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WS 7 Model 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 11:02:51 -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/t1258740264oavm88irgyoyho7.htm/, Retrieved Fri, 20 Nov 2009 19:04:36 +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/t1258740264oavm88irgyoyho7.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:
WS 7 Model 1
 
Dataseries X:
» Textbox « » Textfile « » CSV «
286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 0 280190 0 280408 0 276836 0 275216 0 274352 0 271311 0 289802 0 290726 0 292300 0 278506 0 269826 0 265861 0 269034 0 264176 0 255198 0 253353 0 246057 0 235372 0 258556 0 260993 0 254663 0 250643 0 243422 0 247105 0 248541 0 245039 0 237080 0 237085 0 225554 0 226839 1 247934 1 248333 1 246969 1 245098 1 246263 1 255765 1 264319 1 268347 1 273046 1 273963 1 267430 1 271993 1 292710 1 295881 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
nwwmb[t] = + 267912.577777778 -6253.24444444445dummy_variable[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)267912.5777777782671.648691100.279900
dummy_variable-6253.244444444455343.297382-1.17030.2466680.123334


Multiple Linear Regression - Regression Statistics
Multiple R0.151884696481867
R-squared0.0230689610253889
Adjusted R-squared0.0062253224223785
F-TEST (value)1.36959487015268
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.246667802057425
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation17921.964256143
Sum Squared Residuals18629414562.3111


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1286602267912.57777777718689.4222222226
2283042267912.57777777815129.4222222222
3276687267912.5777777788774.42222222221
4277915267912.57777777810002.4222222222
5277128267912.5777777789215.42222222221
6277103267912.5777777789190.42222222221
7275037267912.5777777787124.42222222221
8270150267912.5777777782237.42222222221
9267140267912.577777778-772.577777777788
10264993267912.577777778-2919.57777777779
11287259267912.57777777819346.4222222222
12291186267912.57777777823273.4222222222
13292300267912.57777777824387.4222222222
14288186267912.57777777820273.4222222222
15281477267912.57777777813564.4222222222
16282656267912.57777777814743.4222222222
17280190267912.57777777812277.4222222222
18280408267912.57777777812495.4222222222
19276836267912.5777777788923.42222222221
20275216267912.5777777787303.42222222221
21274352267912.5777777786439.42222222221
22271311267912.5777777783398.42222222221
23289802267912.57777777821889.4222222222
24290726267912.57777777822813.4222222222
25292300267912.57777777824387.4222222222
26278506267912.57777777810593.4222222222
27269826267912.5777777781913.42222222221
28265861267912.577777778-2051.57777777779
29269034267912.5777777781121.42222222221
30264176267912.577777778-3736.57777777779
31255198267912.577777778-12714.5777777778
32253353267912.577777778-14559.5777777778
33246057267912.577777778-21855.5777777778
34235372267912.577777778-32540.5777777778
35258556267912.577777778-9356.57777777779
36260993267912.577777778-6919.57777777779
37254663267912.577777778-13249.5777777778
38250643267912.577777778-17269.5777777778
39243422267912.577777778-24490.5777777778
40247105267912.577777778-20807.5777777778
41248541267912.577777778-19371.5777777778
42245039267912.577777778-22873.5777777778
43237080267912.577777778-30832.5777777778
44237085267912.577777778-30827.5777777778
45225554267912.577777778-42358.5777777778
46226839261659.333333333-34820.3333333333
47247934261659.333333333-13725.3333333333
48248333261659.333333333-13326.3333333333
49246969261659.333333333-14690.3333333333
50245098261659.333333333-16561.3333333333
51246263261659.333333333-15396.3333333333
52255765261659.333333333-5894.33333333333
53264319261659.3333333332659.66666666667
54268347261659.3333333336687.66666666667
55273046261659.33333333311386.6666666667
56273963261659.33333333312303.6666666667
57267430261659.3333333335770.66666666667
58271993261659.33333333310333.6666666667
59292710261659.33333333331050.6666666667
60295881261659.33333333334221.6666666667


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.02728951289853640.05457902579707280.972710487101464
60.007408116725938060.01481623345187610.992591883274062
70.002537022842699480.005074045685398960.9974629771573
80.002314436682515520.004628873365031040.997685563317484
90.002657268368066330.005314536736132670.997342731631934
100.002959502158938880.005919004317877750.99704049784106
110.003130452954857320.006260905909714640.996869547045143
120.005009178936030.010018357872060.99499082106397
130.007176211964049110.01435242392809820.99282378803595
140.00566421118652250.0113284223730450.994335788813478
150.002930321343102440.005860642686204890.997069678656898
160.001575664513349140.003151329026698280.99842433548665
170.0007830873208205660.001566174641641130.99921691267918
180.0003914014524602860.0007828029049205720.99960859854754
190.0001953145208545450.000390629041709090.999804685479145
200.0001023788618737310.0002047577237474620.999897621138126
215.56853980804253e-050.0001113707961608510.99994431460192
223.73313706641159e-057.46627413282319e-050.999962668629336
236.69654652638743e-050.0001339309305277490.999933034534736
240.0001581682763354940.0003163365526709890.999841831723665
250.0006018687637575950.001203737527515190.999398131236242
260.0005953513838617990.001190702767723600.999404648616138
270.00074256580882380.00148513161764760.999257434191176
280.001215656404002210.002431312808004420.998784343595998
290.001604136780164200.003208273560328400.998395863219836
300.002751997440364010.005503994880728010.997248002559636
310.008522470171039580.01704494034207920.99147752982896
320.02011969015337020.04023938030674030.97988030984663
330.05618468654972630.1123693730994530.943815313450274
340.190113328511860.380226657023720.80988667148814
350.1889390071752510.3778780143505010.81106099282475
360.1918364202404630.3836728404809260.808163579759537
370.1982245965595150.3964491931190300.801775403440485
380.2092775698016110.4185551396032220.79072243019839
390.2376764262052060.4753528524104130.762323573794794
400.2424009789135190.4848019578270380.757599021086481
410.2427431540969220.4854863081938440.757256845903078
420.2476896679084320.4953793358168630.752310332091568
430.2654178981321870.5308357962643730.734582101867813
440.2761077263246250.552215452649250.723892273675375
450.314504723827570.629009447655140.68549527617243
460.4837177512341710.9674355024683420.516282248765829
470.469264979812260.938529959624520.53073502018774
480.4546766691928680.9093533383857350.545323330807132
490.4709182317051780.9418364634103570.529081768294822
500.55477057520020.89045884959960.4452294247998
510.6994232951347790.6011534097304420.300576704865221
520.7504144571474220.4991710857051550.249585542852578
530.7180674755895970.5638650488208070.281932524410403
540.6450791264203550.709841747159290.354920873579645
550.51363936294010.97272127411980.4863606370599


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level210.411764705882353NOK
5% type I error level270.529411764705882NOK
10% type I error level280.549019607843137NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/10j5ol1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/10j5ol1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/12ark1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/12ark1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/2uliy1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/2uliy1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/326351258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/326351258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/4fzbm1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/4fzbm1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/5v38q1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/5v38q1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/69unh1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/69unh1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/7l5id1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/7l5id1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/8pswr1258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/8pswr1258740167.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/993x21258740167.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740264oavm88irgyoyho7/993x21258740167.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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Software written by Ed van Stee & Patrick Wessa


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