WS7 Tutorial

*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, 18 Nov 2010 16:04:53 +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/18/t12900965061gj996g400gk7u2.htm/, Retrieved Thu, 18 Nov 2010 17:08:29 +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/18/t12900965061gj996g400gk7u2.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 «

13 13 14 13 3 12 12 8 13 5 15 10 12 16 6 12 9 7 12 6 10 10 10 11 5 12 12 7 12 3 15 13 16 18 8 9 12 11 11 4 12 12 14 14 4 11 6 6 9 4 11 5 16 14 6 11 12 11 12 6 15 11 16 11 5 7 14 12 12 4 11 14 7 13 6 11 12 13 11 4 10 12 11 12 6 14 11 15 16 6 10 11 7 9 4 6 7 9 11 4 11 9 7 13 2 15 11 14 15 7 11 11 15 10 5 12 12 7 11 4 14 12 15 13 6 15 11 17 16 6 9 11 15 15 7 13 8 14 14 5 13 9 14 14 6 16 12 8 14 4 13 10 8 8 4 12 10 14 13 7 14 12 14 15 7 11 8 8 13 4 9 12 11 11 4 16 11 16 15 6 12 12 10 15 6 10 7 8 9 5 13 11 14 13 6 16 11 16 16 7 14 12 13 13 6 15 9 5 11 3 5 15 8 12 3 8 11 10 12 4 11 11 8 12 6 16 11 13 14 7 17 11 15 14 5 9 15 6 8 4 9 11 12 13 5 13 12 16 16 6 10 12 5 13 6 6 9 15 11 6 12 12 12 14 5 8 12 8 13 4 14 13 13 13 5 12 11 14 13 5 11 9 12 12 4 16 9 16 16 6 8 11 10 15 2 15 11 15 15 8 7 12 8 12 3 16 12 16 14 6 14 9 19 12 6 16 11 14 15 6 9 9 6 12 5 14 12 13 13 5 11 12 15 12 6 13 12 7 12 5 15 12 13 13 6 5 14 4 5 2 15 11 14 13 5 13 12 13 13 5 11 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.303577528406636 + 0.0945470254137575FindingFriends[t] + 0.2438215702385KnowingPeople[t] + 0.348903064267891Liked[t] + 0.627086448309147Celebrity[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) 0.303577528406636 1.425118 0.213 0.831599 0.4158 FindingFriends 0.0945470254137575 0.095958 0.9853 0.326054 0.163027 KnowingPeople 0.2438215702385 0.061374 3.9727 0.00011 5.5e-05 Liked 0.348903064267891 0.096479 3.6164 0.000407 0.000203 Celebrity 0.627086448309147 0.156033 4.0189 9.2e-05 4.6e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.706541003093969 R-squared 0.499200189053031 Adjusted R-squared 0.485933968895496 F-TEST (value) 37.6294214271329 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10551474685275 Sum Squared Residuals 669.412044731376 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.3631900225345 1.63680997746547 2 12 11.059886472308 0.940113527691951 3 15 13.5198743435474 1.48012565645264 4 12 10.8106072098695 1.18939279013047 5 10 10.6606294334218 -0.660629433421751 6 12 9.21298894118337 2.78701105881664 7 15 16.7307807258967 -1.73078072589671 8 9 10.4664586061786 -1.46645860617862 9 12 12.2446325096978 -0.244632509697797 10 11 7.9822624739678 3.01773752603221 11 11 13.3246193688968 -2.32461936889679 12 11 12.0695345670648 -1.06953456706481 13 15 12.2181058802665 2.78189411973349 14 7 11.2482772915125 -4.24827729151253 15 11 11.6322454012062 -0.632245401206211 16 11 10.9541017466556 0.0458982533443776 17 10 12.0695345670648 -2.06953456706481 18 14 14.3458860796766 -0.345886079676616 19 10 8.69881917127508 1.30118082872492 20 6 9.50608033863283 -3.50608033863283 21 11 8.65116448090084 2.34883551909916 22 15 14.3802478934794 0.61975210652063 23 11 11.6253812457601 -0.625381245760121 24 12 9.49117232522462 2.50882767477538 25 14 13.3937239122867 0.606276087713301 26 15 14.8335292201536 0.166470779846384 27 9 14.6240694637179 -5.62406946371787 28 13 12.4935308563519 0.506469143648087 29 13 13.2151643300748 -0.215164330074817 30 16 10.7817030882668 5.21829691173321 31 13 8.49919065183193 4.50080934816807 32 12 13.5878947395298 -1.58789473952983 33 14 14.4747949188931 -0.474794918893128 34 11 10.0546119223439 0.945388077656127 35 9 10.4664586061786 -1.46645860617862 36 16 14.2408045856472 1.75919541435278 37 12 12.87242218963 -0.87242218962998 38 10 9.1915390881677 0.808460911832304 39 13 13.0553553166344 -0.0553553166344411 40 16 15.2167940982243 0.783205901775738 41 14 12.9060807718097 1.0939192281903 42 15 8.0928016601972 6.9071983398028 43 5 9.74045158766314 -4.74045158766314 44 8 10.4769930747943 -2.47699307479425 45 11 11.2435228309355 -0.243522830935547 46 16 13.787523258973 2.21247674102702 47 17 13.0209935028317 3.97900649716831 48 9 8.48428263842372 0.515717361576283 49 9 11.9406257278483 -2.94062572784829 50 13 14.6842546753289 -1.68425467532887 51 10 10.9555082099017 -0.955508209901694 52 6 12.4122767075096 -6.41227670750964 53 12 12.3840758175299 -0.384075817529943 54 8 10.4328000239989 -2.4328000239989 55 14 12.3735413489143 1.62645865108569 56 12 12.4282688683253 -0.428268868325295 57 11 10.7755421644437 0.224457835556259 58 16 14.4006135990876 1.5993864009124 59 8 10.2695293709796 -2.26952937097964 60 15 15.251155912027 -0.251155912027017 61 7 9.45681051142187 -2.45681051142187 62 16 13.9864485467931 2.01355145320691 63 14 13.7364660527315 0.263533947268463 64 16 13.7531614451702 2.24683855482978 65 9 9.93969919132188 -0.939699191321884 66 14 12.2789943235006 1.72100567649945 67 11 13.0448208480188 -2.04482084801881 68 13 10.4671618378017 2.53283816219834 69 15 12.9060807718097 2.0939192281903 70 5 5.60121038311099 -0.601210383110992 71 15 12.4282688683253 2.57173113167471 72 13 12.2789943235006 0.721005676499448 73 11 12.0457072218777 -1.04570722187768 74 11 13.9782324466372 -2.97823244663722 75 12 12.4731651507437 -0.473165150743683 76 12 13.3937239122867 -1.3937239122867 77 12 12.2684598548849 -0.268459854884918 78 12 11.9008062218455 0.0991937781544784 79 14 10.7817030882668 3.21829691173321 80 6 7.99317785836783 -1.99317785836783 81 7 9.84007538949251 -2.84007538949251 82 14 11.9898955550593 2.01010444494074 83 14 13.8582429391996 0.141757060800385 84 10 11.2533540679281 -1.25335406792814 85 13 8.72534580070636 4.27465419929364 86 12 12.4079031627171 -0.407903162717064 87 9 9.29154380578147 -0.291543805781471 88 12 12.0164221844905 -0.016422184490546 89 16 15.0073343417885 0.992665658211484 90 10 10.2331715045558 -0.233171504555754 91 14 13.1267782284841 0.873221771515887 92 10 13.5093398749317 -3.50933987493172 93 16 15.311341123638 0.68865887636198 94 15 13.4484514316977 1.55154856830232 95 12 11.3479010933419 0.652098906658098 96 10 9.73499389546312 0.26500610453688 97 8 10.2389515125944 -2.23895151259441 98 8 8.60972983806134 -0.609729838061339 99 11 12.8424339206198 -1.8424339206198 100 13 12.4184376313327 0.581562368667303 101 16 15.4606156684628 0.539384331537238 102 16 14.7186164891316 1.28138351086837 103 14 15.8149764249307 -1.81497642493067 104 11 8.88515481414674 2.11484518585326 105 4 6.96753760279542 -2.96753760279542 106 14 14.5700451759299 -0.570045175929921 107 9 10.3480842355777 -1.34808423557774 108 14 15.251155912027 -1.25115591202702 109 8 10.4531657296071 -2.45316572960713 110 8 10.9016925957044 -2.9016925957044 111 11 12.1949817667024 -1.19498176670243 112 12 13.6426222589408 -1.64262225894082 113 11 11.4431513503787 -0.443151350378695 114 14 13.6038869003455 0.396113099654519 115 15 14.336054842684 0.663945157315982 116 16 13.4042583809023 2.59574161909767 117 16 13.4988054063161 2.50119459368391 118 11 12.7336821134209 -1.73368211342087 119 14 13.7426269765546 0.25737302344541 120 14 10.9646362152713 3.03536378472874 121 12 11.4080863049529 0.591913695047095 122 14 12.5670089445344 1.4329910554656 123 8 10.2331715045558 -2.23317150455575 124 13 13.8371740019683 -0.837174001968348 125 16 13.7426269765546 2.25737302344541 126 12 10.9211463960989 1.07885360390106 127 16 15.4507844314702 0.549215568529835 128 12 13.3937239122867 -1.3937239122867 129 11 11.5182445753979 -0.518244575397912 130 4 6.42684120345585 -2.42684120345585 131 16 15.4507844314702 0.549215568529835 132 15 12.5677121761574 2.43228782384256 133 10 11.4795092168026 -1.47950921680258 134 13 13.2107907852822 -0.210790785282238 135 15 13.2549838360776 1.74501616392241 136 12 10.6766215942374 1.3233784057626 137 14 13.6480799511408 0.351920048859167 138 7 10.6759183626144 -3.67591836261437 139 19 14.0915300408225 4.90846995917752 140 12 12.6826249071794 -0.682624907179428 141 12 12.2888255604931 -0.288825560493149 142 13 13.4988054063161 -0.49880540631609 143 15 12.9424386382336 2.05756136176642 144 8 8.28902766377315 -0.289027663773149 145 12 10.9204431644759 1.0795568355241 146 10 10.806233665077 -0.806233665076951 147 8 11.4087895365759 -3.40878953657594 148 10 14.3751711170638 -4.37517111706375 149 15 13.8919015213793 1.10809847862067 150 16 14.6142382267253 1.38576177327473 151 13 13.1947986244666 -0.194798624466587 152 16 15.0675195533995 0.932480446600481 153 9 10.2331715045558 -1.23317150455575 154 14 13.1709712792795 0.829028720720535 155 14 12.7064522523665 1.29354774763345 156 12 10.1644478769502 1.83555212304975 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0602548279129953 0.120509655825991 0.939745172087005 9 0.0406954098125639 0.0813908196251279 0.959304590187436 10 0.0170194540356913 0.0340389080713827 0.982980545964309 11 0.033244624108525 0.0664892482170501 0.966755375891475 12 0.0168523905161605 0.0337047810323211 0.98314760948384 13 0.340062248849965 0.68012449769993 0.659937751150035 14 0.687383501588052 0.625232996823897 0.312616498411948 15 0.601209234185372 0.797581531629256 0.398790765814628 16 0.510582167235863 0.978835665528275 0.489417832764137 17 0.453598746628794 0.907197493257588 0.546401253371206 18 0.370723509717003 0.741447019434005 0.629276490282997 19 0.301317999657159 0.602635999314318 0.698682000342841 20 0.59754628609609 0.80490742780782 0.40245371390391 21 0.53486276663169 0.93027446673662 0.46513723336831 22 0.502940395116637 0.994119209766727 0.497059604883363 23 0.432801804411746 0.865603608823492 0.567198195588254 24 0.418583982789439 0.837167965578878 0.581416017210561 25 0.383548025270662 0.767096050541324 0.616451974729338 26 0.329006450590219 0.658012901180438 0.670993549409781 27 0.589952522480592 0.820094955038816 0.410047477519408 28 0.531783445122043 0.936433109755914 0.468216554877957 29 0.470499450120094 0.940998900240188 0.529500549879906 30 0.64591484469755 0.7081703106049 0.35408515530245 31 0.777619464550457 0.444761070899086 0.222380535449543 32 0.738132289899842 0.523735420200317 0.261867710100158 33 0.694547933147884 0.610904133704233 0.305452066852116 34 0.650248296469407 0.699503407061186 0.349751703530593 35 0.642879525215904 0.714240949568192 0.357120474784096 36 0.664526801799945 0.670946396400109 0.335473198200054 37 0.62364987575451 0.75270024849098 0.37635012424549 38 0.574270482321598 0.851459035356803 0.425729517678402 39 0.523417168331546 0.953165663336909 0.476582831668454 40 0.5065545935911 0.9868908128178 0.4934454064089 41 0.478286475802828 0.956572951605655 0.521713524197172 42 0.78471791613157 0.430564167736859 0.21528208386843 43 0.946304186779753 0.107391626440493 0.0536958132202466 44 0.957428016849002 0.0851439663019955 0.0425719831509978 45 0.945018503253557 0.109962993492886 0.0549814967464428 46 0.951914749439327 0.0961705011213454 0.0480852505606727 47 0.977477395616427 0.0450452087671469 0.0225226043835734 48 0.970404632842215 0.0591907343155706 0.0295953671577853 49 0.978046431461814 0.0439071370763724 0.0219535685381862 50 0.974973738015696 0.0500525239686073 0.0250262619843037 51 0.96972041968274 0.060559160634518 0.030279580317259 52 0.997195094467551 0.00560981106489728 0.00280490553244864 53 0.996015186000193 0.00796962799961483 0.00398481399980742 54 0.997066458160068 0.00586708367986411 0.00293354183993206 55 0.996777054212645 0.0064458915747094 0.0032229457873547 56 0.995452163466775 0.00909567306645014 0.00454783653322507 57 0.993698309725151 0.012603380549698 0.006301690274849 58 0.992824492334593 0.0143510153308133 0.00717550766540665 59 0.994875541388604 0.0102489172227923 0.00512445861139614 60 0.993107836698961 0.0137843266020771 0.00689216330103856 61 0.994303559973613 0.0113928800527746 0.0056964400263873 62 0.99461821057237 0.0107635788552586 0.0053817894276293 63 0.992711696750124 0.014576606499751 0.00728830324987549 64 0.99314526274136 0.0137094745172792 0.00685473725863961 65 0.991521033516925 0.0169579329661501 0.00847896648307504 66 0.990640031207434 0.0187199375851319 0.00935996879256594 67 0.990579267686937 0.0188414646261253 0.00942073231306266 68 0.992052782643885 0.0158944347122294 0.00794721735611471 69 0.992179411265123 0.0156411774697543 0.00782058873487717 70 0.989533972961278 0.0209320540774442 0.0104660270387221 71 0.991118815967093 0.0177623680658142 0.0088811840329071 72 0.98829900395178 0.0234019920964386 0.0117009960482193 73 0.985384729647866 0.0292305407042682 0.0146152703521341 74 0.989674735176406 0.020650529647187 0.0103252648235935 75 0.986151873286726 0.0276962534265481 0.013848126713274 76 0.983957392177819 0.032085215644363 0.0160426078221815 77 0.97884823552833 0.0423035289433389 0.0211517644716695 78 0.972145436892618 0.0557091262147639 0.0278545631073819 79 0.982272778178078 0.0354544436438441 0.017727221821922 80 0.98183755445924 0.0363248910815189 0.0181624455407594 81 0.985420684797794 0.029158630404413 0.0145793152022065 82 0.986093198605719 0.0278136027885626 0.0139068013942813 83 0.981307364452055 0.0373852710958895 0.0186926355479448 84 0.977277769911912 0.0454444601761762 0.0227222300880881 85 0.993781837032372 0.0124363259352551 0.00621816296762753 86 0.99153828379201 0.01692343241598 0.00846171620799002 87 0.9885046880255 0.0229906239489984 0.0114953119744992 88 0.984910222563193 0.0301795548736137 0.0150897774368069 89 0.980897193440334 0.0382056131193326 0.0191028065596663 90 0.974775366283342 0.0504492674333157 0.0252246337166578 91 0.96933891151375 0.0613221769724979 0.030661088486249 92 0.983173081675879 0.0336538366482428 0.0168269183241214 93 0.978067041297031 0.0438659174059371 0.0219329587029686 94 0.974586217123195 0.05082756575361 0.025413782876805 95 0.967691233544076 0.0646175329118488 0.0323087664559244 96 0.958871060981457 0.0822578780370851 0.0411289390185426 97 0.956043405139286 0.0879131897214289 0.0439565948607145 98 0.944002390973054 0.111995218053891 0.0559976090269456 99 0.941531041688533 0.116937916622934 0.058468958311467 100 0.92723553591443 0.145528928171139 0.0727644640855697 101 0.909642352011191 0.180715295977617 0.0903576479888085 102 0.89362610063478 0.21274779873044 0.10637389936522 103 0.904692134088707 0.190615731822586 0.0953078659112928 104 0.933253048191239 0.133493903617523 0.0667469518087613 105 0.933078626236996 0.133842747526007 0.0669213737630037 106 0.916329092237754 0.167341815524492 0.0836709077622459 107 0.900331296600664 0.199337406798671 0.0996687033993356 108 0.896841294673983 0.206317410652033 0.103158705326017 109 0.89751900807058 0.204961983858839 0.102480991929419 110 0.919562139162954 0.160875721674091 0.0804378608370456 111 0.9116162700525 0.176767459895001 0.0883837299475005 112 0.938376918856626 0.123246162286748 0.061623081143374 113 0.920727306804311 0.158545386391377 0.0792726931956885 114 0.898613937833284 0.202772124333433 0.101386062166716 115 0.872509371842654 0.254981256314691 0.127490628157346 116 0.871197088327875 0.257605823344251 0.128802911672125 117 0.877952479314964 0.244095041370073 0.122047520685036 118 0.869721702638088 0.260556594723824 0.130278297361912 119 0.836816878194584 0.326366243610833 0.163183121805416 120 0.884467307369234 0.231065385261531 0.115532692630766 121 0.86066277272278 0.278674454554439 0.139337227277219 122 0.838725546795745 0.322548906408511 0.161274453204255 123 0.831160457721601 0.337679084556797 0.168839542278399 124 0.794849771606176 0.410300456787648 0.205150228393824 125 0.7948524106691 0.4102951786618 0.2051475893309 126 0.778503071816987 0.442993856366025 0.221496928183013 127 0.730054198264471 0.539891603471058 0.269945801735529 128 0.705009328627945 0.58998134274411 0.294990671372055 129 0.722948300389997 0.554103399220006 0.277051699610003 130 0.718649310500746 0.562701378998508 0.281350689499254 131 0.662536173180311 0.674927653639378 0.337463826819689 132 0.651205019909617 0.697589960180766 0.348794980090383 133 0.625024074297117 0.749951851405766 0.374975925702883 134 0.553835358999271 0.892329282001459 0.446164641000729 135 0.529031672819813 0.941936654360375 0.470968327180187 136 0.52496898010893 0.95006203978214 0.47503101989107 137 0.451837592005814 0.903675184011628 0.548162407994186 138 0.521851195782836 0.956297608434329 0.478148804217164 139 0.850055444645576 0.299889110708848 0.149944555354424 140 0.87775097711501 0.244498045769981 0.12224902288499 141 0.84421312121048 0.311573757579041 0.155786878789521 142 0.777233315436775 0.44553336912645 0.222766684563225 143 0.749312686280594 0.501374627438812 0.250687313719406 144 0.652220317047529 0.695559365904942 0.347779682952471 145 0.642877004864542 0.714245990270916 0.357122995135458 146 0.763918241013173 0.472163517973654 0.236081758986827 147 0.731674192977648 0.536651614044704 0.268325807022352 148 0.852462448780022 0.295075102439955 0.147537551219978 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0354609929078014 NOK 5% type I error level 43 0.304964539007092 NOK 10% type I error level 57 0.404255319148936 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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