WS7 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: Thu, 02 Dec 2010 21:49:42 +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/02/t1291326490p9an9qot7uv7efx.htm/, Retrieved Thu, 02 Dec 2010 22:48:21 +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/02/t1291326490p9an9qot7uv7efx.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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20 10 11 4 25 25 1 16 11 11 11 23 21 2 18 16 12 7 17 22 2 17 11 13 7 21 25 3 23 13 14 12 19 24 3 30 12 16 10 19 18 4 23 8 11 10 15 22 4 18 12 10 8 16 15 4 15 11 11 8 23 22 6 12 4 15 4 27 28 7 21 9 9 9 22 20 7 15 8 11 8 14 12 8 20 8 17 7 22 24 8 31 14 17 11 23 20 11 27 15 11 9 23 21 12 34 16 18 11 21 20 13 21 9 14 13 19 21 13 31 14 10 8 18 23 13 19 11 11 8 20 28 13 16 8 15 9 23 24 13 20 9 15 6 25 24 13 21 9 13 9 19 24 13 22 9 16 9 24 23 13 17 9 13 6 22 23 13 24 10 9 6 25 29 13 25 16 18 16 26 24 13 26 11 18 5 29 18 13 25 8 12 7 32 25 13 17 9 17 9 25 21 13 32 16 9 6 29 26 13 33 11 9 6 28 22 13 13 16 12 5 17 22 13 32 12 18 12 28 22 13 25 12 12 7 29 23 13 29 14 18 10 26 30 13 22 9 14 9 25 23 13 18 10 15 8 14 17 13 17 9 16 5 25 23 13 20 10 10 8 26 23 14 15 12 11 8 20 25 14 20 14 14 10 18 24 14 33 14 9 6 32 24 14 29 10 12 8 25 23 14 23 14 17 7 25 21 14 26 16 5 4 23 24 14 18 9 12 8 21 24 14 20 10 12 8 20 28 14 11 6 6 4 15 16 14 28 8 24 20 30 20 14 26 13 12 8 24 29 14 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 Org[t] = + 15.5287004980391 -0.0536894023314702concern[t] + 0.199935118355062doubts[t] -0.147908652466377Par_Crit[t] -0.232432985498191Par_Stan[t] + 0.379676563293621Pers_Stan[t] + 0.249702635338725Days[t] -0.035096925566633t + 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) 15.5287004980391 2.347401 6.6153 0 0 concern -0.0536894023314702 0.062701 -0.8563 0.393257 0.196629 doubts 0.199935118355062 0.111662 1.7905 0.075454 0.037727 Par_Crit -0.147908652466377 0.106237 -1.3923 0.165976 0.082988 Par_Stan -0.232432985498191 0.131255 -1.7709 0.078686 0.039343 Pers_Stan 0.379676563293621 0.076536 4.9607 2e-06 1e-06 Days 0.249702635338725 0.14265 1.7505 0.082155 0.041078 t -0.035096925566633 0.013229 -2.6531 0.008864 0.004432 Multiple Linear Regression - Regression Statistics Multiple R 0.514236415207976 R-squared 0.26443909072595 Adjusted R-squared 0.228929253726513 F-TEST (value) 7.44692493885971 F-TEST (DF numerator) 7 F-TEST (DF denominator) 145 p-value 1.20832214567379e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.43911727777500 Sum Squared Residuals 1714.99150929212 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 23.6040563079501 1.39594369204993 2 21 21.8469707203285 -0.846970720328523 3 22 21.2079344916389 0.792065508361099 4 25 21.8473516126753 3.15264838732472 5 24 19.8205618032854 4.17943819671463 6 18 19.6284552444457 -1.62845524444574 7 22 18.3902806709365 3.60971932906345 8 15 20.4158224172039 -5.4158224172039 9 22 23.3510911415430 -1.35109114154303 10 28 24.1840228151258 3.81597718487415 11 20 22.4923010311905 -2.49230103119049 12 12 19.7283112108128 -7.72831121081281 13 24 21.8071608506377 2.19283914936228 14 20 22.5801437368723 -2.58014373687232 15 21 24.56176006012 -3.56176006012 16 20 22.3408954070786 -2.3408954070786 17 21 20.9716303956175 0.0283696043824669 18 23 22.7734380125743 0.226561987425655 19 28 23.3942530340410 4.60574696595896 20 24 23.2353810549208 0.764618945079206 21 24 24.6421137214652 -0.642113721465157 22 24 21.8737863622435 2.12621363775649 23 23 23.2396568934144 -0.239656893414380 24 23 23.8546787668116 -0.854678766811559 25 29 25.3743554430261 3.62564455697393 26 24 23.2093486613727 0.790651338627347 27 18 25.8166792720602 -7.8166792720602 28 25 26.7970820274426 -1.79708202744260 29 21 23.5292902624992 -2.52929026249918 30 26 27.487672559846 -1.48767255984600 31 22 26.0195340768790 -4.01953407687896 32 22 23.6701656215863 -1.67016562158627 33 22 23.4771889612457 -1.47718896124569 34 23 26.2472112575822 -3.24721125758219 35 30 23.6734463982261 6.3265536017739 36 23 23.4588907292745 -0.458890729274526 37 17 19.7465686681908 -2.74656866819082 38 23 24.2910585268586 -1.29105852685862 39 23 25.1143606695887 -2.11436066958867 40 25 23.3216129601614 1.67838703983859 41 24 21.7499942046648 2.25000579533521 42 24 28.0016821392244 -4.00168213922439 43 23 23.8152744781125 -0.815274478112536 44 21 24.3949441631213 -3.39494416312127 45 24 26.3114989267742 -2.31149892677421 46 24 22.5819257555293 1.41807424447074 47 28 22.2597085803611 5.74029141963887 48 16 21.8268768426804 -5.8268768426804 49 20 20.5927952512274 -0.592795251227375 50 29 23.9507929979121 5.04920700208792 51 27 24.5397040885321 2.46029591146789 52 22 23.7828794773891 -1.78287947738909 53 28 24.5571678567985 3.44283214320148 54 16 21.1595767102694 -5.15957671026945 55 25 23.4760421674824 1.52395783251757 56 24 23.9755130549732 0.0244869450268235 57 28 24.0673235328150 3.93267646718496 58 24 24.7084370717368 -0.708437071736818 59 23 23.0906731778823 -0.0906731778822884 60 30 27.087348790829 2.91265120917101 61 24 21.9348623744643 2.06513762553568 62 21 24.3465389067657 -3.34653890676574 63 25 23.5192558999806 1.48074410001940 64 25 24.1589900683566 0.841009931643362 65 22 21.2807140856368 0.719285914363234 66 23 22.7521594201012 0.247840579898821 67 26 23.0522205628555 2.94777943714454 68 23 21.8431255681807 1.15687443181934 69 25 23.1347301509554 1.8652698490446 70 21 21.7908163560116 -0.79081635601161 71 25 23.7889878090036 1.21101219099645 72 24 22.4589743824077 1.54102561759230 73 29 23.7350004201613 5.26499957983867 74 22 23.7972568954409 -1.7972568954409 75 27 23.7006803946040 3.29931960539596 76 26 20.0578203034344 5.94217969656557 77 22 21.5248017026582 0.475198297341756 78 24 22.1131211573691 1.88687884263095 79 27 23.4336441377373 3.56635586226266 80 24 21.6376620343347 2.36233796566531 81 24 24.885098603503 -0.885098603502989 82 29 24.4313672239027 4.56863277609726 83 22 22.3871856042376 -0.387185604237574 84 21 20.8573229383607 0.142677061639320 85 24 20.7178903794631 3.28210962053694 86 24 21.8540788383863 2.14592116161372 87 23 22.0216274154058 0.978372584594233 88 20 22.2429568736669 -2.24295687366690 89 27 21.4512191413187 5.54878085868125 90 26 23.2042742066992 2.79572579330079 91 25 21.9250053187923 3.07499468120767 92 21 20.1085482764634 0.891451723536632 93 21 20.9708946885383 0.0291053114617316 94 19 20.5943230363677 -1.59432303636772 95 21 21.6432362490086 -0.643236249008586 96 21 21.2926008332459 -0.29260083324594 97 16 19.8035111867683 -3.8035111867683 98 22 20.6471691206687 1.35283087933133 99 29 21.7551939401469 7.24480605985306 100 15 21.6358534475275 -6.63585344752746 101 17 20.6786226659200 -3.67862266591996 102 15 19.9210443011139 -4.92104430111389 103 21 21.442712964441 -0.442712964441015 104 21 20.7852861993609 0.214713800639119 105 19 19.1532266241979 -0.153226624197947 106 24 18.0776953794773 5.92230462052272 107 20 21.9642772027555 -1.9642772027555 108 17 24.3597518735404 -7.35975187354037 109 23 24.1847774118242 -1.18477741182424 110 24 21.7913670509557 2.20863294904428 111 14 21.4251043684990 -7.42510436849896 112 19 22.2468142136299 -3.24681421362987 113 24 21.5566096797711 2.44339032022893 114 13 19.9705908359096 -6.9705908359096 115 22 24.5359932646432 -2.53599326464319 116 16 20.4523060855796 -4.45230608557956 117 19 22.3993625558498 -3.39936255584980 118 25 21.9875320672270 3.01246793277304 119 25 23.2289720988706 1.77102790112938 120 23 20.7862146100073 2.21378538999266 121 24 22.7645284135839 1.2354715864161 122 26 22.7425023635532 3.25749763644680 123 26 20.7996604915163 5.20033950848374 124 25 23.3335047637633 1.66649523623675 125 18 21.5367165207630 -3.53671652076304 126 21 19.2316808750871 1.76831912491292 127 26 22.6458380992053 3.35416190079472 128 23 21.0943629315779 1.90563706842211 129 23 19.0578782050849 3.94212179491511 130 22 21.5027700651349 0.497229934865092 131 20 21.3524535768885 -1.35245357688847 132 13 21.0315670505931 -8.03156705059306 133 24 20.3983277064040 3.60167229359597 134 15 20.5444039822562 -5.54440398225622 135 14 22.0328614190784 -8.0328614190784 136 22 22.7560687362669 -0.756068736266917 137 10 16.7500582278710 -6.75005822787096 138 24 23.0769065020551 0.923093497944933 139 22 20.5276080287126 1.47239197128736 140 24 24.2311243350231 -0.231124335023130 141 19 20.3449987784280 -1.34499877842805 142 20 20.7340969111277 -0.734096911127747 143 13 16.1245407751944 -3.1245407751944 144 20 18.8358876597892 1.16411234021085 145 22 21.6624527431894 0.337547256810550 146 24 21.7307932607457 2.26920673925433 147 29 21.5503992597234 7.44960074027656 148 12 19.6951930899155 -7.69519308991555 149 20 19.5512452089045 0.448754791095511 150 21 20.041354902906 0.958645097093987 151 24 22.144684293873 1.85531570612701 152 22 20.6656375918297 1.33436240817029 153 20 17.112228696361 2.887771303639 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.716893198347154 0.566213603305692 0.283106801652846 12 0.785774731310745 0.428450537378511 0.214225268689255 13 0.68061492082909 0.63877015834182 0.31938507917091 14 0.59824498916899 0.80351002166202 0.40175501083101 15 0.602677548974136 0.794644902051727 0.397322451025864 16 0.500796303024003 0.998407393951994 0.499203696975997 17 0.464668576259671 0.929337152519341 0.535331423740329 18 0.616522925898572 0.766954148202856 0.383477074101428 19 0.79205396354958 0.415892072900841 0.207946036450421 20 0.72700045163663 0.54599909672674 0.27299954836337 21 0.675325401594835 0.64934919681033 0.324674598405165 22 0.625427101617398 0.749145796765204 0.374572898382602 23 0.568190757429135 0.86361848514173 0.431809242570865 24 0.498076928264513 0.996153856529025 0.501923071735487 25 0.469511960427748 0.939023920855497 0.530488039572252 26 0.397364971979872 0.794729943959745 0.602635028020128 27 0.698175023092589 0.603649953814822 0.301824976907411 28 0.653552365586799 0.692895268826403 0.346447634413202 29 0.600628611035043 0.798742777929914 0.399371388964957 30 0.546034168106265 0.90793166378747 0.453965831893735 31 0.514847635957721 0.970304728084558 0.485152364042279 32 0.465989730439557 0.931979460879114 0.534010269560443 33 0.41098856700867 0.82197713401734 0.58901143299133 34 0.368203894221564 0.736407788443127 0.631796105778436 35 0.608040657209810 0.783918685580379 0.391959342790190 36 0.549138600950737 0.901722798098526 0.450861399049263 37 0.508884671289471 0.982230657421058 0.491115328710529 38 0.452394819800984 0.904789639601968 0.547605180199016 39 0.40543774311631 0.81087548623262 0.59456225688369 40 0.381545655414374 0.763091310828747 0.618454344585626 41 0.358805561960884 0.717611123921768 0.641194438039116 42 0.348329888864618 0.696659777729236 0.651670111135382 43 0.303334703537916 0.606669407075832 0.696665296462084 44 0.29237808391336 0.58475616782672 0.70762191608664 45 0.265835638622324 0.531671277244649 0.734164361377676 46 0.232071975367675 0.46414395073535 0.767928024632325 47 0.31051673516036 0.62103347032072 0.68948326483964 48 0.400046883877738 0.800093767755476 0.599953116122262 49 0.378643518485982 0.757287036971965 0.621356481514018 50 0.454907281010378 0.909814562020755 0.545092718989622 51 0.428106944536917 0.856213889073833 0.571893055463083 52 0.395210014624035 0.79042002924807 0.604789985375965 53 0.39264428798767 0.78528857597534 0.60735571201233 54 0.468595510651620 0.937191021303241 0.53140448934838 55 0.421811875307868 0.843623750615736 0.578188124692132 56 0.375782704454471 0.751565408908941 0.62421729554553 57 0.38077195690537 0.76154391381074 0.61922804309463 58 0.341497821010063 0.682995642020126 0.658502178989937 59 0.297799979116548 0.595599958233096 0.702200020883452 60 0.277780932135128 0.555561864270256 0.722219067864872 61 0.242107385197613 0.484214770395227 0.757892614802387 62 0.265386421935849 0.530772843871698 0.734613578064151 63 0.230140079423531 0.460280158847062 0.769859920576469 64 0.194188330790771 0.388376661581543 0.805811669209229 65 0.161931615112155 0.323863230224309 0.838068384887845 66 0.134226372209861 0.268452744419723 0.865773627790139 67 0.116002513160506 0.232005026321013 0.883997486839494 68 0.0936880870951785 0.187376174190357 0.906311912904821 69 0.0757253767885398 0.151450753577080 0.92427462321146 70 0.0635643707177557 0.127128741435511 0.936435629282244 71 0.0502194371938501 0.100438874387700 0.94978056280615 72 0.0389193983554841 0.0778387967109682 0.961080601644516 73 0.0446488959899425 0.089297791979885 0.955351104010058 74 0.0412628493071150 0.0825256986142301 0.958737150692885 75 0.0347842383956438 0.0695684767912877 0.965215761604356 76 0.0465588360892819 0.0931176721785639 0.953441163910718 77 0.0364455638670782 0.0728911277341563 0.963554436132922 78 0.0294014452024608 0.0588028904049217 0.97059855479754 79 0.0262344945009501 0.0524689890019002 0.97376550549905 80 0.0204658116744854 0.0409316233489707 0.979534188325515 81 0.0170203495539574 0.0340406991079149 0.982979650446043 82 0.0172093768822258 0.0344187537644516 0.982790623117774 83 0.0147526340252826 0.0295052680505652 0.985247365974717 84 0.0112849299264620 0.0225698598529240 0.988715070073538 85 0.00958686919048707 0.0191737383809741 0.990413130809513 86 0.00787540444259952 0.0157508088851990 0.9921245955574 87 0.00585246598401224 0.0117049319680245 0.994147534015988 88 0.0056514788389303 0.0113029576778606 0.99434852116107 89 0.0088552433410972 0.0177104866821944 0.991144756658903 90 0.00742480658796388 0.0148496131759278 0.992575193412036 91 0.00673381287466156 0.0134676257493231 0.993266187125338 92 0.00572093427823266 0.0114418685564653 0.994279065721767 93 0.00432130101620042 0.00864260203240083 0.9956786989838 94 0.00375563041744314 0.00751126083488628 0.996244369582557 95 0.00297987257529094 0.00595974515058188 0.99702012742471 96 0.00219274982767844 0.00438549965535689 0.997807250172322 97 0.00284121863411939 0.00568243726823878 0.99715878136588 98 0.00213203549685143 0.00426407099370287 0.997867964503149 99 0.00794180860711597 0.0158836172142319 0.992058191392884 100 0.0212978513531616 0.0425957027063232 0.978702148646838 101 0.0238445685399219 0.0476891370798437 0.976155431460078 102 0.0337171401408696 0.0674342802817393 0.96628285985913 103 0.0264302667641975 0.0528605335283951 0.973569733235802 104 0.0194929638217722 0.0389859276435444 0.980507036178228 105 0.0143177879580013 0.0286355759160025 0.985682212041999 106 0.0400853664310051 0.0801707328620103 0.959914633568995 107 0.0398944684147913 0.0797889368295826 0.960105531585209 108 0.0969297701868554 0.193859540373711 0.903070229813145 109 0.082284738070299 0.164569476140598 0.917715261929701 110 0.0700600694596319 0.140120138919264 0.929939930540368 111 0.171171619883192 0.342343239766383 0.828828380116808 112 0.161106455953812 0.322212911907623 0.838893544046188 113 0.152802249846012 0.305604499692025 0.847197750153988 114 0.228453756030011 0.456907512060023 0.771546243969988 115 0.225950839538695 0.451901679077390 0.774049160461305 116 0.254408540727379 0.508817081454758 0.745591459272621 117 0.23902613968181 0.47805227936362 0.76097386031819 118 0.242037925828197 0.484075851656394 0.757962074171803 119 0.247827234867109 0.495654469734218 0.752172765132891 120 0.208691368100152 0.417382736200303 0.791308631899848 121 0.182020285866376 0.364040571732751 0.817979714133624 122 0.1621756796819 0.3243513593638 0.8378243203181 123 0.194557287586439 0.389114575172877 0.805442712413561 124 0.161157441597222 0.322314883194445 0.838842558402778 125 0.142894571769777 0.285789143539553 0.857105428230223 126 0.121787729756878 0.243575459513756 0.878212270243122 127 0.105261709129099 0.210523418258198 0.8947382908709 128 0.0851155840005305 0.170231168001061 0.91488441599947 129 0.175378469995883 0.350756939991767 0.824621530004117 130 0.136908004514851 0.273816009029703 0.863091995485149 131 0.112310890218499 0.224621780436997 0.887689109781501 132 0.166591354976365 0.33318270995273 0.833408645023635 133 0.429172623310088 0.858345246620175 0.570827376689912 134 0.371183056249561 0.742366112499122 0.628816943750439 135 0.501663818434207 0.996672363131587 0.498336181565793 136 0.40477849497815 0.8095569899563 0.59522150502185 137 0.615498724179908 0.769002551640184 0.384501275820092 138 0.622909485677371 0.754181028645258 0.377090514322629 139 0.557224698153065 0.885550603693871 0.442775301846935 140 0.439754771596666 0.879509543193332 0.560245228403334 141 0.335482209087972 0.670964418175945 0.664517790912028 142 0.292733965240929 0.585467930481859 0.70726603475907 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.0454545454545455 NOK 5% type I error level 24 0.181818181818182 NOK 10% type I error level 36 0.272727272727273 NOK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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