Workshop7, Mini-tutorial, 1

*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: Mon, 22 Nov 2010 22:12:50 +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/22/t1290464257u3txd6hhnlq8nex.htm/, Retrieved Mon, 22 Nov 2010 23:17:40 +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/22/t1290464257u3txd6hhnlq8nex.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 «

12 12 11 24 11 8 7 25 14 8 17 17 12 8 10 18 21 9 12 18 12 7 12 16 22 4 11 20 11 11 11 16 10 7 12 18 13 7 13 17 10 12 14 23 8 10 16 30 15 10 11 23 14 8 10 18 10 8 11 15 14 4 15 12 14 9 9 21 11 8 11 15 10 7 17 20 13 11 17 31 7 9 11 27 14 11 18 34 12 13 14 21 14 8 10 31 11 8 11 19 9 9 15 16 11 6 15 20 15 9 13 21 14 9 16 22 13 6 13 17 9 6 9 24 15 16 18 25 10 5 18 26 11 7 12 25 13 9 17 17 8 6 9 32 20 6 9 33 12 5 12 13 10 12 18 32 10 7 12 25 9 10 18 29 14 9 14 22 8 8 15 18 14 5 16 17 11 8 10 20 13 8 11 15 9 10 14 20 11 6 9 33 15 8 12 29 11 7 17 23 10 4 5 26 14 8 12 18 18 8 12 20 14 4 6 11 11 20 24 28 12 8 12 26 13 8 12 22 9 6 14 17 10 4 7 12 15 8 13 14 20 9 12 17 12 6 13 21 12 7 14 19 14 9 8 18 13 5 11 10 11 5 9 29 17 8 11 31 12 8 13 19 13 6 10 9 14 8 11 20 13 7 12 28 15 7 9 19 13 9 15 30 10 11 18 29 11 6 15 26 19 8 12 23 13 6 13 13 17 9 14 21 13 8 10 19 9 6 13 28 11 10 13 23 10 8 11 18 9 8 13 21 12 10 16 20 12 5 8 23 13 7 16 21 1 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 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation ParentalExpectations[t] = + 5.10714357111745 -0.00142234580182886Depression[t] + 0.691744367954341ParentalCriticism[t] + 0.0961766747674232ConcernOverMistakes[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) 5.10714357111745 1.375748 3.7123 0.000286 0.000143 Depression -0.00142234580182886 0.069907 -0.0203 0.983793 0.491897 ParentalCriticism 0.691744367954341 0.085046 8.1338 0 0 ConcernOverMistakes 0.0961766747674232 0.040384 2.3816 0.018453 0.009226 Multiple Linear Regression - Regression Statistics Multiple R 0.612364119037733 R-squared 0.374989814284858 Adjusted R-squared 0.362892842948436 F-TEST (value) 30.9986527913662 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 8.88178419700125e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.75014920716009 Sum Squared Residuals 1172.31470255471 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 15.6992480313658 -4.69924803136577 2 7 13.0298695801176 -6.02986958011764 3 17 12.2561891445728 4.74381085542723 4 10 12.3552105109438 -2.35521051094385 5 12 13.0341537666817 -1.03415376668173 6 12 11.4711127934547 0.528887206545337 7 11 9.76636293064304 1.23363706935696 8 11 14.2395126110739 -3.23951261107386 9 12 11.6663108345932 0.333689165406833 10 13 11.5658671224203 1.43413287757974 11 14 15.605916048202 -1.60591604820199 12 16 14.8985087272689 1.10149127273107 13 11 14.2153155832842 -3.21531558328416 14 10 12.3523658193402 -2.35236581934019 15 11 12.0695251782452 -1.06952517824524 16 15 9.00832829891829 5.99167170108171 17 9 13.3326402115968 -4.3326402115968 18 11 12.0681028324434 -1.06810283244341 19 17 11.858664184128 5.14133581587199 20 17 15.6793180409815 1.32068195901845 21 11 13.9196566808141 -2.91965668081414 22 18 15.966425719482 2.03357428051801 23 14 16.1024623750178 -2.10246237501782 24 10 13.6026625913167 -3.60266259131669 25 11 12.4528095315131 -1.4528095315131 26 15 12.8588685667688 2.14113143323117 27 15 11.1654974703718 3.83450252962816 28 13 13.331217865795 -0.331217865794974 29 16 13.4288168863642 2.57118311363577 30 13 10.8741227544659 2.12587724553408 31 9 11.5530488610452 -2.55304886104519 32 18 18.5581351405451 -0.558135140545055 33 18 11.0522354968239 6.94776450317613 34 12 12.3381252121633 -0.3381252121633 35 17 12.9493558583289 4.05064414167106 36 9 12.3238846049864 -3.32388460498641 37 9 12.4029931301319 -3.40299313013189 38 12 9.79909403324371 2.20090596675629 39 18 16.4715061211088 1.5284938788912 40 12 12.3395475579651 -0.339547557965129 41 18 14.8009097066997 3.19909029330033 42 14 13.4288168863642 0.571183113635774 43 15 12.3608998941512 2.63910010584884 44 16 10.1809560407097 5.81904395929025 45 10 12.5489862062805 -2.54898620628053 46 11 12.0652581408398 -1.06525814083975 47 14 13.9353196337929 0.0646803662071349 48 9 12.4157942423483 -3.41579424234834 49 12 13.40888689598 -1.40888689598002 50 17 12.1457718626285 4.85422813737155 51 5 10.3604911288695 -5.36049112886953 52 12 12.3523658193402 -0.352365819340192 53 12 12.5390297856677 -0.539029785667723 54 6 8.91215162415087 -2.91215162415087 55 24 21.619332019872 2.380667980128 56 12 13.1246239090832 -1.12462390908324 57 12 12.7384948642117 -0.738494864211714 58 14 10.8798121376732 3.12018786232677 59 7 9.0140176821256 -2.01401768212561 60 13 11.9662367744687 1.03376322553133 61 12 12.9393994377161 -0.939399437716137 62 13 11.2602517993374 1.73974820066256 63 14 11.7596428177569 2.24035718224307 64 8 13.0441101872945 -5.04411018729453 65 11 9.50914166313961 1.49085833686039 66 9 11.3393431753243 -2.33934317532431 67 11 13.5983955539112 -2.59839555391121 68 13 12.4513871857113 0.548612814288727 69 10 10.1047093563265 -0.104709356326531 70 11 12.544719168875 -1.54471916887504 71 12 12.6238105448619 -0.623810544861912 72 9 11.7553757803514 -2.75537578035145 73 15 14.1996526303054 0.80034736969456 74 18 15.4912317288522 2.50876827114781 75 15 11.7425575189764 3.25744248102362 76 12 12.8261374641682 -0.826137464168164 77 13 10.4894160553962 2.51058394460378 78 14 13.3283731741913 0.671626825808683 79 10 12.4499648399094 -2.44996483990944 80 13 11.9377555601149 1.06224443988511 81 13 14.2210049664915 -1.22100496649148 82 11 12.3580552025475 -1.35805520254751 83 13 12.6480075726516 0.351992427348394 84 16 13.9310525963874 2.06894740361262 85 8 10.7608607809179 -2.76086078091794 86 16 11.95057382149 4.04942617851005 87 11 10.5670850855813 0.432914914418732 88 9 12.0666804866416 -3.06668048664158 89 16 17.4631764289386 -1.46317642893864 90 12 11.7454193597386 0.254580640261357 91 14 13.1232015632814 0.876798436718593 92 8 10.1980413394903 -2.1980413394903 93 9 10.0862017117442 -1.08620171174415 94 15 11.3521614366994 3.64783856330063 95 11 13.8377206132236 -2.83772061322361 96 21 16.3739071005395 4.62609289946046 97 14 14.2915622676674 -0.291562267667377 98 18 16.1815537510047 1.8184462489953 99 12 11.7610651635588 0.238934836441239 100 13 12.7427619016172 0.257238098382799 101 15 14.2224273122933 0.777572687706694 102 12 10.6775023675256 1.32249763247442 103 19 13.9310525963874 5.06894740361262 104 15 13.7401215926544 1.25987840734564 105 11 14.2138932374823 -3.21389323748233 106 11 10.94325770984 0.056742290160013 107 10 11.9534185130936 -1.95341851309361 108 13 14.3100699122498 -1.31006991224976 109 15 15.0994133007733 -0.0994133007733494 110 12 10.8584769506458 1.1415230493542 111 12 11.1797380775487 0.820261922451264 112 16 16.07968769303 -0.07968769302996 113 9 14.720395984911 -5.72039598491097 114 18 15.0994133007733 2.90058669922665 115 8 13.5648535419001 -5.56485354190006 116 13 10.0904687491496 2.90953125085036 117 17 12.4485424941076 4.55145750589238 118 9 10.8741227544659 -1.87412275446592 119 15 13.7244586396756 1.27554136032436 120 8 9.77631935125585 -1.77631935125585 121 7 10.6419094241627 -3.64190942416266 122 12 11.2759147523162 0.724085247683841 123 14 14.8165726596784 -0.816572659678395 124 6 10.6888811339402 -4.68888113394021 125 8 11.7610651635588 -3.76106516355876 126 17 12.5489862062805 4.45101379371947 127 10 9.30539239803153 0.694607601968468 128 11 12.5504085520824 -1.55040855208235 129 14 13.0483772247 0.95162277529998 130 11 13.7964382866534 -2.79643828665337 131 13 14.8165726596784 -1.81657265967839 132 12 12.1514783949944 -0.151478394994373 133 11 10.1866454239171 0.813354576082939 134 9 9.39161265218615 -0.391612652186154 135 12 12.6437405352461 -0.64374053524612 136 20 14.5052679533883 5.49473204661174 137 12 10.956075971215 1.04392402878495 138 13 13.0441101872945 -0.0441101872945335 139 12 12.9450888209235 -0.945088820923453 140 12 16.2000613955871 -4.20006139558708 141 9 14.2010749761073 -5.20107497610727 142 15 14.8956640356653 0.104335964334732 143 24 21.2303582833968 2.76964171660318 144 7 10.5685074313831 -3.5685074313831 145 17 14.7189736391091 2.28102636089086 146 11 12.0310875432787 -1.03108754327865 147 17 14.2972516508747 2.70274834912531 148 11 11.8543971467225 -0.854397146722527 149 12 12.8560238751652 -0.856023875165174 150 14 14.1134495253094 -0.113449525309423 151 11 13.239308228433 -2.23930822843304 152 16 13.3098655296089 2.69013447039106 153 21 13.5912666757435 7.40873332425654 154 14 11.3564284741049 2.64357152589514 155 20 15.9963292796376 4.0036707203624 156 13 10.8670110254568 2.13298897454323 157 11 13.3127102212126 -2.3127102212126 158 15 14.1205612543186 0.879438745681432 159 19 19.1408845723569 -0.140884572356908 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.679020833345542 0.641958333308916 0.320979166654458 8 0.654299646033697 0.691400707932607 0.345700353966303 9 0.526583278828409 0.946833442343182 0.473416721171591 10 0.406656215159091 0.813312430318182 0.593343784840909 11 0.48243779700899 0.96487559401798 0.51756220299101 12 0.735975557931781 0.528048884136437 0.264024442068219 13 0.669504310792624 0.660991378414752 0.330495689207376 14 0.621998169385751 0.756003661228497 0.378001830614249 15 0.542777750402186 0.914444499195628 0.457222249597814 16 0.592877268950152 0.814245462099695 0.407122731049847 17 0.605121090369446 0.789757819261108 0.394878909630554 18 0.541284472726021 0.917431054547957 0.458715527273979 19 0.668918274916595 0.66216345016681 0.331081725083405 20 0.74877794607754 0.50244410784492 0.25122205392246 21 0.744600461102474 0.510799077795052 0.255399538897526 22 0.785768939409794 0.428462121180413 0.214231060590206 23 0.758178634962274 0.483642730075453 0.241821365037726 24 0.798669213795553 0.402661572408894 0.201330786204447 25 0.760014000712783 0.479971998574433 0.239985999287217 26 0.754384213260845 0.491231573478311 0.245615786739155 27 0.754229625798803 0.491540748402394 0.245770374201197 28 0.704025817828415 0.59194836434317 0.295974182171585 29 0.718630012168797 0.562739975662406 0.281369987831203 30 0.67456979795665 0.650860404086698 0.325430202043349 31 0.709520672709645 0.580958654580709 0.290479327290355 32 0.714283566086916 0.571432867826168 0.285716433913084 33 0.862044575044173 0.275910849911654 0.137955424955827 34 0.831992853802784 0.336014292394432 0.168007146197216 35 0.870831213195895 0.258337573608209 0.129168786804105 36 0.8880499877067 0.223900024586601 0.111950012293301 37 0.895881502713026 0.208236994573948 0.104118497286974 38 0.876614443785595 0.246771112428809 0.123385556214405 39 0.886427823841684 0.227144352316632 0.113572176158316 40 0.859494201480616 0.281011597038767 0.140505798519384 41 0.882373221691769 0.235253556616462 0.117626778308231 42 0.856520477969054 0.286959044061892 0.143479522030946 43 0.844859575846468 0.310280848307065 0.155140424153532 44 0.902928335159587 0.194143329680825 0.0970716648404127 45 0.904244834820473 0.191510330359053 0.0957551651795265 46 0.888530712627776 0.222938574744447 0.111469287372224 47 0.862738769576874 0.274522460846253 0.137261230423126 48 0.876156717716058 0.247686564567885 0.123843282283942 49 0.854031676939984 0.291936646120032 0.145968323060016 50 0.898866887289648 0.202266225420704 0.101133112710352 51 0.955499963848982 0.0890000723020366 0.0445000361510183 52 0.943584739863299 0.112830520273402 0.056415260136701 53 0.929051807948229 0.141896384103542 0.070948192051771 54 0.94423785657101 0.111524286857978 0.0557621434289892 55 0.949096718211675 0.101806563576651 0.0509032817883253 56 0.937344535031457 0.125310929937086 0.062655464968543 57 0.922357427246228 0.155285145507544 0.077642572753772 58 0.923830384760063 0.152339230479873 0.0761696152399366 59 0.92182310444199 0.156353791116021 0.0781768955580106 60 0.905720824729525 0.188558350540949 0.0942791752704746 61 0.886579407930466 0.226841184139068 0.113420592069534 62 0.87209612545408 0.255807749091839 0.12790387454592 63 0.862734186699925 0.274531626600151 0.137265813300075 64 0.914022666006081 0.171954667987837 0.0859773339939187 65 0.90165153456085 0.1966969308783 0.0983484654391501 66 0.894813490368598 0.210373019262804 0.105186509631402 67 0.893553825617062 0.212892348765877 0.106446174382939 68 0.871804317992109 0.256391364015782 0.128195682007891 69 0.8512180463214 0.297563907357201 0.1487819536786 70 0.831123812429552 0.337752375140897 0.168876187570448 71 0.803846720241996 0.392306559516007 0.196153279758004 72 0.80238754388001 0.395224912239979 0.197612456119989 73 0.776479424155193 0.447041151689614 0.223520575844807 74 0.772148624712013 0.455702750575973 0.227851375287987 75 0.785718689046907 0.428562621906185 0.214281310953093 76 0.756330301521301 0.487339396957398 0.243669698478699 77 0.756505550142356 0.486988899715287 0.243494449857644 78 0.722732024167513 0.554535951664975 0.277267975832487 79 0.713572569134285 0.572854861731429 0.286427430865715 80 0.678483226381181 0.643033547237638 0.321516773618819 81 0.644312930529833 0.711374138940335 0.355687069470167 82 0.611821504290155 0.77635699141969 0.388178495709845 83 0.568731101838826 0.862537796322349 0.431268898161174 84 0.551665325216438 0.896669349567123 0.448334674783562 85 0.552608072309082 0.894783855381836 0.447391927690918 86 0.609682519197232 0.780634961605536 0.390317480802768 87 0.565921657893047 0.868156684213905 0.434078342106953 88 0.572717446082102 0.854565107835796 0.427282553917898 89 0.548665449174946 0.902669101650108 0.451334550825054 90 0.505619685138272 0.988760629723456 0.494380314861728 91 0.464044938910098 0.928089877820196 0.535955061089902 92 0.443114493039101 0.886228986078202 0.556885506960899 93 0.403193565405743 0.806387130811486 0.596806434594257 94 0.438230114654234 0.876460229308467 0.561769885345766 95 0.436236815820298 0.872473631640596 0.563763184179702 96 0.511690013130641 0.976619973738718 0.488309986869359 97 0.470771920381169 0.941543840762338 0.529228079618831 98 0.441073789065828 0.882147578131655 0.558926210934172 99 0.396329392677606 0.792658785355212 0.603670607322394 100 0.352364367315688 0.704728734631377 0.647635632684312 101 0.313267839613263 0.626535679226527 0.686732160386736 102 0.283636609433294 0.567273218866588 0.716363390566706 103 0.395604828573456 0.791209657146913 0.604395171426544 104 0.366358632359252 0.732717264718503 0.633641367640748 105 0.388764865424938 0.777529730849876 0.611235134575062 106 0.346994193140696 0.693988386281392 0.653005806859304 107 0.319525776693164 0.639051553386328 0.680474223306836 108 0.291548897275529 0.583097794551058 0.708451102724471 109 0.252368838915551 0.504737677831101 0.74763116108445 110 0.219422621774468 0.438845243548936 0.780577378225532 111 0.192152667457568 0.384305334915135 0.807847332542432 112 0.163039174941625 0.326078349883249 0.836960825058375 113 0.271169043873621 0.542338087747242 0.728830956126379 114 0.263242681729177 0.526485363458353 0.736757318270823 115 0.368227006952715 0.73645401390543 0.631772993047285 116 0.401343257396744 0.802686514793487 0.598656742603256 117 0.496983913843193 0.993967827686386 0.503016086156807 118 0.458237641556438 0.916475283112876 0.541762358443562 119 0.421019851203108 0.842039702406215 0.578980148796892 120 0.384211374837246 0.768422749674491 0.615788625162754 121 0.44629751741614 0.89259503483228 0.55370248258386 122 0.403157324651746 0.806314649303493 0.596842675348254 123 0.352690209297912 0.705380418595824 0.647309790702088 124 0.393036304832908 0.786072609665815 0.606963695167092 125 0.4258861671848 0.8517723343696 0.5741138328152 126 0.529124516278047 0.941750967443905 0.470875483721953 127 0.505049598847387 0.989900802305227 0.494950401152613 128 0.452337850480875 0.90467570096175 0.547662149519125 129 0.413810571314178 0.827621142628357 0.586189428685822 130 0.48813195831145 0.9762639166229 0.51186804168855 131 0.444277626830591 0.888555253661182 0.555722373169409 132 0.386046730994027 0.772093461988054 0.613953269005973 133 0.372072154078262 0.744144308156523 0.627927845921738 134 0.314659004551502 0.629318009103004 0.685340995448498 135 0.25829547523005 0.5165909504601 0.74170452476995 136 0.36530305549662 0.73060611099324 0.63469694450338 137 0.306393176689853 0.612786353379706 0.693606823310147 138 0.249601895020681 0.499203790041362 0.750398104979319 139 0.198341841729884 0.396683683459767 0.801658158270117 140 0.241559003360889 0.483118006721777 0.758440996639111 141 0.555103713119235 0.88979257376153 0.444896286880765 142 0.492948134037833 0.985896268075667 0.507051865962167 143 0.426661406053479 0.853322812106957 0.573338593946521 144 0.488216336444511 0.976432672889022 0.511783663555489 145 0.466313308870428 0.932626617740856 0.533686691129572 146 0.4955629121108 0.9911258242216 0.5044370878892 147 0.40074087033524 0.80148174067048 0.59925912966476 148 0.324023329095929 0.648046658191858 0.675976670904071 149 0.229880209190757 0.459760418381513 0.770119790809243 150 0.170657497626561 0.341314995253122 0.829342502373439 151 0.150491162189829 0.300982324379659 0.84950883781017 152 0.0820364711591598 0.16407294231832 0.91796352884084 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 1 0.00684931506849315 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/104e201290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/104e201290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/1fd5p1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/1fd5p1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/28mma1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/28mma1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/38mma1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/38mma1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/48mma1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/48mma1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/5jdmv1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/5jdmv1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/6jdmv1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/6jdmv1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/7b42f1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/7b42f1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/8b42f1290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/8b42f1290463957.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/94e201290463957.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464257u3txd6hhnlq8nex/94e201290463957.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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