Paper Multiple Regression zonder outliers

*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: Sun, 19 Dec 2010 13:54:47 +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/19/t1292767015jk0kkucaf1837v5.htm/, Retrieved Sun, 19 Dec 2010 14:57:07 +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/19/t1292767015jk0kkucaf1837v5.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 «

41 25 15 9 3 38 25 15 9 4 37 19 14 9 4 42 18 10 8 4 40 23 18 15 3 43 25 14 9 4 40 23 11 11 4 45 30 17 6 5 45 32 21 10 4 44 25 7 11 4 42 26 18 16 4 41 35 18 7 4 38 20 12 10 4 38 21 9 9 4 46 17 11 6 5 42 27 16 12 4 46 25 12 10 4 43 18 14 14 5 38 22 13 9 4 39 23 17 14 4 40 25 13 14 3 37 19 13 9 2 41 20 12 8 4 46 26 12 10 4 37 22 9 9 3 39 25 17 9 4 44 29 18 11 5 38 22 12 10 2 38 32 12 8 0 38 23 9 14 4 33 18 13 10 3 43 26 11 14 4 41 14 13 15 2 45 25 11 10 5 38 23 15 10 4 39 24 11 11 4 40 21 14 10 4 36 17 12 16 2 49 29 8 6 5 41 25 11 11 4 42 25 17 14 3 41 25 16 9 5 43 21 13 11 4 46 23 15 8 3 41 25 16 8 5 39 25 7 11 4 42 24 16 16 4 35 21 13 12 5 36 22 15 14 3 41 20 12 10 4 41 22 15 10 3 36 28 18 12 4 46 25 17 9 4 44 21 15 8 4 43 27 11 16 2 40 19 12 13 5 40 20 14 8 3 39 22 10 8 4 44 26 11 7 4 38 17 12 11 2 39 15 6 6 4 41 27 15 9 5 39 25 14 14 3 40 19 16 12 4 44 18 16 8 4 42 15 11 8 4 46 29 15 12 5 44 24 12 13 4 37 24 13 11 4 39 22 14 12 2 40 22 12 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation StudyForCareer[t] = + 32.354703179194 + 0.252477610175875PersonalStandards[t] -0.106985446432251ParentalExpectations[t] -0.141013216016659Doubts[t] + 1.4793123811832LeaderPreference[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) 32.354703179194 2.205386 14.6708 0 0 PersonalStandards 0.252477610175875 0.072985 3.4593 0.000749 0.000374 ParentalExpectations -0.106985446432251 0.093164 -1.1484 0.253086 0.126543 Doubts -0.141013216016659 0.104376 -1.351 0.179212 0.089606 LeaderPreference 1.4793123811832 0.324385 4.5604 1.2e-05 6e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.544667585985645 R-squared 0.29666277922343 Adjusted R-squared 0.273411962007676 F-TEST (value) 12.7592409535789 F-TEST (DF numerator) 4 F-TEST (DF denominator) 121 p-value 1.07389912518130e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.16129589508423 Sum Squared Residuals 1209.24880008944 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 40.2306799365066 0.769320063493367 2 38 41.70999231769 -3.70999231768996 3 37 40.302112103067 -3.30211210306696 4 42 40.6185894946368 1.38141050536325 5 40 38.5586890807583 1.44131091924170 6 43 41.8169777641222 1.18302223587779 7 40 41.3509524510339 -1.35095245103390 8 45 44.660761504938 0.339238495061987 9 45 42.6944096943109 2.30559030568908 10 44 42.2838494571146 1.71615054288535 11 42 40.6544210764525 1.34557892354753 12 41 44.1958385121853 -3.19583851218528 13 38 40.6275473900907 -2.62754739009068 14 38 41.3419945555800 -3.34199455557997 15 46 42.0204652512451 3.97953474875486 16 42 41.6849224435595 0.315077556440519 17 46 41.8899354409701 4.11006455902995 18 43 40.823880793991 2.17611920600901 19 38 41.1665303800268 -3.16653038002684 20 39 40.2860001243904 -1.28600012439041 21 40 39.739584749288 0.260415250712035 22 37 37.4504727871328 -0.450472787132813 23 41 40.909573822124 0.0904261778760015 24 46 42.1424130511459 3.85758694885407 25 37 40.1151597845726 -3.11515978457264 26 39 41.4960214248255 -2.49602142482546 27 44 43.5962323682466 0.403767631753411 28 38 38.173877848076 -0.173877848076030 29 38 38.0220556195017 -0.0220556195016989 30 38 41.1418836958484 -3.14188369584842 31 33 38.5362943421235 -5.53629434212348 32 43 41.6853456335115 1.31465436648846 33 41 35.3420054401535 5.65799455984652 34 45 43.4762332685855 1.52376673141450 35 38 41.0640238813216 -3.06402388132155 36 39 41.6034300612098 -2.60343006120977 37 40 40.6660541074021 -0.666054107402053 38 36 36.0654105010967 -0.0654105010966984 39 49 45.3711529126524 3.62884708734761 40 41 41.8559076713856 -0.855907671385645 41 42 39.311642963559 2.68835703644104 42 41 43.0823192524409 -2.08231925244091 43 43 40.6320263378176 2.36797366218236 44 46 39.8667379321717 6.13326206782833 45 41 43.2233324684576 -2.22333246845757 46 39 42.2838494571146 -3.28384945711465 47 42 40.3634367489652 1.63656325103478 48 35 41.9703255029842 -6.97032550298418 49 36 38.7681810258958 -2.76818102589584 50 41 40.6275473900907 0.372452609909321 51 41 39.3322338899625 1.66776611003752 52 36 41.7234291608709 -5.72342916087085 53 46 41.4960214248255 4.50397857517454 54 44 40.8410950930031 3.15890490699688 55 43 38.6971720492877 4.3028279507123 56 40 41.431342513048 -1.43134251304803 57 40 39.2162905480763 0.783709451923703 58 39 41.6284999353403 -2.62849993534025 59 44 42.6724381456282 1.32756185437184 60 38 36.77047658118 1.22952341882000 61 39 40.5711248818714 -1.57112488187145 62 41 43.6942599192249 -2.69425991922491 63 39 39.6325993028557 -0.632599302855715 64 40 39.6651015621525 0.334898437847518 65 44 39.9766768160432 4.02332318395675 66 42 39.7541712176769 2.24582878232313 67 46 43.7761754915267 2.22382450847332 68 44 41.2144181827442 2.7855818172558 69 37 41.3894591683453 -4.38945916834527 70 39 37.6778805231782 1.32211947682179 71 40 39.2301505812093 0.769849418790749 72 42 39.311642963559 2.68835703644104 73 37 39.6487112815323 -2.64871128153227 74 33 38.0964412235012 -5.09644122350122 75 35 40.725574941069 -5.725574941069 76 42 35.2851597419822 6.71484025801781 77 36 36.8138854361704 -0.813885436170394 78 44 41.1418836958484 2.85811630415158 79 45 41.1803904131598 3.81960958684021 80 47 43.4141821874313 3.58581781256871 81 40 41.3505292610818 -1.35052926108184 82 48 43.6298369478789 4.37016305212106 83 45 42.8302648322171 2.16973516778291 84 41 41.0210382162832 -0.0210382162832137 85 34 38.6837352061068 -4.68373520610680 86 38 38.3291742871777 -0.329174287177704 87 37 38.8277018595628 -1.82770185956279 88 48 44.3993259993082 3.60067400069179 89 39 42.3563839440104 -3.35638394401043 90 34 40.9364475084858 -6.93644750848579 91 35 36.6590121870208 -1.65901218702078 92 41 40.949606049723 0.0503939502769873 93 43 39.501693607501 3.498306392499 94 41 38.7842930045724 2.21570699542761 95 39 37.7512613899781 1.24873861002189 96 36 40.8796018103145 -4.8796018103145 97 46 41.3169246814495 4.68307531855051 98 42 41.7784710468108 0.221528953189161 99 42 37.2073762623629 4.79262373763707 100 45 40.6111571094705 4.38884289052954 101 39 41.5304723843619 -2.53047238436193 102 45 42.8273113947778 2.17268860522223 103 48 43.7197529833075 4.28024701669255 104 35 38.1693989003491 -3.16939890034907 105 38 39.8199748113021 -1.81997481130210 106 42 39.1471326885719 2.8528673114281 107 36 38.9731940233064 -2.97319402330641 108 37 41.521514488908 -4.521514488908 109 38 39.3187970467816 -1.31879704678158 110 43 40.8634898316379 2.13651016836206 111 35 36.4342546431108 -1.43425464311081 112 36 40.5935196205063 -4.59351962050627 113 33 35.8331006273723 -2.83310062737228 114 39 39.0240352634631 -0.0240352634630974 115 45 39.6827390511167 5.31726094888333 116 35 40.4820552263471 -5.48205522634706 117 38 38.5707453016599 -0.570745301659948 118 36 38.759646320394 -2.75964632039397 119 42 38.3908021783799 3.60919782162015 120 41 39.9860579014492 1.01394209855077 121 35 38.5792800071618 -3.57928000716182 122 43 38.6911675912731 4.30883240872691 123 40 42.3747229248703 -2.37472292487035 124 46 41.6329788830672 4.36702111693279 125 44 42.8302648322171 1.16973516778290 126 35 38.929785168316 -3.92978516831601 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.545009047548961 0.909981904902078 0.454990952451039 9 0.412482517347963 0.824965034695926 0.587517482652037 10 0.277586030542454 0.555172061084908 0.722413969457546 11 0.176983723950777 0.353967447901555 0.823016276049223 12 0.247052937915410 0.494105875830821 0.75294706208459 13 0.206561337268609 0.413122674537218 0.793438662731391 14 0.186915458933043 0.373830917866086 0.813084541066957 15 0.320208158717785 0.64041631743557 0.679791841282215 16 0.237810300102247 0.475620600204493 0.762189699897754 17 0.311538894697874 0.623077789395748 0.688461105302126 18 0.240794578655821 0.481589157311642 0.759205421344179 19 0.238248119592836 0.476496239185672 0.761751880407164 20 0.204048681847240 0.408097363694481 0.79595131815276 21 0.152323416540437 0.304646833080874 0.847676583459563 22 0.119371949072377 0.238743898144754 0.880628050927623 23 0.0848284121012232 0.169656824202446 0.915171587898777 24 0.104087298142713 0.208174596285426 0.895912701857287 25 0.0957073178090307 0.191414635618061 0.904292682190969 26 0.0826426355374807 0.165285271074961 0.91735736446252 27 0.0589492046126065 0.117898409225213 0.941050795387393 28 0.0436374375876331 0.0872748751752662 0.956362562412367 29 0.0341007604883415 0.068201520976683 0.965899239511658 30 0.0429279764485592 0.0858559528971184 0.95707202355144 31 0.075764390518856 0.151528781037712 0.924235609481144 32 0.0564239727605151 0.112847945521030 0.943576027239485 33 0.129694922540084 0.259389845080167 0.870305077459916 34 0.106833090915995 0.213666181831991 0.893166909084005 35 0.104497688289231 0.208995376578462 0.895502311710769 36 0.0972122796189408 0.194424559237882 0.902787720381059 37 0.0737255054980739 0.147451010996148 0.926274494501926 38 0.0555416677781268 0.111083335556254 0.944458332221873 39 0.067434166168498 0.134868332336996 0.932565833831502 40 0.0519168581953949 0.103833716390790 0.948083141804605 41 0.0474336278087159 0.0948672556174319 0.952566372191284 42 0.0391368091288063 0.0782736182576127 0.960863190871194 43 0.0349870258570652 0.0699740517141304 0.965012974142935 44 0.096409420577955 0.19281884115591 0.903590579422045 45 0.0832131941419678 0.166426388283936 0.916786805858032 46 0.0867338634334604 0.173467726866921 0.91326613656654 47 0.0700667253881324 0.140133450776265 0.929933274611868 48 0.17404807295743 0.34809614591486 0.82595192704257 49 0.168456750189495 0.33691350037899 0.831543249810505 50 0.137444650984168 0.274889301968335 0.862555349015832 51 0.117155627043069 0.234311254086138 0.882844372956931 52 0.189458869736687 0.378917739473374 0.810541130263313 53 0.230547689783896 0.461095379567792 0.769452310216104 54 0.228614123611289 0.457228247222578 0.771385876388711 55 0.262666688967479 0.525333377934958 0.737333311032521 56 0.230303790005192 0.460607580010383 0.769696209994808 57 0.193869102117462 0.387738204234924 0.806130897882538 58 0.181695516888541 0.363391033777081 0.81830448311146 59 0.155337689593220 0.310675379186439 0.84466231040678 60 0.130092162644638 0.260184325289277 0.869907837355361 61 0.112249090602327 0.224498181204654 0.887750909397673 62 0.105603619256999 0.211207238513998 0.894396380743 63 0.0845373363136994 0.169074672627399 0.9154626636863 64 0.0660107632517947 0.132021526503589 0.933989236748205 65 0.075030321914732 0.150060643829464 0.924969678085268 66 0.0643645466346569 0.128729093269314 0.935635453365343 67 0.0578369361621563 0.115673872324313 0.942163063837844 68 0.054534491532617 0.109068983065234 0.945465508467383 69 0.0690321333014794 0.138064266602959 0.93096786669852 70 0.0574071525146493 0.114814305029299 0.94259284748535 71 0.0446241142897188 0.0892482285794376 0.955375885710281 72 0.0442458445108059 0.0884916890216118 0.955754155489194 73 0.0406959335342815 0.0813918670685631 0.959304066465718 74 0.059629700012771 0.119259400025542 0.94037029998723 75 0.1181211270564 0.2362422541128 0.8818788729436 76 0.244425865872336 0.488851731744673 0.755574134127664 77 0.208401789529889 0.416803579059778 0.79159821047011 78 0.198064638110256 0.396129276220513 0.801935361889744 79 0.213944481575031 0.427888963150061 0.78605551842497 80 0.220762249801794 0.441524499603587 0.779237750198206 81 0.187215477657188 0.374430955314376 0.812784522342812 82 0.277345708048921 0.554691416097842 0.722654291951079 83 0.246827575426429 0.493655150852857 0.753172424573571 84 0.205283824352681 0.410567648705363 0.794716175647318 85 0.245614305445008 0.491228610890017 0.754385694554992 86 0.205244018385246 0.410488036770491 0.794755981614754 87 0.179988594737792 0.359977189475584 0.820011405262208 88 0.193703162578581 0.387406325157163 0.806296837421419 89 0.207567638841008 0.415135277682016 0.792432361158992 90 0.293672663747095 0.58734532749419 0.706327336252905 91 0.252867986415092 0.505735972830185 0.747132013584908 92 0.207739390612172 0.415478781224343 0.792260609387828 93 0.207706286583307 0.415412573166615 0.792293713416693 94 0.188994001031027 0.377988002062053 0.811005998968973 95 0.152605000763804 0.305210001527608 0.847394999236196 96 0.174434150502102 0.348868301004203 0.825565849497898 97 0.205098481247786 0.410196962495573 0.794901518752213 98 0.162573369473536 0.325146738947072 0.837426630526464 99 0.23676830616447 0.47353661232894 0.76323169383553 100 0.267258743607907 0.534517487215813 0.732741256392093 101 0.246274223406406 0.492548446812813 0.753725776593594 102 0.212575418342830 0.425150836685659 0.78742458165717 103 0.22734191952111 0.45468383904222 0.77265808047889 104 0.195218275414668 0.390436550829335 0.804781724585332 105 0.158712251281727 0.317424502563455 0.841287748718272 106 0.168132100324881 0.336264200649762 0.831867899675119 107 0.145060254542499 0.290120509084998 0.854939745457501 108 0.176414178907608 0.352828357815216 0.823585821092392 109 0.136416149197458 0.272832298394916 0.863583850802542 110 0.108558581240895 0.217117162481790 0.891441418759105 111 0.074471924832197 0.148943849664394 0.925528075167803 112 0.097149287522224 0.194298575044448 0.902850712477776 113 0.0727856472664278 0.145571294532856 0.927214352733572 114 0.0538383517154384 0.107676703430877 0.946161648284562 115 0.0651797448635784 0.130359489727157 0.934820255136422 116 0.169492273102554 0.338984546205108 0.830507726897446 117 0.114405817492183 0.228811634984366 0.885594182507817 118 0.292388629258723 0.584777258517445 0.707611370741277 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 9 0.0810810810810811 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/105x961292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/105x961292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/1yecc1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/1yecc1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/2yecc1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/2yecc1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/39nbx1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/39nbx1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/49nbx1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/49nbx1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/59nbx1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/59nbx1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/62ebi1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/62ebi1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/7uosl1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/7uosl1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/8uosl1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/8uosl1292766875.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/9uosl1292766875.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767015jk0kkucaf1837v5/9uosl1292766875.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