*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, 24 Dec 2010 15:55:06 +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/24/t1293205977dv8gbk52zhvcrzd.htm/, Retrieved Fri, 24 Dec 2010 16:53:09 +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/24/t1293205977dv8gbk52zhvcrzd.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 «

15 10 12 16 6 2 0 0 9 12 9 7 12 6 1 1 2 9 9 12 11 11 4 1 2 1 9 10 12 11 12 6 0 0 0 9 13 9 14 14 6 0 0 0 9 16 11 16 16 7 1 0 0 9 14 12 13 13 6 0 0 0 9 16 11 13 14 7 1 1 0 9 10 12 5 13 6 0 0 0 9 8 12 8 13 4 2 0 1 10 12 11 14 13 5 1 0 0 10 15 11 15 15 8 0 0 0 10 14 12 8 14 4 0 1 0 10 14 6 13 12 6 1 1 2 10 12 13 12 12 6 1 2 1 10 12 11 11 12 5 0 0 0 10 10 12 8 11 4 0 0 0 10 4 10 4 10 2 0 0 0 10 14 11 15 15 8 0 1 0 10 15 12 12 16 7 0 0 0 10 16 12 14 14 6 0 0 0 10 12 12 9 13 4 0 1 0 10 12 11 16 13 4 0 0 0 10 12 12 10 13 4 0 0 1 10 12 12 8 13 5 1 0 1 9 12 12 14 14 4 0 0 0 9 11 6 6 9 4 3 2 1 9 11 5 16 14 6 1 0 0 9 11 12 11 12 6 1 1 0 9 11 14 7 13 6 1 1 0 9 11 12 13 11 4 3 1 1 9 11 9 7 13 2 0 0 0 9 15 11 14 15 7 0 0 0 9 15 11 17 16 6 0 0 0 9 9 11 15 15 7 0 0 0 9 16 12 8 14 4 0 0 0 9 13 10 8 8 4 0 2 1 9 9 12 11 11 4 1 0 0 9 16 11 16 15 6 0 0 0 9 12 12 10 15 6 0 0 0 9 15 9 5 11 3 0 0 2 9 5 15 8 12 3 0 0 0 9 11 11 8 12 6 2 2 0 9 17 11 15 14 5 2 2 0 9 9 15 6 8 4 0 1 1 9 13 12 16 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 Popularity[t] = + 1.65207643482502 + 0.118875597665322FindingFriends[t] + 0.240875196872858KnowingPeople[t] + 0.379030919193094Liked[t] + 0.607799529613716Celebrity[t] -0.0468917198450873B[t] + 0.165306614305527`2B`[t] + 0.499352685427422`3B`[t] -0.214487341055989Month[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) 1.65207643482502 3.68147 0.4488 0.65427 0.327135 FindingFriends 0.118875597665322 0.096603 1.2306 0.220453 0.110226 KnowingPeople 0.240875196872858 0.06174 3.9015 0.000145 7.3e-05 Liked 0.379030919193094 0.097785 3.8762 0.000159 8e-05 Celebrity 0.607799529613716 0.156769 3.877 0.000159 7.9e-05 B -0.0468917198450873 0.223691 -0.2096 0.834249 0.417125 `2B` 0.165306614305527 0.269363 0.6137 0.540366 0.270183 `3B` 0.499352685427422 0.317135 1.5746 0.117504 0.058752 Month -0.214487341055989 0.363362 -0.5903 0.555906 0.277953 Multiple Linear Regression - Regression Statistics Multiple R 0.716996814212143 R-squared 0.514084431590363 Adjusted R-squared 0.487640046915008 F-TEST (value) 19.4402115194413 F-TEST (DF numerator) 8 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10201796085084 Sum Squared Residuals 649.51648763771 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 13.4184571495303 1.58154285046974 2 12 11.7899855957337 0.210014404266271 3 9 11.1814371266787 -2.1814371266787 4 10 11.9929929109058 -1.99299291090584 5 13 13.1170535469146 -0.117053546914642 6 16 15.1555247841458 0.844475215854184 7 14 12.8537742238447 1.14622577615535 8 16 13.8401439694466 2.15985603055342 9 10 10.9267726488618 -0.926772648861791 10 8 10.6248810849342 -2.62488108493419 11 12 12.1065952325374 -0.106595232537396 12 15 14.9758225764827 0.0241774235173207 13 14 10.7636493726956 3.23635062730444 14 14 12.6641226429189 1.33587735708108 15 12 12.9213305585814 -0.921330558581422 16 12 11.0518304425708 0.948169557429184 17 10 9.46125000081075 0.538749999189246 18 4 6.66536803956815 -2.66536803956815 19 14 15.1411291907882 -1.14112919078821 20 15 14.1433039731088 0.856696026891195 21 16 13.2591929988546 2.74080700114538 22 12 10.6254936503753 1.37450634962467 23 12 12.0274378165145 -0.0274378165144826 24 12 11.2004149183701 0.799585081629921 25 12 11.4940596754490 0.505940324551018 26 12 12.2580812806832 -0.258081280683172 27 11 8.41196227824612 2.58803772175388 28 11 13.0764098301540 -2.07640983015398 29 11 12.1114078053663 -1.11140780536628 30 11 11.7646891323986 -0.76468913239859 31 11 11.4040974664287 -0.404097466428718 32 11 8.62069813115668 2.37930186884333 33 15 14.3416351910521 0.658364808947906 34 15 14.8354921712500 0.164507828749955 35 9 14.5825103879250 -5.58251038792495 36 16 10.8128300994460 5.18716990055398 37 13 9.13085930299529 3.86914069700471 38 9 10.3514712126402 -1.35147121264023 39 16 14.2155860551841 1.78441394481591 40 12 12.8892104716123 -0.889210471612268 41 15 8.98739079949333 6.01260920050667 42 5 9.8035955244421 -4.80359552444209 43 11 11.3883215115428 -0.388321511542827 44 17 13.2247101984253 3.77528980157470 45 9 9.07818028327066 -0.078180283270659 46 13 14.7134925720425 -1.71349257204251 47 16 14.1423784379906 1.85762156200945 48 16 13.7409433926003 2.25905660739967 49 14 14.2538022830014 -0.25380228300142 50 16 13.4724566005373 2.5275433994627 51 11 12.7420063573413 -1.74200635734129 52 11 11.809892280957 -0.809892280957004 53 11 13.6830321704420 -2.68303217044197 54 12 12.1606604905852 -0.160660490585163 55 12 13.7388048564222 -1.73880485642224 56 12 12.0122072285200 -0.0122072285200334 57 14 13.6575040427026 0.342495957297375 58 10 10.8391714052153 -0.83917140521532 59 9 9.2939567125634 -0.293956712563391 60 12 12.2127734949162 -0.212773494916232 61 10 9.96228051921138 0.0377194807886161 62 14 12.9348784520841 1.06512154791595 63 8 9.87703212260633 -1.87703212260633 64 16 14.4400069246892 1.55999307531080 65 14 15.6888017417311 -1.68880174173112 66 14 10.6849061098300 3.31509389017004 67 12 11.1828126266884 0.817187373311627 68 14 13.3343008782171 0.665699121782935 69 7 11.0546249546423 -4.05462495464228 70 19 13.8790991149206 5.12090088507943 71 15 12.8016557780134 2.19834422198663 72 8 11.2061422880038 -3.20614228800375 73 10 14.2357259079165 -4.23572590791653 74 13 12.8873356178642 0.112664382135799 75 13 11.3901264295417 1.60987357045832 76 10 10.5275360698955 -0.527536069895532 77 12 9.20609353457326 2.79390646542674 78 15 17.4706883670544 -2.4706883670544 79 7 11.2091285240368 -4.20912852403683 80 14 14.3537417775043 -0.353741777504329 81 10 8.55792470894237 1.44207529105762 82 6 9.81815439332957 -3.81815439332957 83 11 11.3779732930419 -0.377973293041874 84 12 9.43486214499388 2.56513785500612 85 14 14.3342299884452 -0.334229988445212 86 12 13.4646977550006 -1.46469775500058 87 14 14.4605107887174 -0.460510788717415 88 11 10.1951265785125 0.804873421487478 89 10 9.38355801035 0.616441989650003 90 13 13.4751265084796 -0.475126508479611 91 8 10.4176430571402 -2.41764305714023 92 9 11.8862238996928 -2.88622389969276 93 6 12.0063486451522 -6.00634864515223 94 12 13.1214567265049 -1.12145672650494 95 14 12.1503629508403 1.84963704915973 96 11 10.4471549144993 0.552845085500686 97 8 10.5771103800184 -2.57711038001842 98 7 9.23248139039013 -2.23248139039013 99 9 10.4396691769144 -1.43966917691436 100 14 12.1030105277903 1.8969894722097 101 13 10.2072052527447 2.79279474725529 102 15 12.6392868827887 2.36071311721134 103 5 5.24571583426397 -0.24571583426397 104 15 12.1781184071527 2.82188159284725 105 13 12.1967939674805 0.803206032519526 106 12 11.5559849625137 0.44401503748634 107 6 7.71700882799252 -1.71700882799252 108 7 9.59940572313099 -2.59940572313099 109 13 8.50985579977156 4.49014420022844 110 16 14.8533622740703 1.14663772592974 111 10 13.2784731235095 -3.27847312350953 112 16 15.1068047606002 0.893195239399764 113 15 13.1241612780766 1.87583872192341 114 8 8.35241995279641 -0.352419952796407 115 11 12.5549219977727 -1.55492199777271 116 13 13.1528090173870 -0.15280901738695 117 16 15.1819126399627 0.818087360037315 118 11 8.65113552363401 2.34886447636599 119 14 14.3882287066421 -0.388228706642128 120 9 10.1679098794865 -1.16790987948651 121 8 10.2345424271914 -2.23454242719139 122 8 11.0763318517117 -3.07633185171171 123 11 11.8381084404744 -0.838108440474365 124 12 13.2533344154868 -1.25333441548681 125 11 11.0064688221712 -0.00646882217116818 126 14 14.5613607063352 -0.561360706335221 127 11 12.643526830619 -1.64352683061901 128 14 12.2562064269351 1.74379357306490 129 13 14.689172338863 -1.68917233886299 130 12 10.7243918942580 1.27560810574196 131 4 5.85078078205209 -1.85078078205209 132 15 12.8504119482933 2.14958805170674 133 10 11.3564045967762 -1.35640459677622 134 13 13.8175481192878 -0.817548119287846 135 15 14.1354380672970 0.86456193270296 136 12 13.1967164681036 -1.19671646810364 137 13 13.2591929988546 -0.259192998854616 138 8 7.81009460326036 0.189905396739644 139 10 10.4965022689081 -0.496502268908092 140 15 13.622067794935 1.37793220506499 141 16 14.3720725835294 1.62792741647057 142 16 14.8659295637274 1.13407043627262 143 14 12.9187223289714 1.08127767102865 144 14 13.0000231426910 0.999976857309033 145 12 10.6042612720037 1.39573872799628 146 15 13.2556748339584 1.74432516604163 147 13 13.0081459995235 -0.00814599952346191 148 16 13.1403174011893 2.85968259881071 149 14 13.5000681957275 0.499931804272526 150 8 9.96228051921138 -1.96228051921138 151 16 13.665374810033 2.334625189967 152 16 15.8506214763561 0.149378523643902 153 12 13.1210372765344 -1.12103727653438 154 11 12.2076628194322 -1.20766281943218 155 16 15.8506214763561 0.149378523643902 156 9 9.96228051921138 -0.962280519211384 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.32896021364012 0.65792042728024 0.67103978635988 13 0.430347063820874 0.860694127641747 0.569652936179126 14 0.302321610407188 0.604643220814376 0.697678389592812 15 0.195967867432362 0.391935734864723 0.804032132567639 16 0.149433425278951 0.298866850557902 0.85056657472105 17 0.109264500794582 0.218529001589163 0.890735499205418 18 0.169135972250133 0.338271944500266 0.830864027749867 19 0.281094884295363 0.562189768590725 0.718905115704637 20 0.207068979868893 0.414137959737786 0.792931020131107 21 0.233217654939827 0.466435309879655 0.766782345060173 22 0.174368990010263 0.348737980020526 0.825631009989737 23 0.135448191942885 0.270896383885769 0.864551808057116 24 0.0951741577198061 0.190348315439612 0.904825842280194 25 0.070632875932601 0.141265751865202 0.929367124067399 26 0.0566383230383321 0.113276646076664 0.943361676961668 27 0.0806000683312881 0.161200136662576 0.919399931668712 28 0.148411350154335 0.296822700308669 0.851588649845665 29 0.117035344138738 0.234070688277476 0.882964655861262 30 0.0903384878449066 0.180676975689813 0.909661512155093 31 0.066056317437478 0.132112634874956 0.933943682562522 32 0.0583022771088072 0.116604554217614 0.941697722891193 33 0.0415894157954200 0.0831788315908399 0.95841058420458 34 0.0295278087999596 0.0590556175999193 0.97047219120004 35 0.205711811957273 0.411423623914546 0.794288188042727 36 0.407803223801948 0.815606447603896 0.592196776198052 37 0.548008602111476 0.903982795777048 0.451991397888524 38 0.494078825352244 0.988157650704487 0.505921174647756 39 0.47252039425318 0.94504078850636 0.52747960574682 40 0.437572339596923 0.875144679193845 0.562427660403077 41 0.682081959413621 0.635836081172758 0.317918040586379 42 0.843228926728527 0.313542146542946 0.156771073271473 43 0.80874998642989 0.38250002714022 0.19125001357011 44 0.849050993212815 0.301898013574370 0.150949006787185 45 0.823411046966297 0.353177906067407 0.176588953033703 46 0.818539203025999 0.362921593948003 0.181460796974001 47 0.794605124387706 0.410789751224589 0.205394875612294 48 0.81453496938487 0.370930061230259 0.185465030615130 49 0.777892552544747 0.444214894910506 0.222107447455253 50 0.79435208897037 0.411295822059262 0.205647911029631 51 0.771099400130383 0.457801199739234 0.228900599869617 52 0.746586679473186 0.506826641053629 0.253413320526814 53 0.847374306281003 0.305251387437994 0.152625693718997 54 0.815438837314818 0.369122325370363 0.184561162685182 55 0.809423953393434 0.381152093213132 0.190576046606566 56 0.777545799468447 0.444908401063107 0.222454200531553 57 0.738464329730409 0.523071340539183 0.261535670269591 58 0.69856581999184 0.60286836001632 0.30143418000816 59 0.664060228264741 0.671879543470517 0.335939771735259 60 0.642113948128808 0.715772103742384 0.357886051871192 61 0.594604357709274 0.810791284581452 0.405395642290726 62 0.555084592250538 0.889830815498924 0.444915407749462 63 0.536286805315793 0.927426389368414 0.463713194684207 64 0.528090856300788 0.943818287398424 0.471909143699212 65 0.524981559245403 0.950036881509193 0.475018440754597 66 0.594108493790074 0.811783012419852 0.405891506209926 67 0.550788429153248 0.898423141693505 0.449211570846752 68 0.510385001915492 0.979229996169015 0.489614998084508 69 0.674201597134799 0.651596805730402 0.325798402865201 70 0.844384055870127 0.311231888259747 0.155615944129873 71 0.841037382599993 0.317925234800013 0.158962617400007 72 0.874450071761273 0.251099856477454 0.125549928238727 73 0.940192628146165 0.119614743707671 0.0598073718538355 74 0.925185907388453 0.149628185223095 0.0748140926115474 75 0.915979657293713 0.168040685412574 0.0840203427062869 76 0.896546830902256 0.206906338195488 0.103453169097744 77 0.918832782285214 0.162334435429573 0.0811672177147863 78 0.926118960946253 0.147762078107494 0.0738810390537472 79 0.968659621247293 0.0626807575054139 0.0313403787527070 80 0.959570537975871 0.0808589240482575 0.0404294620241288 81 0.955232835588176 0.0895343288236487 0.0447671644118243 82 0.978449661780366 0.043100676439268 0.021550338219634 83 0.9725384090455 0.0549231819089985 0.0274615909544992 84 0.976718021143186 0.0465639577136289 0.0232819788568144 85 0.969324486320533 0.0613510273589334 0.0306755136794667 86 0.964221758791657 0.0715564824166859 0.0357782412083429 87 0.9550371394109 0.0899257211782006 0.0449628605891003 88 0.946482330833396 0.107035338333208 0.0535176691666038 89 0.947742014810473 0.104515970379054 0.0522579851895269 90 0.933510371327346 0.132979257345308 0.066489628672654 91 0.936269089910977 0.127461820178046 0.0637309100890231 92 0.962301191080293 0.075397617839413 0.0376988089197065 93 0.997433857667213 0.00513228466557359 0.00256614233278679 94 0.996467905180277 0.00706418963944601 0.00353209481972301 95 0.995680767898137 0.0086384642037259 0.00431923210186295 96 0.994145524272307 0.0117089514553851 0.00585447572769257 97 0.994577171886353 0.0108456562272931 0.00542282811364655 98 0.995305492615521 0.0093890147689575 0.00469450738447875 99 0.993570554407893 0.0128588911842143 0.00642944559210713 100 0.992294011811768 0.0154119763764638 0.0077059881882319 101 0.99487214946781 0.0102557010643788 0.00512785053218939 102 0.994855587553962 0.0102888248920769 0.00514441244603844 103 0.9928063673531 0.0143872652937992 0.00719363264689962 104 0.994556519435815 0.0108869611283695 0.00544348056418477 105 0.992151452338304 0.0156970953233918 0.00784854766169588 106 0.989637340506016 0.020725318987967 0.0103626594939835 107 0.988632968773223 0.0227340624535534 0.0113670312267767 108 0.992715225382654 0.0145695492346921 0.00728477461734604 109 0.999196910702276 0.00160617859544776 0.000803089297723881 110 0.998826078834382 0.00234784233123571 0.00117392116561786 111 0.999724541436235 0.000550917127529005 0.000275458563764503 112 0.999533943441265 0.00093211311747012 0.00046605655873506 113 0.99946413090732 0.00107173818536121 0.000535869092680606 114 0.999165667361723 0.00166866527655385 0.000834332638276923 115 0.998809387899737 0.00238122420052484 0.00119061210026242 116 0.998028804684133 0.00394239063173328 0.00197119531586664 117 0.996835042450736 0.0063299150985287 0.00316495754926435 118 0.999350714821428 0.00129857035714462 0.00064928517857231 119 0.99901788069341 0.00196423861317857 0.000982119306589283 120 0.998403071815296 0.00319385636940862 0.00159692818470431 121 0.99825395489838 0.00349209020324089 0.00174604510162044 122 0.997821309805526 0.00435738038894845 0.00217869019447422 123 0.996661658080476 0.00667668383904817 0.00333834191952409 124 0.996806288918021 0.00638742216395701 0.00319371108197851 125 0.994628296769586 0.0107434064608278 0.00537170323041389 126 0.991860195116645 0.0162796097667096 0.00813980488335478 127 0.989173802820303 0.0216523943593941 0.0108261971796970 128 0.984374360963883 0.0312512780722343 0.0156256390361172 129 0.991419207719256 0.0171615845614878 0.00858079228074389 130 0.99410042779256 0.0117991444148791 0.00589957220743954 131 0.990859393583142 0.0182812128337157 0.00914060641685786 132 0.989622377635367 0.0207552447292669 0.0103776223646334 133 0.984449545963209 0.0311009080735826 0.0155504540367913 134 0.973963684751102 0.0520726304977959 0.0260363152488980 135 0.95584814707239 0.0883037058552193 0.0441518529276097 136 0.948544467579975 0.102911064840049 0.0514555324200246 137 0.930998434602684 0.138003130794632 0.0690015653973161 138 0.901226268093157 0.197547463813686 0.0987737319068429 139 0.874539518908223 0.250920962183553 0.125460481091777 140 0.805238170246671 0.389523659506657 0.194761829753329 141 0.831736741158426 0.336526517683147 0.168263258841574 142 0.733328209284037 0.533343581431926 0.266671790715963 143 0.6146867160109 0.770626567978201 0.385313283989100 144 0.685372843446449 0.629254313107101 0.314627156553551 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.150375939849624 NOK 5% type I error level 43 0.323308270676692 NOK 10% type I error level 55 0.413533834586466 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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