*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, 14 Dec 2010 17:36:27 +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/14/t1292348106fotvtud7x7rtzd1.htm/, Retrieved Tue, 14 Dec 2010 18:35:16 +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/14/t1292348106fotvtud7x7rtzd1.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 «

1280 1024 1024 768 1120 700 1024 768 1280 800 1280 1024 1280 800 1024 768 1280 800 1280 1024 1280 800 1280 800 1280 1024 1688 949 1440 900 1600 1200 1280 800 1280 800 1280 768 1176 735 1280 800 1503 845 1440 900 1366 768 1280 768 1024 768 1280 800 2560 1440 1280 768 1024 768 1280 1024 1280 800 1440 900 1280 800 1440 900 1024 768 1440 900 1143 857 1280 800 1440 900 1280 800 1366 768 1024 768 1408 880 1366 768 1176 735 1920 1200 1257 785 1280 800 1280 800 1440 900 1680 1050 1440 900 1024 768 1140 641 1280 1024 1280 800 1280 800 1280 800 1280 800 1440 900 1280 800 1152 864 1280 1024 1280 800 1440 900 1280 800 1280 1024 1440 900 1280 800 1280 800 1440 900 1280 800 1280 1024 1600 900 1024 768 1366 768 1280 800 1280 800 1440 900 1366 768 1280 800 1024 768 1280 800 1440 900 1280 800 1280 800 1408 880 1280 800 1600 900 1600 900 1680 1050 1440 900 1440 900 917 550 1280 800 1760 990 1280 800 1280 800 1280 800 1024 768 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 br[t] = + 94.9736438223377 + 1.43774098707423gr[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) 94.9736438223377 87.409215 1.0865 0.279148 0.139574 gr 1.43774098707423 0.102577 14.0161 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.767558899807279 R-squared 0.58914666467336 Adjusted R-squared 0.586147735218421 F-TEST (value) 196.452325246626 F-TEST (DF numerator) 1 F-TEST (DF denominator) 137 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 137.554262316877 Sum Squared Residuals 2592200.98617101 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1280 1567.22041458631 -287.220414586311 2 1024 1199.15872189535 -175.158721895348 3 1120 1101.39233477430 18.6076652257042 4 1024 1199.15872189534 -175.158721895343 5 1280 1245.16643348172 34.8335665182815 6 1280 1567.22041458635 -287.220414586345 7 1280 1245.16643348172 34.8335665182815 8 1024 1199.15872189534 -175.158721895343 9 1280 1245.16643348172 34.8335665182815 10 1280 1567.22041458635 -287.220414586345 11 1280 1245.16643348172 34.8335665182815 12 1280 1245.16643348172 34.8335665182815 13 1280 1567.22041458635 -287.220414586345 14 1688 1459.38984055578 228.610159444222 15 1440 1388.94053218914 51.059467810859 16 1600 1820.26282831141 -220.262828311409 17 1280 1245.16643348172 34.8335665182815 18 1280 1245.16643348172 34.8335665182815 19 1280 1199.15872189534 80.8412781046568 20 1176 1151.71326932189 24.2867306781062 21 1280 1245.16643348172 34.8335665182815 22 1503 1309.86477790006 193.135222099941 23 1440 1388.94053218914 51.059467810859 24 1366 1199.15872189534 166.841278104657 25 1280 1199.15872189534 80.8412781046568 26 1024 1199.15872189534 -175.158721895343 27 1280 1245.16643348172 34.8335665182815 28 2560 2165.32066520922 394.679334790777 29 1280 1199.15872189534 80.8412781046568 30 1024 1199.15872189534 -175.158721895343 31 1280 1567.22041458635 -287.220414586345 32 1280 1245.16643348172 34.8335665182815 33 1440 1388.94053218914 51.059467810859 34 1280 1245.16643348172 34.8335665182815 35 1440 1388.94053218914 51.059467810859 36 1024 1199.15872189534 -175.158721895343 37 1440 1388.94053218914 51.059467810859 38 1143 1327.11766974495 -184.117669744949 39 1280 1245.16643348172 34.8335665182815 40 1440 1388.94053218914 51.059467810859 41 1280 1245.16643348172 34.8335665182815 42 1366 1199.15872189534 166.841278104657 43 1024 1199.15872189534 -175.158721895343 44 1408 1360.18571244766 47.8142875523435 45 1366 1199.15872189534 166.841278104657 46 1176 1151.71326932189 24.2867306781062 47 1920 1820.26282831141 99.7371716885912 48 1257 1223.60031867560 33.3996813243949 49 1280 1245.16643348172 34.8335665182815 50 1280 1245.16643348172 34.8335665182815 51 1440 1388.94053218914 51.059467810859 52 1680 1604.60168025027 75.398319749725 53 1440 1388.94053218914 51.059467810859 54 1024 1199.15872189534 -175.158721895343 55 1140 1016.56561653692 123.434383463083 56 1280 1567.22041458635 -287.220414586345 57 1280 1245.16643348172 34.8335665182815 58 1280 1245.16643348172 34.8335665182815 59 1280 1245.16643348172 34.8335665182815 60 1280 1245.16643348172 34.8335665182815 61 1440 1388.94053218914 51.059467810859 62 1280 1245.16643348172 34.8335665182815 63 1152 1337.18185665447 -185.181856654469 64 1280 1567.22041458635 -287.220414586345 65 1280 1245.16643348172 34.8335665182815 66 1440 1388.94053218914 51.059467810859 67 1280 1245.16643348172 34.8335665182815 68 1280 1567.22041458635 -287.220414586345 69 1440 1388.94053218914 51.059467810859 70 1280 1245.16643348172 34.8335665182815 71 1280 1245.16643348172 34.8335665182815 72 1440 1388.94053218914 51.059467810859 73 1280 1245.16643348172 34.8335665182815 74 1280 1567.22041458635 -287.220414586345 75 1600 1388.94053218914 211.059467810859 76 1024 1199.15872189534 -175.158721895343 77 1366 1199.15872189534 166.841278104657 78 1280 1245.16643348172 34.8335665182815 79 1280 1245.16643348172 34.8335665182815 80 1440 1388.94053218914 51.059467810859 81 1366 1199.15872189534 166.841278104657 82 1280 1245.16643348172 34.8335665182815 83 1024 1199.15872189534 -175.158721895343 84 1280 1245.16643348172 34.8335665182815 85 1440 1388.94053218914 51.059467810859 86 1280 1245.16643348172 34.8335665182815 87 1280 1245.16643348172 34.8335665182815 88 1408 1360.18571244766 47.8142875523435 89 1280 1245.16643348172 34.8335665182815 90 1600 1388.94053218914 211.059467810859 91 1600 1388.94053218914 211.059467810859 92 1680 1604.60168025027 75.398319749725 93 1440 1388.94053218914 51.059467810859 94 1440 1388.94053218914 51.059467810859 95 917 885.731186713162 31.2688132868380 96 1280 1245.16643348172 34.8335665182815 97 1760 1518.33722102582 241.662778974179 98 1280 1245.16643348172 34.8335665182815 99 1280 1245.16643348172 34.8335665182815 100 1280 1245.16643348172 34.8335665182815 101 1024 1199.15872189534 -175.158721895343 102 1366 1199.15872189534 166.841278104657 103 1440 1388.94053218914 51.059467810859 104 1280 1245.16643348172 34.8335665182815 105 1280 1567.22041458635 -287.220414586345 106 1920 1647.73390986250 272.266090137498 107 1024 1199.15872189534 -175.158721895343 108 1024 1199.15872189534 -175.158721895343 109 1600 1388.94053218914 211.059467810859 110 1117 1098.51685280015 18.4831471998526 111 1440 1388.94053218914 51.059467810859 112 983 1154.58875129604 -171.588751296042 113 1024 1199.15872189534 -175.158721895343 114 1024 1015.12787554984 8.87212445015768 115 1280 1245.16643348172 34.8335665182815 116 1440 1388.94053218914 51.059467810859 117 1280 1245.16643348172 34.8335665182815 118 1280 1245.16643348172 34.8335665182815 119 1280 1245.16643348172 34.8335665182815 120 1440 1388.94053218914 51.059467810859 121 1280 1245.16643348172 34.8335665182815 122 1024 1199.15872189534 -175.158721895343 123 1024 1199.15872189534 -175.158721895343 124 1152 1337.18185665447 -185.181856654469 125 1280 1199.15872189534 80.8412781046568 126 1024 1199.15872189534 -175.158721895343 127 1366 1199.15872189534 166.841278104657 128 1680 1604.60168025027 75.398319749725 129 1680 1604.60168025027 75.398319749725 130 1280 1245.16643348172 34.8335665182815 131 1366 1199.15872189534 166.841278104657 132 1024 1199.15872189534 -175.158721895343 133 1440 1388.94053218914 51.059467810859 134 1024 1199.15872189534 -175.158721895343 135 1280 1245.16643348172 34.8335665182815 136 1280 1245.16643348172 34.8335665182815 137 1280 1245.16643348172 34.8335665182815 138 1024 1199.15872189534 -175.158721895343 139 1280 1245.16643348172 34.8335665182815 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.455754716930539 0.911509433861078 0.544245283069461 6 0.302901881262972 0.605803762525943 0.697098118737028 7 0.321628168936851 0.643256337873702 0.678371831063149 8 0.29640473220508 0.59280946441016 0.70359526779492 9 0.301773492286020 0.603546984572041 0.69822650771398 10 0.229158600652843 0.458317201305686 0.770841399347157 11 0.220374018245931 0.440748036491861 0.77962598175407 12 0.199124390323176 0.398248780646353 0.800875609676824 13 0.157749887045832 0.315499774091665 0.842250112954168 14 0.798390146830728 0.403219706338543 0.201609853169272 15 0.807088633667367 0.385822732665266 0.192911366332633 16 0.790697710739689 0.418604578520622 0.209302289260311 17 0.745461915166425 0.509076169667149 0.254538084833574 18 0.694746779001216 0.610506441997567 0.305253220998784 19 0.654009104046486 0.691981791907028 0.345990895953514 20 0.585215232346936 0.829569535306129 0.414784767653064 21 0.525286897788693 0.949426204422613 0.474713102211307 22 0.65423577764231 0.691528444715378 0.345764222357689 23 0.634429841692568 0.731140316614863 0.365570158307432 24 0.647050987082341 0.705898025835318 0.352949012917659 25 0.596686701628343 0.806626596743313 0.403313298371657 26 0.663426339359125 0.67314732128175 0.336573660640875 27 0.608069337059325 0.78386132588135 0.391930662940675 28 0.98639297784758 0.0272140443048402 0.0136070221524201 29 0.982815355493987 0.0343692890120265 0.0171846445060132 30 0.984247008054294 0.0315059838914119 0.0157529919457060 31 0.993737524960999 0.0125249500780025 0.00626247503900123 32 0.991164662999981 0.0176706740000381 0.00883533700001904 33 0.988132013637893 0.0237359727242146 0.0118679863621073 34 0.983700985473636 0.0325980290527276 0.0162990145263638 35 0.97859736565919 0.0428052686816213 0.0214026343408106 36 0.98058691888468 0.0388261622306385 0.0194130811153193 37 0.974840918966398 0.0503181620672036 0.0251590810336018 38 0.978154616135905 0.0436907677281891 0.0218453838640945 39 0.971211324114065 0.0575773517718693 0.0287886758859347 40 0.963480846823275 0.0730383063534492 0.0365191531767246 41 0.95296933193849 0.0940613361230213 0.0470306680615106 42 0.9589187387268 0.0821625225463987 0.0410812612731993 43 0.963225954619348 0.0735480907613045 0.0367740453806523 44 0.953608483279418 0.0927830334411644 0.0463915167205822 45 0.959234812404388 0.0815303751912243 0.0407651875956122 46 0.94724601609936 0.105507967801280 0.0527539839006399 47 0.940979000402846 0.118041999194308 0.0590209995971539 48 0.925748554204258 0.148502891591484 0.074251445795742 49 0.9078169551447 0.1843660897106 0.0921830448553 50 0.88688850016568 0.22622299966864 0.11311149983432 51 0.864843167693721 0.270313664612558 0.135156832306279 52 0.844734226705325 0.310531546589350 0.155265773294675 53 0.817577768581526 0.364844462836949 0.182422231418474 54 0.834111152651114 0.331777694697771 0.165888847348886 55 0.828161863765852 0.343676272468296 0.171838136234148 56 0.911245601371281 0.177508797257437 0.0887543986287187 57 0.891287896115 0.217424207770001 0.108712103885000 58 0.868300792101478 0.263398415797045 0.131699207898522 59 0.842173861245583 0.315652277508834 0.157826138754417 60 0.812869530509964 0.374260938980072 0.187130469490036 61 0.782935981717135 0.43412803656573 0.217064018282865 62 0.747703084961041 0.504593830077918 0.252296915038959 63 0.777495391174173 0.445009217651654 0.222504608825827 64 0.88630359996102 0.227392800077959 0.113696400038979 65 0.862805521240488 0.274388957519025 0.137194478759512 66 0.838097290273552 0.323805419452896 0.161902709726448 67 0.808500870458227 0.382998259083545 0.191499129541773 68 0.916412112833602 0.167175774332797 0.0835878871663985 69 0.89867373650393 0.20265252699214 0.10132626349607 70 0.876869161547538 0.246261676904925 0.123130838452462 71 0.851947396367097 0.296105207265805 0.148052603632903 72 0.825505988686742 0.348988022626516 0.174494011313258 73 0.794336800783273 0.411326398433455 0.205663199216727 74 0.925301042278577 0.149397915442847 0.0746989577214235 75 0.942794412962787 0.114411174074426 0.0572055870372129 76 0.95168667258438 0.0966266548312402 0.0483133274156201 77 0.959791114496883 0.0804177710062332 0.0402088855031166 78 0.94861840049144 0.102763199017118 0.0513815995085588 79 0.93508538142942 0.129829237141158 0.0649146185705791 80 0.919409693019979 0.161180613960043 0.0805903069800215 81 0.932472340240691 0.135055319518618 0.067527659759309 82 0.915820108706271 0.168359782587458 0.0841798912937289 83 0.927463547131503 0.145072905736994 0.0725364528684971 84 0.909675089654962 0.180649820690076 0.0903249103450381 85 0.889141443444858 0.221717113110284 0.110858556555142 86 0.864968111447011 0.270063777105978 0.135031888552989 87 0.837354133630848 0.325291732738303 0.162645866369152 88 0.80622665200949 0.387546695981018 0.193773347990509 89 0.771602561081887 0.456794877836227 0.228397438918113 90 0.810384219666647 0.379231560666707 0.189615780333353 91 0.846462102739901 0.307075794520198 0.153537897260099 92 0.81936509125643 0.361269817487142 0.180634908743571 93 0.785210161199721 0.429579677600558 0.214789838800279 94 0.74738161736553 0.50523676526894 0.25261838263447 95 0.742076055154695 0.515847889690611 0.257923944845305 96 0.702079035588081 0.595841928823837 0.297920964411919 97 0.75696711607652 0.486065767846959 0.243032883923480 98 0.71813090231586 0.563738195368279 0.281869097684140 99 0.676543745698901 0.646912508602198 0.323456254301099 100 0.632652744742957 0.734694510514086 0.367347255257043 101 0.64876129971983 0.70247740056034 0.35123870028017 102 0.699352247095861 0.601295505808277 0.300647752904139 103 0.652544852261487 0.694910295477026 0.347455147738513 104 0.607245261872757 0.785509476254485 0.392754738127243 105 0.890781764412596 0.218436471174807 0.109218235587404 106 0.910376896138908 0.179246207722183 0.0896231038610917 107 0.9180746542139 0.163850691572202 0.081925345786101 108 0.926958634563934 0.146082730872132 0.0730413654360662 109 0.950157323646614 0.0996853527067725 0.0498426763533862 110 0.938605687820113 0.122788624359774 0.0613943121798872 111 0.917988453673456 0.164023092653087 0.0820115463265437 112 0.921076454377672 0.157847091244656 0.078923545622328 113 0.932206308004822 0.135587383990357 0.0677936919951784 114 0.917201410034306 0.165597179931388 0.082798589965694 115 0.892450749494224 0.215098501011553 0.107549250505777 116 0.858404139761363 0.283191720477275 0.141595860238637 117 0.82235566985136 0.355288660297281 0.177644330148640 118 0.781015722083361 0.437968555833277 0.218984277916639 119 0.734733486595997 0.530533026808007 0.265266513404003 120 0.674947876526479 0.650104246947043 0.325052123473521 121 0.619408905435352 0.761182189129296 0.380591094564648 122 0.623185771668364 0.753628456663271 0.376814228331636 123 0.638488067609144 0.723023864781712 0.361511932390856 124 0.729761478952952 0.540477042094096 0.270238521047048 125 0.69744217015298 0.60511565969404 0.30255782984702 126 0.736095786581693 0.527808426836614 0.263904213418307 127 0.818010290273253 0.363979419453495 0.181989709726747 128 0.745959732299655 0.508080535400691 0.254040267700345 129 0.694309429655038 0.611381140689924 0.305690570344962 130 0.601105828113774 0.797788343772452 0.398894171886226 131 0.867679952495014 0.264640095009972 0.132320047504986 132 0.836649300548192 0.326701398903616 0.163350699451808 133 1 2.02666162109634e-59 1.01333081054817e-59 134 1 8.67490392411492e-42 4.33745196205746e-42 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0153846153846154 NOK 5% type I error level 12 0.0923076923076923 NOK 10% type I error level 23 0.176923076923077 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/10kchm1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/10kchm1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/1daka1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/1daka1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/2daka1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/2daka1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/36kjv1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/36kjv1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/46kjv1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/46kjv1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/56kjv1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/56kjv1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/6hbig1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/6hbig1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/792hj1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/792hj1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/892hj1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/892hj1292348177.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/992hj1292348177.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292348106fotvtud7x7rtzd1/992hj1292348177.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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Software written by Ed van Stee & Patrick Wessa

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