Multiple regression: FMPS

*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: Sat, 18 Dec 2010 15:20:43 +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/18/t1292685671hr33jn7fymtk30b.htm/, Retrieved Sat, 18 Dec 2010 16:21:22 +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/18/t1292685671hr33jn7fymtk30b.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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24 14 11 24 26 25 11 7 25 23 17 6 17 30 25 18 12 10 19 23 18 8 12 22 19 16 10 12 22 29 20 10 11 25 25 16 11 11 23 21 18 16 12 17 22 17 11 13 21 25 23 13 14 19 24 30 12 16 19 18 23 8 11 15 22 18 12 10 16 15 15 11 11 23 22 12 4 15 27 28 21 9 9 22 20 15 8 11 14 12 20 8 17 22 24 31 14 17 23 20 27 15 11 23 21 34 16 18 21 20 21 9 14 19 21 31 14 10 18 23 19 11 11 20 28 16 8 15 23 24 20 9 15 25 24 21 9 13 19 24 22 9 16 24 23 17 9 13 22 23 24 10 9 25 29 25 16 18 26 24 26 11 18 29 18 25 8 12 32 25 17 9 17 25 21 32 16 9 29 26 33 11 9 28 22 13 16 12 17 22 32 12 18 28 22 25 12 12 29 23 29 14 18 26 30 22 9 14 25 23 18 10 15 14 17 17 9 16 25 23 20 10 10 26 23 15 12 11 20 25 20 14 14 18 24 33 14 9 32 24 29 10 12 25 23 23 14 17 25 21 26 16 5 23 24 18 9 12 21 24 20 10 12 20 28 11 6 6 15 16 28 8 24 30 20 26 13 12 24 29 22 10 12 26 27 17 8 14 24 22 12 7 7 22 28 14 15 13 14 16 17 9 12 24 25 21 10 13 24 24 19 12 14 24 28 18 13 8 24 24 10 10 11 19 23 29 11 9 31 30 31 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 7.52338981352697 + 0.329234589786872CM[t] -0.360242862076528D[t] + 0.196436099966937PE[t] + 0.399119446996563O[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) 7.52338981352697 2.214293 3.3976 0.000865 0.000433 CM 0.329234589786872 0.055051 5.9805 0 0 D -0.360242862076528 0.105903 -3.4016 0.000853 0.000427 PE 0.196436099966937 0.085046 2.3098 0.02223 0.011115 O 0.399119446996563 0.070569 5.6558 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.605745939016341 R-squared 0.366928142634789 Adjusted R-squared 0.350484717768160 F-TEST (value) 22.3145813971791 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 1.50990331349021e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.39855285935688 Sum Squared Residuals 1778.72487682780 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 22.9195226208873 1.08047737911266 2 25 22.3463830560465 2.65361694395354 3 30 24.2763205417966 5.72367945820337 4 19 20.2708063653626 -1.27080636536265 5 22 20.5081722256164 1.49182777438363 6 22 23.1204117918552 -1.12041179185521 7 25 22.6444362630495 2.35556373695049 8 23 19.3707772538392 3.62922274616076 9 17 18.8235876699938 -1.82358766999384 10 21 21.6893618315462 -0.689361831546238 11 19 22.7416002990848 -3.74160029908479 12 19 23.4046408076239 -4.40464080762391 13 15 23.1552674155735 -8.15526741557349 14 16 17.0778507893901 -1.07785078939014 15 23 19.4406621110489 3.55933788895107 16 27 24.1551194580711 2.84488054192886 17 22 20.9454442799962 1.05455572000378 18 14 16.5301962273129 -2.53019622731288 19 22 24.1444191400076 -2.14441914000762 20 23 24.0080646672178 -1.00806466721779 21 23 21.5513862931887 1.44861370681128 22 21 24.4717188123923 -3.47171881239229 23 19 22.3267442268275 -3.32674422682747 24 18 23.8303703084389 -5.83037030843893 25 20 23.1523171521758 -3.1523171521758 26 23 22.4346085809263 0.56539141907374 27 25 23.3913040779972 1.60869592200278 28 19 23.3276664678502 -4.32766646785022 29 24 23.8470899105413 0.152910089458663 30 22 21.6116086617062 0.388391338293833 31 25 25.1649802102494 -0.164980210249377 32 26 23.1050852922967 2.89491470770331 33 29 22.8408175104868 6.15918248951317 34 32 25.2075310361039 6.79246896389614 35 25 21.5991141675808 3.40088583241921 36 29 24.4400414150955 4.5599585849045 37 28 24.9740125272788 3.02598747272125 38 17 17.1774147210595 -0.177414721059483 39 28 26.0524599751178 1.94754002488222 40 29 22.9683206938046 6.03167930619538 41 26 27.5372260575766 -1.53722605757662 42 25 23.4542177106075 1.54578228939254 43 14 19.578755907371 -5.57875590737100 44 25 22.2009169616070 2.79908303839302 45 26 21.6497612690894 4.35023873091056 46 20 20.2777775899621 -0.277777589962093 47 18 21.3936536676476 -3.39365366764764 48 32 24.6915228350423 7.3084771649577 49 25 25.0057447771052 -0.00574477710516708 50 25 21.7733073959194 3.22669260408062 51 23 20.8806505825134 2.11934941748661 52 21 22.1435265985227 -1.14352659852267 53 20 24.0382307040061 -4.03823070400614 54 15 16.54804088047 -1.54804088047002 55 30 26.5568707700849 3.4431292299151 56 24 25.3320291034943 -1.33202910349435 57 26 24.2975804365833 1.70241956341668 58 24 21.7691681767531 2.23083182324693 59 22 21.5029020721061 0.49709792789394 60 14 15.6686115909104 -1.66861159091044 61 24 22.2134114557324 1.78658854426764 62 24 22.9674236057737 1.03257639422631 63 24 23.3813825900001 0.618617409999919 64 24 19.9168107503488 4.08318924965119 65 19 18.5538514711877 0.446148528812339 66 31 26.8500297441038 4.14997025589623 67 22 26.5873830278616 -4.58738302786159 68 27 21.4718389472868 5.52816105271322 69 19 17.7456910891974 1.25430891080260 70 25 22.284193400973 2.71580659902702 71 20 24.9978764644748 -4.99787646447479 72 21 21.4843334414122 -0.484333441412164 73 27 27.4818888698591 -0.481888869859067 74 23 24.3831470665241 -1.38314706652415 75 25 25.765831063715 -0.765831063715015 76 20 22.2320983443908 -2.23209834439081 77 21 19.2916948861692 1.70830511383083 78 22 22.4433739815876 -0.443373981587572 79 23 22.9947576371289 0.0052423628711022 80 25 24.1135839782121 0.88641602178786 81 25 23.382279678031 1.61772032196899 82 17 23.8260579787784 -6.82605797877844 83 19 21.4486989876275 -2.44869898762751 84 25 23.9479830400407 1.05201695995932 85 19 22.4000991781963 -3.40009917819633 86 20 23.1964890435980 -3.19648904359797 87 26 22.5745514058398 3.42544859416018 88 23 20.7608974538614 2.23910254613858 89 27 24.3426494160364 2.65735058396358 90 17 20.9151599852433 -3.91515998524332 91 17 23.3690612063689 -6.36906120636888 92 19 20.1648769286661 -1.16487692866605 93 17 19.7761439478985 -2.77614394789849 94 22 22.0930526075082 -0.0930526075081821 95 21 23.4736834293323 -2.47368342933229 96 32 28.629497197371 3.37050280262897 97 21 24.6938678781467 -3.69386787814674 98 21 24.3053938966841 -3.30539389668408 99 18 21.2754028473198 -3.27540284731985 100 18 21.3010609605777 -3.30106096057775 101 23 22.8214066442916 0.178593355708382 102 19 20.6789502123254 -1.67895021232541 103 20 20.9840929018925 -0.98409290189246 104 21 22.2948388665069 -1.29483886650688 105 20 23.7876463720903 -3.78764637209027 106 17 18.8584432937121 -1.85844329371212 107 18 20.30476490105 -2.30476490104999 108 19 20.7232952142418 -1.72329521424176 109 22 22.0389043755593 -0.0389043755592504 110 15 18.8157193573635 -3.81571935736346 111 14 18.861999276682 -4.86199927668202 112 18 26.5818597583357 -8.58185975833566 113 24 21.3056871420727 2.69431285792725 114 35 23.5534349220095 11.4465650779905 115 29 19.0762800298061 9.9237199701939 116 21 22.0417363809924 -1.04173638099239 117 25 20.5444758044082 4.45552419559183 118 20 18.5089007496991 1.49109925030089 119 22 23.2362627165489 -1.23626271654894 120 13 16.9054517371134 -3.90545173711341 121 26 23.2642019681974 2.73579803180261 122 17 16.9131469392496 0.086853060750385 123 25 20.0565256122386 4.94347438776143 124 20 20.7365685384335 -0.736568538433521 125 19 18.1234647525965 0.876535247403452 126 21 22.6645711067815 -1.66457110678147 127 22 21.1231934913047 0.876806508695295 128 24 22.6833128479695 1.31668715203046 129 21 22.9743948303731 -1.97439483037314 130 26 25.4835144819727 0.516485518027266 131 24 20.5416986515047 3.45830134849535 132 16 20.2876990779592 -4.28769907795923 133 23 22.416094802762 0.583905197238016 134 18 20.8568725341281 -2.85687253412808 135 16 22.3718680588102 -6.37186805881019 136 26 24.1096817742539 1.89031822574610 137 19 19.1060773622303 -0.106077362230300 138 21 16.8689201952978 4.13107980470218 139 21 22.1745348708123 -1.17453487081232 140 22 18.4274184863950 3.57258151360503 141 23 19.7126245957160 3.28737540428395 142 29 24.8046824956432 4.19531750435677 143 21 19.0872807685126 1.91271923148739 144 21 19.9875926955894 1.01240730441057 145 23 21.8742005254187 1.12579947458127 146 27 23.0469709516756 3.95302904832437 147 25 25.4101595306039 -0.410159530603869 148 21 21.0090818901432 -0.00908189014322001 149 10 17.0947435019867 -7.09474350198672 150 20 22.6171022316943 -2.6171022316943 151 26 22.5278065082894 3.4721934917106 152 24 23.6999168617234 0.300083138276562 153 29 31.7712548047923 -2.77125480479230 154 19 19.0639037936453 -0.0639037936452667 155 24 22.0565210656926 1.94347893430741 156 19 20.8133697677130 -1.81336976771304 157 24 23.4382220860418 0.56177791395819 158 22 21.8105629152717 0.189437084728275 159 17 23.6804511429986 -6.68045114299861 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.313908091714112 0.627816183428223 0.686091908285888 9 0.184161427812675 0.368322855625350 0.815838572187325 10 0.113055352943660 0.226110705887320 0.88694464705634 11 0.228358723830182 0.456717447660365 0.771641276169818 12 0.209735537529444 0.419471075058889 0.790264462470556 13 0.81275056304401 0.374498873911982 0.187249436955991 14 0.74190122158433 0.516197556831339 0.258098778415670 15 0.693429293364596 0.613141413270807 0.306570706635404 16 0.62476569885514 0.750468602289719 0.375234301144860 17 0.544875030289121 0.910249939421758 0.455124969710879 18 0.519120707484585 0.96175858503083 0.480879292515415 19 0.454185870152810 0.908371740305619 0.54581412984719 20 0.451890113889269 0.903780227778537 0.548109886110731 21 0.438511594078955 0.87702318815791 0.561488405921045 22 0.37533295715466 0.75066591430932 0.62466704284534 23 0.352144474222603 0.704288948445205 0.647855525777397 24 0.384517196995652 0.769034393991304 0.615482803004348 25 0.400964584236053 0.801929168472106 0.599035415763947 26 0.336307554187925 0.672615108375850 0.663692445812075 27 0.294853399922711 0.589706799845423 0.705146600077289 28 0.315916371387688 0.631832742775376 0.684083628612312 29 0.264856394702076 0.529712789404151 0.735143605297924 30 0.214634392561454 0.429268785122908 0.785365607438546 31 0.173124834581063 0.346249669162126 0.826875165418937 32 0.179223094879201 0.358446189758401 0.8207769051208 33 0.361651415217500 0.723302830434999 0.6383485847825 34 0.59728455328745 0.8054308934251 0.40271544671255 35 0.571475634319893 0.857048731360213 0.428524365680107 36 0.675196021333216 0.649607957333567 0.324803978666784 37 0.679234296222423 0.641531407555154 0.320765703777577 38 0.627616884363965 0.744766231272069 0.372383115636035 39 0.588863865476317 0.822272269047366 0.411136134523683 40 0.68532488483786 0.629350230324279 0.314675115162139 41 0.655914904165825 0.68817019166835 0.344085095834175 42 0.611267501492562 0.777464997014877 0.388732498507438 43 0.680532468743455 0.63893506251309 0.319467531256545 44 0.65832080898886 0.683358382022279 0.341679191011140 45 0.675512812030156 0.648974375939688 0.324487187969844 46 0.62900258110614 0.74199483778772 0.37099741889386 47 0.624138230638205 0.75172353872359 0.375861769361795 48 0.754353108638781 0.491293782722438 0.245646891361219 49 0.717021540602141 0.565956918795718 0.282978459397859 50 0.719902362680314 0.560195274639371 0.280097637319686 51 0.688933476314936 0.622133047370129 0.311066523685064 52 0.653625703909832 0.692748592180335 0.346374296090168 53 0.689469892175614 0.621060215648773 0.310530107824386 54 0.65294711015571 0.694105779688579 0.347052889844290 55 0.645234269684252 0.709531460631496 0.354765730315748 56 0.613021738006507 0.773956523986986 0.386978261993493 57 0.574416392160035 0.85116721567993 0.425583607839965 58 0.544291477785167 0.911417044429666 0.455708522214833 59 0.497213344533111 0.994426689066222 0.502786655466889 60 0.457758574709084 0.915517149418168 0.542241425290916 61 0.421560516161258 0.843121032322515 0.578439483838742 62 0.37875670660946 0.75751341321892 0.62124329339054 63 0.335740404334552 0.671480808669104 0.664259595665448 64 0.356503041758516 0.713006083517033 0.643496958241484 65 0.314203826821476 0.628407653642952 0.685796173178524 66 0.328798541588361 0.657597083176721 0.67120145841164 67 0.386766831145141 0.773533662290282 0.613233168854859 68 0.460372895375259 0.920745790750519 0.539627104624741 69 0.420219324718961 0.840438649437921 0.57978067528104 70 0.403698209936378 0.807396419872756 0.596301790063622 71 0.461526333698883 0.923052667397766 0.538473666301117 72 0.417422107553176 0.834844215106352 0.582577892446824 73 0.37638820216516 0.75277640433032 0.62361179783484 74 0.340676462671655 0.68135292534331 0.659323537328345 75 0.302708572746511 0.605417145493022 0.69729142725349 76 0.279100202788534 0.558200405577068 0.720899797211466 77 0.251680858250261 0.503361716500521 0.748319141749739 78 0.217539790976247 0.435079581952495 0.782460209023753 79 0.188646320569137 0.377292641138275 0.811353679430863 80 0.161109146881336 0.322218293762673 0.838890853118664 81 0.142432352034499 0.284864704068999 0.8575676479655 82 0.232412287423974 0.464824574847949 0.767587712576026 83 0.214487351911849 0.428974703823699 0.78551264808815 84 0.186502118395167 0.373004236790333 0.813497881604833 85 0.185563848053983 0.371127696107966 0.814436151946017 86 0.179814665337771 0.359629330675543 0.820185334662229 87 0.182409793807212 0.364819587614425 0.817590206192788 88 0.172639636431485 0.345279272862971 0.827360363568515 89 0.162585478391337 0.325170956782673 0.837414521608663 90 0.167948517213653 0.335897034427306 0.832051482786347 91 0.241334617742729 0.482669235485457 0.758665382257271 92 0.20893943701761 0.41787887403522 0.79106056298239 93 0.193705913068455 0.387411826136909 0.806294086931545 94 0.162983760088996 0.325967520177992 0.837016239911004 95 0.146929950032658 0.293859900065317 0.853070049967342 96 0.151256538778794 0.302513077557588 0.848743461221206 97 0.152081860366667 0.304163720733334 0.847918139633333 98 0.147047161493748 0.294094322987496 0.852952838506252 99 0.141381205888916 0.282762411777833 0.858618794111084 100 0.137412310693485 0.27482462138697 0.862587689306515 101 0.112949386229247 0.225898772458493 0.887050613770753 102 0.095119274613827 0.190238549227654 0.904880725386173 103 0.0775192624770602 0.155038524954120 0.92248073752294 104 0.062875943915877 0.125751887831754 0.937124056084123 105 0.0637898211862556 0.127579642372511 0.936210178813744 106 0.0551237573644963 0.110247514728993 0.944876242635504 107 0.0490025614394577 0.0980051228789154 0.950997438560542 108 0.0421038220666769 0.0842076441333539 0.957896177933323 109 0.0321670700054552 0.0643341400109104 0.967832929994545 110 0.0334237492536641 0.0668474985073282 0.966576250746336 111 0.043875132073119 0.087750264146238 0.956124867926881 112 0.144453178232742 0.288906356465483 0.855546821767258 113 0.129192154690002 0.258384309380004 0.870807845309998 114 0.538394111787916 0.923211776424167 0.461605888212084 115 0.888138364029625 0.223723271940750 0.111861635970375 116 0.86092682812201 0.278146343755980 0.139073171877990 117 0.90239189134391 0.195216217312181 0.0976081086560904 118 0.881391745659575 0.23721650868085 0.118608254340425 119 0.858284891281352 0.283430217437295 0.141715108718648 120 0.894615113812526 0.210769772374948 0.105384886187474 121 0.87655186336812 0.246896273263759 0.123448136631879 122 0.844490577281067 0.311018845437867 0.155509422718933 123 0.871604045375132 0.256791909249736 0.128395954624868 124 0.837921861731835 0.324156276536329 0.162078138268165 125 0.80599531994001 0.388009360119982 0.194004680059991 126 0.765495653261683 0.469008693476634 0.234504346738317 127 0.734103367401864 0.531793265196272 0.265896632598136 128 0.698287304790342 0.603425390419316 0.301712695209658 129 0.645833838520459 0.708332322959083 0.354166161479541 130 0.586880510831911 0.826238978336178 0.413119489168089 131 0.586817344832592 0.826365310334816 0.413182655167408 132 0.589229045267082 0.821541909465835 0.410770954732918 133 0.541871641549675 0.91625671690065 0.458128358450325 134 0.495158390907884 0.990316781815767 0.504841609092116 135 0.649441511758549 0.701116976482903 0.350558488241451 136 0.612907870488338 0.774184259023325 0.387092129511662 137 0.545655076054474 0.908689847891052 0.454344923945526 138 0.549902165955774 0.900195668088451 0.450097834044226 139 0.475549976571105 0.95109995314221 0.524450023428895 140 0.454475219699718 0.908950439399436 0.545524780300282 141 0.424878335520443 0.849756671040887 0.575121664479556 142 0.491065817282313 0.982131634564626 0.508934182717687 143 0.616683573847295 0.766632852305411 0.383316426152705 144 0.542083881601001 0.915832236797998 0.457916118398999 145 0.466931403195775 0.93386280639155 0.533068596804225 146 0.492273938949524 0.984547877899049 0.507726061050476 147 0.438778444456133 0.877556888912266 0.561221555543867 148 0.327473281349775 0.65494656269955 0.672526718650225 149 0.561540225645244 0.876919548709513 0.438459774354756 150 0.539603645709571 0.920792708580858 0.460396354290429 151 0.400811779071350 0.801623558142699 0.59918822092865 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 0.0347222222222222 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/10iqg51292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/10iqg51292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/1mgjw1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/1mgjw1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/2mgjw1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/2mgjw1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/3mgjw1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/3mgjw1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/4mgjw1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/4mgjw1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/5mgjw1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/5mgjw1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/6x7ih1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/6x7ih1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/7pyhk1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/7pyhk1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/8pyhk1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/8pyhk1292685631.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/9pyhk1292685631.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292685671hr33jn7fymtk30b/9pyhk1292685631.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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