ws10 Multiple 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: Mon, 13 Dec 2010 08:40:38 +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/13/t1292229736mszftghlqfcz03i.htm/, Retrieved Mon, 13 Dec 2010 09:42:26 +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/13/t1292229736mszftghlqfcz03i.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 12 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 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] = + 6.80689662687928 + 0.337375488932305CM[t] -0.374730059936112D[t] + 0.174440171909908PE[t] + 0.0466548470870721PC[t] + 0.420990395069853O[t] + 0.0111700079917458`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) 6.80689662687928 3.073786 2.2145 0.028283 0.014141 CM 0.337375488932305 0.056942 5.9249 0 0 D -0.374730059936112 0.115686 -3.2392 0.001472 0.000736 PE 0.174440171909908 0.101377 1.7207 0.08734 0.04367 PC 0.0466548470870721 0.128182 0.364 0.716384 0.358192 O 0.420990395069853 0.073288 5.7443 0 0 `H ` 0.0111700079917458 0.125735 0.0888 0.929328 0.464664 Multiple Linear Regression - Regression Statistics Multiple R 0.613973533520472 R-squared 0.376963499863614 Adjusted R-squared 0.352369953805598 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 23.1938379299364 0.806162070063634 2 25 22.5527323694467 2.44726763055333 3 30 24.3584412988746 5.64155870112544 4 19 20.3508644107059 -1.35086441070588 5 22 20.5948682850530 1.40513171494695 6 22 23.2090613878984 -1.20906138789839 7 25 22.6272170981275 2.37278290187246 8 23 19.5679474477758 3.43205255222421 9 17 18.6438192086904 -1.64381920869036 10 21 21.6733554165168 -0.673355416516813 11 19 22.9460422505056 -3.94604225050558 12 19 23.4343690281779 -4.43436902817787 13 15 23.3722515581343 -8.37225155813432 14 16 16.9717712421553 -0.97177124215531 15 23 19.4780877886769 3.52191221132312 16 27 24.1261554111432 2.87384458885678 17 22 21.0629145233035 0.937085476696499 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 -3.53155515827944 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 0.0933175832017827 29 22 21.590029939121 0.409970060879012 30 26 23.3698131165580 2.63018688344197 31 29 22.5640332327775 6.43596676722253 32 32 25.3444493518572 6.65555064814283 33 25 21.5634343618986 3.43656563810136 34 29 24.5257423031722 4.47425769682777 35 28 25.0974865434727 2.90251345652734 36 17 16.9418221257969 0.0581778742030896 37 28 26.1905915923489 1.80940840765113 38 29 22.9812083059895 6.01879169401047 39 26 27.7706385200149 -1.77063852001489 40 25 23.5689720809701 1.43102791902985 41 14 19.3795629717581 -5.37956297175806 42 25 22.0555255997719 2.94447440022810 43 26 21.7527354924592 4.24726450754078 44 20 20.3551589059586 -0.355158905958583 45 18 21.4435360136149 -3.44353601361492 46 32 24.7594271138453 7.2405728861547 47 25 25.1715052606450 -0.171505260645026 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 -1.52762096048366 55 26 24.4714984024148 1.52850159758519 56 24 21.7070397679054 2.29296023209459 57 22 21.5952738480639 0.404726151936134 58 14 15.4647300334008 -1.46473003340083 59 24 22.3751950826285 1.62480491737149 60 24 22.9411121980170 1.05888780198303 61 24 23.3996176835730 0.600382316426967 62 24 20.1060692570986 3.89393074290137 63 19 18.4581362657519 0.54186373424815 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 -0.783760449496019 74 20 22.3164415449032 -2.31644154490324 75 22 22.4948867833241 -0.49488678332412 76 23 23.1806722460821 -0.18067224608207 77 25 24.0413497385003 0.958650261499702 78 25 23.5553635017032 1.44463649829677 79 17 24.0589961434255 -7.05899614342552 80 19 21.4206409661957 -2.42064096619569 81 25 24.0966467570101 0.903353242989863 82 19 22.4163783827431 -3.41637838274309 83 20 23.1586975168811 -3.15869751688114 84 26 22.5902570390771 3.40974296092294 85 23 20.9631200385294 2.03687996147055 86 27 24.5966889949657 2.40331100503427 87 17 20.8979447261035 -3.89794472610345 88 17 23.4526693089768 -6.45266930897682 89 17 19.7140987636228 -2.71409876362277 90 22 21.9657464664732 0.0342535335268337 91 21 23.7753115338017 -2.77531153380174 92 32 28.8769783672484 3.12302163275159 93 21 24.8242218519478 -3.82422185194781 94 21 24.4050846865295 -3.40508468652949 95 18 21.2391647620643 -3.23916476206433 96 18 21.2445053897907 -3.24450538979066 97 23 22.9107317388236 0.0892682611763867 98 19 20.6259781030955 -1.62597810309549 99 20 20.8661440442532 -0.866144044253178 100 21 22.4278148330794 -1.42781483307940 101 20 24.0931439799901 -4.0931439799901 102 17 18.5960751594744 -1.59607515947442 103 18 20.3004839077328 -2.3004839077328 104 19 20.7480145734531 -1.74801457345309 105 22 22.1332173240308 -0.133217324030847 106 15 18.6776186614073 -3.67761866140732 107 14 18.8035111382256 -4.80351113822563 108 18 26.877790354651 -8.87779035465098 109 24 21.5421242854055 2.45787571459450 110 35 23.6068566870257 11.3931433129743 111 29 19.3316095513897 9.66839044861028 112 21 21.9570400261406 -0.957040026140592 113 20 18.4365075353462 1.56349246465378 114 22 23.2805387990828 -1.28053879908277 115 13 16.6661117736317 -3.66611177363171 116 26 23.2946245417577 2.70537545824226 117 17 16.7313852461565 0.268614753843453 118 25 20.0599898632173 4.94001013678267 119 20 20.8885685919793 -0.888568591979345 120 19 18.1256750113904 0.874324988609638 121 21 22.6102566438842 -1.61025664388422 122 22 21.0943692063585 0.905630793641527 123 24 22.8377568056261 1.16224319437393 124 21 23.0965412425226 -2.09654124252263 125 26 25.6784575868679 0.321542413132151 126 24 20.6110894920294 3.3889105079706 127 16 20.3072031663297 -4.30720316632972 128 23 22.4462959254319 0.553704074568088 129 18 20.7804640883523 -2.78046408835229 130 16 22.4501613332031 -6.4501613332031 131 26 24.0583492564563 1.94165074354365 132 19 18.9575638072141 0.042436192785862 133 21 16.6997658148324 4.3002341851676 134 21 22.3289347474948 -1.32893474749477 135 22 18.5175277092119 3.48247229078815 136 23 19.7332112775698 3.26678872243020 137 29 24.9550604445391 4.04493955546088 138 21 19.0989526203443 1.90104737965575 139 21 19.9183159798312 1.08168402016885 140 23 21.9283161671274 1.07168383287259 141 27 23.0540254140307 3.94597458596934 142 25 25.4223704008277 -0.422370400827713 143 21 21.0146197079921 -0.0146197079921060 144 10 16.9635948368745 -6.96359483687448 145 20 22.7162157947920 -2.71621579479203 146 26 22.7440503441452 3.25594965585483 147 24 23.7156705027973 0.284329497202719 148 29 31.8824036716209 -2.88240367162088 149 19 18.8092832019323 0.190716798067711 150 24 22.1038802098397 1.89611979016025 151 19 20.6921991090226 -1.69219910902255 152 24 23.5482497311530 0.451750268847021 153 22 21.8589864571611 0.141013542838921 154 17 23.9180546657576 -6.9180546657576 155 24 23.1938379299365 0.806162070063483 156 25 22.5527323694467 2.44726763055334 157 30 24.3584412988746 5.64155870112545 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 0.304163125120191 0.847918437439904 11 0.452337356991705 0.90467471398341 0.547662643008295 12 0.388213520076801 0.776427040153603 0.611786479923199 13 0.72774522495959 0.54450955008082 0.27225477504041 14 0.639425170459595 0.72114965908081 0.360574829540405 15 0.546943098459527 0.906113803080946 0.453056901540473 16 0.450275285877095 0.90055057175419 0.549724714122905 17 0.491727830322886 0.983455660645771 0.508272169677114 18 0.402736491603866 0.805472983207732 0.597263508396134 19 0.319511209266562 0.639022418533124 0.680488790733438 20 0.26302363029507 0.52604726059014 0.73697636970493 21 0.328072028225222 0.656144056450444 0.671927971774778 22 0.267182130268775 0.534364260537549 0.732817869731225 23 0.310098016762844 0.620196033525688 0.689901983237156 24 0.297119319290263 0.594238638580525 0.702880680709737 25 0.236744935246064 0.473489870492129 0.763255064753936 26 0.186233548854765 0.37246709770953 0.813766451145235 27 0.163966296963311 0.327932593926622 0.83603370303669 28 0.133167677360551 0.266335354721101 0.86683232263945 29 0.107538425330602 0.215076850661203 0.892461574669398 30 0.109353898188991 0.218707796377982 0.89064610181101 31 0.262754405595824 0.525508811191647 0.737245594404176 32 0.543667633490031 0.912664733019938 0.456332366509969 33 0.51686654290675 0.9662669141865 0.48313345709325 34 0.561855210797745 0.87628957840451 0.438144789202255 35 0.531468575211131 0.937062849577737 0.468531424788869 36 0.507283411067722 0.985433177864556 0.492716588932278 37 0.480147248913498 0.960294497826996 0.519852751086502 38 0.580055828923481 0.839888342153038 0.419944171076519 39 0.606866947595257 0.786266104809487 0.393133052404743 40 0.557665975877922 0.884668048244156 0.442334024122078 41 0.597736703494942 0.804526593010117 0.402263296505058 42 0.565712783034667 0.868574433930666 0.434287216965333 43 0.595243569231538 0.809512861536925 0.404756430768462 44 0.546910405172956 0.906179189654089 0.453089594827044 45 0.534308113997382 0.931383772005236 0.465691886002618 46 0.655120065829546 0.689759868340908 0.344879934170454 47 0.62359228919704 0.75281542160592 0.37640771080296 48 0.609212712933452 0.781574574133096 0.390787287066548 49 0.565242477253371 0.869515045493258 0.434757522746629 50 0.522665017079655 0.95466996584069 0.477334982920345 51 0.582939217483258 0.834121565033484 0.417060782516742 52 0.545218339411399 0.909563321177203 0.454781660588601 53 0.595403437830661 0.809193124338677 0.404596562169339 54 0.56556297822273 0.868874043554541 0.434437021777271 55 0.522985056535732 0.954029886928536 0.477014943464268 56 0.490315071654591 0.980630143309183 0.509684928345409 57 0.441726326062757 0.883452652125515 0.558273673937243 58 0.401885733439674 0.803771466879348 0.598114266560326 59 0.367298137342021 0.734596274684041 0.63270186265798 60 0.325895728927786 0.651791457855571 0.674104271072214 61 0.284262193665279 0.568524387330558 0.71573780633472 62 0.299724557771075 0.599449115542151 0.700275442228925 63 0.261428901630255 0.522857803260511 0.738571098369745 64 0.26580440123006 0.53160880246012 0.73419559876994 65 0.360321377224498 0.720642754448997 0.639678622775502 66 0.448895721923045 0.89779144384609 0.551104278076955 67 0.411007696955101 0.822015393910203 0.588992303044899 68 0.389890735766869 0.779781471533738 0.610109264233131 69 0.471999191817478 0.943998383634956 0.528000808182522 70 0.426356301738342 0.852712603476683 0.573643698261658 71 0.387418702801506 0.774837405603011 0.612581297198494 72 0.357365532804649 0.714731065609297 0.642634467195351 73 0.324819324812948 0.649638649625896 0.675180675187052 74 0.304696665279569 0.609393330559139 0.69530333472043 75 0.265700496302875 0.53140099260575 0.734299503697125 76 0.229115117037877 0.458230234075755 0.770884882962123 77 0.200436082402065 0.40087216480413 0.799563917597935 78 0.175548368617213 0.351096737234426 0.824451631382787 79 0.287626527636521 0.575253055273042 0.712373472363479 80 0.265943273546381 0.531886547092763 0.734056726453619 81 0.231877933461132 0.463755866922265 0.768122066538867 82 0.230595632840884 0.461191265681769 0.769404367159116 83 0.229240437203921 0.458480874407842 0.770759562796079 84 0.230780344412659 0.461560688825317 0.769219655587341 85 0.209983013635230 0.419966027270460 0.79001698636477 86 0.195102568498852 0.390205136997704 0.804897431501148 87 0.202217159374713 0.404434318749426 0.797782840625287 88 0.299743741716408 0.599487483432817 0.700256258283592 89 0.279799467196004 0.559598934392009 0.720200532803996 90 0.24333774863356 0.48667549726712 0.75666225136644 91 0.230967455911562 0.461934911823124 0.769032544088438 92 0.225649470280327 0.451298940560653 0.774350529719673 93 0.232771486307609 0.465542972615218 0.767228513692391 94 0.229087213511671 0.458174427023342 0.770912786488329 95 0.219868614062428 0.439737228124855 0.780131385937572 96 0.212745507682769 0.425491015365538 0.787254492317231 97 0.179586439967164 0.359172879934329 0.820413560032836 98 0.154199292176411 0.308398584352821 0.84580070782359 99 0.127877935719618 0.255755871439236 0.872122064280382 100 0.107406561164754 0.214813122329507 0.892593438835246 101 0.119529831573143 0.239059663146285 0.880470168426857 102 0.0993795967937931 0.198759193587586 0.900620403206207 103 0.0881240918238203 0.176248183647641 0.91187590817618 104 0.076695689248106 0.153391378496212 0.923304310751894 105 0.0607958138954348 0.121591627790870 0.939204186104565 106 0.0600019237639285 0.120003847527857 0.939998076236072 107 0.0758206550231698 0.151641310046340 0.92417934497683 108 0.271128028956533 0.542256057913066 0.728871971043467 109 0.250684771183485 0.50136954236697 0.749315228816515 110 0.697817075758572 0.604365848482857 0.302182924241428 111 0.906547886023399 0.186904227953202 0.093452113976601 112 0.883225574503502 0.233548850992996 0.116774425496498 113 0.85998654658264 0.280026906834719 0.140013453417360 114 0.833416878070443 0.333166243859113 0.166583121929557 115 0.857597735214885 0.284804529570229 0.142402264785115 116 0.839959623386584 0.320080753226832 0.160040376613416 117 0.80419669594677 0.391606608106459 0.195803304053229 118 0.846911202071808 0.306177595856384 0.153088797928192 119 0.812525199021855 0.374949601956291 0.187474800978145 120 0.776141083673704 0.447717832652593 0.223858916326296 121 0.736494629908617 0.527010740182766 0.263505370091383 122 0.688584829734065 0.62283034053187 0.311415170265935 123 0.639642744195599 0.720714511608803 0.360357255804402 124 0.595179618530144 0.809640762939713 0.404820381469856 125 0.537464408785764 0.925071182428472 0.462535591214236 126 0.534549818756306 0.930900362487389 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 0.711881524217099 0.355940762108550 131 0.615148768436642 0.769702463126716 0.384851231563358 132 0.552844378593497 0.894311242813007 0.447155621406503 133 0.56390679329217 0.87218641341566 0.43609320670783 134 0.521090831414262 0.957818337171477 0.478909168585738 135 0.505370676694289 0.989258646611423 0.494629323305711 136 0.51068001172829 0.97863997654342 0.48931998827171 137 0.548340475253241 0.903319049493519 0.451659524746759 138 0.803743322159 0.392513355681999 0.196256677841000 139 0.740544028973054 0.518911942053893 0.259455971026946 140 0.677686389382796 0.644627221234408 0.322313610617204 141 0.720288336762336 0.559423326475328 0.279711663237664 142 0.72092458420698 0.55815083158604 0.27907541579302 143 0.630904741141985 0.738190517716031 0.369095258858015 144 0.763077086073737 0.473845827852526 0.236922913926263 145 0.748831576802837 0.502336846394327 0.251168423197163 146 0.643513687301472 0.712972625397057 0.356486312698528 147 0.639744992816221 0.720510014367559 0.360255007183779 148 0.591219617887186 0.817560764225627 0.408780382112814 149 0.50971702309122 0.98056595381756 0.49028297690878 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 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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