workshop 10: Multiple regression 2

*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: Tue, 14 Dec 2010 08:37:33 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292315728fczs62umi86g5mx.htm/, Retrieved Tue, 14 Dec 2010 09:35:31 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292315728fczs62umi86g5mx.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 «

194.9 1.79 195.5 1.95 196 2.26 196.2 2.04 196.2 2.16 196.2 2.75 196.2 2.79 197 2.88 197.7 3.36 198 2.97 198.2 3.1 198.5 2.49 198.6 2.2 199.5 2.25 200 2.09 201.3 2.79 202.2 3.14 202.9 2.93 203.5 2.65 203.5 2.67 204 2.26 204.1 2.35 204.3 2.13 204.5 2.18 204.8 2.9 205.1 2.63 205.7 2.67 206.5 1.81 206.9 1.33 207.1 0.88 207.8 1.28 208 1.26 208.5 1.26 208.6 1.29 209 1.1 209.1 1.37 209.7 1.21 209.8 1.74 209.9 1.76 210 1.48 210.8 1.04 211.4 1.62 211.7 1.49 212 1.79 212.2 1.8 212.4 1.58 212.9 1.86 213.4 1.74 213.7 1.59 214 1.26 214.3 1.13 214.8 1.92 215 2.61 215.9 2.26 216.4 2.41 216.9 2.26 217.2 2.03 217.5 2.86 217.9 2.55 218.1 2.27 218.6 2.26 218.9 2.57 219.3 3.07 220.4 2.76 220.9 2.51 221 2.87 221.8 3.14 222 3.11 222.2 3.16 222.5 2.47 222.9 2.57 223.1 2.89

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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation uurloon[t] = + 208.816893645343 + 0.144566354919626inflatie[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) 208.816893645343 3.568222 58.5213 0 0 inflatie 0.144566354919626 1.566058 0.0923 0.926714 0.463357 Multiple Linear Regression - Regression Statistics Multiple R 0.0110327518319243 R-squared 0.000121721612984829 Adjusted R-squared -0.0141622537925439 F-TEST (value) 0.00852155016576935 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.926713644276811 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.40652619334202 Sum Squared Residuals 4946.87778475418 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 194.9 209.075667420648 -14.1756674206482 2 195.5 209.098798037436 -13.5987980374359 3 196 209.143613607461 -13.143613607461 4 196.2 209.111809009379 -12.9118090093787 5 196.2 209.129156971969 -12.929156971969 6 196.2 209.214451121372 -13.0144511213716 7 196.2 209.220233775568 -13.0202337755684 8 197 209.233244747511 -12.2332447475111 9 197.7 209.302636597873 -11.6026365978726 10 198 209.246255719454 -11.2462557194539 11 198.2 209.265049345593 -11.0650493455935 12 198.5 209.176863869092 -10.6768638690925 13 198.6 209.134939626166 -10.5349396261658 14 199.5 209.142167943912 -9.64216794391176 15 200 209.119037327125 -9.11903732712462 16 201.3 209.220233775568 -7.92023377556835 17 202.2 209.27083199979 -7.07083199979024 18 202.9 209.240473065257 -6.3404730652571 19 203.5 209.19999448588 -5.69999448587961 20 203.5 209.202885812978 -5.70288581297801 21 204 209.143613607461 -5.14361360746096 22 204.1 209.156624579404 -5.05662457940373 23 204.3 209.124819981321 -4.8248199813214 24 204.5 209.132048299067 -4.63204829906739 25 204.8 209.23613607461 -4.43613607460951 26 205.1 209.197103158781 -4.09710315878123 27 205.7 209.202885812978 -3.50288581297802 28 206.5 209.078558747747 -2.57855874774713 29 206.9 209.009166897386 -2.1091668973857 30 207.1 208.944112037672 -1.84411203767188 31 207.8 209.00193857964 -1.20193857963971 32 208 208.999047252541 -0.999047252541332 33 208.5 208.999047252541 -0.499047252541332 34 208.6 209.003384243189 -0.403384243188927 35 209 208.975916635754 0.024083364245808 36 209.1 209.014949551583 0.0850504484175031 37 209.7 208.991818934795 0.708181065204638 38 209.8 209.068439102903 0.731560897097258 39 209.9 209.071330430001 0.82866956999886 40 210 209.030851850624 0.96914814937635 41 210.8 208.967242654459 1.832757345541 42 211.4 209.051091140312 2.34890885968761 43 211.7 209.032297514173 2.66770248582714 44 212 209.075667420649 2.92433257935126 45 212.2 209.077113084198 3.12288691580206 46 212.4 209.045308486116 3.35469151388439 47 212.9 209.085787065493 3.8142129345069 48 213.4 209.068439102903 4.33156089709725 49 213.7 209.046754149665 4.65324585033518 50 214 208.999047252541 5.00095274745867 51 214.3 208.980253626402 5.31974637359823 52 214.8 209.094461046788 5.70553895321172 53 215 209.194211831683 5.80578816831717 54 215.9 209.143613607461 6.75638639253905 55 216.4 209.165298560699 7.2347014393011 56 216.9 209.143613607461 7.75638639253905 57 217.2 209.110363345829 8.08963665417054 58 217.5 209.230353420413 8.26964657958727 59 217.9 209.185537850388 8.71446214961236 60 218.1 209.14505927101 8.95494072898984 61 218.6 209.143613607461 9.45638639253904 62 218.9 209.188429177486 9.71157082251396 63 219.3 209.260712354946 10.0392876450542 64 220.4 209.215896784921 11.1841032150792 65 220.9 209.179755196191 11.7202448038091 66 221 209.231799083962 11.7682009160381 67 221.8 209.27083199979 12.5291680002098 68 222 209.266495009143 12.7335049908574 69 222.2 209.273723326889 12.9262766731114 70 222.5 209.173972541994 13.3260274580059 71 222.9 209.188429177486 13.711570822514 72 223.1 209.23469041106 13.8653095889397 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000123374542553486 0.000246749085106971 0.999876625457446 6 2.07945464228865e-05 4.15890928457729e-05 0.999979205453577 7 1.35331505980224e-06 2.70663011960448e-06 0.99999864668494 8 1.3875871387718e-07 2.77517427754361e-07 0.999999861241286 9 1.27253677695828e-08 2.54507355391657e-08 0.999999987274632 10 9.28373292705801e-09 1.8567465854116e-08 0.999999990716267 11 2.73361447573023e-09 5.46722895146046e-09 0.999999997266386 12 2.39753410457788e-08 4.79506820915577e-08 0.99999997602466 13 1.03295266576916e-07 2.06590533153831e-07 0.999999896704733 14 4.97711365651618e-07 9.95422731303236e-07 0.999999502288634 15 1.88252019114834e-06 3.76504038229667e-06 0.999998117479809 16 7.82230883500204e-06 1.56446176700041e-05 0.999992177691165 17 2.64687818427489e-05 5.29375636854977e-05 0.999973531218157 18 0.000112347961325214 0.000224695922650429 0.999887652038675 19 0.000614559440369245 0.00122911888073849 0.99938544055963 20 0.00228227555148455 0.0045645511029691 0.997717724448515 21 0.00969391109687763 0.0193878221937553 0.990306088903122 22 0.0286371291467823 0.0572742582935645 0.971362870853218 23 0.0690042903253586 0.138008580650717 0.930995709674641 24 0.143144423637652 0.286288847275304 0.856855576362348 25 0.396957989304436 0.793915978608872 0.603042010695564 26 0.765244522742497 0.469510954515006 0.234755477257503 27 0.989230476740164 0.0215390465196718 0.0107695232598359 28 0.999054178103369 0.00189164379326284 0.000945821896631422 29 0.999622347242339 0.000755305515322951 0.000377652757661476 30 0.999544458727897 0.000911082544205415 0.000455541272102708 31 0.999608882285583 0.000782235428833707 0.000391117714416853 32 0.999605390654724 0.000789218690552749 0.000394609345276374 33 0.99955911674952 0.000881766500959874 0.000440883250479937 34 0.999506129113065 0.000987741773870027 0.000493870886935013 35 0.99924970612909 0.0015005877418192 0.0007502938709096 36 0.999199081438848 0.00160183712230467 0.000800918561152334 37 0.998859479949173 0.0022810401016541 0.00114052005082705 38 0.999483217817783 0.00103356436443443 0.000516782182217216 39 0.999807354112359 0.00038529177528286 0.00019264588764143 40 0.999829394952234 0.000341210095531305 0.000170605047765653 41 0.99969612534006 0.000607749319881324 0.000303874659940662 42 0.99974128160401 0.000517436791981286 0.000258718395990643 43 0.999689928262651 0.000620143474698061 0.000310071737349031 44 0.999810267968267 0.000379464063465322 0.000189732031732661 45 0.99988497588815 0.000230048223702377 0.000115024111851189 46 0.999870638382582 0.000258723234835584 0.000129361617417792 47 0.999923503014211 0.00015299397157753 7.64969857887652e-05 48 0.999928090052668 0.000143819894663967 7.19099473319837e-05 49 0.999902050417076 0.000195899165847249 9.79495829236244e-05 50 0.99981025582084 0.000379488358321333 0.000189744179160667 51 0.999679637831264 0.000640724337471942 0.000320362168735971 52 0.999646384752431 0.000707230495137893 0.000353615247568947 53 0.99995513668931 8.97266213799058e-05 4.48633106899529e-05 54 0.999967499123027 6.5001753946655e-05 3.25008769733275e-05 55 0.999980928675157 3.81426496863245e-05 1.90713248431622e-05 56 0.999978981413115 4.20371737699061e-05 2.1018586884953e-05 57 0.999963234047147 7.35319057051092e-05 3.67659528525546e-05 58 0.999988133681447 2.37326371058844e-05 1.18663185529422e-05 59 0.999989182089623 2.16358207539473e-05 1.08179103769737e-05 60 0.999983017453983 3.39650920337079e-05 1.6982546016854e-05 61 0.999976152782438 4.76944351234185e-05 2.38472175617092e-05 62 0.999984557101548 3.08857969039207e-05 1.54428984519604e-05 63 0.999991347611474 1.73047770518231e-05 8.65238852591157e-06 64 0.999985429824424 2.91403511511274e-05 1.45701755755637e-05 65 0.99997383668981 5.23266203820475e-05 2.61633101910238e-05 66 0.99997615280769 4.76943846182326e-05 2.38471923091163e-05 67 0.999729280274863 0.000541439450274884 0.000270719725137442 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 56 0.888888888888889 NOK 5% type I error level 58 0.92063492063492 NOK 10% type I error level 59 0.936507936507937 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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