*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: Thu, 02 Dec 2010 23:03:05 +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/03/t1291330861d6ftcncdc4y99pj.htm/, Retrieved Fri, 03 Dec 2010 00:01:11 +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/03/t1291330861d6ftcncdc4y99pj.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 «

11 12 24 26 38 7 8 25 23 36 17 8 30 25 23 10 8 19 23 30 12 9 22 19 26 12 7 22 29 26 11 4 25 25 30 11 11 23 21 27 12 7 17 22 34 13 7 21 25 28 14 12 19 24 36 16 10 19 18 42 11 10 15 22 31 10 8 16 15 30 11 8 23 22 26 15 4 27 28 16 9 9 22 20 30 11 8 14 12 23 17 7 22 24 28 17 11 23 20 45 11 9 23 21 42 18 11 21 20 50 14 13 19 21 30 10 8 18 23 45 11 8 20 28 30 15 9 23 24 24 15 6 25 24 29 13 9 19 24 30 16 9 24 23 31 13 6 22 23 26 9 6 25 29 34 18 16 26 24 41 18 5 29 18 37 12 7 32 25 33 17 9 25 21 26 9 6 29 26 48 9 6 28 22 44 12 5 17 22 29 18 12 28 22 44 12 7 29 23 37 18 10 26 30 43 14 9 25 23 31 15 8 14 17 28 16 5 25 23 26 10 8 26 23 30 11 8 20 25 27 14 10 18 24 34 9 6 32 24 47 12 8 25 23 39 17 7 25 21 37 5 4 23 24 42 12 8 21 24 27 12 8 20 28 30 6 4 15 16 17 24 20 30 20 36 12 8 24 29 39 12 8 26 27 32 14 6 24 22 25 7 4 22 28 19 13 8 14 16 29 12 9 24 25 26 13 6 24 24 31 14 7 24 28 31 8 9 24 24 31 11 5 19 23 20 9 5 31 30 40 11 8 22 24 39 13 8 27 21 28 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation CM+D[t] = + 13.8648506940409 + 0.152805219548221ParentalExpectations[t] + 0.629365627171892ParentalCriticism[t] + 0.449660665114335PersonalStandards[t] + 0.0677807458976412Organization[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) 13.8648506940409 4.244167 3.2668 0.001341 0.000671 ParentalExpectations 0.152805219548221 0.198679 0.7691 0.443008 0.221504 ParentalCriticism 0.629365627171892 0.247635 2.5415 0.012026 0.006013 PersonalStandards 0.449660665114335 0.143042 3.1436 0.002003 0.001001 Organization 0.0677807458976412 0.153124 0.4427 0.658637 0.329319 Multiple Linear Regression - Regression Statistics Multiple R 0.419463868754593 R-squared 0.175949937190571 Adjusted R-squared 0.154546039455261 F-TEST (value) 8.22046243008849 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 4.91173108119192e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.71059243516357 Sum Squared Residuals 6934.93582795469 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 38 35.6522509912167 2.34774900878331 2 36 32.7698860317577 3.23011396824229 3 23 36.6818030446069 -13.6818030446069 4 30 30.5303376997164 -0.530337699716388 5 26 32.5431727777371 -6.54317277773713 6 26 31.9622489823698 -5.96224898236977 7 30 30.9992058930583 -0.99920589305831 8 27 34.2343209694423 -7.23432096944232 9 34 29.2394804355146 4.7605195644854 10 28 31.3942705532131 -3.39427055321309 11 36 33.7268018324945 2.27319816750554 12 42 32.3669965418613 9.63300345813873 13 31 30.0754507672534 0.92454923274661 14 30 28.6391097371922 1.36089026280777 15 26 32.4140048338243 -6.41400483382428 16 16 32.7130903391728 -16.7130903391728 17 30 32.1525378649901 -2.15253786499011 18 23 27.6892513888189 -4.68925138881886 19 28 32.3873713506227 -4.38737135062267 20 45 35.083371540834 9.916628459166 21 42 32.9755897150985 9.02441028490147 22 50 34.3368554301536 15.6631445698464 23 30 34.1528252219734 -4.15282522197343 24 45 30.0806770346020 14.9193229653980 25 30 31.4717073138671 -1.47170731386713 26 24 33.7901528309843 -9.79015283098434 27 29 32.8013772796973 -3.80137727969734 28 30 31.6858997314306 -1.68589973143056 29 31 34.3248379697493 -3.32483796974926 30 26 31.0790040993603 -5.07900409936025 31 34 32.2234496918962 1.77655030810378 32 41 40.0031098751753 0.996890124824745 33 37 34.0223854962416 2.9776145037584 34 33 36.1877326499226 -3.18773264992255 35 26 34.7917423626165 -8.79174236261653 36 48 33.8187501146606 14.1812498853394 37 44 33.0979664659557 10.9020335340443 38 29 27.9807491811708 1.01925081882918 39 44 38.2494072049211 5.75059279507892 40 37 34.7031891627843 2.29681083721574 41 43 36.6336005875298 6.36639941247025 42 31 34.4688881957671 -3.46888819576715 43 28 28.6393759965000 -0.639375996499952 44 26 32.257036126176 -6.25703612617603 45 30 33.6779623555167 -3.67796235551671 46 27 31.2683650761742 -4.2683650761742 47 34 32.0184099130363 1.98159008696366 48 47 35.0321706182084 11.9678293817916 49 39 33.5339121294988 5.46608787050118 50 37 33.5330111082728 3.46698889172725 51 42 29.1152724996427 12.8847275003573 52 27 31.8030502149391 -4.80305021493912 53 30 31.6245125334153 -1.62451253341535 54 17 25.1285464310951 -8.12854643109508 55 36 44.9649233780189 -8.96492337801892 56 39 33.4909359397703 5.50906406022967 57 32 34.2546957782037 -2.25469577820372 58 25 32.0633499032395 -7.0633499032395 59 19 29.2423452572153 -10.2423452572153 60 29 28.2659848115059 0.734015188494133 61 26 33.8491785833517 -7.84917858335166 62 31 32.0461061754866 -1.04610617548656 63 31 33.0994000057972 -2.09940000579724 64 31 33.1701769592611 -2.17017695926113 65 20 28.7950460377489 -8.79504603774891 66 40 34.359828801308 5.64017119869203 67 39 32.0999056605052 6.90009433949477 68 28 34.4504771874804 -6.45047718748042 69 22 29.4071679371679 -7.40716793716786 70 31 33.5166684017459 -2.51666840174588 71 36 30.5884624308576 5.41153756914239 72 28 30.6474881832249 -2.64748818322492 73 39 35.724356983237 3.27564301676303 74 44 35.4395189980752 8.56048100192485 75 35 32.869158025595 2.13084197440502 76 33 31.1500473121319 1.84995268786814 77 27 30.7649049260412 -3.7649049260412 78 33 33.1876869463218 -0.187686946321788 79 31 32.7356648355595 -1.73566483555955 80 39 32.3602053488056 6.63979465119439 81 37 35.2165715869814 1.78342841301861 82 24 29.9871638267288 -5.98716382672884 83 33 30.9209726124634 2.07902738753661 84 28 35.4716450079331 -7.47164500793313 85 37 28.6077533626948 8.39224663730519 86 32 31.3352448008458 0.66475519915422 87 31 32.0104514394469 -1.01045143944690 88 29 32.5828596160113 -3.58285961601133 89 40 38.7528673550541 1.24713264494592 90 29 29.1716996896170 -0.171699689616964 91 40 30.3100179935782 9.68998200642178 92 15 29.0337767521738 -14.0337767521738 93 27 27.5901142684238 -0.590114268423799 94 32 31.1812723007638 0.81872769923623 95 28 33.1123184874276 -5.1123184874276 96 41 40.7775885076136 0.222411492386357 97 47 32.8058070271051 14.1941929728949 98 42 35.0340018032231 6.96599819677691 99 28 29.6213603547313 -1.6213603547313 100 32 30.2679697096561 1.73203029034387 101 33 34.2161762204633 -1.21617622046331 102 22 29.4416553926737 -7.44165539267374 103 29 33.139511373825 -4.13951137382499 104 26 33.3846356361323 -7.38463563613228 105 37 32.7982193141086 4.20178068589145 106 39 27.3534787403391 11.6465212596609 107 29 29.0446269320443 -0.0446269320442908 108 33 31.7052386455237 1.29476135447632 109 39 34.3958811825209 4.60411881747913 110 31 27.6430127322164 3.3569872677836 111 21 27.6871562024787 -6.68715620247868 112 36 33.5827516064766 2.41724839352343 113 29 34.3105904495626 -5.31059044956257 114 32 40.4287625040613 -8.42876250406132 115 15 36.6094307932789 -21.6094307932789 116 24 30.0677585529717 -6.06775855297167 117 25 33.6879115141612 -8.68791151416115 118 28 29.2973389073481 -1.29733890734813 119 39 33.34049216587 5.65950783412999 120 31 24.3314933022699 6.66850669773007 121 40 30.6343034422868 9.36569655771316 122 25 28.8327959601288 -3.83279596012876 123 36 35.4564964665204 0.543503533479632 124 23 29.2456077240893 -6.24560772408931 125 39 29.7309231252433 9.26907687475669 126 31 32.4992955667826 -1.49929556678259 127 23 29.4296379322694 -6.42963793226944 128 31 33.1347884825292 -2.13478848252918 129 28 32.8735877730027 -4.87358777300274 130 47 33.9663290668602 13.0336709331398 131 33 34.7862498359602 -1.78624983596017 132 25 29.3514046516745 -4.35140465167452 133 26 30.7970309358992 -4.79703093589917 134 24 27.4104093063662 -3.41040930636624 135 31 29.4869661434698 1.51303385653020 136 39 36.3969650594451 2.60303494055493 137 31 29.3738746467761 1.6261253532239 138 30 31.8396328567852 -1.83963285678518 139 25 32.432415842111 -7.43241584211101 140 35 34.7895123028341 0.210487697165861 141 44 32.1955140547186 11.8044859452814 142 42 36.9819209570470 5.01807904295304 143 38 40.2401699330135 -2.2401699330135 144 36 29.1509272356823 6.84907276431766 145 34 35.2189330326293 -1.21893303262929 146 45 33.0894777317331 11.9105222682669 147 40 34.6561808708213 5.34381912917875 148 29 30.7497563846284 -1.74975638462844 149 25 26.7405603209793 -1.74056032097927 150 30 32.6466082596744 -2.64660825967445 151 27 34.3923524563392 -7.39235245633918 152 44 33.763253088475 10.236746911525 153 49 36.4851206141041 12.5148793858959 154 31 29.1372391186914 1.86276088130859 155 31 37.2501791189368 -6.25017911893679 156 26 29.5944606122220 -3.59446061222196 157 42 32.9992269907339 9.0007730092661 158 35 33.8342963012466 1.16570369875338 159 47 35.8378461251039 11.1621538748961 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.181910788133424 0.363821576266847 0.818089211866576 9 0.30072607142964 0.60145214285928 0.69927392857036 10 0.178666271621447 0.357332543242894 0.821333728378553 11 0.153077344319954 0.306154688639908 0.846922655680046 12 0.391630753815655 0.78326150763131 0.608369246184346 13 0.346925888620869 0.693851777241738 0.653074111379131 14 0.284345175811855 0.568690351623709 0.715654824188145 15 0.237780899878409 0.475561799756818 0.762219100121591 16 0.275049143012596 0.550098286025191 0.724950856987404 17 0.207860942085214 0.415721884170427 0.792139057914786 18 0.247208745090777 0.494417490181555 0.752791254909223 19 0.190951267915260 0.381902535830519 0.80904873208474 20 0.358188574304207 0.716377148608414 0.641811425695793 21 0.482902556354582 0.965805112709163 0.517097443645418 22 0.667667513717628 0.664664972564743 0.332332486282371 23 0.737886061174369 0.524227877651263 0.262113938825631 24 0.893132537534067 0.213734924931866 0.106867462465933 25 0.859975951509263 0.280048096981474 0.140024048490737 26 0.879558940474799 0.240882119050402 0.120441059525201 27 0.85048017724193 0.299039645516140 0.149519822758070 28 0.816015226481998 0.367969547036004 0.183984773518002 29 0.775511344864049 0.448977310271902 0.224488655135951 30 0.735576276179786 0.528847447640428 0.264423723820214 31 0.73264209372168 0.534715812556639 0.267357906278319 32 0.683075118188959 0.633849763622082 0.316924881811041 33 0.710152845310168 0.579694309379664 0.289847154689832 34 0.67001298042705 0.6599740391459 0.32998701957295 35 0.689727717544381 0.620544564911237 0.310272282455619 36 0.879709302563428 0.240581394873145 0.120290697436572 37 0.90991321429975 0.180173571400499 0.0900867857002493 38 0.888293266151035 0.223413467697929 0.111706733848965 39 0.881329458736966 0.237341082526069 0.118670541263034 40 0.854835011727248 0.290329976545504 0.145164988272752 41 0.872464855360653 0.255070289278694 0.127535144639347 42 0.851295716263871 0.297408567472257 0.148704283736129 43 0.818737587771821 0.362524824456358 0.181262412228179 44 0.803592492456468 0.392815015087065 0.196407507543532 45 0.782209868574374 0.435580262851251 0.217790131425626 46 0.756132612415768 0.487734775168465 0.243867387584232 47 0.71853634255218 0.56292731489564 0.28146365744782 48 0.786618182269205 0.426763635461589 0.213381817730795 49 0.769604239968527 0.460791520062947 0.230395760031473 50 0.746573390896607 0.506853218206786 0.253426609103393 51 0.825537244835157 0.348925510329687 0.174462755164843 52 0.808921030453734 0.382157939092531 0.191078969546266 53 0.774679316149586 0.450641367700829 0.225320683850414 54 0.801072220104104 0.397855559791791 0.198927779895896 55 0.836072774453677 0.327854451092645 0.163927225546323 56 0.825995031352089 0.348009937295823 0.174004968647912 57 0.797838402117173 0.404323195765654 0.202161597882827 58 0.797517834882795 0.404964330234411 0.202482165117205 59 0.841058949444541 0.317882101110918 0.158941050555459 60 0.811222562353994 0.377554875292012 0.188777437646006 61 0.822920724192292 0.354158551615417 0.177079275807708 62 0.791728566695664 0.416542866608673 0.208271433304336 63 0.760949698315942 0.478100603368116 0.239050301684058 64 0.733442119410413 0.533115761179174 0.266557880589587 65 0.755792983221077 0.488414033557846 0.244207016778923 66 0.74254993581121 0.514900128377581 0.257450064188791 67 0.745233337840863 0.509533324318273 0.254766662159137 68 0.744942503688527 0.510114992622946 0.255057496311473 69 0.750129594824568 0.499740810350865 0.249870405175432 70 0.717584495284246 0.564831009431507 0.282415504715754 71 0.706358888487168 0.587282223025663 0.293641111512832 72 0.672116752722741 0.655766494554517 0.327883247277259 73 0.640897834394399 0.718204331211203 0.359102165605601 74 0.673276111791339 0.653447776417323 0.326723888208661 75 0.639030062478616 0.721939875042768 0.360969937521384 76 0.59818334858928 0.80363330282144 0.40181665141072 77 0.568897882811127 0.862204234377746 0.431102117188873 78 0.523262692086909 0.953474615826182 0.476737307913091 79 0.479606866757076 0.959213733514151 0.520393133242924 80 0.476587063759144 0.953174127518288 0.523412936240856 81 0.433725108681661 0.867450217363322 0.566274891318339 82 0.42220258815704 0.84440517631408 0.57779741184296 83 0.382564792880696 0.765129585761391 0.617435207119304 84 0.395644662374329 0.791289324748658 0.604355337625671 85 0.422569279513321 0.845138559026642 0.577430720486679 86 0.384514623426935 0.769029246853871 0.615485376573065 87 0.342262511565282 0.684525023130564 0.657737488434718 88 0.312078718950188 0.624157437900375 0.687921281049813 89 0.274205210509522 0.548410421019044 0.725794789490478 90 0.237321894261151 0.474643788522302 0.762678105738849 91 0.276625691540811 0.553251383081621 0.723374308459189 92 0.421292023527485 0.84258404705497 0.578707976472515 93 0.377568398288561 0.755136796577122 0.622431601711439 94 0.335429547390774 0.670859094781547 0.664570452609226 95 0.318787312617155 0.63757462523431 0.681212687382845 96 0.278766274474398 0.557532548948796 0.721233725525602 97 0.414860550005862 0.829721100011723 0.585139449994138 98 0.414076372395859 0.828152744791718 0.585923627604141 99 0.372084481334962 0.744168962669923 0.627915518665038 100 0.32948742895362 0.65897485790724 0.67051257104638 101 0.288750627893168 0.577501255786336 0.711249372106832 102 0.305077866790297 0.610155733580593 0.694922133209704 103 0.283743744634842 0.567487489269684 0.716256255365158 104 0.296415444057842 0.592830888115684 0.703584555942158 105 0.269953959357665 0.539907918715329 0.730046040642335 106 0.340661954440699 0.681323908881398 0.659338045559301 107 0.296712880325768 0.593425760651535 0.703287119674232 108 0.258105216447926 0.516210432895853 0.741894783552074 109 0.235312809993043 0.470625619986086 0.764687190006957 110 0.204783205139148 0.409566410278296 0.795216794860852 111 0.208169999478506 0.416339998957013 0.791830000521494 112 0.176506571881085 0.353013143762170 0.823493428118915 113 0.159758335153255 0.319516670306509 0.840241664846745 114 0.179845604628985 0.359691209257971 0.820154395371015 115 0.66445332962361 0.671093340752779 0.335546670376389 116 0.664951967779673 0.670096064440654 0.335048032220327 117 0.738678884139286 0.522642231721427 0.261321115860714 118 0.698440510109737 0.603118979780527 0.301559489890263 119 0.67609509818017 0.64780980363966 0.32390490181983 120 0.705357529260543 0.589284941478915 0.294642470739457 121 0.708840381020582 0.582319237958835 0.291159618979418 122 0.667336270884386 0.665327458231228 0.332663729115614 123 0.618634712072332 0.762730575855336 0.381365287927668 124 0.623623632775241 0.752752734449518 0.376376367224759 125 0.675254137754607 0.649491724490786 0.324745862245393 126 0.625543172194153 0.748913655611693 0.374456827805847 127 0.650968136496522 0.698063727006956 0.349031863503478 128 0.619684524153043 0.760630951693914 0.380315475846957 129 0.612943093829583 0.774113812340835 0.387056906170417 130 0.688564290690787 0.622871418618425 0.311435709309213 131 0.646606675071403 0.706786649857194 0.353393324928597 132 0.602786105107045 0.79442778978591 0.397213894892955 133 0.627119116349346 0.745761767301307 0.372880883650654 134 0.602358094537223 0.795283810925554 0.397641905462777 135 0.534130452179011 0.931739095641979 0.465869547820989 136 0.469333638678377 0.938667277356753 0.530666361321623 137 0.398707177069252 0.797414354138504 0.601292822930748 138 0.342238780372457 0.684477560744915 0.657761219627543 139 0.431360218786554 0.862720437573108 0.568639781213446 140 0.356853881088579 0.713707762177158 0.643146118911421 141 0.550323610246985 0.89935277950603 0.449676389753015 142 0.480866057571906 0.961732115143812 0.519133942428094 143 0.42784406515667 0.85568813031334 0.57215593484333 144 0.357278418437818 0.714556836875637 0.642721581562182 145 0.309094535786457 0.618189071572913 0.690905464213543 146 0.419622418631741 0.839244837263482 0.580377581368259 147 0.372954177166156 0.745908354332313 0.627045822833844 148 0.272396399956919 0.544792799913838 0.727603600043081 149 0.19316073537572 0.38632147075144 0.80683926462428 150 0.142050550908775 0.284101101817550 0.857949449091225 151 0.110888642878924 0.221777285757848 0.889111357121076 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 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/10zm941291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/10zm941291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/1b3cb1291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/1b3cb1291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/2b3cb1291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/2b3cb1291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/3lube1291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/3lube1291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/4lube1291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/4lube1291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/5lube1291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/5lube1291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/6w4az1291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/6w4az1291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/77ds21291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/77ds21291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/87ds21291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/87ds21291330973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/97ds21291330973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291330861d6ftcncdc4y99pj/97ds21291330973.ps (open in new window)

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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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