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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 21 Dec 2009 06:45:07 -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/Dec/21/t1261403167tt3v991jd9vla7h.htm/, Retrieved Mon, 21 Dec 2009 14:46:19 +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/Dec/21/t1261403167tt3v991jd9vla7h.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:

Dataseries X:

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581 1 597 1 587 1 536 1 524 1 537 1 536 1 533 1 528 1 516 1 502 1 506 1 518 1 534 0 528 0 478 0 469 0 490 0 493 0 508 0 517 0 514 0 510 0 527 0 542 0 565 0 555 0 499 0 511 0 526 0 532 0 549 0 561 0 557 0 566 0 588 0 620 0 626 0 620 0 573 0 573 0 574 0 580 0 590 0 593 0 597 0 595 0 612 0 628 0 629 0 621 0 569 0 567 0 573 0 584 0 589 0 591 0 595 0 594 0 611 0

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 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 Y[t] = + 467.571130434783 + 49.8834782608694` `[t] + 26.9059130434780M1[t] + 46.7478260869565M2[t] + 36.2130434782609M3[t] -17.5217391304347M4[t] -22.2565217391304M5[t] -13.5913043478261M6[t] -11.1260869565217M7[t] -4.86086956521739M8[t] -3.19565217391303M9[t] -7.93043478260867M10[t] -12.8652173913043M11[t] + 2.53478260869565t + 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) 467.571130434783 14.050575 33.2777 0 0 ` ` 49.8834782608694 9.939399 5.0188 8e-06 4e-06 M1 26.9059130434780 13.880686 1.9384 0.058729 0.029364 M2 46.7478260869565 13.966667 3.3471 0.001635 0.000817 M3 36.2130434782609 13.927725 2.6001 0.012489 0.006245 M4 -17.5217391304347 13.89279 -1.2612 0.213592 0.106796 M5 -22.2565217391304 13.861892 -1.6056 0.115208 0.057604 M6 -13.5913043478261 13.835058 -0.9824 0.331051 0.165525 M7 -11.1260869565217 13.812311 -0.8055 0.424664 0.212332 M8 -4.86086956521739 13.793673 -0.3524 0.726149 0.363074 M9 -3.19565217391303 13.779158 -0.2319 0.817629 0.408815 M10 -7.93043478260867 13.768782 -0.576 0.567441 0.283721 M11 -12.8652173913043 13.762552 -0.9348 0.354774 0.177387 t 2.53478260869565 0.239105 10.6011 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.888041241395152 R-squared 0.788617246418643 Adjusted R-squared 0.728878642145651 F-TEST (value) 13.2011327686003 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.89785964721523e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.7572209945670 Sum Squared Residuals 21775.3266086956 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 581 546.895304347827 34.104695652173 2 597 569.272 27.7279999999999 3 587 561.272 25.7280000000001 4 536 510.072 25.9280000000001 5 524 507.872 16.1280000000000 6 537 519.072 17.9280000000001 7 536 524.072 11.9280000000001 8 533 532.872 0.12800000000008 9 528 537.072 -9.07199999999994 10 516 534.872 -18.8719999999999 11 502 532.472 -30.4720000000000 12 506 547.872 -41.8719999999999 13 518 577.312695652174 -59.3126956521736 14 534 549.805913043478 -15.8059130434781 15 528 541.805913043478 -13.8059130434783 16 478 490.605913043478 -12.6059130434783 17 469 488.405913043478 -19.4059130434783 18 490 499.605913043478 -9.60591304347826 19 493 504.605913043478 -11.6059130434783 20 508 513.405913043478 -5.40591304347827 21 517 517.605913043478 -0.605913043478274 22 514 515.405913043478 -1.40591304347828 23 510 513.005913043478 -3.00591304347828 24 527 528.405913043478 -1.40591304347825 25 542 557.846608695652 -15.8466086956520 26 565 580.223304347826 -15.2233043478261 27 555 572.223304347826 -17.2233043478261 28 499 521.023304347826 -22.0233043478261 29 511 518.823304347826 -7.8233043478261 30 526 530.023304347826 -4.02330434782611 31 532 535.023304347826 -3.02330434782609 32 549 543.823304347826 5.17669565217392 33 561 548.023304347826 12.9766956521739 34 557 545.823304347826 11.1766956521739 35 566 543.423304347826 22.5766956521739 36 588 558.823304347826 29.1766956521739 37 620 588.264 31.7360000000002 38 626 610.640695652174 15.3593043478261 39 620 602.640695652174 17.3593043478261 40 573 551.440695652174 21.5593043478260 41 573 549.240695652174 23.7593043478261 42 574 560.440695652174 13.5593043478261 43 580 565.440695652174 14.5593043478261 44 590 574.240695652174 15.7593043478261 45 593 578.440695652174 14.5593043478261 46 597 576.240695652174 20.7593043478261 47 595 573.840695652174 21.1593043478261 48 612 589.240695652174 22.7593043478261 49 628 618.681391304348 9.31860869565238 50 629 641.058086956522 -12.0580869565217 51 621 633.058086956522 -12.0580869565218 52 569 581.858086956522 -12.8580869565218 53 567 579.658086956522 -12.6580869565218 54 573 590.858086956522 -17.8580869565218 55 584 595.858086956522 -11.8580869565218 56 589 604.658086956522 -15.6580869565218 57 591 608.858086956522 -17.8580869565218 58 595 606.658086956522 -11.6580869565218 59 594 604.258086956522 -10.2580869565218 60 611 619.658086956522 -8.65808695652178 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00331008180403206 0.00662016360806412 0.996689918195968 18 0.00633017131285227 0.0126603426257045 0.993669828687148 19 0.00701112779350704 0.0140222555870141 0.992988872206493 20 0.0482407733238209 0.0964815466476417 0.95175922667618 21 0.167792583927958 0.335585167855916 0.832207416072042 22 0.321869927099705 0.64373985419941 0.678130072900295 23 0.506300384414559 0.987399231170883 0.493699615585441 24 0.709696501695739 0.580606996608522 0.290303498304261 25 0.880741238367227 0.238517523265547 0.119258761632773 26 0.913926898734206 0.172146202531588 0.0860731012657942 27 0.928642971674956 0.142714056650089 0.0713570283250444 28 0.964858211860916 0.0702835762781683 0.0351417881390841 29 0.983527460906105 0.0329450781877901 0.0164725390938950 30 0.987220210590474 0.0255595788190516 0.0127797894095258 31 0.994756631848337 0.0104867363033254 0.00524336815166272 32 0.997434271003126 0.00513145799374894 0.00256572899687447 33 0.998081456416822 0.00383708716635532 0.00191854358317766 34 0.999795928103154 0.000408143793691373 0.000204071896845687 35 0.999984285615203 3.14287695941118e-05 1.57143847970559e-05 36 0.999999985293208 2.94135839225577e-08 1.47067919612788e-08 37 0.999999994954803 1.00903943443971e-08 5.04519717219855e-09 38 0.999999974904866 5.01902671981372e-08 2.50951335990686e-08 39 0.999999765794193 4.68411613329511e-07 2.34205806664756e-07 40 0.99999796887573 4.06224853845481e-06 2.03112426922741e-06 41 0.999995602505714 8.79498857197069e-06 4.39749428598535e-06 42 0.999931101833304 0.000137796333392322 6.88981666961608e-05 43 0.99998991272377 2.01745524593534e-05 1.00872762296767e-05 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.481481481481481 NOK 5% type I error level 18 0.666666666666667 NOK 10% type I error level 20 0.740740740740741 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/10y16g1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/10y16g1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/1vhlf1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/1vhlf1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/2bebq1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/2bebq1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/3wdp81261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/3wdp81261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/4tx9w1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/4tx9w1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/5cvev1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/5cvev1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/6z6i41261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/6z6i41261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/7mu4l1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/7mu4l1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/85afg1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/85afg1261403100.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/99swq1261403100.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261403167tt3v991jd9vla7h/99swq1261403100.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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