Case - Multiple Regression 1

*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: Sun, 27 Dec 2009 12:53:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka.htm/, Retrieved Sun, 27 Dec 2009 20:56:57 +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/2009/Dec/27/t1261943805vx1rr1uwnbv3vka.htm/}, year = {2009}, } @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 = {2009}, 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 «

11881.4 423.4 10374.2 404.1 13828 500 13490.5 472.6 13092.2 496.1 13184.4 562 12398.4 434.8 13882.3 538.2 15861.5 577.6 13286.1 518.1 15634.9 625.2 14211 561.2 13646.8 523.3 12224.6 536.1 15916.4 607.3 16535.9 637.3 15796 606.9 14418.6 652.9 15044.5 617.2 14944.2 670.4 16754.8 729.9 14254 677.2 15454.9 710 15644.8 844.3 14568.3 748.2 12520.2 653.9 14803 742.6 15873.2 854.2 14755.3 808.4 12875.1 1819 14291.1 1936.5 14205.3 1966.1 15859.4 2083.1 15258.9 1620.1 15498.6 1527.6 15106.5 1795 15023.6 1685.1 12083 1851.8 15761.3 2164.4 16943 1981.8 15070.3 1726.5 13659.6 2144.6 14768.9 1758.2 14725.1 1672.9 15998.1 1837.3 15370.6 1596.1 14956.9 1446 15469.7 1898.4 15101.8 1964.1 11703.7 1755.9 16283.6 2255.3 16726.5 1881.2 14968.9 2117.9 14861 1656.5 14583.3 1544.1 15305.8 2098.9 17903.9 2133.3 16379.4 1963.5 15420.3 1801.2 17870.5 2365.4 15912.8 1936.5 13866.5 1667.6 17823.2 1983.5 17872 2058.6 17420.4 2448.3 16704.4 1858.1 15991.2 1625.4 16583.6 213 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 12086.2267705685 + 2.46058056232764X[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) 12086.2267705685 416.228981 29.0374 0 0 X 2.46058056232764 0.202482 12.1521 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.745550286064503 R-squared 0.555845229050863 Adjusted R-squared 0.552081205568243 F-TEST (value) 147.673156561709 F-TEST (DF numerator) 1 F-TEST (DF denominator) 118 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1820.99706221618 Sum Squared Residuals 391291575.470797 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11881.4 13128.0365806581 -1246.63658065810 2 10374.2 13080.5473758051 -2706.34737580511 3 13828 13316.5170517323 511.482948267663 4 13490.5 13249.0971443246 241.40285567544 5 13092.2 13306.9207875393 -214.720787539259 6 13184.4 13469.0730465967 -284.673046596651 7 12398.4 13156.0871990686 -757.687199068575 8 13882.3 13410.5112292133 471.788770786746 9 15861.5 13507.4581033690 2354.04189663104 10 13286.1 13361.0535599105 -74.9535599104676 11 15634.9 13624.5817381358 2010.31826186424 12 14211 13467.1045821468 743.89541785321 13 13646.8 13373.8485788346 272.951421165428 14 12224.6 13405.3440100324 -1180.74401003237 15 15916.4 13580.5373460701 2335.86265392991 16 16535.9 13654.3547629399 2881.54523706008 17 15796 13579.5531138452 2216.44688615484 18 14418.6 13692.7398197122 725.860180287767 19 15044.5 13604.8970936371 1439.60290636286 20 14944.2 13735.7999795530 1208.40002044703 21 16754.8 13882.2045230115 2872.59547698854 22 14254 13752.5319273768 501.468072623204 23 15454.9 13833.2389698211 1621.66103017886 24 15644.8 14163.6949393417 1481.10506065825 25 14568.3 13927.2331473021 641.06685269794 26 12520.2 13695.2004002746 -1175.00040027456 27 14803 13913.4538961530 889.546103846976 28 15873.2 14188.0546869088 1685.14531309121 29 14755.3 14075.3600971542 679.939902845817 30 12875.1 16562.0228134425 -3686.9228134425 31 14291.1 16851.141029516 -2560.04102951600 32 14205.3 16923.9742141609 -2718.67421416090 33 15859.4 17211.8621399532 -1352.46213995323 34 15258.9 16072.6133395955 -813.713339595531 35 15498.6 15845.0096375802 -346.409637580223 36 15106.5 16502.9688799466 -1396.46887994664 37 15023.6 16232.5510761468 -1208.95107614683 38 12083 16642.7298558868 -4559.72985588685 39 15761.3 17411.9073396705 -1650.60733967047 40 16943 16962.6053289894 -19.6053289894398 41 15070.3 16334.4191114272 -1264.11911142719 42 13659.6 17363.1878445364 -3703.58784453638 43 14768.9 16412.4195152530 -1643.51951525298 44 14725.1 16202.5319932864 -1477.43199328643 45 15998.1 16607.0514377331 -608.951437733095 46 15370.6 16013.5594060997 -642.959406099667 47 14956.9 15644.2262636943 -687.326263694289 48 15469.7 16757.3929100913 -1287.69291009131 49 15101.8 16919.0530530362 -1817.25305303624 50 11703.7 16406.7601799596 -4703.06017995962 51 16283.6 17635.5741127861 -1351.97411278605 52 16726.5 16715.0709244193 11.4290755807209 53 14968.9 17297.4903435222 -2328.59034352223 54 14861 16162.1784720643 -1301.17847206426 55 14583.3 15885.6092168586 -1302.30921685863 56 15305.8 17250.739312838 -1944.93931283801 57 17903.9 17335.3832841821 568.516715817923 58 16379.4 16917.5767046988 -538.176704698844 59 15420.3 16518.2244794331 -1097.92447943307 60 17870.5 17906.4840326983 -35.9840326983246 61 15912.8 16851.141029516 -938.341029515998 62 13866.5 16189.4909163061 -2322.99091630609 63 17823.2 16966.7883159454 856.411684054604 64 17872 17151.5779161762 720.422083823797 65 17420.4 18110.4661613153 -690.066161315285 66 16704.4 16658.2315134295 46.1684865704913 67 15991.2 16085.6544165759 -94.4544165758672 68 16583.6 17328.7397166638 -745.139716663795 69 19123.5 18276.3092912162 847.190708783831 70 17838.7 17573.8135406716 264.886459328374 71 17209.4 17221.2123460901 -11.8123460900742 72 18586.5 17585.6243273708 1000.8756726292 73 16258.1 17253.9380675690 -995.838067569032 74 15141.6 17717.5114455116 -2575.91144551156 75 19202.1 18213.0723707643 989.02762923565 76 17746.5 18419.0229638312 -672.522963831172 77 19090.1 18345.4516050176 744.648394982422 78 18040.3 17018.9526238667 1021.34737613326 79 17515.5 17967.0143145316 -451.514314531584 80 17751.8 17840.0483575155 -88.2483575154786 81 21072.4 18790.0785126302 2282.32148736982 82 17170 17727.1077097046 -557.107709704639 83 19439.5 17957.1719922823 1482.32800771773 84 19795.4 18183.2993459602 1612.10065403982 85 17574.9 17836.6035447282 -261.703544728217 86 16165.4 18496.2851934883 -2330.88519348826 87 19464.6 18387.2814745771 1077.31852542285 88 19932.1 19072.5531611854 859.546838814603 89 19961.2 18009.3363002036 1951.86369979638 90 17343.4 17217.0293591341 126.370640865884 91 18924.2 18817.3909568720 106.809043127983 92 18574.1 18972.6535903549 -398.553590354893 93 21350.6 19598.8713434673 1751.72865653272 94 18594.6 18003.9230229665 590.6769770335 95 19823.1 18168.5358625862 1654.56413741378 96 20844.4 18796.9681382047 2047.43186179530 97 19640.2 18952.9689458563 687.23105414373 98 17735.4 17955.6956439449 -220.295643944876 99 19813.6 19976.3244017283 -162.724401728339 100 22160 18743.5735400022 3416.42645999781 101 20664.3 20743.5334210621 -79.2334210620987 102 17877.4 16896.4157118628 980.984288137175 103 20906.5 18445.1051177918 2461.39488220815 104 21164.1 18325.7669605190 2838.33303948104 105 21374.4 18695.1001029243 2679.29989707567 106 22952.3 19138.2506621995 3814.04933780046 107 21343.5 17589.5612562705 3753.93874372948 108 23899.3 19307.7846629439 4591.51533705608 109 22392.9 18652.5320591961 3740.36794080394 110 18274.1 17920.7553999598 353.344600040174 111 22786.7 19876.1787728416 2910.5212271584 112 22321.5 19190.4149701209 3131.08502987911 113 17842.2 19744.0455966446 -1901.84559664461 114 16373.5 18658.9295686581 -2285.42956865812 115 15993.8 18071.8350464867 -2078.03504648674 116 16446.1 19006.1174860025 -2560.01748600255 117 17729 19703.4460173662 -1974.4460173662 118 16643 19130.6228624563 -2487.62286245633 119 16196.7 18501.6984707254 -2304.99847072538 120 18252.1 19129.6386302314 -877.538630231397 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0420496283266551 0.0840992566533102 0.957950371673345 6 0.0902862707722315 0.180572541544463 0.909713729227769 7 0.0417000311001006 0.0834000622002012 0.9582999688999 8 0.0164525831009072 0.0329051662018143 0.983547416899093 9 0.0157599611122236 0.0315199222244473 0.984240038887776 10 0.00697310443316586 0.0139462088663317 0.993026895566834 11 0.00284073232367573 0.00568146464735146 0.997159267676324 12 0.00110644363156852 0.00221288726313704 0.998893556368431 13 0.00038961919098633 0.00077923838197266 0.999610380809014 14 0.00120388683036931 0.00240777366073862 0.99879611316963 15 0.000707909842807252 0.00141581968561450 0.999292090157193 16 0.0004009945624293 0.0008019891248586 0.99959900543757 17 0.000193873804658484 0.000387747609316969 0.999806126195341 18 0.000625466772549588 0.00125093354509918 0.99937453322745 19 0.000311895719684362 0.000623791439368724 0.999688104280316 20 0.000340958993398081 0.000681917986796163 0.999659041006602 21 0.000214892802091942 0.000429785604183885 0.999785107197908 22 0.000464230854352586 0.000928461708705172 0.999535769145647 23 0.000373476914852201 0.000746953829704403 0.999626523085148 24 0.00130692352274221 0.00261384704548442 0.998693076477258 25 0.00175846227376867 0.00351692454753734 0.998241537726231 26 0.00484122234766101 0.00968244469532202 0.995158777652339 27 0.00425192695547729 0.00850385391095457 0.995748073044523 28 0.00432243219065414 0.00864486438130828 0.995677567809346 29 0.00526630643955707 0.0105326128791141 0.994733693560443 30 0.222408076504546 0.444816153009091 0.777591923495454 31 0.200291968303061 0.400583936606123 0.799708031696939 32 0.177161365717836 0.354322731435672 0.822838634282164 33 0.151410161256871 0.302820322513742 0.848589838743129 34 0.120345887933310 0.240691775866621 0.87965411206669 35 0.0983008842067757 0.196601768413551 0.901699115793224 36 0.0750044543108634 0.150008908621727 0.924995545689137 37 0.0560005550339109 0.112001110067822 0.94399944496609 38 0.119838978522801 0.239677957045602 0.880161021477199 39 0.102469795214209 0.204939590428419 0.89753020478579 40 0.105135025510566 0.210270051021132 0.894864974489434 41 0.0815745003782725 0.163149000756545 0.918425499621727 42 0.102991727989408 0.205983455978817 0.897008272010592 43 0.0816300942062363 0.163260188412473 0.918369905793764 44 0.0631389762538534 0.126277952507707 0.936861023746147 45 0.0524025292637302 0.104805058527460 0.94759747073627 46 0.0402124798906544 0.0804249597813087 0.959787520109346 47 0.0299100119103915 0.059820023820783 0.97008998808961 48 0.0224687681962985 0.044937536392597 0.977531231803701 49 0.0172942497410687 0.0345884994821375 0.982705750258931 50 0.0601319307119548 0.120263861423910 0.939868069288045 51 0.0542427459859444 0.108485491971889 0.945757254014056 52 0.0516750805613612 0.103350161122722 0.948324919438639 53 0.0479127636031398 0.0958255272062797 0.95208723639686 54 0.0370331013591714 0.0740662027183428 0.962966898640829 55 0.0283435796937381 0.0566871593874762 0.971656420306262 56 0.0249278679152145 0.0498557358304291 0.975072132084785 57 0.0327635338655104 0.0655270677310208 0.96723646613449 58 0.0271738841939620 0.0543477683879241 0.972826115806038 59 0.0209777575320431 0.0419555150640862 0.979022242467957 60 0.0227798798653588 0.0455597597307177 0.977220120134641 61 0.0178155762021353 0.0356311524042705 0.982184423797865 62 0.0194545741294543 0.0389091482589085 0.980545425870546 63 0.0224291110808275 0.0448582221616550 0.977570888919173 64 0.0242503007153693 0.0485006014307386 0.975749699284631 65 0.0216043367641358 0.0432086735282715 0.978395663235864 66 0.0174861624048739 0.0349723248097479 0.982513837595126 67 0.0131168688044708 0.0262337376089415 0.98688313119553 68 0.0104725947080618 0.0209451894161236 0.989527405291938 69 0.0130979655311015 0.026195931062203 0.986902034468899 70 0.0114744205647656 0.0229488411295313 0.988525579435234 71 0.00909484892979021 0.0181896978595804 0.99090515107021 72 0.00949754088475706 0.0189950817695141 0.990502459115243 73 0.0075908789457202 0.0151817578914404 0.99240912105428 74 0.0110402444518314 0.0220804889036628 0.988959755548169 75 0.0119413210962473 0.0238826421924946 0.988058678903753 76 0.00990657766960745 0.0198131553392149 0.990093422330393 77 0.0094342659098337 0.0188685318196674 0.990565734090166 78 0.00824601468935766 0.0164920293787153 0.991753985310642 79 0.00647177107132915 0.0129435421426583 0.993528228928671 80 0.00499045138230057 0.00998090276460114 0.9950095486177 81 0.00895225797161268 0.0179045159432254 0.991047742028387 82 0.00710311064432879 0.0142062212886576 0.992896889355671 83 0.00695603061972357 0.0139120612394471 0.993043969380276 84 0.0070577600509123 0.0141155201018246 0.992942239949088 85 0.00528087865820911 0.0105617573164182 0.99471912134179 86 0.00783899894494346 0.0156779978898869 0.992161001055057 87 0.00656017123720367 0.0131203424744073 0.993439828762796 88 0.00528565580345425 0.0105713116069085 0.994714344196546 89 0.00539111964494817 0.0107822392898963 0.994608880355052 90 0.00392053938236959 0.00784107876473918 0.99607946061763 91 0.00273892144831777 0.00547784289663555 0.997261078551682 92 0.00195535417679220 0.00391070835358441 0.998044645823208 93 0.00196111548541044 0.00392223097082089 0.99803888451459 94 0.00132002812771763 0.00264005625543527 0.998679971872282 95 0.00105577268260157 0.00211154536520314 0.998944227317398 96 0.00102073263991634 0.00204146527983269 0.998979267360084 97 0.000644885791967018 0.00128977158393404 0.999355114208033 98 0.000436082610474958 0.000872165220949916 0.999563917389525 99 0.000252536658638809 0.000505073317277617 0.999747463341361 100 0.00055784251705651 0.00111568503411302 0.999442157482944 101 0.000310413728266265 0.000620827456532531 0.999689586271734 102 0.0001819503089903 0.0003639006179806 0.99981804969101 103 0.000176451860829976 0.000352903721659952 0.99982354813917 104 0.000218116576947568 0.000436233153895136 0.999781883423052 105 0.000258409254488234 0.000516818508976469 0.999741590745512 106 0.000893061542284856 0.00178612308456971 0.999106938457715 107 0.00380832223128036 0.00761664446256071 0.99619167776872 108 0.0296669380490479 0.0593338760980958 0.970333061950952 109 0.154047038272177 0.308094076544354 0.845952961727823 110 0.189925864621717 0.379851729243434 0.810074135378283 111 0.341866052901947 0.683732105803895 0.658133947098053 112 0.996431880857547 0.00713623828490533 0.00356811914245266 113 0.988371402557704 0.0232571948845928 0.0116285974422964 114 0.965826894900512 0.0683462101989753 0.0341731050994877 115 0.906427893701437 0.187144212597127 0.0935721062985634 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 38 0.342342342342342 NOK 5% type I error level 76 0.684684684684685 NOK 10% type I error level 87 0.783783783783784 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/10ifgh1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/10ifgh1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/1kui51261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/1kui51261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/2eu0d1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/2eu0d1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/3eqvr1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/3eqvr1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/4prry1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/4prry1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/5tn8z1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/5tn8z1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/6puxu1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/6puxu1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/762at1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/762at1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/8me2y1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/8me2y1261943629.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/99thb1261943629.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/27/t1261943805vx1rr1uwnbv3vka/99thb1261943629.ps (open in new window)

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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