WS07-Multiple Regression

*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: Fri, 20 Nov 2009 18:20:00 -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/Nov/21/t1258766771r9w0yoc73jkviy4.htm/, Retrieved Sat, 21 Nov 2009 02:26:23 +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/Nov/21/t1258766771r9w0yoc73jkviy4.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 «

423.4 0 404.1 0 500 0 472.6 0 496.1 0 562 0 434.8 0 538.2 0 577.6 0 518.1 0 625.2 0 561.2 0 523.3 0 536.1 0 607.3 0 637.3 0 606.9 0 652.9 0 617.2 0 670.4 0 729.9 0 677.2 0 710 0 844.3 0 748.2 0 653.9 0 742.6 0 854.2 0 808.4 0 1819 1 1936.5 1 1966.1 1 2083.1 1 1620.1 1 1527.6 1 1795 1 1685.1 1 1851.8 1 2164.4 1 1981.8 1 1726.5 1 2144.6 1 1758.2 1 1672.9 1 1837.3 1 1596.1 1 1446 1 1898.4 1 1964.1 1 1755.9 1 2255.3 1 1881.2 1 2117.9 1 1656.5 1 1544.1 1 2098.9 1 2133.3 1 1963.5 1 1801.2 1 2365.4 1 1936.5 1 1667.6 1 1983.5 1 2058.6 1 2448.3 1 1858.1 1 1625.4 1 2130.6 1 2515.7 1 2230.2 1 2086.9 1 2235 1 2100.2 1 2288.6 1 2490 1 2573.7 1 2543.8 1 2004.7 1 2390 1 2338.4 1 2724.5 1 2292.5 1 2386 1 2477.9 1 2337 1 2605.1 1 2560.8 1 2839.3 1 2407.2 1 2085.2 1 2735.6 1 2798.7 1 3053.2 1 2405 1 2471.9 1 2727.3 1 2790.7 1 2385.4 1 3206.6 1 2705.6 1 3518.4 1 1954.9 1 2584.3 1 2535.8 1 2685.9 1 2866 1 2236.6 1 2934.9 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(Export_farma_prod)[t] = + 611.496551724142 + 1678.78366805608`X(sprong)`[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) 611.496551724142 74.319942 8.2279 0 0 `X(sprong)` 1678.78366805608 85.344451 19.6707 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.875389579068774 R-squared 0.766306915142206 Adjusted R-squared 0.76432646527053 F-TEST (value) 386.935779643651 F-TEST (DF numerator) 1 F-TEST (DF denominator) 118 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 400.225137425860 Sum Squared Residuals 18901258.9540508 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 423.4 611.49655172413 -188.096551724130 2 404.1 611.496551724125 -207.396551724125 3 500 611.496551724139 -111.496551724139 4 472.6 611.496551724139 -138.896551724139 5 496.1 611.496551724139 -115.396551724139 6 562 611.496551724139 -49.4965517241387 7 434.8 611.496551724139 -176.696551724139 8 538.2 611.496551724139 -73.2965517241387 9 577.6 611.496551724139 -33.8965517241386 10 518.1 611.496551724139 -93.3965517241386 11 625.2 611.496551724139 13.7034482758613 12 561.2 611.496551724139 -50.2965517241387 13 523.3 611.496551724139 -88.1965517241387 14 536.1 611.496551724139 -75.3965517241386 15 607.3 611.496551724139 -4.19655172413875 16 637.3 611.496551724139 25.8034482758613 17 606.9 611.496551724139 -4.59655172413884 18 652.9 611.496551724139 41.4034482758612 19 617.2 611.496551724139 5.70344827586134 20 670.4 611.496551724139 58.9034482758612 21 729.9 611.496551724139 118.403448275861 22 677.2 611.496551724139 65.7034482758613 23 710 611.496551724139 98.5034482758613 24 844.3 611.496551724139 232.803448275861 25 748.2 611.496551724139 136.703448275861 26 653.9 611.496551724139 42.4034482758612 27 742.6 611.496551724139 131.103448275861 28 854.2 611.496551724139 242.703448275861 29 808.4 611.496551724139 196.903448275861 30 1819 2290.28021978022 -471.28021978022 31 1936.5 2290.28021978022 -353.78021978022 32 1966.1 2290.28021978022 -324.18021978022 33 2083.1 2290.28021978022 -207.18021978022 34 1620.1 2290.28021978022 -670.18021978022 35 1527.6 2290.28021978022 -762.68021978022 36 1795 2290.28021978022 -495.28021978022 37 1685.1 2290.28021978022 -605.18021978022 38 1851.8 2290.28021978022 -438.48021978022 39 2164.4 2290.28021978022 -125.880219780220 40 1981.8 2290.28021978022 -308.48021978022 41 1726.5 2290.28021978022 -563.78021978022 42 2144.6 2290.28021978022 -145.68021978022 43 1758.2 2290.28021978022 -532.08021978022 44 1672.9 2290.28021978022 -617.38021978022 45 1837.3 2290.28021978022 -452.98021978022 46 1596.1 2290.28021978022 -694.18021978022 47 1446 2290.28021978022 -844.28021978022 48 1898.4 2290.28021978022 -391.88021978022 49 1964.1 2290.28021978022 -326.18021978022 50 1755.9 2290.28021978022 -534.38021978022 51 2255.3 2290.28021978022 -34.9802197802196 52 1881.2 2290.28021978022 -409.08021978022 53 2117.9 2290.28021978022 -172.380219780220 54 1656.5 2290.28021978022 -633.78021978022 55 1544.1 2290.28021978022 -746.18021978022 56 2098.9 2290.28021978022 -191.380219780220 57 2133.3 2290.28021978022 -156.980219780220 58 1963.5 2290.28021978022 -326.78021978022 59 1801.2 2290.28021978022 -489.08021978022 60 2365.4 2290.28021978022 75.1197802197803 61 1936.5 2290.28021978022 -353.78021978022 62 1667.6 2290.28021978022 -622.68021978022 63 1983.5 2290.28021978022 -306.78021978022 64 2058.6 2290.28021978022 -231.680219780220 65 2448.3 2290.28021978022 158.019780219780 66 1858.1 2290.28021978022 -432.18021978022 67 1625.4 2290.28021978022 -664.88021978022 68 2130.6 2290.28021978022 -159.68021978022 69 2515.7 2290.28021978022 225.41978021978 70 2230.2 2290.28021978022 -60.08021978022 71 2086.9 2290.28021978022 -203.380219780220 72 2235 2290.28021978022 -55.2802197802198 73 2100.2 2290.28021978022 -190.08021978022 74 2288.6 2290.28021978022 -1.68021978021987 75 2490 2290.28021978022 199.719780219780 76 2573.7 2290.28021978022 283.41978021978 77 2543.8 2290.28021978022 253.519780219780 78 2004.7 2290.28021978022 -285.58021978022 79 2390 2290.28021978022 99.7197802197802 80 2338.4 2290.28021978022 48.1197802197803 81 2724.5 2290.28021978022 434.21978021978 82 2292.5 2290.28021978022 2.21978021978022 83 2386 2290.28021978022 95.7197802197802 84 2477.9 2290.28021978022 187.619780219780 85 2337 2290.28021978022 46.7197802197802 86 2605.1 2290.28021978022 314.81978021978 87 2560.8 2290.28021978022 270.519780219780 88 2839.3 2290.28021978022 549.01978021978 89 2407.2 2290.28021978022 116.91978021978 90 2085.2 2290.28021978022 -205.08021978022 91 2735.6 2290.28021978022 445.31978021978 92 2798.7 2290.28021978022 508.41978021978 93 3053.2 2290.28021978022 762.91978021978 94 2405 2290.28021978022 114.719780219780 95 2471.9 2290.28021978022 181.619780219780 96 2727.3 2290.28021978022 437.019780219780 97 2790.7 2290.28021978022 500.41978021978 98 2385.4 2290.28021978022 95.1197802197803 99 3206.6 2290.28021978022 916.31978021978 100 2705.6 2290.28021978022 415.31978021978 101 3518.4 2290.28021978022 1228.11978021978 102 1954.9 2290.28021978022 -335.38021978022 103 2584.3 2290.28021978022 294.019780219780 104 2535.8 2290.28021978022 245.519780219780 105 2685.9 2290.28021978022 395.61978021978 106 2866 2290.28021978022 575.71978021978 107 2236.6 2290.28021978022 -53.6802197802199 108 2934.9 2290.28021978022 644.61978021978 109 2668.6 2290.28021978022 378.31978021978 110 2371.2 2290.28021978022 80.91978021978 111 3165.9 2290.28021978022 875.61978021978 112 2887.2 2290.28021978022 596.91978021978 113 3112.2 2290.28021978022 821.91978021978 114 2671.2 2290.28021978022 380.91978021978 115 2432.6 2290.28021978022 142.31978021978 116 2812.3 2290.28021978022 522.01978021978 117 3095.7 2290.28021978022 805.41978021978 118 2862.9 2290.28021978022 572.61978021978 119 2607.3 2290.28021978022 317.019780219780 120 2862.5 2290.28021978022 572.21978021978 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00254826141355959 0.00509652282711917 0.99745173858644 6 0.00117003755455760 0.00234007510911519 0.998829962445442 7 0.000191984707355903 0.000383969414711806 0.999808015292644 8 4.43102757986334e-05 8.86205515972669e-05 0.999955689724201 9 1.81393787903007e-05 3.62787575806015e-05 0.99998186062121 10 2.86045794958925e-06 5.7209158991785e-06 0.99999713954205 11 2.41033635681395e-06 4.82067271362791e-06 0.999997589663643 12 5.15477922922994e-07 1.03095584584599e-06 0.999999484522077 13 8.25362591969503e-08 1.65072518393901e-07 0.999999917463741 14 1.33269862214333e-08 2.66539724428666e-08 0.999999986673014 15 5.08933655645804e-09 1.01786731129161e-08 0.999999994910663 16 2.99680916336652e-09 5.99361832673305e-09 0.99999999700319 17 8.66036988838159e-10 1.73207397767632e-09 0.999999999133963 18 4.97350627497977e-10 9.94701254995955e-10 0.99999999950265 19 1.40443467144352e-10 2.80886934288703e-10 0.999999999859557 20 8.51649437203201e-11 1.7032988744064e-10 0.999999999914835 21 1.36539899088159e-10 2.73079798176317e-10 0.99999999986346 22 6.22650892332271e-11 1.24530178466454e-10 0.999999999937735 23 4.14555257905999e-11 8.29110515811997e-11 0.999999999958544 24 2.81945665671629e-10 5.63891331343259e-10 0.999999999718054 25 1.94360954801925e-10 3.88721909603849e-10 0.999999999805639 26 5.52135355003007e-11 1.10427071000601e-10 0.999999999944786 27 3.14115776991543e-11 6.28231553983085e-11 0.999999999968588 28 7.40320360954235e-11 1.48064072190847e-10 0.999999999925968 29 6.6856088014826e-11 1.33712176029652e-10 0.999999999933144 30 2.03877853935221e-11 4.07755707870441e-11 0.999999999979612 31 7.1711477352395e-12 1.4342295470479e-11 0.999999999992829 32 2.34951305099513e-12 4.69902610199026e-12 0.99999999999765 33 1.30505372079942e-12 2.61010744159884e-12 0.999999999998695 34 6.55932475923159e-12 1.31186495184632e-11 0.99999999999344 35 4.41142577377296e-11 8.82285154754591e-11 0.999999999955886 36 1.72749089357268e-11 3.45498178714535e-11 0.999999999982725 37 1.11109498785635e-11 2.2221899757127e-11 0.99999999998889 38 4.37975277542928e-12 8.75950555085856e-12 0.99999999999562 39 1.71669627295394e-11 3.43339254590788e-11 0.999999999982833 40 8.79305063279658e-12 1.75861012655932e-11 0.999999999991207 41 5.811583410086e-12 1.1623166820172e-11 0.999999999994188 42 1.00183665636844e-11 2.00367331273687e-11 0.999999999989982 43 6.14506777519582e-12 1.22901355503916e-11 0.999999999993855 44 6.78591656727517e-12 1.35718331345503e-11 0.999999999993214 45 3.22913109145724e-12 6.45826218291447e-12 0.99999999999677 46 7.57870615735575e-12 1.51574123147115e-11 0.999999999992421 47 1.05757148566129e-10 2.11514297132258e-10 0.999999999894243 48 6.37349331129436e-11 1.27469866225887e-10 0.999999999936265 49 4.44673263750856e-11 8.89346527501712e-11 0.999999999955533 50 3.55805164529656e-11 7.11610329059312e-11 0.99999999996442 51 2.13370848512149e-10 4.26741697024299e-10 0.99999999978663 52 1.40681583093066e-10 2.81363166186132e-10 0.999999999859318 53 1.80296170204467e-10 3.60592340408933e-10 0.999999999819704 54 3.60250612081756e-10 7.20501224163511e-10 0.99999999963975 55 2.22015316533750e-09 4.44030633067500e-09 0.999999997779847 56 2.80608857413867e-09 5.61217714827734e-09 0.999999997193911 57 3.9030884825351e-09 7.8061769650702e-09 0.999999996096911 58 3.39140470543664e-09 6.78280941087329e-09 0.999999996608595 59 4.36296816466258e-09 8.72593632932515e-09 0.999999995637032 60 2.81015803495758e-08 5.62031606991517e-08 0.99999997189842 61 2.79264896429318e-08 5.58529792858637e-08 0.99999997207351 62 1.07217018907921e-07 2.14434037815843e-07 0.99999989278298 63 1.23073173294119e-07 2.46146346588238e-07 0.999999876926827 64 1.48775709142014e-07 2.97551418284028e-07 0.99999985122429 65 1.02769631019277e-06 2.05539262038553e-06 0.99999897230369 66 1.85853281889022e-06 3.71706563778044e-06 0.999998141467181 67 1.81257733269860e-05 3.62515466539721e-05 0.999981874226673 68 2.65303370922856e-05 5.30606741845711e-05 0.999973469662908 69 0.000132458627643849 0.000264917255287697 0.999867541372356 70 0.000185362619473375 0.000370725238946749 0.999814637380527 71 0.00026287890495351 0.00052575780990702 0.999737121095047 72 0.000369224679105016 0.000738449358210032 0.999630775320895 73 0.000554544123303652 0.00110908824660730 0.999445455876696 74 0.00081125202184739 0.00162250404369478 0.999188747978153 75 0.00165005375128746 0.00330010750257493 0.998349946248713 76 0.00361798592208201 0.00723597184416402 0.996382014077918 77 0.00604031511440589 0.0120806302288118 0.993959684885594 78 0.0111574355132996 0.0223148710265991 0.9888425644867 79 0.0135549748190601 0.0271099496381202 0.98644502518094 80 0.0160168286154135 0.0320336572308269 0.983983171384587 81 0.0305584592590151 0.0611169185180301 0.969441540740985 82 0.0348302384006325 0.069660476801265 0.965169761599368 83 0.0383270220998013 0.0766540441996027 0.961672977900199 84 0.0421550310164665 0.084310062032933 0.957844968983533 85 0.0469996948069699 0.0939993896139397 0.95300030519303 86 0.0541275213600217 0.108255042720043 0.945872478639978 87 0.057930642406167 0.115861284812334 0.942069357593833 88 0.08544905253227 0.17089810506454 0.91455094746773 89 0.0862606694912308 0.172521338982462 0.91373933050877 90 0.142450864228381 0.284901728456762 0.857549135771619 91 0.155019018077030 0.310038036154060 0.84498098192297 92 0.172866291912561 0.345732583825123 0.827133708087439 93 0.265312127716995 0.53062425543399 0.734687872283005 94 0.262461135165279 0.524922270330557 0.737538864834721 95 0.251736117829264 0.503472235658528 0.748263882170736 96 0.239215464613513 0.478430929227026 0.760784535386487 97 0.231313042299006 0.462626084598011 0.768686957700994 98 0.232748322674252 0.465496645348503 0.767251677325748 99 0.365607272910926 0.731214545821853 0.634392727089074 100 0.328017007781214 0.656034015562428 0.671982992218786 101 0.724481772559428 0.551036454881144 0.275518227440572 102 0.918783384088452 0.162433231823095 0.0812166159115476 103 0.897272482247284 0.205455035505432 0.102727517752716 104 0.878860184762208 0.242279630475585 0.121139815237793 105 0.840863623016767 0.318272753966467 0.159136376983233 106 0.803038608993708 0.393922782012584 0.196961391006292 107 0.898381036569388 0.203237926861224 0.101618963430612 108 0.869844837110212 0.260310325779576 0.130155162889788 109 0.822533860365175 0.354932279269649 0.177466139634825 110 0.88735075847269 0.225298483054619 0.112649241527309 111 0.910894439593809 0.178211120812382 0.0891055604061909 112 0.856152199388167 0.287695601223665 0.143847800611833 113 0.874547390434997 0.250905219130005 0.125452609565003 114 0.784046696776652 0.431906606446695 0.215953303223348 115 0.84977697932924 0.300446041341518 0.150223020670759 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 72 0.648648648648649 NOK 5% type I error level 76 0.684684684684685 NOK 10% type I error level 81 0.72972972972973 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/1041d71258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/1041d71258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/1yra21258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/1yra21258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/2fg881258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/2fg881258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/3uchu1258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/3uchu1258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/48pat1258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/48pat1258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/5uo941258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/5uo941258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/623gw1258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/623gw1258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/7kpki1258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/7kpki1258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/8qksk1258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/8qksk1258766393.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/9r8dv1258766393.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258766771r9w0yoc73jkviy4/9r8dv1258766393.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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