*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: Wed, 29 Dec 2010 12:28:26 +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/29/t12936256389i9b2y3h6sv9yvl.htm/, Retrieved Wed, 29 Dec 2010 13:27:30 +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/29/t12936256389i9b2y3h6sv9yvl.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 «

1567 0 2237 0 2598 0 3729 0 5715 0 5776 0 5852 0 6878 0 5488 0 3583 0 2054 0 2282 0 1552 0 2261 0 2446 0 3519 0 5161 0 5085 0 5711 0 6057 0 5224 0 3363 0 1899 0 2115 0 1491 0 2061 0 2419 0 3430 0 4778 0 4862 0 6176 0 5664 0 5529 0 3418 0 1941 0 2402 0 1579 0 2146 0 2462 0 3695 0 4831 0 5134 0 6250 0 5760 0 6249 0 2917 0 1741 0 2359 0 1511 0 2059 0 2635 0 2867 0 4403 0 5720 0 4502 0 5749 0 5627 0 2846 0 1762 0 2429 0 1169 0 2154 0 2249 0 2687 0 4359 0 5382 0 4459 0 6398 0 4596 0 3024 0 1887 0 2070 0 1351 0 2218 0 2461 0 3028 0 4784 0 4975 1 4607 1 6249 1 4809 1 3157 1 1910 1 2228 1 1673 1 2589 1 2332 1 3785 1 4916 1 5207 1 6055 1 5751 1 5247 1 3387 1 2091 1 2401 1 1664 1 2205 1 2295 1 3762 1 4890 1 5117 1 6099 1 5865 1 5594 1 3229 1 2106 1 2410 1 1583 1 2092 1 2612 1 3665 1 4880 1 5875 1 5892 1 6078 1 6515 1 3164 1 2028 1 2677 1 1580 1 2196 1 2838 1 3087 1 4726 1 6521 1 6739 1 5943 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Aantalhuwelijken[t] = + 2248.6655982906 + 169.478174603174Dummy[t] -813.27090964591M1[t] -105.655525030524M2[t] + 169.036782661784M3[t] + 1065.03678266178M4[t] + 2618.65216727716M5[t] + 3073.69230769231M6[t] + 3246.07692307692M7[t] + 3903.46153846154M8[t] + 3222.84615384615M9[t] + 955.307692307692M10[t] -376.692307692306M11[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) 2248.6655982906 119.134777 18.875 0 0 Dummy 169.478174603174 65.859639 2.5733 0.011091 0.005545 M1 -813.27090964591 160.92428 -5.0537 1e-06 1e-06 M2 -105.655525030524 160.92428 -0.6566 0.512523 0.256261 M3 169.036782661784 160.92428 1.0504 0.295301 0.14765 M4 1065.03678266178 160.92428 6.6182 0 0 M5 2618.65216727716 160.92428 16.2726 0 0 M6 3073.69230769231 160.844515 19.1097 0 0 M7 3246.07692307692 160.844515 20.1815 0 0 M8 3903.46153846154 160.844515 24.2685 0 0 M9 3222.84615384615 160.844515 20.037 0 0 M10 955.307692307692 160.844515 5.9393 0 0 M11 -376.692307692306 160.844515 -2.342 0.020562 0.010281 Multiple Linear Regression - Regression Statistics Multiple R 0.97194288209495 R-squared 0.944672966055038 Adjusted R-squared 0.940030138031685 F-TEST (value) 203.469299595706 F-TEST (DF numerator) 12 F-TEST (DF denominator) 143 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 410.074661434315 Sum Squared Residuals 24047055.5969170 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1567 1435.39468864469 131.60531135531 2 2237 2143.01007326007 93.9899267399274 3 2598 2417.70238095238 180.297619047623 4 3729 3313.70238095238 415.297619047616 5 5715 4867.31776556777 847.682234432233 6 5776 5322.35790598291 453.642094017094 7 5852 5494.74252136751 357.257478632492 8 6878 6152.12713675215 725.872863247851 9 5488 5471.51175213675 16.4882478632508 10 3583 3203.97329059830 379.026709401704 11 2054 1871.97329059828 182.026709401717 12 2282 2248.6655982906 33.3344017094019 13 1552 1435.39468864469 116.605311355312 14 2261 2143.01007326007 117.989926739927 15 2446 2417.70238095238 28.2976190476187 16 3519 3313.70238095238 205.297619047619 17 5161 4867.31776556777 293.682234432235 18 5085 5322.35790598291 -237.357905982906 19 5711 5494.74252136752 216.257478632477 20 6057 6152.12713675214 -95.1271367521358 21 5224 5471.51175213675 -247.511752136752 22 3363 3203.97329059829 159.02670940171 23 1899 1871.97329059829 27.0267094017086 24 2115 2248.6655982906 -133.665598290598 25 1491 1435.39468864469 55.6053113553113 26 2061 2143.01007326007 -82.0100732600734 27 2419 2417.70238095238 1.29761904761871 28 3430 3313.70238095238 116.297619047619 29 4778 4867.31776556777 -89.3177655677652 30 4862 5322.35790598291 -460.357905982906 31 6176 5494.74252136752 681.257478632477 32 5664 6152.12713675214 -488.127136752136 33 5529 5471.51175213675 57.4882478632475 34 3418 3203.97329059829 214.02670940171 35 1941 1871.97329059829 69.0267094017081 36 2402 2248.6655982906 153.334401709402 37 1579 1435.39468864469 143.605311355311 38 2146 2143.01007326007 2.9899267399266 39 2462 2417.70238095238 44.2976190476187 40 3695 3313.70238095238 381.297619047619 41 4831 4867.31776556777 -36.3177655677651 42 5134 5322.35790598291 -188.357905982906 43 6250 5494.74252136752 755.257478632477 44 5760 6152.12713675214 -392.127136752136 45 6249 5471.51175213675 777.488247863247 46 2917 3203.97329059829 -286.97329059829 47 1741 1871.97329059829 -130.973290598291 48 2359 2248.6655982906 110.334401709402 49 1511 1435.39468864469 75.6053113553113 50 2059 2143.01007326007 -84.0100732600734 51 2635 2417.70238095238 217.297619047619 52 2867 3313.70238095238 -446.702380952381 53 4403 4867.31776556777 -464.317765567765 54 5720 5322.35790598291 397.642094017094 55 4502 5494.74252136752 -992.742521367523 56 5749 6152.12713675214 -403.127136752136 57 5627 5471.51175213675 155.488247863247 58 2846 3203.97329059829 -357.97329059829 59 1762 1871.97329059829 -109.973290598291 60 2429 2248.6655982906 180.334401709402 61 1169 1435.39468864469 -266.394688644689 62 2154 2143.01007326007 10.9899267399266 63 2249 2417.70238095238 -168.702380952381 64 2687 3313.70238095238 -626.70238095238 65 4359 4867.31776556777 -508.317765567765 66 5382 5322.35790598291 59.6420940170937 67 4459 5494.74252136752 -1035.74252136752 68 6398 6152.12713675214 245.872863247864 69 4596 5471.51175213675 -875.511752136752 70 3024 3203.97329059829 -179.973290598290 71 1887 1871.97329059829 15.0267094017086 72 2070 2248.6655982906 -178.665598290598 73 1351 1435.39468864469 -84.3946886446887 74 2218 2143.01007326007 74.9899267399265 75 2461 2417.70238095238 43.2976190476187 76 3028 3313.70238095238 -285.702380952381 77 4784 4867.31776556777 -83.3177655677652 78 4975 5491.83608058608 -516.836080586081 79 4607 5664.2206959707 -1057.22069597070 80 6249 6321.60531135531 -72.6053113553099 81 4809 5640.98992673993 -831.989926739926 82 3157 3373.45146520146 -216.451465201465 83 1910 2041.45146520147 -131.451465201466 84 2228 2418.14377289377 -190.143772893772 85 1673 1604.87286324786 68.1271367521368 86 2589 2312.48824786325 276.511752136752 87 2332 2587.18055555556 -255.180555555556 88 3785 3483.18055555556 301.819444444444 89 4916 5036.79594017094 -120.795940170940 90 5207 5491.83608058608 -284.836080586081 91 6055 5664.2206959707 390.779304029303 92 5751 6321.60531135531 -570.60531135531 93 5247 5640.98992673993 -393.989926739927 94 3387 3373.45146520146 13.5485347985350 95 2091 2041.45146520147 49.5485347985342 96 2401 2418.14377289377 -17.1437728937722 97 1664 1604.87286324786 59.1271367521368 98 2205 2312.48824786325 -107.488247863248 99 2295 2587.18055555556 -292.180555555556 100 3762 3483.18055555556 278.819444444445 101 4890 5036.79594017094 -146.795940170940 102 5117 5491.83608058608 -374.836080586081 103 6099 5664.2206959707 434.779304029303 104 5865 6321.60531135531 -456.60531135531 105 5594 5640.98992673993 -46.9899267399269 106 3229 3373.45146520146 -144.451465201465 107 2106 2041.45146520147 64.5485347985342 108 2410 2418.14377289377 -8.1437728937722 109 1583 1604.87286324786 -21.8728632478631 110 2092 2312.48824786325 -220.488247863248 111 2612 2587.18055555556 24.8194444444442 112 3665 3483.18055555556 181.819444444445 113 4880 5036.79594017094 -156.795940170940 114 5875 5491.83608058608 383.163919413919 115 5892 5664.2206959707 227.779304029303 116 6078 6321.60531135531 -243.60531135531 117 6515 5640.98992673993 874.010073260073 118 3164 3373.45146520146 -209.451465201465 119 2028 2041.45146520147 -13.4514652014658 120 2677 2418.14377289377 258.856227106227 121 1580 1604.87286324786 -24.8728632478631 122 2196 2312.48824786325 -116.488247863248 123 2838 2587.18055555556 250.819444444444 124 3087 3483.18055555556 -396.180555555555 125 4726 5036.79594017094 -310.795940170940 126 6521 5491.83608058608 1029.16391941392 127 6739 5664.2206959707 1074.77930402930 128 5943 6321.60531135531 -378.60531135531 129 6265 5640.98992673993 624.010073260073 130 3323 3373.45146520146 -50.451465201465 131 2098 2041.45146520147 56.5485347985342 132 2544 2418.14377289377 125.856227106227 133 1442 1604.87286324786 -162.872863247863 134 2307 2312.48824786325 -5.48824786324774 135 2811 2587.18055555556 223.819444444444 136 3461 3483.18055555556 -22.1805555555554 137 5451 5036.79594017094 414.20405982906 138 5481 5491.83608058608 -10.8360805860811 139 5114 5664.2206959707 -550.220695970697 140 8381 6321.60531135531 2059.39468864469 141 5215 5640.98992673993 -425.989926739927 142 3700 3373.45146520146 326.548534798535 143 2122 2041.45146520147 80.5485347985342 144 2311 2418.14377289377 -107.143772893772 145 1515 1604.87286324786 -89.8728632478631 146 2351 2312.48824786325 38.5117521367523 147 2289 2587.18055555556 -298.180555555556 148 3380 3483.18055555556 -103.180555555555 149 5398 5036.79594017094 361.20405982906 150 5242 5491.83608058608 -249.836080586081 151 5162 5664.2206959707 -502.220695970697 152 6391 6321.60531135531 69.39468864469 153 5958 5640.98992673993 317.010073260073 154 3727 3373.45146520146 353.548534798535 155 1883 2041.45146520147 -158.451465201466 156 2191 2418.14377289377 -227.143772893772 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0224569505085652 0.0449139010171303 0.977543049491435 17 0.106502278896379 0.213004557792758 0.89349772110362 18 0.222203030457395 0.444406060914789 0.777796969542605 19 0.137115485791067 0.274230971582135 0.862884514208933 20 0.275289865607203 0.550579731214407 0.724710134392797 21 0.206275266673710 0.412550533347421 0.79372473332629 22 0.147428028567830 0.294856057135659 0.85257197143217 23 0.0981135054955831 0.196227010991166 0.901886494504417 24 0.063876871516078 0.127753743032156 0.936123128483922 25 0.0386495282021686 0.0772990564043372 0.961350471797831 26 0.024957432584119 0.049914865168238 0.975042567415881 27 0.0145529323346813 0.0291058646693626 0.985447067665319 28 0.00927222547555814 0.0185444509511163 0.990727774524442 29 0.0216401029112766 0.0432802058225532 0.978359897088723 30 0.0313961965548904 0.0627923931097808 0.96860380344511 31 0.0336300899156815 0.067260179831363 0.966369910084318 32 0.0784795782824617 0.156959156564923 0.921520421717538 33 0.0572864466560922 0.114572893312184 0.942713553343908 34 0.0403288841676651 0.0806577683353302 0.959671115832335 35 0.0270739132362832 0.0541478264725663 0.972926086763717 36 0.0194985657368962 0.0389971314737924 0.980501434263104 37 0.0128113215378100 0.0256226430756200 0.98718867846219 38 0.0080917288949488 0.0161834577898976 0.991908271105051 39 0.0050154641316135 0.010030928263227 0.994984535868386 40 0.00362141748142747 0.00724283496285494 0.996378582518572 41 0.00341479101421986 0.00682958202843973 0.99658520898578 42 0.00212945193196431 0.00425890386392861 0.997870548068036 43 0.00293060247147311 0.00586120494294621 0.997069397528527 44 0.00321185407391571 0.00642370814783143 0.996788145926084 45 0.0157331339527781 0.0314662679055562 0.984266866047222 46 0.0186825385237882 0.0373650770475763 0.981317461476212 47 0.0140470475017306 0.0280940950034612 0.98595295249827 48 0.00996888748179733 0.0199377749635947 0.990031112518203 49 0.00690847993058095 0.0138169598611619 0.993091520069419 50 0.00468652003481925 0.0093730400696385 0.99531347996518 51 0.00352181337114639 0.00704362674229279 0.996478186628854 52 0.00752739121825487 0.0150547824365097 0.992472608781745 53 0.0137316776901667 0.0274633553803335 0.986268322309833 54 0.0171306558161259 0.0342613116322518 0.982869344183874 55 0.177205100351373 0.354410200702745 0.822794899648628 56 0.162034353718286 0.324068707436573 0.837965646281714 57 0.138996978151436 0.277993956302873 0.861003021848564 58 0.134246495650416 0.268492991300831 0.865753504349584 59 0.109588688512528 0.219177377025055 0.890411311487472 60 0.0938261171966572 0.187652234393314 0.906173882803343 61 0.0833960498432985 0.166792099686597 0.916603950156702 62 0.0662238124961096 0.132447624992219 0.93377618750389 63 0.0546876815303646 0.109375363060729 0.945312318469635 64 0.0772552403949966 0.154510480789993 0.922744759605003 65 0.0868224410639883 0.173644882127977 0.913177558936012 66 0.0704234310134558 0.140846862026912 0.929576568986544 67 0.208734432661900 0.417468865323800 0.7912655673381 68 0.19521734856645 0.3904346971329 0.80478265143355 69 0.320412635583143 0.640825271166287 0.679587364416857 70 0.282558157928667 0.565116315857334 0.717441842071333 71 0.242104145843017 0.484208291686035 0.757895854156982 72 0.211127380830380 0.422254761660759 0.78887261916962 73 0.178099527915418 0.356199055830835 0.821900472084582 74 0.149295531820929 0.298591063641857 0.850704468179071 75 0.125131339095946 0.250262678191891 0.874868660904054 76 0.107805445782328 0.215610891564656 0.892194554217672 77 0.0868013450275972 0.173602690055194 0.913198654972403 78 0.0809904815703343 0.161980963140669 0.919009518429666 79 0.140837632097271 0.281675264194541 0.85916236790273 80 0.145554974320011 0.291109948640022 0.85444502567999 81 0.189091743339445 0.378183486678889 0.810908256660555 82 0.172543504877151 0.345087009754303 0.827456495122849 83 0.153055114095358 0.306110228190717 0.846944885904642 84 0.131091845730247 0.262183691460495 0.868908154269753 85 0.119028071859263 0.238056143718527 0.880971928140737 86 0.123582555363563 0.247165110727126 0.876417444636437 87 0.102734946123872 0.205469892247743 0.897265053876128 88 0.105789319451817 0.211578638903634 0.894210680548183 89 0.0863050844696556 0.172610168939311 0.913694915530344 90 0.076079824891809 0.152159649783618 0.923920175108191 91 0.0834322856602698 0.166864571320540 0.91656771433973 92 0.098945258755573 0.197890517511146 0.901054741244427 93 0.101665706711472 0.203331413422945 0.898334293288528 94 0.0832028497769755 0.166405699553951 0.916797150223025 95 0.0672631583837464 0.134526316767493 0.932736841616254 96 0.0527752000454015 0.105550400090803 0.947224799954599 97 0.041649357465942 0.083298714931884 0.958350642534058 98 0.0314420113376828 0.0628840226753655 0.968557988662317 99 0.0258712307034809 0.0517424614069617 0.97412876929652 100 0.0236637712176412 0.0473275424352825 0.976336228782359 101 0.0179790737712938 0.0359581475425877 0.982020926228706 102 0.0188000304518922 0.0376000609037845 0.981199969548108 103 0.0200459750592483 0.0400919501184966 0.979954024940752 104 0.026399766076411 0.052799532152822 0.973600233923589 105 0.0226950635024775 0.0453901270049549 0.977304936497523 106 0.0173178299322224 0.0346356598644448 0.982682170067778 107 0.0126399172937594 0.0252798345875189 0.98736008270624 108 0.00890960816274954 0.0178192163254991 0.99109039183725 109 0.00616211360549316 0.0123242272109863 0.993837886394507 110 0.00439018741080737 0.00878037482161474 0.995609812589193 111 0.00296818270959089 0.00593636541918178 0.99703181729041 112 0.00231287492411378 0.00462574984822757 0.997687125075886 113 0.00164855023552359 0.00329710047104719 0.998351449764476 114 0.00142927378683192 0.00285854757366384 0.998570726213168 115 0.00103303176695592 0.00206606353391184 0.998966968233044 116 0.00139253208564243 0.00278506417128486 0.998607467914358 117 0.00373685716957970 0.00747371433915939 0.99626314283042 118 0.00293051030799662 0.00586102061599325 0.997069489692003 119 0.00184456490939793 0.00368912981879586 0.998155435090602 120 0.00138530212946806 0.00277060425893612 0.998614697870532 121 0.000843717270372868 0.00168743454074574 0.999156282729627 122 0.000507034634590998 0.00101406926918200 0.99949296536541 123 0.000346238182095778 0.000692476364191555 0.999653761817904 124 0.000252144945537366 0.000504289891074732 0.999747855054463 125 0.000262000815576652 0.000524001631153304 0.999737999184423 126 0.00189800264273973 0.00379600528547945 0.99810199735726 127 0.0366053905811792 0.0732107811623584 0.96339460941882 128 0.197410532890698 0.394821065781396 0.802589467109302 129 0.248363982048039 0.496727964096078 0.751636017951961 130 0.218327980098889 0.436655960197778 0.78167201990111 131 0.164194721163796 0.328389442327592 0.835805278836204 132 0.129314398937784 0.258628797875569 0.870685601062216 133 0.0898303694761895 0.179660738952379 0.91016963052381 134 0.0586223926950855 0.117244785390171 0.941377607304914 135 0.0486693740867543 0.0973387481735086 0.951330625913246 136 0.0287124702766257 0.0574249405532514 0.971287529723374 137 0.016722024530169 0.033444049060338 0.983277975469831 138 0.0088592226532433 0.0177184453064866 0.991140777346757 139 0.00442666973594812 0.00885333947189624 0.995573330264052 140 0.629076330187278 0.741847339625445 0.370923669812722 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.2 NOK 5% type I error level 53 0.424 NOK 10% type I error level 65 0.52 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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