Workshop 7 Regressiemodel 2

*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: Wed, 24 Nov 2010 00:41:04 +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/24/t1290559507dft9bqkn2ly71jm.htm/, Retrieved Wed, 24 Nov 2010 01:45:07 +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/24/t1290559507dft9bqkn2ly71jm.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 53 18 11 86 11 14 66 12 12 67 16 21 76 18 12 78 14 22 53 14 11 80 15 10 74 15 13 76 17 10 79 19 8 54 10 15 67 16 14 54 18 10 87 14 14 58 14 14 75 17 11 88 14 10 64 16 13 57 18 7 66 11 14 68 14 12 54 12 14 56 17 11 86 9 9 80 16 11 76 14 15 69 15 14 78 11 13 67 16 9 80 13 15 54 17 10 71 15 11 84 14 13 74 16 8 71 9 20 63 15 12 71 17 10 76 13 10 69 15 9 74 16 14 75 16 8 54 12 14 52 12 11 69 11 13 68 15 9 65 15 11 75 17 15 74 13 11 75 16 10 72 14 14 67 11 18 63 12 14 62 12 11 63 15 12 76 16 13 74 15 9 67 12 10 73 12 15 70 8 20 53 13 12 77 11 12 77 14 14 52 15 13 54 10 11 80 11 17 66 12 12 73 15 13 63 15 14 69 14 13 67 16 15 54 15 13 81 15 10 69 13 11 84 12 19 80 17 13 70 13 17 69 15 13 77 13 9 54 15 11 79 16 10 30 15 9 71 16 12 73 15 12 72 14 13 77 15 13 75 14 12 69 13 15 54 7 22 70 17 13 73 13 15 54 15 13 77 14 15 82 13 10 80 16 11 80 12 16 69 14 11 78 17 11 81 15 10 76 17 10 76 12 16 73 16 12 85 11 11 66 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Belonging[t] = + 68.6905883670272 + 0.738682252828208Happiness[t] -0.612064171715593Depression[t] -2.79167918844864M1[t] + 1.16668974198661M2[t] + 5.38629689816489M3[t] -0.570072423785216M4[t] + 0.755352844437453M5[t] + 1.11291391479045M6[t] -1.21360489058126M7[t] -4.53924513891819M8[t] -1.68495950612742M9[t] -3.24013500131986M10[t] -0.27755330990375M11[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) 68.6905883670272 9.652935 7.116 0 0 Happiness 0.738682252828208 0.432176 1.7092 0.089507 0.044753 Depression -0.612064171715593 0.319215 -1.9174 0.057113 0.028556 M1 -2.79167918844864 3.994013 -0.699 0.48567 0.242835 M2 1.16668974198661 3.972069 0.2937 0.769381 0.38469 M3 5.38629689816489 3.995149 1.3482 0.179651 0.089825 M4 -0.570072423785216 4.000206 -0.1425 0.88687 0.443435 M5 0.755352844437453 3.968737 0.1903 0.849315 0.424657 M6 1.11291391479045 4.004802 0.2779 0.781481 0.39074 M7 -1.21360489058126 4.041968 -0.3003 0.764407 0.382204 M8 -4.53924513891819 4.068388 -1.1157 0.266344 0.133172 M9 -1.68495950612742 4.069224 -0.4141 0.679419 0.33971 M10 -3.24013500131986 4.063068 -0.7975 0.426461 0.213231 M11 -0.27755330990375 4.096768 -0.0677 0.946077 0.473038 Multiple Linear Regression - Regression Statistics Multiple R 0.392999624550488 R-squared 0.154448704896824 Adjusted R-squared 0.0801773073539778 F-TEST (value) 2.07951795720182 F-TEST (DF numerator) 13 F-TEST (DF denominator) 148 p-value 0.0184665212073112 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.2844671234392 Sum Squared Residuals 15653.999073939 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 53 68.8956906575865 -15.8956906575865 2 86 76.42085277105 9.57914722894995 3 66 73.6334916422841 -7.6334916422841 4 67 69.6399329165934 -2.63993291659338 5 76 68.4115096506885 7.58849034931145 6 78 75.7550127721383 2.24498722786171 7 53 64.3531232382978 -11.3531232382978 8 80 67.7601888788324 12.2398111211676 9 74 71.965220936167 2.03477906383301 10 76 68.5738529258278 7.42614707417223 11 79 74.849991638047 4.15000836195292 12 54 77.8290377970384 -23.8290377970384 13 67 64.1047691311268 2.89523086887323 14 54 73.1072957502469 -19.1072957502469 15 87 81.252524098944 5.74747590105607 16 58 69.8931690788186 -11.8931690788186 17 75 71.2185943470413 3.78140565295872 18 88 75.6283946910257 12.3716053089743 19 64 71.697893298885 -7.69789329888494 20 57 68.0134250410577 -11.0134250410577 21 66 76.0174602097984 -10.0174602097984 22 68 65.0070597427993 2.99294025720066 23 54 71.4098165361313 -17.4098165361313 24 56 68.9858769969474 -12.9858769969474 25 86 71.7238015877866 14.2761984122134 26 80 70.9968408390274 9.00315916097265 27 76 79.1630954215719 -3.16309542157191 28 69 69.281104907103 -0.281104907103021 29 78 71.9572765998695 6.04272340013051 30 67 69.9721728306252 -2.97217283062524 31 80 73.787321976257 6.21267802374305 32 54 64.5732499391418 -10.5732499391418 33 71 73.4425854418234 -2.4425854418234 34 84 69.797981269259 14.2020187307410 35 74 70.7977523644157 3.20224763558433 36 71 75.6129910385538 -4.6129910385538 37 63 60.3057660197206 2.69423398027940 38 71 73.5927418408498 -2.59274184084983 39 76 80.5138418461157 -4.51384184611572 40 69 71.6027435128528 -2.60274351285278 41 74 75.0175974584475 -1.01759745844745 42 75 73.0535199230507 1.94648007694931 43 54 74.3993861479725 -20.3993861479726 44 52 64.4466318580292 -12.4466318580292 45 69 69.1371100059668 -0.137110005966768 46 68 65.6191239145149 2.38087608548507 47 65 73.9846913041062 -8.98469130410625 48 75 73.0381162705788 1.96188372942119 49 74 69.2755449009242 4.72445509907577 50 75 72.727441506909 2.27255849309099 51 72 79.7751595932875 -7.77515959328751 52 67 69.8931690788186 -2.89316907881861 53 63 66.5542909016943 -3.55429090169429 54 62 70.0987909117379 -8.09879091173786 55 63 69.608464621513 -6.60846462151293 56 76 67.886806959945 8.11319304005496 57 74 70.8677106738484 3.13228932615158 58 67 71.0221096126901 -4.02210961269013 59 73 71.156580373906 1.84341962609397 60 70 68.3738128252318 1.62618717476818 61 53 59.5670837668924 -6.56708376689239 62 77 72.1153773351934 4.88462266480659 63 77 74.8576199857153 2.14238001428472 64 52 69.8931690788186 -17.8931690788186 65 54 72.5693407715851 -18.5693407715851 66 80 70.4576189212282 9.54238107877178 67 66 65.1973973383912 0.802602661608828 68 73 65.6707602014604 7.32923979853959 69 63 70.1290284210202 -7.12902842102021 70 69 67.9617887541122 1.03821124588783 71 67 70.7977523644157 -3.79775236441567 72 54 71.3285418365447 -17.3285418365447 73 81 69.022308738699 11.977691261301 74 69 74.816870184281 -5.81687018428101 75 84 76.9470486630873 7.05295133691271 76 80 65.3554837145842 14.6445162854158 77 70 74.0467052772415 -4.0467052772415 78 69 69.0012806494193 -0.00128064941928921 79 77 70.6003830365664 6.39961696343362 80 54 68.2456349694354 -14.2456349694354 81 79 71.3531567644514 7.6468432355486 82 30 71.1487276938027 -41.1487276938027 83 71 73.9846913041062 -2.98469130410625 84 73 73.1647343516914 -0.164734351691429 85 72 69.6343729104146 2.36562708958541 86 77 72.241995416306 4.75800458369397 87 75 77.2002848253125 -2.20028482531252 88 69 71.1172974222498 -2.1172974222498 89 54 69.8678479224975 -15.8678479224975 90 70 61.5088662738721 8.49113372612792 91 73 72.0777475422228 0.922252457777211 92 54 64.5732499391418 -10.5732499391418 93 77 70.1290284210202 6.87097157897979 94 82 66.6110423295684 15.3889576704316 95 80 71.8952626267343 8.10473737326576 96 80 73.776798523407 6.22320147659298 97 69 64.9700694650676 4.02993053493241 98 78 73.4661237597372 4.53387624026279 99 81 79.9017776744001 1.09822232559988 100 76 73.0801080185092 2.91989198149081 101 76 75.8828977923883 0.117102207611722 102 73 68.8746625683067 4.12533743169332 103 85 71.9511294611102 13.0488705388898 104 66 65.5441421203478 0.455857879652206 105 79 68.2928359058734 10.7071640941266 106 68 60.469374378565 7.53062562143504 107 76 73.4992452135033 2.50075478649673 108 71 69.9777954120009 1.02220458799915 109 54 64.1047691311268 -10.1047691311268 110 46 62.5545605161217 -16.5545605161217 111 82 76.588220653597 5.41177934640307 112 74 67.0650581486184 6.9349418513816 113 88 72.3161046093599 15.6838953906401 114 38 70.9640912456787 -32.9640912456787 115 76 73.4284939667666 2.57150603323341 116 86 69.8496175562044 16.1503824437956 117 54 68.7782819964764 -14.7782819964764 118 70 67.8351706729996 2.16482932700044 119 69 73.246009051278 -4.24600905127804 120 90 69.8511773308882 20.1488226691118 121 54 65.5821336367832 -11.5821336367832 122 76 71.6299312445904 4.37006875540956 123 89 78.4244131687437 10.5755868312563 124 76 74.3042363619404 1.69576363805962 125 73 73.7934691150163 -0.793469115016269 126 79 72.6736656797129 6.32633432028715 127 90 75.1380684008008 14.8619315991992 128 74 70.5882998090326 3.41170019096736 129 81 74.3078857757642 6.69211422423577 130 72 68.5738529258278 3.42614707417223 131 71 71.2831984550186 -0.283198455018649 132 66 63.0974452081692 2.90255479183076 133 77 70.8585012538458 6.14149874615423 134 65 71.756549325703 -6.75654932570305 135 74 77.8123489970281 -3.81234899702811 136 82 71.370533584475 10.6294664155250 137 54 63.4939700431163 -9.49397004311633 138 63 71.5761554173943 -8.57615541739427 139 54 65.8094615101068 -11.8094615101068 140 64 68.4988711316606 -4.49887113166063 141 69 69.2637280870794 -0.263728087079386 142 54 70.4100454409746 -16.4100454409745 143 84 71.6630526983565 12.3369473016435 144 86 71.687369846035 14.3126301539650 145 77 69.6343729104146 7.36562708958541 146 89 74.9434882653936 14.0565117346064 147 76 78.5510312498563 -2.55103124985632 148 60 68.2891864920496 -8.28918649204958 149 75 71.5774223565316 3.42257764346835 150 73 64.8224232946753 8.17757670532473 151 85 71.9511294611102 13.0488705388898 152 79 63.3491215957107 15.6508784042893 153 71 73.3159673607108 -2.31596736071078 154 72 66.9698703390587 5.03012966094126 155 69 63.4319560699811 5.56804393001893 156 78 67.2763025629132 10.7236974370868 157 54 66.3208158896114 -12.3208158896114 158 69 71.6299312445904 -2.62993124459044 159 81 81.3791421800565 -0.379142180056540 160 84 72.2148076845684 11.7851923154316 161 84 67.2929731545225 16.7070268454775 162 69 69.6133448211349 -0.613344821134881 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.908677303549781 0.182645392900438 0.0913226964502189 18 0.86231263221249 0.275374735575019 0.137687367787510 19 0.782980098953491 0.434039802093018 0.217019901046509 20 0.84751646153741 0.304967076925181 0.152483538462590 21 0.823819119836297 0.352361760327406 0.176180880163703 22 0.757452617712629 0.485094764574742 0.242547382287371 23 0.810314665472591 0.379370669054817 0.189685334527409 24 0.802025279322476 0.395949441355048 0.197974720677524 25 0.857976526083733 0.284046947832535 0.142023473916267 26 0.83960212827131 0.320795743457379 0.160397871728689 27 0.787108048271464 0.425783903457073 0.212891951728536 28 0.750392828329162 0.499214343341675 0.249607171670838 29 0.690364914016382 0.619270171967236 0.309635085983618 30 0.65614903280163 0.68770193439674 0.34385096719837 31 0.621117949366442 0.757764101267116 0.378882050633558 32 0.585412098018707 0.829175803962585 0.414587901981293 33 0.519030375182689 0.961939249634622 0.480969624817311 34 0.48777668315745 0.9755533663149 0.51222331684255 35 0.474540402952652 0.949080805905305 0.525459597047348 36 0.454097049586453 0.908194099172906 0.545902950413547 37 0.427526388681407 0.855052777362814 0.572473611318593 38 0.366094987620843 0.732189975241685 0.633905012379158 39 0.315777539166318 0.631555078332636 0.684222460833682 40 0.262758051710513 0.525516103421026 0.737241948289487 41 0.262398199048564 0.524796398097127 0.737601800951436 42 0.214984454204225 0.42996890840845 0.785015545795775 43 0.328571188844325 0.657142377688649 0.671428811155676 44 0.320906534072943 0.641813068145887 0.679093465927057 45 0.275911726462495 0.55182345292499 0.724088273537505 46 0.239339544855024 0.478679089710049 0.760660455144976 47 0.217573897584506 0.435147795169013 0.782426102415494 48 0.244755767050042 0.489511534100084 0.755244232949958 49 0.208134231685536 0.416268463371071 0.791865768314464 50 0.172125427012645 0.344250854025290 0.827874572987355 51 0.152009765411419 0.304019530822838 0.84799023458858 52 0.123275526804002 0.246551053608005 0.876724473195998 53 0.102979609108087 0.205959218216173 0.897020390891913 54 0.0982013265222755 0.196402653044551 0.901798673477725 55 0.084276520262467 0.168553040524934 0.915723479737533 56 0.0879668499601417 0.175933699920283 0.912033150039858 57 0.0739160466184048 0.147832093236810 0.926083953381595 58 0.0736718368582538 0.147343673716508 0.926328163141746 59 0.0620053645019454 0.124010729003891 0.937994635498055 60 0.0637410328985194 0.127482065797039 0.93625896710148 61 0.0539827618848071 0.107965523769614 0.946017238115193 62 0.0438242624486854 0.0876485248973707 0.956175737551315 63 0.0358028485009946 0.0716056970019893 0.964197151499005 64 0.0530783510062719 0.106156702012544 0.946921648993728 65 0.105606001901822 0.211212003803644 0.894393998098178 66 0.0988142724248327 0.197628544849665 0.901185727575167 67 0.0902971333715656 0.180594266743131 0.909702866628434 68 0.0831797316156357 0.166359463231271 0.916820268384364 69 0.0720791703491606 0.144158340698321 0.92792082965084 70 0.0578701340340291 0.115740268068058 0.94212986596597 71 0.0462330744085828 0.0924661488171656 0.953766925591417 72 0.0650539837326382 0.130107967465276 0.934946016267362 73 0.0712373567066487 0.142474713413297 0.928762643293351 74 0.0613469337558191 0.122693867511638 0.93865306624418 75 0.0555861106598281 0.111172221319656 0.944413889340172 76 0.0919287303433824 0.183857460686765 0.908071269656618 77 0.0756485419487278 0.151297083897456 0.924351458051272 78 0.0601237457797434 0.120247491559487 0.939876254220257 79 0.0589530531277833 0.117906106255567 0.941046946872217 80 0.076451667077367 0.152903334154734 0.923548332922633 81 0.0702874982203366 0.140574996440673 0.929712501779663 82 0.682250771750133 0.635498456499734 0.317749228249867 83 0.651087994142834 0.697824011714332 0.348912005857166 84 0.644984202777748 0.710031594444504 0.355015797222252 85 0.602370414492605 0.795259171014791 0.397629585507395 86 0.563338236544006 0.873323526911987 0.436661763455994 87 0.517260660293761 0.965478679412478 0.482739339706239 88 0.477575459854146 0.955150919708292 0.522424540145854 89 0.562308773479255 0.87538245304149 0.437691226520745 90 0.577112085941684 0.845775828116632 0.422887914058316 91 0.5427314781083 0.9145370437834 0.4572685218917 92 0.563730983925632 0.872538032148736 0.436269016074368 93 0.537229572914895 0.92554085417021 0.462770427085105 94 0.598647531176194 0.802704937647612 0.401352468823806 95 0.576389007884624 0.847221984230751 0.423610992115376 96 0.571697505308787 0.856604989382426 0.428302494691213 97 0.54523126767337 0.90953746465326 0.45476873232663 98 0.502724128234412 0.994551743531175 0.497275871765588 99 0.453962199985100 0.907924399970199 0.5460378000149 100 0.414226349536187 0.828452699072375 0.585773650463813 101 0.386727826118109 0.773455652236217 0.613272173881891 102 0.365357561526089 0.730715123052179 0.634642438473911 103 0.379292621528909 0.758585243057817 0.620707378471091 104 0.342046281434419 0.684092562868839 0.657953718565581 105 0.37092421411125 0.7418484282225 0.62907578588875 106 0.384270365446823 0.768540730893647 0.615729634553177 107 0.341060868664609 0.682121737329217 0.658939131335392 108 0.337949252304915 0.67589850460983 0.662050747695085 109 0.316014332930213 0.632028665860426 0.683985667069787 110 0.349420303598081 0.698840607196162 0.650579696401919 111 0.315425939576494 0.630851879152987 0.684574060423506 112 0.288534607250728 0.577069214501457 0.711465392749272 113 0.311841966548235 0.62368393309647 0.688158033451765 114 0.800326392003245 0.39934721599351 0.199673607996755 115 0.77239889346216 0.45520221307568 0.22760110653784 116 0.786622199576577 0.426755600846847 0.213377800423423 117 0.811350440946829 0.377299118106342 0.188649559053171 118 0.774635252481214 0.450729495037573 0.225364747518786 119 0.771374116225186 0.457251767549628 0.228625883774814 120 0.792516009192764 0.414967981614473 0.207483990807236 121 0.782055082462782 0.435889835074437 0.217944917537218 122 0.739346312194446 0.521307375611108 0.260653687805554 123 0.763648756378597 0.472702487242807 0.236351243621403 124 0.720552048917312 0.558895902165376 0.279447951082688 125 0.694421883814572 0.611156232370856 0.305578116185428 126 0.64422241412424 0.711555171751521 0.355777585875760 127 0.63154707241455 0.7369058551709 0.36845292758545 128 0.579397652295763 0.841204695408475 0.420602347704237 129 0.515774015468277 0.968451969063445 0.484225984531723 130 0.466966828923074 0.933933657846148 0.533033171076926 131 0.444617461250195 0.889234922500391 0.555382538749805 132 0.37981017229038 0.75962034458076 0.62018982770962 133 0.325789438626832 0.651578877253663 0.674210561373168 134 0.305905763439575 0.61181152687915 0.694094236560425 135 0.240142850880128 0.480285701760256 0.759857149119872 136 0.202729241087488 0.405458482174977 0.797270758912512 137 0.257807285728822 0.515614571457644 0.742192714271178 138 0.263782705147672 0.527565410295345 0.736217294852328 139 0.325281952530474 0.650563905060949 0.674718047469526 140 0.385103947234928 0.770207894469856 0.614896052765072 141 0.293379501659732 0.586759003319464 0.706620498340268 142 0.477920332889656 0.955840665779311 0.522079667110344 143 0.379873280154126 0.759746560308252 0.620126719845874 144 0.265479574166162 0.530959148332324 0.734520425833838 145 0.260224062851647 0.520448125703294 0.739775937148353 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 3 0.0232558139534884 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Include Monthly 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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