WS 7 Multiple Regression

*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 06:12:12 -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/t12587231034ui1o6yrmgxlmis.htm/, Retrieved Fri, 20 Nov 2009 14:18:35 +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/t12587231034ui1o6yrmgxlmis.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:

SWH WS 7 Multiple Regression

Dataseries X:

» Textbox « » Textfile « » CSV «

14.2 -0.8 13.5 -0.2 11.9 0.2 14.6 1 15.6 0 14.1 -0.2 14.9 1 14.2 0.4 14.6 1 17.2 1.7 15.4 3.1 14.3 3.3 17.5 3.1 14.5 3.5 14.4 6 16.6 5.7 16.7 4.7 16.6 4.2 16.9 3.6 15.7 4.4 16.4 2.5 18.4 -0.6 16.9 -1.9 16.5 -1.9 18.3 0.7 15.1 -0.9 15.7 -1.7 18.1 -3.1 16.8 -2.1 18.9 0.2 19 1.2 18.1 3.8 17.8 4 21.5 6.6 17.1 5.3 18.7 7.6 19 4.7 16.4 6.6 16.9 4.4 18.6 4.6 19.3 6 19.4 4.8 17.6 4 18.6 2.7 18.1 3 20.4 4.1 18.1 4 19.6 2.7 19.9 2.6 19.2 3.1 17.8 4.4 19.2 3 22 2 21.1 1.3 19.5 1.5 22.2 1.3 20.9 3.2 22.2 1.8 23.5 3.3 21.5 1 24.3 2.4 22.8 0.4 20.3 -0.1 23.7 1.3 23.3 -1.1 19.6 -4.4 18 -7.5 17.3 -12.2 16.8 -14.5 18.2 -16 16.5 -16.7 16 -16.3 18.4 -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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 17.9543786350265 + 0.0508054588397703X[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) 17.9543786350265 0.314811 57.0323 0 0 X 0.0508054588397703 0.056957 0.892 0.375407 0.187703 Multiple Linear Regression - Regression Statistics Multiple R 0.105272555849855 R-squared 0.0110823110151609 Adjusted R-squared -0.00284610713955513 F-TEST (value) 0.79566185420765 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 0.375406737257063 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.67377764339768 Sum Squared Residuals 507.585168929663 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14.2 17.9137342679547 -3.71373426795466 2 13.5 17.9442175432585 -4.44421754325854 3 11.9 17.9645397267944 -6.06453972679445 4 14.6 18.0051840938663 -3.40518409386627 5 15.6 17.9543786350265 -2.35437863502650 6 14.1 17.9442175432585 -3.84421754325854 7 14.9 18.0051840938663 -3.10518409386626 8 14.2 17.9747008185624 -3.7747008185624 9 14.6 18.0051840938663 -3.40518409386627 10 17.2 18.0407479150541 -0.840747915054105 11 15.4 18.1118755574298 -2.71187555742978 12 14.3 18.1220366491977 -3.82203664919774 13 17.5 18.1118755574298 -0.611875557429782 14 14.5 18.1321977409657 -3.63219774096569 15 14.4 18.2592113880651 -3.85921138806512 16 16.6 18.2439697504132 -1.64396975041318 17 16.7 18.1931642915734 -1.49316429157342 18 16.6 18.1677615621535 -1.56776156215353 19 16.9 18.1372782868497 -1.23727828684967 20 15.7 18.1779226539215 -2.47792265392148 21 16.4 18.0813922821259 -1.68139228212592 22 18.4 17.9238953597226 0.476104640277366 23 16.9 17.8578482632309 -0.957848263230932 24 16.5 17.8578482632309 -1.35784826323093 25 18.3 17.9899424562143 0.310057543785667 26 15.1 17.9086537220707 -2.8086537220707 27 15.7 17.8680093549989 -2.16800935499889 28 18.1 17.7968817126232 0.303118287376795 29 16.8 17.8476871714630 -1.04768717146298 30 18.9 17.9645397267944 0.93546027320555 31 19 18.0153451856342 0.984654814365781 32 18.1 18.1474393786176 -0.0474393786176201 33 17.8 18.1576004703856 -0.357600470385575 34 21.5 18.2896946633690 3.21030533663102 35 17.1 18.2236475668773 -1.12364756687728 36 18.7 18.3405001222087 0.359499877791251 37 19 18.1931642915734 0.806835708426585 38 16.4 18.2896946633690 -1.88969466336898 39 16.9 18.1779226539215 -1.27792265392149 40 18.6 18.1880837456894 0.411916254310564 41 19.3 18.2592113880651 1.04078861193488 42 19.4 18.1982448374574 1.20175516254261 43 17.6 18.1576004703856 -0.557600470385574 44 18.6 18.0915533738939 0.508446626106127 45 18.1 18.1067950115458 -0.00679501154580392 46 20.4 18.1626810162696 2.23731898373045 47 18.1 18.1576004703856 -0.0576004703855741 48 19.6 18.0915533738939 1.50844662610613 49 19.9 18.0864728280099 1.8135271719901 50 19.2 18.1118755574298 1.08812444257022 51 17.8 18.1779226539215 -0.377922653921483 52 19.2 18.1067950115458 1.09320498845419 53 22 18.0559895527060 3.94401044729396 54 21.1 18.0204257315182 3.07957426848181 55 19.5 18.0305868232861 1.46941317671385 56 22.2 18.0204257315182 4.1795742684818 57 20.9 18.1169561033138 2.78304389668624 58 22.2 18.0458284609381 4.15417153906192 59 23.5 18.1220366491977 5.37796335080226 60 21.5 18.0051840938663 3.49481590613374 61 24.3 18.0763117362419 6.22368826375806 62 22.8 17.9747008185624 4.8252991814376 63 20.3 17.9492980891425 2.35070191085748 64 23.7 18.0204257315182 5.6795742684818 65 23.3 17.8984926303027 5.40150736969725 66 19.6 17.7308346161315 1.86916538386850 67 18 17.5733376937282 0.426662306271783 68 17.3 17.3345520371813 -0.0345520371812967 69 16.8 17.2176994818498 -0.417699481849825 70 18.2 17.1414912935902 1.05850870640983 71 16.5 17.1059274724023 -0.605927472402331 72 16 17.1262496559382 -1.12624965593824 73 18.4 17.0957663806344 1.30423361936562 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.249267006333158 0.498534012666316 0.750732993666842 6 0.131170652069466 0.262341304138933 0.868829347930534 7 0.0709580373917745 0.141916074783549 0.929041962608225 8 0.0347656028469147 0.0695312056938294 0.965234397153085 9 0.0164750486355547 0.0329500972711094 0.983524951364445 10 0.0217782289680795 0.0435564579361591 0.97822177103192 11 0.0156719912001959 0.0313439824003918 0.984328008799804 12 0.0164887496466931 0.0329774992933863 0.983511250353307 13 0.0181397575972296 0.0362795151944593 0.98186024240277 14 0.0186758964835096 0.0373517929670192 0.98132410351649 15 0.0257844131211117 0.0515688262422235 0.974215586878888 16 0.0182920412230832 0.0365840824461663 0.981707958776917 17 0.0136319946667700 0.0272639893335400 0.98636800533323 18 0.0100817259238621 0.0201634518477242 0.989918274076138 19 0.0087021007874287 0.0174042015748574 0.991297899212571 20 0.00668392070538937 0.0133678414107787 0.99331607929461 21 0.00594468869693466 0.0118893773938693 0.994055311303065 22 0.0390359735878665 0.078071947175733 0.960964026412134 23 0.0481540844419458 0.0963081688838916 0.951845915558054 24 0.0462934127126761 0.0925868254253522 0.953706587287324 25 0.0671254772655035 0.134250954531007 0.932874522734496 26 0.0700669402859328 0.140133880571866 0.929933059714067 27 0.0680041651899045 0.136008330379809 0.931995834810096 28 0.0841460612386377 0.168292122477275 0.915853938761362 29 0.0766255024910332 0.153251004982066 0.923374497508967 30 0.106945670853525 0.213891341707049 0.893054329146475 31 0.138999765375892 0.277999530751783 0.861000234624108 32 0.145802336860737 0.291604673721473 0.854197663139263 33 0.145697843232526 0.291395686465053 0.854302156767474 34 0.296260320054996 0.592520640109993 0.703739679945004 35 0.294358860305331 0.588717720610661 0.70564113969467 36 0.274602391267889 0.549204782535779 0.72539760873211 37 0.262394703304646 0.524789406609292 0.737605296695354 38 0.333588295503157 0.667176591006314 0.666411704496843 39 0.381275720086351 0.762551440172701 0.618724279913649 40 0.381557439442471 0.763114878884942 0.618442560557529 41 0.37804022656994 0.75608045313988 0.62195977343006 42 0.375972733980284 0.751945467960568 0.624027266019716 43 0.427415457108425 0.85483091421685 0.572584542891575 44 0.443987496751497 0.887974993502994 0.556012503248503 45 0.491849108561386 0.983698217122772 0.508150891438614 46 0.510121445700852 0.979757108598296 0.489878554299148 47 0.599023626084832 0.801952747830336 0.400976373915168 48 0.620985173717603 0.758029652564795 0.379014826282397 49 0.638566601128064 0.722866797743873 0.361433398871936 50 0.684570967173321 0.630858065653357 0.315429032826679 51 0.897613540606887 0.204772918786225 0.102386459393113 52 0.956946902585663 0.0861061948286731 0.0430530974143365 53 0.964685783857145 0.0706284322857102 0.0353142161428551 54 0.9663361122976 0.0673277754048006 0.0336638877024003 55 0.98576552327472 0.0284689534505588 0.0142344767252794 56 0.985294412670992 0.0294111746580155 0.0147055873290077 57 0.99125831151431 0.0174833769713787 0.00874168848568936 58 0.989387681075589 0.0212246378488225 0.0106123189244112 59 0.987260162348971 0.0254796753020571 0.0127398376510286 60 0.983873748033803 0.0322525039323948 0.0161262519661974 61 0.985835963587762 0.0283280728244759 0.0141640364122380 62 0.979717100746142 0.0405657985077157 0.0202828992538579 63 0.978617469792708 0.0427650604145843 0.0213825302072922 64 0.972457324643057 0.055085350713886 0.027542675356943 65 0.99354601241571 0.0129079751685805 0.00645398758429024 66 0.987360161924767 0.0252796761504652 0.0126398380752326 67 0.964011305550936 0.0719773888981286 0.0359886944490643 68 0.903149676489245 0.193700647021511 0.0968503235107554 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 23 0.359375 NOK 10% type I error level 33 0.515625 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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