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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 07:52:22 -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/t1258556011gym7b278la6ff0g.htm/, Retrieved Wed, 18 Nov 2009 15:53:43 +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/t1258556011gym7b278la6ff0g.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 «
8,2 25,5 8,3 25,5 8,1 25,5 7,4 20,9 7,3 20,9 7,7 20,9 8 22,3 8 22,3 7,7 22,3 6,9 19,9 6,6 19,9 6,9 19,9 7,5 24,1 7,9 24,1 7,7 24,1 6,5 13,8 6,1 13,8 6,4 13,8 6,8 16,2 7,1 16,2 7,3 16,2 7,2 18,6 7 18,6 7 18,6 7 22,4 7,3 22,4 7,5 22,4 7,2 22,6 7,7 22,6 8 22,6 7,9 20 8 20 8 20 7,9 21,8 7,9 21,8 8 21,8 8,1 28,7 8,1 28,7 8,2 28,7 8 19,5 8,3 19,5 8,5 19,5 8,6 19,4 8,7 19,4 8,7 19,4 8,5 21,7 8,4 21,7 8,5 21,7 8,7 26,2 8,7 26,2 8,6 26,2 7,9 19,1 8,1 19,1 8,2 19,1 8,5 21,3 8,6 21,3 8,5 21,3 8,3 24,1 8,2 24,1 8,7 24,1
 
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 4.16181097906056 + 0.140421618562535X[t] -0.296852126957176M1[t] -0.155697745708356M2[t] -0.214543364459535M3[t] + 0.0172250518770039M4[t] + 0.0983794331258246M5[t] + 0.339533814374645M6[t] + 0.428009927372194M7[t] + 0.529164308621014M8[t] + 0.470318689869835M9[t] -0.0223087624976419M10[t] -0.181154381248821M11[t] + 0.018845618751179t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)4.161810979060560.4830818.615100
X0.1404216185625350.022426.263200
M1-0.2968521269571760.262005-1.1330.2630850.131542
M2-0.1556977457083560.261291-0.59590.5541770.277089
M3-0.2145433644595350.26061-0.82320.4146220.207311
M40.01722505187700390.2425130.0710.9436840.471842
M50.09837943312582460.2424130.40580.6867460.343373
M60.3395338143746450.242351.4010.1679230.083962
M70.4280099273721940.2402731.78140.0814580.040729
M80.5291643086210140.2402262.20280.0326590.01633
M90.4703186898698350.2402181.95790.0563250.028163
M10-0.02230876249764190.238499-0.09350.9258820.462941
M11-0.1811543812488210.238441-0.75970.4512840.225642
t0.0188456187511790.0030286.224100


Multiple Linear Regression - Regression Statistics
Multiple R0.863371612166365
R-squared0.745410540694749
Adjusted R-squared0.6734613456737
F-TEST (value)10.3602346138365
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.02096775478344e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.376978214389973
Sum Squared Residuals6.53717840973402


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.27.46455574419920.735444255800796
28.37.62455574419920.675444255800792
38.17.58455574419920.515444255800792
47.47.189230333899260.210769666100737
57.37.289230333899260.0107696661007361
67.77.549230333899260.150769666100736
787.853142331635540.14685766836446
887.973142331635540.0268576683644611
97.77.93314233163554-0.23314233163554
106.97.12234861346916-0.222348613469157
116.66.98234861346916-0.382348613469158
126.97.18234861346916-0.282348613469157
137.57.49411290322580.00588709677419252
147.97.65411290322580.245887096774195
157.77.61411290322580.0858870967741937
166.56.418384267119410.0816157328805864
176.16.51838426711941-0.418384267119414
186.46.77838426711941-0.378384267119413
196.87.22271788341822-0.422717883418224
207.17.34271788341822-0.242717883418224
217.37.30271788341822-0.00271788341822402
227.27.165947934352010.0340520656479897
2377.02594793435201-0.0259479343520098
2477.22594793435201-0.225947934352010
2577.48154357668365-0.481543576683646
267.37.64154357668365-0.341543576683646
277.57.60154357668365-0.101543576683645
287.27.88024193548387-0.68024193548387
297.77.98024193548387-0.28024193548387
3088.24024193548387-0.24024193548387
317.97.98246745897-0.0824674589700051
3288.10246745897-0.102467458970005
3388.06246745897-0.0624674589700053
347.97.841444538766270.0585554612337295
357.97.701444538766270.19855546123373
3687.901444538766270.0985554612337294
378.18.59234719864176-0.492347198641766
388.18.75234719864176-0.652347198641765
398.28.71234719864176-0.512347198641765
4087.671082342954160.32891765704584
418.37.771082342954160.528917657045841
428.58.031082342954160.468917657045841
438.68.124361912846630.475638087153367
448.78.244361912846630.455638087153367
458.78.204361912846630.495638087153367
468.58.053549801924160.446450198075835
478.47.913549801924170.486450198075836
488.58.113549801924170.386450198075835
498.78.467440577249580.232559422750423
508.78.627440577249580.0725594227504237
518.68.587440577249580.0125594227504248
527.97.84106112054330.0589388794567062
538.17.94106112054330.158938879456706
548.28.2010611205433-0.00106112054329452
558.58.6173104131296-0.117310413129598
568.68.7373104131296-0.137310413129598
578.58.6973104131296-0.197310413129597
588.38.6167091114884-0.316709111488397
598.28.4767091114884-0.276709111488398
608.78.67670911148840.0232908885116015


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.09015598335308180.1803119667061640.909844016646918
180.06267148401296370.1253429680259270.937328515987036
190.03755243474037790.07510486948075570.962447565259622
200.02020535488574560.04041070977149120.979794645114254
210.1165989707452930.2331979414905850.883401029254707
220.2629654941308650.525930988261730.737034505869135
230.3488052280940030.6976104561880060.651194771905997
240.3306810393193360.6613620786386710.669318960680664
250.5626274804180990.8747450391638020.437372519581901
260.6893281834865940.6213436330268130.310671816513406
270.8210172986368820.3579654027262360.178982701363118
280.771472916723450.4570541665530990.228527083276550
290.7899878598202940.4200242803594120.210012140179706
300.798493965485330.4030120690293390.201506034514670
310.8183802191056840.3632395617886320.181619780894316
320.8248158651348240.3503682697303510.175184134865176
330.8299347014926780.3401305970146450.170065298507322
340.843779057611260.3124418847774780.156220942388739
350.8692217533817830.2615564932364350.130778246618217
360.9625093434860650.07498131302786980.0374906565139349
370.9624104310484130.07517913790317350.0375895689515867
380.983769738547790.03246052290442040.0162302614522102
390.998055265615130.003889468769739150.00194473438486958
400.9971670471320830.00566590573583460.0028329528679173
410.9947469797174520.01050604056509710.00525302028254853
420.9846068105370720.03078637892585550.0153931894629278
430.952120847699590.09575830460081930.0478791523004096


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.0740740740740741NOK
5% type I error level60.222222222222222NOK
10% type I error level100.370370370370370NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/10g36q1258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/10g36q1258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/1r94h1258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/1r94h1258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/2d9q41258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/2d9q41258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/3cmv31258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/3cmv31258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/4q6x91258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/4q6x91258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/52n001258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/52n001258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/6j65m1258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/6j65m1258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/7o71k1258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/7o71k1258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/8bdfc1258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/8bdfc1258555937.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/97l2s1258555937.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258556011gym7b278la6ff0g/97l2s1258555937.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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