Paper 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 14:32:10 +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/t1292682640imwuzok6b68k3ys.htm/, Retrieved Sat, 18 Dec 2010 15:30:40 +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/t1292682640imwuzok6b68k3ys.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 «

41 25 15 9 3 38 25 15 9 4 37 19 14 9 4 36 18 10 14 2 42 18 10 8 4 44 23 9 14 4 40 23 18 15 3 43 25 14 9 4 40 23 11 11 4 45 24 11 14 4 47 32 9 14 4 45 30 17 6 5 45 32 21 10 4 40 24 16 9 4 49 17 14 14 4 48 30 24 8 5 44 25 7 11 4 29 25 9 10 4 42 26 18 16 4 45 23 11 11 5 32 25 13 11 5 32 25 13 11 5 41 35 18 7 4 29 19 14 13 2 38 20 12 10 4 41 21 12 9 4 38 21 9 9 4 24 23 11 15 3 34 24 8 13 2 38 23 5 16 2 37 19 10 12 3 46 17 11 6 5 48 27 15 4 5 42 27 16 12 4 46 25 12 10 4 43 18 14 14 5 38 22 13 9 4 39 26 10 10 4 34 26 18 14 4 39 23 17 14 4 35 16 12 10 2 41 27 13 9 3 40 25 13 14 3 43 14 11 8 4 37 19 13 9 2 41 20 12 8 4 46 26 12 10 4 26 16 12 9 3 41 18 12 9 3 37 22 9 9 3 39 25 17 9 4 44 29 18 11 5 39 21 7 15 2 36 22 17 8 4 38 22 12 10 2 38 32 12 8 0 38 23 9 14 4 32 31 9 11 4 33 18 13 10 3 46 23 10 12 4 42 24 12 9 4 42 19 10 13 2 43 26 11 14 4 41 14 13 15 2 49 20 6 8 4 45 22 7 7 3 39 24 13 10 4 45 25 11 10 5 31 21 18 13 3 30 21 18 13 3 45 28 9 11 4 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation StudyForCareer[t] = + 32.5202067294365 + 0.174192543560943PersonalStandards[t] + 0.0466789923587195ParentalExpectations[t] -0.217373134461697Doubts[t] + 1.39806533965884LeaderPreference[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) 32.5202067294365 3.250358 10.0051 0 0 PersonalStandards 0.174192543560943 0.10383 1.6777 0.095627 0.047814 ParentalExpectations 0.0466789923587195 0.127944 0.3648 0.715779 0.357889 Doubts -0.217373134461697 0.154972 -1.4027 0.162915 0.081457 LeaderPreference 1.39806533965884 0.482225 2.8992 0.00434 0.00217 Multiple Linear Regression - Regression Statistics Multiple R 0.367916033517428 R-squared 0.135362207719197 Adjusted R-squared 0.110833476023288 F-TEST (value) 5.51851638304525 F-TEST (DF numerator) 4 F-TEST (DF denominator) 141 p-value 0.000371345161075842 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.98212870492208 Sum Squared Residuals 3499.84650696961 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 39.8130430126621 1.18695698733793 2 38 41.2111083523209 -3.21110835232092 3 37 40.1192740985965 -3.11927409859654 4 36 35.8753692339746 0.124630766025435 5 42 39.9757387200624 2.02426127993758 6 44 39.4957836387382 4.50421636126177 7 40 38.3004560958462 1.69954390415382 8 43 41.1644293599622 1.8355706400378 9 40 40.2412610268408 -0.241261026840763 10 45 39.7633341670166 5.23666583298338 11 47 41.0635165307867 5.93648346921328 12 45 44.225613797887 0.774386202112997 13 45 42.4931569769381 2.50684302306186 14 40 41.0835948011187 -1.08359480111870 15 49 38.6840233391662 10.3159766608338 16 48 44.1176204754746 3.88237952452535 17 44 40.4029301445278 3.59706985547223 18 29 40.7136612637069 -11.7136612637069 19 42 40.0037259317261 1.99627406827385 20 45 41.6393263664996 3.3606736335004 21 32 42.0810694383389 -10.0810694383389 22 32 42.0810694383389 -10.0810694383389 23 41 43.5278170339299 -2.52781703392991 24 29 36.4536508814321 -7.45365088143208 25 38 39.9827355229783 -1.98273552297835 26 41 40.374301201001 0.625698798999012 27 38 40.2342642239248 -2.23426422392483 28 24 37.9737031493351 -13.9737031493351 29 34 37.0445396450845 -3.04453964508448 30 38 36.0781907210623 1.92180927893771 31 37 37.8823733861177 -0.882373386117737 32 46 41.6810367774424 4.31896322255758 33 48 44.0444244514101 3.95557554858987 34 42 40.9540530284164 1.04594697158356 35 46 40.8536982407831 5.14630175921693 36 43 40.2562812223860 2.74371877761405 37 38 40.5951727369207 -2.59517273692065 38 39 40.9345327996266 -1.93453279962657 39 34 40.4384722006495 -6.43847220064954 40 39 39.869215577608 -0.86921557760799 41 35 36.4898346694169 -1.48983466941690 42 41 40.0680701150665 0.931929884933467 43 40 38.6328193556362 1.36718064436384 44 43 39.3256475381774 3.67435246182264 45 37 37.2764644269201 -0.27646442692015 46 41 40.4174817919017 0.582518208098259 47 46 41.027890784344 4.97210921565599 48 26 38.1052731435374 -12.1052731435374 49 41 38.4536582306593 2.54634176934068 50 37 39.0103914278269 -2.01039142782694 51 39 41.3044663370384 -2.30446633703836 52 44 43.0112345743763 0.988765425623705 53 39 36.0405367531195 2.95946324688046 54 36 40.9992618408172 -4.99926184081723 55 38 37.5349899307826 0.465010069217436 56 38 36.9155309559977 1.08446904400228 57 38 39.4957836387382 -1.49578363873823 58 32 41.5414433906109 -9.54144339061087 59 33 38.2829640885563 -5.28296408855634 60 46 39.9772089000203 6.02279109997965 61 42 40.8968788316838 1.10312116831618 62 42 36.2669349119972 5.7330650880028 63 43 40.1117192541385 2.88828074586150 64 41 35.1012629023453 5.89873709765475 65 49 40.1374078377494 8.86259216225058 66 45 39.3517797120329 5.64822028796711 67 39 40.7261846895808 -1.72618468958084 68 45 42.2050845880832 2.79491541191682 69 31 38.3868172776477 -7.38681727764768 70 30 38.3868172776477 -8.38681727764768 71 45 41.018865759928 3.98113424007196 72 48 42.3722803287282 5.62771967127181 73 28 38.2422802673268 -10.2422802673268 74 35 37.5314915293246 -2.53149152932460 75 38 40.6453501307373 -2.64535013073734 76 39 40.4154535704017 -1.41545357040171 77 40 40.2502860512567 -0.250286051256730 78 38 38.9460472444866 -0.946047244486551 79 42 38.3592986141552 3.64070138584483 80 36 35.3597884062077 0.640211593792333 81 49 43.6313103230976 5.36868967690241 82 41 40.5896461139627 0.410353886037351 83 18 35.9617304157761 -17.9617304157761 84 36 38.1032449220374 -2.1032449220374 85 42 38.8195353250710 3.18046467492896 86 41 42.6558526843385 -1.65585268433848 87 43 39.9862339244363 3.01376607556369 88 46 39.6820310600019 6.31796893999811 89 37 40.7191878866649 -3.71918788666491 90 38 39.0625970431437 -1.06259704314366 91 43 40.7492033198287 2.25079668017132 92 41 42.8732258188002 -1.87322581880017 93 35 34.6519649860479 0.348035013952111 94 39 40.4029301445278 -1.40293014452777 95 42 39.5619828598868 2.43801714011318 96 36 39.7186833961579 -3.71868339615793 97 35 41.1669261296335 -6.16692612963345 98 33 36.2814865593712 -3.28148655937117 99 36 38.2035997096708 -2.20359970967077 100 48 39.3723265305361 8.62767346946392 101 41 39.9827355229783 1.01726447702165 102 47 38.4495180973383 8.5504819026617 103 41 39.0730922475176 1.92690775248244 104 31 42.1067580219498 -11.1067580219498 105 36 41.2216035566948 -5.22160355669482 106 46 41.3044663370384 4.69553366296164 107 39 38.1559190855253 0.844080914474662 108 44 40.7317113125388 3.26828868746116 109 43 37.0550348494584 5.94496515054162 110 32 41.1157221461035 -9.11572214610345 111 40 40.5544889156912 -0.55448891569115 112 40 39.1127744369603 0.887225563039656 113 46 37.1459210224312 8.85407897756883 114 45 39.1936089958038 5.80639100419615 115 39 40.6725088943062 -1.67250889430619 116 44 41.6333311953704 2.36666880462962 117 35 39.7618639870587 -4.76186398705868 118 38 37.7046824410988 0.295317558901173 119 38 36.4466540785161 1.55334592148385 120 36 37.3542691324769 -1.35426913247690 121 42 38.0620925526367 3.93790744736332 122 39 39.7011913888681 -0.7011913888681 123 41 42.9575587791016 -1.95755877910164 124 41 39.4204757028527 1.57952429714727 125 47 38.7748845542124 8.22511544578764 126 39 38.6794983479949 0.320501652005117 127 40 39.5605126799289 0.439487320071111 128 44 40.2558126742147 3.74418732578527 129 42 39.4998400817383 2.50015991826170 130 35 38.5540130182927 -3.55401301829269 131 46 42.6538244628384 3.34617553716156 132 43 37.668498653114 5.33150134688599 133 40 40.1061926311805 -0.106192631180502 134 44 40.027386293837 3.97261370616297 135 37 40.5088115551191 -3.50881155511914 136 46 40.6760072957642 5.32399270423584 137 44 41.6393263664996 2.36067363350040 138 35 38.674529766579 -3.67452976657898 139 39 37.1936016465766 1.80639835342339 140 40 38.2809358670563 1.71906413294369 141 42 38.8195353250710 3.18046467492896 142 37 38.9295568689834 -1.92955686898343 143 29 39.6016650493296 -10.6016650493296 144 33 37.8422226485037 -4.84222264850373 145 35 39.9290597277037 -4.92905972770369 146 42 35.6620525425129 6.33794745748706 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.209623360905933 0.419246721811867 0.790376639094067 9 0.124782190918213 0.249564381836425 0.875217809081787 10 0.0689524797774847 0.137904959554969 0.931047520222515 11 0.0327723743286261 0.0655447486572523 0.967227625671374 12 0.0146619573212959 0.0293239146425918 0.985338042678704 13 0.00701730563516128 0.0140346112703226 0.992982694364839 14 0.00290988769063062 0.00581977538126124 0.99709011230937 15 0.0297456959922112 0.0594913919844225 0.970254304007789 16 0.0174753335350673 0.0349506670701346 0.982524666464933 17 0.00990393532341799 0.0198078706468360 0.990096064676582 18 0.265533381534683 0.531066763069367 0.734466618465317 19 0.290141279932567 0.580282559865134 0.709858720067433 20 0.226571794433583 0.453143588867167 0.773428205566417 21 0.608355423269853 0.783289153460294 0.391644576730147 22 0.793292586775668 0.413414826448663 0.206707413224332 23 0.744127292770325 0.511745414459351 0.255872707229675 24 0.827311131025054 0.345377737949891 0.172688868974946 25 0.782819323834711 0.434361352330577 0.217180676165289 26 0.739165866509296 0.521668266981409 0.260834133490704 27 0.685206171692053 0.629587656615895 0.314793828307947 28 0.930632255599542 0.138735488800917 0.0693677444004584 29 0.91031412543671 0.17937174912658 0.08968587456329 30 0.896012733923862 0.207974532152276 0.103987266076138 31 0.866578076848953 0.266843846302093 0.133421923151046 32 0.864089683233044 0.271820633533912 0.135910316766956 33 0.855829404658425 0.288341190683151 0.144170595341575 34 0.821104329528161 0.357791340943678 0.178895670471839 35 0.823875889004932 0.352248221990137 0.176124110995068 36 0.788738222873837 0.422523554252326 0.211261777126163 37 0.754766384975769 0.490467230048462 0.245233615024231 38 0.712594382031662 0.574811235936675 0.287405617968338 39 0.746914557248095 0.50617088550381 0.253085442751905 40 0.702428372346569 0.595143255306862 0.297571627653431 41 0.655249412069329 0.689501175861342 0.344750587930671 42 0.612742139387124 0.774515721225751 0.387257860612876 43 0.568466838662756 0.863066322674488 0.431533161337244 44 0.540820203958858 0.918359592082283 0.459179796041142 45 0.48953654776758 0.97907309553516 0.51046345223242 46 0.43692862504431 0.87385725008862 0.56307137495569 47 0.438239343414298 0.876478686828596 0.561760656585702 48 0.654575835891141 0.690848328217717 0.345424164108859 49 0.62718092287587 0.745638154248259 0.372819077124129 50 0.582237566057809 0.835524867884382 0.417762433942191 51 0.540199888811843 0.919600222376315 0.459800111188158 52 0.490375182201818 0.980750364403637 0.509624817798182 53 0.468344553044192 0.936689106088384 0.531655446955808 54 0.46029873521068 0.92059747042136 0.53970126478932 55 0.417628920654950 0.835257841309899 0.58237107934505 56 0.384016017869314 0.768032035738627 0.615983982130686 57 0.34150895974301 0.68301791948602 0.65849104025699 58 0.475289611841533 0.950579223683065 0.524710388158467 59 0.474338070308881 0.948676140617762 0.525661929691119 60 0.497242505266077 0.994485010532155 0.502757494733923 61 0.450726223133082 0.901452446266164 0.549273776866918 62 0.469942158790798 0.939884317581597 0.530057841209202 63 0.435636607940062 0.871273215880124 0.564363392059938 64 0.454480525291663 0.908961050583326 0.545519474708337 65 0.556025090507531 0.887949818984938 0.443974909492469 66 0.564193480720711 0.871613038558578 0.435806519279289 67 0.521913417630937 0.956173164738127 0.478086582369063 68 0.486624850833425 0.97324970166685 0.513375149166575 69 0.539543277307325 0.92091344538535 0.460456722692675 70 0.623402039397222 0.753195921205557 0.376597960602778 71 0.605607530015622 0.788784939968755 0.394392469984378 72 0.621395609910202 0.757208780179595 0.378604390089798 73 0.753263918993778 0.493472162012444 0.246736081006222 74 0.722685621846642 0.554628756306715 0.277314378153358 75 0.69389105904814 0.61221788190372 0.30610894095186 76 0.653228400873408 0.693543198253184 0.346771599126592 77 0.607822719605149 0.784354560789702 0.392177280394851 78 0.563198868530471 0.873602262939059 0.436801131469529 79 0.547389938962039 0.905220122075922 0.452610061037961 80 0.503236418396931 0.993527163206137 0.496763581603069 81 0.542394004139885 0.915211991720231 0.457605995860115 82 0.496818675513802 0.993637351027603 0.503181324486198 83 0.950784553809807 0.0984308923803867 0.0492154461901934 84 0.940759803445022 0.118480393109956 0.0592401965549782 85 0.931980571282796 0.136038857434408 0.0680194287172039 86 0.915098491596973 0.169803016806054 0.0849015084030268 87 0.903230799605212 0.193538400789576 0.096769200394788 88 0.917280560313423 0.165438879373154 0.0827194396865772 89 0.905460612277278 0.189078775445444 0.0945393877227218 90 0.883843842836232 0.232312314327537 0.116156157163768 91 0.862690339003934 0.274619321992133 0.137309660996066 92 0.834981227530137 0.330037544939726 0.165018772469863 93 0.806406862983452 0.387186274033097 0.193593137016548 94 0.774657182184761 0.450685635630478 0.225342817815239 95 0.740818701437841 0.518362597124319 0.259181298562159 96 0.720286410708274 0.559427178583452 0.279713589291726 97 0.74347978145328 0.513040437093441 0.256520218546721 98 0.776518150928931 0.446963698142137 0.223481849071069 99 0.766633316124658 0.466733367750683 0.233366683875341 100 0.837483291283589 0.325033417432822 0.162516708716411 101 0.804027809257954 0.391944381484092 0.195972190742046 102 0.824688221424396 0.350623557151208 0.175311778575604 103 0.789841055394342 0.420317889211316 0.210158944605658 104 0.882707715561165 0.234584568877671 0.117292284438835 105 0.891754429247661 0.216491141504677 0.108245570752339 106 0.88806013293411 0.22387973413178 0.11193986706589 107 0.859952712086751 0.280094575826498 0.140047287913249 108 0.841739924524885 0.316520150950231 0.158260075475115 109 0.846942830853486 0.306114338293027 0.153057169146514 110 0.909156858665438 0.181686282669124 0.0908431413345619 111 0.883386253815632 0.233227492368735 0.116613746184368 112 0.850965716838828 0.298068566322344 0.149034283161172 113 0.90346964967565 0.1930607006487 0.09653035032435 114 0.91153162093979 0.176936758120421 0.0884683790602107 115 0.885207339577812 0.229585320844377 0.114792660422189 116 0.868673240582563 0.262653518834873 0.131326759417437 117 0.874059968138645 0.251880063722711 0.125940031861355 118 0.836059036603053 0.327881926793894 0.163940963396947 119 0.791391895271072 0.417216209457856 0.208608104728928 120 0.752662659267248 0.494674681465504 0.247337340732752 121 0.716343908413226 0.567312183173547 0.283656091586774 122 0.653245572681016 0.693508854637967 0.346754427318984 123 0.589029282805996 0.821941434388008 0.410970717194004 124 0.516756898190163 0.966486203619673 0.483243101809837 125 0.628954283714751 0.742091432570497 0.371045716285249 126 0.552534886179232 0.894930227641537 0.447465113820768 127 0.472949294913665 0.94589858982733 0.527050705086335 128 0.457608918950470 0.915217837900939 0.54239108104953 129 0.394211867142267 0.788423734284533 0.605788132857733 130 0.334792893545842 0.669585787091684 0.665207106454158 131 0.364780825608167 0.729561651216333 0.635219174391833 132 0.301368012735573 0.602736025471145 0.698631987264427 133 0.259140195905667 0.518280391811333 0.740859804094333 134 0.207367343018183 0.414734686036366 0.792632656981817 135 0.141586940139517 0.283173880279034 0.858413059860483 136 0.221599840203288 0.443199680406575 0.778400159796713 137 0.468679990639211 0.937359981278422 0.531320009360789 138 0.31441654638618 0.62883309277236 0.68558345361382 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00763358778625954 OK 5% type I error level 5 0.0381679389312977 OK 10% type I error level 8 0.0610687022900763 OK

Charts produced by software:

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Parameters (Session):

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

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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Software written by Ed van Stee & Patrick Wessa

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