*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: Thu, 19 Nov 2009 11:46:20 -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/19/t1258656759wsfywwxal9j95mh.htm/, Retrieved Thu, 19 Nov 2009 19:52:51 +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/19/t1258656759wsfywwxal9j95mh.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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611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 0 478 0 528 0 534 0 518 1 506 1 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 1 587 1 597 1 581 1

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 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 562.191489361702 -23.6530278232406X[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) 562.191489361702 5.974896 94.0923 0 0 X -23.6530278232406 12.836135 -1.8427 0.070487 0.035243 Multiple Linear Regression - Regression Statistics Multiple R 0.235171212976024 R-squared 0.0553054994126142 Adjusted R-squared 0.0390176631955904 F-TEST (value) 3.39550930373486 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.070486897756235 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 40.961821451658 Sum Squared Residuals 97316.5073649755 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 611 562.191489361702 48.8085106382982 2 594 562.191489361702 31.8085106382979 3 595 562.191489361702 32.8085106382979 4 591 562.191489361702 28.8085106382979 5 589 562.191489361702 26.8085106382979 6 584 562.191489361702 21.8085106382979 7 573 562.191489361702 10.8085106382979 8 567 562.191489361702 4.80851063829787 9 569 562.191489361702 6.80851063829787 10 621 562.191489361702 58.8085106382979 11 629 562.191489361702 66.8085106382979 12 628 562.191489361702 65.8085106382979 13 612 562.191489361702 49.8085106382979 14 595 562.191489361702 32.8085106382979 15 597 562.191489361702 34.8085106382979 16 593 562.191489361702 30.8085106382979 17 590 562.191489361702 27.8085106382979 18 580 562.191489361702 17.8085106382979 19 574 562.191489361702 11.8085106382979 20 573 562.191489361702 10.8085106382979 21 573 562.191489361702 10.8085106382979 22 620 562.191489361702 57.8085106382979 23 626 562.191489361702 63.8085106382979 24 620 562.191489361702 57.8085106382979 25 588 562.191489361702 25.8085106382979 26 566 562.191489361702 3.80851063829787 27 557 562.191489361702 -5.19148936170213 28 561 562.191489361702 -1.19148936170213 29 549 562.191489361702 -13.1914893617021 30 532 562.191489361702 -30.1914893617021 31 526 562.191489361702 -36.1914893617021 32 511 562.191489361702 -51.1914893617021 33 499 562.191489361702 -63.1914893617021 34 555 562.191489361702 -7.19148936170213 35 565 562.191489361702 2.80851063829787 36 542 562.191489361702 -20.1914893617021 37 527 562.191489361702 -35.1914893617021 38 510 562.191489361702 -52.1914893617021 39 514 562.191489361702 -48.1914893617021 40 517 562.191489361702 -45.1914893617021 41 508 562.191489361702 -54.1914893617021 42 493 562.191489361702 -69.1914893617021 43 490 562.191489361702 -72.1914893617021 44 469 562.191489361702 -93.1914893617021 45 478 562.191489361702 -84.1914893617021 46 528 562.191489361702 -34.1914893617021 47 534 562.191489361702 -28.1914893617021 48 518 538.538461538462 -20.5384615384615 49 506 538.538461538462 -32.5384615384615 50 502 538.538461538462 -36.5384615384615 51 516 538.538461538462 -22.5384615384615 52 528 538.538461538462 -10.5384615384615 53 533 538.538461538462 -5.53846153846154 54 536 538.538461538462 -2.53846153846154 55 537 538.538461538462 -1.53846153846154 56 524 538.538461538462 -14.5384615384615 57 536 538.538461538462 -2.53846153846154 58 587 538.538461538462 48.4615384615385 59 597 538.538461538462 58.4615384615385 60 581 538.538461538462 42.4615384615385 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0191196987086397 0.0382393974172794 0.98088030129136 6 0.00714913941716335 0.0142982788343267 0.992850860582837 7 0.00672535916346196 0.0134507183269239 0.993274640836538 8 0.00670459287639376 0.0134091857527875 0.993295407123606 9 0.00408714914956368 0.00817429829912736 0.995912850850436 10 0.00928986187530165 0.0185797237506033 0.990710138124698 11 0.0211205696294501 0.0422411392589003 0.97887943037055 12 0.031408967084831 0.062817934169662 0.96859103291517 13 0.0235536961374826 0.0471073922749652 0.976446303862517 14 0.0138147727362416 0.0276295454724831 0.986185227263758 15 0.0081720306297986 0.0163440612595972 0.991827969370201 16 0.00479274681613789 0.00958549363227579 0.995207253183862 17 0.00284924452970747 0.00569848905941494 0.997150755470293 18 0.00195825290578001 0.00391650581156002 0.99804174709422 19 0.00157034362020517 0.00314068724041033 0.998429656379795 20 0.00125866743077242 0.00251733486154484 0.998741332569228 21 0.0009827964762945 0.001965592952589 0.999017203523705 22 0.00224394919392743 0.00448789838785485 0.997756050806073 23 0.00890816166213439 0.0178163233242688 0.991091838337866 24 0.0290453156717811 0.0580906313435622 0.970954684328219 25 0.0382508045099664 0.0765016090199328 0.961749195490034 26 0.0550599784692554 0.110119956938511 0.944940021530745 27 0.0864118039627778 0.172823607925556 0.913588196037222 28 0.121600243114090 0.243200486228179 0.87839975688591 29 0.181888056788101 0.363776113576201 0.8181119432119 30 0.296476861223953 0.592953722447906 0.703523138776047 31 0.41798342862505 0.8359668572501 0.58201657137495 32 0.579194038328074 0.841611923343852 0.420805961671926 33 0.738646311965449 0.522707376069102 0.261353688034551 34 0.756399546686023 0.487200906627953 0.243600453313977 35 0.819293469456018 0.361413061087964 0.180706530543982 36 0.839450576070787 0.321098847858427 0.160549423929213 37 0.85040477276851 0.299190454462981 0.149595227231490 38 0.864467148800974 0.271065702398052 0.135532851199026 39 0.865896496795584 0.268207006408832 0.134103503204416 40 0.861579628982873 0.276840742034255 0.138420371017127 41 0.855846059967713 0.288307880064574 0.144153940032287 42 0.859679200356536 0.280641599286928 0.140320799643464 43 0.860098044866498 0.279803910267003 0.139901955133502 44 0.910301399594078 0.179397200811844 0.0896986004059222 45 0.942996328964422 0.114007342071157 0.0570036710355784 46 0.913093394155127 0.173813211689745 0.0869066058448726 47 0.868677602138455 0.26264479572309 0.131322397861545 48 0.823638789167184 0.352722421665632 0.176361210832816 49 0.808607290371021 0.382785419257958 0.191392709628979 50 0.826515279734884 0.346969440530232 0.173484720265116 51 0.806861761804161 0.386276476391678 0.193138238195839 52 0.749986481968234 0.500027036063532 0.250013518031766 53 0.670033477349216 0.659933045301567 0.329966522650784 54 0.570762523004971 0.858474953990057 0.429237476995029 55 0.464069744573504 0.928139489147009 0.535930255426496 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.156862745098039 NOK 5% type I error level 18 0.352941176470588 NOK 10% type I error level 21 0.411764705882353 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/10r6rc1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/10r6rc1258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/1nkl21258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/1nkl21258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/26vz11258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/26vz11258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/3hacy1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/3hacy1258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/4b7am1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/4b7am1258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/5b9bv1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/5b9bv1258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/6wuv01258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/6wuv01258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/7j86z1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/7j86z1258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/81nax1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/81nax1258656375.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/9ckag1258656375.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258656759wsfywwxal9j95mh/9ckag1258656375.ps (open in new window)

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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