*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 30 Nov 2010 13:02:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h.htm/, Retrieved Tue, 30 Nov 2010 14:01:51 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h.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 «

2 12 2 11 2 14 1 12 2 21 2 12 2 22 2 11 2 10 2 13 1 10 2 8 1 15 2 14 2 10 1 14 1 14 2 11 1 10 2 13 1 7 2 14 2 12 2 14 1 11 2 9 1 11 2 15 2 14 1 13 2 9 1 15 2 10 2 11 1 13 1 8 1 20 1 12 2 10 1 10 1 9 2 14 1 8 1 14 2 11 2 13 2 9 2 11 2 15 1 11 2 10 1 14 1 18 2 14 1 11 2 12 2 13 2 9 1 10 2 15 1 20 1 12 2 12 2 14 2 13 1 11 2 17 1 12 2 13 1 14 1 13 2 15 2 13 1 10 1 11 2 19 2 13 2 17 1 13 1 9 1 11 1 10 2 9 1 12 2 12 2 13 1 13 2 12 2 15 2 22 2 13 2 15 2 13 2 15 2 10 2 11 2 16 2 11 1 11 1 10 2 10 1 16 2 12 1 11 2 16 1 19 2 11 1 16 1 15 2 24 2 14 2 15 2 11 1 15 2 12 1 10 2 14 2 13 2 9 2 15 2 15 2 14 2 11 2 8 2 11 2 11 1 8 2 10 2 11 2 13 1 11 1 20 2 10 1 15 1 12 2 14 1 23 1 14 2 16 2 11 1 12 2 10 1 14 2 12 1 12 2 11 2 12 1 13 1 11 1 19 2 12 2 17 1 9 2 12 2 19 2 18 2 15 2 14 2 11 2 9 2 18 2 16

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 12.4457068657685 + 0.291998052264244x[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) 12.4457068657685 0.871666 14.2781 0 0 x 0.291998052264244 0.514495 0.5675 0.571141 0.28557 Multiple Linear Regression - Regression Statistics Multiple R 0.0448231217392387 R-squared 0.00200911224245061 Adjusted R-squared -0.00422833080603424 F-TEST (value) 0.322105104100101 F-TEST (DF numerator) 1 F-TEST (DF denominator) 160 p-value 0.571140774666708 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.17284786290018 Sum Squared Residuals 1610.71416977763 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 13.0297029702971 -1.02970297029708 2 11 13.0297029702970 -2.02970297029703 3 14 13.0297029702970 0.97029702970297 4 12 12.7377049180328 -0.737704918032786 5 21 13.0297029702970 7.97029702970297 6 12 13.0297029702970 -1.02970297029703 7 22 13.0297029702970 8.97029702970297 8 11 13.0297029702970 -2.02970297029703 9 10 13.0297029702970 -3.02970297029703 10 13 13.0297029702970 -0.0297029702970298 11 10 12.7377049180328 -2.73770491803279 12 8 13.0297029702970 -5.02970297029703 13 15 12.7377049180328 2.26229508196721 14 14 13.0297029702970 0.97029702970297 15 10 13.0297029702970 -3.02970297029703 16 14 12.7377049180328 1.26229508196721 17 14 12.7377049180328 1.26229508196721 18 11 13.0297029702970 -2.02970297029703 19 10 12.7377049180328 -2.73770491803279 20 13 13.0297029702970 -0.0297029702970298 21 7 12.7377049180328 -5.73770491803279 22 14 13.0297029702970 0.97029702970297 23 12 13.0297029702970 -1.02970297029703 24 14 13.0297029702970 0.97029702970297 25 11 12.7377049180328 -1.73770491803279 26 9 13.0297029702970 -4.02970297029703 27 11 12.7377049180328 -1.73770491803279 28 15 13.0297029702970 1.97029702970297 29 14 13.0297029702970 0.97029702970297 30 13 12.7377049180328 0.262295081967214 31 9 13.0297029702970 -4.02970297029703 32 15 12.7377049180328 2.26229508196721 33 10 13.0297029702970 -3.02970297029703 34 11 13.0297029702970 -2.02970297029703 35 13 12.7377049180328 0.262295081967214 36 8 12.7377049180328 -4.73770491803279 37 20 12.7377049180328 7.26229508196721 38 12 12.7377049180328 -0.737704918032786 39 10 13.0297029702970 -3.02970297029703 40 10 12.7377049180328 -2.73770491803279 41 9 12.7377049180328 -3.73770491803279 42 14 13.0297029702970 0.97029702970297 43 8 12.7377049180328 -4.73770491803279 44 14 12.7377049180328 1.26229508196721 45 11 13.0297029702970 -2.02970297029703 46 13 13.0297029702970 -0.0297029702970298 47 9 13.0297029702970 -4.02970297029703 48 11 13.0297029702970 -2.02970297029703 49 15 13.0297029702970 1.97029702970297 50 11 12.7377049180328 -1.73770491803279 51 10 13.0297029702970 -3.02970297029703 52 14 12.7377049180328 1.26229508196721 53 18 12.7377049180328 5.26229508196721 54 14 13.0297029702970 0.97029702970297 55 11 12.7377049180328 -1.73770491803279 56 12 13.0297029702970 -1.02970297029703 57 13 13.0297029702970 -0.0297029702970298 58 9 13.0297029702970 -4.02970297029703 59 10 12.7377049180328 -2.73770491803279 60 15 13.0297029702970 1.97029702970297 61 20 12.7377049180328 7.26229508196721 62 12 12.7377049180328 -0.737704918032786 63 12 13.0297029702970 -1.02970297029703 64 14 13.0297029702970 0.97029702970297 65 13 13.0297029702970 -0.0297029702970298 66 11 12.7377049180328 -1.73770491803279 67 17 13.0297029702970 3.97029702970297 68 12 12.7377049180328 -0.737704918032786 69 13 13.0297029702970 -0.0297029702970298 70 14 12.7377049180328 1.26229508196721 71 13 12.7377049180328 0.262295081967214 72 15 13.0297029702970 1.97029702970297 73 13 13.0297029702970 -0.0297029702970298 74 10 12.7377049180328 -2.73770491803279 75 11 12.7377049180328 -1.73770491803279 76 19 13.0297029702970 5.97029702970297 77 13 13.0297029702970 -0.0297029702970298 78 17 13.0297029702970 3.97029702970297 79 13 12.7377049180328 0.262295081967214 80 9 12.7377049180328 -3.73770491803279 81 11 12.7377049180328 -1.73770491803279 82 10 12.7377049180328 -2.73770491803279 83 9 13.0297029702970 -4.02970297029703 84 12 12.7377049180328 -0.737704918032786 85 12 13.0297029702970 -1.02970297029703 86 13 13.0297029702970 -0.0297029702970298 87 13 12.7377049180328 0.262295081967214 88 12 13.0297029702970 -1.02970297029703 89 15 13.0297029702970 1.97029702970297 90 22 13.0297029702970 8.97029702970297 91 13 13.0297029702970 -0.0297029702970298 92 15 13.0297029702970 1.97029702970297 93 13 13.0297029702970 -0.0297029702970298 94 15 13.0297029702970 1.97029702970297 95 10 13.0297029702970 -3.02970297029703 96 11 13.0297029702970 -2.02970297029703 97 16 13.0297029702970 2.97029702970297 98 11 13.0297029702970 -2.02970297029703 99 11 12.7377049180328 -1.73770491803279 100 10 12.7377049180328 -2.73770491803279 101 10 13.0297029702970 -3.02970297029703 102 16 12.7377049180328 3.26229508196721 103 12 13.0297029702970 -1.02970297029703 104 11 12.7377049180328 -1.73770491803279 105 16 13.0297029702970 2.97029702970297 106 19 12.7377049180328 6.26229508196721 107 11 13.0297029702970 -2.02970297029703 108 16 12.7377049180328 3.26229508196721 109 15 12.7377049180328 2.26229508196721 110 24 13.0297029702970 10.9702970297030 111 14 13.0297029702970 0.97029702970297 112 15 13.0297029702970 1.97029702970297 113 11 13.0297029702970 -2.02970297029703 114 15 12.7377049180328 2.26229508196721 115 12 13.0297029702970 -1.02970297029703 116 10 12.7377049180328 -2.73770491803279 117 14 13.0297029702970 0.97029702970297 118 13 13.0297029702970 -0.0297029702970298 119 9 13.0297029702970 -4.02970297029703 120 15 13.0297029702970 1.97029702970297 121 15 13.0297029702970 1.97029702970297 122 14 13.0297029702970 0.97029702970297 123 11 13.0297029702970 -2.02970297029703 124 8 13.0297029702970 -5.02970297029703 125 11 13.0297029702970 -2.02970297029703 126 11 13.0297029702970 -2.02970297029703 127 8 12.7377049180328 -4.73770491803279 128 10 13.0297029702970 -3.02970297029703 129 11 13.0297029702970 -2.02970297029703 130 13 13.0297029702970 -0.0297029702970298 131 11 12.7377049180328 -1.73770491803279 132 20 12.7377049180328 7.26229508196721 133 10 13.0297029702970 -3.02970297029703 134 15 12.7377049180328 2.26229508196721 135 12 12.7377049180328 -0.737704918032786 136 14 13.0297029702970 0.97029702970297 137 23 12.7377049180328 10.2622950819672 138 14 12.7377049180328 1.26229508196721 139 16 13.0297029702970 2.97029702970297 140 11 13.0297029702970 -2.02970297029703 141 12 12.7377049180328 -0.737704918032786 142 10 13.0297029702970 -3.02970297029703 143 14 12.7377049180328 1.26229508196721 144 12 13.0297029702970 -1.02970297029703 145 12 12.7377049180328 -0.737704918032786 146 11 13.0297029702970 -2.02970297029703 147 12 13.0297029702970 -1.02970297029703 148 13 12.7377049180328 0.262295081967214 149 11 12.7377049180328 -1.73770491803279 150 19 12.7377049180328 6.26229508196721 151 12 13.0297029702970 -1.02970297029703 152 17 13.0297029702970 3.97029702970297 153 9 12.7377049180328 -3.73770491803279 154 12 13.0297029702970 -1.02970297029703 155 19 13.0297029702970 5.97029702970297 156 18 13.0297029702970 4.97029702970297 157 15 13.0297029702970 1.97029702970297 158 14 13.0297029702970 0.97029702970297 159 11 13.0297029702970 -2.02970297029703 160 9 13.0297029702970 -4.02970297029703 161 18 13.0297029702970 4.97029702970297 162 16 13.0297029702970 2.97029702970297 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.890311882137785 0.21937623572443 0.109688117862215 6 0.835678091070186 0.328643817859628 0.164321908929814 7 0.967359506805803 0.0652809863883943 0.0326404931941972 8 0.967051108276131 0.0658977834477383 0.0329488917238691 9 0.97124642118687 0.0575071576262595 0.0287535788131297 10 0.952844620174595 0.0943107596508092 0.0471553798254046 11 0.931023665218445 0.137952669563110 0.0689763347815549 12 0.962344418926067 0.0753111621478665 0.0376555810739332 13 0.95754928503602 0.084901429927961 0.0424507149639805 14 0.936483306024963 0.127033387950074 0.063516693975037 15 0.932250222631816 0.135499554736368 0.0677497773681841 16 0.908512845111864 0.182974309776271 0.0914871548881356 17 0.877803759480582 0.244392481038836 0.122196240519418 18 0.852392885549283 0.295214228901434 0.147607114450717 19 0.836954172002272 0.326091655995456 0.163045827997728 20 0.789969157273412 0.420061685453176 0.210030842726588 21 0.850812523206204 0.298374953587591 0.149187476793796 22 0.812261981437177 0.375476037125647 0.187738018562823 23 0.769459168695263 0.461081662609475 0.230540831304738 24 0.72187780334191 0.55624439331618 0.27812219665809 25 0.670794817716318 0.658410364567364 0.329205182283682 26 0.696687308262123 0.606625383475753 0.303312691737877 27 0.645456399634279 0.709087200731442 0.354543600365721 28 0.611349623468542 0.777300753062916 0.388650376531458 29 0.558176434913756 0.883647130172489 0.441823565086244 30 0.507620918207734 0.984758163584531 0.492379081792266 31 0.537588636417831 0.924822727164338 0.462411363582169 32 0.52951873842419 0.94096252315162 0.47048126157581 33 0.516531339567294 0.966937320865412 0.483468660432706 34 0.476866646361124 0.953733292722247 0.523133353638876 35 0.425108524832067 0.850217049664133 0.574891475167933 36 0.464446972652359 0.928893945304718 0.535553027347641 37 0.713884456341352 0.572231087317297 0.286115543658648 38 0.667777034782605 0.66444593043479 0.332222965217395 39 0.653353570359294 0.693292859281412 0.346646429640706 40 0.632073907408965 0.73585218518207 0.367926092591035 41 0.63582478862576 0.728350422748481 0.364175211374241 42 0.594583792071748 0.810832415856504 0.405416207928252 43 0.631492225257272 0.737015549485456 0.368507774742728 44 0.599701873454206 0.800596253091589 0.400298126545794 45 0.564738125467717 0.870523749064566 0.435261874532283 46 0.515410129082943 0.969179741834113 0.484589870917057 47 0.533014255892546 0.933971488214909 0.466985744107454 48 0.497252964291201 0.994505928582403 0.502747035708799 49 0.475744195012975 0.95148839002595 0.524255804987025 50 0.435945833612265 0.87189166722453 0.564054166387735 51 0.422980679139512 0.845961358279023 0.577019320860488 52 0.391255770692373 0.782511541384746 0.608744229307627 53 0.494691188328734 0.989382376657468 0.505308811671266 54 0.45576791473588 0.91153582947176 0.54423208526412 55 0.419356373665056 0.838712747330112 0.580643626334944 56 0.376222087348892 0.752444174697785 0.623777912651108 57 0.332970358241738 0.665940716483476 0.667029641758262 58 0.350593608767429 0.701187217534859 0.649406391232571 59 0.33471863049242 0.66943726098484 0.66528136950758 60 0.315964286852916 0.631928573705833 0.684035713147084 61 0.523827366180146 0.952345267639708 0.476172633819854 62 0.479387256915321 0.958774513830642 0.520612743084679 63 0.436965563291438 0.873931126582877 0.563034436708562 64 0.399407258542133 0.798814517084266 0.600592741457867 65 0.356496409742313 0.712992819484625 0.643503590257687 66 0.325548195794705 0.65109639158941 0.674451804205295 67 0.357486948365992 0.714973896731984 0.642513051634008 68 0.317600025738196 0.635200051476392 0.682399974261804 69 0.278441387613626 0.556882775227253 0.721558612386374 70 0.248434635055499 0.496869270110998 0.751565364944501 71 0.214344467255381 0.428688934510762 0.78565553274462 72 0.196828227182862 0.393656454365725 0.803171772817138 73 0.167059779918639 0.334119559837279 0.83294022008136 74 0.159316605542874 0.318633211085747 0.840683394457126 75 0.140677612042492 0.281355224084983 0.859322387957508 76 0.220141291219783 0.440282582439566 0.779858708780217 77 0.188156173527561 0.376312347055121 0.81184382647244 78 0.207254112103335 0.41450822420667 0.792745887896665 79 0.177254062668596 0.354508125337191 0.822745937331404 80 0.189519073674162 0.379038147348325 0.810480926325838 81 0.170086580915433 0.340173161830867 0.829913419084567 82 0.165105982851625 0.33021196570325 0.834894017148375 83 0.182684272698450 0.365368545396900 0.81731572730155 84 0.157793791049837 0.315587582099674 0.842206208950163 85 0.134628911123000 0.269257822245999 0.865371088877 86 0.111753494138726 0.223506988277453 0.888246505861274 87 0.0929210295172339 0.185842059034468 0.907078970482766 88 0.0772271127951671 0.154454225590334 0.922772887204833 89 0.0678832518368949 0.135766503673790 0.932116748163105 90 0.242821755046978 0.485643510093956 0.757178244953022 91 0.208729772405988 0.417459544811975 0.791270227594012 92 0.189150534065514 0.378301068131027 0.810849465934486 93 0.159898143111862 0.319796286223725 0.840101856888138 94 0.143395631364223 0.286791262728445 0.856604368635777 95 0.140933374860930 0.281866749721860 0.85906662513907 96 0.126385568582101 0.252771137164202 0.873614431417899 97 0.123087391903844 0.246174783807687 0.876912608096156 98 0.109775615331437 0.219551230662874 0.890224384668563 99 0.0987940485131316 0.197588097026263 0.901205951486868 100 0.0994346348750596 0.198869269750119 0.90056536512494 101 0.0978481145314125 0.195696229062825 0.902151885468587 102 0.095415535653008 0.190831071306016 0.904584464346992 103 0.0791166628675102 0.158233325735020 0.92088333713249 104 0.071791243162145 0.14358248632429 0.928208756837855 105 0.0692007313019632 0.138401462603926 0.930799268698037 106 0.112504882106532 0.225009764213063 0.887495117893468 107 0.0998508591771636 0.199701718354327 0.900149140822836 108 0.0958005096634936 0.191601019326987 0.904199490336506 109 0.0834543091662693 0.166908618332539 0.91654569083373 110 0.453340851213032 0.906681702426064 0.546659148786968 111 0.41068627869065 0.8213725573813 0.58931372130935 112 0.383387365583242 0.766774731166485 0.616612634416758 113 0.353705506618928 0.707411013237857 0.646294493381072 114 0.323452654819337 0.646905309638673 0.676547345180663 115 0.283830801935407 0.567661603870814 0.716169198064593 116 0.286413042009816 0.572826084019632 0.713586957990184 117 0.249647022729069 0.499294045458137 0.750352977270931 118 0.211438195026787 0.422876390053574 0.788561804973213 119 0.229461281996368 0.458922563992735 0.770538718003632 120 0.206455199339667 0.412910398679334 0.793544800660333 121 0.185311040687228 0.370622081374457 0.814688959312772 122 0.156350860714379 0.312701721428759 0.84364913928562 123 0.136423907499085 0.27284781499817 0.863576092500915 124 0.176993847154302 0.353987694308604 0.823006152845698 125 0.156882827712314 0.313765655424627 0.843117172287686 126 0.138838636272042 0.277677272544085 0.861161363727958 127 0.205550307747893 0.411100615495787 0.794449692252107 128 0.204537441318984 0.409074882637967 0.795462558681016 129 0.185633618830582 0.371267237661164 0.814366381169418 130 0.151091896024199 0.302183792048397 0.848908103975801 131 0.145776408278417 0.291552816556835 0.854223591721583 132 0.246626802797540 0.493253605595080 0.75337319720246 133 0.25294011265139 0.50588022530278 0.74705988734861 134 0.216259236833151 0.432518473666303 0.783740763166849 135 0.186627046517319 0.373254093034638 0.813372953482681 136 0.149482857444099 0.298965714888198 0.850517142555901 137 0.568205950023176 0.863588099953649 0.431794049976824 138 0.510920602777833 0.978158794444334 0.489079397222167 139 0.48414894603838 0.96829789207676 0.51585105396162 140 0.45960056906177 0.91920113812354 0.54039943093823 141 0.397106647643525 0.794213295287051 0.602893352356475 142 0.420645718999328 0.841291437998655 0.579354281000672 143 0.359612386292654 0.719224772585309 0.640387613707346 144 0.316595405942459 0.633190811884918 0.683404594057541 145 0.257096254441670 0.514192508883341 0.74290374555833 146 0.250273198610364 0.500546397220729 0.749726801389636 147 0.220376866206384 0.440753732412767 0.779623133793616 148 0.164784203888478 0.329568407776955 0.835215796111522 149 0.138906887210952 0.277813774421905 0.861093112789048 150 0.363404914361201 0.726809828722403 0.636595085638799 151 0.333752787383088 0.667505574766176 0.666247212616912 152 0.290349170838613 0.580698341677225 0.709650829161387 153 0.212783847381234 0.425567694762469 0.787216152618766 154 0.182681656542127 0.365363313084253 0.817318343457873 155 0.228184145081917 0.456368290163833 0.771815854918083 156 0.250266346010647 0.500532692021294 0.749733653989353 157 0.155825066827269 0.311650133654538 0.844174933172731 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 6 0.0392156862745098 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/10x23l1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/10x23l1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/1q16r1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/1q16r1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/21b5u1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/21b5u1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/31b5u1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/31b5u1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/41b5u1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/41b5u1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/5uk4x1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/5uk4x1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/6uk4x1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/6uk4x1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/7ntm01291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/7ntm01291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/8x23l1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/8x23l1291122157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/9x23l1291122157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911220995l1ao9stm4mg09h/9x23l1291122157.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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