WS7 - Deterministische 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: Sat, 20 Nov 2010 18:14:50 +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/20/t1290276818jlf3r91c8p1d0p0.htm/, Retrieved Sat, 20 Nov 2010 19:13:49 +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/20/t1290276818jlf3r91c8p1d0p0.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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.184727929928006 + 0.102458915938333FindingFriends[t] + 0.241835431638646KnowingPeople[t] + 0.349828593066031Liked[t] + 0.637259261836312Celebrity[t] + 0.0988008593457308Date[t] -0.0064127230084315t + 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 0.241835431638646 0.061846 3.9103 0.00014 7e-05 Liked 0.349828593066031 0.09795 3.5715 0.000478 0.000239 Celebrity 0.637259261836312 0.158123 4.0302 8.9e-05 4.4e-05 Date 0.0988008593457308 0.196706 0.5023 0.616215 0.308107 t -0.0064127230084315 0.011948 -0.5367 0.592247 0.296123 Multiple Linear Regression - Regression Statistics Multiple R 0.707225438473912 R-squared 0.500167820824616 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 1.54567248822804 2 12 11.168961806666 0.831038193334013 3 15 13.6117180193699 1.38828198063014 4 12 10.8943548499658 1.10564515003425 5 10 10.7288194829093 -0.728819482909259 6 12 9.27712836625497 2.72287163374503 7 15 16.8349613115104 -1.83496131151042 8 9 10.5190753155630 -1.51907531556297 9 12 12.2876546666686 -0.287654666668564 10 11 7.98266202959082 3.01733797040918 11 11 13.3158061960333 -2.31580619603329 12 11 12.1177715402679 -1.11777154026790 13 15 12.2309892046120 2.76901079538798 14 7 11.2771808340937 -4.27718083409372 15 11 11.6859380696307 -0.685938069630715 16 11 10.9514443947728 0.048555605227192 17 10 12.0857079252257 -2.08570792522574 18 14 14.3434923850977 -0.343492385097678 19 10 8.77787839319098 1.22212160680902 20 6 9.54495805583857 -3.54495805583857 21 11 8.68493096388895 2.31506903611105 22 15 14.4622375895413 0.537762410458681 23 11 11.6739988091688 -0.673998809168759 24 12 9.54793088021921 2.45206911978079 25 14 13.4503773201246 0.54962267987537 26 15 14.8746623236532 0.125337676346752 27 9 14.6720094061378 -5.67200940613781 28 13 12.4920373869371 0.507962613062922 29 13 13.2253428417033 -0.225342841703291 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 0.885738536501996 35 9 10.5435335130268 -1.54353351302678 36 16 14.31767192821 1.68232807179001 37 12 12.9627055313080 -0.962705531308015 38 10 9.22409654509814 0.775903454901863 39 13 13.1151057097753 -0.115105709775342 40 16 15.2791088910786 0.720891108921396 41 14 12.9629037480582 1.03709625194183 42 15 8.10299585248458 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 0.491118075659151 49 9 11.9300483545774 -2.93004835457742 50 13 14.6801813150963 -1.68018131509631 51 10 10.9640930648647 -0.964093064864686 52 6 12.4678015836414 -6.46780158364138 53 12 12.4554858308938 -0.455485830893791 54 8 10.4946435264284 -2.49464352642844 55 14 12.4371261393879 1.56287386061212 56 12 12.4676310161414 -0.467631016141426 57 11 10.7855417430767 0.214458256923304 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 1.99762768779120 63 14 13.7144319501693 0.285568049830749 64 16 13.7532456800423 2.24675431995765 65 9 9.92048663101368 -0.920486631013682 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 -0.65526965476048 71 15 12.4702410303607 2.52975896963932 72 13 12.3244517916519 0.67554820834806 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 -0.28685393112073 78 12 11.8761397898480 0.123860210151980 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 0.161802036344738 84 10 11.2090818273308 -1.20908182733078 85 13 8.68205582269451 4.31794417730549 86 12 12.3827278226039 -0.382727822603868 87 9 9.32868069070524 -0.328680690705235 88 12 12.0243408260259 -0.0243408260258719 89 16 15.0650478471956 0.934952152804356 90 10 10.2509351394506 -0.250935139450646 91 14 13.1601907440176 0.839809255982396 92 10 13.5294557228591 -3.52945572285908 93 16 15.3380960656073 0.66190393439274 94 15 13.4400204696878 1.55997953031224 95 12 11.3398016495221 0.660198350477908 96 10 9.72325369263371 0.276746307366286 97 8 10.2113803731837 -2.21138037318372 98 8 8.5839638760142 -0.583963876014196 99 11 12.7817660837874 -1.78176608378740 100 13 12.3972848053206 0.602715194679391 101 16 15.4261707972401 0.573829202759879 102 16 14.6887175338267 1.31128246617330 103 14 15.783120023334 -1.78312002333400 104 11 8.80392570606941 2.19607429393059 105 4 6.86893251038793 -2.86893251038793 106 14 14.5434362544404 -0.543436254440421 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 -0.445378539002147 114 14 13.5896355919577 0.41036440804235 115 15 14.3284752922129 0.671524707787085 116 16 13.3663580685751 2.63364193142493 117 16 13.4624042615050 2.53759573849503 118 11 12.7046361347967 -1.70463613479673 119 14 13.6914142471268 0.308585752873246 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 0.627547258774659 128 12 13.2838711469848 -1.28387114698484 129 11 11.3710149332596 -0.371014933259569 130 4 6.26171529119994 -2.26171529119994 131 16 15.3468018491916 0.653198150808385 132 15 12.4302550440968 2.56974495590315 133 10 11.3339267659976 -1.33392676599763 134 13 13.0801691844501 -0.0801691844500615 135 15 13.1051398157146 1.89486018428544 136 12 10.5070382494129 1.49296175058711 137 14 13.4735263170367 0.526473682963345 138 7 10.573267534394 -3.573267534394 139 19 14.0117892393699 4.98821076063011 140 12 12.5715353979438 -0.571535397943801 141 12 12.1641645992487 -0.164164599248651 142 13 13.4008870456399 -0.400887045639915 143 15 12.8196129850909 2.18038701490908 144 8 8.14265477299094 -0.142654772990940 145 12 10.7899600333214 1.21003996667862 146 10 10.7095121600920 -0.709512160092034 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 -0.242075146810151 152 16 15.1131134138541 0.88688658614592 153 9 10.6373404646853 -1.63734046468531 154 14 13.5779794235252 0.422020576474804 155 14 13.1082107005343 0.891789299465702 156 12 10.5269118213967 1.47308817860326 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0738539342406379 0.147707868481276 0.926146065759362 11 0.111412168598258 0.222824337196516 0.888587831401742 12 0.0734578741372406 0.146915748274481 0.92654212586276 13 0.54882734548451 0.90234530903098 0.45117265451549 14 0.718699208630822 0.562601582738355 0.281300791369178 15 0.652090412310228 0.695819175379545 0.347909587689772 16 0.576112492137821 0.847775015724357 0.423887507862179 17 0.48920416864993 0.97840833729986 0.51079583135007 18 0.451879492529463 0.903758985058927 0.548120507470537 19 0.366000416506305 0.73200083301261 0.633999583493695 20 0.510038740501301 0.979922518997399 0.489961259498699 21 0.516426674721425 0.96714665055715 0.483573325278575 22 0.545846586045827 0.908306827908347 0.454153413954173 23 0.472361536131052 0.944723072262104 0.527638463868948 24 0.477945431608221 0.955890863216443 0.522054568391779 25 0.434731365974649 0.869462731949298 0.565268634025351 26 0.374386151119235 0.74877230223847 0.625613848880765 27 0.620073597970519 0.759852804058961 0.379926402029481 28 0.574954642758156 0.850090714483688 0.425045357241844 29 0.519760536276081 0.960478927447838 0.480239463723919 30 0.711763970133492 0.576472059733017 0.288236029866508 31 0.812570598711138 0.374858802577725 0.187429401288862 32 0.776825716797298 0.446348566405405 0.223174283202702 33 0.730783095040026 0.538433809919948 0.269216904959974 34 0.697861985984422 0.604276028031156 0.302138014015578 35 0.69575087166892 0.60849825666216 0.30424912833108 36 0.708445328680888 0.583109342638223 0.291554671319112 37 0.675394706082227 0.649210587835546 0.324605293917773 38 0.626334916756153 0.747330166487694 0.373665083243847 39 0.572897411380088 0.854205177239824 0.427102588619912 40 0.543550964821021 0.912898070357958 0.456449035178979 41 0.502091559029739 0.995816881940522 0.497908440970261 42 0.757528815664885 0.484942368670231 0.242471184335115 43 0.956307047538371 0.087385904923257 0.0436929524616285 44 0.966683420979718 0.0666331580405636 0.0333165790202818 45 0.956290274161252 0.0874194516774967 0.0437097258387484 46 0.961225446856714 0.0775491062865718 0.0387745531432859 47 0.980650982255261 0.0386980354894774 0.0193490177447387 48 0.97421652545787 0.0515669490842622 0.0257834745421311 49 0.982136641646371 0.0357267167072569 0.0178633583536284 50 0.979210150922893 0.0415796981542141 0.0207898490771071 51 0.97446674575257 0.0510665084948611 0.0255332542474306 52 0.997597461351614 0.004805077296772 0.002402538648386 53 0.996534554484524 0.00693089103095228 0.00346544551547614 54 0.997121346101836 0.0057573077963282 0.0028786538981641 55 0.99710451393585 0.00579097212829858 0.00289548606414929 56 0.995913070323251 0.00817385935349715 0.00408692967674857 57 0.994229234073585 0.0115415318528298 0.00577076592641488 58 0.993564980729086 0.0128700385418285 0.00643501927091424 59 0.99514767680476 0.00970464639048047 0.00485232319524023 60 0.993662276710802 0.0126754465783969 0.00633772328919846 61 0.99448678054191 0.0110264389161778 0.00551321945808888 62 0.995041687770348 0.00991662445930408 0.00495831222965204 63 0.993354910372801 0.0132901792543975 0.00664508962719873 64 0.993715406157568 0.0125691876848638 0.0062845938424319 65 0.992074101296807 0.0158517974063868 0.00792589870319338 66 0.991233013479951 0.0175339730400972 0.00876698652004858 67 0.991193655492438 0.0176126890151242 0.00880634450756212 68 0.99240860329775 0.0151827934045007 0.00759139670225035 69 0.99262298900723 0.0147540219855377 0.00737701099276885 70 0.990035459478192 0.0199290810436162 0.0099645405218081 71 0.991512344594023 0.0169753108119531 0.00848765540597653 72 0.988744712009448 0.0225105759811049 0.0112552879905524 73 0.985875535529372 0.028248928941256 0.014124464470628 74 0.989683954110711 0.0206320917785782 0.0103160458892891 75 0.986064984710967 0.0278700305780663 0.0139350152890332 76 0.983814010657477 0.0323719786850452 0.0161859893425226 77 0.978757230581324 0.0424855388373513 0.0212427694186757 78 0.97189841343023 0.0562031731395398 0.0281015865697699 79 0.981928839719816 0.0361423205603687 0.0180711602801844 80 0.981171189093485 0.0376576218130292 0.0188288109065146 81 0.984465618766586 0.0310687624668274 0.0155343812334137 82 0.985531580579376 0.028936838841248 0.014468419420624 83 0.980548112818612 0.0389037743627765 0.0194518871813882 84 0.976025194854872 0.0479496102902564 0.0239748051451282 85 0.993614742822052 0.0127705143558967 0.00638525717794837 86 0.991186158493816 0.0176276830123688 0.00881384150618442 87 0.987937413476295 0.0241251730474103 0.0120625865237051 88 0.984168771851926 0.0316624562961473 0.0158312281480737 89 0.980266995450385 0.0394660090992293 0.0197330045496147 90 0.973933446018777 0.0521331079624469 0.0260665539812234 91 0.96894737673181 0.0621052465363797 0.0310526232681899 92 0.981483206720742 0.0370335865585169 0.0185167932792585 93 0.976077099013598 0.0478458019728039 0.0239229009864019 94 0.972824609097762 0.0543507818044763 0.0271753909022381 95 0.96597903556356 0.068041928872882 0.034020964436441 96 0.957543997112153 0.0849120057756944 0.0424560028878472 97 0.953597370111769 0.0928052597764626 0.0464026298882313 98 0.941028716771498 0.117942566457005 0.0589712832285023 99 0.935332034240117 0.129335931519765 0.0646679657598827 100 0.921498373330872 0.157003253338257 0.0785016266691284 101 0.902660289705945 0.194679420588111 0.0973397102940554 102 0.888687169237796 0.222625661524408 0.111312830762204 103 0.8918904622524 0.216219075495199 0.108109537747600 104 0.928929204993892 0.142141590012215 0.0710707950061076 105 0.925456916449307 0.149086167101386 0.0745430835506932 106 0.90562530027135 0.188749399457301 0.0943746997286506 107 0.88523090970282 0.229538180594359 0.114769090297179 108 0.879548215760314 0.240903568479371 0.120451784239686 109 0.876971448272647 0.246057103454706 0.123028551727353 110 0.896714705031344 0.206570589937312 0.103285294968656 111 0.888818831945975 0.222362336108051 0.111181168054025 112 0.926529602725404 0.146940794549192 0.073470397274596 113 0.904866008509663 0.190267982980675 0.0951339914903373 114 0.882761840721651 0.234476318556697 0.117238159278349 115 0.856578652191078 0.286842695617844 0.143421347808922 116 0.847360482630237 0.305279034739525 0.152639517369763 117 0.845160067878447 0.309679864243105 0.154839932121553 118 0.846213905052698 0.307572189894604 0.153786094947302 119 0.814040652836467 0.371918694327066 0.185959347163533 120 0.851321019990752 0.297357960018496 0.148678980009248 121 0.818990515920393 0.362018968159215 0.181009484079607 122 0.79045236724802 0.419095265503961 0.209547632751980 123 0.782510780887197 0.434978438225605 0.217489219112803 124 0.746706356137427 0.506587287725146 0.253293643862573 125 0.734130909366521 0.531738181266957 0.265869090633479 126 0.715398152194316 0.569203695611368 0.284601847805684 127 0.657211416468591 0.685577167062818 0.342788583531409 128 0.629278984908168 0.741442030183665 0.370721015091832 129 0.636265128901009 0.727469742197983 0.363734871098991 130 0.640084554700864 0.719830890598272 0.359915445299136 131 0.594546146744681 0.810907706510637 0.405453853255319 132 0.553103349561024 0.893793300877953 0.446896650438976 133 0.543699901622874 0.912600196754252 0.456300098377126 134 0.47134678279836 0.94269356559672 0.52865321720164 135 0.414315595537165 0.82863119107433 0.585684404462835 136 0.393702835618114 0.787405671236227 0.606297164381886 137 0.320790451030565 0.64158090206113 0.679209548969435 138 0.411615168913243 0.823230337826486 0.588384831086757 139 0.771364571464273 0.457270857071454 0.228635428535727 140 0.763775101199089 0.472449797601823 0.236224898800911 141 0.709611408881837 0.580777182236327 0.290388591118163 142 0.623349240400772 0.753301519198456 0.376650759599228 143 0.55995155523412 0.880096889531761 0.440048444765880 144 0.434662285853639 0.869324571707278 0.565337714146361 145 0.699580655627806 0.600838688744387 0.300419344372194 146 0.849248587677247 0.301502824645506 0.150751412322753 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

Charts produced by software:

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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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