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*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: Wed, 18 Nov 2009 10:10:28 -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/18/t1258564624mxbhrpyn2asgicu.htm/, Retrieved Wed, 18 Nov 2009 18:17:16 +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/18/t1258564624mxbhrpyn2asgicu.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:
» Textbox « » Textfile « » CSV «
8.9 1.6 8.8 1.8 8.3 1.6 7.5 1.5 7.2 1.5 7.4 1.3 8.8 1.4 9.3 1.4 9.3 1.3 8.7 1.3 8.2 1.2 8.3 1.1 8.5 1.4 8.6 1.2 8.5 1.5 8.2 1.1 8.1 1.3 7.9 1.5 8.6 1.1 8.7 1.4 8.7 1.3 8.5 1.5 8.4 1.6 8.5 1.7 8.7 1.1 8.7 1.6 8.6 1.3 8.5 1.7 8.3 1.6 8 1.7 8.2 1.9 8.1 1.8 8.1 1.9 8 1.6 7.9 1.5 7.9 1.6 8 1.6 8 1.7 7.9 2 8 2 7.7 1.9 7.2 1.7 7.5 1.8 7.3 1.9 7 1.7 7 2 7 2.1 7.2 2.4 7.3 2.5 7.1 2.5 6.8 2.6 6.4 2.2 6.1 2.5 6.5 2.8 7.7 2.8 7.9 2.9 7.5 3 6.9 3.1 6.6 2.9 6.9 2.7
 
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
inflatie[t] = + 6.49479693937611 -0.59211300765156graad[t] + 0.0478987639788073M1[t] + 0.144214243672748M2[t] + 0.0539493819894059M3[t] -0.223684520306063M4[t] -0.305791642142437M5[t] -0.313160682754562M6[t] + 0.136845203060624M7[t] + 0.27605650382578M8[t] + 0.153160682754562M9[t] + 0.0355267804590934M10[t] -0.122895821071219M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)6.494796939376110.60391310.754500
graad-0.592113007651560.074532-7.944400
M10.04789876397880730.2488070.19250.8481690.424085
M20.1442142436727480.248360.58070.564240.28212
M30.05394938198940590.2465330.21880.8277280.413864
M4-0.2236845203060630.245788-0.91010.3674290.183715
M5-0.3057916421424370.246655-1.23980.221220.11061
M6-0.3131606827545620.24723-1.26670.2115130.105756
M70.1368452030606240.2475720.55270.5830540.291527
M80.276056503825780.2485791.11050.2724170.136209
M90.1531606827545620.247230.61950.5385750.269288
M100.03552678045909340.2458110.14450.8857010.44285
M11-0.1228958210712190.245992-0.49960.6196920.309846


Multiple Linear Regression - Regression Statistics
Multiple R0.762889719864329
R-squared0.582000724674674
Adjusted R-squared0.475277505442676
F-TEST (value)5.45336552685413
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value1.05276384025910e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.388596739751561
Sum Squared Residuals7.09734902884049


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.61.272889935256050.327110064743952
21.81.428416715715130.371583284284873
31.61.63420835785756-0.0342083578575625
41.51.83026486168334-0.330264861683343
51.51.92579164214244-0.425791642142438
61.31.8-0.5
71.41.421047675103-0.021047675103001
81.41.264202472042380.135797527957623
91.31.141306650971160.158693349028842
101.31.37894055326663-0.0789405532666269
111.21.51657445556210-0.316574455562096
121.11.58025897586816-0.480258975868157
131.41.50973513831665-0.109735138316653
141.21.54683931724544-0.346839317245438
151.51.51578575632725-0.0157857563272512
161.11.41578575632725-0.315785756327251
171.31.39288993525603-0.0928899352560326
181.51.50394349617422-0.00394349617421958
191.11.53947027663331-0.439470276633314
201.41.61947027663331-0.219470276633314
211.31.49657445556210-0.196574455562095
221.51.497363154796940.00263684520306104
231.61.398151854031780.201848145968217
241.71.461836374337850.238163625662154
251.11.39131253678634-0.291312536786341
261.61.487628016480280.112371983519718
271.31.45657445556210-0.156574455562095
281.71.238151854031780.461848145968217
291.61.274467333725720.32553266627428
301.71.444732195409060.255267804590936
311.91.776315479693940.123684520306062
321.81.97473808122425-0.174738081224250
331.91.851842260153030.0481577398469687
341.61.79341965862272-0.193419658622719
351.51.69420835785756-0.194208357857563
361.61.81710417892878-0.217104178928781
371.61.80579164214243-0.205791642142433
381.71.90210712183637-0.202107121836374
3921.871053560918190.128946439081813
4021.534208357857560.465791642142437
411.91.629735138316660.270264861683343
421.71.91842260153031-0.218422601530312
431.82.19079458505003-0.39079458505003
441.92.4484284873455-0.548428487345498
451.72.50316656856975-0.803166568569748
4622.38553266627428-0.38553266627428
472.12.22711006474397-0.127110064743967
482.42.231583284284870.168416715715126
492.52.220270747498530.279729252501475
502.52.435008828722780.0649911712772213
512.62.522377869334900.0776221306650962
522.22.48158917010006-0.281589170100059
532.52.57711595055915-0.0771159505591534
542.82.332901706886400.467098293113596
552.82.072371983519720.727628016480282
562.92.093160682754560.806839317245438
5732.207110064743970.792889935256033
583.12.444743967039440.655256032960565
592.92.463955267804590.436044732195408
602.72.409217186580340.290782813419658


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.3405233667630100.6810467335260190.65947663323699
170.1906316721187880.3812633442375750.809368327881212
180.1208724967874260.2417449935748520.879127503212574
190.09186137889410340.1837227577882070.908138621105897
200.04664485794657520.09328971589315030.953355142053425
210.02215733654317690.04431467308635380.977842663456823
220.01130520980232530.02261041960465070.988694790197675
230.01005070475254130.02010140950508250.989949295247459
240.01618669345124110.03237338690248220.98381330654876
250.01558843068287290.03117686136574570.984411569317127
260.00780121510077990.01560243020155980.99219878489922
270.005008619818468090.01001723963693620.994991380181532
280.004114148129514840.008228296259029680.995885851870485
290.001983776943420230.003967553886840450.99801622305658
300.001101712196429770.002203424392859530.99889828780357
310.002737649540044870.005475299080089750.997262350459955
320.002153940061986710.004307880123973410.997846059938013
330.001957840441348730.003915680882697470.998042159558651
340.001036998612689640.002073997225379290.99896300138731
350.0005628967154052220.001125793430810440.999437103284595
360.0003659645426300080.0007319290852600160.99963403545737
370.0002264727000346840.0004529454000693690.999773527299965
380.0001167066199129090.0002334132398258190.999883293380087
398.8398809469723e-050.0001767976189394460.99991160119053
408.23543010185547e-050.0001647086020371090.999917645698981
415.48794215708293e-050.0001097588431416590.999945120578429
420.0003159314554920300.0006318629109840610.999684068544508
430.0002997674063778220.0005995348127556430.999700232593622
440.0001854215755436370.0003708431510872740.999814578424456


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level170.586206896551724NOK
5% type I error level240.827586206896552NOK
10% type I error level250.862068965517241NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/101gqe1258564224.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/101gqe1258564224.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/11qnw1258564224.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/11qnw1258564224.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/2jdtu1258564224.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/2jdtu1258564224.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/3i2ov1258564224.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/4nw9c1258564224.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/590dv1258564224.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/6oquy1258564224.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/7x4w51258564224.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/7x4w51258564224.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/8i4s51258564224.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/8i4s51258564224.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/9c4jr1258564224.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258564624mxbhrpyn2asgicu/9c4jr1258564224.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 2 ; par2 = Include Monthly 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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