*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 29 Dec 2010 10:35:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t12936189569ubsj5nieiiea4p.htm/, Retrieved Wed, 29 Dec 2010 11:35:56 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t12936189569ubsj5nieiiea4p.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 13 14 182 13 169 3 39 2 26 12 12 8 96 13 156 5 60 1 12 15 10 12 120 16 160 6 60 0 0 12 9 7 63 12 108 6 54 3 27 10 10 10 100 11 110 5 50 3 30 12 12 7 84 12 144 3 36 1 12 15 13 16 208 18 234 8 104 3 39 9 12 11 132 11 132 4 48 1 12 12 12 14 168 14 168 4 48 4 48 11 6 6 36 9 54 4 24 0 0 11 5 16 80 14 70 6 30 3 15 11 12 11 132 12 144 6 72 2 24 15 11 16 176 11 121 5 55 4 44 7 14 12 168 12 168 4 56 3 42 11 14 7 98 13 182 6 84 1 14 11 12 13 156 11 132 4 48 1 12 10 12 11 132 12 144 6 72 2 24 14 11 15 165 16 176 6 66 3 33 10 11 7 77 9 99 4 44 1 11 6 7 9 63 11 77 4 28 1 7 11 9 7 63 13 117 2 18 2 18 15 11 14 154 15 165 7 77 3 33 11 11 15 165 10 110 5 55 4 44 12 12 7 84 11 132 4 48 2 24 14 12 15 180 13 156 6 72 1 12 15 11 17 187 16 176 6 66 2 22 9 11 15 165 15 165 7 77 2 22 13 8 14 112 14 112 5 40 4 32 13 9 14 126 14 126 6 54 2 18 16 12 8 96 14 168 4 48 3 36 13 10 8 80 8 80 4 40 3 30 12 10 14 140 13 130 7 70 3 30 14 12 14 168 15 180 7 84 4 48 11 8 8 64 13 104 4 32 2 16 9 12 11 132 11 13 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 Popularity[t] = + 7.13071247390462 -0.501068230469552FindingFriends[t] + 0.0144399681786133KnowingPeople[t] + 0.0195920449423166friends_knowning[t] + 0.453370355865983Liked[t] -0.0119296940515774friends_liked[t] -1.04257015127669Celebrity[t] + 0.146732923963820friends_celeb[t] + 1.14069077304853Sum[t] -0.0845908632946571friends_sum[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) 7.13071247390462 5.618027 1.2693 0.20637 0.103185 FindingFriends -0.501068230469552 0.493294 -1.0158 0.311425 0.155712 KnowingPeople 0.0144399681786133 0.39969 0.0361 0.97123 0.485615 friends_knowning 0.0195920449423166 0.035777 0.5476 0.584794 0.292397 Liked 0.453370355865983 0.502072 0.903 0.368014 0.184007 friends_liked -0.0119296940515774 0.047077 -0.2534 0.800308 0.400154 Celebrity -1.04257015127669 1.209949 -0.8617 0.390285 0.195143 friends_celeb 0.146732923963820 0.107187 1.3689 0.173121 0.086561 Sum 1.14069077304853 0.841424 1.3557 0.177298 0.088649 friends_sum -0.0845908632946571 0.075323 -1.123 0.263263 0.131631 Multiple Linear Regression - Regression Statistics Multiple R 0.722001202058945 R-squared 0.521285735774562 Adjusted R-squared 0.491775952363404 F-TEST (value) 17.6648445199185 F-TEST (DF numerator) 9 F-TEST (DF denominator) 146 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09351674679716 Sum Squared Residuals 639.890605891545 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 10.9393262245388 2.06067377546120 2 12 10.8637572173315 1.13624278266855 3 15 12.5380843562029 2.46191564379708 4 12 10.9147903176924 1.08520968230763 5 10 10.9065837761927 -0.906583776192664 6 12 8.86754881001966 3.13245118998034 7 15 17.3348198468565 -2.3348198468565 8 9 10.2737377490074 -1.27373774900742 9 12 12.3298145937458 -0.329814593745755 10 11 7.703695812116 3.296304187884 11 11 12.2356569872936 -1.23565698729358 12 11 12.1460020623454 -1.14600206234544 13 15 12.5400074425859 2.45999255741406 14 7 10.9327752831474 -3.93277528314743 15 11 11.8860311300230 -0.886031130023043 16 11 10.7728267639802 0.227173236019755 17 10 12.1460020623454 -2.14600206234543 18 14 14.2820743220530 -0.282074322053041 19 10 8.62408199434456 1.37591800565544 20 6 9.54277687401174 -3.54277687401174 21 11 9.76931576610675 1.23068423389325 22 15 14.3014701505356 0.69852984946435 23 11 11.9879112587432 -0.98791125874321 24 12 9.40116013257441 2.59883986742559 25 14 13.3287937060255 0.671206293974503 26 15 14.5317879703339 0.468212029666069 27 9 14.3212313362724 -5.32123133627244 28 13 13.0420161354698 -0.0420161354698297 29 13 12.5628021417156 0.437197858284434 30 16 10.7069471353146 5.29305286468537 31 13 9.05888360657696 3.94111639342304 32 12 13.2656904540232 -1.26569045402324 33 14 14.7947034298603 -0.794703429860287 34 11 10.5978043918972 0.402195608102836 35 9 10.3993381625201 -1.39933816252006 36 16 14.4000743401058 1.59992565989419 37 12 12.9527000501128 -0.952700050112832 38 10 10.2816921026549 -0.281692102654871 39 13 12.8754994188057 0.124500581194254 40 16 15.5039013505371 0.496098649462922 41 14 13.0809055180780 0.91909448192204 42 15 8.59442596298533 6.40557403701467 43 5 8.72145244464665 -3.72145244464665 44 8 10.2803705458728 -2.28037054587275 45 11 11.1736409222425 -0.173640922242536 46 16 13.7493739666929 2.25062603330708 47 17 14.3274425279742 2.67255747202575 48 9 8.29370726420258 0.706292735797424 49 9 11.4237199277776 -2.42371992777761 50 13 14.6345807087657 -1.63458070876572 51 10 10.9589490446740 -0.958949044674013 52 6 12.0949341895663 -6.09493418956629 53 12 12.1721492745242 -0.172149274524155 54 8 10.2711326945549 -2.27113269455493 55 14 12.3180862921800 1.68191370781997 56 12 12.9345812369023 -0.934581236902313 57 11 10.9332068487977 0.0667931512023279 58 16 14.3950911126313 1.60490888736870 59 8 10.5242002387326 -2.52420023873258 60 15 14.4723407949832 0.527659205016821 61 7 8.99149290399343 -1.99149290399343 62 16 14.2653534812969 1.7346465187031 63 14 12.4452647828127 1.55473521718731 64 16 13.3095955845957 2.69040441540429 65 9 10.8253687840318 -1.82536878403182 66 14 12.2370801682762 1.76291983172384 67 11 13.3953809193164 -2.39538091931638 68 13 10.3039986825980 2.69600131740202 69 15 13.2065059315906 1.79349406840939 70 5 4.63866377481484 0.361336225185164 71 15 12.9345812369023 2.06541876309769 72 13 12.4882809953014 0.511719004698553 73 11 12.3566762937614 -1.35667629376135 74 11 14.0222084053631 -3.02220840536308 75 12 12.7149926705601 -0.71499267056012 76 12 13.5799945330508 -1.57999453305079 77 12 12.4119671620672 -0.411967162067243 78 12 12.0489431376080 -0.0489431376080456 79 14 10.5813467218020 3.41865327819801 80 6 7.58956533899704 -1.58956533899704 81 7 9.58577374630882 -2.58577374630882 82 14 12.6144008030286 1.38559919697144 83 14 14.0323606737721 -0.0323606737721499 84 10 11.1562354690427 -1.15623546904270 85 13 8.61966062207213 4.38033937792787 86 12 12.6976423672448 -0.697642367244776 87 9 9.3863694549946 -0.386369454994595 88 12 11.8585104760372 0.14148952396285 89 16 14.6627708860537 1.33722911394631 90 10 10.4708006369433 -0.470800636943257 91 14 12.9221207325253 1.07787926747474 92 10 13.5000256756662 -3.50002567566622 93 16 15.6040064720802 0.395993527919833 94 15 13.2616522008653 1.73834779913472 95 12 11.5021975743568 0.497802425643212 96 10 9.39950381303554 0.600496186964465 97 8 9.49370108808758 -1.49370108808758 98 8 8.16051735795124 -0.160517357951236 99 11 12.4720212055406 -1.47202120554065 100 13 12.5818165031051 0.418183496894865 101 16 15.5236625362739 0.476337463726128 102 16 15.0442479373467 0.9557520626533 103 14 16.205090299453 -2.20509029945300 104 11 9.3786282020592 1.62137179794081 105 4 7.74128845004527 -3.74128845004527 106 14 15.1234318658932 -1.12343186589317 107 9 10.9355728477718 -1.93557284777183 108 14 15.1029146254051 -1.10291462540508 109 8 10.4697215653163 -2.46972156531634 110 8 11.0222268640315 -3.02222686403150 111 11 11.7399605772429 -0.739960577242937 112 12 11.7259545405275 0.274045459472454 113 11 11.2068372326215 -0.206837232621550 114 14 13.4501327455468 0.549867254453218 115 15 14.4802280286219 0.51977197137813 116 16 13.4078344169117 2.59216558308832 117 16 13.2638628122735 2.73613718772651 118 11 12.6382246488744 -1.63822464887442 119 14 14.1414093873231 -0.14140938732313 120 14 10.9504667477682 3.04953325223176 121 12 11.3949111380132 0.60508886198677 122 14 12.6519598870773 1.34804011292273 123 8 10.8911831905579 -2.89118319055786 124 13 14.1836397913579 -1.18363979135789 125 16 14.0158089738105 1.98419102618952 126 12 10.5492818160930 1.45071818390697 127 16 15.6975419798839 0.302458020116145 128 12 13.2031932925129 -1.20319329251285 129 11 11.4293830912187 -0.429383091218697 130 4 6.10612877200004 -2.10612877200004 131 16 16.0743432204218 -0.0743432204217874 132 15 12.6257857705249 2.37421422947515 133 10 11.0761743627835 -1.07617436278346 134 13 13.4873970152744 -0.487397015274428 135 15 13.2655191318124 1.73448086818763 136 12 10.3950767885287 1.60492321147130 137 14 13.6377868794558 0.362213120544224 138 7 10.3648158549381 -3.36481585493814 139 19 14.0748221740323 4.92517782596775 140 12 13.0450278327524 -1.04502783275237 141 12 11.9822290424360 0.0177709575640404 142 13 13.5150636392988 -0.515063639298784 143 15 12.4478409941893 2.55215900581071 144 8 9.40102189128402 -1.40102189128402 145 12 10.7702217095278 1.22977829047224 146 10 10.8018247307924 -0.80182473079243 147 8 11.1739712445785 -3.17397124457850 148 10 14.7937263715450 -4.79372637154504 149 15 13.8677393419999 1.13226065800013 150 16 14.5114376971260 1.48856230287396 151 13 13.1972777828502 -0.197277782850192 152 16 15.2288615510811 0.77113844891889 153 9 9.84022680652135 -0.840226806521353 154 14 12.7935752210566 1.20642477894338 155 14 13.1839295279290 0.816070472070982 156 12 10.2218177031707 1.77818229682926 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.789856754638046 0.420286490723908 0.210143245361954 14 0.794290257201509 0.411419485596982 0.205709742798491 15 0.720281079680348 0.559437840639304 0.279718920319652 16 0.652360434596926 0.695279130806148 0.347639565403074 17 0.559647021224978 0.880705957550043 0.440352978775022 18 0.461611528974337 0.923223057948675 0.538388471025663 19 0.366800294452809 0.733600588905618 0.633199705547191 20 0.787485910307698 0.425028179384605 0.212514089692302 21 0.746649252642218 0.506701494715563 0.253350747357782 22 0.71550487307246 0.56899025385508 0.28449512692754 23 0.649591316169457 0.700817367661086 0.350408683830543 24 0.677632001947584 0.644735996104833 0.322367998052416 25 0.612063670996889 0.775872658006223 0.387936329003111 26 0.542401760210633 0.915196479578735 0.457598239789367 27 0.779451156916408 0.441097686167185 0.220548843083592 28 0.722935064379629 0.554129871240743 0.277064935620371 29 0.67363039878558 0.65273920242884 0.32636960121442 30 0.820414569955332 0.359170860089336 0.179585430044668 31 0.863602288904169 0.272795422191662 0.136397711095831 32 0.82953688249718 0.340926235005639 0.170463117502820 33 0.793887141927808 0.412225716144384 0.206112858072192 34 0.748011208619611 0.503977582760778 0.251988791380389 35 0.726702639941763 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0.0218425297868389 53 0.971164838151099 0.0576703236978028 0.0288351618489014 54 0.97667337797608 0.0466532440478394 0.0233266220239197 55 0.978581189897702 0.042837620204595 0.0214188101022975 56 0.973878198000592 0.0522436039988154 0.0261218019994077 57 0.965858522295067 0.0682829554098653 0.0341414777049327 58 0.959475176615094 0.0810496467698111 0.0405248233849056 59 0.972211977397613 0.0555760452047747 0.0277880226023874 60 0.966988960278706 0.0660220794425878 0.0330110397212939 61 0.966475616449684 0.0670487671006323 0.0335243835503162 62 0.963719585700957 0.0725608285980868 0.0362804142990434 63 0.975166711134009 0.0496665777319821 0.0248332888659910 64 0.97952499290963 0.0409500141807413 0.0204750070903706 65 0.979991337015718 0.0400173259685643 0.0200086629842821 66 0.978033533804374 0.0439329323912527 0.0219664661956263 67 0.981027901073737 0.0379441978525253 0.0189720989262627 68 0.984639352940902 0.0307212941181954 0.0153606470590977 69 0.98325874118567 0.0334825176286591 0.0167412588143296 70 0.978464810038453 0.0430703799230932 0.0215351899615466 71 0.978438755695841 0.0431224886083175 0.0215612443041588 72 0.971736232525735 0.0565275349485301 0.0282637674742651 73 0.96722932069742 0.0655413586051594 0.0327706793025797 74 0.983171346943996 0.0336573061120083 0.0168286530560041 75 0.978631496071623 0.0427370078567547 0.0213685039283773 76 0.97635682845968 0.0472863430806395 0.0236431715403197 77 0.969335964613115 0.0613280707737694 0.0306640353868847 78 0.959907761006206 0.0801844779875881 0.0400922389937940 79 0.97487213722366 0.0502557255526806 0.0251278627763403 80 0.973524285597228 0.0529514288055441 0.0264757144027721 81 0.979794345741268 0.0404113085174646 0.0202056542587323 82 0.97938721677699 0.0412255664460189 0.0206127832230095 83 0.972650243757005 0.0546995124859892 0.0273497562429946 84 0.967176595754993 0.0656468084900142 0.0328234042450071 85 0.989707413712195 0.0205851725756101 0.0102925862878050 86 0.98649381468275 0.0270123706344991 0.0135061853172496 87 0.981899927358457 0.0362001452830859 0.0181000726415430 88 0.975755405295073 0.0484891894098548 0.0242445947049274 89 0.970320439332827 0.0593591213343467 0.0296795606671734 90 0.961635292062185 0.0767294158756301 0.0383647079378151 91 0.95349478122867 0.0930104375426596 0.0465052187713298 92 0.977456689084616 0.0450866218307681 0.0225433109153841 93 0.969990325502287 0.0600193489954257 0.0300096744977128 94 0.964419862773051 0.0711602744538975 0.0355801372269487 95 0.953778692720702 0.0924426145585966 0.0462213072792983 96 0.940649793686263 0.118700412627473 0.0593502063137367 97 0.927789235403593 0.144421529192814 0.0722107645964068 98 0.910113670632 0.179772658736000 0.0898863293680002 99 0.907106610992191 0.185786778015618 0.0928933890078088 100 0.884607078733033 0.230785842533934 0.115392921266967 101 0.860615361519267 0.278769276961466 0.139384638480733 102 0.835871566962959 0.328256866074083 0.164128433037041 103 0.875796479709198 0.248407040581604 0.124203520290802 104 0.914359596350102 0.171280807299796 0.0856404036498978 105 0.925043542953848 0.149912914092304 0.074956457046152 106 0.909435769665579 0.181128460668843 0.0905642303344213 107 0.905858722900244 0.188282554199512 0.0941412770997558 108 0.910164860487342 0.179670279025317 0.0898351395126584 109 0.908865267778054 0.182269464443892 0.0911347322219461 110 0.90122116403938 0.197557671921241 0.0987788359606207 111 0.886025292846051 0.227949414307897 0.113974707153949 112 0.899915057077614 0.200169885844773 0.100084942922386 113 0.871777571593193 0.256444856813615 0.128222428406807 114 0.841065216834469 0.317869566331062 0.158934783165531 115 0.802814400797228 0.394371198405545 0.197185599202772 116 0.792288192023945 0.415423615952109 0.207711807976055 117 0.80106321391162 0.397873572176758 0.198936786088379 118 0.79285086230577 0.41429827538846 0.20714913769423 119 0.745725907062648 0.508548185874703 0.254274092937352 120 0.815871346278011 0.368257307443978 0.184128653721989 121 0.783472604704189 0.433054790591622 0.216527395295811 122 0.73960066909439 0.520798661811219 0.260399330905610 123 0.731701256823727 0.536597486352547 0.268298743176273 124 0.677187246593197 0.645625506813606 0.322812753406803 125 0.682576594490698 0.634846811018605 0.317423405509303 126 0.652292041346899 0.695415917306202 0.347707958653101 127 0.588959466234945 0.82208106753011 0.411040533765055 128 0.552166421609133 0.895667156781733 0.447833578390867 129 0.499035241259993 0.998070482519987 0.500964758740007 130 0.444943808642562 0.889887617285123 0.555056191357438 131 0.374981421696104 0.749962843392207 0.625018578303896 132 0.375366110833359 0.750732221666717 0.624633889166641 133 0.37547158393236 0.75094316786472 0.62452841606764 134 0.335005100297719 0.670010200595438 0.664994899702281 135 0.299849971717293 0.599699943434585 0.700150028282707 136 0.301040174722990 0.602080349445979 0.69895982527701 137 0.226501992443877 0.453003984887755 0.773498007556123 138 0.351490911221516 0.702981822443032 0.648509088778484 139 0.61800047648068 0.763999047038641 0.381999523519320 140 0.813317324653413 0.373365350693175 0.186682675346587 141 0.746032629348773 0.507934741302454 0.253967370651227 142 0.71953424887232 0.56093150225536 0.28046575112768 143 0.610057764065747 0.779884471868507 0.389942235934253 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 22 0.16793893129771 NOK 10% type I error level 44 0.33587786259542 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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