WS 10 - MR: Organization

*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: Tue, 14 Dec 2010 16:06:02 +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/14/t1292342661m4siwggwrsfkono.htm/, Retrieved Tue, 14 Dec 2010 17:04:35 +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/14/t1292342661m4siwggwrsfkono.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 «

0 25 11 7 8 25 23 0 17 6 17 8 30 25 0 18 8 12 9 22 19 0 16 10 12 7 22 29 0 20 10 11 4 25 25 0 16 11 11 11 23 21 0 18 16 12 7 17 22 0 17 11 13 7 21 25 0 30 12 16 10 19 18 0 23 8 11 10 15 22 0 18 12 10 8 16 15 0 21 9 9 9 22 20 0 31 14 17 11 23 20 0 27 15 11 9 23 21 0 21 9 14 13 19 21 0 16 8 15 9 23 24 0 20 9 15 6 25 24 0 17 9 13 6 22 23 0 25 16 18 16 26 24 0 26 11 18 5 29 18 0 25 8 12 7 32 25 0 17 9 17 9 25 21 0 32 12 18 12 28 22 0 22 9 14 9 25 23 0 17 9 16 5 25 23 0 20 14 14 10 18 24 0 29 10 12 8 25 23 0 23 14 17 7 25 21 0 20 10 12 8 20 28 0 11 6 6 4 15 16 0 26 13 12 8 24 29 0 22 10 12 8 26 27 0 14 15 13 8 14 16 0 19 12 14 7 24 28 0 20 11 11 8 25 25 0 28 8 12 7 20 22 0 19 9 9 7 21 23 0 30 9 15 9 27 26 0 29 15 18 11 23 23 0 26 9 15 6 25 25 0 23 10 12 8 20 21 0 21 12 14 9 22 24 0 28 11 13 6 25 22 0 23 14 13 10 25 27 0 18 6 11 8 17 26 0 20 8 16 10 25 24 0 21 10 11 5 26 24 0 28 12 16 14 27 22 0 10 5 8 6 19 24 0 22 10 15 6 22 20 0 31 10 21 12 32 26 0 29 13 18 12 21 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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation O[t] = + 15.1221163728982 + 1.88594086825902Gender[t] -0.0545464258288678CM[t] + 0.14601855026369D[t] -0.107909720696322PE[t] -0.222522303520102PC[t] + 0.419080093545205PS[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) 15.1221163728982 1.966696 7.6891 0 0 Gender 1.88594086825902 0.580382 3.2495 0.001423 0.000712 CM -0.0545464258288678 0.061246 -0.8906 0.374541 0.187271 D 0.14601855026369 0.111494 1.3097 0.192289 0.096144 PE -0.107909720696322 0.10194 -1.0586 0.291481 0.14574 PC -0.222522303520102 0.126918 -1.7533 0.08157 0.040785 PS 0.419080093545205 0.073368 5.712 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.522382553604487 R-squared 0.272883532310344 Adjusted R-squared 0.244181566480490 F-TEST (value) 9.50748579132165 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 7.26832949382583e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.39491293472217 Sum Squared Residuals 1751.86594282028 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 23 23.3061156456720 -0.306115645672036 2 25 24.0286975617474 0.97130243825255 3 19 21.2305737880458 -2.23057378804582 4 29 22.0767483472711 6.92325165272886 5 25 23.8912795558479 1.10872044415209 6 21 21.8596674976960 -0.859667497695954 7 22 20.7483663294695 1.25163367053048 8 25 21.6412306574644 3.35876934253556 9 18 19.2486894122132 -1.24868941221316 10 22 17.9096684212613 4.09033157873873 11 15 19.7385091727421 -4.7385091727421 12 20 21.5366822229119 -1.53668222291188 13 20 20.8320684368761 -0.832068436876072 14 21 22.2887756216734 -1.28877562167337 15 21 18.8498041247142 2.15019587528576 16 24 21.4350175711598 2.5649824288402 17 24 22.8685775157587 1.13142248424127 18 23 21.9907959540024 1.00920404599763 19 24 21.4881031347154 2.51189686528456 20 18 24.4084495769249 -6.40844957692486 21 25 25.484594349736 -0.484594349736 22 21 22.1488304412924 -1.14883044129239 23 22 22.2504533540294 -0.250453354029424 24 23 22.199827474237 0.800172525762988 25 23 23.1468293760691 -0.146829376069117 26 24 19.8829301188767 4.11706988112334 27 23 22.4023627886114 0.597637211388627 28 21 22.9966892446778 -1.99668924467783 29 28 20.7978801533452 7.20211984665484 30 16 20.1468708552825 -4.14687085528253 31 29 22.5849776233438 6.41502237665616 32 27 23.2032678629587 3.79673213704135 33 16 19.2328611776693 -3.23286117766927 34 28 22.8274869160097 5.17251308399031 35 25 23.1472088920312 1.85279110796880 36 22 20.2919939497069 1.70800605029306 37 23 21.6717395880646 1.32826041193539 38 26 22.4937065340002 3.50629346599984 39 23 20.9792701181012 2.02072988189882 40 25 22.5412989607855 2.45870103921447 41 21 20.6342408758586 0.365759124141444 42 24 21.4351892702213 2.56481072977866 43 22 22.9400626510478 -0.940062651047814 44 27 22.7607612169028 4.23923878309718 45 26 19.1735682440088 6.82643175599116 46 24 21.7245600307183 2.27543996928169 47 24 24.0332909200441 -0.03329092004415 48 22 21.8203337981521 0.179666201847870 49 24 21.0708550565957 2.92914494340432 50 20 21.6482629337291 -1.64826293372907 51 26 23.3655538914228 2.63444610857723 52 21 19.6265505269633 1.37344947303672 53 19 19.7427173939007 -0.742717393900692 54 21 21.122707387365 -0.122707387365001 55 16 19.451448951167 -3.45144895116701 56 22 20.2652422288916 1.73475777110845 57 15 20.6274585758766 -5.62745857587660 58 17 20.0514781848112 -3.05147818481125 59 15 19.4616414784843 -4.46164147848427 60 21 20.9560863396967 0.0439136603032818 61 19 18.5957097758687 0.404290224131271 62 24 17.9095833622307 6.09041663776927 63 17 25.0582685418496 -8.05826854184958 64 23 24.3496094505398 -1.34960945053977 65 24 21.7027660395424 2.29723396045756 66 14 21.8242042423637 -7.82420424236368 67 22 24.3970992499823 -2.39709924998229 68 16 20.2364592814665 -4.23645928146655 69 19 22.4848756185153 -3.48487561851526 70 25 21.8710781131803 3.12892188681974 71 24 22.7226440245256 1.27735597547442 72 26 22.728128798486 3.27187120151401 73 26 20.8877113536354 5.11228864636464 74 25 23.2952411005922 1.70475889940781 75 18 21.7356495948753 -3.73564959487531 76 21 19.1937269322161 1.80627306778388 77 23 21.0996869452122 1.90031305478778 78 20 21.3709931692890 -1.37099316928897 79 13 21.2876581748591 -8.28765817485906 80 15 20.8523916219684 -5.85239162196839 81 14 22.1949372353157 -8.19493723531572 82 22 23.5474000683615 -1.54740006836153 83 10 17.6176644540326 -7.61766445403256 84 22 21.2315141449011 0.76848585509894 85 24 24.6695886050205 -0.66958860502045 86 19 21.3851804796882 -2.38518047968824 87 20 21.4013737208431 -1.4013737208431 88 13 16.4567240674248 -3.45672406742479 89 20 19.7358861527272 0.264113847272804 90 22 22.7596924810015 -0.759692481001539 91 24 22.4823015396919 1.51769846030811 92 29 22.9851186978493 6.01488130215072 93 12 20.3529138235261 -8.3529138235261 94 20 20.6443297946186 -0.644329794618582 95 21 20.7335556733668 0.266444326633248 96 22 21.1962293704397 0.803770629560266 97 20 17.2811940171391 2.71880598286093 98 26 23.9438504001402 2.05614959985980 99 23 22.8816903216367 0.118309678363270 100 24 21.4332486458904 2.56675135410962 101 22 24.4677217023441 -2.46772170234414 102 28 25.7440018334609 2.25599816653914 103 12 20.2579452096462 -8.25794520964623 104 24 22.9129178082057 1.08708219179430 105 20 21.9003372203891 -1.90033722038913 106 23 22.0455437928436 0.954456207156377 107 28 22.9922957183931 5.00770428160695 108 24 21.73374392775 2.26625607225001 109 23 23.4508688075582 -0.450868807558179 110 29 25.3298095551439 3.6701904448561 111 26 27.4458698242759 -1.44586982427592 112 22 26.2421505535834 -4.24215055358339 113 22 23.3520839339131 -1.35208393391308 114 23 26.6973691384142 -3.69736913841416 115 30 24.1989550202522 5.80104497974778 116 17 19.9547041499017 -2.95470414990172 117 23 25.4141210242680 -2.41412102426805 118 25 23.3564999719722 1.64350002802778 119 24 28.3565265785553 -4.35652657855528 120 24 26.1353513078034 -2.13535130780339 121 24 23.0659754165434 0.934024583456574 122 20 22.1810291593008 -2.18102915930081 123 22 24.4609687383918 -2.46096873839178 124 28 24.9499347820965 3.05006521790352 125 25 24.1552398194878 0.844760180512194 126 24 24.6427298563 -0.64272985630001 127 24 25.116406477499 -1.11640647749899 128 23 23.5856818176043 -0.585681817604278 129 30 27.9400988410546 2.05990115894542 130 24 22.7378431447460 1.26215685525402 131 21 25.4179998312895 -4.41799983128947 132 25 23.9636713114004 1.03632868859956 133 25 24.4059351833501 0.594064816649902 134 29 24.5034642699887 4.49653573001132 135 22 22.3943218820612 -0.394321882061161 136 27 23.7843816449727 3.21561835502728 137 24 22.5661765667738 1.43382343322619 138 29 25.1215967945279 3.87840320547214 139 21 21.7036494703175 -0.703649470317532 140 24 21.4675569456575 2.53244305434253 141 23 22.782081067197 0.217918932803005 142 27 22.6742941043707 4.32570589562932 143 25 22.9406599877012 2.05934001229877 144 21 21.9767110135990 -0.976711013599046 145 21 22.5444620134524 -1.54446201345244 146 29 22.7671210588285 6.23287894117155 147 21 21.7811786394597 -0.78117863945972 148 20 23.6697201209574 -3.66972012095741 149 19 23.7622526184836 -4.76225261848364 150 24 23.2870718149959 0.712928185004062 151 13 21.2180070139171 -8.21800701391713 152 25 24.4336340428301 0.566365957169871 153 23 22.7093710619315 0.290628938068539 154 26 24.7341586607193 1.26584133928067 155 23 20.9529542215945 2.04704577840551 156 22 24.0007563060825 -2.00075630608249 157 24 22.7519809885885 1.24801901141150 158 24 24.9855629546809 -0.98556295468088 159 24 24.6157539109051 -0.615753910905134 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.667360977907146 0.665278044185708 0.332639022092854 11 0.882627431680766 0.234745136638468 0.117372568319234 12 0.815044557601717 0.369910884796565 0.184955442398283 13 0.727910098935921 0.544179802128158 0.272089901064079 14 0.626495802972272 0.747008394055456 0.373504197027728 15 0.566120607327706 0.867758785344589 0.433879392672294 16 0.468126731255751 0.936253462511502 0.531873268744249 17 0.377975272594961 0.755950545189922 0.622024727405039 18 0.299028110839056 0.598056221678112 0.700971889160944 19 0.271105134785659 0.542210269571317 0.728894865214341 20 0.431190666832706 0.862381333665412 0.568809333167294 21 0.360421640856411 0.720843281712822 0.639578359143589 22 0.326641172473848 0.653282344947696 0.673358827526152 23 0.265063604966092 0.530127209932184 0.734936395033908 24 0.206708530991929 0.413417061983858 0.793291469008071 25 0.156525729705042 0.313051459410084 0.843474270294958 26 0.153477477917775 0.306954955835550 0.846522522082225 27 0.126313790409779 0.252627580819558 0.873686209590221 28 0.0984160414402037 0.196832082880407 0.901583958559796 29 0.215751534946184 0.431503069892368 0.784248465053816 30 0.318666475512378 0.637332951024757 0.681333524487622 31 0.495536956058978 0.991073912117957 0.504463043941022 32 0.497898525315504 0.995797050631009 0.502101474684496 33 0.518517133347139 0.962965733305723 0.481482866652861 34 0.580942027412914 0.838115945174173 0.419057972587086 35 0.529177257844229 0.941645484311543 0.470822742155771 36 0.486997888929162 0.973995777858324 0.513002111070838 37 0.432644324740772 0.865288649481543 0.567355675259228 38 0.419641226316025 0.83928245263205 0.580358773683975 39 0.375271539142877 0.750543078285755 0.624728460857123 40 0.346523539296928 0.693047078593856 0.653476460703072 41 0.297347717664609 0.594695435329218 0.702652282335391 42 0.267778229598947 0.535556459197894 0.732221770401053 43 0.228713482707738 0.457426965415475 0.771286517292262 44 0.233634688349059 0.467269376698119 0.76636531165094 45 0.339671111746255 0.679342223492509 0.660328888253745 46 0.303159338430546 0.606318676861092 0.696840661569454 47 0.259026682962303 0.518053365924606 0.740973317037697 48 0.232665655432323 0.465331310864647 0.767334344567677 49 0.213919044938378 0.427838089876756 0.786080955061622 50 0.188572284528821 0.377144569057641 0.81142771547118 51 0.168968786724960 0.337937573449921 0.83103121327504 52 0.142372588712727 0.284745177425454 0.857627411287273 53 0.121146741749319 0.242293483498638 0.878853258250681 54 0.102302319441870 0.204604638883741 0.89769768055813 55 0.115320557742797 0.230641115485594 0.884679442257203 56 0.0980011599096147 0.196002319819229 0.901998840090385 57 0.127353177724174 0.254706355448348 0.872646822275826 58 0.128305768646930 0.256611537293861 0.87169423135307 59 0.162400118738880 0.324800237477759 0.83759988126112 60 0.135709401881264 0.271418803762528 0.864290598118736 61 0.11169288256294 0.22338576512588 0.88830711743706 62 0.177569042447071 0.355138084894141 0.822430957552929 63 0.431362113798148 0.862724227596297 0.568637886201852 64 0.4136908285648 0.8273816571296 0.5863091714352 65 0.395768987237999 0.791537974475998 0.604231012762001 66 0.583616429767779 0.832767140464442 0.416383570232221 67 0.552716942208569 0.894566115582862 0.447283057791431 68 0.577128830183909 0.845742339632182 0.422871169816091 69 0.582257997223764 0.835484005552473 0.417742002776236 70 0.58808004329838 0.82383991340324 0.41191995670162 71 0.554701213408912 0.890597573182176 0.445298786591088 72 0.564398297379662 0.871203405240676 0.435601702620338 73 0.64387289026425 0.712254219471499 0.356127109735750 74 0.622393451479182 0.755213097041636 0.377606548520818 75 0.628417271135854 0.743165457728293 0.371582728864147 76 0.617139952997445 0.765720094005111 0.382860047002555 77 0.616204893379555 0.76759021324089 0.383795106620445 78 0.575971116458307 0.848057767083385 0.424028883541693 79 0.749701943966494 0.500596112067013 0.250298056033506 80 0.800046198560187 0.399907602879625 0.199953801439813 81 0.900356903362721 0.199286193274558 0.0996430966372788 82 0.88054685836132 0.238906283277361 0.119453141638680 83 0.956560139525645 0.0868797209487105 0.0434398604743553 84 0.945460084372517 0.109079831254966 0.0545399156274828 85 0.931538640822981 0.136922718354037 0.0684613591770187 86 0.921859036626176 0.156281926747648 0.0781409633738238 87 0.905400733608073 0.189198532783855 0.0945992663919274 88 0.901365128956814 0.197269742086373 0.0986348710431864 89 0.879937233121763 0.240125533756474 0.120062766878237 90 0.855409846610792 0.289180306778417 0.144590153389208 91 0.831863766007233 0.336272467985534 0.168136233992767 92 0.907245023647143 0.185509952705715 0.0927549763528573 93 0.964498432373311 0.0710031352533778 0.0355015676266889 94 0.956999923750577 0.0860001524988458 0.0430000762494229 95 0.944537595644048 0.110924808711904 0.0554624043559522 96 0.93073350918427 0.138532981631461 0.0692664908157305 97 0.918836296934597 0.162327406130807 0.0811637030654034 98 0.900337345768944 0.199325308462113 0.0996626542310564 99 0.878368090541405 0.24326381891719 0.121631909458595 100 0.859303872820741 0.281392254358518 0.140696127179259 101 0.854452943095928 0.291094113808145 0.145547056904072 102 0.845524027576096 0.308951944847807 0.154475972423904 103 0.956200949867877 0.0875981002642452 0.0437990501321226 104 0.94748296546564 0.105034069068718 0.0525170345343591 105 0.939879673827892 0.120240652344216 0.0601203261721082 106 0.923581764542929 0.152836470914143 0.0764182354570714 107 0.941992440087715 0.116015119824570 0.0580075599122851 108 0.932732207823616 0.134535584352768 0.0672677921763839 109 0.914014315222112 0.171971369555776 0.085985684777888 110 0.929442148601935 0.141115702796130 0.0705578513980652 111 0.912536997909618 0.174926004180765 0.0874630020903823 112 0.913570182130401 0.172859635739198 0.0864298178695991 113 0.899359527596499 0.201280944807002 0.100640472403501 114 0.900510722989115 0.198978554021770 0.0994892770108849 115 0.941424690781391 0.117150618437217 0.0585753092186086 116 0.93973431901922 0.120531361961561 0.0602656809807805 117 0.930168101127397 0.139663797745206 0.0698318988726032 118 0.91158937849851 0.176821243002982 0.0884106215014908 119 0.922830225556402 0.154339548887196 0.077169774443598 120 0.921901636390081 0.156196727219838 0.0780983636099188 121 0.901138355428982 0.197723289142036 0.0988616445710179 122 0.901683378869523 0.196633242260954 0.0983166211304771 123 0.88225869716127 0.235482605677460 0.117741302838730 124 0.905739701003877 0.188520597992246 0.0942602989961232 125 0.877315623056737 0.245368753886525 0.122684376943263 126 0.84192353840785 0.316152923184301 0.158076461592151 127 0.830916755824925 0.338166488350149 0.169083244175075 128 0.78811733701752 0.423765325964960 0.211882662982480 129 0.78862974384603 0.422740512307939 0.211370256153970 130 0.778214521341099 0.443570957317801 0.221785478658901 131 0.806559869088251 0.386880261823497 0.193440130911749 132 0.756360700760065 0.48727859847987 0.243639299239935 133 0.699979767905974 0.600040464188052 0.300020232094026 134 0.714064011611768 0.571871976776464 0.285935988388232 135 0.653405300873577 0.693189398252845 0.346594699126423 136 0.741057455635575 0.517885088728851 0.258942544364425 137 0.693751057306632 0.612497885386737 0.306248942693368 138 0.653596279610249 0.692807440779502 0.346403720389751 139 0.57374322181139 0.85251355637722 0.42625677818861 140 0.525379793488492 0.949240413023017 0.474620206511508 141 0.471089704345162 0.942179408690325 0.528910295654838 142 0.465104023158177 0.930208046316355 0.534895976841823 143 0.402927838183914 0.805855676367828 0.597072161816086 144 0.312501176014207 0.625002352028414 0.687498823985793 145 0.228604961793762 0.457209923587524 0.771395038206238 146 0.382010303173662 0.764020606347323 0.617989696826338 147 0.269470504443929 0.538941008887859 0.73052949555607 148 0.330640092450667 0.661280184901334 0.669359907549333 149 0.425543663816575 0.85108732763315 0.574456336183425 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 4 0.0285714285714286 OK

Charts produced by software:

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Parameters (Session):

par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 7 ; 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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