workshop 7

*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: Thu, 02 Dec 2010 21:18:09 +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/02/t1291324623xrr91hw5ln1lw25.htm/, Retrieved Thu, 02 Dec 2010 22:17:03 +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/02/t1291324623xrr91hw5ln1lw25.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

4 4 1 4 2 4 2 1 4 2 4 3 2 5 2 4 2 1 3 2 4 2 2 4 2 5 2 1 3 2 4 1 3 4 3 3 1 1 3 3 4 1 1 2 4 4 2 1 4 2 4 2 2 2 3 4 2 4 2 4 4 2 2 2 2 2 2 1 1 3 3 1 1 4 2 4 3 3 4 1 3 2 2 2 2 2 2 2 2 2 4 2 3 3 2 3 2 3 3 2 3 3 1 3 4 4 4 2 4 4 3 2 2 3 3 3 2 2 2 4 4 2 2 2 3 4 1 3 4 2 4 2 2 4 3 4 2 2 3 2 4 2 2 4 2 4 2 2 2 2 5 4 2 4 3 4 2 3 4 4 4 4 2 5 4 4 3 2 5 2 3 1 2 4 2 4 4 2 4 4 3 3 2 4 2 4 2 1 2 3 4 4 2 4 4 3 2 1 4 4 5 3 2 4 5 4 3 2 3 3 3 2 2 2 2 3 1 2 3 2 3 2 2 4 2 4 1 3 3 3 4 2 2 2 3 4 4 2 4 4 4 2 2 4 2 4 2 4 3 4 4 2 1 4 4 4 2 2 3 2 5 2 2 4 2 3 1 1 2 1 3 2 5 4 2 5 3 2 4 3 5 2 2 4 2 4 2 2 4 2 4 1 1 3 2 3 1 2 1 4 4 2 2 3 3 4 2 2 3 2 5 1 2 4 2 4 2 2 2 4 4 1 1 3 2 5 4 1 5 2 4 4 2 4 3 3 1 2 4 2 4 1 1 3 2 4 3 2 4 2 4 4 2 2 2 4 2 1 3 2 4 4 3 4 2 4 4 3 3 4 4 3 3 4 2 3 4 2 4 2 4 2 2 3 4 3 2 2 3 3 5 2 1 2 2 4 2 4 4 2 5 2 3 3 3 5 2 2 2 1 4 2 2 2 4 4 1 2 3 2 4 3 1 2 4 4 3 2 2 3 4 2 3 4 3 5 4 1 4 4 4 4 2 4 4 3 2 2 2 2 4 2 2 2 4 3 1 1 4 1 4 1 1 2 3 4 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation right [t] = + 3.08781260356635 -0.175565703273633neat[t] + 0.170884076111847failure[t] + 0.0577259776688666performance[t] -0.036240515598931goals[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) 3.08781260356635 0.391143 7.8943 0 0 neat -0.175565703273633 0.084998 -2.0655 0.040549 0.020275 failure 0.170884076111847 0.084734 2.0167 0.045463 0.022731 performance 0.0577259776688666 0.07786 0.7414 0.459575 0.229788 goals -0.036240515598931 0.085975 -0.4215 0.673959 0.336979 Multiple Linear Regression - Regression Statistics Multiple R 0.250034454595201 R-squared 0.0625172284847196 Adjusted R-squared 0.0381670266271799 F-TEST (value) 2.56742136473755 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 0.040330704676335 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.95802062625422 Sum Squared Residuals 141.341742130593 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.98185001019235 -0.981850010192352 2 2 2.64008185796866 -0.640081857968656 3 2 2.83245139615044 -0.83245139615044 4 2 2.67632237356759 -0.676322373567588 5 2 2.69780783563752 -0.697807835637523 6 2 2.50075667029395 -0.500756670293955 7 3 2.58464973719454 0.415350262805458 8 3 2.68100400072937 0.318995999270627 9 4 2.54167881305467 1.45832118694533 10 2 2.64008185796866 -0.640081857968656 11 3 2.77028886683539 0.229711133164615 12 4 2.88574082217312 1.11425917782688 13 2 2.77028886683539 -0.770288866835385 14 3 3.09993481131272 -0.0999348113127153 15 2 2.64476348513044 -0.644763485130442 16 1 2.92641788941824 -1.92641788941824 17 2 2.94585457010902 -0.945854570109018 18 2 3.12142027338265 -1.12142027338265 19 2 2.79177432890532 -0.79177432890532 20 2 2.96734003217895 -0.967340032178953 21 4 3.02277215295307 0.977227847046932 22 4 3.03957598786122 0.960424012138782 23 3 2.90961405451009 0.0903859454899132 24 4 2.94585457010902 1.05414542989098 25 3 2.77028886683539 0.229711133164615 26 2 2.58464973719454 -0.584649737194542 27 3 2.69780783563752 0.302192164362477 28 2 2.73404835123645 -0.734048351236454 29 2 2.69780783563752 -0.697807835637523 30 2 2.77028886683539 -0.770288866835385 31 3 2.86401028458758 0.135989715412415 32 4 2.75553381330639 1.24446618669361 33 4 3.00333547226229 0.996664527737713 34 2 2.83245139615044 -0.83245139615044 35 2 2.70248946279931 -0.702489462799308 36 4 3.03957598786122 0.960424012138782 37 2 3.04425761502300 -1.04425761502300 38 3 2.71256288916652 0.287437110833481 39 4 3.03957598786122 0.960424012138782 40 4 2.81564756124229 1.18435243875771 41 5 2.69312620847574 2.30687379152426 42 3 2.9049324273483 0.0950675726516984 43 2 2.94585457010902 -0.945854570109018 44 2 2.73872997839824 -0.73872997839824 45 2 2.87337353891116 -0.873373538911156 46 3 2.62089025279347 0.379109747206527 47 3 2.77028886683539 0.229711133164615 48 4 3.03957598786122 0.960424012138782 49 2 2.69780783563752 -0.697807835637523 50 4 2.84950030657419 1.15049969342581 51 4 2.64008185796866 1.35991814203134 52 2 2.73404835123645 -0.734048351236454 53 2 2.52224213236389 -0.52224213236389 54 1 2.71724451632830 -1.71724451632830 55 2 3.04655147191776 -1.04655147191776 56 3 2.69312620847574 0.306873791524262 57 2 2.52224213236389 -0.52224213236389 58 2 2.69780783563752 -0.697807835637523 59 2 2.50543829745574 -0.50543829745574 60 4 2.8112110095961 1.18878899040390 61 3 2.73404835123645 0.265951648763546 62 2 2.73404835123645 -0.734048351236454 63 2 2.35135805625204 -0.351358056252043 64 4 2.77028886683539 1.22971113316461 65 2 2.50543829745574 -0.50543829745574 66 2 2.77004379131979 -0.770043791319787 67 3 3.03957598786122 -0.039575987861218 68 2 2.70248946279931 -0.702489462799308 69 2 2.50543829745574 -0.50543829745574 70 2 2.86869191174937 -0.86869191174937 71 2 3.11205701905908 -1.11205701905908 72 2 2.67632237356759 -0.676322373567588 73 2 3.09730196553008 -1.09730196553008 74 4 3.13354248112902 0.866457518870985 75 2 2.92641788941824 -0.926417889418237 76 2 3.21514169113485 -1.21514169113485 77 4 2.73404835123645 1.26595164876355 78 3 2.90961405451009 0.0903859454899132 79 2 2.53699718589289 -0.536997185892886 80 2 2.81325979097526 -0.813259790975256 81 3 2.61620862563169 0.383791374368312 82 1 2.59472316356175 -1.59472316356175 83 4 2.77028886683539 1.22971113316461 84 2 2.56316427512461 -0.563164275124607 85 4 2.88344696527837 1.11655303472163 86 3 2.94117294294723 0.0588270570527674 87 3 2.75553381330639 0.244466186693610 88 4 2.80628430691872 1.19371569308128 89 4 3.03957598786122 0.960424012138782 90 2 2.94585457010902 -0.945854570109018 91 4 2.77028886683539 1.22971113316461 92 1 2.64476348513044 -1.64476348513044 93 3 2.54167881305467 0.458321186945329 94 2 2.56316427512461 -0.563164275124607 95 2 2.73404835123645 -0.734048351236454 96 2 2.77701927537633 -0.777019275376325 97 4 2.9049324273483 1.09506757265170 98 3 3.33059364647258 -0.330593646472584 99 2 2.85188807684122 -0.85188807684122 100 2 3.00358054777788 -1.00358054777788 101 3 3.21514169113485 -0.215141691134851 102 2 2.90961405451009 -0.909614054510087 103 2 3.3715157892333 -1.3715157892333 104 2 2.96734003217895 -0.967340032178953 105 4 2.52224213236389 1.47775786763611 106 4 3.44170296353641 0.55829703646359 107 2 3.02745378011485 -1.02745378011485 108 2 3.11673864622087 -1.11673864622087 109 4 2.96734003217895 1.03265996782105 110 4 3.04893924218479 0.951060757815211 111 4 2.95053619727080 1.04946380272920 112 3 2.73404835123645 0.265951648763546 113 2 3.06130652544675 -1.06130652544675 114 3 3.47016390966288 -0.470163909662884 115 4 3.26303931795211 0.736960682047895 116 2 3.35471195432515 -1.35471195432515 117 4 3.40775630483223 0.592243695167768 118 4 3.23687222872038 0.763127771279616 119 2 2.96734003217895 -0.967340032178953 120 3 3.05362086934657 -0.0536208693465743 121 3 2.81794141813704 0.182058581862958 122 3 3.26074546105735 -0.260745461057353 123 4 3.14290573545259 0.857094264547414 124 4 3.12610190054444 0.873898099455564 125 4 3.01269872658586 0.987301273414142 126 3 3.2923043494945 -0.292304349494498 127 4 2.89042244933490 1.10957755066510 128 4 3.20063171312145 0.799368286878547 129 4 3.23687222872038 0.763127771279616 130 2 2.84950030657419 -0.849500306574187 131 4 3.21538676665045 0.784613233349551 132 5 2.94585457010902 2.05414542989098 133 4 2.99350712141067 1.00649287858933 134 4 3.22006839381223 0.779931606187766 135 4 3.08517975778372 0.91482024221628 136 3 3.33059364647258 -0.330593646472584 137 1 3.35471195432515 -2.35471195432515 138 4 3.14290573545259 0.857094264547414 139 3 3.17914625105152 -0.179146251051517 140 3 2.96734003217895 0.0326599678210465 141 3 2.96734003217895 0.0326599678210465 142 1 3.06130652544675 -2.06130652544675 143 4 3.34739748138073 0.652602518619266 144 5 2.52692375952568 2.47307624047432 145 4 3.42694791000741 0.573052089992585 146 3 2.98882549424889 0.0111745057511110 147 4 3.1382241082908 0.861775891709199 148 3 3.17914625105152 -0.179146251051517 149 4 3.20301948338849 0.796980516611514 150 4 3.12142027338265 0.878579726617349 151 4 3.06598815260854 0.934011847391463 152 5 2.77701927537632 2.22298072462368 153 2 3.45611902817753 -1.45611902817753 154 3 3.15766078898158 -0.157660788981582 155 3 3.19595008595967 -0.195950085959668 156 4 3.17914625105152 0.820853748948483 157 4 2.69780783563752 1.30219216436248 158 3 3.23687222872038 -0.236872228720384 159 4 3.03957598786122 0.960424012138782 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0511807051359942 0.102361410271988 0.948819294864006 9 0.122822258896010 0.245644517792020 0.87717774110399 10 0.0580179552345656 0.116035910469131 0.941982044765434 11 0.0409182095720266 0.0818364191440533 0.959081790427973 12 0.0185276643227372 0.0370553286454744 0.981472335677263 13 0.0647022040058219 0.129404408011644 0.935297795994178 14 0.0415348756782752 0.0830697513565504 0.958465124321725 15 0.0279434073529204 0.0558868147058407 0.97205659264708 16 0.0696090576309877 0.139218115261975 0.930390942369012 17 0.0739986381229636 0.147997276245927 0.926001361877036 18 0.0591766129155215 0.118353225831043 0.940823387084478 19 0.0488243801977298 0.0976487603954595 0.95117561980227 20 0.0338770937052131 0.0677541874104262 0.966122906294787 21 0.184232655613504 0.368465311227009 0.815767344386496 22 0.382343598467759 0.764687196935518 0.617656401532241 23 0.332203666739291 0.664407333478582 0.667796333260709 24 0.360444675823887 0.720889351647774 0.639555324176113 25 0.296666860074501 0.593333720149002 0.703333139925499 26 0.242895507710748 0.485791015421496 0.757104492289252 27 0.221640383170941 0.443280766341881 0.77835961682906 28 0.196095747671122 0.392191495342245 0.803904252328878 29 0.159635862175683 0.319271724351365 0.840364137824317 30 0.156216938088856 0.312433876177712 0.843783061911144 31 0.130794087047222 0.261588174094444 0.869205912952778 32 0.211682883395490 0.423365766790981 0.78831711660451 33 0.267231174119264 0.534462348238528 0.732768825880736 34 0.237059707530097 0.474119415060195 0.762940292469903 35 0.200682550424173 0.401365100848345 0.799317449575827 36 0.209699856859217 0.419399713718434 0.790300143140783 37 0.199883827425212 0.399767654850423 0.800116172574788 38 0.163819122868419 0.327638245736838 0.836180877131581 39 0.166135648367663 0.332271296735325 0.833864351632338 40 0.226889266808770 0.453778533617539 0.77311073319123 41 0.435509735116889 0.871019470233777 0.564490264883111 42 0.382901604392085 0.76580320878417 0.617098395607915 43 0.370824837456217 0.741649674912433 0.629175162543783 44 0.333345572328125 0.66669114465625 0.666654427671875 45 0.304916743744519 0.609833487489038 0.695083256255481 46 0.274251012834580 0.548502025669159 0.72574898716542 47 0.232980091892471 0.465960183784942 0.767019908107529 48 0.224429622450318 0.448859244900635 0.775570377549682 49 0.203095229512620 0.406190459025241 0.79690477048738 50 0.219926726282021 0.439853452564041 0.78007327371798 51 0.272307944588187 0.544615889176374 0.727692055411813 52 0.258696839310591 0.517393678621182 0.741303160689409 53 0.239730761074667 0.479461522149335 0.760269238925333 54 0.303099601239161 0.606199202478322 0.696900398760839 55 0.289829706242271 0.579659412484541 0.71017029375773 56 0.250820823984834 0.501641647969668 0.749179176015166 57 0.230905621057066 0.461811242114132 0.769094378942934 58 0.210603841369426 0.421207682738852 0.789396158630574 59 0.184451219511376 0.368902439022753 0.815548780488624 60 0.217615058412158 0.435230116824317 0.782384941587842 61 0.185869577553590 0.371739155107181 0.81413042244641 62 0.174514228554434 0.349028457108868 0.825485771445566 63 0.149832817175586 0.299665634351171 0.850167182824415 64 0.160878899254248 0.321757798508496 0.839121100745752 65 0.140419676827673 0.280839353655346 0.859580323172327 66 0.14259556932957 0.28519113865914 0.85740443067043 67 0.118260994176738 0.236521988353476 0.881739005823262 68 0.107085332924824 0.214170665849647 0.892914667075176 69 0.0936940335198297 0.187388067039659 0.90630596648017 70 0.0931091570786377 0.186218314157275 0.906890842921362 71 0.121133106190348 0.242266212380696 0.878866893809652 72 0.113454528558602 0.226909057117204 0.886545471441398 73 0.124984981391691 0.249969962783381 0.87501501860831 74 0.118275499279239 0.236550998558479 0.88172450072076 75 0.119063958539250 0.238127917078499 0.88093604146075 76 0.132363275013276 0.264726550026552 0.867636724986724 77 0.149961791861424 0.299923583722847 0.850038208138576 78 0.127852840094986 0.255705680189973 0.872147159905014 79 0.123322427239046 0.246644854478093 0.876677572760953 80 0.118576829192744 0.237153658385488 0.881423170807256 81 0.0978071167862947 0.195614233572589 0.902192883213705 82 0.170321763707552 0.340643527415104 0.829678236292448 83 0.182049716878433 0.364099433756865 0.817950283121567 84 0.172606623974853 0.345213247949707 0.827393376025147 85 0.171883312774960 0.343766625549919 0.82811668722504 86 0.144173312361743 0.288346624723486 0.855826687638257 87 0.123736372847667 0.247472745695335 0.876263627152333 88 0.122524959985277 0.245049919970555 0.877475040014723 89 0.118861178987333 0.237722357974666 0.881138821012667 90 0.119352538709592 0.238705077419185 0.880647461290408 91 0.128509204082299 0.257018408164597 0.871490795917701 92 0.222535296412863 0.445070592825725 0.777464703587137 93 0.193457053550455 0.386914107100909 0.806542946449545 94 0.195352390116881 0.390704780233762 0.80464760988312 95 0.205593590564341 0.411187181128681 0.79440640943566 96 0.229828364030750 0.459656728061501 0.77017163596925 97 0.227062535714599 0.454125071429197 0.772937464285401 98 0.194147572373697 0.388295144747393 0.805852427626303 99 0.220654269957017 0.441308539914034 0.779345730042983 100 0.233792155673685 0.467584311347369 0.766207844326316 101 0.203291041370562 0.406582082741124 0.796708958629438 102 0.237586376001162 0.475172752002324 0.762413623998838 103 0.252621336338159 0.505242672676318 0.747378663661841 104 0.286882844565382 0.573765689130764 0.713117155434618 105 0.284957470426016 0.569914940852032 0.715042529573984 106 0.28867453905156 0.57734907810312 0.71132546094844 107 0.359846943269406 0.719693886538812 0.640153056730594 108 0.404556239998433 0.809112479996866 0.595443760001567 109 0.411334867444594 0.822669734889188 0.588665132555406 110 0.429102941090919 0.858205882181839 0.570897058909081 111 0.435693123028542 0.871386246057085 0.564306876971458 112 0.411339352246558 0.822678704493116 0.588660647753442 113 0.436078419554279 0.872156839108559 0.563921580445721 114 0.387627303297391 0.775254606594782 0.612372696702609 115 0.418367780372238 0.836735560744476 0.581632219627762 116 0.449266327529099 0.898532655058198 0.550733672470901 117 0.460879804527603 0.921759609055205 0.539120195472397 118 0.472781326104399 0.945562652208799 0.527218673895601 119 0.568899440350754 0.862201119298492 0.431100559649246 120 0.593310959827829 0.813378080344342 0.406689040172171 121 0.587950906866126 0.824098186267747 0.412049093133874 122 0.574974411943241 0.850051176113517 0.425025588056759 123 0.546785883995838 0.906428232008324 0.453214116004162 124 0.515137178232019 0.969725643535962 0.484862821767981 125 0.510579051620995 0.97884189675801 0.489420948379005 126 0.464026296935766 0.928052593871532 0.535973703064234 127 0.463886978937676 0.927773957875351 0.536113021062324 128 0.443995245266567 0.887990490533135 0.556004754733433 129 0.470770460822468 0.941540921644935 0.529229539177532 130 0.541930200677311 0.916139598645378 0.458069799322689 131 0.575110661686604 0.849778676626792 0.424889338313396 132 0.698562743273628 0.602874513452744 0.301437256726372 133 0.653727524429497 0.692544951141007 0.346272475570503 134 0.728870386199199 0.542259227601603 0.271129613800801 135 0.677313325725747 0.645373348548507 0.322686674274253 136 0.629902825654615 0.74019434869077 0.370097174345385 137 0.918579401702393 0.162841196595214 0.0814205982976071 138 0.889393191317017 0.221213617365965 0.110606808682983 139 0.847376610060405 0.305246779879190 0.152623389939595 140 0.819950033918167 0.360099932163667 0.180049966081833 141 0.793041831986755 0.41391633602649 0.206958168013245 142 0.98036124475297 0.0392775104940607 0.0196387552470303 143 0.97368557048833 0.0526288590233392 0.0263144295116696 144 0.9645000031825 0.0709999936349993 0.0354999968174996 145 0.953223162881812 0.0935536742363751 0.0467768371181876 146 0.98361757084036 0.0327648583192808 0.0163824291596404 147 0.976150853265447 0.0476982934691065 0.0238491467345532 148 0.964718971442618 0.070562057114763 0.0352810285573815 149 0.949166756998338 0.101666486003324 0.0508332430016619 150 0.897903440363582 0.204193119272835 0.102096559636417 151 0.824655298132912 0.350689403734175 0.175344701867088 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 4 0.0277777777777778 OK 10% type I error level 13 0.0902777777777778 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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