0.812809256857317 0.374381486285366 0.187190743142683 117 0.825383224190319 0.349233551619362 0.174616775809681 118 0.814932503182843 0.370134993634314 0.185067496817157 119 0.77335508183685 0.453289836326299 0.226644918163149 120 0.834561940220552 0.330876119558896 0.165438059779448 121 0.804605728069574 0.390788543860852 0.195394271930426 122 0.777411502658302 0.445176994683396 0.222588497341698 123 0.775776866225366 0.448446267549267 0.224223133774634 124 0.734242845611249 0.531514308777503 0.265757154388751 125 0.730358805270345 0.539282389459311 0.269641194729655 126 0.713783863286044 0.572432273427912 0.286216136713956 127 0.658185458685668 0.683629082628665 0.341814541314332 128 0.627021379630045 0.745957240739911 0.372978620369955 129 0.64415478841531 0.71169042316938 0.35584521158469 130 0.638798730395771 0.722402539208457 0.361201269604229 131 0.573070752088402 0.853858495823196 0.426929247911598 132 0.560025620009999 0.879948759980003 0.439974379990001 133 0.527713477627487 0.944573044745026 0.472286522372513 134 0.460117286236233 0.920234572472466 0.539882713763767 135 0.43375822299254 0.86751644598508 0.56624177700746 136 0.428314954748377 0.856629909496753 0.571685045251623 137 0.355929452694262 0.711858905388523 0.644070547305738 138 0.440052178741233 0.880104357482467 0.559947821258767 139 0.789116061544987 0.421767876910026 0.210883938455013 140 0.811338309789578 0.377323380420843 0.188661690210422 141 0.768312391354073 0.463375217291854 0.231687608645927 142 0.68483083624476 0.630338327510479 0.315169163755239 143 0.642263362748481 0.715473274503038 0.357736637251519 144 0.527945014239736 0.944109971520527 0.472054985760264 145 0.508045768189991 0.983908463620018 0.491954231810009 146 0.672796693169096 0.654406613661808 0.327203306830904 147 0.571448072484721 0.857103855030559 0.428551927515279 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 0.230215827338130 NOK 10% type I error level 45 0.323741007194245 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/10o8lo1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/10o8lo1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/1agng1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/1agng1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/2agng1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/2agng1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/3agng1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/3agng1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/4274j1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/4274j1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/5274j1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/5274j1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/6274j1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/6274j1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/7dhml1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/7dhml1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/8o8lo1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/8o8lo1291123190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/9o8lo1291123190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291123212r53wf9rjpn9g3wv/9o8lo1291123190.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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by