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WS7 Multiple Regression 1 (eenvoudigste model)

*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 06:48:22 -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/t1258725139ot68frauw2ws9l5.htm/, Retrieved Fri, 20 Nov 2009 14:52:31 +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/t1258725139ot68frauw2ws9l5.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 92.9 114.1 107.7 110.3 103.5 103.9 91.1 101.6 79.8 94.6 71.9 95.9 82.9 104.7 90.1 102.8 100.7 98.1 90.7 113.9 108.8 80.9 44.1 95.7 93.6 113.2 107.4 105.9 96.5 108.8 93.6 102.3 76.5 99 76.7 100.7 84 115.5 103.3 100.7 88.5 109.9 99 114.6 105.9 85.4 44.7 100.5 94 114.8 107.1 116.5 104.8 112.9 102.5 102 77.7 106 85.2 105.3 91.3 118.8 106.5 106.1 92.4 109.3 97.5 117.2 107 92.5 51.1 104.2 98.6 112.5 102.2 122.4 114.3 113.3 99.4 100 72.5 110.7 92.3 112.8 99.4 109.8 85.9 117.3 109.4 109.1 97.6 115.9 104.7 96 56.9 99.8 86.7 116.8 108.5 115.7 103.4 99.4 86.2 94.3 71 91 75.9 93.2 87.1 103.1 102 94.1 88.5 91.8 87.8 102.7 100.8 82.6 50.6
 
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'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Totind[t] = + 59.9181251189299 + 0.494158060055627Bouw[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)59.91812511892993.60208116.634300
Bouw0.4941580600556270.03915612.620400


Multiple Linear Regression - Regression Statistics
Multiple R0.856186966701773
R-squared0.733056121949982
Adjusted R-squared0.728453641293947
F-TEST (value)159.274134262530
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.93290987300361
Sum Squared Residuals1411.34878928024


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
196.8105.825408898098-9.02540889809781
2114.1113.1389481869210.961051813079056
3110.3111.063484334687-0.763484334687316
4103.9104.935924389998-1.03592438999753
5101.699.3519383113692.24806168863105
694.695.4480896369295-0.848089636929504
795.9100.883828297541-4.98382829754139
8104.7104.4417663299420.258233670058096
9102.8109.679841766532-6.87984176653156
1098.1104.738261165975-6.63826116597529
11113.9113.6825220529820.21747794701787
1280.981.710495567383-0.810495567383055
1395.7106.171319540137-10.4713195401366
14113.2112.9907007689040.209299231095741
15105.9107.604377914298-1.70437791429792
16108.8106.1713195401372.62868045986340
17102.397.72121671318544.57878328681462
189997.82004832519651.17995167480349
19100.7101.427402163603-0.727402163602581
20115.5110.9646527226764.53534727732381
21100.7103.651113433853-2.95111343385290
22109.9108.8397730644371.06022693556301
23114.6112.2494636788212.35053632117917
2485.482.00699040341643.39300959658357
25100.5106.368982764159-5.86898276415886
26114.8112.8424533508881.95754664911243
27116.5111.7058898127604.79411018724037
28112.9110.5693262746322.33067372536832
2910298.31420638525213.68579361474787
30106102.0203918356693.97960816433066
31105.3105.0347560020090.265243997991337
32118.8112.5459585148546.2540414851458
33106.1105.5783298680700.52167013193014
34109.3108.0985359743541.20146402564645
35117.2112.7930375448824.40696245511799
3692.585.16960198777257.33039801222755
37104.2108.642109840415-4.44210984041473
38112.5110.4210788566152.078921143385
39122.4116.4003913832885.99960861671192
40113.3109.0374362884594.26256371154075
4110095.74458447296294.25541552703713
42110.7105.5289140620645.17108593793572
43112.8109.0374362884593.76256371154075
44109.8102.3663024777087.43369752229172
45117.3113.9790168890163.32098311098448
46109.1108.1479517803590.952048219640884
47115.9111.6564740067544.24352599324594
489688.03571873609517.96428126390491
4999.8102.761628925753-2.96162892575278
50116.8113.5342746349653.26572536503455
51115.7111.0140685286824.68593147131825
5299.4102.514549895725-3.11454989572496
5394.395.0033473828794-0.703347382879434
549197.424721877152-6.42472187715201
5593.2102.959292149775-9.75929214977502
56103.1110.322247244604-7.22224724460388
5794.1103.651113433853-9.55111343385291
5891.8103.305202791814-11.5052027918140
59102.7109.729257572537-7.02925757253712
6082.684.9225229577446-2.32252295774464


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.6155460640368840.7689078719262310.384453935963116
60.4459835083894950.8919670167789890.554016491610505
70.3741257337137010.7482514674274030.625874266286299
80.2701097503699820.5402195007399630.729890249630018
90.2891691870527950.578338374105590.710830812947205
100.2861259771840510.5722519543681030.713874022815949
110.2297387929447070.4594775858894140.770261207055293
120.1588746032565430.3177492065130850.841125396743457
130.3449798293008850.689959658601770.655020170699115
140.2958079382481810.5916158764963620.704192061751819
150.2253528030967280.4507056061934560.774647196903272
160.2283573959417460.4567147918834910.771642604058254
170.2737040726499880.5474081452999750.726295927350012
180.2200115237077330.4400230474154670.779988476292267
190.1632966248748630.3265932497497260.836703375125137
200.1955208100827600.3910416201655200.80447918991724
210.1540680326981310.3081360653962630.845931967301869
220.1189901540505490.2379803081010970.881009845949451
230.09925253412348440.1985050682469690.900747465876516
240.08465741507318240.1693148301463650.915342584926818
250.09253660817723240.1850732163544650.907463391822768
260.07459750148643120.1491950029728620.925402498513569
270.0829048697080180.1658097394160360.917095130291982
280.06478335985113650.1295667197022730.935216640148864
290.05652455379466150.1130491075893230.943475446205339
300.05057255501155560.1011451100231110.949427444988444
310.03362529757715660.06725059515431330.966374702422843
320.04472379566588270.08944759133176540.955276204334117
330.02950292480992910.05900584961985820.97049707519007
340.01928354248409670.03856708496819340.980716457515903
350.01740663844985700.03481327689971390.982593361550143
360.02972468124635990.05944936249271980.97027531875364
370.02696910765943020.05393821531886050.97303089234057
380.01829238025833290.03658476051666580.981707619741667
390.02166008952541560.04332017905083130.978339910474584
400.01903546788089420.03807093576178850.980964532119106
410.01717861529925220.03435723059850440.982821384700748
420.01857109396218870.03714218792437740.981428906037811
430.01599505690287050.0319901138057410.98400494309713
440.03493460647464680.06986921294929350.965065393525353
450.03271328152393540.06542656304787070.967286718476065
460.02368769580788190.04737539161576380.976312304192118
470.03562085380916810.07124170761833630.964379146190832
480.1437361752094770.2874723504189540.856263824790523
490.1060867570726590.2121735141453180.893913242927341
500.1725865919459790.3451731838919570.827413408054021
510.7719471929711070.4561056140577870.228052807028893
520.7851064262589670.4297871474820660.214893573741033
530.8710746974984840.2578506050030310.128925302501516
540.783216696759520.433566606480960.21678330324048
550.7073273405882160.5853453188235680.292672659411784


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level90.176470588235294NOK
10% type I error level170.333333333333333NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/10rfym1258724895.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/10rfym1258724895.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/1b47n1258724895.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/1b47n1258724895.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/2af8c1258724895.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/2af8c1258724895.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/3zi6z1258724895.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/419sk1258724895.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/5hove1258724895.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/7t8sz1258724895.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/8lzwy1258724895.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/8lzwy1258724895.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/9zqey1258724895.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258725139ot68frauw2ws9l5/9zqey1258724895.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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