Model 3 MLR

*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, 26 Nov 2010 10:26:32 +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/26/t12907671438731sldmtdk4eqf.htm/, Retrieved Fri, 26 Nov 2010 11:25:54 +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/26/t12907671438731sldmtdk4eqf.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 «

0 13 13 0 14 0 13 0 3 0 1 12 12 12 8 8 13 13 5 5 1 15 10 10 12 12 16 16 6 6 1 12 9 9 7 7 12 12 6 6 0 10 10 0 10 0 11 0 5 0 0 12 12 0 7 0 12 0 3 0 1 15 13 13 16 16 18 18 8 8 1 9 12 12 11 11 11 11 4 4 1 12 12 12 14 14 14 14 4 4 1 11 6 6 6 6 9 9 4 4 0 11 5 0 16 0 14 0 6 0 1 11 12 12 11 11 12 12 6 6 1 15 11 11 16 16 11 11 5 5 0 7 14 0 12 0 12 0 4 0 0 11 14 0 7 0 13 0 6 0 1 11 12 12 13 13 11 11 4 4 1 10 12 12 11 11 12 12 6 6 0 14 11 0 15 0 16 0 6 0 1 10 11 11 7 7 9 9 4 4 0 6 7 0 9 0 11 0 4 0 1 11 9 9 7 7 13 13 2 2 0 15 11 0 14 0 15 0 7 0 1 11 11 11 15 15 10 10 5 5 0 12 12 0 7 0 11 0 4 0 1 14 12 12 15 15 13 13 6 6 0 15 11 0 17 0 16 0 6 0 0 9 11 0 15 0 15 0 7 0 1 13 8 8 14 14 14 14 5 5 0 13 9 0 14 0 14 0 6 0 1 16 12 12 8 8 14 14 4 4 1 13 10 10 8 8 8 8 4 4 0 12 10 0 14 0 13 0 7 0 1 14 12 12 14 14 15 15 7 7 0 11 8 0 8 0 13 0 4 0 1 9 12 12 11 11 11 11 4 4 0 16 11 0 16 0 15 0 6 0 1 12 12 12 10 10 15 15 6 6 0 10 7 0 8 0 9 0 5 0 1 13 11 11 14 14 13 13 6 6 1 16 11 11 16 16 16 16 7 7 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = -1.42983001087090 + 2.84020419065591G[t] + 0.255310644726744FindingFriends[t] -0.280871718072335`Findingfriends*G`[t] + 0.239737612907330KnowingPeople[t] + 0.0307639092683181`Knowingpeople*G`[t] + 0.269027325629948Liked[t] + 0.129060192292371`Liked*G`[t] + 0.736542054753873Celebrity[t] -0.197707988203980`Celebrity*G`[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) -1.42983001087090 2.268179 -0.6304 0.529427 0.264714 G 2.84020419065591 2.903248 0.9783 0.329552 0.164776 FindingFriends 0.255310644726744 0.13989 1.8251 0.070032 0.035016 `Findingfriends*G` -0.280871718072335 0.194346 -1.4452 0.150542 0.075271 KnowingPeople 0.239737612907330 0.110822 2.1633 0.032148 0.016074 `Knowingpeople*G` 0.0307639092683181 0.13355 0.2304 0.818138 0.409069 Liked 0.269027325629948 0.151062 1.7809 0.077007 0.038504 `Liked*G` 0.129060192292371 0.197536 0.6534 0.514558 0.257279 Celebrity 0.736542054753873 0.294309 2.5026 0.01343 0.006715 `Celebrity*G` -0.197707988203980 0.34718 -0.5695 0.569913 0.284957 Multiple Linear Regression - Regression Statistics Multiple R 0.723716252676761 R-squared 0.523765214388493 Adjusted R-squared 0.494408275549428 F-TEST (value) 17.8412748433946 F-TEST (DF numerator) 9 F-TEST (DF denominator) 146 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.08808807120738 Sum Squared Residuals 636.576321795309 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 10.9525163487302 2.04748365126979 2 12 11.1369615427827 0.863038457217288 3 15 14.0031863984933 0.996813601506686 4 12 11.0838897892714 0.916110210728603 5 10 10.1626634211686 -0.162663421168614 6 12 8.75001508802231 3.24998491197769 7 15 16.8823524361036 -1.88235243610357 8 9 10.6134570069151 -1.61345700691512 9 12 12.6192241272090 -0.61922412720902 10 11 8.61814080026579 2.38185919973421 11 11 11.8681599066226 -0.868159906622589 12 11 12.0892126579372 -1.08921265793722 13 15 12.5303597576888 2.46964024231116 14 7 11.1958664967663 -4.19586649676633 15 11 11.7392898673674 -0.73928986736737 16 11 11.1544600512664 -0.154460051266414 17 10 12.0892126579372 -2.08921265793722 18 14 13.6983408133356 0.301659186664381 19 10 8.76083695571348 1.23916304428652 20 6 8.42045181932718 -2.42045181932718 21 11 9.32664104099415 1.67335895900585 22 15 13.9261179295522 1.07388207044779 23 11 11.8617707175909 -0.861770717590873 24 12 9.21752981714624 2.78247018285376 25 14 13.5693062645621 0.430693735437869 26 15 14.1778160391503 0.822183960849721 27 9 14.1658555424595 -5.16585554245954 28 13 13.2603024871413 -0.260302487141271 29 13 12.4099272597149 0.590072740285095 30 16 10.9962149941551 5.00378500584487 31 13 8.6588120333124 4.3411879666876 32 12 13.1327526335656 -1.13275263356557 33 14 14.6338138447810 -0.633813844781013 34 11 8.9740795024065 2.02592049759351 35 9 10.6134570069151 -1.61345700691512 36 16 13.669051100613 2.330948899387 37 12 13.0129736895285 -1.01297368952853 38 10 8.37920160991383 1.62079839008617 39 13 13.3243658157321 -0.324365815732074 40 16 15.5984654804002 0.401534519599783 41 14 12.6670942553579 1.33290574464214 42 15 8.52829702734811 6.47170297265189 43 5 9.58452267172383 -4.58452267172383 44 8 9.95045933677143 -1.95045933677143 45 11 11.3032691647559 -0.303269164755869 46 16 13.4173529910149 2.58264700898506 47 17 13.4541207892801 3.54587921071985 48 9 8.9366421615293 0.0633578384707 49 9 12.2445287048309 -3.24452870483089 50 13 15.0340703405047 -2.03407034050474 51 10 10.8642910428057 -0.864291042805654 52 6 11.8425828957324 -5.84258289573239 53 12 11.9598419133266 0.0401580866733938 54 8 9.99532208131347 -1.99532208131347 55 14 12.1858628453307 1.81413715466927 56 12 12.7855317491822 -0.785531749182182 57 11 11.3587292670499 -0.358729267049855 58 16 15.1107535605415 0.889246439458495 59 8 9.28445720415353 -1.28445720415353 60 15 15.4687105068521 -0.468710506852143 61 7 8.98975270092965 -1.98975270092965 62 16 13.6553344197098 2.34466558029020 63 14 14.3299080553792 -0.329908055379173 64 16 14.1205408515767 1.87945914842329 65 9 10.2745542005459 -1.27455420054586 66 14 12.4894691536609 1.51053084633906 67 11 12.8775421555426 -1.87754215554257 68 13 10.2230991975301 2.77690080246994 69 15 13.0283032202108 1.97169677978916 70 5 5.92169020459031 -0.921690204590309 71 15 12.7855317491822 2.21446825081782 72 13 12.4894691536609 0.510530846339056 73 11 11.4647936556925 -0.464793655692533 74 11 12.4510773024245 -1.45107730242452 75 12 12.8089238447264 -0.808923844726368 76 12 13.5693062645621 -1.56930626456213 77 12 12.3363220845687 -0.336322084568683 78 12 12.5917134470433 -0.591713447043304 79 14 10.9962149941551 3.00378500584487 80 6 8.1832812629371 -2.18328126293710 81 7 9.4865571427762 -2.48655714277619 82 14 12.7835821423621 1.21641785763794 83 14 14.2481268473234 -0.248126847323382 84 10 11.6015007380785 -1.60150073807851 85 13 8.27053986220766 4.72946013779234 86 12 12.4136399615473 -0.413639961547326 87 9 8.93292945969688 0.0670705403031203 88 12 12.8724465118822 -0.872446511882236 89 16 15.1982089846765 0.801791015323505 90 10 9.7107217238641 0.289278276135895 91 14 13.4366222807964 0.563377719203561 92 10 13.8500393294011 -3.85003932940106 93 16 15.5729044070546 0.427095592945374 94 15 13.8909299334290 1.10907006657104 95 12 10.9267390044326 1.07326099556736 96 10 9.80195244038818 0.198047559611824 97 8 10.7215948873580 -2.72159488735796 98 8 8.46727108148916 -0.467271081489165 99 11 11.6871018858642 -0.687101885864238 100 13 12.4873001758595 0.512699824140459 101 16 15.8689670025759 0.131032997424135 102 16 14.9043153669567 1.09568463304334 103 14 15.4818026245904 -1.48180262459041 104 11 9.29891098984716 1.70108901015284 105 4 6.24558425383307 -2.24558425383307 106 14 14.4631682672050 -0.463168267205043 107 9 10.9219201229010 -1.92192012290104 108 14 15.4687105068521 -1.46871050685214 109 8 11.0495061186477 -3.04950611864772 110 8 11.7926094009810 -3.79260940098105 111 11 12.6681772960988 -1.66817729609879 112 12 14.2103846244944 -2.21038462449438 113 11 11.4052940871569 -0.405294087156949 114 14 13.8244782560555 0.175521743944527 115 15 13.9709806740942 1.02901932590575 116 16 13.7224533336544 2.27754666634561 117 16 13.6968922603088 2.3031077396912 118 11 12.2754881677111 -1.27548816771105 119 14 13.4155968068025 0.584403193197533 120 14 10.4299345625861 3.57006543741391 121 12 11.6801335649354 0.319866435064596 122 14 12.1254270689693 1.87457293103072 123 8 9.7107217238641 -1.71072172386410 124 13 13.6709074515292 -0.670907451529211 125 16 13.4155968068025 2.58440319319753 126 12 10.9940460163537 1.00595398364627 127 16 15.5707354292532 0.429264570746776 128 12 13.5693062645621 -1.56930626456213 129 11 12.1782963984387 -1.17829639843868 130 4 6.57658106396301 -2.57658106396301 131 16 15.5707354292532 0.429264570746776 132 15 12.7833627713808 2.21663722861922 133 10 11.7923900299998 -1.79239002999977 134 13 13.2579141383586 -0.257914138358588 135 15 12.9361215809878 2.06387841901219 136 12 10.8686289984085 1.13137100159154 137 14 13.1602861620757 0.839713837924277 138 7 11.0137135026388 -4.01371350263884 139 19 14.3654813004068 4.63451869959323 140 12 13.2091803404501 -1.20918034045009 141 12 11.6579123398454 0.342087660154638 142 13 13.1758591938951 -0.175859193895138 143 15 13.4153991630537 1.58460083694635 144 8 8.080984738265 -0.0809847382650022 145 12 11.1391305205841 0.860869479415891 146 10 10.5682284472844 -0.568228447284417 147 8 11.0008914616973 -3.00089146169729 148 10 14.4505560666126 -4.45055606661265 149 15 13.4000237749831 1.59997622501695 150 16 14.6316448669796 1.36835513302039 151 13 13.3221968379307 -0.322196837930670 152 16 15.3024028848790 0.69759711512102 153 9 10.4961025538317 -1.49610255383173 154 14 12.4547900042569 1.54520999574306 155 14 12.3824938979085 1.61750610209150 156 12 10.7556125009279 1.24438749907212 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.43006961522312 0.86013923044624 0.56993038477688 14 0.274888764574927 0.549777529149854 0.725111235425073 15 0.506026789806373 0.987946420387255 0.493973210193627 16 0.375166525712514 0.750333051425029 0.624833474287485 17 0.318875913845688 0.637751827691377 0.681124086154312 18 0.230799664956415 0.461599329912829 0.769200335043585 19 0.188984045098721 0.377968090197441 0.81101595490128 20 0.330147775667823 0.660295551335647 0.669852224332177 21 0.251700848401222 0.503401696802444 0.748299151598778 22 0.255607402386979 0.511214804773958 0.744392597613021 23 0.212313050608448 0.424626101216897 0.787686949391552 24 0.28648442578635 0.5729688515727 0.71351557421365 25 0.234265454143884 0.468530908287768 0.765734545856116 26 0.179541095764657 0.359082191529314 0.820458904235343 27 0.346553527185448 0.693107054370897 0.653446472814551 28 0.322788808224502 0.645577616449004 0.677211191775498 29 0.296309579479623 0.592619158959246 0.703690420520377 30 0.544032645726404 0.911934708547193 0.455967354273596 31 0.654968626300755 0.69006274739849 0.345031373699245 32 0.66377215225915 0.672455695481698 0.336227847740849 33 0.605012027841110 0.789975944317781 0.394987972158891 34 0.558794794488372 0.882410411023257 0.441205205511628 35 0.563512980439374 0.872974039121252 0.436487019560626 36 0.6048861801856 0.7902276396288 0.3951138198144 37 0.56171174699452 0.87657650601096 0.43828825300548 38 0.605394950500548 0.789210098998903 0.394605049499452 39 0.547033852166425 0.90593229566715 0.452966147833575 40 0.506119494644498 0.987761010711004 0.493880505355502 41 0.502298318708823 0.995403362582354 0.497701681291177 42 0.76025985248557 0.479480295028859 0.239740147514430 43 0.882446326927137 0.235107346145727 0.117553673072863 44 0.89201293222915 0.215974135541699 0.107987067770850 45 0.868384760568134 0.263230478863731 0.131615239431866 46 0.892444156730834 0.215111686538332 0.107555843269166 47 0.928652958343993 0.142694083312015 0.0713470416560073 48 0.90970323573131 0.180593528537380 0.0902967642686898 49 0.942853451368332 0.114293097263336 0.0571465486316681 50 0.941243581084431 0.117512837831138 0.0587564189155688 51 0.926038714763267 0.147922570473466 0.0739612852367332 52 0.983457593554058 0.0330848128918844 0.0165424064459422 53 0.977964156375552 0.0440716872488960 0.0220358436244480 54 0.984456487508796 0.0310870249824081 0.0155435124912041 55 0.984882036535365 0.0302359269292693 0.0151179634646347 56 0.980526484830116 0.0389470303397688 0.0194735151698844 57 0.97837906436449 0.0432418712710215 0.0216209356355108 58 0.972105548624488 0.0557889027510246 0.0278944513755123 59 0.973218009020024 0.0535639819599515 0.0267819909799757 60 0.965632642242348 0.0687347155153034 0.0343673577576517 61 0.964923897947721 0.070152204104557 0.0350761020522785 62 0.970263611405282 0.0594727771894363 0.0297363885947181 63 0.96157515433289 0.0768496913342197 0.0384248456671098 64 0.960153614321478 0.0796927713570447 0.0398463856785223 65 0.961843718708436 0.0763125625831282 0.0381562812915641 66 0.958179148000494 0.0836417039990122 0.0418208519995061 67 0.95731082560228 0.0853783487954407 0.0426891743977204 68 0.96429687637811 0.0714062472437784 0.0357031236218892 69 0.966022795118322 0.0679544097633558 0.0339772048816779 70 0.957271413416693 0.0854571731666132 0.0427285865833066 71 0.95976924116351 0.0804615176729782 0.0402307588364891 72 0.949151092919736 0.101697814160527 0.0508489070802636 73 0.93672650961414 0.126546980771719 0.0632734903858594 74 0.942326184308426 0.115347631383149 0.0576738156915744 75 0.930248108586298 0.139503782827404 0.069751891413702 76 0.923288147136211 0.153423705727578 0.0767118528637891 77 0.90654790374247 0.186904192515060 0.0934520962575302 78 0.897788435090235 0.204423129819531 0.102211564909765 79 0.922516867755525 0.154966264488951 0.0774831322444753 80 0.928685400972062 0.142629198055875 0.0713145990279376 81 0.936562572292374 0.126874855415252 0.063437427707626 82 0.948484365202093 0.103031269595815 0.0515156347979073 83 0.934447231901997 0.131105536196005 0.0655527680980027 84 0.927185396527686 0.145629206944629 0.0728146034723145 85 0.990505441397758 0.0189891172044847 0.00949455860224233 86 0.987003894656189 0.0259922106876229 0.0129961053438114 87 0.98228448264463 0.0354310347107399 0.0177155173553700 88 0.982014655666862 0.035970688666277 0.0179853443331385 89 0.97741463776668 0.0451707244666378 0.0225853622333189 90 0.971043633528738 0.0579127329425233 0.0289563664712616 91 0.963318846180935 0.0733623076381308 0.0366811538190654 92 0.984916147078963 0.0301677058420733 0.0150838529210367 93 0.980287379600092 0.0394252407998152 0.0197126203999076 94 0.977620320722816 0.0447593585543682 0.0223796792771841 95 0.971935732090093 0.0561285358198145 0.0280642679099072 96 0.962745888704103 0.0745082225917935 0.0372541112958968 97 0.96360399763183 0.0727920047363401 0.0363960023681701 98 0.962866782924813 0.0742664341503751 0.0371332170751875 99 0.983888543524648 0.0322229129507048 0.0161114564753524 100 0.978212342726523 0.0435753145469530 0.0217876572734765 101 0.970452619276104 0.059094761447792 0.029547380723896 102 0.962836934973764 0.0743261300524723 0.0371630650262361 103 0.953359576154336 0.0932808476913281 0.0466404238456641 104 0.97127905570085 0.0574418885983013 0.0287209442991507 105 0.965761982290385 0.0684760354192304 0.0342380177096152 106 0.960923334957236 0.0781533300855287 0.0390766650427644 107 0.954728249858872 0.0905435002822569 0.0452717501411284 108 0.955678188686967 0.0886436226260652 0.0443218113130326 109 0.96054329618955 0.0789134076209016 0.0394567038104508 110 0.965206657705316 0.0695866845893683 0.0347933422946842 111 0.95972910361321 0.0805417927735781 0.0402708963867891 112 0.961852712872646 0.0762945742547086 0.0381472871273543 113 0.94811713829389 0.103765723412219 0.0518828617061094 114 0.93234757929272 0.135304841414559 0.0676524207072793 115 0.91451642374583 0.17096715250834 0.08548357625417 116 0.915296163677018 0.169407672645964 0.0847038363229822 117 0.916635724857786 0.166728550284428 0.0833642751422142 118 0.899184794195659 0.201630411608683 0.100815205804341 119 0.869480774562666 0.261038450874669 0.130519225437334 120 0.950853862932875 0.0982922741342507 0.0491461370671254 121 0.933064059092508 0.133871881814983 0.0669359409074917 122 0.915181044858135 0.169637910283729 0.0848189551418647 123 0.88942872373317 0.221142552533660 0.110571276266830 124 0.853712135783922 0.292575728432155 0.146287864216078 125 0.865949380095356 0.268101239809289 0.134050619904644 126 0.840054927240337 0.319890145519325 0.159945072759663 127 0.799459838610168 0.401080322779664 0.200540161389832 128 0.808944729074374 0.382110541851251 0.191055270925626 129 0.761343649908805 0.47731270018239 0.238656350091195 130 0.718842669339033 0.562314661321933 0.281157330660967 131 0.68071751531851 0.63856496936298 0.31928248468149 132 0.697295346869192 0.605409306261616 0.302704653130808 133 0.80819043348079 0.38361913303842 0.19180956651921 134 0.800638798962864 0.398722402074271 0.199361201037136 135 0.852804160225776 0.294391679548448 0.147195839774224 136 0.831967804465356 0.336064391069288 0.168032195534644 137 0.764880005134963 0.470239989730074 0.235119994865037 138 0.977796206690889 0.0444075866182231 0.0222037933091115 139 0.996900374872304 0.00619925025539215 0.00309962512769608 140 0.994662528161493 0.0106749436770132 0.0053374718385066 141 0.985511284904342 0.0289774301913165 0.0144887150956582 142 0.957137969176596 0.0857240616468082 0.0428620308234041 143 0.892498843441303 0.215002313117394 0.107501156558697 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00763358778625954 OK 5% type I error level 20 0.152671755725191 NOK 10% type I error level 54 0.412213740458015 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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