Ws 7 - Deterministic 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: Sun, 21 Nov 2010 15:54:23 +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/t1290354848mb1qxhmqno0jkz4.htm/, Retrieved Sun, 21 Nov 2010 16:54:08 +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/t1290354848mb1qxhmqno0jkz4.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 «

13 13 14 13 3 1 12 12 8 13 5 1 15 10 12 16 6 1 12 9 7 12 6 1 10 10 10 11 5 1 12 12 7 12 3 1 15 13 16 18 8 1 9 12 11 11 4 1 12 12 14 14 4 1 11 6 6 9 4 1 11 5 16 14 6 1 11 12 11 12 6 1 15 11 16 11 5 1 7 14 12 12 4 1 11 14 7 13 6 1 11 12 13 11 4 1 10 12 11 12 6 1 14 11 15 16 6 1 10 11 7 9 4 2 6 7 9 11 4 2 11 9 7 13 2 2 15 11 14 15 7 2 11 11 15 10 5 2 12 12 7 11 4 2 14 12 15 13 6 2 15 11 17 16 6 2 9 11 15 15 7 2 13 8 14 14 5 2 13 9 14 14 6 2 16 12 8 14 4 2 13 10 8 8 4 2 12 10 14 13 7 2 14 12 14 15 7 2 11 8 8 13 4 3 9 12 11 11 4 3 16 11 16 15 6 3 12 12 10 15 6 3 10 7 8 9 5 3 13 11 14 13 6 3 16 11 16 16 7 3 14 12 13 13 6 3 15 9 5 11 3 3 5 15 8 12 3 3 8 11 10 12 4 3 11 11 8 12 6 3 16 11 13 14 7 3 17 11 15 14 5 3 9 15 6 8 4 3 9 11 12 13 5 3 13 12 16 16 6 3 10 12 5 13 6 3 6 9 15 11 6 4 12 12 12 14 5 4 8 12 8 13 4 4 14 13 13 13 5 4 12 11 14 13 5 4 11 9 12 12 4 4 16 9 16 16 6 4 8 11 10 15 2 4 15 11 15 15 8 4 7 12 8 12 3 4 16 12 16 14 6 4 14 9 19 12 6 4 16 11 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.184727929928006 + 0.102458915938333FindingFriends[t] + 0.241835431638645KnowingPeople[t] + 0.349828593066031Liked[t] + 0.637259261836313Celebrity[t] + 0.0988008593457305`Date `[t] -0.00641272300843145t + 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) 0.184727929928006 1.456114 0.1269 0.899219 0.44961 FindingFriends 0.102458915938333 0.097707 1.0486 0.296043 0.148022 KnowingPeople 0.241835431638645 0.061846 3.9103 0.00014 7e-05 Liked 0.349828593066031 0.09795 3.5715 0.000478 0.000239 Celebrity 0.637259261836313 0.158123 4.0302 8.9e-05 4.4e-05 `Date ` 0.0988008593457305 0.196706 0.5023 0.616215 0.308107 t -0.00641272300843145 0.011948 -0.5367 0.592247 0.296123 Multiple Linear Regression - Regression Statistics Multiple R 0.707225438473912 R-squared 0.500167820824617 Adjusted R-squared 0.480040350522252 F-TEST (value) 24.8500091323379 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.11754990906277 Sum Squared Residuals 668.118624988388 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.4543275117720 1.54567248822798 2 12 11.168961806666 0.83103819333401 3 15 13.6117180193699 1.38828198063012 4 12 10.8943548499658 1.10564515003424 5 10 10.7288194829093 -0.72881948290926 6 12 9.27712836625497 2.72287163374504 7 15 16.8349613115104 -1.83496131151042 8 9 10.5190753155630 -1.51907531556296 9 12 12.2876546666686 -0.287654666668562 10 11 7.98266202959082 3.01733797040918 11 11 13.3158061960333 -2.31580619603328 12 11 12.1177715402679 -1.11777154026790 13 15 12.2309892046120 2.76901079538799 14 7 11.2771808340937 -4.27718083409372 15 11 11.6859380696307 -0.685938069630715 16 11 10.9514443947728 0.0485556052271954 17 10 12.0857079252257 -2.08570792522574 18 14 14.3434923850977 -0.343492385097677 19 10 8.77787839319097 1.22212160680903 20 6 9.54495805583856 -3.54495805583856 21 11 8.68493096388894 2.31506903611106 22 15 14.4622375895413 0.537762410458682 23 11 11.6739988091688 -0.673998809168755 24 12 9.54793088021921 2.45206911978079 25 14 13.4503773201246 0.549622679875371 26 15 14.8746623236532 0.125337676346754 27 9 14.6720094061378 -5.67200940613781 28 13 12.4920373869371 0.507962613062925 29 13 13.2253428417033 -0.225342841703290 30 16 10.8007757530054 5.19922424699464 31 13 8.49047363972408 4.50952636027592 32 12 13.5959942573866 -1.59599425738661 33 14 14.4941565523869 -0.494156552386905 34 11 10.114261463498 0.885738536501998 35 9 10.5435335130268 -1.54353351302678 36 16 14.31767192821 1.68232807179001 37 12 12.9627055313080 -0.962705531308016 38 10 9.22409654509813 0.775903454901866 39 13 13.1151057097753 -0.115105709775341 40 16 15.2791088910786 0.720891108921397 41 14 12.9629037480582 1.03709625194183 42 15 8.10299585248457 6.89700414751543 43 5 9.7866715130881 -4.78667151308811 44 8 10.4913532514399 -2.49135325143995 45 11 11.2757881888268 -0.275788188826849 46 16 13.8154690719800 2.18453092801998 47 17 13.0182086885763 3.98179131142375 48 9 8.50888192434085 0.491118075659152 49 9 11.9300483545774 -2.93004835457742 50 13 14.6801813150963 -1.68018131509631 51 10 10.9640930648647 -0.964093064864687 52 6 12.4678015836414 -6.46780158364138 53 12 12.4554858308938 -0.455485830893791 54 8 10.4946435264284 -2.49464352642843 55 14 12.4371261393879 1.56287386061212 56 12 12.4676310161414 -0.467631016141424 57 11 10.7855417430767 0.214458256923307 58 16 14.4203036425596 1.57969635744041 59 8 10.2689305211847 -2.26893052118467 60 15 15.2952505273873 -0.295250527387342 61 7 9.46266661046707 -2.46266661046707 62 16 14.0023723122088 1.9976276877912 63 14 13.7144319501692 0.285568049830753 64 16 13.7532456800423 2.24675431995765 65 9 9.92048663101368 -0.92048663101368 66 14 12.2641272703568 1.73587272964320 67 11 13.0288160793959 -2.02881607939594 68 13 10.4504606414420 2.54953935855797 69 15 12.9809492225135 2.01905077748645 70 5 5.65526965476048 -0.655269654760477 71 15 12.4702410303607 2.52975896963932 72 13 12.3244517916519 0.675548208348061 73 11 12.0817378824939 -1.08173788249391 74 11 13.9752819157442 -2.97528191574416 75 12 12.4957196209476 -0.495719620947646 76 12 13.4197310247318 -1.41973102473182 77 12 12.2868539311207 -0.286853931120729 78 12 11.8761397898480 0.123860210151982 79 14 10.7829549036294 3.21704509637059 80 6 7.96886701447297 -1.96886701447297 81 7 9.82863683984184 -2.82863683984184 82 14 11.9330017347079 2.06699826529209 83 14 13.8381979636553 0.161802036344736 84 10 11.2090818273308 -1.20908182733077 85 13 8.6820558226945 4.31794417730549 86 12 12.3827278226039 -0.382727822603868 87 9 9.32868069070523 -0.328680690705233 88 12 12.0243408260259 -0.0243408260258715 89 16 15.0650478471956 0.934952152804355 90 10 10.2509351394506 -0.250935139450645 91 14 13.1601907440176 0.839809255982394 92 10 13.5294557228591 -3.52945572285908 93 16 15.3380960656073 0.661903934392739 94 15 13.4400204696878 1.55997953031224 95 12 11.3398016495221 0.660198350477909 96 10 9.72325369263371 0.276746307366287 97 8 10.2113803731837 -2.21138037318372 98 8 8.5839638760142 -0.583963876014194 99 11 12.7817660837874 -1.78176608378739 100 13 12.3972848053206 0.60271519467939 101 16 15.4261707972401 0.573829202759878 102 16 14.6887175338267 1.31128246617330 103 14 15.783120023334 -1.78312002333401 104 11 8.8039257060694 2.19607429393059 105 4 6.86893251038793 -2.86893251038793 106 14 14.5434362544404 -0.543436254440425 107 9 10.3345009862217 -1.33450098622172 108 14 15.2838424010198 -1.28384240101982 109 8 10.4296687016322 -2.42966870163224 110 8 10.8611316540725 -2.86113165407251 111 11 12.1750326425653 -1.17503264256529 112 12 13.6138983132027 -1.61389831320273 113 11 11.4453785390021 -0.44537853900215 114 14 13.5896355919577 0.410364408042348 115 15 14.3284752922129 0.671524707787082 116 16 13.3663580685751 2.63364193142493 117 16 13.4624042615050 2.53759573849503 118 11 12.7046361347967 -1.70463613479673 119 14 13.6914142471268 0.308585752873245 120 14 10.8828606034594 3.11713939654063 121 12 11.3287353894553 0.6712646105447 122 14 12.4746361458334 1.5253638541666 123 8 10.1381161395181 -2.13811613951814 124 13 13.7618095480229 -0.76180954802293 125 16 13.6529379090762 2.34706209092383 126 12 10.8327470394836 1.16725296051639 127 16 15.3724527412253 0.627547258774656 128 12 13.2838711469848 -1.28387114698484 129 11 11.3710149332596 -0.371014933259570 130 4 6.26171529119994 -2.26171529119994 131 16 15.3468018491916 0.653198150808382 132 15 12.4302550440968 2.56974495590315 133 10 11.3339267659976 -1.33392676599763 134 13 13.0801691844501 -0.080169184450065 135 15 13.1051398157146 1.89486018428544 136 12 10.5070382494129 1.49296175058711 137 14 13.4735263170367 0.526473682963344 138 7 10.573267534394 -3.573267534394 139 19 14.0117892393699 4.98821076063011 140 12 12.5715353979438 -0.571535397943801 141 12 12.1641645992487 -0.164164599248650 142 13 13.4008870456399 -0.400887045639917 143 15 12.8196129850909 2.18038701490908 144 8 8.14265477299094 -0.142654772990937 145 12 10.7899600333214 1.21003996667861 146 10 10.7095121600920 -0.709512160092038 147 8 11.2805515789296 -3.28055157892957 148 10 14.261451480109 -4.261451480109 149 15 13.7372099319199 1.26279006808015 150 16 14.5890623743796 1.41093762562044 151 13 13.2420751468102 -0.242075146810153 152 16 15.1131134138541 0.886886586145918 153 9 10.6373404646853 -1.63734046468531 154 14 13.5779794235252 0.422020576474805 155 14 13.1082107005343 0.891789299465703 156 12 10.5269118213967 1.47308817860326 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0738539342406383 0.147707868481277 0.926146065759362 11 0.111412168598257 0.222824337196515 0.888587831401742 12 0.0734578741372411 0.146915748274482 0.926542125862759 13 0.54882734548451 0.90234530903098 0.45117265451549 14 0.718699208630822 0.562601582738355 0.281300791369178 15 0.652090412310227 0.695819175379545 0.347909587689773 16 0.576112492137822 0.847775015724356 0.423887507862178 17 0.48920416864993 0.97840833729986 0.51079583135007 18 0.451879492529462 0.903758985058924 0.548120507470538 19 0.366000416506306 0.732000833012613 0.633999583493694 20 0.510038740501302 0.979922518997395 0.489961259498698 21 0.516426674721423 0.967146650557155 0.483573325278577 22 0.545846586045827 0.908306827908346 0.454153413954173 23 0.472361536131051 0.944723072262103 0.527638463868949 24 0.477945431608222 0.955890863216444 0.522054568391778 25 0.434731365974649 0.869462731949298 0.565268634025351 26 0.374386151119236 0.748772302238472 0.625613848880764 27 0.62007359797052 0.759852804058961 0.379926402029481 28 0.574954642758156 0.850090714483688 0.425045357241844 29 0.51976053627608 0.96047892744784 0.48023946372392 30 0.71176397013349 0.576472059733021 0.288236029866510 31 0.812570598711138 0.374858802577725 0.187429401288862 32 0.776825716797297 0.446348566405406 0.223174283202703 33 0.730783095040027 0.538433809919946 0.269216904959973 34 0.697861985984421 0.604276028031158 0.302138014015579 35 0.695750871668919 0.608498256662162 0.304249128331081 36 0.708445328680888 0.583109342638225 0.291554671319112 37 0.675394706082227 0.649210587835545 0.324605293917773 38 0.626334916756152 0.747330166487696 0.373665083243848 39 0.57289741138009 0.85420517723982 0.42710258861991 40 0.54355096482102 0.91289807035796 0.45644903517898 41 0.50209155902974 0.995816881940519 0.497908440970259 42 0.757528815664884 0.484942368670232 0.242471184335116 43 0.956307047538371 0.0873859049232579 0.0436929524616289 44 0.966683420979718 0.0666331580405634 0.0333165790202817 45 0.956290274161252 0.0874194516774964 0.0437097258387482 46 0.961225446856714 0.0775491062865716 0.0387745531432858 47 0.980650982255261 0.0386980354894772 0.0193490177447386 48 0.974216525457869 0.0515669490842624 0.0257834745421312 49 0.982136641646371 0.0357267167072569 0.0178633583536285 50 0.979210150922893 0.0415796981542144 0.0207898490771072 51 0.97446674575257 0.0510665084948609 0.0255332542474305 52 0.997597461351614 0.00480507729677206 0.00240253864838603 53 0.996534554484524 0.00693089103095237 0.00346544551547619 54 0.997121346101836 0.00575730779632819 0.00287865389816409 55 0.99710451393585 0.00579097212829866 0.00289548606414933 56 0.995913070323251 0.00817385935349709 0.00408692967674855 57 0.994229234073585 0.0115415318528297 0.00577076592641486 58 0.993564980729086 0.0128700385418285 0.00643501927091427 59 0.99514767680476 0.00970464639048043 0.00485232319524021 60 0.993662276710802 0.0126754465783970 0.00633772328919849 61 0.994486780541911 0.0110264389161778 0.00551321945808889 62 0.995041687770348 0.00991662445930408 0.00495831222965204 63 0.993354910372801 0.0132901792543976 0.00664508962719878 64 0.993715406157568 0.0125691876848637 0.00628459384243185 65 0.992074101296807 0.0158517974063868 0.00792589870319338 66 0.991233013479951 0.0175339730400972 0.0087669865200486 67 0.991193655492438 0.0176126890151239 0.00880634450756193 68 0.99240860329775 0.0151827934045008 0.0075913967022504 69 0.992622989007231 0.0147540219855378 0.00737701099276888 70 0.990035459478192 0.0199290810436164 0.0099645405218082 71 0.991512344594023 0.0169753108119530 0.00848765540597649 72 0.988744712009448 0.0225105759811049 0.0112552879905525 73 0.985875535529372 0.0282489289412562 0.0141244644706281 74 0.98968395411071 0.0206320917785783 0.0103160458892892 75 0.986064984710967 0.0278700305780664 0.0139350152890332 76 0.983814010657478 0.0323719786850447 0.0161859893425223 77 0.978757230581325 0.0424855388373509 0.0212427694186755 78 0.97189841343023 0.0562031731395393 0.0281015865697696 79 0.981928839719815 0.036142320560369 0.0180711602801845 80 0.981171189093485 0.0376576218130295 0.0188288109065148 81 0.984465618766586 0.0310687624668274 0.0155343812334137 82 0.985531580579376 0.0289368388412482 0.0144684194206241 83 0.980548112818612 0.0389037743627762 0.0194518871813881 84 0.976025194854872 0.0479496102902564 0.0239748051451282 85 0.993614742822052 0.0127705143558967 0.00638525717794835 86 0.991186158493816 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0.216219075495198 0.108109537747599 104 0.928929204993892 0.142141590012215 0.0710707950061076 105 0.925456916449307 0.149086167101387 0.0745430835506933 106 0.90562530027135 0.188749399457301 0.0943746997286505 107 0.885230909702821 0.229538180594358 0.114769090297179 108 0.879548215760315 0.240903568479370 0.120451784239685 109 0.876971448272647 0.246057103454706 0.123028551727353 110 0.896714705031345 0.206570589937311 0.103285294968655 111 0.888818831945975 0.222362336108050 0.111181168054025 112 0.926529602725404 0.146940794549192 0.0734703972745962 113 0.904866008509663 0.190267982980674 0.095133991490337 114 0.882761840721651 0.234476318556697 0.117238159278349 115 0.856578652191078 0.286842695617844 0.143421347808922 116 0.847360482630238 0.305279034739525 0.152639517369762 117 0.845160067878448 0.309679864243104 0.154839932121552 118 0.846213905052698 0.307572189894603 0.153786094947302 119 0.814040652836466 0.371918694327068 0.185959347163534 120 0.851321019990752 0.297357960018496 0.148678980009248 121 0.818990515920393 0.362018968159214 0.181009484079607 122 0.79045236724802 0.419095265503961 0.209547632751980 123 0.782510780887198 0.434978438225603 0.217489219112802 124 0.746706356137427 0.506587287725146 0.253293643862573 125 0.734130909366523 0.531738181266955 0.265869090633477 126 0.715398152194316 0.569203695611367 0.284601847805683 127 0.657211416468591 0.685577167062817 0.342788583531409 128 0.629278984908165 0.74144203018367 0.370721015091835 129 0.636265128901008 0.727469742197983 0.363734871098992 130 0.640084554700865 0.719830890598271 0.359915445299135 131 0.594546146744681 0.810907706510639 0.405453853255319 132 0.553103349561024 0.893793300877953 0.446896650438976 133 0.543699901622874 0.912600196754253 0.456300098377126 134 0.471346782798363 0.942693565596725 0.528653217201637 135 0.414315595537165 0.82863119107433 0.585684404462835 136 0.393702835618114 0.787405671236229 0.606297164381886 137 0.320790451030566 0.641580902061132 0.679209548969434 138 0.411615168913242 0.823230337826484 0.588384831086758 139 0.771364571464273 0.457270857071455 0.228635428535727 140 0.76377510119909 0.472449797601821 0.236224898800910 141 0.709611408881837 0.580777182236326 0.290388591118163 142 0.623349240400771 0.753301519198457 0.376650759599229 143 0.559951555234119 0.880096889531761 0.440048444765881 144 0.434662285853637 0.869324571707275 0.565337714146363 145 0.699580655627783 0.600838688744433 0.300419344372217 146 0.849248587677245 0.30150282464551 0.150751412322755 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.0510948905109489 NOK 5% type I error level 42 0.306569343065693 NOK 10% type I error level 55 0.401459854014599 NOK

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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