*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 15:33:51 +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/t129052635025pzoo36p9oicpe.htm/, Retrieved Tue, 23 Nov 2010 16:32:41 +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/t129052635025pzoo36p9oicpe.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 24 11 12 24 26 237,588 11 25 7 8 25 23 164,083 6 17 17 8 30 25 278,261 12 18 10 8 19 23 220,36 8 18 12 9 22 19 253,967 10 16 12 7 22 29 422,31 10 20 11 4 25 25 136,921 11 16 11 11 23 21 143,495 16 18 12 7 17 22 189,785 11 17 13 7 21 25 219,529 13 23 14 12 19 24 217,761 12 30 16 10 19 18 221,754 8 23 11 10 15 22 159,854 12 18 10 8 16 15 209,464 11 15 11 8 23 22 174,283 4 12 15 4 27 28 154,55 9 21 9 9 22 20 153,024 8 15 11 8 14 12 162,49 8 20 17 7 22 24 154,462 14 31 17 11 23 20 249,671 15 27 11 9 23 21 259,473 16 34 18 11 21 20 155,337 9 21 14 13 19 21 151,289 14 31 10 8 18 23 276,614 11 19 11 8 20 28 188,214 8 16 15 9 23 24 181,098 9 20 15 6 25 24 240,898 9 21 13 9 19 24 244,551 9 22 16 9 24 23 250,238 9 17 13 6 22 23 183,129 10 24 9 6 25 29 310,331 16 25 18 16 26 24 281,942 11 26 18 5 29 18 230,343 8 25 12 7 32 25 161,563 9 17 17 9 25 21 392,527 16 32 9 6 29 26 1077,414 11 33 9 6 28 22 248,275 16 13 12 5 17 22 557,386 12 32 18 12 28 22 731,874 12 25 12 7 29 23 301,42 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 Doubts[t] = + 7.47325443163413 + 0.246741956415152Concern[t] -0.111829096401947Expectations[t] + 0.144344598465124Criticism[t] -0.191710784726768Standards[t] + 0.105802868004161Organization[t] + 0.00078421221897491Time[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) 7.47325443163413 1.57409 4.7477 5e-06 2e-06 Concern 0.246741956415152 0.039835 6.1941 0 0 Expectations -0.111829096401947 0.073618 -1.5191 0.130826 0.065413 Criticism 0.144344598465124 0.092378 1.5625 0.12024 0.06012 Standards -0.191710784726768 0.056446 -3.3963 0.000872 0.000436 Organization 0.105802868004161 0.05638 1.8766 0.062488 0.031244 Time 0.00078421221897491 0.000476 1.6492 0.101178 0.050589 Multiple Linear Regression - Regression Statistics Multiple R 0.502906482662687 R-squared 0.252914930304155 Adjusted R-squared 0.223424730184582 F-TEST (value) 8.57623648800857 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 4.93064412632194e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.46791871367676 Sum Squared Residuals 925.774662152027 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 12.2332116541052 1.76678834589478 2 11 11.7831286943728 -0.783128694372844 3 6 8.03349367414476 -2.03349367414476 4 12 10.9148455296688 1.08515447033121 5 8 9.86354312917616 -1.86354312917616 6 10 10.2714153370361 -0.271415337036119 7 10 9.71502909654533 0.284970903454673 8 11 9.70383896870502 1.29616103129498 9 16 10.800484151254 5.199515848746 10 11 10.0158041717835 0.984195828216502 11 13 12.3823820204443 0.61761797955569 12 12 12.9655424769816 -0.965542476981638 13 8 12.9390061386545 -4.93900613865447 14 12 10.6350101634779 1.36498983652214 15 11 9.15401041069645 1.84598958930355 16 4 7.24158897138357 -3.24158897138358 17 9 10.9658984216116 -1.96589842161165 18 8 9.81213057849738 -1.81213057849739 19 8 9.9601736662382 -1.96017366623820 20 14 12.7114553850783 1.28854461492166 21 15 12.2202626570737 2.77973734292628 22 16 13.6492958519106 2.35070414808939 23 9 11.6637059474469 -2.66370594744695 24 14 14.3583168219588 -0.358316821958762 25 11 11.3618526589849 -0.361852658984872 26 8 9.31473072224958 -1.31473072224958 27 9 9.53213907375598 -0.53213907375598 28 9 11.5887024539669 -2.58870245396692 29 9 10.4400601444275 -1.44006014442754 30 9 9.4395977278126 -0.439597727812599 31 10 11.7735460248492 -1.77354602484916 32 16 11.7142839728660 4.28571602713403 33 11 9.12282121767261 1.87717878232739 34 8 9.94729264202712 -1.94729264202712 35 9 8.80278951764046 0.197210482359536 36 16 13.2647857948188 2.73521420518124 37 11 12.6298061289154 -1.62980612891540 38 16 9.56636236815538 6.43363763184462 39 12 12.6219141405575 -0.62191414055751 40 12 10.4205038864182 1.57949611358175 41 14 12.4264133322057 1.57358666779426 42 9 10.4443875981524 -1.44438759815237 43 10 10.6302760676848 -0.630276067684837 44 9 8.41285649951002 0.587143500489982 45 10 10.0605970475122 -0.0605970475122338 46 12 10.2162227403744 1.78377725962557 47 14 11.4976254626734 2.50237453732661 48 14 12.0583959174247 1.94160408257527 49 10 12.2699104652829 -2.26991046528291 50 14 10.0838079571160 3.91619204288402 51 16 12.1537183567663 3.84628164323374 52 9 10.4080720919727 -1.40807209197273 53 10 11.4860241642348 -1.48602416423478 54 6 9.04630480316662 -3.04630480316662 55 8 11.2012190384819 -3.20121903848192 56 13 12.4077706211257 0.592229378874307 57 10 10.7955707721772 -0.79557077217719 58 8 8.97843353799814 -0.978433537998137 59 7 9.25669117887252 -2.25669117887252 60 15 9.93723097316711 5.06276902683289 61 9 9.8233367355582 -0.823336735558207 62 10 10.2195910413457 -0.219591041345750 63 12 10.1137527188050 1.88624728119504 64 13 10.4880074166183 2.51199258338166 65 10 8.50922841505382 1.49077158494618 66 11 11.7558457066626 -0.755845706662588 67 8 13.5390973756636 -5.53909737566361 68 9 9.1136956908828 -0.113695690882796 69 13 8.57700023764982 4.42299976235018 70 11 10.3892631889348 0.610736811065243 71 8 12.8169921451353 -4.81699214513528 72 9 10.9750928729583 -1.97509287295826 73 9 12.2008612179035 -3.20086121790354 74 15 12.3149501349260 2.68504986507395 75 9 11.0627938181380 -2.06279381813795 76 10 11.5371291738712 -1.53712917387119 77 14 8.85910601391733 5.14089398608267 78 12 10.8621735758763 1.13782642412371 79 12 11.0652322321941 0.934767767805863 80 11 11.5513942484139 -0.551394248413907 81 14 11.4818101195682 2.51818988043184 82 6 11.5198774729132 -5.51987747291315 83 12 11.2971445690057 0.702855430994276 84 8 10.0042506590629 -2.00425065906291 85 14 12.4070975513490 1.59290244865095 86 11 10.8904995581690 0.109500441831029 87 10 9.88605471850173 0.113945281498267 88 14 10.1601326751095 3.83986732489046 89 12 11.8902147364706 0.109785263529372 90 10 11.0034395261537 -1.00343952615374 91 14 12.9197933882695 1.08020661173051 92 5 8.99164437425524 -3.99164437425524 93 11 10.4157158987174 0.584284101282608 94 10 10.3703698902126 -0.370369890212591 95 9 11.3849025088244 -2.38490250882443 96 10 11.2438482309453 -1.24384823094527 97 16 15.0766093687621 0.923390631237886 98 13 12.7048508259988 0.295149174001184 99 9 10.8939000661556 -1.89390006615560 100 10 11.3417193884507 -1.3417193884507 101 10 10.8830217158585 -0.883021715858534 102 7 9.46168471635747 -2.46168471635747 103 9 9.62973979688686 -0.629739796886863 104 8 10.2091805605624 -2.20918056056239 105 14 12.7519490787475 1.24805092125254 106 14 11.6766424024919 2.32335759750806 107 8 11.0316556205765 -3.03165562057653 108 9 11.5000012063194 -2.50000120631942 109 14 11.7443694436946 2.25563055630543 110 14 10.7275945748817 3.27240542511827 111 8 9.79765924036386 -1.79765924036386 112 8 13.5734367608051 -5.57343676080506 113 8 11.3361615474807 -3.33616154748066 114 7 8.4950420371341 -1.4950420371341 115 6 7.3474157870404 -1.34741578704041 116 8 9.34873114203093 -1.34873114203093 117 6 8.28221095627665 -2.28221095627665 118 11 9.8584082404761 1.14159175952389 119 14 11.784363469849 2.21563653015099 120 11 11.1104437069811 -0.110443706981125 121 11 11.9974163414266 -0.997416341426569 122 11 9.19606079188431 1.80393920811569 123 14 10.3470848191907 3.65291518080926 124 8 10.3320739391197 -2.33207393911968 125 20 11.4098550822654 8.59014491773456 126 11 10.2554295322568 0.744570467743242 127 8 9.1165046294495 -1.11650462944949 128 11 10.6609746912370 0.339025308763027 129 10 10.5694490964196 -0.569449096419625 130 14 13.5702125569339 0.42978744306611 131 11 10.4773717393613 0.522628260638734 132 9 10.6226581695311 -1.62265816953110 133 9 9.65307314391648 -0.65307314391648 134 8 10.1412980275125 -2.14129802751249 135 10 11.9931543524394 -1.99315435243945 136 13 10.6272421396325 2.37275786036745 137 13 10.2615114061883 2.7384885938117 138 12 9.30469987998887 2.69530012001113 139 8 10.2751602523702 -2.27516025237017 140 13 10.9349276892883 2.06507231071165 141 14 12.4358476370457 1.56415236295426 142 12 11.5964601840543 0.403539815945663 143 14 10.8265529975164 3.17344700248358 144 15 11.2441382719679 3.75586172803209 145 13 14.1351354883011 -1.13513548830110 146 16 11.7367516513755 4.26324834862451 147 9 11.8970837246303 -2.89708372463025 148 9 10.4257500610686 -1.42575006106859 149 9 11.0490897011570 -2.04908970115697 150 8 11.3025504625713 -3.30255046257126 151 7 9.96492669641727 -2.96492669641727 152 16 11.8668176039625 4.13318239603754 153 11 13.1669923249122 -2.16699232491221 154 9 9.96199394897339 -0.961993948973386 155 11 9.70637373227855 1.29362626772145 156 9 9.79759721826525 -0.797597218265245 157 14 12.4394044834054 1.56059551659457 158 13 10.9620909258838 2.0379090741162 159 16 14.2238620943191 1.77613790568094 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.173197259770479 0.346394519540958 0.826802740229521 11 0.273907888038019 0.547815776076038 0.726092111961981 12 0.158192279437898 0.316384558875796 0.841807720562102 13 0.854289793723402 0.291420412553197 0.145710206276598 14 0.795270669647719 0.409458660704562 0.204729330352281 15 0.721312026543243 0.557375946913513 0.278687973456757 16 0.766232092342619 0.467535815314762 0.233767907657381 17 0.74304904246318 0.513901915073641 0.256950957536820 18 0.721458620836174 0.557082758327653 0.278541379163826 19 0.652173790202345 0.69565241959531 0.347826209797655 20 0.639326806453078 0.721346387093844 0.360673193546922 21 0.626853099723956 0.746293800552087 0.373146900276044 22 0.614054125421809 0.771891749156382 0.385945874578191 23 0.5934109691749 0.8131780616502 0.4065890308251 24 0.55819204056871 0.88361591886258 0.44180795943129 25 0.485411645902276 0.970823291804552 0.514588354097724 26 0.418696709542333 0.837393419084665 0.581303290457667 27 0.352552818354199 0.705105636708398 0.647447181645801 28 0.350011735534441 0.700023471068882 0.649988264465559 29 0.302643542941081 0.605287085882162 0.697356457058919 30 0.247441266081039 0.494882532162078 0.752558733918961 31 0.235031213010194 0.470062426020388 0.764968786989806 32 0.301402051117222 0.602804102234444 0.698597948882778 33 0.267465099797721 0.534930199595442 0.732534900202279 34 0.252029277415976 0.504058554831952 0.747970722584024 35 0.208926429094547 0.417852858189095 0.791073570905453 36 0.178773348834503 0.357546697669005 0.821226651165497 37 0.15870507841515 0.3174101568303 0.84129492158485 38 0.340678938147761 0.681357876295521 0.659321061852239 39 0.370234002668579 0.740468005337158 0.629765997331421 40 0.344940287128443 0.689880574256886 0.655059712871557 41 0.326462741000383 0.652925482000765 0.673537258999617 42 0.290647774972176 0.581295549944352 0.709352225027824 43 0.250409067091932 0.500818134183865 0.749590932908068 44 0.211942796848789 0.423885593697578 0.788057203151211 45 0.174950920706222 0.349901841412443 0.825049079293778 46 0.150196776334395 0.300393552668790 0.849803223665605 47 0.153176201678914 0.306352403357828 0.846823798321086 48 0.156254805504373 0.312509611008746 0.843745194495627 49 0.151033742661009 0.302067485322019 0.84896625733899 50 0.167033579681665 0.33406715936333 0.832966420318335 51 0.240020822358969 0.480041644717938 0.75997917764103 52 0.214610456289071 0.429220912578143 0.785389543710929 53 0.189150306477050 0.378300612954101 0.81084969352295 54 0.209967072215288 0.419934144430575 0.790032927784712 55 0.231001344244210 0.462002688488421 0.76899865575579 56 0.195355125242636 0.390710250485273 0.804644874757364 57 0.16557225611368 0.33114451222736 0.83442774388632 58 0.144413984110149 0.288827968220298 0.855586015889851 59 0.146026999935799 0.292053999871598 0.853973000064201 60 0.219558606936411 0.439117213872822 0.780441393063589 61 0.187084904120101 0.374169808240203 0.812915095879899 62 0.156432141297783 0.312864282595566 0.843567858702217 63 0.149778883373045 0.299557766746091 0.850221116626955 64 0.154528473106934 0.309056946213868 0.845471526893066 65 0.132164181163122 0.264328362326243 0.867835818836878 66 0.108758892830893 0.217517785661786 0.891241107169107 67 0.233561662603693 0.467123325207387 0.766438337396307 68 0.198328478985759 0.396656957971519 0.80167152101424 69 0.286183082686903 0.572366165373806 0.713816917313097 70 0.249386010402551 0.498772020805102 0.750613989597449 71 0.390245451733287 0.780490903466573 0.609754548266713 72 0.400270317923234 0.800540635846468 0.599729682076766 73 0.419250010304747 0.838500020609494 0.580749989695253 74 0.444039215143047 0.888078430286094 0.555960784856953 75 0.423568586474444 0.847137172948887 0.576431413525556 76 0.39617255980595 0.7923451196119 0.60382744019405 77 0.568101286622599 0.863797426754802 0.431898713377401 78 0.533406191117502 0.933187617764996 0.466593808882498 79 0.492877788034578 0.985755576069156 0.507122211965422 80 0.449473990386641 0.898947980773282 0.550526009613359 81 0.445106048258516 0.890212096517033 0.554893951741484 82 0.631942719683474 0.736114560633053 0.368057280316526 83 0.589391303044569 0.821217393910862 0.410608696955431 84 0.570347880449597 0.859304239100806 0.429652119550403 85 0.540085632129906 0.919828735740189 0.459914367870094 86 0.495503093087175 0.99100618617435 0.504496906912825 87 0.448873981446928 0.897747962893856 0.551126018553072 88 0.527240942336692 0.945518115326616 0.472759057663308 89 0.482895481290959 0.965790962581918 0.517104518709041 90 0.443305356566582 0.886610713133165 0.556694643433418 91 0.406475304156725 0.81295060831345 0.593524695843275 92 0.467821017418560 0.935642034837121 0.53217898258144 93 0.426338586035084 0.852677172070167 0.573661413964916 94 0.384230231831992 0.768460463663984 0.615769768168008 95 0.379362915115978 0.758725830231955 0.620637084884022 96 0.344779992539524 0.689559985079047 0.655220007460476 97 0.324048143441059 0.648096286882118 0.675951856558941 98 0.283098339856433 0.566196679712866 0.716901660143567 99 0.265020556158495 0.53004111231699 0.734979443841505 100 0.237012639429637 0.474025278859273 0.762987360570363 101 0.205382099399729 0.410764198799458 0.794617900600271 102 0.198505146337349 0.397010292674697 0.801494853662651 103 0.166802371210806 0.333604742421611 0.833197628789194 104 0.159092442030445 0.318184884060889 0.840907557969555 105 0.135927420603657 0.271854841207315 0.864072579396343 106 0.132025857949457 0.264051715898913 0.867974142050543 107 0.142860866705681 0.285721733411361 0.85713913329432 108 0.146690648297019 0.293381296594038 0.853309351702981 109 0.137531909140799 0.275063818281598 0.862468090859201 110 0.160969500698802 0.321939001397604 0.839030499301198 111 0.141828832631687 0.283657665263374 0.858171167368313 112 0.335526718837888 0.671053437675775 0.664473281162112 113 0.419280900145971 0.838561800291941 0.580719099854029 114 0.382704359781257 0.765408719562515 0.617295640218743 115 0.369947420920901 0.739894841841801 0.6300525790791 116 0.327536871881042 0.655073743762084 0.672463128118958 117 0.312314593609307 0.624629187218614 0.687685406390693 118 0.273466021175358 0.546932042350715 0.726533978824642 119 0.25582327982725 0.5116465596545 0.74417672017275 120 0.214126813557713 0.428253627115426 0.785873186442287 121 0.190179778407857 0.380359556815713 0.809820221592143 122 0.178769744166124 0.357539488332249 0.821230255833876 123 0.191291143452804 0.382582286905609 0.808708856547196 124 0.201849232129082 0.403698464258164 0.798150767870918 125 0.769118573779935 0.46176285244013 0.230881426220065 126 0.733293881004225 0.53341223799155 0.266706118995775 127 0.682288743737281 0.635422512525438 0.317711256262719 128 0.623215537331073 0.753568925337853 0.376784462668927 129 0.56082038712176 0.87835922575648 0.43917961287824 130 0.499280335418379 0.998560670836758 0.500719664581621 131 0.440621738754771 0.881243477509541 0.559378261245229 132 0.384752309929138 0.769504619858277 0.615247690070862 133 0.321911670721122 0.643823341442245 0.678088329278878 134 0.280624190830818 0.561248381661637 0.719375809169182 135 0.247531765233157 0.495063530466314 0.752468234766843 136 0.233455887137588 0.466911774275176 0.766544112862412 137 0.267275884150423 0.534551768300846 0.732724115849577 138 0.279501688434267 0.559003376868534 0.720498311565733 139 0.280281538643503 0.560563077287005 0.719718461356497 140 0.221413321284013 0.442826642568026 0.778586678715987 141 0.166386519982344 0.332773039964689 0.833613480017656 142 0.122387060065051 0.244774120130101 0.87761293993495 143 0.155574180500688 0.311148361001376 0.844425819499312 144 0.144026865613261 0.288053731226522 0.855973134386739 145 0.135733966506997 0.271467933013994 0.864266033493003 146 0.191930262841260 0.383860525682519 0.80806973715874 147 0.155085798761212 0.310171597522423 0.844914201238788 148 0.0929256594203078 0.185851318840616 0.907074340579692 149 0.056362116530027 0.112724233060054 0.943637883469973 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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