Mini-Tutorial Determistic Trend

*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: Mon, 22 Nov 2010 22:57:36 +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/Nov/22/t1290466610f9r8hb6baj9m97s.htm/, Retrieved Mon, 22 Nov 2010 23:56:50 +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/Nov/22/t1290466610f9r8hb6baj9m97s.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:

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13 26 9 15 6 25 25 16 20 9 15 6 25 24 19 21 9 14 13 19 21 15 31 14 10 8 18 23 14 21 8 10 7 18 17 13 18 8 12 9 22 19 19 26 11 18 5 29 18 15 22 10 12 8 26 27 14 22 9 14 9 25 23 15 29 15 18 11 23 23 16 15 14 9 8 23 29 16 16 11 11 11 23 21 16 24 14 11 12 24 26 17 17 6 17 8 30 25 15 19 20 8 7 19 25 15 22 9 16 9 24 23 20 31 10 21 12 32 26 18 28 8 24 20 30 20 16 38 11 21 7 29 29 16 26 14 14 8 17 24 19 25 11 7 8 25 23 16 25 16 18 16 26 24 17 29 14 18 10 26 30 17 28 11 13 6 25 22 16 15 11 11 8 23 22 15 18 12 13 9 21 13 14 21 9 13 9 19 24 15 25 7 18 11 35 17 12 23 13 14 12 19 24 14 23 10 12 8 20 21 16 19 9 9 7 21 23 14 18 9 12 8 21 24 7 18 13 8 9 24 24 10 26 16 5 4 23 24 14 18 12 10 8 19 23 16 18 6 11 8 17 26 16 28 14 11 8 24 24 16 17 14 12 6 15 21 14 29 10 12 8 25 23 20 12 4 15 4 27 28 14 25 12 12 7 29 23 14 28 12 16 14 27 22 11 20 14 14 10 18 24 15 17 9 17 9 25 21 16 17 9 13 6 22 23 14 20 10 10 8 26 23 16 31 14 17 11 23 20 14 21 10 12 8 16 23 12 19 9 13 8 27 21 16 23 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Confidence[t] = + 13.1859586294866 + 0.00507128374736726Concern[t] -0.278644023837285Doubts[t] + 0.101708935008028ParentalExpectations[t] + 0.00158176421768097ParentalCriticism[t] + 0.0217139022837344PersonalStandards[t] + 0.149270127306556Organization[t] -0.00580718049086313t + 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) 13.1859586294866 1.571231 8.3921 0 0 Concern 0.00507128374736726 0.037631 0.1348 0.892989 0.446495 Doubts -0.278644023837285 0.068906 -4.0438 8.6e-05 4.3e-05 ParentalExpectations 0.101708935008028 0.062726 1.6215 0.107131 0.053566 ParentalCriticism 0.00158176421768097 0.078903 0.02 0.984034 0.492017 PersonalStandards 0.0217139022837344 0.049043 0.4428 0.658616 0.329308 Organization 0.149270127306556 0.049894 2.9917 0.003272 0.001636 t -0.00580718049086313 0.003975 -1.461 0.146216 0.073108 Multiple Linear Regression - Regression Statistics Multiple R 0.467944300630389 R-squared 0.218971868492464 Adjusted R-squared 0.180470481728008 F-TEST (value) 5.68737614133464 F-TEST (DF numerator) 7 F-TEST (DF denominator) 142 p-value 8.27082807408619e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.05762788096972 Sum Squared Residuals 601.204214509241 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.6139339620755 -3.6139339620755 2 16 16.4284289517939 -0.428428951793902 3 19 15.7589626739441 3.24103732605593 4 15 14.2727300029493 0.727269997050687 5 14 14.9908715999515 -0.99087159995147 6 13 15.5618278304180 -2.56182783041797 7 19 15.3673125902512 3.63268740974878 8 15 16.2926454201209 -1.29264542012085 9 14 16.1516874861911 -2.15168748619105 10 15 14.8760866128081 0.123913387191945 11 16 15.0534205398054 0.946579460194623 12 16 14.9026188587904 1.09738114120961 13 16 14.8710961798008 1.12890382019920 14 17 17.6438820433499 -0.643882043349945 15 15 12.5913859922208 2.40861400777919 16 15 16.2927411904873 -1.29274119048733 17 20 17.1887431077682 2.81125689223178 18 18 17.1037424740686 0.896257525931451 19 16 17.3087435631608 -1.30874356316084 20 16 14.6888506614136 1.31114933858640 21 19 14.8263828145943 4.17361718540565 22 16 14.7297919433371 1.27020805666289 23 17 16.1876881240435 0.812311875956463 24 17 15.2819950786701 1.71800492132989 25 16 14.9665790633153 1.03342093668469 26 15 13.5154823941365 1.48451760586348 27 14 15.9593647322043 -1.95936473220427 28 15 16.3453704832468 -1.34537048324680 29 12 14.9497710710292 -2.94977107102921 30 14 15.1440545555275 -1.14405455552749 31 16 15.4101518515395 0.589848148460479 32 14 15.8552520838496 -1.85525208384961 33 7 14.3947565390464 -7.39475653904638 34 10 13.2588380286264 -3.25883802862638 35 14 14.6057826689751 -0.605782668975087 36 16 16.7779311438682 -0.777931143868164 37 16 14.4471416715257 1.55285832847428 38 16 13.8408602739132 2.15913972608680 39 14 15.5293273996257 -1.52932739962571 40 20 18.1977507277069 1.80224927229308 41 14 15.0254137008972 -1.02541370089720 42 14 15.2600305293303 -1.26003052933029 43 11 14.5497352383586 -3.54973523835864 44 15 15.9296663006850 -0.929666300684979 45 16 15.7456766352709 0.25432336472913 46 14 15.2613316147310 -1.26133161473104 47 16 14.4004882090504 1.59951179094956 48 14 15.2410673846754 -1.24106738467539 49 12 15.5457832660431 -3.54578326604307 50 16 15.0223975890625 0.977602410937516 51 9 13.9633980484456 -4.96339804844555 52 14 14.4875496896335 -0.487549689633468 53 16 15.7408222337379 0.259177766262083 54 16 15.1609716522175 0.839028347782451 55 15 15.2122243633186 -0.212224363318575 56 16 14.8521819555621 1.14781804443789 57 12 13.5401323121032 -1.54013231210324 58 16 16.5217287955254 -0.521728795525386 59 16 16.1761543938631 -0.176154393863125 60 14 16.3933353283843 -2.39333532838426 61 16 12.6016606260921 3.39833937390794 62 17 15.9824204316697 1.01757956833026 63 18 14.7070871914091 3.29291280859092 64 18 15.4249220914617 2.5750779085383 65 12 14.5025949683924 -2.50259496839241 66 16 15.8687302617883 0.131269738211660 67 10 14.3910440418816 -4.39104404188163 68 14 12.7095949087348 1.29040509126520 69 18 15.4179556648222 2.58204433517785 70 18 16.2653622499863 1.73463775001372 71 16 15.5290289855346 0.470971014465363 72 16 15.4825531524353 0.517446847564721 73 16 14.7271359945953 1.27286400540465 74 13 14.6752984396829 -1.67529843968288 75 16 15.0670808830758 0.932919116924178 76 16 14.7744375095125 1.22556249048753 77 20 15.9482652208551 4.05173477914486 78 16 15.2387419322767 0.761258067723293 79 15 12.8063237050544 2.19367629494562 80 15 15.2913349665646 -0.291334966564635 81 16 15.7955961048069 0.204403895193115 82 14 14.0345813427015 -0.0345813427015287 83 15 13.2216000839889 1.77839991601113 84 12 14.9066365866886 -2.90663658668858 85 17 15.9601126792037 1.03988732079633 86 16 15.1289356585966 0.871064341403366 87 15 13.0445065581465 1.95549344185345 88 13 14.3081944139494 -1.30819441394942 89 16 15.8588474413305 0.141152558669501 90 16 15.2054735820545 0.794526417945482 91 16 16.1312662650405 -0.131266265040474 92 16 15.7713969342266 0.228603065773409 93 14 15.5486865554169 -1.54868655541693 94 16 14.0673890109121 1.93261098908791 95 16 15.0422581528602 0.95774184713982 96 20 16.2692340013688 3.73076599863119 97 15 15.3992262599508 -0.39922625995077 98 16 13.9980326565390 2.00196734346102 99 13 14.2957655650165 -1.29576556501655 100 17 15.7672289610709 1.23277103892914 101 16 14.0679683586658 1.93203164133423 102 12 13.2356636412037 -1.23566364120369 103 16 14.9111800497967 1.08881995020325 104 16 15.1422387177507 0.857761282249325 105 17 15.3478860085924 1.65211399140764 106 13 13.0595149855268 -0.0595149855268156 107 12 15.7081076497185 -3.7081076497185 108 18 15.6443489143162 2.35565108568384 109 14 13.5387860906722 0.461213909327788 110 14 14.3394650263327 -0.339465026332685 111 13 13.6382368874932 -0.638236887493229 112 16 15.2773937903488 0.722606209651224 113 13 12.4904083485798 0.509591651420171 114 16 15.1215593021966 0.878440697803391 115 13 14.6830274621508 -1.68302746215077 116 16 15.6426034269247 0.35739657307529 117 15 14.5204570156667 0.479542984333252 118 16 15.0933210796492 0.906678920350833 119 15 14.7316609277932 0.268339072206798 120 17 15.4196193486458 1.58038065135420 121 15 15.6157457213473 -0.615745721347312 122 12 13.4724342652028 -1.47243426520282 123 16 14.2133702098931 1.78662979010686 124 10 13.9459293229077 -3.94592932290766 125 16 14.1745922844059 1.82540771559412 126 14 14.4995566223463 -0.499556622346274 127 15 16.0999575797433 -1.09995757974331 128 13 14.2367854122844 -1.23678541228445 129 15 15.1040846437896 -0.104084643789639 130 11 13.4618815468193 -2.46188154681932 131 12 13.9762152487714 -1.97621524877138 132 8 14.2452353733339 -6.24523537333395 133 16 15.9461048056350 0.0538951943649715 134 15 14.5211473010084 0.478852698991634 135 17 15.0337438609766 1.96625613902335 136 16 15.0927711898981 0.907228810101923 137 10 14.6538827628817 -4.65388276288175 138 18 13.6255610961421 4.37443890385786 139 13 13.5183347163529 -0.518334716352945 140 15 13.9670488488242 1.03295115117577 141 16 14.2929461263752 1.70705387362481 142 16 14.6224575461024 1.37754245389761 143 14 13.0799227119239 0.920077288076148 144 10 12.7967484861264 -2.7967484861264 145 17 15.6116818497519 1.38831815024812 146 13 13.9868871063324 -0.98688710633238 147 15 15.4647590285849 -0.46475902858487 148 16 15.5470842456070 0.452915754392974 149 12 14.9184477267086 -2.91844772670861 150 13 13.2806196571575 -0.280619657157512 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.79843571586637 0.403128568267260 0.201564284133630 12 0.70719864925925 0.5856027014815 0.29280135074075 13 0.577455876553119 0.845088246893762 0.422544123446881 14 0.707313306260085 0.58537338747983 0.292686693739915 15 0.613076936846848 0.773846126306304 0.386923063153152 16 0.510973728725096 0.978052542549808 0.489026271274904 17 0.519993265923904 0.96001346815219 0.480006734076095 18 0.527531548362266 0.944936903275468 0.472468451637734 19 0.438392147098584 0.876784294197168 0.561607852901416 20 0.390845282710078 0.781690565420156 0.609154717289922 21 0.480732488081969 0.961464976163938 0.519267511918031 22 0.472004725721639 0.944009451443278 0.527995274278361 23 0.400294851361374 0.800589702722748 0.599705148638626 24 0.333147851964483 0.666295703928965 0.666852148035517 25 0.272628096991176 0.545256193982353 0.727371903008823 26 0.251179307318538 0.502358614637075 0.748820692681462 27 0.211705337592410 0.423410675184821 0.78829466240759 28 0.309300113228680 0.618600226457361 0.69069988677132 29 0.395248439268546 0.790496878537091 0.604751560731454 30 0.335470221732142 0.670940443464284 0.664529778267858 31 0.303423487416557 0.606846974833114 0.696576512583443 32 0.256324411472861 0.512648822945722 0.743675588527139 33 0.902799714274697 0.194400571450605 0.0972002857253027 34 0.925461464447135 0.14907707110573 0.074538535552865 35 0.906782062169122 0.186435875661757 0.0932179378308783 36 0.905443091787589 0.189113816424823 0.0945569082124114 37 0.900819591137584 0.198360817724832 0.099180408862416 38 0.902482992566613 0.195034014866774 0.097517007433387 39 0.881566402755432 0.236867194489136 0.118433597244568 40 0.912843883385941 0.174312233228118 0.0871561166140589 41 0.891304334968484 0.217391330063032 0.108695665031516 42 0.869748998191234 0.260502003617532 0.130251001808766 43 0.912855731845383 0.174288536309233 0.0871442681546167 44 0.891930747177383 0.216138505645235 0.108069252822618 45 0.870542990710397 0.258914018579207 0.129457009289603 46 0.846577890027168 0.306844219945664 0.153422109972832 47 0.8326311333831 0.3347377332338 0.1673688666169 48 0.805725862082261 0.388548275835478 0.194274137917739 49 0.844812756904374 0.310374486191252 0.155187243095626 50 0.829594174648924 0.340811650702152 0.170405825351076 51 0.924154376364671 0.151691247270657 0.0758456236353285 52 0.9141155193318 0.1717689613364 0.0858844806682 53 0.907134498977458 0.185731002045083 0.0928655010225417 54 0.900827651264732 0.198344697470537 0.0991723487352683 55 0.884305664476058 0.231388671047884 0.115694335523942 56 0.884297794851036 0.231404410297928 0.115702205148964 57 0.873794175594201 0.252411648811598 0.126205824405799 58 0.850811302214444 0.298377395571112 0.149188697785556 59 0.825766668536981 0.348466662926038 0.174233331463019 60 0.840518934841716 0.318962130316567 0.159481065158284 61 0.880861302019607 0.238277395960785 0.119138697980393 62 0.866429814714177 0.267140370571646 0.133570185285823 63 0.898157642013416 0.203684715973168 0.101842357986584 64 0.91149915841015 0.177001683179699 0.0885008415898493 65 0.928874502975021 0.142250994049958 0.0711254970249788 66 0.913787862006614 0.172424275986773 0.0862121379933863 67 0.968689057366647 0.0626218852667062 0.0313109426333531 68 0.961232706876615 0.0775345862467696 0.0387672931233848 69 0.968337476513819 0.0633250469723626 0.0316625234861813 70 0.96661428919433 0.0667714216113394 0.0333857108056697 71 0.957271897179262 0.0854562056414768 0.0427281028207384 72 0.946299626794865 0.107400746410269 0.0537003732051345 73 0.934159009387402 0.131681981225196 0.0658409906125981 74 0.940225985127095 0.119548029745810 0.0597740148729049 75 0.927786928464003 0.144426143071993 0.0722130715359965 76 0.912713441387291 0.174573117225417 0.0872865586127086 77 0.945423803922236 0.109152392155529 0.0545761960777644 78 0.93052257809335 0.138954843813301 0.0694774219066503 79 0.92398382848846 0.152032343023078 0.0760161715115392 80 0.908096221636062 0.183807556727877 0.0919037783639384 81 0.88630890554857 0.227382188902862 0.113691094451431 82 0.862932805631603 0.274134388736794 0.137067194368397 83 0.851215519141086 0.297568961717829 0.148784480858915 84 0.89816460851048 0.203670782979038 0.101835391489519 85 0.87884975668889 0.242300486622221 0.121150243311110 86 0.852414238425507 0.295171523148986 0.147585761574493 87 0.836584356011868 0.326831287976263 0.163415643988132 88 0.830210491755858 0.339579016488283 0.169789508244142 89 0.805824290497749 0.388351419004503 0.194175709502251 90 0.769907464468067 0.460185071063866 0.230092535531933 91 0.739742178841851 0.520515642316297 0.260257821158149 92 0.699206159619448 0.601587680761105 0.300793840380552 93 0.731946435987902 0.536107128024195 0.268053564012098 94 0.718500745961405 0.562998508077189 0.281499254038595 95 0.675586120939414 0.648827758121173 0.324413879060587 96 0.720008390931779 0.559983218136442 0.279991609068221 97 0.681754472241316 0.636491055517368 0.318245527758684 98 0.679876163949377 0.640247672101246 0.320123836050623 99 0.669827176947889 0.660345646104221 0.330172823052111 100 0.629825815122613 0.740348369754773 0.370174184877386 101 0.61270592578572 0.77458814842856 0.38729407421428 102 0.584831108841493 0.830337782317014 0.415168891158507 103 0.534576066721204 0.930847866557591 0.465423933278796 104 0.500687247600614 0.998625504798773 0.499312752399386 105 0.478856609775188 0.957713219550376 0.521143390224812 106 0.425228681158729 0.850457362317458 0.574771318841271 107 0.596017621392183 0.807964757215634 0.403982378607817 108 0.581267300660983 0.837465398678033 0.418732699339017 109 0.563409654954614 0.873180690090771 0.436590345045386 110 0.510455523415996 0.979088953168008 0.489544476584004 111 0.457763162996382 0.915526325992764 0.542236837003618 112 0.402297400625652 0.804594801251304 0.597702599374348 113 0.365239715166137 0.730479430332275 0.634760284833862 114 0.327027810437883 0.654055620875766 0.672972189562117 115 0.314342516233273 0.628685032466545 0.685657483766727 116 0.262502214251584 0.525004428503169 0.737497785748416 117 0.234911936155590 0.469823872311181 0.76508806384441 118 0.238462304461922 0.476924608923845 0.761537695538078 119 0.192256057369963 0.384512114739927 0.807743942630037 120 0.165486544505742 0.330973089011484 0.834513455494258 121 0.131805397843157 0.263610795686314 0.868194602156843 122 0.117565063444904 0.235130126889808 0.882434936555096 123 0.109630033191465 0.219260066382931 0.890369966808535 124 0.148748910308133 0.297497820616266 0.851251089691867 125 0.119798918079296 0.239597836158591 0.880201081920704 126 0.097419892017348 0.194839784034696 0.902580107982652 127 0.0721565981199034 0.144313196239807 0.927843401880097 128 0.0611420477853251 0.122284095570650 0.938857952214675 129 0.0412616739864623 0.0825233479729246 0.958738326013538 130 0.0426074268135283 0.0852148536270565 0.957392573186472 131 0.0353838000527565 0.070767600105513 0.964616199947243 132 0.486788137830947 0.973576275661894 0.513211862169053 133 0.401834786588614 0.803669573177227 0.598165213411386 134 0.313822407412951 0.627644814825902 0.686177592587049 135 0.265062973364862 0.530125946729724 0.734937026635138 136 0.182145016266821 0.364290032533642 0.817854983733179 137 0.625912160903189 0.748175678193621 0.374087839096811 138 0.519688615826267 0.960622768347466 0.480311384173733 139 0.382829775313453 0.765659550626906 0.617170224686547 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 8 0.062015503875969 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/10yscv1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/10yscv1290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/199x21290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/199x21290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/22iwn1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/22iwn1290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/32iwn1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/32iwn1290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/42iwn1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/42iwn1290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/5d9w71290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/5d9w71290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/6d9w71290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/6d9w71290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/7njva1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/7njva1290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/8njva1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/8njva1290466645.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/9yscv1290466645.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290466610f9r8hb6baj9m97s/9yscv1290466645.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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') }

Copyright

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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