*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, 22 Dec 2010 20:28:14 +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/22/t1293049786xq1916d6sjljtvh.htm/, Retrieved Wed, 22 Dec 2010 21:29:46 +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/22/t1293049786xq1916d6sjljtvh.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 «

13 11 23 1 6 12 22 24 2 5 26 23 24 2 20 16 21 21 2 12 18 19 21 2 11 12 12 19 2 12 18 24 12 1 11 20 21 21 1 9 18 21 25 2 13 24 26 27 2 9 17 18 21 1 14 19 21 27 1 12 12 22 20 1 18 25 26 16 2 9 23 20 26 1 15 22 20 24 2 12 23 26 25 2 12 16 27 25 1 12 16 27 27 1 15 15 16 23 2 11 24 26 22 1 13 18 20 10 1 10 23 25 25 2 17 18 16 18 1 13 19 20 21 1 17 17 20 20 1 15 22 24 18 1 13 22 24 25 1 17 8 22 28 1 21 12 18 27 1 12 22 21 20 2 12 16 17 20 1 15 12 15 20 2 8 28 28 27 2 15 15 23 23 1 16 17 19 23 2 9 16 15 22 2 13 24 26 26 1 11 27 20 21 1 9 10 11 17 1 15 20 17 27 2 9 17 16 16 2 15 20 21 26 1 14 16 18 17 1 8 16 17 24 2 11 22 21 23 2 14 19 18 20 1 14 11 16 10 1 12 11 13 21 1 15 28 28 25 1 11 12 25 28 1 11 22 24 25 2 9 15 15 20 2 8 19 21 20 1 13 12 11 27 1 12 18 27 26 1 24 21 23 19 2 11 21 21 26 1 11 15 16 20 2 16 12 20 22 1 12 25 21 19 2 18 12 10 23 2 12 25 18 28 2 14 17 20 22 2 16 26 21 27 2 24 24 24 14 1 13 18 26 25 1 11 20 23 22 1 14 17 22 24 1 16 11 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation E/Introjected[t] = + 7.19886437536333 + 0.537098324370937`I/Accomp.`[t] + 0.139674730633224`E/Ext.Regulation`[t] -0.669211159060354gender[t] + 0.0867952854772109PE[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) 7.19886437536333 2.588791 2.7808 0.006154 0.003077 `I/Accomp.` 0.537098324370937 0.067589 7.9465 0 0 `E/Ext.Regulation` 0.139674730633224 0.083014 1.6826 0.094644 0.047322 gender -0.669211159060354 0.641333 -1.0435 0.298492 0.149246 PE 0.0867952854772109 0.090217 0.9621 0.337636 0.168818 Multiple Linear Regression - Regression Statistics Multiple R 0.570779891253353 R-squared 0.325789684259189 Adjusted R-squared 0.306930654448258 F-TEST (value) 17.2749970452002 F-TEST (DF numerator) 4 F-TEST (DF denominator) 143 p-value 1.39434019885698e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.58298406921987 Sum Squared Residuals 1835.80180216053 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 17.2452219505526 -6.24522195055256 2 22 16.0917919122773 5.90820808772271 3 23 24.9130977356286 -1.91309773562856 4 21 18.4287280162018 2.57127198379816 5 19 19.4161293794665 -0.416129379466504 6 12 16.0009852574516 -4.00098525745165 7 24 18.8282679628278 5.17173203717216 8 21 20.9859466163143 0.014053383685691 9 21 20.1484188729538 0.85158112704618 10 26 23.3031771385370 2.69682286146296 11 18 19.8086280705876 -1.80862807058755 12 21 21.5472825321743 -0.547282532174348 13 22 17.3306428600085 4.66935713999151 14 26 22.3038534259425 3.69614657405748 15 20 23.8163869554565 -3.8163869554565 16 20 22.0703421543271 -2.07034215432713 17 26 22.7471152093313 3.25288479066871 18 27 19.6566380977951 7.34336190220491 19 27 20.1963734154932 6.80362658450683 20 16 18.0841838676201 -2.08418386762014 21 26 23.6211957863401 2.37880421365988 22 20 18.4621232160842 1.53787678391581 23 25 23.1810916367173 1.81890836328265 24 16 19.8399069175816 -3.83990691758161 25 20 21.1432105757611 -1.14321057576106 26 20 19.7557486254315 0.244251374568459 27 24 21.9883002150654 2.01169978493464 28 24 23.3132044714068 0.686795528593236 29 22 16.5600332640222 5.43996673597783 30 18 17.7875942615778 0.212405738422207 31 21 21.5116432317942 -0.511643231794236 32 17 19.2186503010606 -2.21865030106060 33 15 15.7934788461760 -0.793478846176028 34 28 25.9723421488841 2.02765785111594 35 23 19.1873714540666 3.81262854593345 36 19 18.9847899454076 0.0152100545924071 37 15 18.6551980323123 -3.65519803231228 38 26 24.0063041379186 1.99369586208140 39 20 24.7456348869109 -4.74563488691086 40 11 15.5770361629353 -4.57703616293531 41 17 21.1547838410533 -4.1547838410533 42 16 18.5278385438383 -2.52783854383829 43 21 22.1182966968665 -1.11829669686648 44 18 18.1920591108205 -0.192059110820457 45 17 18.7609569226243 -1.76095692262430 46 21 22.1042579946483 -1.10425799464833 47 18 20.7431499886962 -2.74314998869620 48 16 14.8760255164421 1.12397448355795 49 13 16.6728334098391 -3.67283340983915 50 28 26.0150227047691 1.98497729523088 51 25 17.8404737067338 7.1595262932662 52 24 21.9496310285287 2.05036897147128 53 15 17.4047738192888 -2.40477381928884 54 21 20.656354703219 0.343645296781008 55 11 17.7875942615778 -6.78759426157779 56 27 21.9120529028967 5.08794709710328 57 23 20.7480748913129 2.25192510868713 58 21 22.3950091648058 -1.39500916480579 59 16 18.0991361031065 -2.09913610310652 60 20 17.0892206084117 2.91077939158833 61 21 23.5040351871371 -2.50403518713709 62 10 16.5596841799845 -6.55968417998454 63 18 24.4139266209273 -6.41392662092726 64 20 19.4526822131148 0.547317786885155 65 21 25.6793030694371 -4.67930306943708 66 24 22.5037979412743 1.49620205872567 67 26 20.6440394610598 5.35596053894025 68 23 21.5595977743336 1.44040222566641 69 22 20.4012428334416 1.59875716655835 70 13 16.6917970146740 -3.69179701467396 71 27 26.3458772351703 0.654122764829708 72 24 18.2454591964153 5.75454080358468 73 19 22.7774805230571 -3.77748052305712 74 17 19.0812634797169 -2.0812634797169 75 16 21.4415236418623 -5.44152364186232 76 20 20.5193169659129 -0.519316965912912 77 8 16.6970710013282 -8.69707100132825 78 16 21.3909321059958 -5.39093210599583 79 17 19.8615075157436 -2.86150751574357 80 23 23.3207663673506 -0.320766367350571 81 18 19.011143889785 -1.01114388978498 82 24 23.6238327796673 0.376167220332733 83 17 17.8188731085718 -0.818873108571847 84 20 21.9759849729061 -1.97598497290611 85 22 19.5774047082617 2.42259529173831 86 22 19.2552031347089 2.74479686529105 87 20 19.3433727962074 0.656627203792555 88 18 20.9885836096415 -2.98858360964145 89 21 19.9532277038374 1.04677229616256 90 23 19.1318550155834 3.86814498441661 91 28 22.9973021764920 5.00269782350803 92 19 21.4076078015411 -2.40760780154112 93 22 19.9143869608996 2.08561303910042 94 17 20.6828802039976 -3.68288020399761 95 25 23.4022876661735 1.59771233382651 96 22 22.0364263140059 -0.0364263140059339 97 21 19.3293340939893 1.67066590601071 98 15 19.1847344607394 -4.18473446073941 99 20 20.7308347465370 -0.730834746536964 100 25 18.6767986304742 6.32320136952576 101 21 20.4488482919434 0.551151708056627 102 24 23.4502422087128 0.549757791287155 103 23 20.75071188464 2.24928811535999 104 22 23.6740752314961 -1.67407523149614 105 14 20.5748334043961 -6.57483340439607 106 11 22.0993330920317 -11.0993330920317 107 22 16.8314717453072 5.16852825469281 108 22 22.0654172517105 -0.0654172517104694 109 6 15.4316945528184 -9.43169455281842 110 15 20.8851126286189 -5.88511262861895 111 26 22.2240555871785 3.77594441282149 112 26 22.8237116055376 3.17628839446245 113 20 17.9109423807033 2.08905761929666 114 26 22.7205897085527 3.27941029144733 115 15 16.6415545628451 -1.64155456284509 116 25 20.7912760876368 4.20872391236322 117 22 23.6261206889568 -1.62612068895679 118 20 21.9157151882075 -1.91571518820752 119 18 17.8025464970642 0.197453502935824 120 23 17.6113666972962 5.38863330270377 121 22 20.0739388296358 1.92606117036415 122 23 20.709234148375 2.29076585162499 123 17 22.3231661148150 -5.32316611481496 124 20 16.7785923001512 3.22140769984883 125 21 20.6612796058357 0.338720394164346 126 23 24.4186799671427 -1.41867996714269 127 25 23.4119659150056 1.58803408499441 128 25 21.0992674025701 3.90073259742986 129 21 17.1958930319919 3.80410696800807 130 22 19.1996866962258 2.80031330377421 131 18 19.2904933510514 -1.29049335105143 132 18 20.2373305113193 -2.23733051131932 133 18 22.3593698644257 -4.35936986442568 134 21 19.5897199504209 1.41028004957907 135 21 17.1716554405028 3.82834455949717 136 25 21.0490249507413 3.95097504925873 137 24 21.1811377854307 2.81886221456931 138 24 21.7521519501228 2.24784804987718 139 28 24.4086526342730 3.59134736572703 140 24 23.144538803069 0.855461196930994 141 22 22.067705161 -0.0677051609999881 142 22 21.5595977743336 0.440402225666413 143 20 21.7671041856092 -1.76710418560921 144 25 21.7860677904440 3.21393220955598 145 13 18.3004549944596 -5.30045499445963 146 21 19.9672664060556 1.03273359394441 147 23 19.6715903332815 3.32840966671853 148 18 21.1358202362185 -3.13582023621848 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.625219082871111 0.749561834257778 0.374780917128889 9 0.574786782404529 0.850426435190942 0.425213217595471 10 0.55134590856311 0.89730818287378 0.44865409143689 11 0.562045872850061 0.875908254299879 0.437954127149939 12 0.559355429744674 0.881289140510652 0.440644570255326 13 0.805915261495679 0.388169477008642 0.194084738504321 14 0.73903484294201 0.521930314115981 0.260965157057990 15 0.690919757167675 0.618160485664651 0.309080242832325 16 0.641931181461952 0.716137637076095 0.358068818538048 17 0.617517552903602 0.764964894192796 0.382482447096398 18 0.838583997057778 0.322832005884443 0.161416002942222 19 0.90836516827706 0.183269663445879 0.0916348317229396 20 0.895311846567973 0.209376306864054 0.104688153432027 21 0.863694547318501 0.272610905362997 0.136305452681499 22 0.823504293687136 0.352991412625728 0.176495706312864 23 0.779875963375406 0.440248073249187 0.220124036624594 24 0.811849190481306 0.376301619037388 0.188150809518694 25 0.773747943798687 0.452504112402626 0.226252056201313 26 0.721026939310984 0.557946121378032 0.278973060689016 27 0.671869935356056 0.656260129287888 0.328130064643944 28 0.611445654438889 0.777108691122223 0.388554345561111 29 0.630529331493489 0.738941337013022 0.369470668506511 30 0.576812168208226 0.846375663583549 0.423187831791774 31 0.519447934311011 0.961104131377977 0.480552065688989 32 0.503498918189717 0.993002163620567 0.496501081810283 33 0.454151403505304 0.908302807010608 0.545848596494696 34 0.406414821845102 0.812829643690205 0.593585178154898 35 0.387663235867459 0.775326471734918 0.612336764132541 36 0.333708221376937 0.667416442753874 0.666291778623063 37 0.354488803032411 0.708977606064822 0.645511196967589 38 0.309129593695623 0.618259187391245 0.690870406304377 39 0.354298365935955 0.70859673187191 0.645701634064045 40 0.412205541595499 0.824411083190999 0.5877944584045 41 0.440202368908227 0.880404737816454 0.559797631091773 42 0.410886815328927 0.821773630657855 0.589113184671073 43 0.371426477466958 0.742852954933916 0.628573522533042 44 0.321364671024955 0.64272934204991 0.678635328975045 45 0.286441014945663 0.572882029891326 0.713558985054337 46 0.246572171929706 0.493144343859413 0.753427828070294 47 0.233563649093096 0.467127298186191 0.766436350906904 48 0.200109470669690 0.400218941339380 0.79989052933031 49 0.211641893451548 0.423283786903096 0.788358106548452 50 0.184332604319601 0.368665208639202 0.815667395680399 51 0.27712611092426 0.55425222184852 0.72287388907574 52 0.248382503606571 0.496765007213142 0.751617496393429 53 0.224946118302909 0.449892236605819 0.77505388169709 54 0.188410803157508 0.376821606315017 0.811589196842492 55 0.318212360637278 0.636424721274557 0.681787639362721 56 0.347605467158589 0.695210934317179 0.652394532841411 57 0.322063282430472 0.644126564860944 0.677936717569528 58 0.287702336236942 0.575404672473883 0.712297663763058 59 0.261782124541873 0.523564249083747 0.738217875458127 60 0.244995913003484 0.489991826006968 0.755004086996516 61 0.225652932298838 0.451305864597677 0.774347067701162 62 0.320489915922763 0.640979831845526 0.679510084077237 63 0.41815023834618 0.83630047669236 0.58184976165382 64 0.373055789771798 0.746111579543595 0.626944210228202 65 0.407272197187736 0.814544394375471 0.592727802812264 66 0.369725054257422 0.739450108514844 0.630274945742578 67 0.421227529143608 0.842455058287216 0.578772470856392 68 0.381339006752366 0.762678013504732 0.618660993247634 69 0.343000570197361 0.686001140394722 0.656999429802639 70 0.351502180563348 0.703004361126697 0.648497819436652 71 0.310018459969289 0.620036919938577 0.689981540030711 72 0.374208357423378 0.748416714846757 0.625791642576622 73 0.381786634552541 0.763573269105081 0.61821336544746 74 0.354417787999559 0.708835575999118 0.645582212000441 75 0.41413897859494 0.82827795718988 0.58586102140506 76 0.369042613914912 0.738085227829823 0.630957386085088 77 0.611999076339175 0.77600184732165 0.388000923660825 78 0.671256895969383 0.657486208061234 0.328743104030617 79 0.655120498605713 0.689759002788575 0.344879501394287 80 0.613254137997769 0.773491724004461 0.386745862002231 81 0.56950398777743 0.86099202444514 0.43049601222257 82 0.522264490897494 0.955471018205013 0.477735509102506 83 0.476883311184503 0.953766622369006 0.523116688815497 84 0.440550964207413 0.881101928414825 0.559449035792587 85 0.410818949381432 0.821637898762865 0.589181050618568 86 0.386333723432061 0.772667446864122 0.613666276567939 87 0.341653256747404 0.683306513494808 0.658346743252596 88 0.325903727641001 0.651807455282002 0.674096272358999 89 0.286586305018355 0.57317261003671 0.713413694981645 90 0.290187408383079 0.580374816766158 0.709812591616921 91 0.339091175309499 0.678182350618999 0.660908824690501 92 0.312016731230835 0.624033462461669 0.687983268769165 93 0.283935649973957 0.567871299947914 0.716064350026043 94 0.298086486388145 0.596172972776291 0.701913513611855 95 0.262489954860211 0.524979909720422 0.737510045139789 96 0.225674531019452 0.451349062038904 0.774325468980548 97 0.194757073338284 0.389514146676568 0.805242926661716 98 0.204472215442050 0.408944430884100 0.79552778455795 99 0.171221805993964 0.342443611987929 0.828778194006036 100 0.218296435801806 0.436592871603611 0.781703564198194 101 0.182871802067567 0.365743604135135 0.817128197932433 102 0.152287562384571 0.304575124769142 0.847712437615429 103 0.130787755357460 0.261575510714919 0.86921224464254 104 0.108236687760495 0.216473375520989 0.891763312239505 105 0.170443639025534 0.340887278051067 0.829556360974467 106 0.604068257077055 0.791863485845889 0.395931742922945 107 0.655651264962481 0.688697470075038 0.344348735037519 108 0.607035507355478 0.785928985289045 0.392964492644523 109 0.90416859104793 0.191662817904142 0.0958314089520709 110 0.952945033314 0.0941099333720012 0.0470549666860006 111 0.950898868812397 0.0982022623752061 0.0491011311876031 112 0.950531735048548 0.0989365299029044 0.0494682649514522 113 0.93426728323831 0.131465433523382 0.065732716761691 114 0.938464696205439 0.123070607589122 0.0615353037945612 115 0.943938947452944 0.112122105094112 0.0560610525470561 116 0.937017295672097 0.125965408655807 0.0629827043279035 117 0.919188999695008 0.161622000609984 0.0808110003049922 118 0.91774536058335 0.164509278833300 0.0822546394166502 119 0.89801313967597 0.203973720648058 0.101986860324029 120 0.909311733725858 0.181376532548283 0.0906882662741415 121 0.879495885758244 0.241008228483512 0.120504114241756 122 0.863953751178075 0.272092497643849 0.136046248821925 123 0.919702381725241 0.160595236549518 0.0802976182747589 124 0.899692476627508 0.200615046744984 0.100307523372492 125 0.863599489504553 0.272801020990894 0.136400510495447 126 0.828840132477814 0.342319735044371 0.171159867522186 127 0.79022282503378 0.41955434993244 0.20977717496622 128 0.795987209786223 0.408025580427553 0.204012790213777 129 0.750629019600389 0.498741960799223 0.249370980399611 130 0.697325230889518 0.605349538220963 0.302674769110482 131 0.628346348425389 0.743307303149223 0.371653651574611 132 0.565352790110102 0.869294419779795 0.434647209889898 133 0.709220481273436 0.581559037453127 0.290779518726564 134 0.617913429584487 0.764173140831026 0.382086570415513 135 0.839527481829145 0.320945036341709 0.160472518170855 136 0.877434016605878 0.245131966788244 0.122565983394122 137 0.799296789626272 0.401406420747455 0.200703210373728 138 0.693107831878569 0.613784336242863 0.306892168121431 139 0.57987638352974 0.84024723294052 0.42012361647026 140 0.411964625048686 0.823929250097372 0.588035374951314 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 3 0.0225563909774436 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/10unnt1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/10unnt1293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/13he91293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/13he91293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/23he91293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/23he91293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/33he91293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/33he91293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/4w8wu1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/4w8wu1293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/5w8wu1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/5w8wu1293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/6w8wu1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/6w8wu1293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/71eoq1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/71eoq1293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/81eoq1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/81eoq1293049684.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/9unnt1293049684.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049786xq1916d6sjljtvh/9unnt1293049684.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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