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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: Fri, 20 Nov 2009 05:53:28 -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/20/t125872170594e0b17jp0rxva1.htm/, Retrieved Fri, 20 Nov 2009 13:55:17 +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/t125872170594e0b17jp0rxva1.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 «
1.4 2 1.2 2 1 2 1.7 2 2.4 2 2 2 2.1 2 2 2 1.8 2 2.7 2 2.3 2 1.9 2 2 2 2.3 2 2.8 2 2.4 2 2.3 2 2.7 2 2.7 2 2.9 2 3 2 2.2 2 2.3 2 2.8 2.21 2.8 2.25 2.8 2.25 2.2 2.45 2.6 2.5 2.8 2.5 2.5 2.64 2.4 2.75 2.3 2.93 1.9 3 1.7 3.17 2 3.25 2.1 3.39 1.7 3.5 1.8 3.5 1.8 3.65 1.8 3.75 1.3 3.75 1.3 3.9 1.3 4 1.2 4 1.4 4 2.2 4 2.9 4 3.1 4 3.5 4 3.6 4 4.4 4 4.1 4 5.1 4 5.8 4 5.9 4.18 5.4 4.25 5.5 4.25 4.8 3.97 3.2 3.42 2.7 2.75
 
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
Y[t] = + 2.07836940516536 -0.776305498871819X[t] + 0.482562816317725M1[t] + 0.468406500301148M2[t] + 0.548591569205598M3[t] + 0.577724418155176M4[t] + 0.7635681021386M5[t] + 0.814437505056589M6[t] + 0.820833017952014M7[t] + 0.665491976879028M8[t] + 0.562203937846657M9[t] + 0.47096890085490M10[t] + 0.143839867944373M11[t] + 0.0741563160165766t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2.078369405165360.7028562.9570.0048890.002445
X-0.7763054988718190.379015-2.04820.0462710.023135
M10.4825628163177250.6753220.71460.4784880.239244
M20.4684065003011480.6706390.69840.4884130.244207
M30.5485915692055980.671550.81690.4181950.209097
M40.5777244181551760.6694560.8630.3926280.196314
M50.76356810213860.6654211.14750.2571090.128555
M60.8144375050565890.6655721.22370.227310.113655
M70.8208330179520140.667311.23010.2249280.112464
M80.6654919768790280.6671320.99750.3237210.16186
M90.5622039378466570.6644190.84620.4018440.200922
M100.470968900854900.6599110.71370.4790270.239514
M110.1438398679443730.6541870.21990.8269410.41347
t0.07415631601657660.0194193.81874e-042e-04


Multiple Linear Regression - Regression Statistics
Multiple R0.624576730303413
R-squared0.390096092036502
Adjusted R-squared0.217731944133774
F-TEST (value)2.26320900711121
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.0211618067216435
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.03215027135484
Sum Squared Residuals49.0053724022618


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.41.082477539756020.317522460243977
21.21.142477539756020.057522460243976
311.29681892467705-0.296818924677053
41.71.400108089643210.299891910356793
52.41.660108089643210.739891910356793
621.785133808577770.214866191422228
72.11.865685637489770.234314362510226
821.784500912433370.215499087566634
91.81.755369189417570.0446308105824288
102.71.738290468442390.961709531557609
112.31.485317751548440.81468224845156
121.91.415634199620640.484365800379356
1321.972353331954950.0276466680450549
142.32.032353331954940.267646668045055
152.82.186694716875970.613305283124028
162.42.289983881842130.110016118157873
172.32.54998388184213-0.249983881842126
182.72.675009600776690.0249903992233081
192.72.75556142968869-0.0555614296886936
202.92.674376704632290.225623295367715
2132.645244981616490.35475501838351
222.22.62816626064131-0.42816626064131
232.32.37519354374736-0.0751935437473595
242.82.142485837056480.657514162943519
252.82.668152749435910.13184725056409
262.82.728152749435910.0718472505640904
272.22.72723303458257-0.527233034582573
282.62.79170692460514-0.191706924605136
292.83.05170692460514-0.251706924605136
302.53.06804987369765-0.568049873697647
312.43.06320809773375-0.66320809773375
322.32.84228838288041-0.542288382880413
331.92.75881527494359-0.858815274943591
341.72.6097646191602-0.909764619160202
3522.29468746235651-0.294687462356506
362.12.11632114058665-0.0163211405866546
371.72.58764666804506-0.887646668045056
381.82.64764666804506-0.847646668045056
391.82.68554222813531-0.88554222813531
401.82.71120084321428-0.911200843214282
411.32.97120084321428-1.67120084321428
421.32.97978073731808-1.67978073731808
431.32.98270201634290-1.68270201634290
441.22.90151729128649-1.70151729128649
451.42.87238556827069-1.47238556827069
462.22.85530684729551-0.655306847295512
472.92.602334130401560.297665869598439
483.12.532650578473760.567349421526235
493.53.089369710808070.410630289191934
503.63.149369710808070.450630289191934
514.43.303711095729091.09628890427091
524.13.407000260695250.692999739304753
535.13.667000260695251.43299973930475
545.83.792025979629812.00797402037019
555.93.732842818744892.16715718125511
565.43.597316708767451.80268329123255
575.53.568184985751661.93181501424834
584.83.768471804460591.03152819553941
593.23.94246711194613-0.742467111946135
602.74.39290824426246-1.69290824426246


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1260075415665080.2520150831330160.873992458433492
180.04786747211171470.09573494422342950.952132527888285
190.01682422977932900.03364845955865810.98317577022067
200.005493324082715540.01098664816543110.994506675917284
210.00212885514836790.00425771029673580.997871144851632
220.004252879414654460.008505758829308920.995747120585346
230.002393004712019780.004786009424039550.99760699528798
240.001216210111160590.002432420222321190.99878378988884
250.0004768569079774150.000953713815954830.999523143092023
260.0001866820923049660.0003733641846099310.999813317907695
270.0001088855747223190.0002177711494446390.999891114425278
284.14383915722353e-058.28767831444706e-050.999958561608428
291.72779775627681e-053.45559551255361e-050.999982722022437
306.55690455161648e-061.31138091032330e-050.999993443095448
312.50258945404973e-065.00517890809946e-060.999997497410546
321.36765347839472e-062.73530695678945e-060.999998632346522
339.789827975231e-071.9579655950462e-060.999999021017203
348.31081662289104e-071.66216332457821e-060.999999168918338
354.75537323903766e-069.51074647807532e-060.999995244626761
366.07590257616875e-050.0001215180515233750.999939240974238
370.0001332117460737370.0002664234921474740.999866788253926
380.001694840100952960.003389680201905920.998305159899047
390.004790877396164250.00958175479232850.995209122603836
400.05270314162732460.1054062832546490.947296858372675
410.04995681261400360.09991362522800710.950043187385996
420.06979864947804530.1395972989560910.930201350521955
430.1130313657849530.2260627315699060.886968634215047


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.703703703703704NOK
5% type I error level210.777777777777778NOK
10% type I error level230.851851851851852NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/10dxmr1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/10dxmr1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/1xmdq1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/1xmdq1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/2pwhz1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/2pwhz1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/35twd1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/35twd1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/4fao31258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/4fao31258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/5v7re1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/5v7re1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/6q4pr1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/6q4pr1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/71cgl1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/71cgl1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/84sbs1258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/84sbs1258721604.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/9y3s01258721604.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872170594e0b17jp0rxva1/9y3s01258721604.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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