BEL20-MR2

*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, 22 Dec 2010 17:26:34 +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/Dec/22/t1293038692ma9prxkfdytuen3.htm/, Retrieved Wed, 22 Dec 2010 18:24:55 +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/Dec/22/t1293038692ma9prxkfdytuen3.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:

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3.04 493 9 3.030 9.026 25.64 104.8 3.28 481 11 2.803 9.787 27.97 105.2 3.51 462 13 2.768 9.536 27.62 105.6 3.69 457 12 2.883 9.490 23.31 105.8 3.92 442 13 2.863 9.736 29.07 106.1 4.29 439 15 2.897 9.694 29.58 106.5 4.31 488 13 3.013 9.647 28.63 106.71 4.42 521 16 3.143 9.753 29.92 106.68 4.59 501 10 3.033 10.070 32.68 107.41 4.76 485 14 3.046 10.137 31.54 107.15 4.83 464 14 3.111 9.984 32.43 107.5 4.83 460 45 3.013 9.732 26.54 107.22 4.76 467 13 2.987 9.103 25.85 107.11 4.99 460 8 2.996 9.155 27.60 107.57 4.78 448 7 2.833 9.308 25.71 107.81 5.06 443 3 2.849 9.394 25.38 108.75 4.65 436 3 2.795 9.948 28.57 109.43 4.54 431 4 2.845 10.177 27.64 109.62 4.51 484 4 2.915 10.002 25.36 109.54 4.49 510 0 2.893 9.728 25.90 109.53 3.99 513 -4 2.604 10.002 26.29 109.84 3.97 503 -14 2.642 10.063 21.74 109.67 3.51 471 -18 2.660 10.018 19.20 109.79 3.34 471 -8 2.639 9.960 19.32 109.56 3.29 476 -1 2.720 10.236 19.82 110.22 3.28 475 1 2.746 10.893 20.36 110.4 3.26 470 2 2.736 10.756 24.31 110.69 3.32 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation BEL20[t] = + 33.6449842417089 + 0.464260281041345Eonia[t] + 0.00349273190392421Werkloosheid[t] + 0.0201133517056931Consumentenvertrouwen[t] -0.000543752892766527Goudprijs[t] + 0.0181403452647249Olieprijs[t] -0.33406999136402CPI[t] + 0.071913678995696t + 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) 33.6449842417089 5.739412 5.8621 0 0 Eonia 0.464260281041345 0.054682 8.4902 0 0 Werkloosheid 0.00349273190392421 0.001174 2.9741 0.003538 0.001769 Consumentenvertrouwen 0.0201133517056931 0.006096 3.2992 0.001268 0.000634 Goudprijs -0.000543752892766527 0.018628 -0.0292 0.976761 0.48838 Olieprijs 0.0181403452647249 0.003524 5.1477 1e-06 1e-06 CPI -0.33406999136402 0.054304 -6.1518 0 0 t 0.071913678995696 0.009639 7.4606 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.88067962642104 R-squared 0.775596604393103 Adjusted R-squared 0.762825679439865 F-TEST (value) 60.7314354467686 F-TEST (DF numerator) 7 F-TEST (DF denominator) 123 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.369739069066535 Sum Squared Residuals 16.8149584408851 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.03 2.48086161308435 0.549138386915652 2 2.803 2.57073689206409 0.232263107935912 3 2.768 2.58345459752394 0.184545402476058 4 2.883 2.55638424215106 0.326615757848936 5 2.863 2.70693378703709 0.156066212962913 6 2.897 2.85601869487859 0.0409813051214084 7 3.013 2.98077226957404 0.0322277304259561 8 3.143 3.31272029475665 -0.169720294756646 9 3.033 3.07904736278463 -0.0460473627846305 10 3.046 3.32059675862638 -0.27459675862638 11 3.111 3.25096489181336 -0.139964891813355 12 3.013 3.91925153577151 -0.906251535771515 13 2.987 3.36406174522654 -0.377061745226538 14 2.996 3.29578454004121 -0.299784540041206 15 2.833 3.09363218079515 -0.260632180795145 16 2.849 2.87756280357171 -0.0285628035717093 17 2.795 2.56507951217733 0.229920487822671 18 2.845 2.50810591357675 0.336894086423252 19 2.915 2.73666734391097 0.178332656089031 20 2.893 2.82293891461431 0.0700610853856927 21 2.604 2.49611129101611 0.107888708983892 22 2.642 2.29689908694573 0.345100913054268 23 2.66 1.87689180185815 0.78310819814185 24 2.639 2.15005922724702 0.488940772752978 25 2.72 2.14545091618383 0.57454908381617 26 2.746 2.19876190622345 0.547238093776547 27 2.736 2.2388886322308 0.497111367769197 28 2.812 2.28698746040853 0.525012539591471 29 2.799 2.29006208013389 0.508937919866113 30 2.555 2.45052776133524 0.104472238664756 31 2.305 2.58895506212718 -0.283955062127175 32 2.215 2.66302268744789 -0.448022687447893 33 2.066 2.67952964391377 -0.613529643913767 34 1.94 2.75298012693505 -0.81298012693505 35 2.042 2.74774266540487 -0.705742665404869 36 1.995 2.68641812856085 -0.691418128560847 37 1.947 2.50978028586011 -0.562780285860113 38 1.766 2.26122835521364 -0.495228355213641 39 1.635 2.05226421084548 -0.417264210845476 40 1.833 2.17635172653929 -0.343351726539289 41 1.91 2.37842256105382 -0.468422561053817 42 1.96 2.21113522467887 -0.251135224678874 43 1.97 2.32277152314176 -0.352771523141764 44 2.061 2.4064611698153 -0.345461169815299 45 2.093 2.39671818493358 -0.303718184933581 46 2.121 2.37993050653204 -0.258930506532038 47 2.175 2.47530420583926 -0.300304205839265 48 2.197 2.65541010771124 -0.458410107711241 49 2.35 2.70348526526969 -0.353485265269685 50 2.44 2.67334930460244 -0.233349304602443 51 2.409 2.6568207384519 -0.247820738451901 52 2.473 2.50822064984165 -0.0352206498416507 53 2.408 2.41239825104509 -0.00439825104509185 54 2.455 2.61840407860452 -0.163404078604522 55 2.448 2.71634085538346 -0.268340855383456 56 2.498 2.90127632840411 -0.403276328404106 57 2.646 2.97800389802161 -0.332003898021611 58 2.757 2.91564261828691 -0.158642618286909 59 2.849 2.86333890088732 -0.0143389008873174 60 2.921 2.98773304022167 -0.066733040221674 61 2.982 3.0255625254386 -0.0435625254385994 62 3.081 2.91032790602562 0.170672093974376 63 3.106 2.87088501450873 0.235114985491272 64 3.119 2.7608991162046 0.3581008837954 65 3.061 2.60322643795181 0.457773562048193 66 3.097 2.62035500634724 0.476644993652763 67 3.162 2.68687972617366 0.475120273826342 68 3.257 2.8769643395703 0.380035660429696 69 3.277 2.82836427864529 0.448635721354707 70 3.295 2.945144465504 0.349855534495999 71 3.364 2.90166191456493 0.462338085435071 72 3.494 3.17906309525127 0.314936904748728 73 3.667 3.44424894667615 0.22275105332385 74 3.813 3.28809543106726 0.524904568932735 75 3.918 3.38063570106254 0.537364298937457 76 3.896 3.40219150179543 0.493808498204573 77 3.801 3.32610573026569 0.474894269734314 78 3.57 3.50053641791751 0.0694635820824871 79 3.702 3.73476284973515 -0.0327628497351461 80 3.862 3.85046757065559 0.0115324293444066 81 3.97 3.86485250577405 0.105147494225947 82 4.139 4.02412078917276 0.11487921082724 83 4.2 3.91099286300552 0.28900713699448 84 4.291 3.85162080242572 0.439379197574276 85 4.444 3.95063432439014 0.493365675609858 86 4.503 3.86446332585935 0.63853667414065 87 4.357 3.95431520515095 0.40268479484905 88 4.591 4.04603993553927 0.544960064460728 89 4.697 4.10241677478432 0.594583225215682 90 4.621 4.24221877215946 0.37878122784054 91 4.563 4.43224918606564 0.130750813934359 92 4.203 4.49510021537037 -0.292100215370371 93 4.296 4.52948812117335 -0.233488121173351 94 4.435 4.41026381149716 0.024736188502843 95 4.105 4.13215522661303 -0.0271552266130301 96 4.117 4.08026496930281 0.0367350306971933 97 3.844 4.049063698524 -0.205063698523998 98 3.721 3.88719350859549 -0.166193508595492 99 3.674 3.78507018775872 -0.111070187758724 100 3.858 3.74801738654477 0.109982613455234 101 3.801 3.59610113608821 0.204898863911789 102 3.504 3.57879277567125 -0.0747927756712535 103 3.033 3.69768554661102 -0.664685546611017 104 3.047 3.79161411335089 -0.74461411335089 105 2.962 3.4978125443806 -0.535812544380601 106 2.198 2.76816883146949 -0.570168831469492 107 2.014 2.3046264828118 -0.290626482811797 108 1.863 1.94009952518179 -0.0770995251817943 109 1.905 1.82175414159858 0.0832458584014193 110 1.811 1.40362100383087 0.407378996169125 111 1.67 1.70367740341148 -0.0336774034114783 112 1.864 1.69270883222404 0.171291167775957 113 2.052 1.90785658347214 0.144143416527859 114 2.03 2.2880863461164 -0.258086346116403 115 2.071 2.36511266205473 -0.294112662054733 116 2.293 2.58935710226036 -0.296357102260359 117 2.443 2.63904873543087 -0.196048735430866 118 2.513 2.69888621513693 -0.185886215136926 119 2.467 2.75476199743275 -0.28776199743275 120 2.503 2.67132907130013 -0.168329071300131 121 2.54 2.59936748789993 -0.059367487899927 122 2.483 2.41834496154234 0.0646550384576649 123 2.626 2.42691942086076 0.199080579139238 124 2.656 2.51806556901304 0.137934430986956 125 2.447 2.12106762989885 0.325932370101146 126 2.467 2.26687180923024 0.200128190769759 127 2.462 2.60726362771483 -0.145263627714833 128 2.505 2.73647771294044 -0.231477712940444 129 2.579 2.62887380098885 -0.0498738009888447 130 2.649 2.81992046513924 -0.170920465139243 131 2.637 2.81915051673211 -0.182150516732106 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.00226865293627894 0.00453730587255789 0.99773134706372 12 0.000323813933571711 0.000647627867143422 0.999676186066428 13 0.00225271557849577 0.00450543115699155 0.997747284421504 14 0.00054385423095881 0.00108770846191762 0.999456145769041 15 0.000112436896583701 0.000224873793167402 0.999887563103416 16 2.1966615653425e-05 4.39332313068499e-05 0.999978033384347 17 6.81983318514308e-06 1.36396663702862e-05 0.999993180166815 18 3.62037029353353e-06 7.24074058706706e-06 0.999996379629706 19 6.91785781221209e-07 1.38357156244242e-06 0.999999308214219 20 2.25953748836903e-07 4.51907497673806e-07 0.999999774046251 21 5.77994829872174e-07 1.15598965974435e-06 0.99999942200517 22 1.47710783286933e-07 2.95421566573866e-07 0.999999852289217 23 3.25921265994698e-07 6.51842531989395e-07 0.999999674078734 24 1.60948143545646e-07 3.21896287091291e-07 0.999999839051856 25 1.18796103685547e-07 2.37592207371093e-07 0.999999881203896 26 6.1672891316429e-08 1.23345782632858e-07 0.999999938327109 27 2.42707384809939e-08 4.85414769619877e-08 0.999999975729261 28 1.47681781329152e-08 2.95363562658304e-08 0.999999985231822 29 8.95388918508898e-09 1.7907778370178e-08 0.99999999104611 30 2.64549157268988e-08 5.29098314537976e-08 0.999999973545084 31 4.94583212609509e-07 9.89166425219018e-07 0.999999505416787 32 1.01494639595963e-06 2.02989279191925e-06 0.999998985053604 33 3.24974790478932e-06 6.49949580957863e-06 0.999996750252095 34 1.08639834225282e-05 2.17279668450564e-05 0.999989136016577 35 8.89219326593396e-06 1.77843865318679e-05 0.999991107806734 36 4.8973188656034e-06 9.7946377312068e-06 0.999995102681134 37 2.29694857715806e-06 4.59389715431612e-06 0.999997703051423 38 1.06249077876106e-06 2.12498155752212e-06 0.999998937509221 39 4.50841964984938e-07 9.01683929969876e-07 0.999999549158035 40 3.66368559036476e-07 7.32737118072951e-07 0.99999963363144 41 4.32588324388048e-07 8.65176648776096e-07 0.999999567411676 42 1.87419460036724e-06 3.74838920073448e-06 0.9999981258054 43 6.47114869296222e-06 1.29422973859244e-05 0.999993528851307 44 1.47716984243331e-05 2.95433968486661e-05 0.999985228301576 45 1.09539063384154e-05 2.19078126768307e-05 0.999989046093662 46 5.15315630583993e-05 0.000103063126116799 0.999948468436942 47 0.000120063933811744 0.000240127867623487 0.999879936066188 48 0.000438329099000169 0.000876658198000338 0.999561670901 49 0.00226176559045543 0.00452353118091086 0.997738234409545 50 0.00786999239289116 0.0157399847857823 0.99213000760711 51 0.0209574938204985 0.0419149876409971 0.979042506179502 52 0.0361886795785084 0.0723773591570168 0.963811320421492 53 0.0493885303939758 0.0987770607879516 0.950611469606024 54 0.0711314884070467 0.142262976814093 0.928868511592953 55 0.104986205244026 0.209972410488051 0.895013794755974 56 0.188626753656638 0.377253507313277 0.811373246343362 57 0.349744274900269 0.699488549800537 0.650255725099731 58 0.477418546897052 0.954837093794105 0.522581453102948 59 0.671038646428254 0.657922707143492 0.328961353571746 60 0.915073152736143 0.169853694527714 0.084926847263857 61 0.985606805224838 0.028786389550325 0.0143931947751625 62 0.993697176933417 0.0126056461331665 0.00630282306658327 63 0.99542560334017 0.00914879331966152 0.00457439665983076 64 0.996334589801791 0.00733082039641748 0.00366541019820874 65 0.996335811784165 0.00732837643167004 0.00366418821583502 66 0.996058127861218 0.00788374427756454 0.00394187213878227 67 0.994742503676982 0.0105149926460351 0.00525749632301754 68 0.993276099504867 0.0134478009902659 0.00672390049513294 69 0.9941729180341 0.0116541639318004 0.0058270819659002 70 0.99214156496863 0.0157168700627405 0.00785843503137027 71 0.991101341594114 0.0177973168117727 0.00889865840588633 72 0.989974659998604 0.0200506800027917 0.0100253400013959 73 0.992098729769037 0.0158025404619266 0.0079012702309633 74 0.98932314030111 0.0213537193977811 0.0106768596988905 75 0.98662460147549 0.0267507970490221 0.0133753985245111 76 0.9821146086602 0.0357707826796016 0.0178853913398008 77 0.981211618097709 0.0375767638045825 0.0187883819022913 78 0.994461773771057 0.0110764524578868 0.00553822622894342 79 0.99682266591366 0.00635466817268157 0.00317733408634079 80 0.996671349045593 0.00665730190881353 0.00332865095440676 81 0.996634396334947 0.00673120733010623 0.00336560366505311 82 0.998942401265229 0.0021151974695416 0.0010575987347708 83 0.999709202483023 0.00058159503395367 0.000290797516976835 84 0.999726428515031 0.000547142969937293 0.000273571484968647 85 0.999777948782705 0.000444102434590565 0.000222051217295282 86 0.999709581475445 0.000580837049109359 0.000290418524554679 87 0.999521656284252 0.000956687431496716 0.000478343715748358 88 0.999251285623542 0.00149742875291672 0.000748714376458362 89 0.9991861518576 0.00162769628480171 0.000813848142400854 90 0.998838613589464 0.00232277282107155 0.00116138641053578 91 0.999403642514316 0.00119271497136886 0.000596357485684429 92 0.999132029803016 0.0017359403939677 0.00086797019698385 93 0.998732821884183 0.00253435623163368 0.00126717811581684 94 0.998826552601106 0.00234689479778777 0.00117344739889388 95 0.9993410174652 0.00131796506959969 0.000658982534799843 96 0.999707856019072 0.000584287961856772 0.000292143980928386 97 0.99984853061499 0.000302938770018914 0.000151469385009457 98 0.999917204381037 0.000165591237925285 8.27956189626427e-05 99 0.999936207569461 0.000127584861077484 6.3792430538742e-05 100 0.999977910858954 4.41782820916607e-05 2.20891410458303e-05 101 0.999999291882942 1.41623411536778e-06 7.08117057683889e-07 102 0.999999863249575 2.73500850653814e-07 1.36750425326907e-07 103 0.999999926749726 1.4650054837389e-07 7.32502741869448e-08 104 0.999999855500015 2.88999970725167e-07 1.44499985362584e-07 105 0.999999948980435 1.02039129323568e-07 5.10195646617842e-08 106 0.99999988246964 2.35060720305119e-07 1.17530360152559e-07 107 0.999999597731312 8.04537376012204e-07 4.02268688006102e-07 108 0.99999853831204 2.92337591999203e-06 1.46168795999602e-06 109 0.999998518873466 2.96225306718417e-06 1.48112653359208e-06 110 0.999999939561734 1.20876531664664e-07 6.0438265832332e-08 111 0.99999978308173 4.33836539636767e-07 2.16918269818384e-07 112 0.999999038737713 1.92252457422294e-06 9.6126228711147e-07 113 0.999999409810234 1.18037953194212e-06 5.90189765971062e-07 114 0.99999696900965 6.06198069992919e-06 3.0309903499646e-06 115 0.999999122841316 1.75431736705341e-06 8.77158683526707e-07 116 0.99999837718971 3.24562058169918e-06 1.62281029084959e-06 117 0.999985984306324 2.80313873513958e-05 1.40156936756979e-05 118 0.999917945560616 0.000164108878767984 8.2054439383992e-05 119 0.999544985548285 0.000910028903430571 0.000455014451715286 120 0.99611936413917 0.00776127172165928 0.00388063586082964 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 85 0.772727272727273 NOK 5% type I error level 101 0.918181818181818 NOK 10% type I error level 103 0.936363636363636 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/10dcvy1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/10dcvy1293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/1hkf71293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/1hkf71293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/2hkf71293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/2hkf71293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/3hkf71293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/3hkf71293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/4abws1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/4abws1293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/5abws1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/5abws1293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/6abws1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/6abws1293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/732ev1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/732ev1293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/8dcvy1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/8dcvy1293038783.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/9dcvy1293038783.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293038692ma9prxkfdytuen3/9dcvy1293038783.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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