Paper: 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: Thu, 09 Dec 2010 12:18:23 +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/09/t1291897078qri95mbfnd3298p.htm/, Retrieved Thu, 09 Dec 2010 13:17:58 +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/09/t1291897078qri95mbfnd3298p.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 «

24 14 11 12 24 26 10 25 11 7 8 25 23 14 17 6 17 8 30 25 18 18 12 10 8 19 23 15 18 8 12 9 22 19 18 16 10 12 7 22 29 11 20 10 11 4 25 25 17 16 11 11 11 23 21 19 18 16 12 7 17 22 7 17 11 13 7 21 25 12 23 13 14 12 19 24 13 30 12 16 10 19 18 15 23 8 11 10 15 22 14 18 12 10 8 16 15 14 15 11 11 8 23 22 16 12 4 15 4 27 28 16 21 9 9 9 22 20 12 15 8 11 8 14 12 12 20 8 17 7 22 24 13 31 14 17 11 23 20 16 27 15 11 9 23 21 9 21 9 14 13 19 21 11 31 14 10 8 18 23 12 19 11 11 8 20 28 11 16 8 15 9 23 24 14 20 9 15 6 25 24 18 21 9 13 9 19 24 11 22 9 16 9 24 23 14 17 9 13 6 22 23 17 25 16 18 16 26 24 12 26 11 18 5 29 18 14 25 8 12 7 32 25 14 17 9 17 9 25 21 15 32 16 9 6 29 26 11 33 11 9 6 28 22 15 13 16 12 5 17 22 14 32 12 18 12 28 22 11 25 12 12 7 29 23 12 29 14 18 10 26 30 17 22 9 14 9 25 23 15 18 10 15 8 14 17 9 17 9 16 5 25 23 16 20 10 10 8 26 23 13 15 12 11 8 20 25 15 20 14 14 10 18 24 11 33 14 9 6 32 24 10 29 10 12 8 25 23 16 23 14 17 7 25 21 13 26 16 5 4 23 2 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation PS[t] = + 6.80689662687926 + 0.337375488932305CM[t] -0.374730059936113D[t] + 0.174440171909909PE[t] + 0.0466548470870712PC[t] + 0.420990395069853O[t] + 0.0111700079917464`H `[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) 6.80689662687926 3.073786 2.2145 0.028283 0.014141 CM 0.337375488932305 0.056942 5.9249 0 0 D -0.374730059936113 0.115686 -3.2392 0.001472 0.000736 PE 0.174440171909909 0.101377 1.7207 0.08734 0.04367 PC 0.0466548470870712 0.128182 0.364 0.716384 0.358192 O 0.420990395069853 0.073288 5.7443 0 0 `H ` 0.0111700079917464 0.125735 0.0888 0.929328 0.464664 Multiple Linear Regression - Regression Statistics Multiple R 0.613973533520472 R-squared 0.376963499863614 Adjusted R-squared 0.352369953805599 F-TEST (value) 15.3277408216924 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.07580611086178e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.42600565680683 Sum Squared Residuals 1784.10224359181 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.1938379299365 0.806162070063475 2 25 22.5527323694467 2.44726763055335 3 30 24.3584412988746 5.64155870112544 4 19 20.3508644107059 -1.35086441070588 5 22 20.5948682850530 1.40513171494695 6 22 23.2090613878984 -1.20906138789838 7 25 22.6272170981275 2.37278290187246 8 23 19.5679474477758 3.43205255222421 9 17 18.6438192086904 -1.64381920869035 10 21 21.6733554165168 -0.673355416516811 11 19 22.9460422505056 -3.94604225050558 12 19 23.4343690281779 -4.43436902817787 13 15 23.3722515581343 -8.37225155813431 14 16 16.9717712421553 -0.971771242155311 15 23 19.4780877886769 3.52191221132312 16 27 24.1261554111432 2.87384458885678 17 22 21.0629145233035 0.937085476696502 18 14 16.3476939858197 -2.34769398581970 19 22 24.0976123636836 -2.09761236368359 20 23 24.0965302143664 -1.09653021436639 21 23 21.5751478121951 1.42485218780491 22 19 22.5315551582794 -3.53155515827943 23 18 23.9537756229784 -5.95377562297838 24 20 23.2976820748665 -3.29768207486649 25 23 22.5037097663004 0.496290233699556 26 25 23.3831971527993 1.61680284720068 27 19 23.4334667832308 -4.4334667832308 28 24 23.9066824167982 0.0933175832017823 29 22 21.590029939121 0.409970060879009 30 26 23.369813116558 2.63018688344198 31 29 22.5640332327775 6.43596676722252 32 32 25.3444493518572 6.65555064814283 33 25 21.5634343618986 3.43656563810136 34 29 24.5257423031722 4.47425769682777 35 28 25.0974865434727 2.90251345652733 36 17 16.9418221257969 0.0581778742030905 37 28 26.1905915923489 1.80940840765113 38 29 22.9812083059895 6.01879169401048 39 26 27.7706385200149 -1.77063852001489 40 25 23.5689720809701 1.43102791902985 41 14 19.3795629717581 -5.37956297175806 42 25 22.0555255997719 2.9444744002281 43 26 21.7527354924592 4.24726450754078 44 20 20.3551589059586 -0.355158905958581 45 18 21.4435360136149 -3.44353601361491 46 32 24.7594271138453 7.2405728861547 47 25 25.1715052606450 -0.171505260645027 48 25 21.5983872856543 3.40161271434573 49 23 20.8460981816414 2.15390181835858 50 21 22.2337553214121 -1.23375532141214 51 20 24.2400778356035 -4.24007783560355 52 15 16.4063035063195 -1.40630350631953 53 30 26.9514189183557 3.04858108164434 54 24 25.5276209604837 -1.52762096048365 55 26 24.4714984024148 1.52850159758519 56 24 21.7070397679054 2.29296023209459 57 22 21.5952738480639 0.404726151936135 58 14 15.4647300334008 -1.46473003340083 59 24 22.3751950826285 1.62480491737149 60 24 22.9411121980170 1.05888780198303 61 24 23.3996176835730 0.60038231642697 62 24 20.1060692570986 3.89393074290138 63 19 18.4581362657519 0.541863734248147 64 31 27.0134028612565 3.98659713874353 65 22 26.8534365895336 -4.85343658953355 66 27 21.4490897730696 5.55091022693044 67 19 17.6772560383528 1.32274396164716 68 25 22.4167664105562 2.58323358944378 69 20 25.115944649428 -5.11594464942802 70 21 21.5913350604495 -0.591335060449544 71 27 27.7165573575398 -0.716557357539801 72 23 24.4732905256934 -1.47329052569339 73 25 25.783760449496 -0.783760449496022 74 20 22.3164415449032 -2.31644154490324 75 22 22.4948867833241 -0.494886783324118 76 23 23.1806722460821 -0.180672246082066 77 25 24.0413497385003 0.958650261499702 78 25 23.5553635017032 1.44463649829678 79 17 24.0589961434255 -7.05899614342552 80 19 21.4206409661957 -2.42064096619568 81 25 24.0966467570101 0.903353242989863 82 19 22.4163783827431 -3.41637838274308 83 20 23.1586975168811 -3.15869751688114 84 26 22.5902570390771 3.40974296092294 85 23 20.9631200385294 2.03687996147056 86 27 24.5966889949657 2.40331100503428 87 17 20.8979447261035 -3.89794472610345 88 17 23.4526693089768 -6.45266930897682 89 17 19.7140987636228 -2.71409876362277 90 22 21.9657464664732 0.0342535335268300 91 21 23.7753115338017 -2.77531153380173 92 32 28.8769783672484 3.12302163275159 93 21 24.8242218519478 -3.82422185194781 94 21 24.4050846865295 -3.40508468652948 95 18 21.2391647620643 -3.23916476206433 96 18 21.2445053897907 -3.24450538979066 97 23 22.9107317388236 0.0892682611763867 98 19 20.6259781030955 -1.62597810309550 99 20 20.8661440442532 -0.866144044253181 100 21 22.4278148330794 -1.42781483307941 101 20 24.0931439799901 -4.0931439799901 102 17 18.5960751594744 -1.59607515947442 103 18 20.3004839077328 -2.30048390773280 104 19 20.7480145734531 -1.74801457345310 105 22 22.1332173240308 -0.133217324030845 106 15 18.6776186614073 -3.67761866140732 107 14 18.8035111382256 -4.80351113822563 108 18 26.8777903546510 -8.87779035465097 109 24 21.5421242854055 2.4578757145945 110 35 23.6068566870257 11.3931433129743 111 29 19.3316095513897 9.66839044861029 112 21 21.9570400261406 -0.957040026140595 113 20 18.4365075353462 1.56349246465377 114 22 23.2805387990828 -1.28053879908277 115 13 16.6661117736317 -3.66611177363172 116 26 23.2946245417577 2.70537545824226 117 17 16.7313852461565 0.268614753843451 118 25 20.0599898632173 4.94001013678267 119 20 20.8885685919793 -0.888568591979344 120 19 18.1256750113904 0.874324988609644 121 21 22.6102566438842 -1.61025664388422 122 22 21.0943692063585 0.905630793641523 123 24 22.8377568056261 1.16224319437393 124 21 23.0965412425226 -2.09654124252263 125 26 25.6784575868678 0.321542413132153 126 24 20.6110894920294 3.38891050797060 127 16 20.3072031663297 -4.30720316632972 128 23 22.4462959254319 0.553704074568086 129 18 20.7804640883523 -2.78046408835229 130 16 22.4501613332031 -6.45016133320309 131 26 24.0583492564563 1.94165074354365 132 19 18.9575638072141 0.0424361927858609 133 21 16.6997658148324 4.30023418516759 134 21 22.3289347474948 -1.32893474749477 135 22 18.5175277092118 3.48247229078815 136 23 19.7332112775698 3.2667887224302 137 29 24.9550604445391 4.04493955546088 138 21 19.0989526203442 1.90104737965575 139 21 19.9183159798311 1.08168402016885 140 23 21.9283161671274 1.07168383287259 141 27 23.0540254140307 3.94597458596934 142 25 25.4223704008277 -0.422370400827714 143 21 21.0146197079921 -0.0146197079921077 144 10 16.9635948368745 -6.96359483687447 145 20 22.7162157947920 -2.71621579479203 146 26 22.7440503441452 3.25594965585483 147 24 23.7156705027973 0.284329497202718 148 29 31.8824036716209 -2.88240367162089 149 19 18.8092832019323 0.190716798067704 150 24 22.1038802098397 1.89611979016026 151 19 20.6921991090226 -1.69219910902255 152 24 23.5482497311530 0.451750268847024 153 22 21.8589864571611 0.141013542838923 154 17 23.9180546657576 -6.91805466575759 155 24 23.1938379299365 0.806162070063492 156 25 22.5527323694467 2.44726763055334 157 30 24.3584412988746 5.64155870112544 158 19 20.3508644107059 -1.35086441070588 159 22 20.5948682850530 1.40513171494695 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.152081562560096 0.304163125120192 0.847918437439904 11 0.452337356991705 0.90467471398341 0.547662643008295 12 0.388213520076802 0.776427040153604 0.611786479923198 13 0.72774522495959 0.54450955008082 0.27225477504041 14 0.639425170459596 0.721149659080809 0.360574829540404 15 0.546943098459525 0.90611380308095 0.453056901540475 16 0.450275285877095 0.90055057175419 0.549724714122905 17 0.491727830322884 0.983455660645769 0.508272169677116 18 0.402736491603864 0.805472983207727 0.597263508396136 19 0.31951120926656 0.63902241853312 0.68048879073344 20 0.263023630295069 0.526047260590139 0.73697636970493 21 0.328072028225221 0.656144056450442 0.671927971774779 22 0.267182130268775 0.53436426053755 0.732817869731225 23 0.310098016762845 0.62019603352569 0.689901983237155 24 0.297119319290263 0.594238638580525 0.702880680709737 25 0.236744935246065 0.473489870492131 0.763255064753935 26 0.186233548854765 0.37246709770953 0.813766451145235 27 0.163966296963311 0.327932593926621 0.83603370303669 28 0.13316767736055 0.2663353547211 0.86683232263945 29 0.107538425330600 0.215076850661201 0.8924615746694 30 0.109353898188990 0.218707796377979 0.89064610181101 31 0.262754405595823 0.525508811191646 0.737245594404177 32 0.543667633490033 0.912664733019934 0.456332366509967 33 0.51686654290675 0.9662669141865 0.48313345709325 34 0.561855210797746 0.876289578404507 0.438144789202254 35 0.531468575211132 0.937062849577735 0.468531424788868 36 0.50728341106772 0.98543317786456 0.49271658893228 37 0.480147248913496 0.960294497826991 0.519852751086504 38 0.58005582892348 0.83988834215304 0.41994417107652 39 0.60686694759526 0.78626610480948 0.39313305240474 40 0.55766597587792 0.88466804824416 0.44233402412208 41 0.597736703494942 0.804526593010116 0.402263296505058 42 0.565712783034664 0.868574433930672 0.434287216965336 43 0.595243569231536 0.809512861536928 0.404756430768464 44 0.546910405172955 0.90617918965409 0.453089594827045 45 0.53430811399738 0.93138377200524 0.46569188600262 46 0.655120065829547 0.689759868340906 0.344879934170453 47 0.623592289197042 0.752815421605916 0.376407710802958 48 0.609212712933453 0.781574574133094 0.390787287066547 49 0.565242477253369 0.869515045493261 0.434757522746631 50 0.522665017079657 0.954669965840687 0.477334982920343 51 0.582939217483258 0.834121565033484 0.417060782516742 52 0.5452183394114 0.9095633211772 0.4547816605886 53 0.595403437830661 0.809193124338678 0.404596562169339 54 0.565562978222728 0.868874043554545 0.434437021777272 55 0.522985056535733 0.954029886928534 0.477014943464267 56 0.490315071654591 0.980630143309182 0.509684928345409 57 0.441726326062757 0.883452652125514 0.558273673937243 58 0.401885733439674 0.803771466879348 0.598114266560326 59 0.367298137342021 0.734596274684042 0.632701862657979 60 0.325895728927786 0.651791457855572 0.674104271072214 61 0.284262193665279 0.568524387330559 0.715737806334721 62 0.299724557771075 0.599449115542151 0.700275442228924 63 0.261428901630255 0.522857803260509 0.738571098369745 64 0.265804401230059 0.531608802460117 0.734195598769941 65 0.360321377224498 0.720642754448997 0.639678622775501 66 0.448895721923045 0.89779144384609 0.551104278076955 67 0.4110076969551 0.8220153939102 0.5889923030449 68 0.38989073576687 0.77978147153374 0.61010926423313 69 0.47199919181748 0.94399838363496 0.52800080818252 70 0.426356301738342 0.852712603476684 0.573643698261658 71 0.387418702801505 0.77483740560301 0.612581297198495 72 0.357365532804649 0.714731065609298 0.642634467195351 73 0.324819324812949 0.649638649625899 0.67518067518705 74 0.304696665279571 0.609393330559141 0.69530333472043 75 0.265700496302874 0.531400992605748 0.734299503697126 76 0.229115117037878 0.458230234075757 0.770884882962122 77 0.200436082402063 0.400872164804126 0.799563917597937 78 0.175548368617216 0.351096737234432 0.824451631382784 79 0.28762652763652 0.57525305527304 0.71237347236348 80 0.265943273546382 0.531886547092764 0.734056726453618 81 0.231877933461133 0.463755866922265 0.768122066538867 82 0.230595632840887 0.461191265681773 0.769404367159113 83 0.229240437203919 0.458480874407838 0.770759562796081 84 0.23078034441266 0.46156068882532 0.76921965558734 85 0.209983013635230 0.419966027270461 0.79001698636477 86 0.19510256849885 0.3902051369977 0.80489743150115 87 0.202217159374712 0.404434318749423 0.797782840625288 88 0.299743741716408 0.599487483432816 0.700256258283592 89 0.279799467196003 0.559598934392007 0.720200532803997 90 0.243337748633561 0.486675497267121 0.75666225136644 91 0.230967455911560 0.461934911823121 0.76903254408844 92 0.225649470280327 0.451298940560653 0.774350529719673 93 0.232771486307608 0.465542972615216 0.767228513692392 94 0.229087213511668 0.458174427023336 0.770912786488332 95 0.219868614062428 0.439737228124857 0.780131385937572 96 0.212745507682768 0.425491015365535 0.787254492317232 97 0.179586439967165 0.359172879934331 0.820413560032835 98 0.154199292176412 0.308398584352824 0.845800707823588 99 0.127877935719618 0.255755871439236 0.872122064280382 100 0.107406561164753 0.214813122329506 0.892593438835247 101 0.119529831573143 0.239059663146286 0.880470168426857 102 0.0993795967937933 0.198759193587587 0.900620403206207 103 0.0881240918238202 0.176248183647640 0.91187590817618 104 0.0766956892481051 0.153391378496210 0.923304310751895 105 0.0607958138954348 0.121591627790870 0.939204186104565 106 0.0600019237639292 0.120003847527858 0.93999807623607 107 0.0758206550231696 0.151641310046339 0.92417934497683 108 0.271128028956533 0.542256057913066 0.728871971043467 109 0.250684771183485 0.50136954236697 0.749315228816515 110 0.69781707575857 0.60436584848286 0.30218292424143 111 0.906547886023399 0.186904227953202 0.093452113976601 112 0.883225574503502 0.233548850992996 0.116774425496498 113 0.85998654658264 0.280026906834719 0.140013453417360 114 0.833416878070445 0.33316624385911 0.166583121929555 115 0.857597735214886 0.284804529570228 0.142402264785114 116 0.839959623386584 0.320080753226833 0.160040376613416 117 0.804196695946771 0.391606608106458 0.195803304053229 118 0.846911202071809 0.306177595856382 0.153088797928191 119 0.812525199021854 0.374949601956291 0.187474800978146 120 0.776141083673704 0.447717832652592 0.223858916326296 121 0.736494629908617 0.527010740182765 0.263505370091383 122 0.688584829734065 0.622830340531869 0.311415170265935 123 0.639642744195598 0.720714511608804 0.360357255804402 124 0.595179618530144 0.809640762939711 0.404820381469856 125 0.537464408785764 0.925071182428473 0.462535591214236 126 0.534549818756306 0.930900362487387 0.465450181243694 127 0.570829755077969 0.858340489844063 0.429170244922031 128 0.508115228685312 0.983769542629375 0.491884771314688 129 0.468187017304523 0.936374034609046 0.531812982695477 130 0.64405923789145 0.7118815242171 0.35594076210855 131 0.615148768436642 0.769702463126717 0.384851231563358 132 0.552844378593497 0.894311242813006 0.447155621406503 133 0.56390679329217 0.87218641341566 0.43609320670783 134 0.521090831414262 0.957818337171475 0.478909168585738 135 0.505370676694288 0.989258646611423 0.494629323305712 136 0.51068001172829 0.97863997654342 0.48931998827171 137 0.54834047525324 0.903319049493521 0.451659524746761 138 0.803743322159 0.392513355682 0.196256677841 139 0.740544028973054 0.518911942053892 0.259455971026946 140 0.677686389382795 0.64462722123441 0.322313610617205 141 0.720288336762335 0.55942332647533 0.279711663237665 142 0.720924584206979 0.558150831586042 0.279075415793021 143 0.630904741141986 0.738190517716027 0.369095258858014 144 0.763077086073738 0.473845827852523 0.236922913926262 145 0.748831576802836 0.502336846394328 0.251168423197164 146 0.643513687301471 0.712972625397058 0.356486312698529 147 0.639744992816221 0.720510014367558 0.360255007183779 148 0.591219617887185 0.81756076422563 0.408780382112815 149 0.509717023091222 0.980565953817557 0.490282976908778 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:

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/10ei9x1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/10ei9x1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/17ycl1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/17ycl1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/27ycl1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/27ycl1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/37ycl1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/37ycl1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/4iqto1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/4iqto1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/5iqto1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/5iqto1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/6sza81291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/6sza81291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/7sza81291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/7sza81291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/8lqrb1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/8lqrb1291897092.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/9lqrb1291897092.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897078qri95mbfnd3298p/9lqrb1291897092.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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