Hypothesis Testing Connected Paper

*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, 23 Nov 2010 10:02:46 +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/23/t1290506632smmjfw6ziqtzlrs.htm/, Retrieved Tue, 23 Nov 2010 11:04:04 +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/23/t1290506632smmjfw6ziqtzlrs.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 «

14 12 41 18 11 39 11 14 30 12 12 31 16 21 34 18 12 35 14 22 39 14 11 34 15 10 36 15 13 37 17 10 38 19 8 36 10 15 38 16 14 39 18 10 33 14 14 32 14 14 36 17 11 38 14 10 39 16 13 32 18 7 32 11 14 31 14 12 39 12 14 37 17 11 39 9 9 41 16 11 36 14 15 33 15 14 33 11 13 34 16 9 31 13 15 27 17 10 37 15 11 34 14 13 34 16 8 32 9 20 29 15 12 36 17 10 29 13 10 35 15 9 37 16 14 34 16 8 38 12 14 35 12 11 38 11 13 37 15 9 38 15 11 33 17 15 36 13 11 38 16 10 32 14 14 32 11 18 32 12 14 34 12 11 32 15 12 37 16 13 39 15 9 29 12 10 37 12 15 35 8 20 30 13 12 38 11 12 34 14 14 31 15 13 34 10 11 35 11 17 36 12 12 30 15 13 39 15 14 35 14 13 38 16 15 31 15 13 34 15 10 38 13 11 34 12 19 39 17 13 37 13 17 34 15 13 28 13 9 37 15 11 33 16 10 37 15 9 35 16 12 37 15 12 32 14 13 33 15 13 38 14 12 33 13 15 29 7 22 33 17 13 31 13 15 36 15 13 35 14 15 32 13 10 29 16 11 39 12 16 37 14 11 35 17 11 37 15 10 32 17 10 38 12 16 37 16 12 36 11 11 32 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 51 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Conn[t] = + 33.2324706807633 + 0.158472808251304Happ[t] -0.0645138156938048Depr[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) 33.2324706807633 2.822206 11.7754 0 0 Happ 0.158472808251304 0.134913 1.1746 0.241898 0.120949 Depr -0.0645138156938048 0.099608 -0.6477 0.518127 0.259064 Multiple Linear Regression - Regression Statistics Multiple R 0.151458819815009 R-squared 0.0229397740997553 Adjusted R-squared 0.0106497083651611 F-TEST (value) 1.86652981319571 F-TEST (DF numerator) 2 F-TEST (DF denominator) 159 p-value 0.158032381913384 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.35710886629123 Sum Squared Residuals 1791.95861048086 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 34.6769242079564 6.32307579204359 2 39 35.375329256655 3.624670743345 3 30 34.0724781518145 -4.07247815181446 4 31 34.3599785914534 -3.35997859145337 5 34 34.4132454832143 -0.413245483214345 6 35 35.3108154409612 -0.310815440961197 7 39 34.0317860510179 4.96821394898207 8 34 34.7414380236498 -0.741438023649784 9 36 34.9644246475949 1.03557535240511 10 37 34.7708832005135 2.22911679948652 11 38 35.2813702640975 2.7186297359025 12 36 35.7273435119877 0.272656488012279 13 38 33.8494915278693 4.15050847213065 14 39 34.864842193071 4.13515780692902 15 33 35.4398430723488 -2.43984307234881 16 32 34.5478965765684 -2.54789657656837 17 36 34.5478965765684 1.45210342343163 18 38 35.2168564484037 2.7831435515963 19 39 34.8059518393436 4.19404816065641 20 32 34.9293560087648 -2.92935600876478 21 32 35.6333845194302 -3.63338451943022 22 31 34.0724781518145 -3.07247815181446 23 39 34.676924207956 4.32307579204402 24 37 34.2309509600658 2.76904903993424 25 39 35.2168564484037 3.7831435515963 26 41 34.0781016137809 6.92189838621913 27 36 35.0583836401524 0.941616359847607 28 33 34.4833827608746 -1.48338276087456 29 33 34.7063693848197 -1.70636938481967 30 34 34.1369919675083 -0.136991967508261 31 31 35.18741127154 -4.18741127154 32 27 34.3249099526233 -7.32490995262326 33 37 35.2813702640975 1.71862973590250 34 34 34.8999108319011 -0.899910831901089 35 34 34.6124103922622 -0.612410392262174 36 32 35.2519250872338 -3.25192508723381 37 29 33.368449641149 -4.36844964114902 38 36 34.8353970162073 1.16460298379272 39 29 35.2813702640975 -6.2813702640975 40 35 34.6474790310923 0.352520968907715 41 37 35.0289384632887 1.9710615367113 42 34 34.864842193071 -0.864842193070979 43 38 35.2519250872338 2.74807491276619 44 35 34.2309509600658 0.769049039934239 45 38 34.4244924071472 3.57550759285282 46 37 34.1369919675083 2.86300803249174 47 38 35.0289384632887 2.9710615367113 48 33 34.8999108319011 -1.89991083190109 49 36 34.9588011856285 1.04119881437152 50 38 34.5829652153985 3.41703478460152 51 32 35.1228974558462 -3.1228974558462 52 32 34.5478965765684 -2.54789657656837 53 32 33.8144228890392 -1.81442288903924 54 34 34.2309509600658 -0.230950960065761 55 32 34.4244924071472 -2.42449240714718 56 37 34.8353970162073 2.16460298379272 57 39 34.9293560087648 4.07064399123522 58 29 35.0289384632887 -6.0289384632887 59 37 34.489006222841 2.51099377715902 60 35 34.1664371443720 0.833562855628044 61 30 33.2099768328977 -3.20997683289771 62 38 34.5184513997047 3.48154860029532 63 34 34.2015057832021 -0.201505783202066 64 31 34.5478965765684 -3.54789657656837 65 34 34.7708832005135 -0.77088320051348 66 35 34.1075467906446 0.892453209355433 67 36 33.8789367047330 2.12106329526696 68 30 34.3599785914534 -4.35997859145337 69 39 34.7708832005135 4.22911679948652 70 35 34.7063693848197 0.293630615180326 71 38 34.6124103922622 3.38758960773783 72 31 34.8003283773772 -3.80032837737717 73 34 34.7708832005135 -0.77088320051348 74 38 34.9644246475949 3.03557535240511 75 34 34.5829652153985 -0.58296521539848 76 39 33.9083818815967 5.09161811840326 77 37 35.0878288170161 1.91217118298391 78 34 34.1958823212357 -0.195882321235650 79 28 34.7708832005135 -6.77088320051348 80 37 34.7119928467861 2.28800715321391 81 33 34.8999108319011 -1.89991083190109 82 37 35.1228974558462 1.87710254415380 83 35 35.0289384632887 -0.0289384632886986 84 37 34.9938698244586 2.00613017554141 85 32 34.8353970162073 -2.83539701620728 86 33 34.6124103922622 -1.61241039226218 87 38 34.7708832005135 3.22911679948652 88 33 34.676924207956 -1.67692420795598 89 29 34.3249099526233 -5.32490995262326 90 33 32.9224763932588 0.0775236067412003 91 31 35.0878288170161 -4.08782881701609 92 36 34.3249099526233 1.67509004737674 93 35 34.7708832005135 0.229116799486521 94 32 34.4833827608746 -2.48338276087456 95 29 34.6474790310923 -5.64747903109228 96 39 35.0583836401524 3.94161635984761 97 37 34.1019233286782 2.89807667132185 98 35 34.7414380236498 0.258561976350216 99 37 35.2168564484037 1.7831435515963 100 32 34.9644246475949 -2.96442464759489 101 38 35.2813702640975 2.7186297359025 102 37 34.1019233286782 2.89807667132185 103 36 34.9938698244586 1.00613017554141 104 32 34.2660195988959 -2.26601959889587 105 33 34.5773417534321 -1.57734175343207 106 40 33.4329634568428 6.56703654315718 107 38 35.0583836401524 2.94161635984761 108 41 34.5773417534321 6.42265824656794 109 36 33.8494915278693 2.15050847213065 110 43 33.2688671866251 9.7311328133749 111 30 34.7063693848197 -4.70636938481967 112 31 34.0079643361207 -3.00796433612065 113 32 34.5829652153985 -2.58296521539848 114 32 34.4833827608746 -2.48338276087456 115 37 35.3108154409612 1.68918455903880 116 37 35.1228974558462 1.87710254415380 117 33 34.5478965765684 -1.54789657656837 118 34 34.6124103922622 -0.612410392262174 119 33 34.8704656550374 -1.87046565503739 120 38 34.4833827608746 3.51661723912544 121 33 34.1664371443720 -1.16643714437196 122 31 34.5478965765684 -3.54789657656837 123 38 34.8999108319011 3.10008916809891 124 37 35.0934522789825 1.90654772101750 125 33 34.8999108319011 -1.89991083190109 126 31 34.5829652153985 -3.58296521539848 127 39 35.4103978954851 3.58960210451489 128 44 35.2813702640975 8.7186297359025 129 33 35.5338020649063 -2.53380206490631 130 35 34.7708832005135 0.229116799486521 131 32 34.5829652153985 -2.58296521539848 132 28 33.368449641149 -5.36844964114902 133 40 34.9644246475949 5.03557535240511 134 27 34.6418555691259 -7.64185556912587 135 37 34.8353970162073 2.16460298379272 136 32 34.864842193071 -2.86484219307098 137 28 33.4918538105702 -5.49185381057021 138 34 34.5478965765684 -0.54789657656837 139 30 33.9434505204268 -3.94345052042685 140 35 34.8999108319011 0.100089168098911 141 31 34.5184513997047 -3.51845139970468 142 32 34.9644246475949 -2.96442464759489 143 30 34.864842193071 -4.86484219307098 144 30 34.676924207956 -4.67692420795598 145 31 34.8353970162073 -3.83539701620728 146 40 35.0583836401524 4.94161635984761 147 32 34.9938698244586 -2.99386982445859 148 36 34.1369919675083 1.86300803249174 149 32 34.4244924071472 -2.42449240714718 150 35 33.4329634568428 1.56703654315718 151 38 34.9938698244586 3.00613017554141 152 42 34.1958823212357 7.80411767876435 153 34 35.18741127154 -1.18741127154000 154 35 34.3599785914534 0.64002140854663 155 35 33.4329634568428 1.56703654315718 156 33 34.1313685055418 -1.13136850554185 157 36 34.3249099526233 1.67509004737674 158 32 34.5478965765684 -2.54789657656837 159 33 35.5338020649063 -2.53380206490631 160 34 34.7119928467861 -0.71199284678609 161 32 33.9728956972905 -1.97289569729054 162 34 34.2603961369295 -0.260396136929455 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.824448587133094 0.351102825733811 0.175551412866906 7 0.875152960676748 0.249694078646503 0.124847039323252 8 0.795971857734683 0.408056284530635 0.204028142265317 9 0.701732516621466 0.596534966757068 0.298267483378534 10 0.611017537271302 0.777964925457396 0.388982462728698 11 0.51174928220538 0.97650143558924 0.48825071779462 12 0.454415908618031 0.908831817236062 0.545584091381969 13 0.530935591564318 0.938128816871364 0.469064408435682 14 0.491242875238056 0.982485750476112 0.508757124761944 15 0.510585272161981 0.978829455676037 0.489414727838019 16 0.51955046964345 0.9608990607131 0.48044953035655 17 0.440164302730598 0.880328605461197 0.559835697269402 18 0.386944697269370 0.773889394538741 0.61305530273063 19 0.407591554891182 0.815183109782363 0.592408445108819 20 0.446229342495599 0.892458684991199 0.553770657504401 21 0.47104527367512 0.94209054735024 0.52895472632488 22 0.479442074056506 0.958884148113012 0.520557925943494 23 0.504783754310584 0.990432491378831 0.495216245689416 24 0.463869075301878 0.927738150603755 0.536130924698123 25 0.453511366525577 0.907022733051153 0.546488633474423 26 0.601659888169338 0.796680223661325 0.398340111830662 27 0.540267140200854 0.919465719598292 0.459732859799146 28 0.515595421990575 0.968809156018851 0.484404578009425 29 0.490069597003824 0.980139194007647 0.509930402996176 30 0.4417446124378 0.8834892248756 0.5582553875622 31 0.500542668047802 0.998914663904395 0.499457331952198 32 0.745748847690676 0.508502304618649 0.254251152309324 33 0.706018648564251 0.587962702871498 0.293981351435749 34 0.663259735711836 0.673480528576329 0.336740264288164 35 0.615729459775372 0.768541080449256 0.384270540224628 36 0.617518624830169 0.764962750339662 0.382481375169831 37 0.66354595657011 0.672908086859781 0.336454043429891 38 0.616482330585353 0.767035338829293 0.383517669414647 39 0.736460552130613 0.527078895738773 0.263539447869387 40 0.691425693933450 0.617148612133099 0.308574306066550 41 0.656991676253503 0.686016647492994 0.343008323746497 42 0.610926874015612 0.778146251968775 0.389073125984388 43 0.58816740633227 0.82366518733546 0.41183259366773 44 0.53874021338851 0.92251957322298 0.46125978661149 45 0.533972917371333 0.932054165257335 0.466027082628667 46 0.51049886316493 0.97900227367014 0.48950113683507 47 0.490608328964138 0.981216657928276 0.509391671035862 48 0.461367796695968 0.922735593391936 0.538632203304032 49 0.417571462527344 0.835142925054688 0.582428537472656 50 0.409103969608414 0.818207939216828 0.590896030391586 51 0.409093939026166 0.818187878052332 0.590906060973834 52 0.392368729763977 0.784737459527954 0.607631270236023 53 0.361098681638402 0.722197363276805 0.638901318361598 54 0.31741792107817 0.63483584215634 0.68258207892183 55 0.304625833237851 0.609251666475702 0.695374166762149 56 0.278759069429513 0.557518138859026 0.721240930570487 57 0.296871969339177 0.593743938678354 0.703128030660823 58 0.404773840941812 0.809547681883624 0.595226159058188 59 0.381159143688013 0.762318287376027 0.618840856311987 60 0.338790105618212 0.677580211236424 0.661209894381788 61 0.335528885267076 0.671057770534153 0.664471114732924 62 0.335976406466843 0.671952812933686 0.664023593533157 63 0.295314618144911 0.590629236289821 0.70468538185509 64 0.300549536163233 0.601099072326466 0.699450463836767 65 0.263266332150722 0.526532664301444 0.736733667849278 66 0.229736665094668 0.459473330189336 0.770263334905332 67 0.209848170220837 0.419696340441674 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0.271453788410827 0.864273105794586 86 0.117403655365432 0.234807310730865 0.882596344634568 87 0.115468656692941 0.230937313385882 0.884531343307059 88 0.0994486905604637 0.198897381120927 0.900551309439536 89 0.131295504176331 0.262591008352662 0.86870449582367 90 0.108615780810933 0.217231561621866 0.891384219189067 91 0.119664056457201 0.239328112914402 0.880335943542799 92 0.103413088916294 0.206826177832588 0.896586911083706 93 0.0843628980097781 0.168725796019556 0.915637101990222 94 0.0765553897289935 0.153110779457987 0.923444610271007 95 0.106657132852256 0.213314265704511 0.893342867147744 96 0.113992690389064 0.227985380778128 0.886007309610936 97 0.108188436653544 0.216376873307088 0.891811563346456 98 0.0885780746693378 0.177156149338676 0.911421925330662 99 0.0758357275801614 0.151671455160323 0.924164272419839 100 0.0709462342507449 0.141892468501490 0.929053765749255 101 0.0656544055826057 0.131308811165211 0.934345594417394 102 0.0617573996853411 0.123514799370682 0.93824260031466 103 0.0499260399922404 0.0998520799844809 0.95007396000776 104 0.042763862063379 0.085527724126758 0.957236137936621 105 0.0350016562584371 0.0700033125168743 0.964998343741563 106 0.0683848961683259 0.136769792336652 0.931615103831674 107 0.0647709566159952 0.129541913231990 0.935229043384005 108 0.112191240522072 0.224382481044144 0.887808759477928 109 0.102064588708985 0.204129177417970 0.897935411291015 110 0.426208898089382 0.852417796178763 0.573791101910618 111 0.458823223778669 0.917646447557338 0.541176776221331 112 0.437250638295025 0.874501276590051 0.562749361704975 113 0.415449306450323 0.830898612900646 0.584550693549677 114 0.38503326871535 0.7700665374307 0.61496673128465 115 0.352465723788319 0.704931447576638 0.647534276211681 116 0.320098546329095 0.640197092658191 0.679901453670905 117 0.281516306633623 0.563032613267245 0.718483693366377 118 0.240879373437175 0.481758746874349 0.759120626562825 119 0.217456540753208 0.434913081506416 0.782543459246792 120 0.239518909783075 0.47903781956615 0.760481090216925 121 0.203417822179801 0.406835644359602 0.7965821778202 122 0.195810086375089 0.391620172750179 0.80418991362491 123 0.190777575762706 0.381555151525411 0.809222424237294 124 0.163552714740271 0.327105429480543 0.836447285259729 125 0.140160080264683 0.280320160529366 0.859839919735317 126 0.143685255257320 0.287370510514641 0.85631474474268 127 0.140649913467957 0.281299826935914 0.859350086532043 128 0.414768472246689 0.829536944493378 0.585231527753311 129 0.3705596504439 0.7411193008878 0.6294403495561 130 0.324507768206085 0.64901553641217 0.675492231793915 131 0.300534883631931 0.601069767263862 0.699465116368069 132 0.348023516060503 0.696047032121006 0.651976483939497 133 0.446126655933015 0.89225331186603 0.553873344066985 134 0.613052195694029 0.773895608611942 0.386947804305971 135 0.604770789139639 0.790458421720722 0.395229210860361 136 0.558269803994182 0.883460392011635 0.441730196005818 137 0.675725578579411 0.648548842841178 0.324274421420589 138 0.612983289171736 0.774033421656528 0.387016710828264 139 0.65252256144601 0.69495487710798 0.34747743855399 140 0.59636386370175 0.807272272596499 0.403636136298250 141 0.581609379506343 0.836781240987315 0.418390620493657 142 0.532347019344282 0.935305961311437 0.467652980655718 143 0.585518054101218 0.828963891797564 0.414481945898782 144 0.641731820909463 0.716536358181074 0.358268179090537 145 0.663147260634487 0.673705478731025 0.336852739365513 146 0.79802485319331 0.403950293613382 0.201975146806691 147 0.772750504239737 0.454498991520525 0.227249495760263 148 0.719975142590934 0.560049714818132 0.280024857409066 149 0.676319807792869 0.647360384414262 0.323680192207131 150 0.583028051891924 0.833943896216153 0.416971948108076 151 0.60508698773666 0.78982602452668 0.39491301226334 152 0.994749219653908 0.0105015606921842 0.0052507803460921 153 0.985440148371776 0.029119703256448 0.014559851628224 154 0.963903083515065 0.0721938329698692 0.0360969164849346 155 0.923832694747377 0.152334610505246 0.0761673052526229 156 0.823890226235866 0.352219547528268 0.176109773764134 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 2 0.0132450331125828 OK 10% type I error level 6 0.0397350993377483 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/10awkz1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/10awkz1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/1e4mq1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/1e4mq1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/2e4mq1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/2e4mq1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/3e4mq1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/3e4mq1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/4pvlb1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/4pvlb1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/5pvlb1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/5pvlb1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/6pvlb1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/6pvlb1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/7z4kw1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/7z4kw1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/8awkz1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/8awkz1290506514.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/9awkz1290506514.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290506632smmjfw6ziqtzlrs/9awkz1290506514.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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