statistiek Multiple Regression + lineaire trend

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 18 Dec 2010 19:32:07 +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/t1292700637rbzljlk8jxl1cxx.htm/, Retrieved Sat, 18 Dec 2010 20:30:48 +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/t1292700637rbzljlk8jxl1cxx.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

6.5 8.9 -0.6 9 6.3 8.4 1.1 11 5.9 8.1 1.4 13 5.5 8.3 1.4 12 5.2 8.1 1.3 13 4.9 8 1.4 15 5.4 8.7 -0.1 13 5.8 9.2 1.8 16 5.7 9 1.5 10 5.6 8.9 1.5 14 5.5 8.5 1.4 14 5.4 8.1 1.6 15 5.4 7.5 1.6 13 5.4 7.1 1.6 8 5.5 6.9 1.4 7 5.8 7.1 1.7 3 5.7 7 1.8 3 5.4 6.7 1.9 4 5.6 7 2.2 4 5.8 7.3 2.1 0 6.2 7.7 2.4 -4 6.8 8.4 2.6 -14 6.7 8.4 2.8 -18 6.7 8.8 2.7 -8 6.4 9.1 2.6 -1 6.3 9 2.9 1 6.3 8.6 2.8 2 6.4 7.9 2.2 0 6.3 7.7 2.2 1 6 7.8 2.2 0 6.3 9.2 2 -1 6.3 9.4 2 -3 6.6 9.2 1.7 -3 7.5 8.7 1.4 -3 7.8 8.4 1.3 -4 7.9 8.6 1.4 -8 7.8 9 1.3 -9 7.6 9.1 1.3 -13 7.5 8.7 1.4 -18 7.6 8.2 2 -11 7.5 7.9 1.7 -9 7.3 7.9 1.8 -10 7.6 9.1 1.7 -13 7.5 9.4 1.6 -11 7.6 9.4 1.7 -5 7.9 9.1 1.9 -15 7.9 9 1.8 -6 8.1 9.3 1.7 -6 8.2 9.9 1.6 -3 8 9.8 1.8 -1 7.5 9.3 1.6 -3 6.8 8.3 1.5 -4 6.5 8 1.5 -6 6.6 8.5 1.3 0 7.6 10.4 1.4 -4 8 11.1 1.4 -2 8.1 10.9 1.3 -2 7.7 10 1.3 -6 7.5 9.2 1.2 -7 7.6 9.2 1.1 -6 7.8 9.5 1.4 -6 7.8 9.6 1.2 -3 7.8 9.5 1.5 -2 7.5 9.1 1.1 -5 7.5 8.9 1.3 -11 7.1 9 1.5 -1 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Mannen[t] = + 3.51184532722517 + 0.424759546585032Vrouwen[t] -0.431370175281263Inflatie[t] -0.0540453662063982Consumvertr[t] + 0.00511209506842643t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 3.51184532722517 0.546731 6.4234 0 0 Vrouwen 0.424759546585032 0.052987 8.0163 0 0 Inflatie -0.431370175281263 0.093452 -4.6159 1e-05 5e-06 Consumvertr -0.0540453662063982 0.006619 -8.1651 0 0 t 0.00511209506842643 0.001651 3.0959 0.002465 0.001232 Multiple Linear Regression - Regression Statistics Multiple R 0.842249326263617 R-squared 0.709383927591517 Adjusted R-squared 0.699275542464266 F-TEST (value) 70.1777701048472 F-TEST (DF numerator) 4 F-TEST (DF denominator) 115 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.473901715520587 Sum Squared Residuals 25.8270261369358 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.5 7.06973119621155 -0.569731196211554 2 6.3 6.02104348759652 0.278956512403478 3 5.9 5.66122593369226 0.238774066307739 4 5.5 5.8053353042841 -0.305335304284093 5 5.2 5.71458714135724 -0.514587141357239 6 4.9 5.52599553182624 -0.62599553182624 7 5.4 6.58358530483888 -1.18358530483888 8 5.8 5.81933774154623 -0.0193377415462284 9 5.7 6.19318117712042 -0.493181177120417 10 5.6 5.93963585270475 -0.339635852704748 11 5.5 5.81798114666729 -0.317981146667287 12 5.4 5.51287002183905 -0.112870021839050 13 5.4 5.37121712136925 0.0287828786307469 14 5.4 5.47665222883566 -0.0766522288356578 15 5.5 5.53713181584973 -0.0371318158497295 16 5.8 5.71396623247638 0.0860337675236239 17 5.7 5.63346535535817 0.0665346446418273 18 5.4 5.41396720271657 -0.0139672027165651 19 5.6 5.41709610917612 0.182903890823877 20 5.8 5.80895455057378 -0.00895455057377787 21 6.2 6.07074087651743 0.129259123482569 22 6.8 6.82736428120311 -0.0273642812031101 23 6.7 6.96238380604088 -0.262383806040876 24 6.7 6.64008307520746 0.0599169247925401 25 6.4 6.43744248833473 -0.037442488334734 26 6.3 6.16257684374748 0.137423156252517 27 6.3 5.98687677150362 0.313123228496376 28 6.4 6.06157002154408 0.338429978455918 29 6.3 5.9276848410891 0.372315158910896 30 6 6.02931825702243 -0.0293182570224317 31 6.3 6.76941311857255 -0.469413118572554 32 6.3 6.96756785537078 -0.667567855370784 33 6.6 7.01713909370658 -0.417139093706582 34 7.5 6.93928246806687 0.560717531933129 35 7.8 6.91414908289431 0.885850917105687 36 7.9 7.17725753457721 0.722742465422788 37 7.8 7.44945583201418 0.350544167985824 38 7.6 7.7132253465667 -0.113225346566699 39 7.5 7.77552343650498 -0.275523436504977 40 7.6 6.93111608966734 0.668883910332658 41 7.5 6.83012064093184 0.669879359068159 42 7.3 6.84614108467854 0.45385891532146 43 7.6 7.56623775179633 0.0337622482036743 44 7.5 7.63382399595559 -0.133823995955591 45 7.6 7.2715268762575 0.328473123742497 46 7.9 7.60339073435815 0.296609265641852 47 7.9 7.12275559643861 0.777244403561386 48 8.1 7.29843257301068 0.801567426989323 49 8.2 7.43940131493905 0.760598685060946 50 8 7.20767268787993 0.792327312120072 51 7.5 7.19476977712489 0.305230222875112 52 6.8 6.8723047093428 -0.0723047093428067 53 6.5 6.85807967284852 -0.358079672848520 54 6.6 6.83757337902732 -0.237573379027325 55 7.6 7.82277305990478 -0.222773059904780 56 8 8.01712610516993 -0.0171261051699311 57 8.1 7.98042330844948 0.119576691550522 58 7.7 7.81943327641697 -0.119433276416968 59 7.5 7.5819201179519 -0.0819201179518932 60 7.6 7.57612386434205 0.0238761356579520 61 7.8 7.5792527708016 0.220747229198395 62 7.8 7.55097875696559 0.249021243034407 63 7.8 7.33015847858474 0.469841521415261 64 7.5 7.50005092375085 -5.09237508521318e-05 65 7.5 7.65820927168441 -0.158209271684409 66 7.1 7.61952328635509 -0.519523286355086 67 7.5 8.26441895277955 -0.764418952779553 68 7.5 8.1710265383742 -0.671026538374209 69 7.6 8.39298116113785 -0.792981161137851 70 7.7 7.73269129596062 -0.0326912959606161 71 7.7 7.5788079210733 0.121192078926699 72 7.9 7.36707748844651 0.532922511553487 73 8.1 7.4573061785166 0.642693821483393 74 8.2 7.3007785521508 0.899221447849199 75 8.2 7.51248588910579 0.687514110894206 76 8.2 7.20605263853831 0.993947361461689 77 7.9 7.36239248354766 0.537607516452341 78 7.3 7.10818609626237 0.191813903737633 79 6.9 7.36683179354257 -0.466831793542566 80 6.6 7.50003281545613 -0.900032815456126 81 6.7 7.37705598367942 -0.67705598367942 82 6.9 7.08301789321412 -0.183017893214115 83 7 7.05788450804156 -0.0578845080415568 84 7.1 7.50626788143944 -0.406267881439441 85 7.2 7.17553836772158 0.0244616322784173 86 7.1 7.02942271284909 0.070577287150913 87 6.9 7.01321448774593 -0.113214487745930 88 7 6.89866643885367 0.101333561146335 89 6.8 6.77701173281621 0.0229882671837939 90 6.4 6.71006345585477 -0.310063455854767 91 6.7 6.82260522046637 -0.122605220466367 92 6.6 6.71119780023756 -0.111197800237556 93 6.4 6.63268011172822 -0.232680111728221 94 6.3 6.53928769732288 -0.239287697322878 95 6.2 6.87958033830797 -0.679580338307965 96 6.5 6.58157587062492 -0.0815758706249231 97 6.8 6.60916572591952 0.190834274080483 98 6.8 6.32471385839324 0.475286141606762 99 6.4 6.07430916264102 0.325690837358978 100 6.1 6.34072292867204 -0.240722928672038 101 5.8 6.19708683959337 -0.397086839593372 102 6.1 6.35078243312423 -0.250782433124230 103 7.2 7.01617267116599 0.183827328834007 104 7.3 7.08243678958601 0.217563210413987 105 6.9 6.7664173160795 0.133582683920496 106 6.1 6.99085150463698 -0.890851504636977 107 5.8 7.18256064715963 -1.38256064715963 108 6.2 7.56351073987902 -1.36351073987902 109 7.1 7.7264608648486 -0.626460864848601 110 7.7 7.86081932681674 -0.160819326816744 111 8 7.86725354762442 0.132746452375583 112 7.8 7.38000812974465 0.419991870255351 113 7.4 7.18249136014425 0.217508639855754 114 7.4 7.30412297050991 0.0958770294900898 115 7.7 7.93744922538648 -0.237449225386482 116 7.8 7.74571698719203 0.0542830128079709 117 7.8 7.49465122857019 0.30534877142981 118 8 7.429025077348 0.570974922652003 119 8.1 7.32670750287325 0.773292497126749 120 8.4 7.81508726513581 0.584912734864194 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.107879455448015 0.215758910896029 0.892120544551985 9 0.0635432549429895 0.127086509885979 0.93645674505701 10 0.0641880504319815 0.128376100863963 0.935811949568018 11 0.157160100198054 0.314320200396108 0.842839899801946 12 0.237719457591210 0.475438915182419 0.76228054240879 13 0.227213517896932 0.454427035793864 0.772786482103068 14 0.156382312267814 0.312764624535629 0.843617687732186 15 0.105080934041066 0.210161868082133 0.894919065958934 16 0.0665690861852334 0.133138172370467 0.933430913814767 17 0.0411245832880739 0.0822491665761479 0.958875416711926 18 0.0265328424135454 0.0530656848270908 0.973467157586455 19 0.0151697819157403 0.0303395638314806 0.98483021808426 20 0.0095562436310046 0.0191124872620092 0.990443756368995 21 0.00529401021730387 0.0105880204346077 0.994705989782696 22 0.00357607923910717 0.00715215847821433 0.996423920760893 23 0.00337006593863634 0.00674013187727268 0.996629934061364 24 0.00245676647646566 0.00491353295293131 0.997543233523534 25 0.0016106296878035 0.003221259375607 0.998389370312196 26 0.00103301883327683 0.00206603766655366 0.998966981166723 27 0.00086626311284255 0.0017325262256851 0.999133736887157 28 0.000923581988004788 0.00184716397600958 0.999076418011995 29 0.000736259502936229 0.00147251900587246 0.999263740497064 30 0.000425730664088876 0.000851461328177752 0.999574269335911 31 0.000362958527921033 0.000725917055842067 0.999637041472079 32 0.000423844731382511 0.000847689462765021 0.999576155268618 33 0.000282700623550093 0.000565401247100186 0.99971729937645 34 0.00429017464551027 0.00858034929102054 0.99570982535449 35 0.0278337597774432 0.0556675195548864 0.972166240222557 36 0.0427285468921628 0.0854570937843256 0.957271453107837 37 0.0334267493827452 0.0668534987654904 0.966573250617255 38 0.0260730971294723 0.0521461942589445 0.973926902870528 39 0.0251390003380828 0.0502780006761657 0.974860999661917 40 0.0247203743611432 0.0494407487222863 0.975279625638857 41 0.0214005318509492 0.0428010637018984 0.97859946814905 42 0.0157256327034959 0.0314512654069918 0.984274367296504 43 0.0113896486463379 0.0227792972926759 0.988610351353662 44 0.00899880357962838 0.0179976071592568 0.991001196420372 45 0.00640687633435754 0.0128137526687151 0.993593123665642 46 0.00482690674604272 0.00965381349208544 0.995173093253957 47 0.00658802623578987 0.0131760524715797 0.99341197376421 48 0.0102192376291713 0.0204384752583426 0.989780762370829 49 0.0143075500654408 0.0286151001308816 0.98569244993456 50 0.0208268689522337 0.0416537379044675 0.979173131047766 51 0.0209445054915973 0.0418890109831947 0.979055494508403 52 0.0375663796974661 0.0751327593949321 0.962433620302534 53 0.0840210559219864 0.168042111843973 0.915978944078014 54 0.107421808367256 0.214843616734512 0.892578191632744 55 0.101601194452958 0.203202388905916 0.898398805547042 56 0.0824165060763141 0.164833012152628 0.917583493923686 57 0.0664239157429601 0.132847831485920 0.93357608425704 58 0.0567982969024378 0.113596593804876 0.943201703097562 59 0.0485761121812084 0.0971522243624169 0.951423887818792 60 0.038123331818163 0.076246663636326 0.961876668181837 61 0.0310067291578798 0.0620134583157595 0.96899327084212 62 0.0239252456612378 0.0478504913224756 0.976074754338762 63 0.0232674064296305 0.046534812859261 0.97673259357037 64 0.0183911255084545 0.036782251016909 0.981608874491545 65 0.0170552705912858 0.0341105411825716 0.982944729408714 66 0.0261519928672272 0.0523039857344545 0.973848007132773 67 0.0484660642200261 0.0969321284400522 0.951533935779974 68 0.0668951266039352 0.133790253207870 0.933104873396065 69 0.111063181170264 0.222126362340527 0.888936818829736 70 0.0888213214350519 0.177642642870104 0.911178678564948 71 0.0695412917533678 0.139082583506736 0.930458708246632 72 0.0714198668764713 0.142839733752943 0.928580133123529 73 0.0733384609226863 0.146676921845373 0.926661539077314 74 0.132994231885458 0.265988463770917 0.867005768114542 75 0.177221393462785 0.354442786925569 0.822778606537215 76 0.468656715725288 0.937313431450576 0.531343284274712 77 0.723925989634934 0.552148020730133 0.276074010365066 78 0.817716984129412 0.364566031741175 0.182283015870588 79 0.83786364871154 0.324272702576921 0.162136351288460 80 0.903182651801079 0.193634696397843 0.0968173481989214 81 0.9180739021301 0.163852195739800 0.0819260978698998 82 0.898647782385862 0.202704435228276 0.101352217614138 83 0.874837027078193 0.250325945843615 0.125162972921807 84 0.873529039470195 0.25294192105961 0.126470960529805 85 0.860122880978352 0.279754238043295 0.139877119021648 86 0.83778702900701 0.324425941985981 0.162212970992990 87 0.809777172917662 0.380445654164676 0.190222827082338 88 0.773972759004977 0.452054481990046 0.226027240995023 89 0.729374196934483 0.541251606131034 0.270625803065517 90 0.695955591316622 0.608088817366756 0.304044408683378 91 0.643957677801542 0.712084644396915 0.356042322198458 92 0.591563572971027 0.816872854057947 0.408436427028973 93 0.536054893324444 0.927890213351111 0.463945106675556 94 0.489682497451089 0.979364994902178 0.510317502548911 95 0.50952662834296 0.98094674331408 0.49047337165704 96 0.448102430753173 0.896204861506346 0.551897569246827 97 0.391442467319564 0.782884934639127 0.608557532680436 98 0.372894404472233 0.745788808944466 0.627105595527767 99 0.331536362812071 0.663072725624142 0.668463637187929 100 0.27385746893732 0.54771493787464 0.72614253106268 101 0.242069026213412 0.484138052426824 0.757930973786588 102 0.198763926849258 0.397527853698517 0.801236073150742 103 0.195356475548809 0.390712951097617 0.804643524451191 104 0.259839579675318 0.519679159350636 0.740160420324682 105 0.591730126596658 0.816539746806684 0.408269873403342 106 0.598304448872959 0.803391102254083 0.401695551127041 107 0.708582417140141 0.582835165719717 0.291417582859859 108 0.988240853675928 0.0235182926481441 0.0117591463240720 109 0.973331914639 0.0533361707219993 0.0266680853609996 110 0.93795438053974 0.124091238920522 0.0620456194602608 111 0.955529967150477 0.0889400656990463 0.0444700328495232 112 0.99584140767631 0.00831718464738266 0.00415859232369133 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.142857142857143 NOK 5% type I error level 34 0.323809523809524 NOK 10% type I error level 49 0.466666666666667 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/10qgk51292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/10qgk51292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/1jw4t1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/1jw4t1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/2jw4t1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/2jw4t1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/3c64x1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/3c64x1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/4c64x1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/4c64x1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/5c64x1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/5c64x1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/6mf3z1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/6mf3z1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/7mf3z1292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/7mf3z1292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/8x6221292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/8x6221292700717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/9x6221292700717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292700637rbzljlk8jxl1cxx/9x6221292700717.ps (open in new window)

Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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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