*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, 28 Dec 2010 11:30:45 +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/28/t1293535915l14mros99nim7b6.htm/, Retrieved Tue, 28 Dec 2010 12:32:11 +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/28/t1293535915l14mros99nim7b6.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 «

9 14 11 12 24 26 9 11 7 8 25 23 9 6 17 8 30 25 9 12 10 8 19 23 9 8 12 9 22 19 9 10 12 7 22 29 10 10 11 4 25 25 10 11 11 11 23 21 10 16 12 7 17 22 10 11 13 7 21 25 10 13 14 12 19 24 10 12 16 10 19 18 10 8 11 10 15 22 10 12 10 8 16 15 10 11 11 8 23 22 10 4 15 4 27 28 10 9 9 9 22 20 10 8 11 8 14 12 10 8 17 7 22 24 10 14 17 11 23 20 10 15 11 9 23 21 10 16 18 11 21 20 10 9 14 13 19 21 10 14 10 8 18 23 10 11 11 8 20 28 10 8 15 9 23 24 10 9 15 6 25 24 10 9 13 9 19 24 10 9 16 9 24 23 10 9 13 6 22 23 10 10 9 6 25 29 10 16 18 16 26 24 10 11 18 5 29 18 10 8 12 7 32 25 10 9 17 9 25 21 10 16 9 6 29 26 10 11 9 6 28 22 10 16 12 5 17 22 10 12 18 12 28 22 10 12 12 7 29 23 10 14 18 10 26 30 10 9 14 9 25 23 10 10 15 8 14 17 10 9 16 5 25 23 10 10 10 8 26 23 10 12 11 8 20 25 10 14 14 10 18 24 10 14 9 6 32 24 10 10 12 8 25 23 10 14 17 7 25 21 10 16 5 4 23 24 10 9 12 8 21 24 10 10 12 8 20 28 10 6 6 4 15 16 10 8 24 20 30 20 10 13 12 8 24 29 10 10 12 8 26 27 10 8 14 6 24 22 10 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 19.3022138771632 -1.09313336363418Maand[t] -0.113100006049102DoubtsAboutActions[t] + 0.339616385684055ParentalExpectations[t] + 0.0926111824644228ParentalCriticism[t] + 0.440453149254567`Organization `[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) 19.3022138771632 16.145395 1.1955 0.233732 0.116866 Maand -1.09313336363418 1.594907 -0.6854 0.494135 0.247068 DoubtsAboutActions -0.113100006049102 0.109722 -1.0308 0.304267 0.152134 ParentalExpectations 0.339616385684055 0.109455 3.1028 0.002284 0.001142 ParentalCriticism 0.0926111824644228 0.142598 0.6495 0.517016 0.258508 `Organization ` 0.440453149254567 0.079412 5.5465 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.474394730418846 R-squared 0.22505036024917 Adjusted R-squared 0.199725208623326 F-TEST (value) 8.88643683457784 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 1.99000035228103e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.77241020116043 Sum Squared Residuals 2177.35504505035 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.1795098324844 -0.179509832484445 2 25 21.4685401302742 3.53145986972577 3 30 26.3111103158694 3.68888968413056 4 19 22.3742892812773 -3.3742892812773 5 22 21.836720662288 0.16327933771202 6 22 25.8298297778066 -3.82982977780661 7 25 22.3574338840768 2.64256611592317 8 23 21.1307995582604 1.86920044173958 9 17 20.9749243330958 -3.97492433309584 10 21 23.2014001967891 -2.20140019678910 11 19 23.3374193334425 -4.3374193334425 12 19 21.3018108504035 -2.30181085040347 13 15 21.8179415431979 -6.81794154319787 14 16 17.7575307236066 -1.75753072360659 15 23 21.2934191601217 1.70658083987828 16 27 25.7158589108714 1.28414108912864 17 22 20.0520912848071 1.9479087151929 18 14 17.2281876857234 -3.22818768572335 19 22 24.4587126084181 -2.45871260841806 20 23 22.3887447049629 0.611255295037127 21 23 20.4931771691352 2.50682283086484 22 21 22.5021610785487 -1.50216107854872 23 19 22.5610710923396 -3.56107109233963 24 18 21.0549559055449 -3.05495590554492 25 20 23.9361380556491 -3.93613805564912 26 23 23.9647022019788 -0.9647022019788 27 25 23.5737686485364 1.42623135146357 28 19 23.1723694245616 -4.17236942456159 29 24 23.7507654323592 0.249234567640815 30 22 22.4540827279138 -0.454082727913752 31 25 23.6252360746558 1.37476392534417 32 26 24.7270295878891 1.27297041211089 33 29 21.6310877154986 7.36891228450144 34 32 23.2010838292524 8.79891617074765 35 25 23.2094755195341 1.79052448046589 36 29 21.6252765905975 7.37472340940248 37 28 20.4289640238248 7.57103597617524 38 17 20.789701968167 -3.78970196816699 39 28 23.9280785837187 4.07192141628131 40 29 21.8677775065468 7.13222249345319 41 26 27.0402814007282 -1.04028140072818 42 25 23.0715326609911 1.92846733900892 43 14 20.5627189626342 -6.5627189626342 44 25 23.3803207025015 1.61967929749851 45 26 21.5073559297413 4.49264407025867 46 20 22.5016786018363 -2.50167860183632 47 18 23.0390969624646 -5.03909696246455 48 32 20.9705703041866 11.0294296958134 49 25 22.1865887011094 2.81341129889056 50 25 22.4587531243597 2.54124687564025 51 23 19.2006823844233 3.79931761557668 52 21 22.7401418564131 -1.74014185641311 53 20 24.3888544473823 -4.38885444738228 54 15 17.1476736365619 -2.14767363656186 55 30 26.2781600832257 3.72183991677432 56 24 24.4900075784895 -0.490007578489537 57 26 23.9484012981277 2.05159870187229 58 24 22.4663459703923 1.53365402960766 59 22 22.6596278072516 -0.659627807251617 60 14 18.877533011766 -4.87753301176601 61 24 23.2732061881321 0.7267938118679 62 24 22.7814358711192 1.21856412888078 63 24 24.7492760241878 -0.749276024187759 64 24 21.0218874719449 2.97811252805510 65 19 21.5691387680321 -2.56913876803212 66 31 23.8599780353969 7.14002196460312 67 22 22.5136254767782 -0.513625476778157 68 27 21.7583987943335 5.24160120566654 69 19 21.8637398451743 -2.86373984517431 70 25 22.6147786078854 2.38522139211458 71 20 21.8797243814887 -1.87972438148865 72 21 21.1882283676420 -0.188228367641955 73 27 24.7325084944388 2.26749150556117 74 23 23.9366205323615 -0.936620532361528 75 25 24.014221797791 0.985778202209004 76 20 21.3056824026003 -1.30568240260031 77 21 22.7694889961774 -1.76948899617737 78 22 23.1726857920983 -1.17268579209834 79 23 23.9238748131705 -0.923874813170529 80 25 21.7874295665610 3.21257043343902 81 25 24.0208400245442 0.9791599754558 82 17 23.6207317873855 -6.6207317873855 83 19 21.8595519254407 -2.85955192544072 84 25 24.3969297701273 0.603070229872722 85 19 21.8597021838018 -2.85970218380181 86 20 23.7797962045867 -3.7797962045867 87 26 22.0095919172867 3.99040808271332 88 23 23.3580584153883 -0.35805841538827 89 27 23.4340681772794 3.56593182272057 90 17 21.2130712201359 -4.21307122013588 91 17 22.8538745975357 -5.85387459753571 92 19 21.6488539729445 -2.64885397294445 93 17 20.7768059906149 -3.77680599061490 94 22 21.6988560454691 0.301143954530942 95 21 23.9071072834216 -2.9071072834216 96 32 26.9349403498873 5.06505965011267 97 21 23.1607389171565 -2.16073891715649 98 21 23.374525428415 -2.37452542841502 99 18 21.326171226185 -3.32617122618499 100 18 20.7643924897752 -2.76439248977523 101 23 22.5097539245813 0.490246075418683 102 19 21.4597600558188 -2.45976005581877 103 20 21.7790537270938 -1.77905372709380 104 21 23.1764070859341 -2.17640708593409 105 20 24.2225135516852 -4.22251355168523 106 17 17.5931135497992 -0.593113549799169 107 18 18.9982258638477 -0.998225863847708 108 19 19.3009022637349 -0.300902263734906 109 22 22.1499650828493 -0.149965082849330 110 15 20.6680600134750 -5.66806001347505 111 14 20.5583649337250 -6.55836493372495 112 18 24.5821521350561 -6.58215213505612 113 24 20.3504136557850 3.64958634421495 114 35 22.1987016852269 12.8012983147731 115 29 21.5583567299629 7.4416432700371 116 21 22.915024700753 -1.91502470075300 117 25 20.3729923104350 4.62700768956498 118 20 19.1076045760611 0.892395423938942 119 22 23.2861021656842 -1.28610216568419 120 13 15.9400469299208 -2.94004692992075 121 26 19.5645088875278 6.4354911124722 122 17 18.8977054678139 -1.89770546781394 123 25 20.9294423986561 4.07055760134386 124 20 21.0707743326836 -1.07077433268360 125 19 20.4854182139269 -1.48541821392691 126 21 23.7715706234806 -2.77157062348061 127 22 21.8035643612364 0.196435638763590 128 24 23.05523175714 0.944768242860015 129 21 24.2797921027057 -3.27979210270568 130 26 22.2754785897381 3.72452141026189 131 24 20.4886728818648 3.51132711813517 132 16 21.4187824086494 -5.41878240864941 133 23 23.0035982218449 -0.00359822184492027 134 18 21.0234948262978 -3.02349482629779 135 16 22.1865887011094 -6.18658870110944 136 26 24.3089889841089 1.69101101589115 137 19 20.3407068702696 -1.34070687026959 138 21 17.9880847646140 3.01191523538596 139 21 22.9458530449266 -1.94585304492664 140 22 18.7867194012477 3.21328059875229 141 23 16.8438723590342 6.15612764096582 142 29 22.7240070617377 6.27599293826232 143 21 21.1950285543854 -0.195028554385392 144 21 20.0856263443050 0.914373655695048 145 23 23.3827510095211 -0.382751009521110 146 27 21.4236030634565 5.57639693654351 147 25 22.3285692210250 2.67143077897503 148 21 20.5461016912464 0.453898308753637 149 10 17.9877683970773 -7.9877683970773 150 20 21.9558844017409 -1.9558844017409 151 26 21.8384303667825 4.16156963321745 152 24 23.3069073568056 0.693092643194387 153 29 27.6801438792798 1.31985612072019 154 19 17.9487144717976 1.05128552820243 155 24 23.9321162450912 0.067883754908809 156 19 21.5731764294046 -2.57317642940462 157 24 21.8350254404835 2.16497455951646 158 22 22.6109070556886 -0.610907055688577 159 17 23.3048333765549 -6.30483337655489 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.519481478592316 0.961037042815368 0.480518521407684 10 0.423875242886899 0.847750485773799 0.576124757113101 11 0.362764797226806 0.725529594453611 0.637235202773194 12 0.243981598593985 0.48796319718797 0.756018401406015 13 0.607228287268035 0.78554342546393 0.392771712731965 14 0.504807301689688 0.990385396620624 0.495192698310312 15 0.472291065004565 0.94458213000913 0.527708934995435 16 0.375898477609545 0.75179695521909 0.624101522390455 17 0.316039568252978 0.632079136505956 0.683960431747022 18 0.301894066432194 0.603788132864388 0.698105933567806 19 0.236881047696959 0.473762095393918 0.763118952303041 20 0.246953383417575 0.49390676683515 0.753046616582425 21 0.262791723713176 0.525583447426352 0.737208276286824 22 0.204245148458703 0.408490296917406 0.795754851541297 23 0.1644555088605 0.328911017721 0.8355444911395 24 0.137096295558384 0.274192591116767 0.862903704441616 25 0.120340969839388 0.240681939678777 0.879659030160612 26 0.088001630233359 0.176003260466718 0.91199836976664 27 0.069470080587295 0.13894016117459 0.930529919412705 28 0.0619906856211283 0.123981371242257 0.938009314378872 29 0.0465716063882221 0.0931432127764442 0.953428393611778 30 0.0320122948684838 0.0640245897369675 0.967987705131516 31 0.0260345249066770 0.0520690498133539 0.973965475093323 32 0.0299179078770836 0.0598358157541672 0.970082092122916 33 0.0672234318439303 0.134446863687861 0.93277656815607 34 0.274074227831137 0.548148455662275 0.725925772168863 35 0.234729703971434 0.469459407942868 0.765270296028566 36 0.360169024191121 0.720338048382242 0.639830975808879 37 0.492619323597903 0.985238647195806 0.507380676402097 38 0.560061061311946 0.879877877376108 0.439938938688054 39 0.590593132772741 0.818813734454519 0.409406867227259 40 0.690760897322878 0.618478205354245 0.309239102677122 41 0.646374604893719 0.707250790212563 0.353625395106281 42 0.607695781312439 0.784608437375122 0.392304218687561 43 0.707380550235707 0.585238899528587 0.292619449764293 44 0.665557400142472 0.668885199715056 0.334442599857528 45 0.676353932092491 0.647292135815018 0.323646067907509 46 0.655757217493275 0.68848556501345 0.344242782506725 47 0.684269922104255 0.63146015579149 0.315730077895745 48 0.890486260624858 0.219027478750284 0.109513739375142 49 0.87635082392922 0.247298352141558 0.123649176070779 50 0.858835701710217 0.282328596579566 0.141164298289783 51 0.845145657935587 0.309708684128826 0.154854342064413 52 0.822598384266035 0.35480323146793 0.177401615733965 53 0.838600644732248 0.322798710535505 0.161399355267752 54 0.826512828704134 0.346974342591732 0.173487171295866 55 0.870313477756179 0.259373044487643 0.129686522243821 56 0.844623031689563 0.310753936620873 0.155376968310437 57 0.82127177914747 0.35745644170506 0.17872822085253 58 0.792584033800938 0.414831932398123 0.207415966199062 59 0.759965555173892 0.480068889652217 0.240034444826108 60 0.784739952810326 0.430520094379348 0.215260047189674 61 0.748985529472131 0.502028941055737 0.251014470527869 62 0.713535381159232 0.572929237681536 0.286464618840768 63 0.677398778547435 0.64520244290513 0.322601221452565 64 0.658660727377545 0.68267854524491 0.341339272622455 65 0.639387114545896 0.721225770908208 0.360612885454104 66 0.733653177296641 0.532693645406718 0.266346822703359 67 0.694593100199406 0.610813799601187 0.305406899800594 68 0.732061552941342 0.535876894117315 0.267938447058658 69 0.720129335052101 0.559741329895798 0.279870664947899 70 0.69571780402744 0.60856439194512 0.30428219597256 71 0.664487898205593 0.671024203588815 0.335512101794407 72 0.621425454281528 0.757149091436945 0.378574545718472 73 0.594006236278305 0.81198752744339 0.405993763721695 74 0.550573669638024 0.898852660723953 0.449426330361976 75 0.511508559190438 0.976982881619123 0.488491440809562 76 0.469816335951798 0.939632671903595 0.530183664048202 77 0.437107983616314 0.874215967232627 0.562892016383686 78 0.395798819208499 0.791597638416998 0.604201180791501 79 0.356877964394846 0.713755928789692 0.643122035605154 80 0.348180192709431 0.696360385418861 0.65181980729057 81 0.309934077575163 0.619868155150325 0.690065922424837 82 0.393343308113855 0.78668661622771 0.606656691886145 83 0.37243499518249 0.74486999036498 0.62756500481751 84 0.330883889319076 0.661767778638152 0.669116110680924 85 0.314190839496031 0.628381678992062 0.685809160503969 86 0.311078400304826 0.622156800609652 0.688921599695174 87 0.321737423514638 0.643474847029275 0.678262576485362 88 0.28193191758914 0.56386383517828 0.71806808241086 89 0.278879598864288 0.557759197728577 0.721120401135712 90 0.283464270243136 0.566928540486272 0.716535729756864 91 0.33220452992499 0.66440905984998 0.66779547007501 92 0.307346823545459 0.614693647090917 0.692653176454541 93 0.301908465949577 0.603816931899153 0.698091534050423 94 0.262822654684782 0.525645309369564 0.737177345315218 95 0.245549797908869 0.491099595817737 0.754450202091131 96 0.281638347674940 0.563276695349879 0.71836165232506 97 0.252925597509073 0.505851195018146 0.747074402490927 98 0.227925611034910 0.455851222069819 0.77207438896509 99 0.215710338794078 0.431420677588156 0.784289661205922 100 0.197226782160497 0.394453564320995 0.802773217839503 101 0.16611475907843 0.33222951815686 0.83388524092157 102 0.146768060461599 0.293536120923198 0.853231939538401 103 0.124638653021135 0.24927730604227 0.875361346978865 104 0.107679249363384 0.215358498726767 0.892320750636616 105 0.112845013202983 0.225690026405967 0.887154986797017 106 0.0912096802584886 0.182419360516977 0.908790319741511 107 0.0742996080015195 0.148599216003039 0.92570039199848 108 0.0595120769132103 0.119024153826421 0.94048792308679 109 0.0462917349239518 0.0925834698479035 0.953708265076048 110 0.0604981063925752 0.120996212785150 0.939501893607425 111 0.0953094284634925 0.190618856926985 0.904690571536507 112 0.151574925107431 0.303149850214861 0.84842507489257 113 0.141696807568731 0.283393615137461 0.85830319243127 114 0.584365803569274 0.831268392861452 0.415634196430726 115 0.724327232308886 0.551345535382229 0.275672767691114 116 0.686486144429656 0.627027711140688 0.313513855570344 117 0.736185254734636 0.527629490530728 0.263814745265364 118 0.690330183772103 0.619339632455795 0.309669816227898 119 0.650943159801918 0.698113680396164 0.349056840198082 120 0.652848622405789 0.694302755188421 0.347151377594211 121 0.727167620167449 0.545664759665102 0.272832379832551 122 0.697168350085918 0.605663299828164 0.302831649914082 123 0.692824428588809 0.614351142822382 0.307175571411191 124 0.639762498392042 0.720475003215916 0.360237501607958 125 0.666550476138439 0.666899047723122 0.333449523861561 126 0.636636060336399 0.726727879327203 0.363363939663602 127 0.579223944977798 0.841552110044404 0.420776055022202 128 0.522232412404737 0.955535175190527 0.477767587595263 129 0.488390317861649 0.976780635723298 0.511609682138351 130 0.456553528266256 0.913107056532513 0.543446471733744 131 0.454568477651944 0.909136955303888 0.545431522348056 132 0.492384657294839 0.984769314589678 0.507615342705161 133 0.425037108970963 0.850074217941926 0.574962891029037 134 0.399065597889605 0.79813119577921 0.600934402110395 135 0.52686396307558 0.94627207384884 0.47313603692442 136 0.464632508783106 0.929265017566212 0.535367491216894 137 0.43737437571738 0.87474875143476 0.56262562428262 138 0.386123278124523 0.772246556249046 0.613876721875477 139 0.337906655438569 0.675813310877139 0.662093344561431 140 0.304442418916989 0.608884837833978 0.695557581083011 141 0.41601709527614 0.83203419055228 0.58398290472386 142 0.540947880171498 0.918104239657005 0.459052119828502 143 0.672766681928406 0.654466636143187 0.327233318071594 144 0.609086881259463 0.781826237481075 0.390913118740537 145 0.507321418189199 0.985357163621602 0.492678581810801 146 0.513062301677756 0.973875396644487 0.486937698322244 147 0.49534768405517 0.99069536811034 0.50465231594483 148 0.368535894545484 0.737071789090967 0.631464105454516 149 0.562338170860514 0.875323658278972 0.437661829139486 150 0.467320178667623 0.934640357335245 0.532679821332377 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 5 0.0352112676056338 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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