PAPER BAEYENS (Multiple Linear Regression)

*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: Tue, 21 Dec 2010 11:33:46 +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/21/t1292931571x5p5u80vxoiv8vf.htm/, Retrieved Tue, 21 Dec 2010 12:39:44 +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/21/t1292931571x5p5u80vxoiv8vf.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 14 5 12 18 3 15 11 0 12 12 7 10 16 4 12 18 1 15 14 6 9 14 3 12 15 12 11 15 0 11 17 5 11 19 6 15 10 6 7 16 6 11 18 2 11 14 1 10 14 5 14 17 7 10 14 3 6 16 3 11 18 3 15 11 7 11 14 8 12 12 6 14 17 3 15 9 5 9 16 5 13 14 10 13 15 2 16 11 6 13 16 4 12 13 6 14 17 8 11 15 4 9 14 5 16 16 10 12 9 6 10 15 7 13 17 4 16 13 10 14 15 4 15 16 3 5 16 3 8 12 3 11 12 3 16 11 7 17 15 15 9 15 0 9 17 0 13 13 4 10 16 5 6 14 5 12 11 2 8 12 3 14 12 0 12 15 9 11 16 2 16 15 7 8 12 7 15 12 0 7 8 0 16 13 10 14 11 2 16 14 1 9 15 8 14 10 6 11 11 11 13 12 3 15 15 8 5 15 6 15 14 9 13 16 9 11 15 8 11 15 8 12 13 7 12 12 6 12 17 5 12 13 4 14 15 6 6 13 3 7 15 2 14 16 12 14 15 8 10 16 5 13 15 9 12 14 6 9 15 5 12 14 2 16 13 4 10 7 7 14 17 5 10 13 6 16 15 7 15 14 8 12 13 6 10 16 0 8 12 1 8 14 5 11 17 5 13 15 5 16 17 7 16 12 7 14 16 1 11 11 3 4 15 4 14 9 8 9 16 6 14 15 6 8 10 2 8 10 2 11 15 3 12 11 3 11 13 0 14 14 2 15 18 8 16 16 8 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 21 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation HS[t] = + 15.0179951973243 -0.0858344714341663IEP[t] + 0.0108385179567776WP[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) 15.0179951973243 0.79794 18.821 0 0 IEP -0.0858344714341663 0.066922 -1.2826 0.201569 0.100784 WP 0.0108385179567776 0.063132 0.1717 0.863916 0.431958 Multiple Linear Regression - Regression Statistics Multiple R 0.104501600715015 R-squared 0.0109205845520004 Adjusted R-squared -0.00200855813359424 F-TEST (value) 0.844648776609741 F-TEST (DF numerator) 2 F-TEST (DF denominator) 153 p-value 0.431701946955386 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.34103922960213 Sum Squared Residuals 838.511095204031 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 13.9563396584643 0.0436603415356564 2 18 14.0204970939847 3.97950290601531 3 11 13.7304781258118 -2.73047812581185 4 12 14.0638511658118 -2.06385116581179 5 16 14.2030045548098 1.79699544519021 6 18 13.9988200580711 4.00117994192887 7 14 13.7955092335525 0.204490766447482 8 14 14.2780005082872 -0.278000508287183 9 15 14.1180437555957 0.881956244404317 10 15 14.0738160115485 0.926183988451483 11 17 14.1280086013324 2.87199139866759 12 19 14.1388471192892 4.86115288071082 13 10 13.7955092335525 -3.79550923355252 14 16 14.4821850050258 1.51781499497415 15 18 14.0954930474621 3.90450695253793 16 14 14.0846545295053 -0.084654529505295 17 14 14.2138430727666 -0.213843072766572 18 17 13.8921822229435 3.10781777705654 19 14 14.1921660368530 -0.192166036853017 20 16 14.5355039225897 1.46449607741032 21 18 14.1063315654189 3.89366843458115 22 11 13.8063477515093 -2.80634775150930 23 14 14.1605241552027 -0.160524155202739 24 12 14.0530126478550 -2.05301264785502 25 17 13.8488281511164 3.15117184888365 26 9 13.7846707155957 -4.78467071559574 27 16 14.2996775442007 1.70032245579926 28 14 14.0105322482480 -0.0105322482479615 29 15 13.9238241045937 1.07617589540626 30 11 13.7096747621184 -2.70967476211835 31 16 13.9455011405073 2.05449885949271 32 13 14.0530126478550 -1.05301264785502 33 17 13.9030207409002 3.09697925909976 34 15 14.1171700833756 0.882829916624372 35 14 14.2996775442007 -0.299677544200738 36 16 13.7530288339455 2.24697116605454 37 9 14.0530126478550 -5.05301264785502 38 15 14.2355201086801 0.764479891319872 39 17 13.9455011405073 3.05449885949271 40 13 13.7530288339455 -0.753028833945462 41 15 13.8596666690731 1.14033333092687 42 16 13.7629936796822 2.23700632031782 43 16 14.6213383940238 1.37866160597615 44 12 14.3638349797214 -2.36383497972135 45 12 14.1063315654189 -2.10633156541885 46 11 13.7205132800751 -2.72051328007513 47 15 13.7213869522952 1.27861304770482 48 15 14.2454849544169 0.75451504558315 49 17 14.2454849544168 2.75451504558315 50 13 13.9455011405073 -0.945501140507295 51 16 14.2138430727666 1.78615692723343 52 14 14.5571809585032 -0.557180958503238 53 11 14.0096585760279 -3.00965857602791 54 12 14.3638349797214 -2.36383497972135 55 12 13.8163125972460 -1.81631259724602 56 15 14.0855282017253 0.91447179827465 57 16 14.0954930474621 1.90450695253793 58 15 13.7205132800751 1.27948671992487 59 12 14.4071890515485 -2.40718905154846 60 12 13.7304781258119 -1.73047812581185 61 8 14.4171538972852 -6.41715389728518 62 13 13.7530288339455 -0.753028833945462 63 11 13.8379896331596 -2.83798963315957 64 14 13.6554821723345 0.344517827665537 65 15 14.3321930980711 0.667806901928929 66 10 13.8813437049867 -3.88134370498668 67 11 14.1930397090731 -3.19303970907307 68 12 13.9346626225505 -1.93466262255052 69 15 13.8171862694661 1.18281373053393 70 15 14.6538539478942 0.346146052105818 71 14 13.8280247874229 0.171975212577149 72 16 13.9996937302912 2.00030626970882 73 15 14.1605241552027 0.839475844797261 74 15 14.1605241552027 0.839475844797261 75 13 14.0638511658118 -1.06385116581179 76 12 14.0530126478550 -2.05301264785502 77 17 14.0421741298982 2.95782587010176 78 13 14.0313356119415 -1.03133561194146 79 15 13.8813437049867 1.11865629501332 80 13 14.5355039225897 -1.53550392258968 81 15 14.4388309331987 0.561169066801262 82 16 13.9463748127274 2.05362518727265 83 15 13.9030207409002 1.09697925909976 84 16 14.2138430727666 1.78615692723343 85 15 13.9996937302912 1.00030626970882 86 14 14.0530126478550 -0.0530126478550171 87 15 14.2996775442007 0.700322455799262 88 14 14.0096585760279 -0.00965857602790628 89 13 13.6879977262048 -0.687997726204796 90 7 14.2355201086801 -7.23552010868013 91 17 13.8705051870299 3.12949481297009 92 13 14.2246815907233 -1.22468159072335 93 15 13.7205132800751 1.27948671992487 94 14 13.8171862694661 0.182813730533927 95 13 14.0530126478550 -1.05301264785502 96 16 14.1596504829827 1.84034951701732 97 12 14.3421579438078 -2.34215794380779 98 14 14.3855120156349 -0.385512015634905 99 17 14.1280086013324 2.87199139866759 100 15 13.9563396584641 1.04366034153593 101 17 13.7205132800751 3.27948671992487 102 12 13.7205132800751 -1.72051328007513 103 16 13.8271511152028 2.17284888479720 104 11 14.1063315654189 -3.10633156541885 105 15 14.7180113834148 0.281988616585207 106 9 13.9030207409002 -4.90302074090024 107 16 14.3105160621575 1.68948393784248 108 15 13.8813437049867 1.11865629501332 109 10 14.3529964617646 -4.35299646176457 110 10 14.3529964617646 -4.35299646176457 111 15 14.1063315654189 0.89366843458115 112 11 14.0204970939847 -3.02049709398468 113 13 14.0738160115485 -1.07381601154852 114 14 13.8379896331596 0.162010366840426 115 18 13.8171862694661 4.18281373053393 116 16 13.7313517980319 2.26864820196809 117 14 13.6446436543777 0.355356345622314 118 14 14.1280086013324 -0.128008601332406 119 14 13.9138592588570 0.0861407411429825 120 14 13.8813437049867 0.118656295013316 121 12 14.0530126478550 -2.05301264785502 122 14 13.8488281511164 0.151171848883649 123 15 14.428866087462 0.571133912537984 124 15 13.9780166943776 1.02198330562237 125 15 13.7313517980319 1.26864820196809 126 13 13.9879815401144 -0.98798154011435 127 17 13.7205132800751 3.27948671992487 128 17 13.9879815401144 3.01201845988565 129 19 14.1280086013324 4.87199139866759 130 15 14.6746573115877 0.325342688412318 131 13 13.7963829057726 -0.796382905772573 132 9 13.7846707155957 -4.78467071559574 133 15 14.1813275188962 0.818672481103761 134 15 13.9888552123344 1.01114478766559 135 15 13.7738321976390 1.22616780236104 136 16 14.0096585760279 1.99034142397209 137 11 13.8813437049867 -2.88134370498668 138 14 14.4496694511555 -0.449669451155516 139 11 13.4413328298591 -2.44133282985907 140 15 14.0855282017253 0.91447179827465 141 13 14.0204970939847 -1.02049709398468 142 15 13.9346626225505 1.06533737744948 143 16 13.7304781258119 2.26952187418815 144 14 14.4397046054188 -0.439704605418793 145 15 14.0313356119415 0.968664388058538 146 16 14.1813275188962 1.81867248110376 147 16 14.3638349797214 1.63616502027865 148 11 14.2680356625505 -3.26803566255046 149 12 13.8063477515093 -1.80634775150930 150 9 13.6446436543777 -4.64464365437769 151 16 13.9671781764209 2.03282182357915 152 13 13.7313517980319 -0.731351798031907 153 16 14.2454849544168 1.75451504558315 154 12 13.8596666690731 -1.85966666907313 155 9 13.9246977768138 -4.92469777681380 156 13 14.0421741298982 -1.04217412989824 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.637551056969338 0.724897886061324 0.362448943030662 7 0.720617812831196 0.558764374337608 0.279382187168804 8 0.763183089335232 0.473633821329535 0.236816910664767 9 0.682644568335627 0.634710863328746 0.317355431664373 10 0.577183414591579 0.845633170816843 0.422816585408421 11 0.53062958619693 0.93874082760614 0.46937041380307 12 0.644995162109308 0.710009675781385 0.355004837890692 13 0.689751426538875 0.620497146922251 0.310248573461125 14 0.678423667664331 0.643152664671338 0.321576332335669 15 0.684830830731022 0.630338338537957 0.315169169268978 16 0.646409448449967 0.707181103100065 0.353590551550033 17 0.6161224813945 0.767755037210999 0.383877518605499 18 0.676774103764049 0.646451792471902 0.323225896235951 19 0.643206668556978 0.713586662886044 0.356793331443022 20 0.593743583984733 0.812512832030534 0.406256416015267 21 0.630187152724656 0.739625694550688 0.369812847275344 22 0.646511400341089 0.706977199317822 0.353488599658911 23 0.591852064598802 0.816295870802395 0.408147935401198 24 0.601339140581727 0.797321718836546 0.398660859418273 25 0.63906302267517 0.72187395464966 0.36093697732483 26 0.77308888796043 0.453822224079139 0.226911112039569 27 0.729752564523102 0.540494870953796 0.270247435476898 28 0.677886185106977 0.644227629786047 0.322113814893023 29 0.62686297053188 0.74627405893624 0.37313702946812 30 0.603066938021515 0.79386612395697 0.396933061978485 31 0.583960930317577 0.832078139364846 0.416039069682423 32 0.545497667363443 0.909004665273114 0.454502332636557 33 0.623573875586237 0.752852248827526 0.376426124413763 34 0.571089195725676 0.857821608548648 0.428910804274324 35 0.54679338764463 0.906413224710741 0.453206612355371 36 0.586612747080974 0.826774505838053 0.413387252919026 37 0.790876666685112 0.418246666629776 0.209123333314888 38 0.751864855295353 0.496270289409295 0.248135144704648 39 0.770325440021571 0.459349119956857 0.229674559978429 40 0.729449330929487 0.541101338141026 0.270550669070513 41 0.693262316717197 0.613475366565606 0.306737683282803 42 0.68696037991598 0.626079240168039 0.313039620084020 43 0.654557867040719 0.690884265918562 0.345442132959281 44 0.704389143923399 0.591221712153202 0.295610856076601 45 0.71559899595781 0.568802008084381 0.284401004042190 46 0.720991408507736 0.558017182984528 0.279008591492264 47 0.706389975037518 0.587220049924964 0.293610024962482 48 0.666026646785828 0.667946706428344 0.333973353214172 49 0.664083980918152 0.671832038163695 0.335916019081848 50 0.628851678645324 0.742296642709353 0.371148321354676 51 0.600159768078885 0.79968046384223 0.399840231921115 52 0.574637254980505 0.85072549003899 0.425362745019495 53 0.620346281530829 0.759307436938343 0.379653718469171 54 0.643246948108792 0.713506103782416 0.356753051891208 55 0.624863440895589 0.750273118208823 0.375136559104411 56 0.583408414272063 0.833183171455875 0.416591585727937 57 0.563123727041314 0.873752545917372 0.436876272958686 58 0.531919219138087 0.936161561723826 0.468080780861913 59 0.551045658979276 0.897908682041448 0.448954341020724 60 0.528873195501561 0.942253608996879 0.471126804498439 61 0.809388475057755 0.381223049884489 0.190611524942245 62 0.77961016127656 0.440779677446879 0.220389838723440 63 0.792268303161123 0.415463393677754 0.207731696838877 64 0.758837196633692 0.482325606732616 0.241162803366308 65 0.72383426884173 0.55233146231654 0.27616573115827 66 0.785176160404594 0.429647679190813 0.214823839595406 67 0.813898015360898 0.372203969278204 0.186101984639102 68 0.802715331089464 0.394569337821072 0.197284668910536 69 0.778081956905337 0.443836086189326 0.221918043094663 70 0.743750844072478 0.512498311855043 0.256249155927522 71 0.705208729720822 0.589582540558355 0.294791270279178 72 0.693641877123563 0.612716245752875 0.306358122876437 73 0.657311473999847 0.685377052000307 0.342688526000153 74 0.61966377802614 0.760672443947721 0.380336221973861 75 0.583881136125261 0.832237727749478 0.416118863874739 76 0.572309387928658 0.855381224142685 0.427690612071342 77 0.598246048947302 0.803507902105396 0.401753951052698 78 0.561340652990534 0.877318694018931 0.438659347009466 79 0.525927397941247 0.948145204117506 0.474072602058753 80 0.499677925886341 0.999355851772682 0.500322074113659 81 0.456587701381454 0.913175402762907 0.543412298618546 82 0.447100448470919 0.894200896941838 0.552899551529081 83 0.41215164477292 0.82430328954584 0.58784835522708 84 0.394495200787876 0.788990401575753 0.605504799212124 85 0.360243120021496 0.720486240042991 0.639756879978504 86 0.317923229367163 0.635846458734326 0.682076770632837 87 0.282535102090438 0.565070204180876 0.717464897909562 88 0.244452773547738 0.488905547095476 0.755547226452262 89 0.2123774526913 0.4247549053826 0.7876225473087 90 0.559662350568005 0.88067529886399 0.440337649431995 91 0.595036803259768 0.809926393480464 0.404963196740232 92 0.559924691784747 0.880150616430507 0.440075308215253 93 0.527524991407672 0.944950017184656 0.472475008592328 94 0.480921424657558 0.961842849315116 0.519078575342442 95 0.442046698583682 0.884093397167364 0.557953301416318 96 0.423061386268074 0.846122772536149 0.576938613731926 97 0.421237492954222 0.842474985908444 0.578762507045778 98 0.375934096633020 0.751868193266041 0.624065903366980 99 0.399310271258378 0.798620542516757 0.600689728741622 100 0.363222970244405 0.72644594048881 0.636777029755595 101 0.411972887183636 0.823945774367271 0.588027112816364 102 0.386008688033116 0.772017376066232 0.613991311966884 103 0.379303996590173 0.758607993180346 0.620696003409827 104 0.409804896681414 0.819609793362829 0.590195103318586 105 0.363163741690477 0.726327483380954 0.636836258309523 106 0.51189867051671 0.97620265896658 0.48810132948329 107 0.489427258365971 0.978854516731943 0.510572741634029 108 0.452101094379446 0.904202188758891 0.547898905620554 109 0.574627830695144 0.850744338609713 0.425372169304856 110 0.712645062781417 0.574709874437166 0.287354937218583 111 0.6713500473926 0.657299905214799 0.328649952607399 112 0.710917611852416 0.578164776295168 0.289082388147584 113 0.684288175498208 0.631423649003584 0.315711824501792 114 0.635615086387275 0.72876982722545 0.364384913612725 115 0.764265798922241 0.471468402155518 0.235734201077759 116 0.787394205605657 0.425211588788686 0.212605794394343 117 0.746200228024773 0.507599543950454 0.253799771975227 118 0.700377182349814 0.599245635300372 0.299622817650186 119 0.655189171966836 0.689621656066327 0.344810828033164 120 0.604130319248102 0.791739361503795 0.395869680751898 121 0.589999227511724 0.820001544976552 0.410000772488276 122 0.533664065888501 0.932671868222998 0.466335934111499 123 0.477530357562256 0.955060715124511 0.522469642437744 124 0.437307543697191 0.874615087394382 0.562692456302809 125 0.427291242301688 0.854582484603377 0.572708757698312 126 0.393923606110952 0.787847212221904 0.606076393889048 127 0.533684480144685 0.932631039710631 0.466315519855315 128 0.548741502993851 0.902516994012298 0.451258497006149 129 0.769180884162331 0.461638231675337 0.230819115837669 130 0.75237030736816 0.495259385263679 0.247629692631840 131 0.75990745082608 0.48018509834784 0.24009254917392 132 0.854619618995018 0.290760762009963 0.145380381004982 133 0.811084046693603 0.377831906612795 0.188915953306397 134 0.81513656089773 0.369726878204539 0.184863439102269 135 0.81313132356621 0.373737352867578 0.186868676433789 136 0.794914580125507 0.410170839748986 0.205085419874493 137 0.774391734837517 0.451216530324966 0.225608265162483 138 0.763260143994852 0.473479712010296 0.236739856005148 139 0.704247915735937 0.591504168528126 0.295752084264063 140 0.716275789935131 0.567448420129738 0.283724210064869 141 0.660293755927273 0.679412488145455 0.339706244072727 142 0.600642543730638 0.798714912538723 0.399357456269362 143 0.640154087707467 0.719691824585067 0.359845912292534 144 0.547333319322612 0.905333361354775 0.452666680677388 145 0.485396860912044 0.970793721824089 0.514603139087956 146 0.408304402302718 0.816608804605436 0.591695597697282 147 0.310227649141305 0.62045529828261 0.689772350858695 148 0.383583493888627 0.767166987777254 0.616416506111373 149 0.266190863963274 0.532381727926547 0.733809136036726 150 0.347370537818238 0.694741075636476 0.652629462181762 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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