workshop 7 month-effect

*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, 19 Nov 2010 13:22:14 +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/19/t1290172888vetvfnevkvj9n0j.htm/, Retrieved Fri, 19 Nov 2010 14:21:28 +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/19/t1290172888vetvfnevkvj9n0j.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 «

9 26 24 14 11 12 24 9 23 25 11 7 8 25 9 25 17 6 17 8 30 9 23 18 12 10 8 19 9 19 18 8 12 9 22 9 29 16 10 12 7 22 10 25 20 10 11 4 25 10 21 16 11 11 11 23 10 22 18 16 12 7 17 10 25 17 11 13 7 21 10 24 23 13 14 12 19 10 18 30 12 16 10 19 10 22 23 8 11 10 15 10 15 18 12 10 8 16 10 22 15 11 11 8 23 10 28 12 4 15 4 27 10 20 21 9 9 9 22 10 12 15 8 11 8 14 10 24 20 8 17 7 22 10 20 31 14 17 11 23 10 21 27 15 11 9 23 10 20 34 16 18 11 21 10 21 21 9 14 13 19 10 23 31 14 10 8 18 10 28 19 11 11 8 20 10 24 16 8 15 9 23 10 24 20 9 15 6 25 10 24 21 9 13 9 19 10 23 22 9 16 9 24 10 23 17 9 13 6 22 10 29 24 10 9 6 25 10 24 25 16 18 16 26 10 18 26 11 18 5 29 10 25 25 8 12 7 32 10 21 17 9 17 9 25 10 26 32 16 9 6 29 10 22 33 11 9 6 28 10 22 13 16 12 5 17 10 22 32 12 18 12 28 10 23 25 12 12 7 29 10 30 29 14 18 10 26 10 23 22 9 14 9 25 10 17 18 10 15 8 14 10 23 17 9 16 5 25 10 23 20 10 10 8 26 10 25 15 12 11 8 20 10 24 20 14 14 10 18 10 24 33 14 9 6 32 10 23 29 10 12 8 25 10 21 23 14 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 35 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation D[t] = + 4.09848461408953 + 0.322678071995212M[t] + 0.113329495895667O[t] + 0.246895780354797CM[t] -0.109244278297376PE[t] + 0.151547174570634PC[t] -0.189756878633375PS[t] + 0.000994111036614365t + 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) 4.09848461408953 11.14169 0.3679 0.713499 0.35675 M 0.322678071995212 1.115152 0.2894 0.772704 0.386352 O 0.113329495895667 0.058093 1.9508 0.052929 0.026464 CM 0.246895780354797 0.040538 6.0905 0 0 PE -0.109244278297376 0.074902 -1.4585 0.146781 0.073391 PC 0.151547174570634 0.094178 1.6091 0.109673 0.054836 PS -0.189756878633375 0.057396 -3.3061 0.001182 0.000591 t 0.000994111036614365 0.004693 0.2118 0.832533 0.416267 Multiple Linear Regression - Regression Statistics Multiple R 0.490382703106539 R-squared 0.240475195506076 Adjusted R-squared 0.205265436357351 F-TEST (value) 6.82978814170003 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 4.7523723134546e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.49660665392697 Sum Squared Residuals 941.189762449295 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 11.938360941261 2.06163905873900 2 11 11.4872938812390 -0.487293881238988 3 6 7.69855356508792 -1.69855356508792 4 12 10.5718200777368 1.42817992226324 5 8 9.48328418726646 -1.48328418726646 6 10 9.82068734740888 0.179312652591118 7 10 9.76395678696258 0.236043213037422 8 11 9.76439377225853 1.23560622774147 9 16 10.7956172351207 5.20438276487926 10 11 10.0214322606587 0.97856773934132 11 13 12.4184769097510 0.581523090249047 12 12 12.9461816021611 -0.946181602161122 13 8 12.9774721403172 -4.97747214031721 14 12 10.5670739288329 1.43292607116709 15 11 9.1831447413438 1.81685525865620 16 4 7.32123516068448 -3.32123516068448 17 9 10.9996412635532 -1.99964126355323 18 8 9.76064402319735 -1.76064402319735 19 8 10.0310031133341 -2.03100311333405 20 14 12.7109646443399 1.28903535566008 21 15 12.190076450496 2.80992354950399 22 16 13.7239096864469 2.27609031355308 23 9 11.7481733683644 -2.74817336836436 24 14 14.31378239371 -0.31378239370999 25 11 11.4299165844033 -0.429916584403251 26 8 9.38220479627381 -1.38220479627381 27 9 9.53662674775096 -0.536626747750961 28 9 11.5961879912493 -2.59618799124928 29 9 10.4542311586860 -1.45423115868602 30 9 9.47335143639562 -0.473351436395625 31 10 11.7502994625792 -1.75029946257920 32 16 11.7740582368889 4.22594176311115 33 11 9.10568159672916 1.89431840327084 34 8 10.0423757817061 -2.04237578170605 35 9 8.70005677440964 0.299943225590365 36 16 12.6314202583801 3.36857974161986 37 11 12.6157490448223 -1.61574904482226 38 16 9.2868732042673 6.7131267957327 39 12 12.2969260292881 -0.296926029288111 40 12 10.3909520920345 1.60904790796547 41 14 12.5412822855878 1.45871771441223 42 9 10.4958862801234 -1.49588628012338 43 10 10.6558545064659 -0.655854506465924 44 9 8.43871834554534 0.561281654454662 45 10 10.1007501125091 -0.100750112509129 46 12 10.1232213070660 1.87677869293403 47 14 11.6002400954968 2.39975990450321 48 14 12.0943157434829 1.90568425651715 49 10 12.2980569018874 -2.29805690188738 50 14 9.89324877294636 4.10675122705364 51 16 12.2107222858577 3.78927771414227 52 9 10.4575426615236 -1.45754266152362 53 10 11.5954031954859 -1.59540319548587 54 6 9.01244269724991 -3.01244269724992 55 8 11.2759876621775 -3.27598766217748 56 13 12.4340621920867 0.565937807913336 57 10 10.841300432646 -0.841300432646008 58 8 8.89909901396103 -0.899099013961035 59 7 9.18672055480478 -2.18672055480478 60 15 9.79033033336827 5.20966966663173 61 9 9.91519991506453 -0.915199915064533 62 10 10.2265618496154 -0.226561849615389 63 12 10.2293852797983 1.77061472020167 64 13 10.4887256458230 2.51127435417699 65 10 8.4160868781178 1.58391312188221 66 11 11.8428133001595 -0.842813300159467 67 8 13.6015868713492 -5.6015868713492 68 9 9.13257018067962 -0.132570180679624 69 13 8.6606179865688 4.3393820134312 70 11 10.4327744805518 0.56722551944818 71 8 12.7569392870387 -4.75693928703867 72 9 10.7871768270365 -1.78717682703654 73 9 12.3531004172197 -3.35310041721967 74 15 12.5015992889971 2.49840071100287 75 9 11.1790482555329 -2.17904825553290 76 10 11.5656486191227 -1.56564861912273 77 14 8.94890740412202 5.05109259587798 78 12 10.9673786288825 1.03262137111751 79 12 11.1369017186733 0.863098281326655 80 11 11.5563104403333 -0.556310440333316 81 14 11.4956618273568 2.50433817264318 82 6 11.5822967772443 -5.58229677724426 83 12 11.2726579319011 0.7273420680989 84 8 10.0902354968231 -2.09023549682314 85 14 12.4266650619372 1.57333493806277 86 11 10.8332623687061 0.166737631293862 87 10 9.93884225028812 0.0611577497118831 88 14 10.2675098748811 3.73249012511894 89 12 12.0703882440690 -0.0703882440690387 90 10 11.0097065135456 -1.00970651354563 91 14 13.0120181927287 0.987981807271295 92 5 9.03553738146481 -4.03553738146481 93 11 10.5232989831333 0.47670101686672 94 10 10.2129764002312 -0.212976400231175 95 9 11.4995123315785 -2.49951233157848 96 10 11.4732522121774 -1.47325221217737 97 16 13.7583109166552 2.24168908334482 98 13 12.8298598939219 0.170140106078073 99 9 10.8288966342418 -1.82889663424179 100 10 11.3862219908247 -1.38622199082472 101 10 10.9965922733871 -0.9965922733871 102 7 9.50299179272843 -2.50299179272843 103 9 9.82353919762823 -0.823539197628225 104 8 10.2579389578854 -2.25793895788538 105 14 12.9134524337885 1.08654756621148 106 14 11.6331599260423 2.36684007395765 107 8 11.0958116562564 -3.09581165625638 108 9 11.5479859267525 -2.54798592675245 109 14 11.8396407755936 2.16035922440638 110 14 10.7637637562644 3.23623624373556 111 8 9.89181980729455 -1.89181980729455 112 8 13.7246293482616 -5.72462934826161 113 8 11.0186565149427 -3.01865651494273 114 7 8.59672109006802 -1.59672109006802 115 6 7.5583437455759 -1.5583437455759 116 8 9.46348840514807 -1.46348840514807 117 6 8.3305117942813 -2.33051179428131 118 11 9.92400609449128 1.07599390550872 119 14 11.8864760245055 2.11352397549451 120 11 11.1211527618446 -0.121152761844630 121 11 12.0065792151989 -1.00657921519892 122 11 9.24039168546497 1.75960831453502 123 14 10.4261856396477 3.57381436035225 124 8 10.4438890102675 -2.4438890102675 125 20 11.5552817393326 8.44471826066744 126 11 10.3653475515601 0.634652448439868 127 8 9.21395662788415 -1.21395662788415 128 11 10.7935192952045 0.206480704795506 129 10 10.6938068211101 -0.693806821110145 130 14 13.5123094087277 0.487690591272336 131 11 10.6198101889757 0.380189811024253 132 9 10.6520758892231 -1.65207588922305 133 9 9.79291786424465 -0.792917864244648 134 8 10.2227534824305 -2.22275348243046 135 10 12.1161961158982 -2.11619611589821 136 13 10.7699109692417 2.23008903075835 137 13 10.1651435241787 2.83485647582134 138 12 9.33871465209339 2.66128534790662 139 8 10.4486817159249 -2.44868171592491 140 13 11.0806210853237 1.91937891467633 141 14 12.4752392012792 1.52476079872079 142 12 11.7404095124673 0.259590487532716 143 14 10.9504032607241 3.04959673927593 144 15 11.3812680857315 3.61873191426848 145 13 10.5929297121601 2.40707028783991 146 16 11.934451340224 4.065548659776 147 9 12.0412791436863 -3.04127914368626 148 9 10.5511480018923 -1.55114800189227 149 9 11.0524282560510 -2.05242825605105 150 8 11.3635933521282 -3.36359335212824 151 7 10.1350992827678 -3.13509928276784 152 16 12.0196638196434 3.9803361803566 153 11 13.4097102544819 -2.40971025448192 154 9 10.0445020094602 -1.04450200946020 155 11 9.91492068599586 1.08507931400414 156 9 9.94122107111783 -0.941221071117826 157 14 12.5708557663134 1.42914423368665 158 13 11.1094471966484 1.89055280335164 159 16 14.526934666488 1.47306533351201 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.0858038157986438 0.171607631597288 0.914196184201356 12 0.0311388328683760 0.0622776657367521 0.968861167131624 13 0.304625697495613 0.609251394991225 0.695374302504387 14 0.492329737864451 0.984659475728901 0.50767026213555 15 0.652614745536412 0.694770508927177 0.347385254463588 16 0.581383240328433 0.837233519343133 0.418616759671567 17 0.488605910463522 0.977211820927044 0.511394089536478 18 0.415433694355205 0.83086738871041 0.584566305644795 19 0.381673344697804 0.763346689395608 0.618326655302196 20 0.569146547006841 0.861706905986319 0.430853452993159 21 0.655379203417038 0.689241593165925 0.344620796582962 22 0.640845941785108 0.718308116429785 0.359154058214892 23 0.608419781860623 0.783160436278754 0.391580218139377 24 0.534840639600805 0.93031872079839 0.465159360399195 25 0.469752142047922 0.939504284095844 0.530247857952078 26 0.403081457747574 0.806162915495148 0.596918542252426 27 0.34219518872364 0.68439037744728 0.65780481127636 28 0.299747187925588 0.599494375851176 0.700252812074412 29 0.244870824682179 0.489741649364359 0.75512917531782 30 0.207910820784677 0.415821641569354 0.792089179215323 31 0.170361431949054 0.340722863898108 0.829638568050946 32 0.283067245674559 0.566134491349118 0.716932754325441 33 0.270316637094823 0.540633274189646 0.729683362905177 34 0.2571493432061 0.5142986864122 0.7428506567939 35 0.216765227922384 0.433530455844768 0.783234772077616 36 0.251986646250178 0.503973292500356 0.748013353749822 37 0.237929554025635 0.47585910805127 0.762070445974365 38 0.650441650958341 0.699116698083317 0.349558349041659 39 0.6017083986221 0.7965832027558 0.3982916013779 40 0.561100317608191 0.877799364783617 0.438899682391808 41 0.51521617013444 0.96956765973112 0.48478382986556 42 0.492396983288679 0.984793966577357 0.507603016711321 43 0.450306919640215 0.90061383928043 0.549693080359785 44 0.397607376291124 0.795214752582249 0.602392623708876 45 0.346319223754878 0.692638447509755 0.653680776245122 46 0.317079734035208 0.634159468070416 0.682920265964792 47 0.295981527330942 0.591963054661884 0.704018472669058 48 0.268117089910055 0.53623417982011 0.731882910089945 49 0.282592035349495 0.565184070698991 0.717407964650504 50 0.336775896500894 0.673551793001789 0.663224103499106 51 0.370792769777342 0.741585539554684 0.629207230222658 52 0.361104707823910 0.722209415647821 0.63889529217609 53 0.347412812569508 0.694825625139016 0.652587187430492 54 0.375239224031239 0.750478448062479 0.62476077596876 55 0.394336161800894 0.788672323601788 0.605663838199106 56 0.349041081226948 0.698082162453897 0.650958918773052 57 0.308474979890597 0.616949959781194 0.691525020109403 58 0.269839198752162 0.539678397504324 0.730160801247838 59 0.253607093667185 0.507214187334371 0.746392906332815 60 0.402506486830677 0.805012973661354 0.597493513169323 61 0.358464436891629 0.716928873783259 0.641535563108371 62 0.315873446267094 0.631746892534188 0.684126553732906 63 0.293859771920227 0.587719543840455 0.706140228079773 64 0.302982330926661 0.605964661853323 0.697017669073339 65 0.277194667858765 0.55438933571753 0.722805332141235 66 0.245183598557636 0.490367197115272 0.754816401442364 67 0.428811311698768 0.857622623397536 0.571188688301232 68 0.382745278825647 0.765490557651293 0.617254721174354 69 0.479903355215208 0.959806710430416 0.520096644784792 70 0.437478221857140 0.874956443714281 0.56252177814286 71 0.550596682282995 0.89880663543401 0.449403317717005 72 0.52211392678118 0.95577214643764 0.47788607321882 73 0.542069975804689 0.915860048390621 0.457930024195311 74 0.553643363353634 0.892713273292731 0.446356636646366 75 0.532762122010308 0.934475755979384 0.467237877989692 76 0.497792059069483 0.995584118138966 0.502207940930517 77 0.663497945339606 0.673004109320788 0.336502054660394 78 0.632510322134064 0.734979355731872 0.367489677865936 79 0.596079587356566 0.807840825286868 0.403920412643434 80 0.550056557404441 0.899886885191118 0.449943442595559 81 0.559925938025181 0.880148123949637 0.440074061974819 82 0.711607074825696 0.576785850348608 0.288392925174304 83 0.677932237775237 0.644135524449527 0.322067762224763 84 0.653435467736099 0.693129064527803 0.346564532263901 85 0.63092699416984 0.738146011660321 0.369073005830160 86 0.589880483893529 0.820239032212942 0.410119516106471 87 0.546337990976119 0.907324018047763 0.453662009023881 88 0.632733252950352 0.734533494099296 0.367266747049648 89 0.587448140875335 0.825103718249329 0.412551859124665 90 0.543968537860284 0.912062924279432 0.456031462139716 91 0.511257639908837 0.977484720182325 0.488742360091163 92 0.554485158738185 0.89102968252363 0.445514841261815 93 0.51722295738873 0.96555408522254 0.48277704261127 94 0.472653710734202 0.945307421468403 0.527346289265798 95 0.454513496408201 0.909026992816403 0.545486503591799 96 0.412435755054985 0.824871510109971 0.587564244945015 97 0.413720410321425 0.82744082064285 0.586279589678575 98 0.369891718757121 0.739783437514241 0.63010828124288 99 0.335607354931775 0.67121470986355 0.664392645068225 100 0.296577998195954 0.593155996391908 0.703422001804046 101 0.256453648091751 0.512907296183502 0.743546351908249 102 0.237556104187564 0.475112208375128 0.762443895812436 103 0.200942998485037 0.401885996970073 0.799057001514963 104 0.181595477622872 0.363190955245744 0.818404522377128 105 0.158707550647705 0.317415101295409 0.841292449352295 106 0.167046775198966 0.334093550397931 0.832953224801034 107 0.166380396706854 0.332760793413707 0.833619603293146 108 0.158847598483307 0.317695196966613 0.841152401516693 109 0.156399077164869 0.312798154329739 0.84360092283513 110 0.199630460600614 0.399260921201228 0.800369539399386 111 0.171521914328050 0.343043828656101 0.82847808567195 112 0.345764320114815 0.691528640229629 0.654235679885185 113 0.405465460602407 0.810930921204815 0.594534539397593 114 0.374330180067251 0.748660360134502 0.625669819932749 115 0.367888738057406 0.735777476114812 0.632111261942594 116 0.327246972285951 0.654493944571903 0.672753027714049 117 0.329008673321288 0.658017346642575 0.670991326678712 118 0.287877595467373 0.575755190934745 0.712122404532627 119 0.260283096540281 0.520566193080563 0.739716903459719 120 0.217012660512034 0.434025321024068 0.782987339487966 121 0.203100683036967 0.406201366073934 0.796899316963033 122 0.181240976574764 0.362481953149528 0.818759023425236 123 0.185090443596285 0.37018088719257 0.814909556403715 124 0.200209067941851 0.400418135883702 0.799790932058149 125 0.723947485280983 0.552105029438034 0.276052514719017 126 0.680929692253162 0.638140615493676 0.319070307746838 127 0.625275071556267 0.749449856887466 0.374724928443733 128 0.562348010854703 0.875303978290595 0.437651989145298 129 0.497716602182155 0.99543320436431 0.502283397817845 130 0.434319989708159 0.868639979416317 0.565680010291841 131 0.379134114736902 0.758268229473804 0.620865885263098 132 0.326860236335412 0.653720472670824 0.673139763664588 133 0.269520940495752 0.539041880991504 0.730479059504248 134 0.238643713635137 0.477287427270274 0.761356286364863 135 0.238829350733864 0.477658701467727 0.761170649266136 136 0.197887620191867 0.395775240383733 0.802112379808133 137 0.203971828744408 0.407943657488816 0.796028171255592 138 0.208335899438685 0.416671798877371 0.791664100561315 139 0.232037630659643 0.464075261319287 0.767962369340357 140 0.177179864214274 0.354359728428549 0.822820135785726 141 0.129925000857303 0.259850001714606 0.870074999142697 142 0.0949552124591357 0.189910424918271 0.905044787540864 143 0.0966968206972837 0.193393641394567 0.903303179302716 144 0.0869216071763363 0.173843214352673 0.913078392823664 145 0.095986374084967 0.191972748169934 0.904013625915033 146 0.305867826794156 0.611735653588313 0.694132173205844 147 0.202998205543034 0.405996411086067 0.797001794456966 148 0.122980635953369 0.245961271906738 0.877019364046631 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 1 0.0072463768115942 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/1053u51290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/1053u51290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/1y2fb1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/1y2fb1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/2rtfw1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/2rtfw1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/3rtfw1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/3rtfw1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/4rtfw1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/4rtfw1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/512wh1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/512wh1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/612wh1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/612wh1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/7cuvk1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/7cuvk1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/8cuvk1290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/8cuvk1290172895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/953u51290172895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290172888vetvfnevkvj9n0j/953u51290172895.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = 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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