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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSun, 09 Nov 2014 20:25:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/09/t1415564715ghglgs9dxp6eszy.htm/, Retrieved Sun, 19 May 2024 13:53:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=253223, Retrieved Sun, 19 May 2024 13:53:17 +0000
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Original text written by user:
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User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [] [2014-11-09 20:25:00] [e63466588bf3c49b37383cc70d2c7b07] [Current]
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Dataseries X:
41 38 13 12 14 12 53
39 32 16 11 18 11 83
30 35 19 15 11 14 66
31 33 15 6 12 12 67
34 37 14 13 16 21 76
35 29 13 10 18 12 78
39 31 19 12 14 22 53
34 36 15 14 14 11 80
36 35 14 12 15 10 74
37 38 15 9 15 13 76
38 31 16 10 17 10 79
36 34 16 12 19 8 54
38 35 16 12 10 15 67
39 38 16 11 16 14 54
33 37 17 15 18 10 87
32 33 15 12 14 14 58
36 32 15 10 14 14 75
38 38 20 12 17 11 88
39 38 18 11 14 10 64
32 32 16 12 16 13 57
32 33 16 11 18 9.5 66
31 31 16 12 11 14 68
39 38 19 13 14 12 54
37 39 16 11 12 14 56
39 32 17 12 17 11 86
41 32 17 13 9 9 80
36 35 16 10 16 11 76
33 37 15 14 14 15 69
33 33 16 12 15 14 78
34 33 14 10 11 13 67
31 31 15 12 16 9 80
27 32 12 8 13 15 54
37 31 14 10 17 10 71
34 37 16 12 15 11 84
34 30 14 12 14 13 74
32 33 10 7 16 8 71
29 31 10 9 9 20 63
36 33 14 12 15 12 71
29 31 16 10 17 10 76
35 33 16 10 13 10 69
37 32 16 10 15 9 74
34 33 14 12 16 14 75
38 32 20 15 16 8 54
35 33 14 10 12 14 52
38 28 14 10 15 11 69
37 35 11 12 11 13 68
38 39 14 13 15 9 65
33 34 15 11 15 11 75
36 38 16 11 17 15 74
38 32 14 12 13 11 75
32 38 16 14 16 10 72
32 30 14 10 14 14 67
32 33 12 12 11 18 63
34 38 16 13 12 14 62
32 32 9 5 12 11 63
37 35 14 6 15 14.5 76
39 34 16 12 16 13 74
29 34 16 12 15 9 67
37 36 15 11 12 10 73
35 34 16 10 12 15 70
30 28 12 7 8 20 53
38 34 16 12 13 12 77
34 35 16 14 11 12 80
31 35 14 11 14 14 52
34 31 16 12 15 13 54
35 37 17 13 10 11 80
36 35 18 14 11 17 66
30 27 18 11 12 12 73
39 40 12 12 15 13 63
35 37 16 12 15 14 69
38 36 10 8 14 13 67
31 38 14 11 16 15 54
34 39 18 14 15 13 81
38 41 18 14 15 10 69
34 27 16 12 13 11 84
39 30 17 9 12 19 80
37 37 16 13 17 13 70
34 31 16 11 13 17 69
28 31 13 12 15 13 77
37 27 16 12 13 9 54
33 36 16 12 15 11 79
35 37 16 12 15 9 71
37 33 15 12 16 12 73
32 34 15 11 15 12 72
33 31 16 10 14 13 77
38 39 14 9 15 13 75
33 34 16 12 14 12 69
29 32 16 12 13 15 54
33 33 15 12 7 22 70
31 36 12 9 17 13 73
36 32 17 15 13 15 54
35 41 16 12 15 13 77
32 28 15 12 14 15 82
29 30 13 12 13 12.5 80
39 36 16 10 16 11 80
37 35 16 13 12 16 69
35 31 16 9 14 11 78
37 34 16 12 17 11 81
32 36 14 10 15 10 76
38 36 16 14 17 10 76
37 35 16 11 12 16 73
36 37 20 15 16 12 85
32 28 15 11 11 11 66
33 39 16 11 15 16 79
40 32 13 12 9 19 68
38 35 17 12 16 11 76
41 39 16 12 15 16 71
36 35 16 11 10 15 54
43 42 12 7 10 24 46
30 34 16 12 15 14 85
31 33 16 14 11 15 74
32 41 17 11 13 11 88
32 33 13 11 14 15 38
37 34 12 10 18 12 76
37 32 18 13 16 10 86
33 40 14 13 14 14 54
34 40 14 8 14 13 67
33 35 13 11 14 9 69
38 36 16 12 14 15 90
33 37 13 11 12 15 54
31 27 16 13 14 14 76
38 39 13 12 15 11 89
37 38 16 14 15 8 76
36 31 15 13 15 11 73
31 33 16 15 13 11 79
39 32 15 10 17 8 90
44 39 17 11 17 10 74
33 36 15 9 19 11 81
35 33 12 11 15 13 72
32 33 16 10 13 11 71
28 32 10 11 9 20 66
40 37 16 8 15 10 77
27 30 12 11 15 15 65
37 38 14 12 15 12 74
32 29 15 12 16 14 85
28 22 13 9 11 23 54
34 35 15 11 14 14 63
30 35 11 10 11 16 54
35 34 12 8 15 11 64
31 35 11 9 13 12 69
32 34 16 8 15 10 54
30 37 15 9 16 14 84
30 35 17 15 14 12 86
31 23 16 11 15 12 77
40 31 10 8 16 11 89
32 27 18 13 16 12 76
36 36 13 12 11 13 60
32 31 16 12 12 11 75
35 32 13 9 9 19 73
38 39 10 7 16 12 85
42 37 15 13 13 17 79
34 38 16 9 16 9 71
35 39 16 6 12 12 72
38 34 14 8 9 19 69
33 31 10 8 13 18 78
36 32 17 15 13 15 54
32 37 13 6 14 14 69
33 36 15 9 19 11 81
34 32 16 11 13 9 84
32 38 12 8 12 18 84
34 36 13 8 13 16 69
27 26 13 10 10 24 66
31 26 12 8 14 14 81
38 33 17 14 16 20 82
34 39 15 10 10 18 72
24 30 10 8 11 23 54
30 33 14 11 14 12 78
26 25 11 12 12 14 74
34 38 13 12 9 16 82
27 37 16 12 9 18 73
37 31 12 5 11 20 55
36 37 16 12 16 12 72
41 35 12 10 9 12 78
29 25 9 7 13 17 59
36 28 12 12 16 13 72
32 35 15 11 13 9 78
37 33 12 8 9 16 68
30 30 12 9 12 18 69
31 31 14 10 16 10 67
38 37 12 9 11 14 74
36 36 16 12 14 11 54
35 30 11 6 13 9 67
31 36 19 15 15 11 70
38 32 15 12 14 10 80
22 28 8 12 16 11 89
32 36 16 12 13 19 76
36 34 17 11 14 14 74
39 31 12 7 15 12 87
28 28 11 7 13 14 54
32 36 11 5 11 21 61
32 36 14 12 11 13 38
38 40 16 12 14 10 75
32 33 12 3 15 15 69
35 37 16 11 11 16 62
32 32 13 10 15 14 72
37 38 15 12 12 12 70
34 31 16 9 14 19 79
33 37 16 12 14 15 87
33 33 14 9 8 19 62
26 32 16 12 13 13 77
30 30 16 12 9 17 69
24 30 14 10 15 12 69
34 31 11 9 17 11 75
34 32 12 12 13 14 54
33 34 15 8 15 11 72
34 36 15 11 15 13 74
35 37 16 11 14 12 85
35 36 16 12 16 15 52
36 33 11 10 13 14 70
34 33 15 10 16 12 84
34 33 12 12 9 17 64
41 44 12 12 16 11 84
32 39 15 11 11 18 87
30 32 15 8 10 13 79
35 35 16 12 11 17 67
28 25 14 10 15 13 65
33 35 17 11 17 11 85
39 34 14 10 14 12 83
36 35 13 8 8 22 61
36 39 15 12 15 14 82
35 33 13 12 11 12 76
38 36 14 10 16 12 58
33 32 15 12 10 17 72
31 32 12 9 15 9 72
34 36 13 9 9 21 38
32 36 8 6 16 10 78
31 32 14 10 19 11 54
33 34 14 9 12 12 63
34 33 11 9 8 23 66
34 35 12 9 11 13 70
34 30 13 6 14 12 71
33 38 10 10 9 16 67
32 34 16 6 15 9 58
41 33 18 14 13 17 72
34 32 13 10 16 9 72
36 31 11 10 11 14 70
37 30 4 6 12 17 76
36 27 13 12 13 13 50
29 31 16 12 10 11 72
37 30 10 7 11 12 72
27 32 12 8 12 10 88
35 35 12 11 8 19 53
28 28 10 3 12 16 58
35 33 13 6 12 16 66
37 31 15 10 15 14 82
29 35 12 8 11 20 69
32 35 14 9 13 15 68
36 32 10 9 14 23 44
19 21 12 8 10 20 56
21 20 12 9 12 16 53
31 34 11 7 15 14 70
33 32 10 7 13 17 78
36 34 12 6 13 11 71
33 32 16 9 13 13 72
37 33 12 10 12 17 68
34 33 14 11 12 15 67
35 37 16 12 9 21 75
31 32 14 8 9 18 62
37 34 13 11 15 15 67
35 30 4 3 10 8 83
27 30 15 11 14 12 64
34 38 11 12 15 12 68
40 36 11 7 7 22 62
29 32 14 9 14 12 72




\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Engine error message & 
Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases
Calls: lm -> lm.fit
In addition: Warning messages:
1: In model.matrix.default(mt, mf, contrasts) :
  the response appeared on the right-hand side and was dropped
2: In model.matrix.default(mt, mf, contrasts) :
  problem with term 1 in model.matrix: no columns are assigned
Execution halted
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=253223&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Engine error message[/C][C]
Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases
Calls: lm -> lm.fit
In addition: Warning messages:
1: In model.matrix.default(mt, mf, contrasts) :
  the response appeared on the right-hand side and was dropped
2: In model.matrix.default(mt, mf, contrasts) :
  problem with term 1 in model.matrix: no columns are assigned
Execution halted
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=253223&T=0



Parameters (Session):
par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = ; 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
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, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
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,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
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,signif(numsignificant1,6))
a<-table.element(a,signif(numsignificant1/numgqtests,6))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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')
}