statistiek Multiple Regression

*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, 18 Dec 2010 19:19:51 +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/18/t1292699881f3krt0n0f5flkto.htm/, Retrieved Sat, 18 Dec 2010 20:18:12 +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/18/t1292699881f3krt0n0f5flkto.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 «

6,5 8,9 -0,6 9 6,3 8,4 1,1 11 5,9 8,1 1,4 13 5,5 8,3 1,4 12 5,2 8,1 1,3 13 4,9 8 1,4 15 5,4 8,7 -0,1 13 5,8 9,2 1,8 16 5,7 9 1,5 10 5,6 8,9 1,5 14 5,5 8,5 1,4 14 5,4 8,1 1,6 15 5,4 7,5 1,6 13 5,4 7,1 1,6 8 5,5 6,9 1,4 7 5,8 7,1 1,7 3 5,7 7 1,8 3 5,4 6,7 1,9 4 5,6 7 2,2 4 5,8 7,3 2,1 0 6,2 7,7 2,4 -4 6,8 8,4 2,6 -14 6,7 8,4 2,8 -18 6,7 8,8 2,7 -8 6,4 9,1 2,6 -1 6,3 9 2,9 1 6,3 8,6 2,8 2 6,4 7,9 2,2 0 6,3 7,7 2,2 1 6 7,8 2,2 0 6,3 9,2 2 -1 6,3 9,4 2 -3 6,6 9,2 1,7 -3 7,5 8,7 1,4 -3 7,8 8,4 1,3 -4 7,9 8,6 1,4 -8 7,8 9 1,3 -9 7,6 9,1 1,3 -13 7,5 8,7 1,4 -18 7,6 8,2 2 -11 7,5 7,9 1,7 -9 7,3 7,9 1,8 -10 7,6 9,1 1,7 -13 7,5 9,4 1,6 -11 7,6 9,4 1,7 -5 7,9 9,1 1,9 -15 7,9 9 1,8 -6 8,1 9,3 1,7 -6 8,2 9,9 1,6 -3 8 9,8 1,8 -1 7,5 9,3 1,6 -3 6,8 8,3 1,5 -4 6,5 8 1,5 -6 6,6 8,5 1,3 0 7,6 10,4 1,4 -4 8 11,1 1,4 -2 8,1 10,9 1,3 -2 7,7 10 1,3 -6 7,5 9,2 1,2 -7 7,6 9,2 1,1 -6 7,8 9,5 1,4 -6 7,8 9,6 1,2 -3 7,8 9,5 1,5 -2 7,5 9,1 1,1 -5 7,5 8,9 1,3 -11 7,1 9 1,5 -1 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Mannen[t] = + 3.68452713026474 + 0.426921611066371Vrouwen[t] -0.393998879715656Inflatie[t] -0.0659007049273914Consumvertr[t] + 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) 3.68452713026474 0.563644 6.537 0 0 Vrouwen 0.426921611066371 0.054908 7.7752 0 0 Inflatie -0.393998879715656 0.096037 -4.1026 7.6e-05 3.8e-05 Consumvertr -0.0659007049273914 0.005595 -11.7783 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.827745529807599 R-squared 0.685162662116463 Adjusted R-squared 0.677020317171199 F-TEST (value) 84.148076103678 F-TEST (DF numerator) 3 F-TEST (DF denominator) 116 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.49112439590422 Sum Squared Residuals 27.9795679812651 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.5 7.12742245223832 -0.627422452238318 2 6.3 6.11236214133374 0.187637858666263 3 5.9 5.73428458424434 0.165715415755657 4 5.5 5.88556961138501 -0.385569611385008 5 5.2 5.77368447221591 -0.573684472215908 6 4.9 5.55979101328292 -0.659791013282922 7 5.4 6.58143587045765 -1.18143587045765 8 5.8 5.84859668974891 -0.0485966897489136 9 5.7 6.27681626101469 -0.576816261014685 10 5.6 5.97052128019848 -0.370521280198483 11 5.5 5.8391525237435 -0.339152523743499 12 5.4 5.52368339844643 -0.123683398446428 13 5.4 5.39933184166139 0.000668158338611988 14 5.4 5.5580667218718 -0.158066721871797 15 5.5 5.61738288052905 -0.117382880529046 16 5.8 5.84817035853719 -0.0481703585371886 17 5.7 5.76607830945899 -0.0660783094589857 18 5.4 5.53270123324012 -0.132701233240117 19 5.6 5.54257805264533 0.0574219473546677 20 5.8 5.97365724364637 -0.173657243646375 21 6.2 6.28982904386779 -0.089829043867792 22 6.8 7.16888144494504 -0.368881444945035 23 6.7 7.35368448871147 -0.653684488711469 24 6.7 6.90484597183567 -0.204845971835669 25 6.4 6.6110174086354 -0.211017408635406 26 6.3 6.31832417375929 -0.0183241737592898 27 6.3 6.12105471237692 0.178945287623085 28 6.4 6.19041032231463 0.209589677685368 29 6.3 6.03912529517397 0.260874704826034 30 6 6.147718161208 -0.147718161207995 31 6.3 6.89010889757144 -0.590108897571437 32 6.3 7.1072946296395 -0.807294629639494 33 6.6 7.14010997134092 -0.540109971340917 34 7.5 7.04484882972243 0.455151170277573 35 7.8 7.02207293930147 0.777927060698526 36 7.9 7.33166019325275 0.568339806747253 37 7.8 7.60772943057825 0.192270569421747 38 7.6 7.91402441139446 -0.314024411394456 39 7.5 8.0333594036333 -0.533359403633299 40 7.6 7.12219433577898 0.47780566422102 41 7.5 6.98051610651898 0.519483893481017 42 7.3 7.00701692347481 0.292983076525191 43 7.6 7.7564248595082 -0.156424859508194 44 7.5 7.79209982094489 -0.292099820944888 45 7.6 7.35729570340897 0.242704296591026 46 7.9 7.80942649341984 0.0905735065801552 47 7.9 7.21302787593825 0.686972124061749 48 8.1 7.38050424722973 0.719495752770271 49 8.2 7.47835498705894 0.721645012941057 50 8 7.22506164015439 0.774938359845609 51 7.5 7.22220202041912 0.277797979580880 52 6.8 6.90058100225171 -0.100581002251706 53 6.5 6.90430592878658 -0.404305928786577 54 6.6 6.80116228069855 -0.201162280698545 55 7.6 7.83651627346265 -0.236516273462651 56 8 8.00355999135433 -0.00355999135432682 57 8.1 7.95757555711262 0.142424442887381 58 7.7 7.83694892686245 -0.13694892686245 59 7.5 7.60071223090831 -0.10071223090831 60 7.6 7.57421141395248 0.0257885860475155 61 7.8 7.5840882333577 0.215911766642301 62 7.8 7.5078780556253 0.292121944374707 63 7.8 7.28108552567657 0.518914474323432 64 7.5 7.46561854791846 0.0343814520815443 65 7.5 7.6968386793264 -0.196838679326399 66 7.1 7.6607310644899 -0.560731064489905 67 7.5 8.28794438854917 -0.787944388549175 68 7.5 8.18922834192036 -0.689228341920362 69 7.6 8.44953888849486 -0.849538888494856 70 7.7 7.71918191634755 -0.0191819163475530 71 7.7 7.57491408887683 0.12508591112317 72 7.9 7.31460354230234 0.585396457697663 73 8.1 7.3300922115288 0.769907788471198 74 8.2 7.19899347659836 1.00100652340163 75 8.2 7.42951093308196 0.770489066918038 76 8.2 7.12062635405503 1.07937364594497 77 7.9 7.29182765188138 0.608172348118618 78 7.3 6.98882494420025 0.311175055799749 79 6.9 7.25156245711022 -0.351562457110217 80 6.6 7.37634666729506 -0.776346667295057 81 6.7 7.25156245711022 -0.551562457110217 82 6.9 6.89269849578216 0.00730150421783795 83 7 6.8699226053612 0.130077394638792 84 7.1 7.42362906173616 -0.323629061736165 85 7.2 7.00501628835106 0.194983711648938 86 7.1 6.83381499052471 0.266185009475286 87 6.9 6.8474167364648 0.0525832635352007 88 7 6.69240678278926 0.307593217210738 89 6.8 6.56103802633428 0.238961973665720 90 6.4 6.49227770167162 -0.0922777016716169 91 6.7 6.62737138466147 0.0726286153385288 92 6.6 6.52579571829739 0.074204281702614 93 6.4 6.43382684981397 -0.0338268498139682 94 6.3 6.33511080318515 -0.0351108031851547 95 6.2 6.75701584970533 -0.557015849705329 96 6.5 6.4179055271877 0.0820944728122966 97 6.8 6.46761488796428 0.332385112035716 98 6.8 6.1418362898622 0.658163710137802 99 6.4 5.88897559635745 0.511024403642554 100 6.1 6.18210148463336 -0.0821014846333637 101 5.8 6.06762674725354 -0.267626747253538 102 6.1 6.25199713762017 -0.151997137620173 103 7.2 6.93879664186124 0.261203358138762 104 7.3 6.98105614956807 0.318943850431925 105 6.9 6.63908620731518 0.260913792684822 106 6.1 6.9561233143362 -0.856123314336196 107 5.8 7.19365797048974 -1.39365797048974 108 6.2 7.59823634453495 -1.39823634453495 109 7.1 7.67919306528901 -0.579193065289009 110 7.7 7.86728838219052 -0.167288382190515 111 8 7.86070383592037 0.139296164079629 112 7.8 7.35454979551107 0.445450204488931 113 7.4 7.10427870021704 0.295721299782957 114 7.4 7.20585436658113 0.194145633418871 115 7.7 7.80985914681964 -0.109859146819645 116 7.8 7.54253140057521 0.257468599424792 117 7.8 7.29296298020553 0.507037019794471 118 8 7.21761810927272 0.782381890727277 119 8.1 7.08252442628287 1.01747557371713 120 8.4 7.62219648331794 0.777803516682061 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.371898082465908 0.743796164931816 0.628101917534092 8 0.251730794010919 0.503461588021838 0.74826920598908 9 0.54574599183176 0.908508016336479 0.454254008168239 10 0.424140127407054 0.848280254814108 0.575859872592946 11 0.317981380002062 0.635962760004124 0.682018619997938 12 0.240967300826959 0.481934601653918 0.759032699173041 13 0.170695156938326 0.341390313876652 0.829304843061674 14 0.131505607981956 0.263011215963913 0.868494392018044 15 0.0896824488235724 0.179364897647145 0.910317551176428 16 0.0596897723697587 0.119379544739517 0.94031022763024 17 0.0391063850781463 0.0782127701562926 0.960893614921854 18 0.0276751360232245 0.055350272046449 0.972324863976776 19 0.0166286529226134 0.0332573058452267 0.983371347077387 20 0.0118625034961129 0.0237250069922257 0.988137496503887 21 0.0069156487538201 0.0138312975076402 0.99308435124618 22 0.00428522596993973 0.00857045193987947 0.99571477403006 23 0.00349238548498683 0.00698477096997365 0.996507614515013 24 0.00207861037962961 0.00415722075925922 0.99792138962037 25 0.00112939554302189 0.00225879108604377 0.998870604456978 26 0.000624265169103494 0.00124853033820699 0.999375734830896 27 0.000442842376913901 0.000885684753827803 0.999557157623086 28 0.000483971612896719 0.000967943225793438 0.999516028387103 29 0.000492597178990225 0.00098519435798045 0.99950740282101 30 0.000279917472457482 0.000559834944914965 0.999720082527543 31 0.000216914075621245 0.00043382815124249 0.999783085924379 32 0.000263443901212857 0.000526887802425713 0.999736556098787 33 0.000180419942309369 0.000360839884618738 0.99981958005769 34 0.00491646648024632 0.00983293296049264 0.995083533519754 35 0.0608641858213145 0.121728371642629 0.939135814178686 36 0.117123153872368 0.234246307744736 0.882876846127632 37 0.109844158114402 0.219688316228804 0.890155841885598 38 0.0877741576511475 0.175548315302295 0.912225842348853 39 0.0841244609337334 0.168248921867467 0.915875539066267 40 0.095556883551824 0.191113767103648 0.904443116448176 41 0.103858183698499 0.207716367396998 0.8961418163015 42 0.0869645852597672 0.173929170519534 0.913035414740233 43 0.0662831782903852 0.132566356580770 0.933716821709615 44 0.0510967101069132 0.102193420213826 0.948903289893087 45 0.0511992767540234 0.102398553508047 0.948800723245977 46 0.040264401770251 0.080528803540502 0.959735598229749 47 0.0727526648952477 0.145505329790495 0.927247335104752 48 0.126746027388126 0.253492054776252 0.873253972611874 49 0.204474880557329 0.408949761114658 0.795525119442671 50 0.296903459349063 0.593806918698127 0.703096540650937 51 0.266210114915575 0.53242022983115 0.733789885084425 52 0.233819783767987 0.467639567535974 0.766180216232013 53 0.247496610474995 0.49499322094999 0.752503389525005 54 0.239748473359731 0.479496946719461 0.76025152664027 55 0.205815443615118 0.411630887230235 0.794184556384882 56 0.171522663643838 0.343045327287677 0.828477336356162 57 0.146845641288626 0.293691282577253 0.853154358711374 58 0.119524722758276 0.239049445516552 0.880475277241724 59 0.0983302381795049 0.196660476359010 0.901669761820495 60 0.0792557843624406 0.158511568724881 0.92074421563756 61 0.064528210232103 0.129056420464206 0.935471789767897 62 0.054394298511313 0.108788597022626 0.945605701488687 63 0.0564336107773984 0.112867221554797 0.943566389222602 64 0.0444788650633094 0.0889577301266188 0.95552113493669 65 0.0370605526644852 0.0741211053289704 0.962939447335515 66 0.0461963928858566 0.0923927857717132 0.953803607114143 67 0.078383661124857 0.156767322249714 0.921616338875143 68 0.100063384474804 0.200126768949609 0.899936615525196 69 0.170898377458503 0.341796754917007 0.829101622541497 70 0.143240610258524 0.286481220517048 0.856759389741476 71 0.117435498124612 0.234870996249224 0.882564501875388 72 0.125104616022163 0.250209232044325 0.874895383977837 73 0.151166041979441 0.302332083958881 0.84883395802056 74 0.253185098505182 0.506370197010364 0.746814901494818 75 0.287370917941285 0.574741835882571 0.712629082058715 76 0.459110648124279 0.918221296248559 0.54088935187572 77 0.470259450421639 0.940518900843278 0.529740549578361 78 0.427860109719806 0.855720219439612 0.572139890280194 79 0.394178837104038 0.788357674208076 0.605821162895962 80 0.474670127291805 0.94934025458361 0.525329872708195 81 0.504055442247718 0.991889115504564 0.495944557752282 82 0.463595113800152 0.927190227600303 0.536404886199848 83 0.420411675365874 0.840823350731749 0.579588324634126 84 0.433647619399842 0.867295238799684 0.566352380600158 85 0.387860399337857 0.775720798675714 0.612139600662143 86 0.341990235438495 0.68398047087699 0.658009764561505 87 0.298289951910688 0.596579903821377 0.701710048089312 88 0.254097581364017 0.508195162728034 0.745902418635983 89 0.215729730396148 0.431459460792297 0.784270269603851 90 0.226669813213679 0.453339626427358 0.773330186786321 91 0.214405536968969 0.428811073937937 0.785594463031031 92 0.198698739745807 0.397397479491615 0.801301260254192 93 0.225916375361554 0.451832750723109 0.774083624638446 94 0.265576071476616 0.531152142953231 0.734423928523384 95 0.460719615407099 0.921439230814199 0.5392803845929 96 0.449243234380078 0.898486468760156 0.550756765619922 97 0.385528312306976 0.771056624613952 0.614471687693024 98 0.34196934864505 0.6839386972901 0.65803065135495 99 0.291469910778403 0.582939821556807 0.708530089221597 100 0.283820813001128 0.567641626002256 0.716179186998872 101 0.305959546492602 0.611919092985204 0.694040453507398 102 0.281509511652742 0.563019023305484 0.718490488347258 103 0.237896466104520 0.475792932209041 0.76210353389548 104 0.234107832569596 0.468215665139191 0.765892167430404 105 0.273402804741132 0.546805609482263 0.726597195258868 106 0.24174247611224 0.48348495222448 0.75825752388776 107 0.455952003393071 0.911904006786143 0.544047996606929 108 0.891798041393471 0.216403917213057 0.108201958606529 109 0.97145406124368 0.05709187751264 0.02854593875632 110 0.93893247055608 0.122135058887840 0.0610675294439202 111 0.90439058994209 0.191218820115818 0.095609410057909 112 0.987042880709796 0.0259142385804083 0.0129571192902042 113 0.956813610501623 0.0863727789967539 0.0431863894983769 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.121495327102804 NOK 5% type I error level 17 0.158878504672897 NOK 10% type I error level 25 0.233644859813084 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/10tyit1292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/10tyit1292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/1mf3z1292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/1mf3z1292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/2x6221292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/2x6221292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/3x6221292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/3x6221292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/4x6221292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/4x6221292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/5x6221292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/5x6221292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/6qgk51292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/6qgk51292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/7ip1q1292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/7ip1q1292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/8ip1q1292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/8ip1q1292699982.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/9ip1q1292699982.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292699881f3krt0n0f5flkto/9ip1q1292699982.ps (open in new window)

Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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