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oilpricemulregr

*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: Tue, 30 Nov 2010 20:36:28 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e.htm/, Retrieved Tue, 30 Nov 2010 21:41:53 +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/2010/Nov/30/t1291149703ds3h3xjdskkyt3e.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
46.85 48.05 54.63 53.22 49.87 56.42 59.03 64.99 65.55 62.27 58.34 59.45 65.54 61.93 62.97 70.16 70.96 70.97 74.46 73.08 63.90 59.14 59.40 62.09 54.35 59.39 60.74 64.04 63.53 67.53 74.15 72.36 79.63 85.66 94.63 91.74 92.93 95.35 105.42 112.46 125.46 134.02 133.48 116.69 103.76 76.72 57.44 42.04 41.92 39.26 48.06 49.95 59.21 69.70 64.29 71.14 69.47 75.82 78.15 74.60
 
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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Crudeoilprice[t] = + 52.80975 -1.64053472222217M1[t] -1.52848611111111M2[t] + 3.6735625M3[t] + 6.90961111111112M4[t] + 10.3836597222222M5[t] + 15.9397083333333M6[t] + 16.9277569444445M7[t] + 15.1318055555556M8[t] + 11.5758541666667M9[t] + 6.6699027777778M10[t] + 3.9739513888889M11[t] + 0.365951388888888t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)52.8097511.4678384.6053.2e-051.6e-05
M1-1.6405347222221713.951267-0.11760.9068930.453447
M2-1.5284861111111113.930422-0.10970.9130960.456548
M33.673562513.9115360.26410.7928840.396442
M46.9096111111111213.8946160.49730.6213050.310653
M510.383659722222213.879670.74810.4581150.229058
M615.939708333333313.8667041.14950.2561680.128084
M716.927756944444513.8557221.22170.2279080.113954
M815.131805555555613.8467311.09280.2800480.140024
M911.575854166666713.8397340.83640.407150.203575
M106.669902777777813.8347340.48210.6319630.315982
M113.973951388888913.8317330.28730.775140.38757
t0.3659513888888880.1663582.19980.0327750.016388


Multiple Linear Regression - Regression Statistics
Multiple R0.430197138182165
R-squared0.185069577700125
Adjusted R-squared-0.0229977641636727
F-TEST (value)0.889469611339932
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.563345577233602
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21.8683087123745
Sum Squared Residuals22476.4775191667


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
146.8551.5351666666665-4.68516666666653
248.0552.0131666666667-3.96316666666669
354.6357.5811666666667-2.95116666666668
453.2261.1831666666666-7.96316666666663
549.8765.0231666666667-15.1531666666667
656.4270.9451666666667-14.5251666666667
759.0372.2991666666667-13.2691666666667
864.9970.8691666666667-5.87916666666668
965.5567.6791666666667-2.12916666666667
1062.2763.1391666666667-0.869166666666666
1158.3460.8091666666667-2.46916666666667
1259.4557.20116666666672.24883333333334
1365.5455.92658333333349.61341666666665
1461.9356.40458333333335.52541666666666
1562.9761.97258333333330.99741666666666
1670.1665.57458333333334.58541666666666
1770.9669.41458333333331.54541666666666
1870.9775.3365833333333-4.36658333333334
1974.4676.6905833333333-2.23058333333335
2073.0875.2605833333333-2.18058333333334
2163.972.0705833333333-8.17058333333334
2259.1467.5305833333333-8.39058333333334
2359.465.2005833333333-5.80058333333334
2462.0961.59258333333330.497416666666681
2554.3560.318-5.96800000000004
2659.3960.796-1.40600000000000
2760.7466.364-5.624
2864.0469.966-5.92599999999999
2963.5373.806-10.276
3067.5379.728-12.198
3174.1581.082-6.932
3272.3679.652-7.292
3379.6376.4623.168
3485.6671.92213.738
3594.6369.59225.038
3691.7465.98425.756
3792.9364.709416666666728.2205833333333
3895.3565.187416666666730.1625833333333
39105.4270.755416666666734.6645833333333
40112.4674.357416666666738.1025833333333
41125.4678.197416666666747.2625833333333
42134.0284.119416666666749.9005833333334
43133.4885.473416666666748.0065833333333
44116.6984.043416666666732.6465833333333
45103.7680.853416666666722.9065833333333
4676.7276.31341666666670.406583333333334
4757.4473.9834166666667-16.5434166666667
4842.0470.3754166666667-28.3354166666667
4941.9269.1008333333334-27.1808333333334
5039.2669.5788333333333-30.3188333333333
5148.0675.1468333333333-27.0868333333333
5249.9578.7488333333333-28.7988333333333
5359.2182.5888333333333-23.3788333333333
5469.788.5108333333333-18.8108333333333
5564.2989.8648333333333-25.5748333333333
5671.1488.4348333333333-17.2948333333333
5769.4785.2448333333333-15.7748333333333
5875.8280.7048333333333-4.88483333333333
5978.1578.3748333333333-0.224833333333324
6074.674.7668333333333-0.166833333333314


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.002630538869311930.005261077738623870.997369461130688
170.000631868575592170.001263737151184340.999368131424408
187.34641743466015e-050.0001469283486932030.999926535825653
197.56746256307722e-061.51349251261544e-050.999992432537437
202.88995603352467e-065.77991206704933e-060.999997110043966
211.3740556288444e-052.7481112576888e-050.999986259443712
221.82225554028152e-053.64451108056304e-050.999981777444597
237.52575243867712e-061.50515048773542e-050.999992474247561
242.22725955859776e-064.45451911719552e-060.999997772740441
252.76103348583162e-065.52206697166324e-060.999997238966514
268.20603256876916e-071.64120651375383e-060.999999179396743
273.06150426693875e-076.12300853387751e-070.999999693849573
281.05196928216101e-072.10393856432202e-070.999999894803072
294.60776990022425e-089.21553980044849e-080.999999953922301
303.04172723222194e-086.08345446444388e-080.999999969582728
311.92152636098083e-083.84305272196167e-080.999999980784736
322.11392849930122e-084.22785699860244e-080.999999978860715
333.03014407716362e-086.06028815432723e-080.99999996969856
341.60663035611125e-073.21326071222249e-070.999999839336964
352.62510739550891e-065.25021479101782e-060.999997374892605
365.25595625307418e-061.05119125061484e-050.999994744043747
378.52552973774598e-061.70510594754920e-050.999991474470262
381.18880723280486e-052.37761446560972e-050.999988111927672
392.7223710540691e-055.4447421081382e-050.99997277628946
407.76653677387382e-050.0001553307354774760.99992233463226
410.0007142054858487430.001428410971697490.99928579451415
420.004879080512337270.009758161024674550.995120919487663
430.04443977851602510.08887955703205010.955560221483975
440.1183998725769860.2367997451539730.881600127423014


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level270.93103448275862NOK
5% type I error level270.93103448275862NOK
10% type I error level280.96551724137931NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/1022ng1291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/1022ng1291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/1e1qm1291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/1e1qm1291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/2osp71291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/2osp71291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/3osp71291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/3osp71291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/4osp71291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/4osp71291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/5z2ps1291149381.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/6z2ps1291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/6z2ps1291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/7sb6d1291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/7sb6d1291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/8sb6d1291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/8sb6d1291149381.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/922ng1291149381.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291149703ds3h3xjdskkyt3e/922ng1291149381.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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