Multiple Regression X1

*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, 28 Dec 2010 18:52:01 +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/28/t1293562202332oyb8raqrvdpz.htm/, Retrieved Tue, 28 Dec 2010 19:50:02 +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/28/t1293562202332oyb8raqrvdpz.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 «

621 0 587 0 655 0 517 0 646 0 657 0 382 0 345 0 625 0 654 0 606 0 510 0 614 0 647 0 580 0 614 0 636 0 388 0 356 0 639 0 753 0 611 0 639 0 630 0 586 0 695 0 552 0 619 0 681 0 421 0 307 0 754 0 690 0 644 0 643 0 608 0 651 0 691 0 627 0 634 0 731 0 475 0 337 0 803 0 722 0 590 0 724 0 627 0 696 0 825 0 677 0 656 0 785 0 412 0 352 0 839 0 729 0 696 0 641 0 695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 706 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 0 344 0 792 0 852 0 649 0 629 0 685 0 617 0 715 0 715 0 629 0 916 0 531 1 357 1 917 1 828 1 708 1 858 1 775 1 785 1 1006 1 789 1 734 1 906 1 532 1 387 1 991 1 841 1 892 1 782 1 813 1 793 1 978 1 775 1 797 1 946 1 594 1 438 1 1022 1 868 1 795 1

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 628.524752475248 + 145.199385455787X1[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) 628.524752475248 14.217859 44.2067 0 0 X1 145.199385455787 30.102799 4.8235 4e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.392182037649388 R-squared 0.153806750654826 Adjusted R-squared 0.147195865894317 F-TEST (value) 23.2656832219505 F-TEST (DF numerator) 1 F-TEST (DF denominator) 128 p-value 3.93801559650520e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 142.887712175676 Sum Squared Residuals 2613362.98122226 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 621 628.524752475246 -7.52475247524569 2 587 628.524752475247 -41.5247524752474 3 655 628.524752475248 26.4752475247525 4 517 628.524752475248 -111.524752475248 5 646 628.524752475248 17.4752475247525 6 657 628.524752475248 28.4752475247525 7 382 628.524752475248 -246.524752475248 8 345 628.524752475248 -283.524752475248 9 625 628.524752475248 -3.52475247524755 10 654 628.524752475248 25.4752475247525 11 606 628.524752475248 -22.5247524752475 12 510 628.524752475248 -118.524752475248 13 614 628.524752475248 -14.5247524752475 14 647 628.524752475248 18.4752475247525 15 580 628.524752475248 -48.5247524752476 16 614 628.524752475248 -14.5247524752475 17 636 628.524752475248 7.47524752475245 18 388 628.524752475248 -240.524752475248 19 356 628.524752475248 -272.524752475248 20 639 628.524752475248 10.4752475247525 21 753 628.524752475248 124.475247524752 22 611 628.524752475248 -17.5247524752475 23 639 628.524752475248 10.4752475247525 24 630 628.524752475248 1.47524752475245 25 586 628.524752475248 -42.5247524752476 26 695 628.524752475248 66.4752475247525 27 552 628.524752475248 -76.5247524752475 28 619 628.524752475248 -9.52475247524755 29 681 628.524752475248 52.4752475247524 30 421 628.524752475248 -207.524752475248 31 307 628.524752475248 -321.524752475248 32 754 628.524752475248 125.475247524752 33 690 628.524752475248 61.4752475247524 34 644 628.524752475248 15.4752475247525 35 643 628.524752475248 14.4752475247525 36 608 628.524752475248 -20.5247524752475 37 651 628.524752475248 22.4752475247525 38 691 628.524752475248 62.4752475247525 39 627 628.524752475248 -1.52475247524755 40 634 628.524752475248 5.47524752475245 41 731 628.524752475248 102.475247524752 42 475 628.524752475248 -153.524752475248 43 337 628.524752475248 -291.524752475248 44 803 628.524752475248 174.475247524752 45 722 628.524752475248 93.4752475247525 46 590 628.524752475248 -38.5247524752476 47 724 628.524752475248 95.4752475247525 48 627 628.524752475248 -1.52475247524755 49 696 628.524752475248 67.4752475247525 50 825 628.524752475248 196.475247524752 51 677 628.524752475248 48.4752475247524 52 656 628.524752475248 27.4752475247525 53 785 628.524752475248 156.475247524752 54 412 628.524752475248 -216.524752475248 55 352 628.524752475248 -276.524752475248 56 839 628.524752475248 210.475247524752 57 729 628.524752475248 100.475247524752 58 696 628.524752475248 67.4752475247525 59 641 628.524752475248 12.4752475247525 60 695 628.524752475248 66.4752475247525 61 638 628.524752475248 9.47524752475245 62 762 628.524752475248 133.475247524752 63 635 628.524752475248 6.47524752475245 64 721 628.524752475248 92.4752475247525 65 854 628.524752475248 225.475247524752 66 418 628.524752475248 -210.524752475248 67 367 628.524752475248 -261.524752475248 68 824 628.524752475248 195.475247524752 69 687 628.524752475248 58.4752475247524 70 601 628.524752475248 -27.5247524752475 71 676 628.524752475248 47.4752475247524 72 740 628.524752475248 111.475247524752 73 691 628.524752475248 62.4752475247525 74 683 628.524752475248 54.4752475247524 75 594 628.524752475248 -34.5247524752476 76 729 628.524752475248 100.475247524752 77 731 628.524752475248 102.475247524752 78 386 628.524752475248 -242.524752475248 79 331 628.524752475248 -297.524752475248 80 706 628.524752475248 77.4752475247525 81 715 628.524752475248 86.4752475247525 82 657 628.524752475248 28.4752475247525 83 653 628.524752475248 24.4752475247525 84 642 628.524752475248 13.4752475247525 85 643 628.524752475248 14.4752475247525 86 718 628.524752475248 89.4752475247525 87 654 628.524752475248 25.4752475247525 88 632 628.524752475248 3.47524752475245 89 731 628.524752475248 102.475247524752 90 392 628.524752475248 -236.524752475248 91 344 628.524752475248 -284.524752475248 92 792 628.524752475248 163.475247524752 93 852 628.524752475248 223.475247524752 94 649 628.524752475248 20.4752475247525 95 629 628.524752475248 0.47524752475245 96 685 628.524752475248 56.4752475247524 97 617 628.524752475248 -11.5247524752475 98 715 628.524752475248 86.4752475247525 99 715 628.524752475248 86.4752475247525 100 629 628.524752475248 0.47524752475245 101 916 628.524752475248 287.475247524752 102 531 773.724137931034 -242.724137931034 103 357 773.724137931034 -416.724137931034 104 917 773.724137931034 143.275862068966 105 828 773.724137931035 54.2758620689655 106 708 773.724137931034 -65.7241379310345 107 858 773.724137931035 84.2758620689655 108 775 773.724137931035 1.27586206896552 109 785 773.724137931035 11.2758620689655 110 1006 773.724137931034 232.275862068966 111 789 773.724137931035 15.2758620689655 112 734 773.724137931035 -39.7241379310345 113 906 773.724137931034 132.275862068966 114 532 773.724137931034 -241.724137931034 115 387 773.724137931034 -386.724137931034 116 991 773.724137931034 217.275862068966 117 841 773.724137931035 67.2758620689655 118 892 773.724137931035 118.275862068966 119 782 773.724137931035 8.27586206896552 120 813 773.724137931035 39.2758620689655 121 793 773.724137931035 19.2758620689655 122 978 773.724137931034 204.275862068966 123 775 773.724137931035 1.27586206896552 124 797 773.724137931035 23.2758620689655 125 946 773.724137931034 172.275862068966 126 594 773.724137931034 -179.724137931034 127 438 773.724137931035 -335.724137931035 128 1022 773.724137931034 248.275862068966 129 868 773.724137931035 94.2758620689655 130 795 773.724137931035 21.2758620689655 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.101967259796059 0.203934519592119 0.89803274020394 6 0.0481904091862635 0.096380818372527 0.951809590813737 7 0.285090922642108 0.570181845284215 0.714909077357892 8 0.497218641072876 0.994437282145752 0.502781358927124 9 0.40476542933056 0.80953085866112 0.59523457066944 10 0.340355818911244 0.680711637822487 0.659644181088756 11 0.252599571758748 0.505199143517495 0.747400428241252 12 0.193556460409365 0.38711292081873 0.806443539590635 13 0.138503420339819 0.277006840679638 0.86149657966018 14 0.105325037307872 0.210650074615744 0.894674962692128 15 0.0687785688913393 0.137557137782679 0.93122143110866 16 0.0450701565299002 0.0901403130598005 0.9549298434701 17 0.0305470819674404 0.0610941639348807 0.96945291803256 18 0.0610832640737716 0.122166528147543 0.938916735926228 19 0.124589446757307 0.249178893514613 0.875410553242693 20 0.099434362567026 0.198868725134052 0.900565637432974 21 0.132943886492660 0.265887772985320 0.86705611350734 22 0.0994670696266012 0.198934139253202 0.900532930373399 23 0.0764557155862519 0.152911431172504 0.923544284413748 24 0.0566009894565718 0.113201978913144 0.943399010543428 25 0.0393761488839641 0.0787522977679282 0.960623851116036 26 0.0354626984796741 0.0709253969593483 0.964537301520326 27 0.0250633889469848 0.0501267778939697 0.974936611053015 28 0.0171389626894795 0.034277925378959 0.98286103731052 29 0.014008979825059 0.028017959650118 0.985991020174941 30 0.0202232243806782 0.0404464487613564 0.979776775619322 31 0.0755915344328923 0.151183068865785 0.924408465567108 32 0.090489619384448 0.180979238768896 0.909510380615552 33 0.0803228938609034 0.160645787721807 0.919677106139097 34 0.0631086030879065 0.126217206175813 0.936891396912093 35 0.0488056224822818 0.0976112449645636 0.951194377517718 36 0.0358769803956430 0.0717539607912859 0.964123019604357 37 0.0273799303503834 0.0547598607007668 0.972620069649617 38 0.0231344512556504 0.0462689025113008 0.97686554874435 39 0.0165890037982222 0.0331780075964445 0.983410996201778 40 0.0118157527766461 0.0236315055532921 0.988184247223354 41 0.0116836588925859 0.0233673177851718 0.988316341107414 42 0.0118539030901095 0.0237078061802189 0.98814609690989 43 0.0349241558644654 0.0698483117289309 0.965075844135535 44 0.0503693043470406 0.100738608694081 0.94963069565296 45 0.0468160933763461 0.0936321867526921 0.953183906623654 46 0.0354806948663376 0.0709613897326752 0.964519305133662 47 0.0327776244908352 0.0655552489816704 0.967222375509165 48 0.0243494488790097 0.0486988977580193 0.97565055112099 49 0.0201192155366323 0.0402384310732646 0.979880784463368 50 0.0313018759823402 0.0626037519646803 0.96869812401766 51 0.0245530571519995 0.0491061143039989 0.975446942848 52 0.0183928495970397 0.0367856991940794 0.98160715040296 53 0.0214084000914462 0.0428168001828923 0.978591599908554 54 0.0321955829671425 0.064391165934285 0.967804417032857 55 0.0693499281267011 0.138699856253402 0.930650071873299 56 0.0979863984677395 0.195972796935479 0.90201360153226 57 0.0890023676137902 0.178004735227580 0.91099763238621 58 0.0749155632877815 0.149831126575563 0.925084436712219 59 0.0588384391468559 0.117676878293712 0.941161560853144 60 0.0484879631698764 0.0969759263397528 0.951512036830124 61 0.0371499260657483 0.0742998521314967 0.962850073934252 62 0.0364788483401324 0.0729576966802647 0.963521151659868 63 0.0275029658082947 0.0550059316165894 0.972497034191705 64 0.023320835788123 0.046641671576246 0.976679164211877 65 0.0364808015909070 0.0729616031818141 0.963519198409093 66 0.0508261183796412 0.101652236759282 0.949173881620359 67 0.0927298056914554 0.185459611382911 0.907270194308545 68 0.110894992812626 0.221789985625252 0.889105007187374 69 0.0919561860646452 0.183912372129290 0.908043813935355 70 0.0738756411582807 0.147751282316561 0.92612435884172 71 0.0591895699246266 0.118379139849253 0.940810430075373 72 0.052883502987658 0.105767005975316 0.947116497012342 73 0.0424351033637309 0.0848702067274618 0.95756489663627 74 0.0333123017866179 0.0666246035732358 0.966687698213382 75 0.0255284901015169 0.0510569802030338 0.974471509898483 76 0.0215869691760692 0.0431739383521383 0.97841303082393 77 0.0182861351781461 0.0365722703562923 0.981713864821854 78 0.0327167757014804 0.0654335514029607 0.96728322429852 79 0.0829135739718866 0.165827147943773 0.917086426028113 80 0.0684641705537883 0.136928341107577 0.931535829446212 81 0.0568225643628162 0.113645128725632 0.943177435637184 82 0.0438599401464551 0.0877198802929101 0.956140059853545 83 0.0333234273467227 0.0666468546934455 0.966676572653277 84 0.0249195869389600 0.0498391738779199 0.97508041306104 85 0.0183595459820243 0.0367190919640486 0.981640454017976 86 0.0144536324889842 0.0289072649779684 0.985546367511016 87 0.0103574020199093 0.0207148040398186 0.98964259798009 88 0.00731777775852073 0.0146355555170415 0.99268222224148 89 0.00575293002711743 0.0115058600542349 0.994247069972883 90 0.0121248860851501 0.0242497721703002 0.98787511391485 91 0.0418728150570935 0.083745630114187 0.958127184942906 92 0.0383532100349159 0.0767064200698317 0.961646789965084 93 0.0449372049591846 0.0898744099183693 0.955062795040815 94 0.0341207668393071 0.0682415336786142 0.965879233160693 95 0.026258800886467 0.052517601772934 0.973741199113533 96 0.0194050765201820 0.0388101530403641 0.980594923479818 97 0.0155101814116762 0.0310203628233524 0.984489818588324 98 0.0114448048370667 0.0228896096741333 0.988555195162933 99 0.00840066000170275 0.0168013200034055 0.991599339998297 100 0.00884720297452181 0.0176944059490436 0.991152797025478 101 0.00975062871119724 0.0195012574223945 0.990249371288803 102 0.0127874601430448 0.0255749202860896 0.987212539856955 103 0.0701954259288513 0.140390851857703 0.929804574071149 104 0.101520109710646 0.203040219421293 0.898479890289353 105 0.0874667892575287 0.174933578515057 0.912533210742471 106 0.0702053230403538 0.140410646080708 0.929794676959646 107 0.0589142952679325 0.117828590535865 0.941085704732068 108 0.0429103424695152 0.0858206849390305 0.957089657530485 109 0.0303712804017107 0.0607425608034214 0.96962871959829 110 0.0462834041467522 0.0925668082935044 0.953716595853248 111 0.0319480517602288 0.0638961035204576 0.968051948239771 112 0.0219848400703313 0.0439696801406626 0.978015159929669 113 0.0187491886843999 0.0374983773687998 0.9812508113156 114 0.0336780987736985 0.067356197547397 0.966321901226302 115 0.249661765337511 0.499323530675023 0.750338234662489 116 0.287547499153111 0.575094998306223 0.712452500846888 117 0.223954366465432 0.447908732930863 0.776045633534568 118 0.184600311178405 0.36920062235681 0.815399688821595 119 0.129977718902003 0.259955437804006 0.870022281097997 120 0.0864303368962711 0.172860673792542 0.913569663103729 121 0.0534545073456529 0.106909014691306 0.946545492654347 122 0.0606872603070071 0.121374520614014 0.939312739692993 123 0.0333489217738492 0.0666978435476984 0.96665107822615 124 0.0163510985933275 0.032702197186655 0.983648901406672 125 0.0151742483555465 0.030348496711093 0.984825751644454 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 34 0.28099173553719 NOK 10% type I error level 71 0.586776859504132 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/10ihng1293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/10ihng1293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/1tyq41293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/1tyq41293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/24qq71293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/24qq71293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/34qq71293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/34qq71293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/44qq71293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/44qq71293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/5xzps1293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/5xzps1293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/6xzps1293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/6xzps1293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/778od1293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/778od1293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/878od1293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/878od1293562311.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/9ihng1293562311.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562202332oyb8raqrvdpz/9ihng1293562311.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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