Multiple Regression-1

*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, 20 Nov 2009 08:14:20 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258730190xxcvstzie70jlm9.htm/, Retrieved Fri, 20 Nov 2009 16:16:43 +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/2009/Nov/20/t1258730190xxcvstzie70jlm9.htm/}, year = {2009}, } @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 = {2009}, 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:

Yt: werkloosheidsgraad mannen Xt: Economische groei

Dataseries X:

» Textbox « » Textfile « » CSV «

7.3 -0.8 7.6 -0.2 7.5 0.2 7.6 1 7.9 0 7.9 -0.2 8.1 1 8.2 0.4 8 1 7.5 1.7 6.8 3.1 6.5 3.3 6.6 3.1 7.6 3.5 8 6 8.1 5.7 7.7 4.7 7.5 4.2 7.6 3.6 7.8 4.4 7.8 2.5 7.8 -0.6 7.5 -1.9 7.5 -1.9 7.1 0.7 7.5 -0.9 7.5 -1.7 7.6 -3.1 7.7 -2.1 7.7 0.2 7.9 1.2 8.1 3.8 8.2 4 8.2 6.6 8.2 5.3 7.9 7.6 7.3 4.7 6.9 6.6 6.6 4.4 6.7 4.6 6.9 6 7 4.8 7.1 4 7.2 2.7 7.1 3 6.9 4.1 7 4 6.8 2.7 6.4 2.6 6.7 3.1 6.6 4.4 6.4 3 6.3 2 6.2 1.3 6.5 1.5 6.8 1.3 6.8 3.2 6.4 1.8 6.1 3.3 5.8 1 6.1 2.4 7.2 0.4 7.3 -0.1 6.9 1.3 6.1 -1.1 5.8 -4.4 6.2 -7.5 7.1 -12.2 7.7 -14.5 7.9 -16 7.7 -16.7 7.4 -16.3 7.5 -16.9

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WGM[t] = + 7.2296929775596 -0.00837328842482997EcGr[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) 7.2296929775596 0.076331 94.7146 0 0 EcGr -0.00837328842482997 0.01381 -0.6063 0.546241 0.27312 Multiple Linear Regression - Regression Statistics Multiple R 0.0717705598154886 R-squared 0.00515101325622863 Adjusted R-squared -0.00886094430354278 F-TEST (value) 0.367615533679411 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 0.546240609795597 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.648303404675179 Sum Squared Residuals 29.8411086204534 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.3 7.23639160829941 0.0636083917005848 2 7.6 7.23136763524456 0.368632364755444 3 7.5 7.22801831987462 0.271981680125376 4 7.6 7.22131968913476 0.37868031086524 5 7.9 7.22969297755959 0.67030702244041 6 7.9 7.23136763524456 0.668632364755444 7 8.1 7.22131968913476 0.87868031086524 8 8.2 7.22634366218966 0.973656337810341 9 8 7.22131968913476 0.77868031086524 10 7.5 7.21545838723738 0.284541612762621 11 6.8 7.20373578344262 -0.403735783442617 12 6.5 7.20206112575765 -0.702061125757651 13 6.6 7.20373578344262 -0.603735783442617 14 7.6 7.20038646807268 0.399613531927315 15 8 7.17945324701061 0.82054675298939 16 8.1 7.18196523353806 0.91803476646194 17 7.7 7.19033852196289 0.509661478037111 18 7.5 7.1945251661753 0.305474833824696 19 7.6 7.1995491392302 0.400450860769798 20 7.8 7.19285050849034 0.607149491509662 21 7.8 7.20875975649751 0.591240243502485 22 7.8 7.23471695061449 0.565283049385512 23 7.5 7.24560222556677 0.254397774433233 24 7.5 7.24560222556677 0.254397774433233 25 7.1 7.22383167566221 -0.123831675662209 26 7.5 7.23722893714194 0.262771062858063 27 7.5 7.2439275678818 0.256072432118199 28 7.6 7.25565017167656 0.344349828323437 29 7.7 7.24727688325173 0.452723116748267 30 7.7 7.22801831987462 0.471981680125376 31 7.9 7.2196450314498 0.680354968550206 32 8.1 7.19787448154524 0.902125518454764 33 8.2 7.19619982386027 1.00380017613973 34 8.2 7.17442927395571 1.02557072604429 35 8.2 7.18531454890799 1.01468545109201 36 7.9 7.16605598553088 0.733944014469118 37 7.3 7.19033852196289 0.109661478037111 38 6.9 7.17442927395571 -0.274429273955712 39 6.6 7.19285050849034 -0.592850508490338 40 6.7 7.19117585080537 -0.491175850805372 41 6.9 7.17945324701061 -0.27945324701061 42 7 7.1895011931204 -0.189501193120406 43 7.1 7.19619982386027 -0.0961998238602704 44 7.2 7.20708509881255 -0.00708509881254887 45 7.1 7.2045731122851 -0.104573112285100 46 6.9 7.19536249501779 -0.295362495017787 47 7 7.19619982386027 -0.19619982386027 48 6.8 7.20708509881255 -0.407085098812549 49 6.4 7.20792242765503 -0.807922427655032 50 6.7 7.20373578344262 -0.503735783442617 51 6.6 7.19285050849034 -0.592850508490338 52 6.4 7.2045731122851 -0.8045731122851 53 6.3 7.21294640070993 -0.91294640070993 54 6.2 7.21880770260731 -1.01880770260731 55 6.5 7.21713304492235 -0.717133044922345 56 6.8 7.21880770260731 -0.418807702607311 57 6.8 7.20289845460013 -0.402898454600134 58 6.4 7.2146210583949 -0.814621058394896 59 6.1 7.20206112575765 -1.10206112575765 60 5.8 7.22131968913476 -1.42131968913476 61 6.1 7.20959708534 -1.10959708534 62 7.2 7.22634366218966 -0.0263436621896578 63 7.3 7.23053030640207 0.0694696935979269 64 6.9 7.21880770260731 -0.318807702607311 65 6.1 7.2389035948269 -1.13890359482690 66 5.8 7.26653544662884 -1.46653544662884 67 6.2 7.29249264074581 -1.09249264074581 68 7.1 7.33184709634252 -0.231847096342516 69 7.7 7.35110565971962 0.348894340280376 70 7.9 7.36366559235687 0.536334407643131 71 7.7 7.36952689425425 0.33047310574575 72 7.4 7.36617757888432 0.0338224211156819 73 7.5 7.37120155193922 0.128798448060784 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.052229536129485 0.10445907225897 0.947770463870515 6 0.0365525907221283 0.0731051814442566 0.963447409277872 7 0.0230143397242191 0.0460286794484383 0.976985660275781 8 0.0248228846890094 0.0496457693780187 0.97517711531099 9 0.0105149371043286 0.0210298742086571 0.989485062895672 10 0.0150540536667704 0.0301081073335409 0.98494594633323 11 0.0458998581975117 0.0917997163950234 0.954100141802488 12 0.0546360141290879 0.109272028258176 0.945363985870912 13 0.040620199579322 0.081240399158644 0.959379800420678 14 0.0609179090891885 0.121835818178377 0.939082090910812 15 0.204496405391552 0.408992810783104 0.795503594608448 16 0.263141574432277 0.526283148864554 0.736858425567723 17 0.213463182953886 0.426926365907773 0.786536817046114 18 0.160889141320917 0.321778282641834 0.839110858679083 19 0.120805670966144 0.241611341932288 0.879194329033856 20 0.100295130510108 0.200590261020215 0.899704869489892 21 0.0812190011065105 0.162438002213021 0.91878099889349 22 0.063380684141342 0.126761368282684 0.936619315858658 23 0.0456254841074948 0.0912509682149895 0.954374515892505 24 0.0320114739614549 0.0640229479229097 0.967988526038545 25 0.0278642567800772 0.0557285135601544 0.972135743219923 26 0.0189856400759342 0.0379712801518685 0.981014359924066 27 0.0126819760334363 0.0253639520668725 0.987318023966564 28 0.00851411245668041 0.0170282249133608 0.99148588754332 29 0.00610622937352159 0.0122124587470432 0.993893770626478 30 0.00449610625283803 0.00899221250567607 0.995503893747162 31 0.00451207025123755 0.0090241405024751 0.995487929748762 32 0.00772901835562975 0.0154580367112595 0.99227098164437 33 0.0179801060305608 0.0359602120611216 0.98201989396944 34 0.0455913367172144 0.0911826734344288 0.954408663282786 35 0.124358066500839 0.248716133001677 0.875641933499161 36 0.238871233553591 0.477742467107182 0.761128766446409 37 0.277273652078123 0.554547304156246 0.722726347921877 38 0.353389000030109 0.706778000060219 0.64661099996989 39 0.45517540615307 0.91035081230614 0.54482459384693 40 0.503640884956908 0.992718230086185 0.496359115043092 41 0.518894792767544 0.962210414464912 0.481105207232456 42 0.526339685222463 0.947320629555075 0.473660314777537 43 0.540063952553885 0.91987209489223 0.459936047446115 44 0.565300463991825 0.86939907201635 0.434699536008175 45 0.588366745317697 0.823266509364605 0.411633254682303 46 0.605810703600496 0.788378592799007 0.394189296399504 47 0.64180323046581 0.716393539068381 0.358196769534190 48 0.65093663682687 0.698126726346259 0.349063363173129 49 0.681201336090124 0.637597327819752 0.318798663909876 50 0.678713707180051 0.642572585639898 0.321286292819949 51 0.6783572667524 0.643285466495201 0.321642733247600 52 0.677294340477203 0.645411319045594 0.322705659522797 53 0.683154702216572 0.633690595566855 0.316845297783428 54 0.701447667148651 0.597104665702698 0.298552332851349 55 0.666980909656907 0.666038180686185 0.333019090343093 56 0.632495860476559 0.735008279046882 0.367504139523441 57 0.625974649551012 0.748050700897977 0.374025350448988 58 0.582796507150364 0.834406985699271 0.417203492849636 59 0.556276149244599 0.887447701510802 0.443723850755401 60 0.633382728566159 0.733234542867683 0.366617271433841 61 0.605943153869633 0.788113692260734 0.394056846130367 62 0.618685300267284 0.762629399465432 0.381314699732716 63 0.769750323175447 0.460499353649107 0.230249676824553 64 0.97628701521148 0.0474259695770406 0.0237129847885203 65 0.99136165535022 0.0172766892995594 0.00863834464977968 66 0.97868012345065 0.0426397530987002 0.0213198765493501 67 0.963836770622863 0.072326458754274 0.036163229377137 68 0.957087287952566 0.0858254240948678 0.0429127120474339 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.03125 NOK 5% type I error level 15 0.234375 NOK 10% type I error level 24 0.375 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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