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 08:24:29 -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/t1258730743k38ldwl5uuf1gka.htm/, Retrieved Fri, 20 Nov 2009 16:25:55 +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/t1258730743k38ldwl5uuf1gka.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: werkloosheidsgraad vrouwen

Dataseries X:

» Textbox « » Textfile « » CSV «

7.3 7.9 7.6 9.1 7.5 9.4 7.6 9.4 7.9 9.1 7.9 9 8.1 9.3 8.2 9.9 8 9.8 7.5 9.3 6.8 8.3 6.5 8 6.6 8.5 7.6 10.4 8 11.1 8.1 10.9 7.7 10 7.5 9.2 7.6 9.2 7.8 9.5 7.8 9.6 7.8 9.5 7.5 9.1 7.5 8.9 7.1 9 7.5 10.1 7.5 10.3 7.6 10.2 7.7 9.6 7.7 9.2 7.9 9.3 8.1 9.4 8.2 9.4 8.2 9.2 8.2 9 7.9 9 7.3 9 6.9 9.8 6.6 10 6.7 9.8 6.9 9.3 7 9 7.1 9 7.2 9.1 7.1 9.1 6.9 9.1 7 9.2 6.8 8.8 6.4 8.3 6.7 8.4 6.6 8.1 6.4 7.7 6.3 7.9 6.2 7.9 6.5 8 6.8 7.9 6.8 7.6 6.4 7.1 6.1 6.8 5.8 6.5 6.1 6.9 7.2 8.2 7.3 8.7 6.9 8.3 6.1 7.9 5.8 7.5 6.2 7.8 7.1 8.3 7.7 8.4 7.9 8.2 7.7 7.7 7.4 7.2 7.5 7.3

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] = + 3.36968734844189 + 0.437044298126638WGV[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) 3.36968734844189 0.535835 6.2887 0 0 WGV 0.437044298126638 0.060395 7.2364 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.651518181907633 R-squared 0.424475941356227 Adjusted R-squared 0.416369968699273 F-TEST (value) 52.3658244753696 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 4.31893965036068e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.493095981202252 Sum Squared Residuals 17.2631989141246 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.3 6.8223373036423 0.4776626963577 2 7.6 7.3467904613943 0.253209538605704 3 7.5 7.47790375083229 0.0220962491677145 4 7.6 7.47790375083229 0.122096249167714 5 7.9 7.3467904613943 0.553209538605707 6 7.9 7.30308603158163 0.59691396841837 7 8.1 7.43419932101962 0.665800678980378 8 8.2 7.6964258998956 0.503574100104395 9 8 7.65272147008294 0.347278529917059 10 7.5 7.43419932101962 0.0658006789803782 11 6.8 6.99715502289298 -0.197155022892983 12 6.5 6.86604173345499 -0.366041733454991 13 6.6 7.08456388251831 -0.484563882518311 14 7.6 7.91494804895892 -0.314948048958924 15 8 8.22087905764757 -0.220879057647571 16 8.1 8.13347019802224 -0.0334701980222437 17 7.7 7.74013032970827 -0.0401303297082684 18 7.5 7.39049489120696 0.109505108793043 19 7.6 7.39049489120696 0.209505108793042 20 7.8 7.52160818064495 0.278391819355051 21 7.8 7.56531261045761 0.234687389542387 22 7.8 7.52160818064495 0.278391819355051 23 7.5 7.3467904613943 0.153209538605706 24 7.5 7.25938160176897 0.240618398231034 25 7.1 7.30308603158163 -0.203086031581630 26 7.5 7.78383475952093 -0.283834759520932 27 7.5 7.87124361914626 -0.37124361914626 28 7.6 7.8275391893336 -0.227539189333596 29 7.7 7.56531261045761 0.134687389542387 30 7.7 7.39049489120696 0.309505108793043 31 7.9 7.43419932101962 0.465800678980378 32 8.1 7.47790375083229 0.622096249167714 33 8.2 7.47790375083229 0.722096249167714 34 8.2 7.39049489120696 0.809505108793042 35 8.2 7.30308603158163 0.89691396841837 36 7.9 7.30308603158163 0.59691396841837 37 7.3 7.30308603158163 -0.00308603158163013 38 6.9 7.65272147008294 -0.75272147008294 39 6.6 7.74013032970827 -1.14013032970827 40 6.7 7.65272147008294 -0.95272147008294 41 6.9 7.43419932101962 -0.534199321019621 42 7 7.30308603158163 -0.30308603158163 43 7.1 7.30308603158163 -0.203086031581630 44 7.2 7.3467904613943 -0.146790461394293 45 7.1 7.3467904613943 -0.246790461394294 46 6.9 7.3467904613943 -0.446790461394293 47 7 7.39049489120696 -0.390494891206957 48 6.8 7.2156771719563 -0.415677171956303 49 6.4 6.99715502289298 -0.597155022892983 50 6.7 7.04085945270565 -0.340859452705647 51 6.6 6.90974616326765 -0.309746163267655 52 6.4 6.734928444017 -0.334928444017000 53 6.3 6.82233730364233 -0.522337303642328 54 6.2 6.82233730364233 -0.622337303642328 55 6.5 6.86604173345499 -0.366041733454991 56 6.8 6.82233730364233 -0.0223373036423278 57 6.8 6.69122401420434 0.108775985795664 58 6.4 6.47270186514102 -0.0727018651410161 59 6.1 6.34158857570302 -0.241588575703025 60 5.8 6.21047528626503 -0.410475286265034 61 6.1 6.38529300551569 -0.285293005515689 62 7.2 6.95345059308032 0.246549406919681 63 7.3 7.17197274214364 0.128027257856362 64 6.9 6.99715502289298 -0.0971550228929829 65 6.1 6.82233730364233 -0.722337303642328 66 5.8 6.64751958439167 -0.847519584391672 67 6.2 6.77863287382966 -0.578632873829663 68 7.1 6.99715502289298 0.102844977107016 69 7.7 7.04085945270565 0.659140547294353 70 7.9 6.95345059308032 0.946549406919682 71 7.7 6.734928444017 0.965071555983 72 7.4 6.51640629495368 0.88359370504632 73 7.5 6.56011072476634 0.939889275233656 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0787070369835165 0.157414073967033 0.921292963016484 6 0.0658207654406015 0.131641530881203 0.934179234559398 7 0.073912051551343 0.147824103102686 0.926087948448657 8 0.0455554815541079 0.0911109631082159 0.954444518445892 9 0.0205581783204671 0.0411163566409342 0.979441821679533 10 0.017384393214777 0.034768786429554 0.982615606785223 11 0.0390512711271619 0.0781025422543239 0.960948728872838 12 0.0546145793104445 0.109229158620889 0.945385420689555 13 0.0897142756089452 0.179428551217890 0.910285724391055 14 0.167438713415036 0.334877426830072 0.832561286584964 15 0.158295943684141 0.316591887368282 0.84170405631586 16 0.112157315885757 0.224314631771514 0.887842684114243 17 0.0774244905339165 0.154848981067833 0.922575509466084 18 0.0503187796805782 0.100637559361156 0.949681220319422 19 0.0326718122346828 0.0653436244693656 0.967328187765317 20 0.0219962366072546 0.0439924732145092 0.978003763392745 21 0.0139993752553923 0.0279987505107846 0.986000624744608 22 0.00908684443798559 0.0181736888759712 0.990913155562014 23 0.00526182367372777 0.0105236473474555 0.994738176326272 24 0.00310517674326068 0.00621035348652136 0.99689482325674 25 0.00247638196585891 0.00495276393171782 0.997523618034141 26 0.00210958368523794 0.00421916737047588 0.997890416314762 27 0.00200727111798453 0.00401454223596905 0.997992728882015 28 0.00132513036648096 0.00265026073296191 0.99867486963352 29 0.000729730840771316 0.00145946168154263 0.999270269159229 30 0.000473611263804757 0.000947222527609515 0.999526388736195 31 0.000454374796508908 0.000908749593017817 0.999545625203491 32 0.00077601609668745 0.0015520321933749 0.999223983903313 33 0.00195187912042198 0.00390375824084397 0.998048120879578 34 0.0061979704692192 0.0123959409384384 0.99380202953078 35 0.0233427979982893 0.0466855959965786 0.976657202001711 36 0.0346713830529367 0.0693427661058735 0.965328616947063 37 0.0278451660220432 0.0556903320440864 0.972154833977957 38 0.0522469638770029 0.104493927754006 0.947753036122997 39 0.166863181935858 0.333726363871716 0.833136818064142 40 0.271213147166153 0.542426294332307 0.728786852833847 41 0.277048417930283 0.554096835860566 0.722951582069717 42 0.247037375994743 0.494074751989485 0.752962624005257 43 0.207459655224115 0.414919310448231 0.792540344775885 44 0.167248449116426 0.334496898232851 0.832751550883574 45 0.136572402579732 0.273144805159464 0.863427597420268 46 0.126646183812787 0.253292367625573 0.873353816187213 47 0.111096629917350 0.222193259834700 0.88890337008265 48 0.104373157362922 0.208746314725845 0.895626842637078 49 0.127610604796285 0.255221209592571 0.872389395203715 50 0.113748921824915 0.227497843649829 0.886251078175085 51 0.0970657854557446 0.194131570911489 0.902934214544255 52 0.0814070613196417 0.162814122639283 0.918592938680358 53 0.0852419525863986 0.170483905172797 0.914758047413601 54 0.105289574409093 0.210579148818186 0.894710425590907 55 0.0960557768436908 0.192111553687382 0.90394422315631 56 0.0682568784347498 0.136513756869500 0.93174312156525 57 0.0462891920228297 0.0925783840456594 0.95371080797717 58 0.0296596366294137 0.0593192732588275 0.970340363370586 59 0.0190165788045483 0.0380331576090965 0.980983421195452 60 0.0142378378500935 0.0284756757001870 0.985762162149906 61 0.0115653100534281 0.0231306201068563 0.988434689946572 62 0.00671380334875118 0.0134276066975024 0.993286196651249 63 0.00348133992102653 0.00696267984205306 0.996518660078973 64 0.00186019557763051 0.00372039115526103 0.99813980442237 65 0.00615203109569612 0.0123040621913922 0.993847968904304 66 0.090040469447654 0.180080938895308 0.909959530552346 67 0.735254198462193 0.529491603075614 0.264745801537807 68 0.971403288339588 0.057193423320824 0.028596711660412 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 12 0.1875 NOK 5% type I error level 25 0.390625 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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