eigen tutorial workshop 7

*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: Thu, 02 Dec 2010 23:26:25 +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/03/t12913322918nv0mn84ijp1irz.htm/, Retrieved Fri, 03 Dec 2010 00:24:52 +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/03/t12913322918nv0mn84ijp1irz.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 «

2 9 2 1 4 3 3 3 3 3 9 2 3 4 3 3 4 3 3 9 4 2 3 4 4 4 3 3 9 3 3 2 3 3 3 3 3 9 3 2 3 3 2 2 2 3 9 1 2 4 3 3 2 2 2 9 4 4 5 4 4 5 4 3 9 2 2 4 2 2 3 2 3 9 2 2 4 4 3 2 3 4 9 2 2 2 2 2 2 2 3 9 4 2 2 3 2 4 4 3 9 3 3 4 3 2 3 3 2 9 3 2 4 4 4 3 3 3 9 2 2 5 3 4 2 3 9 3 3 5 3 3 4 3 3 9 2 2 4 3 2 2 2 3 9 3 3 3 3 3 3 3 3 9 3 3 4 4 4 4 3 2 9 2 2 4 2 2 2 2 4 9 2 2 2 3 2 2 3 3 9 1 1 4 3 3 3 2 2 9 4 3 4 4 4 4 3 3 9 3 2 4 3 3 2 3 3 9 2 2 4 3 3 2 2 2 9 3 3 4 3 4 3 3 2 9 3 3 4 4 4 4 3 4 9 4 3 4 4 2 4 4 2 9 3 2 3 4 3 3 3 3 9 3 3 3 4 3 3 3 2 9 2 2 4 4 4 4 2 4 9 2 2 3 2 4 2 2 3 9 4 3 4 3 3 3 4 2 9 4 3 4 4 3 4 4 3 9 2 2 4 3 2 3 3 3 9 2 2 4 3 2 2 3 1 9 3 3 4 4 4 4 4 3 9 3 3 4 3 3 4 3 3 9 3 2 3 2 2 2 2 3 9 3 3 4 3 3 3 3 2 9 4 3 4 4 4 4 4 3 9 3 3 4 3 4 4 3 9 1 2 3 2 2 3 3 5 9 2 1 5 2 1 4 2 4 9 2 2 4 3 2 3 2 3 9 3 3 4 3 2 3 3 2 9 4 3 4 4 4 3 4 2 9 3 2 4 4 4 3 4 3 9 2 2 5 2 2 2 2 4 9 2 3 4 3 3 4 3 2 9 3 3 4 4 3 4 3 3 9 3 3 4 3 2 4 3 4 10 4 2 3 3 1 2 2 3 10 3 2 4 4 3 3 4 4 10 2 2 4 3 2 3 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Y[t] = + 10.1280554387145 -0.470936587537932month[t] -0.0930357075258933X1t[t] + 0.693450393160914X2t[t] + 0.194198919311925X3t[t] -0.380079809268144X4t[t] -0.446582546175459X5t[t] -0.109724075319391X6t[t] -0.575762104826707X7t[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) 10.1280554387145 1.019136 9.9379 0 0 month -0.470936587537932 0.073403 -6.4158 0 0 X1t -0.0930357075258933 0.157682 -0.59 0.556081 0.278041 X2t 0.693450393160914 0.140499 4.9356 2e-06 1e-06 X3t 0.194198919311925 0.1186 1.6374 0.10368 0.05184 X4t -0.380079809268144 0.047458 -8.0088 0 0 X5t -0.446582546175459 0.052889 -8.4438 0 0 X6t -0.109724075319391 0.129533 -0.8471 0.39833 0.199165 X7t -0.575762104826707 0.057452 -10.0216 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.77836401948727 R-squared 0.60585054683238 Adjusted R-squared 0.58440023645591 F-TEST (value) 28.2443720486671 F-TEST (DF numerator) 8 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.51291998127982 Sum Squared Residuals 336.472249854092 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.63735519946088 -0.637355199460879 2 3 3.91453191046331 -0.91453191046331 3 3 2.01414882749508 0.98585117250492 4 3 3.54282243963296 -0.54282243963296 5 3 4.17563969210553 -1.17563969210553 6 3 4.10932748029378 -1.10932748029378 7 2 3.10396127229466 -1.10396127229466 8 3 4.7332300528921 -1.7332300528921 9 3 3.06044985867303 -0.0604498586730324 10 4 4.45455628958764 -0.45455628958764 11 3 2.51743270497551 0.482567295024489 12 3 4.37780282443227 -1.37780282443227 13 2 2.41110752965229 -0.411107529652291 14 3 3.18814604107764 -0.188146041077645 15 9 7.50295912431884 1.49704087568116 16 9 8.75645000316021 0.243549996839792 17 9 6.56264088417247 2.43735911582753 18 9 7.19938994602842 1.80061005397158 19 9 7.98648897902158 1.01351102097842 20 9 7.25982514151899 1.74017485848101 21 9 9.06952204760714 -0.0695220476071383 22 9 6.15269125366378 2.84730874633622 23 9 7.79570953103474 1.20429046896526 24 9 8.95213229871877 0.0478677012812281 25 9 7.45177357289195 1.54822642710805 26 9 6.047865736375 2.952134263625 27 9 7.37888890170738 1.62111109829262 28 9 6.84987551101029 2.15012448898971 29 9 7.33260190831111 1.66739809168889 30 9 6.72156210675822 2.27843789324178 31 9 7.10864107215108 1.89135892784892 32 9 7.25119271930277 1.74880728069723 33 9 6.42304698761253 2.57695301238747 34 9 8.20014338166536 0.799856618334642 35 9 9.79825013749423 -0.798250137494232 36 9 6.51390376588232 2.48609623411768 37 9 6.80950873115793 2.19049126884207 38 9 7.39786410314944 1.60213589685056 39 9 7.8318533821601 1.16814661783990 40 9 6.04296717834439 2.95703282165561 41 9 2.97485629292954 6.02514370707046 42 1 2.47190737963854 -1.47190737963854 43 2 2.73880044503947 -0.738800445039467 44 2 3.7383527620878 -1.73835276208780 45 3 2.9305577036938 0.0694422963061973 46 4 3.56582338930311 0.434176610696893 47 3 3.92703590152165 -0.927035901521648 48 2 3.22222239534975 -1.22222239534975 49 2 2.74467681373758 -0.744676813737584 50 3 3.32840313157911 -0.328403131579106 51 3 1.75526763896017 1.24473236103983 52 4 3.44150725474321 0.558492745256792 53 3 3.04735080206362 -0.0473508020636241 54 2 2.71600811108564 -0.716008111085636 55 2 2.0938511084702 -0.0938511084702017 56 2 2.32954636754024 -0.329546367540238 57 2 3.68724554182292 -1.68724554182292 58 3 2.48356903209537 0.516430967904633 59 1 4.19815189564958 -3.19815189564958 60 5 2.39053332456947 2.60946667543053 61 2 3.54905240080649 -1.54905240080649 62 3 2.94683994606432 0.0531600539356767 63 4 3.30716573255477 0.69283426744523 64 4 3.51081224112815 0.489187758871851 65 2 2.14390831176167 -0.143908311761672 66 3 2.65782340353403 0.342176596465974 67 3 2.88585298903509 0.114147010964912 68 3 3.46651365189241 -0.466513651892411 69 3 1.69708293140856 1.30291706859144 70 1 3.96930846483143 -2.96930846483143 71 3 2.37077930179178 0.629220698208224 72 3 1.97382059963457 1.02617940036543 73 3 3.80641720640376 -0.806417206403759 74 4 3.28195284693751 0.718047153062494 75 3 2.43927044285963 0.560729557140371 76 4 2.91020703039756 1.08979296960244 77 3 2.81717132287167 0.182828677128333 78 3 3.02012163081252 -0.0201216308125202 79 2 2.66727099279548 -0.66727099279548 80 1 2.63615385700680 -1.63615385700680 81 2 6.61905578312423 -4.61905578312423 82 3 3.8166428702124 -0.816642870212404 83 4 3.29568542509259 0.704314574907406 84 3 3.81016203344423 -0.810162033444226 85 4 3.84277882726735 0.157221172732646 86 5 4.12204924109036 0.877950758909642 87 2 3.21771156082402 -1.21771156082402 88 2 3.35367049568929 -1.35367049568929 89 4 3.8714475299193 0.128552470080698 90 4 3.43656306094426 0.563436939055741 91 3 3.1859613497732 -0.185961349773203 92 4 4.12363151982792 -0.12363151982792 93 4 4.14031988762142 -0.140319887621417 94 4 3.64745034804968 0.352549651950318 95 4 4.12204924109036 -0.122049241090358 96 4 4.49978682985707 -0.499786829857073 97 2 5.89070373802253 -3.89070373802253 98 4 4.29124176325308 -0.291241763253080 99 4 3.75211257409313 0.247887425906866 100 4 4.40036918805393 -0.400369188053926 101 4 4.03059581230203 -0.0305958123020261 102 4 4.03697774657928 -0.0369777465792789 103 5 5.43260268767979 -0.43260268767979 104 4 4.63966298407505 -0.63966298407505 105 4 2.92883026649424 1.07116973350576 106 4 4.5402453422719 -0.540245342271903 107 3 3.44452727395908 -0.444527273959075 108 4 4.64140855405793 -0.641408554057934 109 4 4.33425661319710 -0.334256613197095 110 4 4.22253029047496 -0.222530290474955 111 3 3.83340055313204 -0.833400553132043 112 3 4.01977050762967 -1.01977050762967 113 3 3.23328440694286 -0.233284406942864 114 3 2.81501674707846 0.184983252921540 115 4 3.02269565928328 0.97730434071672 116 3 2.56814890009301 0.431851099906994 117 3 2.56814890009301 0.431851099906994 118 4 3.31582315585695 0.684176844143055 119 3 3.59539210912579 -0.595392109125789 120 3 3.88262673596361 -0.882626735963607 121 3 3.67986695311832 -0.679866953118323 122 3 3.6058890677376 -0.6058890677376 123 3 2.98946164361269 0.0105383563873116 124 3 3.26159929325392 -0.261599293253920 125 4 3.20893036558039 0.79106963441961 126 3 1.78932847297517 1.21067152702483 127 4 3.45579821256584 0.544201787434155 128 3 4.34866476547092 -1.34866476547092 129 4 6.33516935992365 -2.33516935992365 130 1 2.31685837746780 -1.31685837746780 131 4 3.26159929325392 0.73840070674608 132 3 3.41169014842568 -0.411690148425675 133 4 2.9592312335521 1.04076876644790 134 4 3.01077060131988 0.989229398680119 135 4 4.10514054158659 -0.105140541586589 136 3 3.23328440694286 -0.233284406942864 137 3 4.31602782869201 -1.31602782869201 138 3 2.80844417774782 0.191555822252182 139 4 3.47614888586209 0.523851114137913 140 3 4.77027604843645 -1.77027604843645 141 3 2.6611846076189 0.3388153923811 142 3 3.59539210912579 -0.595392109125789 143 4 3.51285336021171 0.487146639788293 144 2 3.75314863786652 -1.75314863786652 145 3 3.32632011446876 -0.326320114468757 146 3 4.908974755032 -1.90897475503200 147 3 2.83309675855613 0.166903241443869 148 3 2.69762699819009 0.302373001809906 149 3 2.70529267175907 0.294707328240931 150 4 2.31576527322947 1.68423472677053 151 3 2.68553864898137 0.314461351018628 152 4 4.5878669388874 -0.587866938887403 153 3 3.67956841367248 -0.679568413672482 154 4 3.22838584891225 0.771614151087753 155 4 6.73131985650659 -2.73131985650659 156 4 11.4066936912507 -7.40669369125069 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.0371083521600687 0.0742167043201375 0.962891647839931 13 0.0109387864560099 0.0218775729120198 0.98906121354399 14 0.0148915450360187 0.0297830900720373 0.985108454963981 15 0.00475303848227053 0.00950607696454107 0.99524696151773 16 0.00275757446730251 0.00551514893460503 0.997242425532697 17 0.00286251035876125 0.00572502071752251 0.997137489641239 18 0.00116786971943370 0.00233573943886739 0.998832130280566 19 0.000471799849218926 0.000943599698437853 0.999528200150781 20 0.000159163755544881 0.000318327511089762 0.999840836244455 21 0.00069980109850204 0.00139960219700408 0.999300198901498 22 0.00369656890617874 0.00739313781235748 0.996303431093821 23 0.00291436897108812 0.00582873794217624 0.997085631028912 24 0.00193021832953655 0.00386043665907311 0.998069781670463 25 0.00100862521357267 0.00201725042714533 0.998991374786427 26 0.000899338793923123 0.00179867758784625 0.999100661206077 27 0.000676791007148967 0.00135358201429793 0.99932320899285 28 0.000564202916576533 0.00112840583315307 0.999435797083423 29 0.000307281006981923 0.000614562013963847 0.999692718993018 30 0.000222997260909954 0.000445994521819908 0.99977700273909 31 0.000144103270458126 0.000288206540916251 0.999855896729542 32 0.000135710312623425 0.000271420625246849 0.999864289687377 33 0.000172773474269882 0.000345546948539764 0.99982722652573 34 0.000187559636334677 0.000375119272669354 0.999812440363665 35 0.000289114077002658 0.000578228154005316 0.999710885922997 36 0.000361136415264608 0.000722272830529217 0.999638863584735 37 0.000481553968794002 0.000963107937588003 0.999518446031206 38 0.000940380524368385 0.00188076104873677 0.999059619475632 39 0.00286725267349243 0.00573450534698486 0.997132747326508 40 0.0302459000495314 0.0604918000990627 0.969754099950469 41 0.390192674592843 0.780385349185686 0.609807325407157 42 0.999727209653477 0.000545580693046889 0.000272790346523444 43 0.999980907209158 3.81855816838302e-05 1.90927908419151e-05 44 0.99999554888028 8.90223943861814e-06 4.45111971930907e-06 45 0.999994059535147 1.18809297068773e-05 5.94046485343867e-06 46 0.999992408579107 1.51828417852545e-05 7.59142089262726e-06 47 0.999995291240107 9.41751978632208e-06 4.70875989316104e-06 48 0.99999181868119 1.63626376204768e-05 8.18131881023839e-06 49 0.999992235350524 1.55292989523701e-05 7.76464947618506e-06 50 0.999987394613281 2.52107734378343e-05 1.26053867189171e-05 51 0.999982889914211 3.42201715777468e-05 1.71100857888734e-05 52 0.999993041806544 1.39163869118612e-05 6.9581934559306e-06 53 0.99999073795274 1.85240945198547e-05 9.26204725992735e-06 54 0.999988542253839 2.29154923223367e-05 1.14577461611683e-05 55 0.999988571061697 2.28578766059488e-05 1.14289383029744e-05 56 0.999984885493036 3.02290139278071e-05 1.51145069639036e-05 57 0.9999821359664 3.57280672007225e-05 1.78640336003612e-05 58 0.999971067077636 5.78658447274362e-05 2.89329223637181e-05 59 0.999990218026788 1.95639464243207e-05 9.78197321216033e-06 60 0.999998621491981 2.75701603784113e-06 1.37850801892056e-06 61 0.999998606456674 2.7870866519079e-06 1.39354332595395e-06 62 0.999997866180884 4.26763823190473e-06 2.13381911595236e-06 63 0.999998609617224 2.78076555119283e-06 1.39038277559641e-06 64 0.999998477403535 3.04519293040867e-06 1.52259646520433e-06 65 0.999997994341782 4.01131643624052e-06 2.00565821812026e-06 66 0.999996419862766 7.16027446710829e-06 3.58013723355414e-06 67 0.999996728726843 6.54254631321411e-06 3.27127315660705e-06 68 0.99999517599862 9.64800276110497e-06 4.82400138055249e-06 69 0.999992205525492 1.55889490157074e-05 7.79447450785368e-06 70 0.99999742866022 5.14267956012637e-06 2.57133978006319e-06 71 0.999995768762748 8.4624745032881e-06 4.23123725164405e-06 72 0.99999290543809 1.41891238187715e-05 7.09456190938574e-06 73 0.999989602157378 2.07956852449075e-05 1.03978426224537e-05 74 0.999994910769054 1.01784618922854e-05 5.08923094614271e-06 75 0.999992987782886 1.40244342282366e-05 7.01221711411828e-06 76 0.999997090963094 5.81807381210726e-06 2.90903690605363e-06 77 0.999995402309564 9.19538087215001e-06 4.59769043607501e-06 78 0.999995888892954 8.22221409286725e-06 4.11110704643362e-06 79 0.999997068397521 5.86320495768564e-06 2.93160247884282e-06 80 0.999998979862036 2.04027592772741e-06 1.02013796386371e-06 81 0.999999909326724 1.81346551372957e-07 9.06732756864786e-08 82 0.999999999348272 1.30345562395921e-09 6.51727811979607e-10 83 0.999999999562695 8.74609305685168e-10 4.37304652842584e-10 84 0.999999999788423 4.2315346536554e-10 2.1157673268277e-10 85 0.999999999595667 8.08665858549837e-10 4.04332929274919e-10 86 0.999999999752837 4.94325519560956e-10 2.47162759780478e-10 87 0.999999999964218 7.1564641048951e-11 3.57823205244755e-11 88 0.999999999997758 4.48386513322387e-12 2.24193256661194e-12 89 0.99999999999591 8.17826987507567e-12 4.08913493753783e-12 90 0.99999999999089 1.82210220584228e-11 9.1105110292114e-12 91 0.999999999994761 1.04775313495304e-11 5.23876567476519e-12 92 0.99999999998695 2.61000400960766e-11 1.30500200480383e-11 93 0.999999999968804 6.23916158768394e-11 3.11958079384197e-11 94 0.99999999992183 1.56338319405852e-10 7.81691597029262e-11 95 0.999999999812904 3.74191336449721e-10 1.87095668224860e-10 96 0.99999999974253 5.14940213398722e-10 2.57470106699361e-10 97 0.99999999999941 1.17920133039631e-12 5.89600665198157e-13 98 0.999999999998422 3.15675839025762e-12 1.57837919512881e-12 99 0.999999999996372 7.25690701058384e-12 3.62845350529192e-12 100 0.99999999999032 1.93602740244101e-11 9.68013701220507e-12 101 0.999999999974124 5.17526028879048e-11 2.58763014439524e-11 102 0.999999999930438 1.39124251165612e-10 6.95621255828058e-11 103 0.999999999894025 2.119497276052e-10 1.059748638026e-10 104 0.99999999981566 3.68680287764508e-10 1.84340143882254e-10 105 0.99999999993093 1.38140279899204e-10 6.90701399496018e-11 106 0.99999999983207 3.35859493401371e-10 1.67929746700686e-10 107 0.99999999957781 8.44380718125326e-10 4.22190359062663e-10 108 0.999999999135905 1.72819022934115e-09 8.64095114670575e-10 109 0.999999999320955 1.35809057123596e-09 6.79045285617981e-10 110 0.999999999940597 1.18806821073849e-10 5.94034105369244e-11 111 0.99999999987295 2.54099582304186e-10 1.27049791152093e-10 112 0.999999999693586 6.12827910313761e-10 3.06413955156880e-10 113 0.999999999313539 1.37292227464985e-09 6.86461137324923e-10 114 0.999999998459375 3.08125005049882e-09 1.54062502524941e-09 115 0.999999997131894 5.73621154742483e-09 2.86810577371241e-09 116 0.999999994111326 1.17773470514040e-08 5.88867352570201e-09 117 0.999999988463052 2.30738958861672e-08 1.15369479430836e-08 118 0.999999981681026 3.66379488040377e-08 1.83189744020189e-08 119 0.999999967522718 6.49545640216566e-08 3.24772820108283e-08 120 0.999999916918456 1.66163087120146e-07 8.30815435600731e-08 121 0.999999870691035 2.58617930843937e-07 1.29308965421968e-07 122 0.99999966071478 6.78570441005672e-07 3.39285220502836e-07 123 0.999999208261567 1.58347686526893e-06 7.91738432634464e-07 124 0.999998842355047 2.31528990646820e-06 1.15764495323410e-06 125 0.999997367120327 5.26575934505582e-06 2.63287967252791e-06 126 0.9999947718589 1.04562821998286e-05 5.22814109991432e-06 127 0.99998963704246 2.07259150803818e-05 1.03629575401909e-05 128 0.999980418916875 3.91621662498303e-05 1.95810831249151e-05 129 0.999962040133758 7.59197324839148e-05 3.79598662419574e-05 130 0.999974906588492 5.01868230167533e-05 2.50934115083767e-05 131 0.999951930187783 9.61396244336881e-05 4.80698122168441e-05 132 0.999875878276926 0.000248243446147416 0.000124121723073708 133 0.999796869025172 0.000406261949656845 0.000203130974828422 134 0.999866984648811 0.000266030702377936 0.000133015351188968 135 0.99985175984958 0.000296480300839017 0.000148240150419509 136 0.999616251822612 0.000767496354776566 0.000383748177388283 137 0.999231688341617 0.00153662331676608 0.00076831165838304 138 0.998686583001593 0.002626833996814 0.001313416998407 139 0.99641677890384 0.00716644219232013 0.00358322109616006 140 0.992566572260358 0.0148668554792835 0.00743342773964173 141 0.980903496949325 0.0381930061013499 0.0190965030506749 142 0.953731259806953 0.0925374803860948 0.0462687401930474 143 0.92290897992582 0.154182040148359 0.0770910200741797 144 0.876898114393133 0.246203771213734 0.123101885606867 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 123 0.924812030075188 NOK 5% type I error level 127 0.954887218045113 NOK 10% type I error level 130 0.977443609022556 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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