workshop 7 - tutorial 4

*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, 19 Nov 2010 15:44:14 +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/19/t12901814095tihr0h2zbose66.htm/, Retrieved Fri, 19 Nov 2010 16:43:29 +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/19/t12901814095tihr0h2zbose66.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 «

9 26 24 14 11 12 24 9 23 25 11 7 8 25 9 25 17 6 17 8 30 9 23 18 12 10 8 19 9 19 18 8 12 9 22 9 29 16 10 12 7 22 10 25 20 10 11 4 25 10 21 16 11 11 11 23 10 22 18 16 12 7 17 10 25 17 11 13 7 21 10 24 23 13 14 12 19 10 18 30 12 16 10 19 10 22 23 8 11 10 15 10 15 18 12 10 8 16 10 22 15 11 11 8 23 10 28 12 4 15 4 27 10 20 21 9 9 9 22 10 12 15 8 11 8 14 10 24 20 8 17 7 22 10 20 31 14 17 11 23 10 21 27 15 11 9 23 10 20 34 16 18 11 21 10 21 21 9 14 13 19 10 23 31 14 10 8 18 10 28 19 11 11 8 20 10 24 16 8 15 9 23 10 24 20 9 15 6 25 10 24 21 9 13 9 19 10 23 22 9 16 9 24 10 23 17 9 13 6 22 10 29 24 10 9 6 25 10 24 25 16 18 16 26 10 18 26 11 18 5 29 10 25 25 8 12 7 32 10 21 17 9 17 9 25 10 26 32 16 9 6 29 10 22 33 11 9 6 28 10 22 13 16 12 5 17 10 22 32 12 18 12 28 10 23 25 12 12 7 29 10 30 29 14 18 10 26 10 23 22 9 14 9 25 10 17 18 10 15 8 14 10 23 17 9 16 5 25 10 23 20 10 10 8 26 10 25 15 12 11 8 20 10 24 20 14 14 10 18 10 24 33 14 9 6 32 10 23 29 10 12 8 25 10 21 23 14 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 30 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation O[t] = + 18.2651799335288 -0.080823679576423maand[t] -0.0591540614026575CM[t] + 0.216924456733212D[t] -0.132556183679637PE[t] -0.254001352868106PC[t] + 0.39567410079133`PS `[t] -0.0147661337424250t + 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) 18.2651799335288 15.349762 1.1899 0.23594 0.11797 maand -0.080823679576423 1.54324 -0.0524 0.958301 0.47915 CM -0.0591540614026575 0.06241 -0.9478 0.344732 0.172366 D 0.216924456733212 0.111196 1.9508 0.052929 0.026464 PE -0.132556183679637 0.103796 -1.2771 0.203534 0.101767 PC -0.254001352868106 0.129774 -1.9573 0.05216 0.02608 `PS ` 0.39567410079133 0.075665 5.2293 1e-06 0 t -0.0147661337424250 0.006382 -2.3138 0.02203 0.011015 Multiple Linear Regression - Regression Statistics Multiple R 0.502263051134702 R-squared 0.252268172535140 Adjusted R-squared 0.217605107685776 F-TEST (value) 7.27772266045789 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 1.63300429067981e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.45408407493565 Sum Squared Residuals 1801.53521630534 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 24.1302897682984 1.86971023170157 2 23 25.347500449936 -2.34750044993602 3 25 25.3741531909091 -0.374153190909075 4 23 23.1772579132161 -0.177257913216094 5 19 22.9627025346874 -3.96270253468743 6 29 24.0080961429530 4.99190385704704 7 25 25.7574726286814 -0.757472628681422 8 21 23.6268895256234 -2.62688952562344 9 22 23.0878421757866 -1.08784217578657 10 25 23.4977480392664 1.50225196073358 11 24 21.3679953009716 2.63200469902835 12 18 20.9651166190543 -2.96511661905435 13 22 19.5768156034305 2.42318439656946 14 15 21.7617505938414 -6.76175059384143 15 22 24.3446847094334 -2.34468470943344 16 28 25.0573866426857 2.94261335731430 17 20 23.1418160737661 -3.14181607376606 18 12 20.0885460308846 -8.08854603088456 19 24 22.4020666472498 1.59793335275023 20 20 22.4178212677963 -2.41782126779629 21 21 24.1599356442117 -3.15993564421174 22 20 21.7207713443076 -1.72077134430760 23 21 20.1874106390669 0.81258936093309 24 23 22.0702835732317 0.929716426768283 25 28 22.7733848240246 5.22661517597543 26 24 22.6881037190778 1.31189628092218 27 24 24.2069980566450 -0.206998056644952 28 24 21.2621415655068 2.73785843449316 29 23 22.7689233232795 0.231076676720498 30 23 23.4182519046109 -0.418251904610932 31 29 24.9235788348757 4.07642116512435 32 24 22.8138602991234 1.18613970087661 33 18 25.6363550042354 -7.6363550042354 34 25 26.5043262604116 -1.50432626041159 35 21 23.2392147449499 -2.23921474494993 36 26 27.2607588185069 -1.26075881850686 37 22 25.7065422389044 -3.70654223890439 38 22 23.4633973100057 -1.46339731000574 39 22 23.2360747192300 -1.23607471923004 40 23 26.0964049825159 -3.0964049825159 41 30 23.5345080535731 6.46549194642686 42 23 23.2377500527786 -0.237750052778580 43 17 19.4455546818638 -2.44555468186384 44 23 24.2548811364202 -1.25488113642017 45 23 24.7085844194678 -1.70858441946782 46 25 22.9168367177775 2.08316328222252 47 24 21.3431297321304 2.65687026786958 48 24 27.7775845411027 -3.77758454110267 49 23 23.4563468637236 -0.456346863723594 50 21 24.2554233597999 -3.25542335979988 51 24 26.0583740164932 -2.05837401649321 52 24 22.263122278027 1.73687772197298 53 28 21.9512983774212 6.04870162257884 54 16 21.4341929789634 -5.4341929789634 55 20 20.332735274589 -0.332735274589016 56 29 23.7855453811429 5.2144546188571 57 27 24.1479703243941 2.85202967560587 58 22 23.4466677209928 -1.44666772099284 59 28 24.1552952274415 3.8447047725585 60 16 20.7808813048786 -4.78088130487857 61 25 23.1224020852537 1.87759791474626 62 24 23.7173920375586 0.282607962441427 63 28 23.8682254035401 4.13177459645985 64 24 24.4168721842752 -0.416872184275199 65 23 22.8645315280313 0.135468471968741 66 30 26.9559642612268 3.04403573877321 67 24 21.5839333013938 2.41606669860615 68 21 24.2091984978139 -3.20919849781390 69 25 23.3939492554754 1.60605074452461 70 25 24.0281252481694 0.971874751830566 71 22 21.0324279182379 0.96757208176207 72 23 22.5603154456829 0.439684554317123 73 26 22.9655594334452 3.03444056655483 74 23 21.8231264415642 1.17687355843577 75 25 23.1432992685926 1.85670073140740 76 21 21.4342151171374 -0.434215117137412 77 25 23.6498080472023 1.35019195279768 78 24 22.2290743672796 1.77092563272042 79 29 23.5125165447205 5.48748345527954 80 22 23.6501217579009 -1.65012175790086 81 27 23.5658938898989 3.43410611010106 82 26 19.7192246760689 6.28077532393105 83 22 21.3547789327412 0.64522106725879 84 24 21.9998423814415 2.00015761855855 85 27 23.0655724329200 3.93442756708003 86 24 21.3455629774012 2.65443702259875 87 24 24.658700615808 -0.658700615807987 88 29 24.1826426837953 4.81735731620468 89 22 22.0958198385512 -0.0958198385511527 90 21 20.5310845408482 0.468915459151793 91 24 20.4508240839927 3.54917591600735 92 24 21.5248908314905 2.47510916850947 93 23 21.7868440373372 1.21315596266276 94 20 22.1292611274564 -2.12926112745638 95 27 21.1935779436435 5.80642205635649 96 26 23.2047380959745 2.79526190402554 97 25 21.8290009382884 3.17099906171155 98 21 19.9895407638288 1.01045923617116 99 21 20.5769389812245 0.4230610187755 100 19 20.2150775834596 -1.21507758345957 101 21 21.3464128191757 -0.346412819175655 102 21 20.9850833658009 0.0149166341991343 103 16 19.5601712420730 -3.56017124207303 104 22 20.3726876099126 1.62731239008742 105 29 21.4982485434834 7.50175145651664 106 15 21.4481587489022 -6.44815874890216 107 17 20.3886896991058 -3.38868969910585 108 15 19.6493873290368 -4.64938732903676 109 21 21.3279979997044 -0.327997999704353 110 21 20.6844209670233 0.315579032976684 111 19 18.9550488848328 0.0449511151671882 112 24 17.8354367341568 6.16456326584323 113 20 21.7906882736065 -1.79068827360649 114 17 24.4817908931081 -7.48179089310812 115 23 24.1480825171234 -1.14808251712339 116 24 21.8489212595086 2.1510787404914 117 14 21.5133116379342 -7.51331163793424 118 19 22.2915575818798 -3.29155758187984 119 24 21.6883393680163 2.31166063198369 120 13 19.9554033140636 -6.95540331406356 121 22 24.6845701216641 -2.68457012166414 122 16 20.5712630248371 -4.57126302483711 123 19 22.618312797572 -3.618312797572 124 25 22.0681640830699 2.93183591693012 125 25 23.5050873634967 1.49491263650334 126 23 20.8231882533505 2.17681174664951 127 24 22.7929918544429 1.20700814555707 128 26 22.7760153903175 3.22398460968255 129 26 20.8239407163661 5.17605928363388 130 25 23.4196018963803 1.58039810361965 131 18 21.5862924403213 -3.58629244032127 132 21 19.2217691974817 1.77823080251832 133 26 22.8121279501599 3.18787204984014 134 23 21.1803346373576 1.81966536264239 135 23 19.0986249459743 3.90137505402567 136 22 21.8271507081582 0.172849291841752 137 20 21.5923532410073 -1.59235324100729 138 13 21.2574506098304 -8.25745060983036 139 24 20.5666968942374 3.43330310576262 140 15 20.7204514264666 -5.72045142646664 141 14 22.2587253215388 -8.25872532153882 142 22 23.1348164241320 -1.13481642413203 143 10 17.0104115841435 -7.01041158414355 144 24 23.4535075069177 0.546492493082284 145 22 20.9466707072865 1.05332929271347 146 24 24.7574857221061 -0.757485722106147 147 19 20.7572509061611 -1.75725090616112 148 20 21.1138228524966 -1.11382285249664 149 13 16.3426989662444 -3.34269896624437 150 20 19.1937112950387 0.806288704961293 151 22 22.1060433360234 -0.106043336023381 152 24 22.3702370545459 1.62976294545413 153 29 22.2488989615374 6.75110103846262 154 12 19.9719025274833 -7.97190252748331 155 20 19.9143173618147 0.0856826381852847 156 21 20.3706967506914 0.629303249308614 157 24 22.5253383907655 1.4746616092345 158 22 20.8189965266684 1.18100347333161 159 20 16.8900138546179 3.10998614538215 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.388811920578961 0.777623841157921 0.611188079421039 12 0.327160950618601 0.654321901237201 0.6728390493814 13 0.605495952675451 0.789008094649098 0.394504047324549 14 0.798945739969245 0.40210852006151 0.201054260030755 15 0.735893075039497 0.528213849921007 0.264106924960503 16 0.72879973008847 0.542400539823061 0.271200269911530 17 0.646254838127297 0.707490323745405 0.353745161872703 18 0.770551048550574 0.458897902898852 0.229448951449426 19 0.712553677704219 0.574892644591562 0.287446322295781 20 0.658537073561994 0.682925852876011 0.341462926438006 21 0.590212787110068 0.819574425779863 0.409787212889932 22 0.514603673818742 0.970792652362516 0.485396326181258 23 0.501911470857161 0.996177058285677 0.498088529142838 24 0.541661035104423 0.916677929791154 0.458338964895577 25 0.675128752435191 0.649742495129617 0.324871247564809 26 0.608206676099197 0.783586647801605 0.391793323900803 27 0.549677876024811 0.900644247950379 0.450322123975189 28 0.513206161249926 0.973587677500147 0.486793838750074 29 0.451042830699177 0.902085661398354 0.548957169300823 30 0.394921652974088 0.789843305948177 0.605078347025912 31 0.391136588719123 0.782273177438246 0.608863411280877 32 0.330310655675182 0.660621311350363 0.669689344324818 33 0.621934224127771 0.756131551744458 0.378065775872229 34 0.577676870859508 0.844646258280984 0.422323129140492 35 0.553222368002801 0.893555263994397 0.446777631997199 36 0.497071699790775 0.99414339958155 0.502928300209225 37 0.483014894221729 0.966029788443458 0.516985105778271 38 0.431904453052255 0.863808906104509 0.568095546947746 39 0.382554841510071 0.765109683020141 0.617445158489929 40 0.359526273483612 0.719052546967225 0.640473726516388 41 0.509702399344671 0.980595201310658 0.490297600655329 42 0.455954759667728 0.911909519335456 0.544045240332272 43 0.437020250325767 0.874040500651534 0.562979749674233 44 0.390414502856325 0.78082900571265 0.609585497143675 45 0.350904247156312 0.701808494312624 0.649095752843688 46 0.320169561111552 0.640339122223105 0.679830438888448 47 0.290611800735791 0.581223601471581 0.70938819926421 48 0.287170564955714 0.574341129911428 0.712829435044286 49 0.248734756939317 0.497469513878633 0.751265243060683 50 0.252832407244922 0.505664814489843 0.747167592755078 51 0.23206809490451 0.46413618980902 0.76793190509549 52 0.199720958883983 0.399441917767967 0.800279041116017 53 0.258190265874029 0.516380531748058 0.741809734125971 54 0.344858192202929 0.689716384405859 0.655141807797071 55 0.330972549409438 0.661945098818877 0.669027450590562 56 0.383485768692166 0.766971537384333 0.616514231307834 57 0.357941919372067 0.715883838744135 0.642058080627933 58 0.329596310027961 0.659192620055922 0.670403689972039 59 0.328065180554834 0.656130361109668 0.671934819445166 60 0.417917511374841 0.835835022749681 0.58208248862516 61 0.373373720916406 0.746747441832812 0.626626279083594 62 0.330689568258154 0.661379136516308 0.669310431741846 63 0.328468944731044 0.656937889462088 0.671531055268956 64 0.294505633280539 0.589011266561078 0.705494366719461 65 0.2562162389695 0.512432477939 0.7437837610305 66 0.238331788299948 0.476663576599897 0.761668211700052 67 0.207879657763905 0.415759315527811 0.792120342236095 68 0.231608170155643 0.463216340311287 0.768391829844357 69 0.198505794065882 0.397011588131764 0.801494205934118 70 0.166937051044758 0.333874102089516 0.833062948955242 71 0.138905492660454 0.277810985320908 0.861094507339546 72 0.115186507443096 0.230373014886192 0.884813492556904 73 0.0986535742556519 0.197307148511304 0.901346425744348 74 0.0796446357753087 0.159289271550617 0.920355364224691 75 0.0639384679718367 0.127876935943673 0.936061532028163 76 0.0537745581134186 0.107549116226837 0.946225441886581 77 0.0421841842859154 0.0843683685718308 0.957815815714085 78 0.0325714936344662 0.0651429872689323 0.967428506365534 79 0.0367772619625666 0.0735545239251331 0.963222738037433 80 0.0343594767159229 0.0687189534318459 0.965640523284077 81 0.0284797695401812 0.0569595390803624 0.971520230459819 82 0.0369907498994122 0.0739814997988243 0.963009250100588 83 0.0289147906172595 0.057829581234519 0.97108520938274 84 0.0225211247673651 0.0450422495347302 0.977478875232635 85 0.020172500793945 0.04034500158789 0.979827499206055 86 0.0156704633593251 0.0313409267186502 0.984329536640675 87 0.0128165373229335 0.0256330746458670 0.987183462677066 88 0.0131118070203099 0.0262236140406199 0.98688819297969 89 0.0110968105968429 0.0221936211936858 0.988903189403157 90 0.00843563267366763 0.0168712653473353 0.991564367326332 91 0.0070098823118746 0.0140197646237492 0.992990117688125 92 0.00568428565598308 0.0113685713119662 0.994315714344017 93 0.0041723857249848 0.0083447714499696 0.995827614275015 94 0.00410715901212643 0.00821431802425286 0.995892840987874 95 0.00609503281571097 0.0121900656314219 0.993904967184289 96 0.00492354079248395 0.0098470815849679 0.995076459207516 97 0.00413259207391536 0.00826518414783072 0.995867407926085 98 0.00318351954673601 0.00636703909347201 0.996816480453264 99 0.00241600278218349 0.00483200556436698 0.997583997217817 100 0.00204547654334775 0.00409095308669551 0.997954523456652 101 0.00162138327085168 0.00324276654170336 0.998378616729148 102 0.00119482477691668 0.00238964955383335 0.998805175223083 103 0.00151434149814439 0.00302868299628878 0.998485658501856 104 0.00117804904661226 0.00235609809322451 0.998821950953388 105 0.00514478791412113 0.0102895758282423 0.994855212085879 106 0.0129752278327987 0.0259504556655975 0.987024772167201 107 0.0137621860354896 0.0275243720709791 0.98623781396451 108 0.0188453267634506 0.0376906535269012 0.98115467323655 109 0.0146869602282290 0.0293739204564581 0.98531303977177 110 0.0106390880770078 0.0212781761540156 0.989360911922992 111 0.00768036915345235 0.0153607383069047 0.992319630846548 112 0.0221277538532921 0.0442555077065842 0.977872246146708 113 0.0221182592226325 0.044236518445265 0.977881740777368 114 0.0553284859649874 0.110656971929975 0.944671514035013 115 0.0471363917056571 0.0942727834113141 0.952863608294343 116 0.0394274799568147 0.0788549599136294 0.960572520043185 117 0.103765893295208 0.207531786590416 0.896234106704792 118 0.0979247994118948 0.195849598823790 0.902075200588105 119 0.0872458316209407 0.174491663241881 0.91275416837906 120 0.152343613253838 0.304687226507675 0.847656386746162 121 0.149510112328811 0.299020224657621 0.85048988767119 122 0.189821231467135 0.379642462934270 0.810178768532865 123 0.189201762348385 0.37840352469677 0.810798237651615 124 0.179172696914950 0.358345393829901 0.82082730308505 125 0.155186382087894 0.310372764175788 0.844813617912106 126 0.124362819044806 0.248725638089611 0.875637180955194 127 0.0973190447625353 0.194638089525071 0.902680955237465 128 0.094740436050506 0.189480872101012 0.905259563949494 129 0.132633760853391 0.265267521706781 0.86736623914661 130 0.114656101010854 0.229312202021707 0.885343898989146 131 0.0961070124188935 0.192214024837787 0.903892987581106 132 0.0852673361991737 0.170534672398347 0.914732663800826 133 0.083324993768901 0.166649987537802 0.916675006231099 134 0.0740955530721009 0.148191106144202 0.9259044469279 135 0.173101013538592 0.346202027077184 0.826898986461408 136 0.138030968134926 0.276061936269851 0.861969031865074 137 0.115666778336239 0.231333556672478 0.88433322166376 138 0.163171768623359 0.326343537246719 0.83682823137664 139 0.394903450352563 0.789806900705125 0.605096549647437 140 0.340483058981573 0.680966117963145 0.659516941018427 141 0.484493738052017 0.968987476104034 0.515506261947983 142 0.393268068007085 0.786536136014171 0.606731931992915 143 0.556428664297233 0.887142671405535 0.443571335702767 144 0.502585613078458 0.994828773843085 0.497414386921542 145 0.405643386007729 0.811286772015458 0.594356613992271 146 0.300847635283382 0.601695270566765 0.699152364716618 147 0.292262080086770 0.584524160173541 0.70773791991323 148 0.174421108847449 0.348842217694897 0.825578891152551 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.0797101449275362 NOK 5% type I error level 30 0.217391304347826 NOK 10% type I error level 39 0.282608695652174 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/106avp1290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/106avp1290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/1h9yv1290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/1h9yv1290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/2h9yv1290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/2h9yv1290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/3s0gy1290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/3s0gy1290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/4s0gy1290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/4s0gy1290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/5s0gy1290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/5s0gy1290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/62ax11290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/62ax11290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/7vje41290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/7vje41290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/8vje41290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/8vje41290181421.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/9vje41290181421.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t12901814095tihr0h2zbose66/9vje41290181421.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = 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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