WS8: model 1

*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: Fri, 26 Nov 2010 13:29:55 +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/26/t12907785571ykwqt6mhd7tbml.htm/, Retrieved Fri, 26 Nov 2010 14:35:57 +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/26/t12907785571ykwqt6mhd7tbml.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 «

2 14 2 18 2 11 1 12 2 16 2 18 2 14 2 14 2 15 2 15 1 17 2 19 1 10 2 16 2 18 1 14 1 14 2 17 1 14 2 16 1 18 2 11 2 14 2 12 1 17 2 9 1 16 2 14 2 15 1 11 2 16 1 13 2 17 2 15 1 14 1 16 1 9 1 15 2 17 1 13 1 15 2 16 1 16 1 12 2 12 2 11 2 15 2 15 2 17 1 13 2 16 1 14 1 11 2 12 1 12 2 15 2 16 2 15 1 12 2 12 1 8 1 13 2 11 2 14 2 15 1 10 2 11 1 12 2 15 1 15 1 14 2 16 2 15 1 15 1 13 2 12 2 17 2 13 1 15 1 13 1 15 1 16 2 15 1 16 2 15 2 14 1 15 2 14 2 13 2 7 2 17 2 13 2 15 2 14 2 13 2 16 2 12 2 14 1 17 1 15 2 17 1 12 2 16 1 11 2 15 1 9 2 16 1 15 1 10 2 10 2 15 2 11 2 13 1 14 2 18 1 16 2 14 2 14 2 14 2 14 2 12 2 14 2 15 2 15 2 15 2 13 1 17 2 17 2 19 2 15 1 13 1 9 2 15 1 15 1 15 2 16 1 11 1 14 2 11 2 15 1 13 2 15 1 16 2 14 1 15 2 16 2 16 1 11 1 12 1 9 2 16 2 13 1 16 2 12 2 9 2 13 2 13 2 14 2 19 2 13 2 12 2 13

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 16 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 12.6172699237137 + 0.874533354974842x[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) 12.6172699237137 0.633471 19.9177 0 0 x 0.874533354974842 0.373902 2.3389 0.020575 0.010287 Multiple Linear Regression - Regression Statistics Multiple R 0.181826835929637 R-squared 0.0330609982641832 Adjusted R-squared 0.0270176295033342 F-TEST (value) 5.47062401327624 F-TEST (DF numerator) 1 F-TEST (DF denominator) 160 p-value 0.0205749436237584 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.30582339712113 Sum Squared Residuals 850.6914461938 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 14.3663366336634 -0.366336633663402 2 18 14.3663366336634 3.63366336633664 3 11 14.3663366336634 -3.36633663366337 4 12 13.4918032786885 -1.49180327868852 5 16 14.3663366336634 1.63366336633663 6 18 14.3663366336634 3.63366336633663 7 14 14.3663366336634 -0.366336633663366 8 14 14.3663366336634 -0.366336633663366 9 15 14.3663366336634 0.633663366336634 10 15 14.3663366336634 0.633663366336634 11 17 13.4918032786885 3.50819672131148 12 19 14.3663366336634 4.63366336633663 13 10 13.4918032786885 -3.49180327868853 14 16 14.3663366336634 1.63366336633663 15 18 14.3663366336634 3.63366336633663 16 14 13.4918032786885 0.508196721311475 17 14 13.4918032786885 0.508196721311475 18 17 14.3663366336634 2.63366336633663 19 14 13.4918032786885 0.508196721311475 20 16 14.3663366336634 1.63366336633663 21 18 13.4918032786885 4.50819672131148 22 11 14.3663366336634 -3.36633663366337 23 14 14.3663366336634 -0.366336633663366 24 12 14.3663366336634 -2.36633663366337 25 17 13.4918032786885 3.50819672131148 26 9 14.3663366336634 -5.36633663366337 27 16 13.4918032786885 2.50819672131148 28 14 14.3663366336634 -0.366336633663366 29 15 14.3663366336634 0.633663366336634 30 11 13.4918032786885 -2.49180327868852 31 16 14.3663366336634 1.63366336633663 32 13 13.4918032786885 -0.491803278688525 33 17 14.3663366336634 2.63366336633663 34 15 14.3663366336634 0.633663366336634 35 14 13.4918032786885 0.508196721311475 36 16 13.4918032786885 2.50819672131148 37 9 13.4918032786885 -4.49180327868852 38 15 13.4918032786885 1.50819672131148 39 17 14.3663366336634 2.63366336633663 40 13 13.4918032786885 -0.491803278688525 41 15 13.4918032786885 1.50819672131148 42 16 14.3663366336634 1.63366336633663 43 16 13.4918032786885 2.50819672131148 44 12 13.4918032786885 -1.49180327868852 45 12 14.3663366336634 -2.36633663366337 46 11 14.3663366336634 -3.36633663366337 47 15 14.3663366336634 0.633663366336634 48 15 14.3663366336634 0.633663366336634 49 17 14.3663366336634 2.63366336633663 50 13 13.4918032786885 -0.491803278688525 51 16 14.3663366336634 1.63366336633663 52 14 13.4918032786885 0.508196721311475 53 11 13.4918032786885 -2.49180327868852 54 12 14.3663366336634 -2.36633663366337 55 12 13.4918032786885 -1.49180327868852 56 15 14.3663366336634 0.633663366336634 57 16 14.3663366336634 1.63366336633663 58 15 14.3663366336634 0.633663366336634 59 12 13.4918032786885 -1.49180327868852 60 12 14.3663366336634 -2.36633663366337 61 8 13.4918032786885 -5.49180327868852 62 13 13.4918032786885 -0.491803278688525 63 11 14.3663366336634 -3.36633663366337 64 14 14.3663366336634 -0.366336633663366 65 15 14.3663366336634 0.633663366336634 66 10 13.4918032786885 -3.49180327868853 67 11 14.3663366336634 -3.36633663366337 68 12 13.4918032786885 -1.49180327868852 69 15 14.3663366336634 0.633663366336634 70 15 13.4918032786885 1.50819672131148 71 14 13.4918032786885 0.508196721311475 72 16 14.3663366336634 1.63366336633663 73 15 14.3663366336634 0.633663366336634 74 15 13.4918032786885 1.50819672131148 75 13 13.4918032786885 -0.491803278688525 76 12 14.3663366336634 -2.36633663366337 77 17 14.3663366336634 2.63366336633663 78 13 14.3663366336634 -1.36633663366337 79 15 13.4918032786885 1.50819672131148 80 13 13.4918032786885 -0.491803278688525 81 15 13.4918032786885 1.50819672131148 82 16 13.4918032786885 2.50819672131148 83 15 14.3663366336634 0.633663366336634 84 16 13.4918032786885 2.50819672131148 85 15 14.3663366336634 0.633663366336634 86 14 14.3663366336634 -0.366336633663366 87 15 13.4918032786885 1.50819672131148 88 14 14.3663366336634 -0.366336633663366 89 13 14.3663366336634 -1.36633663366337 90 7 14.3663366336634 -7.36633663366337 91 17 14.3663366336634 2.63366336633663 92 13 14.3663366336634 -1.36633663366337 93 15 14.3663366336634 0.633663366336634 94 14 14.3663366336634 -0.366336633663366 95 13 14.3663366336634 -1.36633663366337 96 16 14.3663366336634 1.63366336633663 97 12 14.3663366336634 -2.36633663366337 98 14 14.3663366336634 -0.366336633663366 99 17 13.4918032786885 3.50819672131148 100 15 13.4918032786885 1.50819672131148 101 17 14.3663366336634 2.63366336633663 102 12 13.4918032786885 -1.49180327868852 103 16 14.3663366336634 1.63366336633663 104 11 13.4918032786885 -2.49180327868852 105 15 14.3663366336634 0.633663366336634 106 9 13.4918032786885 -4.49180327868852 107 16 14.3663366336634 1.63366336633663 108 15 13.4918032786885 1.50819672131148 109 10 13.4918032786885 -3.49180327868853 110 10 14.3663366336634 -4.36633663366337 111 15 14.3663366336634 0.633663366336634 112 11 14.3663366336634 -3.36633663366337 113 13 14.3663366336634 -1.36633663366337 114 14 13.4918032786885 0.508196721311475 115 18 14.3663366336634 3.63366336633663 116 16 13.4918032786885 2.50819672131148 117 14 14.3663366336634 -0.366336633663366 118 14 14.3663366336634 -0.366336633663366 119 14 14.3663366336634 -0.366336633663366 120 14 14.3663366336634 -0.366336633663366 121 12 14.3663366336634 -2.36633663366337 122 14 14.3663366336634 -0.366336633663366 123 15 14.3663366336634 0.633663366336634 124 15 14.3663366336634 0.633663366336634 125 15 14.3663366336634 0.633663366336634 126 13 14.3663366336634 -1.36633663366337 127 17 13.4918032786885 3.50819672131148 128 17 14.3663366336634 2.63366336633663 129 19 14.3663366336634 4.63366336633663 130 15 14.3663366336634 0.633663366336634 131 13 13.4918032786885 -0.491803278688525 132 9 13.4918032786885 -4.49180327868852 133 15 14.3663366336634 0.633663366336634 134 15 13.4918032786885 1.50819672131148 135 15 13.4918032786885 1.50819672131148 136 16 14.3663366336634 1.63366336633663 137 11 13.4918032786885 -2.49180327868852 138 14 13.4918032786885 0.508196721311475 139 11 14.3663366336634 -3.36633663366337 140 15 14.3663366336634 0.633663366336634 141 13 13.4918032786885 -0.491803278688525 142 15 14.3663366336634 0.633663366336634 143 16 13.4918032786885 2.50819672131148 144 14 14.3663366336634 -0.366336633663366 145 15 13.4918032786885 1.50819672131148 146 16 14.3663366336634 1.63366336633663 147 16 14.3663366336634 1.63366336633663 148 11 13.4918032786885 -2.49180327868852 149 12 13.4918032786885 -1.49180327868852 150 9 13.4918032786885 -4.49180327868852 151 16 14.3663366336634 1.63366336633663 152 13 14.3663366336634 -1.36633663366337 153 16 13.4918032786885 2.50819672131148 154 12 14.3663366336634 -2.36633663366337 155 9 14.3663366336634 -5.36633663366337 156 13 14.3663366336634 -1.36633663366337 157 13 14.3663366336634 -1.36633663366337 158 14 14.3663366336634 -0.366336633663366 159 19 14.3663366336634 4.63366336633663 160 13 14.3663366336634 -1.36633663366337 161 12 14.3663366336634 -2.36633663366337 162 13 14.3663366336634 -1.36633663366337 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.827120803337438 0.345758393325124 0.172879196662562 6 0.842154000555798 0.315691998888404 0.157845999444202 7 0.771109571435118 0.457780857129765 0.228890428564882 8 0.68664573426683 0.626708531466339 0.313354265733169 9 0.577598084895057 0.844803830209886 0.422401915104943 10 0.468031112662852 0.936062225325705 0.531968887337148 11 0.598759691238616 0.802480617522769 0.401240308761384 12 0.732462165953955 0.535075668092091 0.267537834046046 13 0.811623300014233 0.376753399971534 0.188376699985767 14 0.755251378227499 0.489497243545002 0.244748621772501 15 0.763935357878007 0.472129284243986 0.236064642121993 16 0.706486533251013 0.587026933497975 0.293513466748987 17 0.641628974707846 0.716742050584309 0.358371025292154 18 0.599488121936204 0.801023756127592 0.400511878063796 19 0.530188885090307 0.939622229819386 0.469811114909693 20 0.462993367089153 0.925986734178305 0.537006632910847 21 0.627458797481147 0.745082405037707 0.372541202518853 22 0.775260718613719 0.449478562772562 0.224739281386281 23 0.738972182421354 0.522055635157292 0.261027817578646 24 0.774683200642711 0.450633598714577 0.225316799357289 25 0.794099387247822 0.411801225504356 0.205900612752178 26 0.939862651353344 0.120274697293312 0.0601373486466562 27 0.930725375850375 0.138549248299250 0.0692746241496248 28 0.910881281435606 0.178237437128788 0.0891187185643941 29 0.88560742381401 0.228785152371979 0.114392576185990 30 0.906061671148585 0.187876657702829 0.0939383288514147 31 0.888201610885907 0.223596778228185 0.111798389114093 32 0.865348891018073 0.269302217963853 0.134651108981927 33 0.862141903063667 0.275716193872665 0.137858096936333 34 0.830306791645397 0.339386416709205 0.169693208354603 35 0.794228253559332 0.411543492881336 0.205771746440668 36 0.783879341748973 0.432241316502055 0.216120658251027 37 0.889054955575734 0.221890088848531 0.110945044424266 38 0.869626259671274 0.260747480657451 0.130373740328725 39 0.866876245898224 0.266247508203552 0.133123754101776 40 0.840740428280944 0.318519143438112 0.159259571719056 41 0.81710827013777 0.365783459724458 0.182891729862229 42 0.79200573853187 0.41598852293626 0.20799426146813 43 0.78772340460079 0.424553190798421 0.212276595399210 44 0.773581879122761 0.452836241754477 0.226418120877239 45 0.788628672769059 0.422742654461883 0.211371327230941 46 0.836610362982362 0.326779274035276 0.163389637017638 47 0.80559911207586 0.38880177584828 0.19440088792414 48 0.771447094236372 0.457105811527257 0.228552905763628 49 0.772973840002015 0.454052319995969 0.227026159997985 50 0.739263758385519 0.521472483228962 0.260736241614481 51 0.713340913347128 0.573318173305744 0.286659086652872 52 0.672255844147722 0.655488311704557 0.327744155852278 53 0.686988777586059 0.626022444827882 0.313011222413941 54 0.69924879424213 0.601502411515741 0.300751205757870 55 0.677672544191755 0.64465491161649 0.322327455808245 56 0.636209239496294 0.727581521007411 0.363790760503706 57 0.608678781336563 0.782642437326875 0.391321218663437 58 0.565245054098223 0.869509891803554 0.434754945901777 59 0.540560875272915 0.91887824945417 0.459439124727085 60 0.552587886979654 0.894824226040691 0.447412113020346 61 0.748884804267338 0.502230391465325 0.251115195732662 62 0.71215435580507 0.575691288389861 0.287845644194931 63 0.760000232769349 0.479999534461303 0.239999767230651 64 0.724737614509978 0.550524770980045 0.275262385490022 65 0.687630077709121 0.624739844581758 0.312369922290879 66 0.734945453225843 0.530109093548314 0.265054546774157 67 0.777469243735742 0.445061512528516 0.222530756264258 68 0.756340007403303 0.487319985193395 0.243659992596697 69 0.721807276845492 0.556385446309015 0.278192723154508 70 0.700118510381317 0.599762979237367 0.299881489618683 71 0.661751267303426 0.676497465393147 0.338248732696573 72 0.639377748152498 0.721244503695004 0.360622251847502 73 0.59924445403875 0.801511091922499 0.400755545961249 74 0.574048123575166 0.851903752849667 0.425951876424834 75 0.531292808219847 0.937414383560307 0.468707191780153 76 0.535197864078432 0.929604271843137 0.464802135921568 77 0.546856147941563 0.906287704116873 0.453143852058437 78 0.518645013874195 0.96270997225161 0.481354986125805 79 0.492542081237707 0.985084162475414 0.507457918762293 80 0.449671246028819 0.899342492057639 0.55032875397118 81 0.423773513539913 0.847547027079826 0.576226486460087 82 0.431151792315832 0.862303584631665 0.568848207684168 83 0.390677030654657 0.781354061309314 0.609322969345343 84 0.39870880211536 0.79741760423072 0.60129119788464 85 0.359224992598095 0.718449985196191 0.640775007401905 86 0.319327623651605 0.638655247303211 0.680672376348395 87 0.297336437114614 0.594672874229228 0.702663562885386 88 0.260625869795522 0.521251739591044 0.739374130204478 89 0.237336804871619 0.474673609743239 0.76266319512838 90 0.621010018182109 0.757979963635783 0.378989981817891 91 0.634238977211812 0.731522045576376 0.365761022788188 92 0.605403977577235 0.78919204484553 0.394596022422765 93 0.564420542825694 0.871158914348612 0.435579457174306 94 0.520012118311554 0.959975763376891 0.479987881688446 95 0.489548457880548 0.979096915761096 0.510451542119452 96 0.467047735882649 0.934095471765298 0.532952264117351 97 0.467583326844136 0.935166653688271 0.532416673155864 98 0.422975476518414 0.845950953036827 0.577024523481586 99 0.48899574764547 0.97799149529094 0.51100425235453 100 0.468129104417515 0.93625820883503 0.531870895582485 101 0.482931723102586 0.965863446205172 0.517068276897414 102 0.451692224017544 0.903384448035087 0.548307775982456 103 0.429865285686111 0.859730571372222 0.570134714313889 104 0.429878459463466 0.859756918926932 0.570121540536534 105 0.388294651815864 0.776589303631729 0.611705348184136 106 0.507329358067536 0.985341283864927 0.492670641932464 107 0.486185099147082 0.972370198294164 0.513814900852918 108 0.460702464991797 0.921404929983594 0.539297535008203 109 0.517745108272248 0.964509783455505 0.482254891727752 110 0.632274809816886 0.735450380366228 0.367725190183114 111 0.589680330450407 0.820639339099185 0.410319669549593 112 0.639522863641396 0.720954272717208 0.360477136358604 113 0.608558363523585 0.782883272952831 0.391441636476415 114 0.562330709764795 0.87533858047041 0.437669290235205 115 0.635888179699077 0.728223640601846 0.364111820300923 116 0.648118340859484 0.703763318281031 0.351881659140516 117 0.60054571003669 0.79890857992662 0.39945428996331 118 0.551186541776989 0.897626916446022 0.448813458223011 119 0.50076882592805 0.9984623481439 0.49923117407195 120 0.450081312691069 0.900162625382138 0.549918687308931 121 0.450211008497606 0.900422016995211 0.549788991502394 122 0.399971077757246 0.799942155514492 0.600028922242754 123 0.353306754527817 0.706613509055635 0.646693245472183 124 0.308622410194243 0.617244820388486 0.691377589805757 125 0.266498911719991 0.532997823439982 0.733501088280009 126 0.237086532284946 0.474173064569893 0.762913467715054 127 0.30424855701515 0.6084971140303 0.69575144298485 128 0.317957013882352 0.635914027764704 0.682042986117648 129 0.492558004618627 0.985116009237255 0.507441995381373 130 0.444943169559055 0.88988633911811 0.555056830440945 131 0.389114890170909 0.778229780341819 0.610885109829091 132 0.524135446174477 0.951729107651047 0.475864553825523 133 0.475524845733831 0.951049691467661 0.524475154266169 134 0.446309731394092 0.892619462788184 0.553690268605908 135 0.422699614031334 0.845399228062668 0.577300385968666 136 0.409772698796282 0.819545397592563 0.590227301203718 137 0.40192277577738 0.80384555155476 0.59807722422262 138 0.347106282227297 0.694212564454593 0.652893717772703 139 0.381021233098573 0.762042466197146 0.618978766901427 140 0.330490870168415 0.66098174033683 0.669509129831585 141 0.271879669789715 0.543759339579429 0.728120330210285 142 0.228386348649465 0.45677269729893 0.771613651350535 143 0.259100868905332 0.518201737810665 0.740899131094668 144 0.204535503002915 0.409071006005831 0.795464496997085 145 0.209432881693859 0.418865763387719 0.79056711830614 146 0.200610983433491 0.401221966866982 0.799389016566509 147 0.199569362609872 0.399138725219744 0.800430637390128 148 0.162519887274473 0.325039774548946 0.837480112725527 149 0.118848766169374 0.237697532338748 0.881151233830626 150 0.293406323234508 0.586812646469017 0.706593676765492 151 0.313108790312441 0.626217580624882 0.686891209687559 152 0.232779717402770 0.465559434805539 0.76722028259723 153 0.165289204119251 0.330578408238502 0.834710795880749 154 0.119080219176281 0.238160438352561 0.88091978082372 155 0.296651740413946 0.593303480827891 0.703348259586054 156 0.202997089707311 0.405994179414621 0.79700291029269 157 0.125220425926081 0.250440851852161 0.87477957407392 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:

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Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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