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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: Thu, 19 Nov 2009 03:06:32 -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/19/t1258626341kdjdcuz539hl65l.htm/, Retrieved Thu, 19 Nov 2009 11:25:53 +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/2009/Nov/19/t1258626341kdjdcuz539hl65l.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 «
96.8 610763 114.1 612613 110.3 611324 103.9 594167 101.6 595454 94.6 590865 95.9 589379 104.7 584428 102.8 573100 98.1 567456 113.9 569028 80.9 620735 95.7 628884 113.2 628232 105.9 612117 108.8 595404 102.3 597141 99 593408 100.7 590072 115.5 579799 100.7 574205 109.9 572775 114.6 572942 85.4 619567 100.5 625809 114.8 619916 116.5 587625 112.9 565742 102 557274 106 560576 105.3 548854 118.8 531673 106.1 525919 109.3 511038 117.2 498662 92.5 555362 104.2 564591 112.5 541657 122.4 527070 113.3 509846 100 514258 110.7 516922 112.8 507561 109.8 492622 117.3 490243 109.1 469357 115.9 477580 96 528379 99.8 533590 116.8 517945 115.7 506174 99.4 501866 94.3 516141 91 528222 93.2 532638 103.1 536322 94.1 536535 91.8 523597 102.7 536214 82.6 586570 89.1 596594
 
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
Tot_nietwerkende_werkzoekenden[t] = + 838838.18799994 -2239.06649810638Tot_ind_productie[t] + 25644.8903432349M1[t] + 45056.4124976968M2[t] + 31267.1814830794M3[t] + 2946.30621054342M4[t] -9776.7235398718M5[t] -5649.07194513298M6[t] -5301.24720247713M7[t] + 7360.59494601442M8[t] -9755.17904712758M9[t] -20474.7993209117M10[t] + 3900.0507567845M11[t] -1690.05696515542t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)838838.1879999444098.41098719.02200
Tot_ind_productie-2239.06649810638484.43716-4.6223e-051.5e-05
M125644.890343234914160.5669971.8110.0765340.038267
M245056.412497696819007.243272.37050.0219180.010959
M331267.181483079418958.9170671.64920.1057740.052887
M42946.3062105434216970.2498670.17360.8629130.431456
M5-9776.723539871815149.022085-0.64540.5218260.260913
M6-5649.0719451329815183.182751-0.37210.711520.35576
M7-5301.2472024771315446.860603-0.34320.7329840.366492
M87360.5949460144217738.5064620.4150.6800670.340033
M9-9755.1790471275816039.319974-0.60820.545980.27299
M10-20474.799320911715903.31724-1.28750.204240.10212
M113900.050756784518513.8006540.21070.8340660.417033
t-1690.05696515542161.692331-10.452300


Multiple Linear Regression - Regression Statistics
Multiple R0.890095379048494
R-squared0.792269783803483
Adjusted R-squared0.734812489961893
F-TEST (value)13.7888461295754
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value6.57685017557696e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21892.9363583838
Sum Squared Residuals22527131132.4354


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1610763646051.384361324-35288.3843613239
2612613625036.999133389-12423.9991333891
3611324618066.163846421-6742.16384642067
4594167602385.25719661-8218.25719661001
5595454593122.0234266842331.97657331597
6590865611233.083543012-20368.0835430122
7589379606980.064872974-17601.0648729742
8584428598248.064872974-13820.0648729742
9573100583696.460261079-10596.4602610789
10567456581810.39556324-14354.3955632393
11569028569117.938005699-89.9380056993582
12620735637417.02472127-16682.02472127
13628884628233.673927375650.326072625002
14628232606771.4753998221460.5246001800
15612117607637.3728562244479.6271437763
16595404571133.14777402424270.8522259763
17597141571273.99329614525867.0067038554
18593408581100.50736947912307.4926305210
19590072575951.86210019914120.1378998014
20579799553785.4631115626013.5368884397
21574205568117.8163252376087.18367476267
22572775535108.72730371937666.2726962809
23572942547269.9078751625672.0921248401
24619567607060.54189792612506.4581020737
25625809597205.471154628603.5288454006
26619916582908.28542098537007.7145790153
27587625563622.58439443124002.4156055689
28565742541672.29154992324069.7084500774
29557274551665.0296637125608.9703362885
30560576545146.35830086915429.6416991306
31548854545371.4726270443482.52737295573
32531673526115.8600859445557.13991405572
33525919535746.173653598-9827.17365359789
34511038516171.483620718-5133.48362071788
35498662521167.651398218-22505.6513982183
36555362570882.486179506-15520.4861795060
37564591568640.241529741-4049.24152974076
38541657567777.454784764-26120.4547847644
39527070530131.408473738-3061.40847373838
40509846520495.981368815-10649.981368815
41514258535862.479078059-21604.4790780593
42516922514342.0621779042579.93782209561
43507561508297.790309381-736.790309381435
44492622525986.774987037-33364.7749870367
45490243490387.945292941-144.945292941415
46469357496338.613338474-26981.6133384741
47477580503797.754263892-26217.7542638916
48528379542765.069854269-14386.0698542686
49533590558211.450539544-24621.4505395439
50517945537868.785261042-19923.7852610419
51506174524852.470429186-18678.4704291862
52501866531338.322110629-29472.3221106287
53516141528344.4745354-12203.4745354006
54528222538170.988608735-9948.98860873506
55532638531902.810090401735.189909598565
56536322520707.83694248415614.1630575156
57536535522053.60446714414481.3955328556
58523597514793.780173858803.21982615045
59536214513072.74845703123141.2515429692
60586570552487.87734702934082.1226529709
61596594561888.77848741734705.2215125829


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.04494564637302260.08989129274604510.955054353626977
180.01209484578590710.02418969157181430.987905154214093
190.003016502335146090.006033004670292180.996983497664854
200.0006918966267494560.001383793253498910.99930810337325
210.0002512919509081340.0005025839018162670.999748708049092
220.0001087094464705070.0002174188929410140.99989129055353
232.53150873273935e-055.0630174654787e-050.999974684912673
246.54273682993918e-061.30854736598784e-050.99999345726317
251.28483206443595e-062.5696641288719e-060.999998715167935
261.31865181637720e-062.63730363275439e-060.999998681348184
279.5789886066480e-050.0001915797721329600.999904210113933
280.001884867551706380.003769735103412760.998115132448294
290.02634946011835690.05269892023671380.973650539881643
300.03774217965259340.07548435930518680.962257820347407
310.05726577904697810.1145315580939560.942734220953022
320.1284191004031060.2568382008062120.871580899596894
330.1522195587885070.3044391175770140.847780441211493
340.2551413720620210.5102827441240420.744858627937979
350.3730691235185230.7461382470370460.626930876481477
360.3503537851335240.7007075702670480.649646214866476
370.3114051860148150.6228103720296290.688594813985185
380.3615608108573070.7231216217146140.638439189142693
390.5162561420667790.9674877158664420.483743857933221
400.6928935958957380.6142128082085250.307106404104262
410.9013985019878740.1972029960242520.098601498012126
420.9560807186955330.08783856260893330.0439192813044667
430.9857215085362310.02855698292753710.0142784914637686
440.999982387177093.52256458211766e-051.76128229105883e-05


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level110.392857142857143NOK
5% type I error level130.464285714285714NOK
10% type I error level170.607142857142857NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/10encb1258625187.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/10encb1258625187.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/143e41258625187.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/23jiv1258625187.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/23jiv1258625187.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/35q241258625187.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/4jmr21258625187.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/5rlvz1258625187.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/6t5w71258625187.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/7a0tq1258625187.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/88ez21258625187.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/88ez21258625187.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/97psm1258625187.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258626341kdjdcuz539hl65l/97psm1258625187.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 2 ; 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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