multiple regression

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 21 Nov 2010 15:21:47 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/21/t12903529268e570phu358xke9.htm/, Retrieved Sun, 21 Nov 2010 16:22:17 +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/21/t12903529268e570phu358xke9.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:

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24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 14 6 24 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 7.96604226904438 + 0.329539554855599ConcernoverMistakes[t] -0.359820551945857Doubtsaboutactions[t] + 0.188740986166915ParentalExpectations[t] + 0.0212197379128775ParentalCriticism[t] + 0.389772656468926Organization[t] -0.00400911738275325t + 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) 7.96604226904438 2.379902 3.3472 0.001029 0.000514 ConcernoverMistakes 0.329539554855599 0.055687 5.9177 0 0 Doubtsaboutactions -0.359820551945857 0.107409 -3.35 0.001019 0.00051 ParentalExpectations 0.188740986166915 0.101382 1.8617 0.064579 0.032289 ParentalCriticism 0.0212197379128775 0.128902 0.1646 0.869462 0.434731 Organization 0.389772656468926 0.074001 5.2671 0 0 t -0.00400911738275325 0.006096 -0.6576 0.511774 0.255887 Multiple Linear Regression - Regression Statistics Multiple R 0.60733895095595 R-squared 0.368860601348274 Adjusted R-squared 0.343947204033075 F-TEST (value) 14.8057126325052 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.75557354711964e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.41561362661657 Sum Squared Residuals 1773.29529984198 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.2983715119366 0.70162848806344 2 25 22.6942027395211 2.30579726047887 3 30 24.5199351176299 5.4800648823701 4 19 20.5858100273213 -1.58581002732133 5 22 20.860694202093 1.13930579790698 6 22 23.3332519599709 -1.33325195997087 7 25 22.8359102362292 2.16408976377076 8 23 19.7433698869927 3.25663011300733 9 17 19.0929718105762 -2.09297181057616 10 21 21.9165848536408 -0.91658485364079 11 19 23.0752389807623 -4.07523898076229 12 19 23.7342338570091 -4.7342338570091 13 15 23.4781157584617 -8.47811575846172 14 16 17.4275376017424 -1.42753760174238 15 23 19.7118799531881 3.28812004681191 16 27 24.2467169666893 2.75328303331074 17 22 21.2649326040891 0.73506739591091 18 14 16.8815876921881 -2.88158769218814 19 22 24.3137744057991 -2.31377440579911 20 23 24.3015654059286 -1.30156540592860 21 23 21.8344647808193 1.16553521918072 22 21 24.7512657180051 -3.75126571800509 23 19 22.6592344387476 -3.65923443874758 24 18 24.0700007888973 -6.07000078889733 25 20 23.3285829375965 -3.32858293759652 26 23 22.6325098681894 0.367490131810628 27 25 23.5231792045445 1.47682079545548 28 19 23.5348868834222 -4.53488688342217 29 24 24.0368676229268 -0.0368676229268342 30 22 21.7552785590267 0.244721440973291 31 25 25.2818977678332 -0.281897767833189 32 26 23.4105078659173 2.58949213408273 33 29 22.9630880072642 6.03691199273582 34 32 25.3474031449702 6.65259685502984 35 25 21.7743108175814 3.22568918241862 36 29 24.5699273386823 4.43007266131771 37 28 25.1354699100087 2.86453008999129 38 17 17.2865701563726 -0.286570156372563 39 28 26.2640788714213 1.73592112857875 40 29 23.1045209199524 5.89547908004764 41 26 27.6235426441229 -1.62354264412289 42 25 23.6072671246172 1.39273287538279 43 14 19.7541645453067 -5.75416454530668 44 25 22.2441541362560 2.75584586374397 45 26 21.8001564282314 4.19984357176864 46 20 20.3970947317837 -0.397094731783665 47 18 21.5400320626448 -3.54003206264476 48 32 24.7914532758987 7.2085467241013 49 25 25.1274579247346 -0.127457924734565 50 25 21.8498691504186 3.15013084958137 51 23 20.9556045153761 2.04439548462387 52 21 22.2400886775895 -1.24008867758950 53 20 24.0944287438478 -4.0944287438478 54 15 16.6692490942680 -1.66924909426796 55 30 26.8437154890249 3.1562845109751 56 24 25.3699497214645 -1.36994972146448 57 26 24.3476987275591 1.65230127244095 58 24 21.8018121539535 2.19818784604654 59 22 21.4849353740580 0.515064625942025 60 14 15.8014939418454 -1.80149394184544 61 24 22.2854594606709 1.71454053932907 62 24 22.9750971267241 1.02490287327593 63 24 23.3614191456939 0.638580854306098 64 24 20.0189528544582 3.98104714554175 65 19 18.5496603044486 0.450339695551412 66 31 26.798008800325 4.20199119967499 67 22 26.6350456957499 -4.63504569574993 68 27 21.5249053710812 5.47509462891882 69 19 17.7366466889082 1.26335331109178 70 25 22.3083942408214 2.69160575917856 71 20 25.0183664969683 -5.01836649696831 72 21 21.5122305319075 -0.512230531907487 73 27 27.4773598801703 -0.477359880170346 74 23 24.4242323611766 -1.42423236117657 75 25 25.6977515557749 -0.697751555774884 76 20 22.2624291133288 -2.26242911332878 77 21 19.2291343758235 1.77086562417652 78 22 22.4437103446138 -0.443710344613850 79 23 22.953301717284 0.0466982827160052 80 25 24.07034403294 0.92965596706001 81 25 23.3729177194378 1.62708228056219 82 17 23.7900811387154 -6.79008113871542 83 19 21.4341587206824 -2.43415872068244 84 25 23.9281000034919 1.07189999650813 85 19 22.3070776295078 -3.30707762950784 86 20 23.1065004540058 -3.10650045400576 87 26 22.4761674819085 3.52383251809147 88 23 20.6906793513582 2.30932064864181 89 27 24.4104222863531 2.58957771364688 90 17 20.8669235126350 -3.86692351263496 91 17 23.2984287511115 -6.29842875111146 92 19 20.0852863307246 -1.08528633072460 93 17 19.6773398225854 -2.6773398225854 94 22 21.9947362717897 0.00526372821031451 95 21 23.4202526440523 -2.42025264405233 96 32 28.5509743140169 3.44902568598311 97 21 24.613423111583 -3.61342311158302 98 21 24.2893290728572 -3.28932907285723 99 18 21.1906620081360 -3.19066200813604 100 18 21.2458664145162 -3.24586641451617 101 23 22.7708636130865 0.22913638691355 102 19 20.5588978025442 -1.55889780254422 103 20 20.9401479280230 -0.940147928023032 104 21 22.2205522470208 -1.22055224702084 105 20 23.6787622428558 -3.67876224285576 106 17 18.7709163550548 -1.77091635505484 107 18 20.2409161325215 -2.24091613252153 108 19 20.7160419870612 -1.71604198706124 109 22 21.9798073138651 0.0201926861349317 110 15 18.6671601095724 -3.66716010957239 111 14 18.7455905094174 -4.74559050941741 112 18 26.4946006314453 -8.49460063144532 113 24 21.2823173631164 2.71768263688361 114 35 23.4856379231973 11.5143620768027 115 29 19.0200425572153 9.97995744278472 116 21 21.8093283797562 -0.809328379756237 117 25 20.434475624549 4.56552437545098 118 20 18.3687805549093 1.63121944509066 119 22 23.0665946336186 -1.06659463361856 120 13 16.7795645839044 -3.7795645839044 121 26 23.0606243822755 2.93937561772454 122 17 16.7822501478184 0.217749852181626 123 25 19.9667747068350 5.03322529316504 124 20 20.537521377052 -0.537521377052012 125 19 17.9325255659881 1.06747443401193 126 21 22.4367842714509 -1.43678427145089 127 22 20.8482458372767 1.15175416272327 128 24 22.4656380890907 1.53436191090932 129 21 22.7498131103562 -1.74981311035621 130 26 25.2723997551415 0.727600244858547 131 24 20.4356497809747 3.56435021902534 132 16 20.0909622078513 -4.09096220785126 133 23 22.1129557277632 0.887044272236804 134 18 20.5712079278172 -2.57120792781721 135 16 22.146357390973 -6.146357390973 136 26 23.8731791007228 2.12682089927719 137 19 18.8585013905706 0.141498609429418 138 21 16.7383044297567 4.26169557024325 139 21 21.9427962002931 -0.942796200293108 140 22 18.3643071408902 3.63569285910977 141 23 19.5959193437852 3.40408065621478 142 29 24.5833982369600 4.41660176304003 143 21 19.1161050635558 1.8838949364442 144 21 19.6935810866946 1.30641891330535 145 23 21.6443960494122 1.35560395058783 146 27 22.7382424214086 4.26175757859139 147 25 25.1592981257535 -0.159298125753546 148 21 20.7452411686009 0.254758831399111 149 10 16.9258456985059 -6.92584569850592 150 20 22.3860047677318 -2.38600476773182 151 26 22.2748397091080 3.72516029089204 152 24 23.3707925689168 0.629207431083179 153 29 31.3326302350857 -2.33263023508567 154 19 18.807087542852 0.19291245714798 155 24 21.8235235460094 2.17647645399060 156 19 20.4705844558619 -1.47058445586194 157 24 23.1266831550602 0.873316844939805 158 22 21.5231153680453 0.476884631954731 159 17 23.5082376477324 -6.5082376477324 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.305144732294912 0.610289464589824 0.694855267705088 11 0.347301195412733 0.694602390825465 0.652698804587267 12 0.250709545422878 0.501419090845756 0.749290454577122 13 0.344294876675323 0.688589753350646 0.655705123324677 14 0.263939216007886 0.527878432015773 0.736060783992114 15 0.532873731577465 0.93425253684507 0.467126268422535 16 0.469870562789765 0.93974112557953 0.530129437210235 17 0.492979769545617 0.985959539091234 0.507020230454383 18 0.466473240331405 0.93294648066281 0.533526759668595 19 0.383194930395246 0.766389860790491 0.616805069604754 20 0.488711530954049 0.977423061908098 0.511288469045951 21 0.540672970282667 0.918654059434666 0.459327029717333 22 0.476706749290985 0.95341349858197 0.523293250709015 23 0.416106462561341 0.832212925122682 0.583893537438659 24 0.417751726552838 0.835503453105676 0.582248273447162 25 0.362624988252893 0.725249976505786 0.637375011747107 26 0.322292174946879 0.644584349893757 0.677707825053121 27 0.305948533733473 0.611897067466945 0.694051466266527 28 0.283433666374725 0.56686733274945 0.716566333625275 29 0.256816034638236 0.513632069276471 0.743183965361764 30 0.212606265538741 0.425212531077481 0.78739373446126 31 0.184231378270535 0.368462756541071 0.815768621729465 32 0.24896158665029 0.49792317330058 0.75103841334971 33 0.421585099521228 0.843170199042457 0.578414900478772 34 0.656248400063437 0.687503199873127 0.343751599936563 35 0.624778176067693 0.750443647864614 0.375221823932307 36 0.659844947338662 0.680310105322676 0.340155052661338 37 0.636468429941092 0.727063140117816 0.363531570058908 38 0.608572766925045 0.78285446614991 0.391427233074955 39 0.567298926059778 0.865402147880443 0.432701073940222 40 0.61740633110276 0.76518733779448 0.38259366889724 41 0.596251617027615 0.80749676594477 0.403748382972385 42 0.543902116438828 0.912195767122343 0.456097883561172 43 0.671149778927836 0.657700442144328 0.328850221072164 44 0.637121301607273 0.725757396785453 0.362878698392727 45 0.634390603829408 0.731218792341184 0.365609396170592 46 0.591846184677295 0.81630763064541 0.408153815322705 47 0.59988851810902 0.80022296378196 0.40011148189098 48 0.68650294343089 0.62699411313822 0.31349705656911 49 0.651190641797329 0.697618716405341 0.348809358202671 50 0.631840278997894 0.736319442004211 0.368159721002106 51 0.593799492218066 0.812401015563869 0.406200507781934 52 0.562381185986479 0.875237628027042 0.437618814013521 53 0.611420651440753 0.777158697118494 0.388579348559247 54 0.581362625892006 0.837274748215987 0.418637374107994 55 0.618696203745988 0.762607592508024 0.381303796254012 56 0.59088608603834 0.81822782792332 0.40911391396166 57 0.548659599131576 0.902680801736847 0.451340400868424 58 0.514631885919935 0.97073622816013 0.485368114080065 59 0.468161156796891 0.936322313593781 0.531838843203109 60 0.428344827522361 0.856689655044721 0.57165517247764 61 0.390583398376658 0.781166796753317 0.609416601623342 62 0.351421690672435 0.702843381344869 0.648578309327565 63 0.311109532984218 0.622219065968437 0.688890467015782 64 0.330896982995788 0.661793965991575 0.669103017004212 65 0.290563368920192 0.581126737840385 0.709436631079808 66 0.302317462086313 0.604634924172626 0.697682537913687 67 0.378830692110058 0.757661384220115 0.621169307889943 68 0.448974335490026 0.897948670980053 0.551025664509974 69 0.410723766234703 0.821447532469406 0.589276233765297 70 0.394075005360847 0.788150010721694 0.605924994639153 71 0.472103121922502 0.944206243845005 0.527896878077498 72 0.428682798044118 0.857365596088235 0.571317201955882 73 0.390575127823842 0.781150255647685 0.609424872176157 74 0.356060327457454 0.712120654914907 0.643939672542546 75 0.326688080209756 0.653376160419513 0.673311919790244 76 0.300887002924743 0.601774005849486 0.699112997075257 77 0.282083223767013 0.564166447534025 0.717916776232987 78 0.246028322757991 0.492056645515981 0.753971677242009 79 0.213614018360786 0.427228036721572 0.786385981639214 80 0.189761758658899 0.379523517317798 0.8102382413411 81 0.171388313715941 0.342776627431882 0.828611686284059 82 0.261140258810000 0.522280517620001 0.73885974119 83 0.236924875516303 0.473849751032607 0.763075124483697 84 0.210480319928581 0.420960639857163 0.789519680071419 85 0.205891867858765 0.41178373571753 0.794108132141235 86 0.194577788870004 0.389155577740009 0.805422211129996 87 0.214075424189101 0.428150848378203 0.785924575810899 88 0.20941206157256 0.41882412314512 0.79058793842744 89 0.206456280470041 0.412912560940081 0.79354371952996 90 0.201158917133057 0.402317834266115 0.798841082866943 91 0.258808836419247 0.517617672838495 0.741191163580753 92 0.222289288200024 0.444578576400047 0.777710711799976 93 0.198549168998540 0.397098337997079 0.80145083100146 94 0.170437969774509 0.340875939549018 0.829562030225491 95 0.150010645739372 0.300021291478743 0.849989354260628 96 0.167466138460375 0.334932276920749 0.832533861539625 97 0.157172789244172 0.314345578488344 0.842827210755828 98 0.142918617372631 0.285837234745262 0.857081382627369 99 0.129095463012943 0.258190926025886 0.870904536987057 100 0.118050748957174 0.236101497914349 0.881949251042826 101 0.0975065841982819 0.195013168396564 0.902493415801718 102 0.0790251936373992 0.158050387274798 0.9209748063626 103 0.0628376200929484 0.125675240185897 0.937162379907052 104 0.0498485528788142 0.0996971057576284 0.950151447121186 105 0.0509450177733726 0.101890035546745 0.949054982226627 106 0.0410953733360213 0.0821907466720426 0.958904626663979 107 0.0362771522452653 0.0725543044905306 0.963722847754735 108 0.0334370908858646 0.0668741817717291 0.966562909114135 109 0.0266274074698381 0.0532548149396763 0.973372592530162 110 0.0275661706112704 0.0551323412225408 0.97243382938873 111 0.0385756582476330 0.0771513164952659 0.961424341752367 112 0.255214276787618 0.510428553575235 0.744785723212382 113 0.269089231818209 0.538178463636418 0.730910768181791 114 0.637719985007595 0.724560029984811 0.362280014992406 115 0.883328157361206 0.233343685277588 0.116671842638794 116 0.854962120379124 0.290075759241753 0.145037879620876 117 0.88300426131917 0.233991477361660 0.116995738680830 118 0.857817540390761 0.284364919218477 0.142182459609239 119 0.838630389866766 0.322739220266468 0.161369610133234 120 0.889820255457616 0.220359489084768 0.110179744542384 121 0.866236375418491 0.267527249163018 0.133763624581509 122 0.835590738785668 0.328818522428665 0.164409261214332 123 0.84440320844075 0.311193583118499 0.155596791559249 124 0.805484138582272 0.389031722835456 0.194515861417728 125 0.77477823580955 0.450443528380901 0.225221764190450 126 0.739062941008436 0.521874117983127 0.260937058991564 127 0.694220162670129 0.611559674659743 0.305779837329872 128 0.645187494032652 0.709625011934696 0.354812505967348 129 0.592326627560472 0.815346744879056 0.407673372439528 130 0.543238316969201 0.913523366061598 0.456761683030799 131 0.516764350992005 0.96647129801599 0.483235649007995 132 0.541789972750493 0.916420054499013 0.458210027249507 133 0.477796333387527 0.955592666775055 0.522203666612473 134 0.449201231028115 0.89840246205623 0.550798768971885 135 0.746691243837481 0.506617512325038 0.253308756162519 136 0.68500600883738 0.629987982325241 0.314993991162620 137 0.674481865412014 0.651036269175973 0.325518134587986 138 0.624387479122084 0.751225041755833 0.375612520877916 139 0.650627730836693 0.698744538326614 0.349372269163307 140 0.579724419212119 0.840551161575762 0.420275580787881 141 0.521673858335851 0.956652283328298 0.478326141664149 142 0.482807706385197 0.965615412770394 0.517192293614803 143 0.508398277240507 0.983203445518987 0.491601722759493 144 0.452072853242826 0.904145706485652 0.547927146757174 145 0.347550551506844 0.695101103013688 0.652449448493156 146 0.313190490057939 0.626380980115878 0.686809509942061 147 0.272332555492666 0.544665110985332 0.727667444507334 148 0.174878158751466 0.349756317502931 0.825121841248534 149 0.347435872663227 0.694871745326454 0.652564127336773 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 7 0.05 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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