WS10 MR

*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: Sun, 12 Dec 2010 20:02:08 +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/12/t1292184077a9olm1hcyysls09.htm/, Retrieved Sun, 12 Dec 2010 21:01:17 +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/12/t1292184077a9olm1hcyysls09.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 «

6 73 62 66 4 58 54 54 5 68 41 82 4 62 49 61 4 65 49 65 6 81 72 77 6 73 78 66 4 64 58 66 4 68 58 66 6 51 23 48 4 68 39 57 6 61 63 80 5 69 46 60 4 73 58 70 6 61 39 85 3 62 44 59 5 63 49 72 6 69 57 70 4 47 76 74 6 66 63 70 2 58 18 51 7 63 40 70 5 69 59 71 2 59 62 72 4 59 70 50 4 63 65 69 6 65 56 73 6 65 45 66 5 71 57 73 6 60 50 58 6 81 40 78 4 67 58 83 6 66 49 76 6 62 49 77 6 63 27 79 2 73 51 71 4 55 75 79 5 59 65 60 3 64 47 73 7 63 49 70 5 64 65 42 3 73 61 74 8 54 46 68 8 76 69 83 5 74 55 62 6 63 78 79 3 73 58 61 5 67 34 86 4 68 67 64 5 66 45 75 5 62 68 59 6 71 49 82 5 63 19 61 6 75 72 69 6 77 59 60 4 62 46 59 8 74 56 81 6 67 45 65 4 56 53 60 6 60 67 60 5 58 73 45 5 65 46 75 6 49 70 84 6 61 38 77 6 66 54 64 6 64 46 54 6 65 46 72 6 46 45 56 7 65 47 67 4 81 25 81 4 72 63 73 3 65 46 67 6 74 69 72 5 59 43 69 5 69 49 71 3 58 39 77 5 71 65 63 4 79 54 49 3 68 50 74 7 66 42 76 4 62 45 65 4 69 50 65 5 63 55 69 6 62 38 71 2 61 40 68 2 65 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Celebrity[t] = + 3.04956856198265 + 0.00142148984412118TotNV[t] + 0.00448627811678545TotANX[t] + 0.0260840758692566TotGR[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) 3.04956856198265 1.183817 2.576 0.011015 0.005507 TotNV 0.00142148984412118 0.016259 0.0874 0.930454 0.465227 TotANX 0.00448627811678545 0.009196 0.4879 0.626392 0.313196 TotGR 0.0260840758692566 0.01218 2.1415 0.033943 0.016971 Multiple Linear Regression - Regression Statistics Multiple R 0.191480225727988 R-squared 0.0366646768448413 Adjusted R-squared 0.0163125221302958 F-TEST (value) 1.80151327262843 F-TEST (DF numerator) 3 F-TEST (DF denominator) 142 p-value 0.149630239154723 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.38309910883036 Sum Squared Residuals 271.64076656832 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6 5.15303557121513 0.846964428784874 2 4 4.78281408818795 -0.782814088187947 3 5 5.46906149545013 -0.469061495450133 4 4 4.9486571880653 -0.948657188065301 5 4 5.05725796107469 -1.05725796107469 6 6 5.49619510569777 0.503804894302226 7 6 5.22481602108369 0.775183978916305 8 4 5.12229705015089 -1.12229705015090 9 4 5.12798300952738 -1.12798300952738 10 6 4.47728458244321 1.52271541755679 11 4 4.80798704248515 -0.807987042485147 12 6 5.50564103337205 0.494358966627948 13 5 4.91906470675454 0.080935293245464 14 4 5.23942676222501 -1.23942676222501 15 6 5.52839073791548 0.471609262084516 16 3 4.87405764574286 -1.87405764574286 17 5 5.23700351247124 -0.237003512471245 18 6 5.22925452473174 0.770745475268258 19 4 5.38755733585703 -1.38755733585703 20 6 5.25190772390009 0.748092276099909 21 2 4.5430558483759 -2.5430558483759 22 7 5.14445885768166 1.85554114231834 23 5 5.26431115683457 -0.264311156834570 24 2 5.28963916861297 -3.28963916861297 25 4 4.75167972442361 -0.751679724423609 26 4 5.23053173473204 -1.23053173473204 27 6 5.29733451484624 0.702665485153758 28 6 5.06539692447681 0.934603075523194 29 5 5.31034973202775 -0.310349732027754 30 6 4.87204825888607 1.12795174111393 31 6 5.3787182818299 0.621281718170103 32 4 5.56999080946062 -1.56999080946062 33 6 5.34560428548063 0.654395714519365 34 6 5.36600240197341 0.633997598026593 35 6 5.32089392498676 0.679106075013239 36 2 5.23410689127677 -3.23410689127677 37 4 5.52486335583949 -1.52486335583949 38 5 4.99008909253225 0.00991090746775223 39 3 5.25553652195105 -2.25553652195105 40 7 5.18483536073273 1.81516463926727 41 5 4.52768317610623 0.472316823893766 42 3 5.35722190005239 -2.35722190005239 43 8 5.10641496604677 2.89358503395323 44 8 5.63213327734235 2.36786672265765 45 5 5.01871681076472 -0.0187168107647241 46 6 5.54969410894282 0.450305891057181 47 3 5.0046700794017 -2.00467007940170 48 5 5.54057236226554 -0.54057236226554 49 4 5.11619136083994 -1.11619136083994 50 5 5.30157509714424 -0.301575097144236 51 5 4.98172832054571 0.018271679454289 52 6 5.50921618991678 0.49078381008322 53 5 4.81549033440586 0.184509665594142 54 6 5.27899355967899 0.721006440321006 55 6 4.98875824102572 1.01124175897428 56 4 4.88303020197643 -0.883030201976431 57 8 5.51880053039739 2.48119946960261 58 6 5.04215582829579 0.957844171704209 59 4 4.93198928559846 -0.931989285598459 60 6 5.00048313860994 0.99951686139006 61 5 4.63329668958356 0.366703310416439 62 5 5.3046398854169 -0.304639885416901 63 6 5.62432340553712 0.375676594462878 64 6 5.31523185284465 0.684768147155355 65 6 5.05502676563348 0.944973234366517 66 6 4.75545280231839 1.24454719768161 67 6 5.22638765780913 0.77361234219087 68 6 4.77754785874594 1.22245214125406 69 7 5.10045355657963 1.89954644342037 70 4 5.38967633768588 -1.38967633768588 71 4 5.33868889057259 -1.33868889057259 72 3 5.09596727846285 -2.09596727846285 73 6 5.34236546309229 0.657634536907713 74 5 5.12614765678628 -0.126147656786278 75 5 5.21944837566672 -0.219448375666715 76 3 5.31545366142907 -2.31545366142907 77 5 5.08539919826947 -0.0853991982694717 78 4 4.68224499556821 -0.682244995568209 79 3 5.30076539154715 -2.30076539154715 80 7 5.31420033866314 1.68579966133686 81 4 5.03504837907519 -1.03504837907519 82 4 5.06743019856796 -1.06743019856796 83 5 5.18566895356419 -0.185668953564188 84 6 5.16014888747323 0.839851112526773 85 2 5.08944772625491 -3.08944772625491 86 2 4.64888530340015 -2.64888530340016 87 6 5.60360206448496 0.396397935515041 88 4 4.94743361957123 -0.947433619571232 89 5 5.39336368784296 -0.393363687842963 90 6 4.60876036320537 1.39123963679463 91 7 5.2876965328594 1.71230346714060 92 8 5.00628949059588 2.99371050940412 93 6 4.797472603798 1.20252739620200 94 6 4.9101399249897 1.08986007501030 95 3 4.87209603335481 -1.87209603335481 96 7 4.8473378983922 2.1526621016078 97 3 5.18976525601836 -2.18976525601836 98 6 5.146347851929 0.853652148071004 99 4 5.09361569041219 -1.09361569041219 100 4 5.41694111818036 -1.41694111818036 101 6 5.13676351144839 0.863236488551609 102 6 5.17591644600539 0.824083553994608 103 6 4.4614682930047 1.5385317069953 104 4 4.77712812881146 -0.777128128811462 105 7 5.09047337339892 1.90952662660108 106 5 5.1879001490054 -0.187900149005396 107 7 5.42471399315423 1.57528600684577 108 4 5.24090189357536 -1.24090189357536 109 6 5.28551897892443 0.714481021075572 110 6 5.59484544979832 0.405154550201684 111 6 4.58733073253109 1.41266926746891 112 5 4.40108951616096 0.598910483839035 113 5 5.15392280555282 -0.153922805552815 114 6 5.27156875293649 0.72843124706351 115 7 5.03897064741367 1.96102935258633 116 4 5.15654397665664 -1.15654397665664 117 4 5.22866662771908 -1.22866662771908 118 8 5.24979692106834 2.75020307893166 119 6 5.08228663552807 0.91771336447193 120 3 4.90119712302799 -1.90119712302799 121 4 5.07503490646364 -1.07503490646364 122 5 5.19853989090188 -0.198539890901879 123 5 5.33503620528726 -0.335036205287259 124 6 5.34646176554646 0.65353823445354 125 8 5.20930002540781 2.79069997459219 126 2 4.75668223784995 -2.75668223784995 127 4 4.86042477727682 -0.86042477727682 128 7 5.24761936713336 1.75238063286664 129 5 5.05400111848947 -0.0540011184894671 130 6 5.60379411879752 0.396205881202482 131 6 5.27331346734 0.726686532659997 132 4 5.23504776712069 -1.23504776712069 133 5 5.02284286749076 -0.02284286749076 134 6 4.96331570367536 1.03668429632464 135 6 5.66574453236669 0.334255467633311 136 6 5.56597203574705 0.434027964252951 137 6 5.37637256081673 0.62362743918327 138 5 5.33255931402726 -0.332559314027260 139 5 4.86068944973009 0.139310550269906 140 6 4.98204663450522 1.01795336549478 141 4 5.235924223821 -1.23592422382100 142 6 5.07292410363189 0.927075896368114 143 3 5.59025775570656 -2.59025775570656 144 6 5.17522126598026 0.824778734019736 145 8 5.1963623369669 2.8036376630331 146 4 5.12263925134477 -1.12263925134477 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.069737003680679 0.139474007361358 0.930262996319321 8 0.0365677606476424 0.0731355212952847 0.963432239352358 9 0.0331736024455212 0.0663472048910423 0.966826397554479 10 0.121944273648085 0.243888547296169 0.878055726351915 11 0.248967927181529 0.497935854363058 0.751032072818471 12 0.226410864826282 0.452821729652564 0.773589135173718 13 0.154013779184872 0.308027558369744 0.845986220815128 14 0.135365155756924 0.270730311513849 0.864634844243076 15 0.0992362993171653 0.198472598634331 0.900763700682835 16 0.132713228192409 0.265426456384817 0.867286771807591 17 0.0891711918931123 0.178342383786225 0.910828808106888 18 0.077510514163456 0.155021028326912 0.922489485836544 19 0.065532765935673 0.131065531871346 0.934467234064327 20 0.058466404246092 0.116932808492184 0.941533595753908 21 0.101941836630101 0.203883673260202 0.898058163369899 22 0.176496443293910 0.352992886587820 0.82350355670609 23 0.132946575205768 0.265893150411537 0.867053424794232 24 0.340395609507993 0.680791219015985 0.659604390492007 25 0.285190688859021 0.570381377718042 0.714809311140979 26 0.249824832570574 0.499649665141147 0.750175167429426 27 0.224116061767712 0.448232123535425 0.775883938232288 28 0.212613041709487 0.425226083418974 0.787386958290513 29 0.170648770392996 0.341297540785992 0.829351229607004 30 0.194623604637420 0.389247209274839 0.80537639536258 31 0.155493100989330 0.310986201978661 0.84450689901067 32 0.165617195526032 0.331234391052064 0.834382804473968 33 0.141800880778730 0.283601761557460 0.85819911922127 34 0.122242845259491 0.244485690518983 0.877757154740509 35 0.0986111652173973 0.197222330434795 0.901388834782603 36 0.288297622555878 0.576595245111756 0.711702377444122 37 0.270616587186931 0.541233174373863 0.729383412813069 38 0.236117579020869 0.472235158041739 0.76388242097913 39 0.300142993543634 0.600285987087268 0.699857006456366 40 0.36461595701868 0.72923191403736 0.63538404298132 41 0.335294887281541 0.670589774563082 0.664705112718459 42 0.418918993653452 0.837837987306904 0.581081006346548 43 0.626818942196987 0.746362115606025 0.373181057803013 44 0.732543271358307 0.534913457283387 0.267456728641693 45 0.687942529501652 0.624114940996696 0.312057470498348 46 0.650943863844776 0.698112272310448 0.349056136155224 47 0.685844813110375 0.628310373779249 0.314155186889625 48 0.647822501347449 0.704354997305102 0.352177498652551 49 0.622654301808245 0.754691396383509 0.377345698191755 50 0.574719735759592 0.850560528480816 0.425280264240408 51 0.52864912012491 0.94270175975018 0.47135087987509 52 0.484673893413848 0.969347786827697 0.515326106586152 53 0.435857480491559 0.871714960983118 0.564142519508441 54 0.406792633879559 0.813585267759119 0.59320736612044 55 0.38944999877976 0.77889999755952 0.61055000122024 56 0.356676801015155 0.713353602030311 0.643323198984844 57 0.456947470382198 0.913894940764396 0.543052529617802 58 0.433775709810177 0.867551419620355 0.566224290189823 59 0.401852571060287 0.803705142120573 0.598147428939713 60 0.390074499155761 0.780148998311523 0.609925500844239 61 0.355670385794703 0.711340771589406 0.644329614205297 62 0.312570962099043 0.625141924198086 0.687429037900957 63 0.275782798646504 0.551565597293009 0.724217201353496 64 0.246554770030541 0.493109540061082 0.753445229969459 65 0.227916261836269 0.455832523672539 0.77208373816373 66 0.223860731600222 0.447721463200445 0.776139268399778 67 0.199690217881134 0.399380435762267 0.800309782118866 68 0.195293949228973 0.390587898457946 0.804706050771027 69 0.225065101900196 0.450130203800392 0.774934898099804 70 0.225189734127994 0.450379468255989 0.774810265872006 71 0.221599683317101 0.443199366634202 0.778400316682899 72 0.26802428250793 0.53604856501586 0.73197571749207 73 0.238178848036447 0.476357696072894 0.761821151963553 74 0.202598359683659 0.405196719367318 0.797401640316341 75 0.170953065292854 0.341906130585707 0.829046934707146 76 0.228707354572314 0.457414709144627 0.771292645427686 77 0.193973008883171 0.387946017766342 0.806026991116829 78 0.170276560500717 0.340553121001435 0.829723439499283 79 0.228899206115859 0.457798412231717 0.771100793884141 80 0.244444799531278 0.488889599062557 0.755555200468721 81 0.228116984467691 0.456233968935383 0.771883015532309 82 0.214982854192684 0.429965708385369 0.785017145807316 83 0.182143874778489 0.364287749556977 0.817856125221511 84 0.161807426044283 0.323614852088566 0.838192573955717 85 0.308210802583933 0.616421605167865 0.691789197416067 86 0.446610560031051 0.893221120062102 0.553389439968949 87 0.402205527712021 0.804411055424043 0.597794472287979 88 0.382594232622049 0.765188465244097 0.617405767377951 89 0.339614799476692 0.679229598953385 0.660385200523308 90 0.335520270721755 0.67104054144351 0.664479729278245 91 0.349912731590214 0.699825463180427 0.650087268409786 92 0.507088950764969 0.985822098470063 0.492911049235031 93 0.487938075637488 0.975876151274976 0.512061924362512 94 0.462828028840124 0.925656057680249 0.537171971159876 95 0.518920363786292 0.962159272427416 0.481079636213708 96 0.584862885822468 0.830274228355064 0.415137114177532 97 0.668608648430891 0.662782703138217 0.331391351569109 98 0.63440614907709 0.73118770184582 0.36559385092291 99 0.637413201489675 0.72517359702065 0.362586798510325 100 0.655123063194037 0.689753873611927 0.344876936805963 101 0.621094028712292 0.757811942575415 0.378905971287708 102 0.585642339900746 0.828715320198509 0.414357660099254 103 0.569969825924528 0.860060348150944 0.430030174075472 104 0.54558970668907 0.90882058662186 0.45441029331093 105 0.573850355657696 0.852299288684607 0.426149644342304 106 0.52236131570321 0.95527736859358 0.47763868429679 107 0.520936233469756 0.958127533060489 0.479063766530244 108 0.523296154813352 0.953407690373295 0.476703845186648 109 0.476068425972473 0.952136851944946 0.523931574027527 110 0.421586983946358 0.843173967892716 0.578413016053642 111 0.421587480571290 0.843174961142579 0.57841251942871 112 0.382490327285058 0.764980654570116 0.617509672714942 113 0.333705297707215 0.66741059541443 0.666294702292785 114 0.304224552539106 0.608449105078212 0.695775447460894 115 0.334036132036239 0.668072264072479 0.665963867963761 116 0.330640447153009 0.661280894306019 0.66935955284699 117 0.340513616857655 0.68102723371531 0.659486383142345 118 0.520588161967075 0.95882367606585 0.479411838032925 119 0.505065857585284 0.989868284829433 0.494934142414716 120 0.585502814925888 0.828994370148224 0.414497185074112 121 0.588630386394711 0.822739227210578 0.411369613605289 122 0.554786045136029 0.890427909727942 0.445213954863971 123 0.523563445835329 0.952873108329342 0.476436554164671 124 0.456323465605897 0.912646931211793 0.543676534394103 125 0.594996760093997 0.810006479812006 0.405003239906003 126 0.838167405280868 0.323665189438263 0.161832594719132 127 0.923291404057483 0.153417191885034 0.0767085959425172 128 0.927941243982535 0.144117512034929 0.0720587560174647 129 0.89195343561112 0.216093128777760 0.108046564388880 130 0.861664242891221 0.276671514217558 0.138335757108779 131 0.811686780431174 0.376626439137653 0.188313219568826 132 0.954052664785666 0.0918946704286687 0.0459473352143344 133 0.958472510146785 0.0830549797064303 0.0415274898532151 134 0.92852449433592 0.142951011328158 0.071475505664079 135 0.953531276749416 0.0929374465011681 0.0464687232505841 136 0.909160213853127 0.181679572293746 0.0908397861468732 137 0.947847300026635 0.104305399946731 0.0521526999733654 138 0.902406969289006 0.195186061421987 0.0975930307109936 139 0.788804787070352 0.422390425859296 0.211195212929648 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 5 0.037593984962406 OK

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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