*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, 24 Dec 2010 15:21:29 +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/24/t1293203993nm7y1rh06agx4cj.htm/, Retrieved Fri, 24 Dec 2010 16:20:05 +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/24/t1293203993nm7y1rh06agx4cj.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 «

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

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 1.04499634277411 + 0.119499232591394FindingFriends[t] + 0.241564101757528KnowingPeople[t] + 0.378018708974302Liked[t] + 0.607491789609728Celebrity[t] -0.0489828130821504B[t] + 0.174147430517712`2B`[t] + 0.508543630098061`3B`[t] -0.136999283939156Month[t] -0.00188085357862904t + 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) 1.04499634277411 3.928053 0.266 0.790588 0.395294 FindingFriends 0.119499232591394 0.096875 1.2335 0.219357 0.109678 KnowingPeople 0.241564101757528 0.061926 3.9008 0.000146 7.3e-05 Liked 0.378018708974302 0.098076 3.8543 0.000173 8.7e-05 Celebrity 0.607491789609728 0.157196 3.8645 0.000167 8.3e-05 B -0.0489828130821504 0.224347 -0.2183 0.827473 0.413736 `2B` 0.174147430517712 0.270802 0.6431 0.521181 0.26059 `3B` 0.508543630098061 0.318646 1.596 0.112661 0.056331 Month -0.136999283939156 0.40264 -0.3403 0.734156 0.367078 t -0.00188085357862904 0.00416 -0.4522 0.651825 0.325912 Multiple Linear Regression - Regression Statistics Multiple R 0.717470503794906 R-squared 0.514763923815717 Adjusted R-squared 0.484852110900247 F-TEST (value) 17.2093856454115 F-TEST (DF numerator) 9 F-TEST (DF denominator) 146 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10772912266704 Sum Squared Residuals 648.608219962662 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 13.4991679358302 1.50083206416975 2 12 11.8981100087714 0.10188999122863 3 9 11.2935847722229 -2.29358477222292 4 10 12.0768505287867 -2.07685052878672 5 13 13.1972017006551 -0.197201700655100 6 16 15.2319939102505 0.768006089749506 7 14 12.9323548805402 1.06764511945981 8 16 13.9216499103898 2.07835008961024 9 10 10.9960803593227 -0.996080359322713 10 8 10.7774869517918 -2.77748695179182 11 12 12.2534224487608 -0.253422448760775 12 15 15.1206012967996 -0.120601296799614 13 14 10.9134325266142 3.08656747338582 14 14 12.8294273946596 1.17057260534035 15 12 13.0880808678829 -1.08808086788290 16 12 11.1902899797029 0.809710020297105 17 10 9.59770555485905 0.402294445140954 18 4 6.79756754087376 -2.79756754087376 19 14 15.2815827522669 -1.28158275226692 20 15 14.2708883148540 0.729111685146033 21 16 13.3886064572321 2.61139354276794 22 12 10.7600502371897 1.23994976281026 23 12 12.1554714328047 -0.155471432804704 24 12 11.3322488313704 0.667751168629636 25 12 11.5427480347434 0.457251965256587 26 12 12.3012178940586 -0.301217894058613 27 11 8.46962533788692 2.53037466211308 28 11 13.1100905284140 -2.11009052841396 29 11 12.1549938067566 -1.15499380675656 30 11 11.8038737203049 -0.803873720304908 31 11 11.4519360188544 -0.451936018854355 32 11 8.6474840743162 2.35251592568380 33 15 14.3690467642203 0.630953235779697 34 15 14.8623851352788 0.137614864721169 35 9 14.6068491588206 -5.60684915882057 36 16 10.8330247477272 5.16697525227284 37 13 9.18087166625341 3.81912833374659 38 9 10.3709164058374 -1.37091640583742 39 16 14.2333980566539 1.76660194334614 40 12 12.9016318251215 -0.901631825121455 41 15 9.01596982045074 5.98403017954927 42 5 9.81670811647123 -4.81670811647123 43 11 11.4096349362273 -0.409634936227334 44 17 13.2472484232903 3.75275157670972 45 9 9.10604536654858 -0.106045366548582 46 13 14.7177500231691 -1.71775002316915 47 16 14.2203721878772 1.77962781212282 48 16 13.8209516141241 2.17904838587587 49 14 14.3483495841271 -0.348349584127119 50 16 13.5435983667526 2.45640163324742 51 11 12.8177075336821 -1.81770753368211 52 11 11.8786166688209 -0.878616668820854 53 11 13.7454798740905 -2.74547987409047 54 12 12.2263929114652 -0.226392911465155 55 12 13.8219110758755 -1.82191107587552 56 12 12.0787466070131 -0.078746607013105 57 14 13.7158698120011 0.284130187998903 58 10 10.8938292706448 -0.89382927064478 59 9 9.36948662402635 -0.369486624026353 60 12 12.2721352488986 -0.272135248898607 61 10 10.0150315755398 -0.015031575539804 62 14 12.9817732388354 1.01822676116463 63 8 9.91845471742309 -1.91845471742309 64 16 14.4858215406104 1.51417845938958 65 14 15.7326316930428 -1.73263169304281 66 14 10.7303196129192 3.26968038708076 67 12 11.2259567009063 0.774043299093691 68 14 13.3732883951205 0.626711604879522 69 7 11.1119568444562 -4.11195684445617 70 19 13.9160274426111 5.08397255738893 71 15 12.8356176170298 2.16438238297025 72 8 11.2358065245671 -3.23580652456708 73 10 14.2688825796494 -4.26888257964936 74 13 12.9157668620937 0.0842331379063027 75 13 11.3430448027132 1.65695519728685 76 10 10.4753560056011 -0.475356005601083 77 12 9.15081644168751 2.84918355831249 78 15 17.4307739990282 -2.43077399902825 79 7 11.1523826850283 -4.15238268502825 80 14 14.2927376671468 -0.292737667146839 81 10 8.49722945746842 1.50277054253158 82 6 9.778959586541 -3.77895958654100 83 11 11.3135254367911 -0.31352543679111 84 12 9.36712354727253 2.63287645272747 85 14 14.2858637651183 -0.285863765118304 86 12 13.3938248740130 -1.39382487401296 87 14 14.3869799035657 -0.386979903565729 88 11 10.1295339571697 0.870466042830311 89 10 9.31280240685697 0.687197593143026 90 13 13.4068525327782 -0.406852532778176 91 8 10.3371693538776 -2.33716935387761 92 9 11.8039272023981 -2.80392720239807 93 6 12.0021952766312 -6.00219527663121 94 12 13.1287885999813 -1.12878859998133 95 14 12.1418479246633 1.85815207533665 96 11 10.4348955403776 0.565104459622418 97 8 10.5675183131860 -2.56751831318605 98 7 9.21588333435467 -2.21588333435467 99 9 10.4441986498397 -1.44419864983974 100 14 12.0891262285322 1.91087377146778 101 13 10.1836602510807 2.81633974891929 102 15 12.6166745066313 2.38332549336872 103 5 5.22559837218436 -0.225598372184357 104 15 12.1546848703017 2.84531512969832 105 13 12.1776875868034 0.822312413196627 106 12 11.5236623723415 0.476337627658545 107 6 7.68133413696577 -1.68133413696577 108 7 9.56300248642058 -2.56300248642058 109 13 8.47050163971716 4.52949836028284 110 16 14.819878161772 1.180121838228 111 10 13.2362850097808 -3.23628500978083 112 16 15.0641061926502 0.935893807349795 113 15 13.0816789573562 1.91832104264385 114 8 8.30768738998187 -0.307687389981865 115 11 12.5043362098399 -1.50433620983993 116 13 13.1382002746666 -0.138200274666611 117 16 15.1277839808410 0.872216019158957 118 11 8.59259420130102 2.40740579869898 119 14 14.3285466292558 -0.328546629255758 120 9 10.1143989090423 -1.11439890904234 121 8 10.1727908583271 -2.17279085832707 122 8 11.0159195208167 -3.01591952081667 123 11 11.7691753077400 -0.769175307740024 124 12 13.1879187906606 -1.18791879066065 125 11 10.9280990114490 0.0719009885509587 126 14 14.5188061294066 -0.518806129406618 127 11 12.5720705896542 -1.57207058965423 128 14 12.1874548876841 1.81254511231592 129 13 14.6398066696386 -1.63980666963858 130 12 10.6435888134915 1.35641118650846 131 4 5.77603215019459 -1.77603215019459 132 15 12.7839109993750 2.21608900062505 133 10 11.2696200846096 -1.26962008460959 134 13 13.7567513171914 -0.756751317191425 135 15 14.0748769251425 0.925123074857496 136 12 13.1336737189485 -1.13367371894854 137 13 13.1704274421111 -0.170427442111091 138 8 7.72415846530569 0.275841534694312 139 10 10.3945396148313 -0.394539614831347 140 15 13.5284138522989 1.47158614770114 141 16 14.2727781124753 1.72722188752472 142 16 14.7661164835338 1.23388351646619 143 14 12.8150343609158 1.18496563908423 144 14 12.9154330640543 1.08456693594569 145 12 10.5149301647128 1.48506983528721 146 15 13.1038147889474 1.89618521105255 147 13 12.8368377178223 0.163162282177728 148 16 13.0302388201548 2.96976117984522 149 14 13.3894213009251 0.61057869907493 150 8 9.84763560704182 -1.84763560704182 151 16 13.5598070242855 2.44019297571448 152 16 15.7469438831333 0.253056116866661 153 12 13.0038791776363 -1.00387917763625 154 11 12.1176937259202 -1.11769372592018 155 16 15.7413013223975 0.258698677602548 156 9 9.83635048557004 -0.836350485570045 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.565235017893787 0.869529964212425 0.434764982106213 14 0.395844308804128 0.791688617608256 0.604155691195872 15 0.269509968134723 0.539019936269445 0.730490031865277 16 0.186636967441124 0.373273934882248 0.813363032558876 17 0.120239139388344 0.240478278776689 0.879760860611656 18 0.217017024159083 0.434034048318165 0.782982975840917 19 0.364243292701171 0.728486585402342 0.635756707298829 20 0.275005018713093 0.550010037426185 0.724994981286907 21 0.283088104208519 0.566176208417038 0.716911895791481 22 0.210887010571301 0.421774021142601 0.7891129894287 23 0.176694478721541 0.353388957443083 0.823305521278459 24 0.125654982914780 0.251309965829560 0.87434501708522 25 0.0866417828838418 0.173283565767684 0.913358217116158 26 0.0765812365536047 0.153162473107209 0.923418763446395 27 0.067101538870047 0.134203077740094 0.932898461129953 28 0.172415686860241 0.344831373720482 0.827584313139759 29 0.144493922184316 0.288987844368633 0.855506077815684 30 0.1148369847796 0.2296739695592 0.8851630152204 31 0.0847809535732146 0.169561907146429 0.915219046426785 32 0.0728711260172475 0.145742252034495 0.927128873982753 33 0.0518076382115338 0.103615276423068 0.948192361788466 34 0.0379218229756792 0.0758436459513583 0.962078177024321 35 0.225157413559948 0.450314827119896 0.774842586440052 36 0.44613091630831 0.89226183261662 0.55386908369169 37 0.577861687757512 0.844276624484975 0.422138312242488 38 0.524759880017355 0.95048023996529 0.475240119982645 39 0.495880210901419 0.991760421802838 0.504119789098581 40 0.46781126322247 0.93562252644494 0.53218873677753 41 0.699023071202616 0.601953857594768 0.300976928797384 42 0.85881548724376 0.28236902551248 0.14118451275624 43 0.827155014403285 0.34568997119343 0.172844985596715 44 0.863579993966096 0.272840012067808 0.136420006033904 45 0.837186335844403 0.325627328311194 0.162813664155597 46 0.836228403939023 0.327543192121954 0.163771596060977 47 0.81430041480588 0.371399170388238 0.185699585194119 48 0.824409901755058 0.351180196489884 0.175590098244942 49 0.789352148479074 0.421295703041851 0.210647851520926 50 0.795803066118476 0.408393867763047 0.204196933881524 51 0.77224823331352 0.455503533372959 0.227751766686479 52 0.75928905642826 0.48142188714348 0.24071094357174 53 0.865944463348877 0.268111073302247 0.134055536651123 54 0.836170975523148 0.327658048953705 0.163829024476852 55 0.827198761776506 0.345602476446989 0.172801238223494 56 0.796107818027485 0.407784363945029 0.203892181972515 57 0.759485827938305 0.481028344123391 0.240514172061695 58 0.71911742880809 0.561765142383819 0.280882571191910 59 0.685380388094898 0.629239223810203 0.314619611905102 60 0.664386453757087 0.671227092485827 0.335613546242913 61 0.618521528683077 0.762956942633845 0.381478471316923 62 0.585334957621423 0.829330084757155 0.414665042378577 63 0.558549411223517 0.882901177552966 0.441450588776483 64 0.559571123606092 0.880857752787817 0.440428876393908 65 0.547553139729245 0.90489372054151 0.452446860270755 66 0.632981773528818 0.734036452942365 0.367018226471182 67 0.595982954574342 0.808034090851316 0.404017045425658 68 0.561406758864246 0.877186482271509 0.438593241135754 69 0.697139419948196 0.605721160103608 0.302860580051804 70 0.881308796297056 0.237382407405889 0.118691203702944 71 0.892818244579678 0.214363510840645 0.107181755420322 72 0.90767336535317 0.184653269293659 0.0923266346468293 73 0.94842616692006 0.103147666159878 0.0515738330799391 74 0.936156595506957 0.127686808986085 0.0638434044930427 75 0.929024153402011 0.141951693195979 0.0709758465979893 76 0.911499692139989 0.177000615720023 0.0885003078600114 77 0.932844757086761 0.134310485826478 0.0671552429132392 78 0.934912594926411 0.130174810147178 0.0650874050735889 79 0.97112368128819 0.0577526374236194 0.0288763187118097 80 0.96214294606661 0.0757141078667812 0.0378570539333906 81 0.959431357363502 0.0811372852729951 0.0405686426364976 82 0.977480615906263 0.0450387681874737 0.0225193840937368 83 0.97121752101839 0.057564957963219 0.0287824789816095 84 0.977142269322926 0.0457154613541484 0.0228577306770742 85 0.969794988119506 0.0604100237609889 0.0302050118804944 86 0.963184775566766 0.0736304488664676 0.0368152244332338 87 0.953074449887289 0.0938511002254219 0.0469255501127109 88 0.945970004105975 0.108059991788050 0.0540299958940251 89 0.950468259915745 0.0990634801685103 0.0495317400842551 90 0.937362904954242 0.125274190091517 0.0626370950457583 91 0.934860491214444 0.130279017571112 0.065139508785556 92 0.954056048692625 0.0918879026147508 0.0459439513073754 93 0.996063614766598 0.00787277046680392 0.00393638523340196 94 0.994402529207958 0.0111949415840838 0.00559747079204192 95 0.993580566514058 0.0128388669718848 0.00641943348594238 96 0.991405820205138 0.0171883595897232 0.0085941797948616 97 0.991430563688612 0.0171388726227768 0.00856943631138839 98 0.992487052784944 0.0150258944301113 0.00751294721505564 99 0.989469729272089 0.0210605414558221 0.0105302707279111 100 0.988305806983068 0.0233883860338648 0.0116941930169324 101 0.992325520224263 0.0153489595514739 0.00767447977573696 102 0.992727005229716 0.0145459895405683 0.00727299477028416 103 0.989896971569295 0.0202060568614103 0.0101030284307051 104 0.992825164871735 0.0143496702565307 0.00717483512826537 105 0.989949408274573 0.0201011834508546 0.0100505917254273 106 0.987266617746458 0.0254667645070842 0.0127333822535421 107 0.98528166614647 0.0294366677070614 0.0147183338535307 108 0.989717739714185 0.0205645205716299 0.0102822602858150 109 0.998983993828767 0.00203201234246683 0.00101600617123342 110 0.998671567811605 0.00265686437678947 0.00132843218839473 111 0.999577555351422 0.000844889297155976 0.000422444648577988 112 0.999304829128739 0.00139034174252301 0.000695170871261506 113 0.999293458297452 0.00141308340509546 0.000706541702547729 114 0.998843361918988 0.00231327616202400 0.00115663808101200 115 0.998266299464972 0.00346740107005558 0.00173370053502779 116 0.99713469342585 0.00573061314829891 0.00286530657414946 117 0.99557115566991 0.00885768866018059 0.00442884433009030 118 0.99928575384014 0.00142849231972000 0.000714246159859999 119 0.99875689838233 0.00248620323533879 0.00124310161766940 120 0.997906634033036 0.00418673193392749 0.00209336596696375 121 0.99737515821669 0.00524968356661817 0.00262484178330908 122 0.996628323039009 0.0067433539219827 0.00337167696099135 123 0.994724900840254 0.0105501983194925 0.00527509915974623 124 0.994622704684837 0.0107545906303261 0.00537729531516306 125 0.991111858656729 0.0177762826865428 0.00888814134327138 126 0.98706737337536 0.0258652532492800 0.0129326266246400 127 0.983650942186366 0.032698115627268 0.016349057813634 128 0.97589199526384 0.048216009472322 0.024108004736161 129 0.987690671533919 0.0246186569321619 0.0123093284660809 130 0.989789219226607 0.0204215615467852 0.0102107807733926 131 0.984899765858125 0.0302004682837506 0.0151002341418753 132 0.981996106931669 0.0360077861366615 0.0180038930683308 133 0.97488405455083 0.0502318908983413 0.0251159454491706 134 0.96221397071084 0.0755720585783199 0.0377860292891600 135 0.937878628501461 0.124242742997078 0.0621213714985389 136 0.953839477303385 0.0923210453932298 0.0461605226966149 137 0.972144179918852 0.0557116401622958 0.0278558200811479 138 0.947584174198594 0.104831651602812 0.0524158258014058 139 0.90425799252785 0.191484014944301 0.0957420074721503 140 0.853858044619189 0.292283910761622 0.146141955380811 141 0.773120447739717 0.453759104520566 0.226879552260283 142 0.709951349663682 0.580097300672636 0.290048650336318 143 0.554429649931078 0.891140700137844 0.445570350068922 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.114503816793893 NOK 5% type I error level 42 0.320610687022901 NOK 10% type I error level 56 0.427480916030534 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/10l6vl1293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/10l6vl1293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/1w5g91293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/1w5g91293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/2w5g91293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/2w5g91293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/37wfc1293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/37wfc1293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/47wfc1293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/47wfc1293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/57wfc1293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/57wfc1293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/60owy1293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/60owy1293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/7sfe01293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/7sfe01293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/8sfe01293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/8sfe01293204076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/9sfe01293204076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203993nm7y1rh06agx4cj/9sfe01293204076.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

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