Workshop 7 Linear Trend

*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 01:12:17 +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/t1290561056c6tb2x4fr8pe7s8.htm/, Retrieved Wed, 24 Nov 2010 02:11:07 +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/t1290561056c6tb2x4fr8pe7s8.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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Belonging[t] = + 62.5511357635815 + 0.925603289655825Happiness[t] -0.635347076551754Depression[t] + 0.0414054045932947t + 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) 62.5511357635815 8.56179 7.3058 0 0 Happiness 0.925603289655825 0.405143 2.2846 0.023665 0.011833 Depression -0.635347076551754 0.300117 -2.117 0.035826 0.017913 t 0.0414054045932947 0.017081 2.4241 0.016474 0.008237 Multiple Linear Regression - Regression Statistics Multiple R 0.365747082062413 R-squared 0.133770928037170 Adjusted R-squared 0.117323540594837 F-TEST (value) 8.13326301859167 F-TEST (DF numerator) 3 F-TEST (DF denominator) 158 p-value 4.53014548817965e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.0746625058079 Sum Squared Residuals 16036.8142877371 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 53 67.9268223047357 -14.9268223047357 2 86 72.3059879445037 13.6940120554963 3 66 63.962129091851 2.03787090814907 4 67 66.1998319392035 0.800168060796447 5 76 64.2255268134544 11.7744731865457 6 78 71.8362624863251 6.16373751367492 7 53 61.8217839667775 -8.82178396677753 8 80 68.8520072134401 11.1479927865599 9 74 70.454362984241 3.545637015759 10 76 68.589727159179 7.41027284082097 11 79 72.3883803727392 6.61161962726076 12 54 75.5516865097477 -21.5516865097477 13 67 62.8152327715763 4.18476722842372 14 54 69.0456049906563 -15.0456049906563 15 87 73.4796052807682 13.5203947192318 16 58 67.2772092205312 -9.27720922053122 17 75 67.3186146251245 7.68138537487549 18 88 72.0428711283406 15.9571288716595 19 64 69.9428137405181 -5.94281374051812 20 57 69.9293844947678 -12.9293844947678 21 66 75.6340789379833 -9.63407893798327 22 68 64.7488317791235 3.25116822087649 23 54 68.8377412057878 -14.8377412057878 24 56 65.7572458779659 -9.75724587796593 25 86 72.3327089604936 13.6672910395064 26 80 66.2399822009438 13.7600177990562 27 76 71.4899164800244 4.51008351997563 28 69 67.138726999099 1.86127300090100 29 78 68.7410827698999 9.25891723010012 30 67 65.7154220924216 1.28457790757837 31 80 72.9262322515011 7.07376774849894 32 54 66.3787453278164 -12.3787453278164 33 71 73.2992992737917 -2.29929927379172 34 84 70.8541510225216 13.1458489774784 35 74 68.6992589843556 5.30074101564443 36 71 73.7686063510193 -2.76860635101929 37 63 59.7066238094008 3.29337619059924 38 71 70.384425564343 0.615574435656963 39 76 73.5477317013515 2.45226829864851 40 69 69.8867239473215 -0.886723947321485 41 74 72.4146830077782 1.58531699222182 42 75 70.2049563192685 4.79504368073147 43 54 74.0584441831724 -20.0584441831724 44 52 66.5853539698318 -14.5853539698318 45 69 68.5328006040804 0.467199395919621 46 68 66.3779085659143 1.62209143408566 47 65 72.663115435338 -7.66311543533795 48 75 71.4338266868277 3.56617331317226 49 74 70.7850503645257 3.21494963547433 50 75 69.6654309167027 5.33456908329732 51 72 73.1189932668152 -1.11899326681520 52 67 68.7678037858898 -1.76780378588983 53 63 63.4910110153086 -0.491011015308632 54 62 66.9994080157648 -4.99940801576477 55 63 68.9468546500133 -5.94685465001333 56 76 71.1297228470223 4.87027715297766 57 74 71.4613844647197 2.53861553528029 58 67 73.1185748858642 -6.11857488586419 59 73 69.7478233449383 3.25217665506174 60 70 66.6124933667728 3.38750663322722 61 53 59.774750229984 -6.774750229984 62 77 69.5269486952705 7.47305130472954 63 77 67.7171475205521 9.2828524794479 64 52 69.2646686410094 -17.2646686410094 65 54 70.8670244118102 -16.8670244118102 66 80 67.5511075212279 12.4488924787721 67 66 64.7060337561665 1.29396624383349 68 73 68.8497778331744 4.1502221668256 69 63 71.0326460301834 -8.03264603018342 70 69 70.438704358225 -1.43870435822496 71 67 70.1898535497142 -3.18985354971418 72 54 70.8117713805156 -16.8117713805156 73 81 71.1982676485566 9.8017323514434 74 69 73.1457142828052 -4.14571428280516 75 84 70.700566031535 13.2994339684650 76 80 64.7335915340585 15.2664084659415 77 70 73.2150958462414 -3.21509584624143 78 69 67.0126997860044 1.98730021399560 79 77 71.4467000761164 5.55329992388364 80 54 72.178287207605 -18.1782872076050 81 79 72.8002050384065 6.19979496159354 82 30 74.4025608092073 -44.4025608092073 83 71 74.1537100006966 -3.15371000069656 84 73 73.2146774652904 -0.214677465290417 85 72 72.3304795802279 -0.330479580227887 86 77 70.8109346186136 6.1890653813864 87 75 71.7779433128627 3.22205668713728 88 69 71.529092504352 -2.52909250435195 89 54 68.7388533896342 -14.7388533896342 90 70 58.7792095204302 11.2207904795698 91 73 73.7947715105475 -0.794771510547551 92 54 68.863069603414 -14.8630696034140 93 77 72.0263757404225 4.97362425957751 94 82 69.8714837022565 12.1285162977435 95 80 72.1640211999527 7.8359788000473 96 80 74.3468893969617 5.65311060303829 97 69 67.509146260173 1.49085373982707 98 78 72.5784936268366 5.42150637316335 99 81 75.3967089003974 5.60329109960258 100 76 74.2222548022308 1.77774519776918 101 76 76.1148667861358 -0.114866786135760 102 73 67.7161732831394 5.2838267168606 103 85 74.001380152563 10.9986198474370 104 66 70.0501161854289 -4.05011618542894 105 79 70.6171993658868 8.38280063411324 106 68 63.1989438028898 4.80105619711015 107 76 74.802348847488 1.19765115251205 108 71 70.7414155796667 0.258584420333352 109 54 66.7901516125326 -12.7901516125326 110 46 61.11343332816 -15.1134333281601 111 82 72.13632594655 9.86367405344996 112 74 67.8399711159683 6.16002888403172 113 88 72.2739714060802 15.7260285939198 114 38 70.6995917941223 -32.6995917941223 115 76 76.3494515869942 -0.349451586994203 116 86 75.8103445653794 10.1896554346206 117 54 71.459155084454 -17.459155084454 118 70 72.135907565599 -2.13590756559903 119 69 74.7187012763993 -5.71870127639934 120 90 70.9480242216821 19.0519757783179 121 54 69.1382230469638 -15.1382230469638 122 76 71.6661821074205 4.33381789257954 123 89 74.5392320313248 14.4607679686752 124 76 76.4866786655734 -0.486678665573397 125 73 74.6220428405114 -1.62204284051143 126 79 72.812241665793 6.18775833420693 127 90 78.462101458665 11.5378985413351 128 74 77.2328127101547 -3.23281271015472 129 81 78.490077617508 2.50992238249209 130 72 73.5583757103744 -1.55837571037439 131 71 73.0192686887596 -2.01926868875955 132 66 63.6401372457638 2.35986275423625 133 77 75.5886331538095 1.41136684619046 134 65 72.453303175644 -7.45330317564406 135 74 74.4007498098926 -0.400749809892622 136 82 74.0970643510382 7.90293564896177 137 54 63.7923296183866 -9.79232961838661 138 63 72.3286685809132 -9.32866858091317 139 54 68.3225699634355 -14.3225699634355 140 64 75.2431239094109 -11.2431239094108 141 69 72.7979756581407 -3.79797565814074 142 54 75.9612817951492 -21.9612817951492 143 84 74.3869021831913 9.6130978168087 144 86 73.8477951615764 12.1522048384236 145 77 74.8148038558256 2.18519614417443 146 89 76.4171596266264 12.5828403733736 147 76 75.823217954668 0.176782045332018 148 60 70.6012598344304 -10.6012598344304 149 75 72.838962681783 2.16103731821697 150 73 65.0207816049948 7.97921839500519 151 85 75.9888395730412 9.01116042695884 152 79 70.0766997259082 8.9233002740918 153 71 77.977691611883 -6.97769161188301 154 72 72.4106426281977 -0.410642628197746 155 69 65.2278086279613 3.77219137203871 156 78 69.6069742677296 8.39302573227036 157 54 71.5544209019782 -17.5544209019782 158 69 73.156776672779 -4.15677667277907 159 81 79.7322397553068 1.26776024469325 160 84 75.4907195750686 8.5092804249314 161 84 68.8883980010403 15.1116019989597 162 69 71.1261008483929 -2.12610084839291 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.802443379726021 0.395113240547958 0.197556620273979 8 0.703300751647251 0.593398496705498 0.296699248352749 9 0.613489915357881 0.773020169284238 0.386510084642119 10 0.488229015945317 0.976458031890635 0.511770984054682 11 0.397035394802989 0.794070789605977 0.602964605197011 12 0.880822588199103 0.238354823601794 0.119177411800897 13 0.833481791093288 0.333036417813425 0.166518208906712 14 0.858227372422462 0.283545255155075 0.141772627577538 15 0.897165556435136 0.205668887129729 0.102834443564864 16 0.876303742946226 0.247392514107548 0.123696257053774 17 0.8631081762873 0.273783647425400 0.136891823712700 18 0.89328710544078 0.213425789118441 0.106712894559221 19 0.871297096797706 0.257405806404588 0.128702903202294 20 0.88360021360424 0.232799572791519 0.116399786395760 21 0.866136571640335 0.267726856719331 0.133863428359665 22 0.838372368942621 0.323255262114757 0.161627631057379 23 0.846249237192924 0.307501525614152 0.153750762807076 24 0.815191232105391 0.369617535789217 0.184808767894609 25 0.873013765161725 0.25397246967655 0.126986234838275 26 0.906389483120741 0.187221033758518 0.0936105168792588 27 0.885255925071109 0.229488149857782 0.114744074928891 28 0.8546233434018 0.290753313196400 0.145376656598200 29 0.845662894871325 0.30867421025735 0.154337105128675 30 0.807498901887399 0.385002196225203 0.192501098112601 31 0.779315465609514 0.441369068780973 0.220684534390486 32 0.796964791172118 0.406070417655764 0.203035208827882 33 0.755783449322146 0.488433101355708 0.244216550677854 34 0.777659330278803 0.444681339442393 0.222340669721197 35 0.742800214991739 0.514399570016522 0.257199785008261 36 0.704009505656441 0.591980988687118 0.295990494343559 37 0.659056943749676 0.681886112500647 0.340943056250324 38 0.607866142796160 0.784267714407679 0.392133857203839 39 0.556753610992037 0.886492778015926 0.443246389007963 40 0.505416077328899 0.989167845342201 0.494583922671101 41 0.452943371212964 0.905886742425928 0.547056628787036 42 0.410483639364009 0.820967278728018 0.589516360635991 43 0.564491011422897 0.871017977154206 0.435508988577103 44 0.605283827663962 0.789432344672076 0.394716172336038 45 0.556041401517654 0.887917196964691 0.443958598482345 46 0.508406211867466 0.983187576265068 0.491593788132534 47 0.476642296500898 0.953284593001795 0.523357703499102 48 0.438308468579777 0.876616937159553 0.561691531420223 49 0.397831585755551 0.795663171511101 0.602168414244449 50 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0.307556913484066 85 0.653916295258584 0.692167409482832 0.346083704741416 86 0.632711389868369 0.734577220263262 0.367288610131631 87 0.597121046488671 0.805757907022657 0.402878953511329 88 0.554989639972516 0.890020720054968 0.445010360027484 89 0.600547978639125 0.79890404272175 0.399452021360875 90 0.622196533422049 0.755606933155902 0.377803466577951 91 0.582995667899279 0.834008664201441 0.417004332100721 92 0.63138101823494 0.737237963530121 0.368618981765061 93 0.601838865459368 0.796322269081265 0.398161134540632 94 0.625180927277911 0.749638145444178 0.374819072722089 95 0.611994916005316 0.776010167989368 0.388005083994684 96 0.583444866647581 0.833110266704838 0.416555133352419 97 0.539575986017841 0.920848027964319 0.460424013982159 98 0.509216474933197 0.981567050133606 0.490783525066803 99 0.478066456474799 0.956132912949598 0.521933543525201 100 0.4338266804041 0.8676533608082 0.5661733195959 101 0.389621512840665 0.77924302568133 0.610378487159335 102 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0.930496906276876 0.465248453138438 137 0.521925776082615 0.95614844783477 0.478074223917385 138 0.485089362584628 0.970178725169256 0.514910637415372 139 0.534892834556801 0.930214330886397 0.465107165443199 140 0.53471556888003 0.93056886223994 0.46528443111997 141 0.469114232457609 0.938228464915218 0.530885767542391 142 0.785315753988075 0.429368492023850 0.214684246011925 143 0.730829485579493 0.538341028841013 0.269170514420506 144 0.723829235251503 0.552341529496993 0.276170764748497 145 0.649701625352685 0.70059674929463 0.350298374647315 146 0.684516409036449 0.630967181927102 0.315483590963551 147 0.599299736610547 0.801400526778906 0.400700263389453 148 0.630294457573192 0.739411084853616 0.369705542426808 149 0.53419019901572 0.93161960196856 0.46580980098428 150 0.439403581149058 0.878807162298116 0.560596418850942 151 0.428253873406906 0.856507746813812 0.571746126593094 152 0.421411452383239 0.842822904766477 0.578588547616761 153 0.304519956781488 0.609039913562975 0.695480043218512 154 0.201887094425443 0.403774188850886 0.798112905574557 155 0.121299936006469 0.242599872012938 0.878700063993531 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:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/101n791290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/101n791290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/1v4ax1290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/1v4ax1290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/2v4ax1290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/2v4ax1290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/35vr01290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/35vr01290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/45vr01290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/45vr01290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/55vr01290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/55vr01290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/63qfr1290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/63qfr1290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/7rwqo1290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/7rwqo1290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/8rwqo1290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/8rwqo1290561126.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/9rwqo1290561126.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290561056c6tb2x4fr8pe7s8/9rwqo1290561126.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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