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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: Fri, 20 Nov 2009 09:45:13 -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/t1258735572j9lq8dinp73713p.htm/, Retrieved Fri, 20 Nov 2009 17:46:24 +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/t1258735572j9lq8dinp73713p.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 «
111.4 0 87.4 0 96.8 0 114.1 0 110.3 0 103.9 0 101.6 0 94.6 0 95.9 0 104.7 0 102.8 0 98.1 0 113.9 0 80.9 0 95.7 0 113.2 0 105.9 0 108.8 0 102.3 0 99 0 100.7 0 115.5 0 100.7 0 109.9 0 114.6 0 85.4 0 100.5 0 114.8 0 116.5 0 112.9 0 102 0 106 0 105.3 0 118.8 0 106.1 0 109.3 0 117.2 0 92.5 0 104.2 0 112.5 0 122.4 0 113.3 0 100 0 110.7 0 112.8 0 109.8 0 117.3 0 109.1 0 115.9 0 96 0 99.8 0 116.8 1 115.7 1 99.4 1 94.3 1 91 1 93.2 1 103.1 1 94.1 1 91.8 1 102.7 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 time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 98.85059602649 -14.9166390728477X[t] + 9.55899144591611M1[t] -16.0242356512141M2[t] -5.28014486754967M3[t] + 12.3672737306843M4[t] + 12.0313645143488M5[t] + 5.31545529801325M6[t] -2.52045391832229M7[t] -2.51636313465784M8[t] -1.41227235099337M9[t] + 7.17181843267108M10[t] + 0.775909216335541M11[t] + 0.215909216335541t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)98.850596026492.30862542.81800
X-14.91663907284771.978489-7.539400
M19.558991445916112.6132363.65790.0006410.000321
M2-16.02423565121412.745086-5.837400
M3-5.280144867549672.742979-1.9250.0602980.030149
M412.36727373068432.7435484.50784.3e-052.2e-05
M512.03136451434882.7388624.39286.3e-053.2e-05
M65.315455298013252.7347941.94360.057940.02897
M7-2.520453918322292.731347-0.92280.3608310.180415
M8-2.516363134657842.728524-0.92220.3611120.180556
M9-1.412272350993372.726326-0.5180.6068790.30344
M107.171818432671082.7247552.63210.0114450.005722
M110.7759092163355412.7238120.28490.7770020.388501
t0.2159092163355410.0413855.21714e-062e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.911311400399914
R-squared0.830488468498853
Adjusted R-squared0.783602300211301
F-TEST (value)17.712867116918
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value7.07212066686225e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.30622765600411
Sum Squared Residuals871.549041390728


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1111.4108.6254966887422.77450331125823
287.483.2581788079474.14182119205302
396.894.2181788079472.58182119205298
4114.1112.0815066225172.01849337748342
5110.3111.961506622517-1.66150662251656
6103.9105.461506622517-1.56150662251655
7101.697.84150662251653.75849337748346
894.698.0615066225166-3.46150662251656
995.999.3815066225166-3.48150662251655
10104.7108.181506622517-3.48150662251655
11102.8102.0015066225170.798493377483445
1298.1101.441506622517-3.34150662251656
13113.9111.2164072847682.6835927152318
1480.985.8490894039735-4.94908940397352
1595.796.8090894039735-1.10908940397351
16113.2114.672417218543-1.47241721854304
17105.9114.552417218543-8.65241721854304
18108.8108.0524172185430.747582781456949
19102.3100.4324172185431.86758278145695
2099100.652417218543-1.65241721854304
21100.7101.972417218543-1.27241721854305
22115.5110.7724172185434.72758278145695
23100.7104.592417218543-3.89241721854304
24109.9104.0324172185435.86758278145696
25114.6113.8073178807950.792682119205299
2685.488.44-3.04000000000001
27100.599.41.10000000000000
28114.8117.263327814570-2.46332781456953
29116.5117.143327814570-0.643327814569542
30112.9110.6433278145702.25667218543047
31102103.023327814570-1.02332781456954
32106103.2433278145702.75667218543047
33105.3104.5633278145700.736672185430459
34118.8113.3633278145705.43667218543046
35106.1107.183327814570-1.08332781456954
36109.3106.6233278145702.67667218543046
37117.2116.3982284768210.801771523178817
3892.591.03091059602651.46908940397350
39104.2101.9909105960262.20908940397351
40112.5119.854238410596-7.35423841059602
41122.4119.7342384105962.66576158940398
42113.3113.2342384105960.0657615894039687
43100105.614238410596-5.61423841059603
44110.7105.8342384105964.86576158940398
45112.8107.1542384105965.64576158940397
46109.8115.954238410596-6.15423841059603
47117.3109.7742384105967.52576158940397
48109.1109.214238410596-0.114238410596029
49115.9118.989139072848-3.08913907284767
509693.6218211920532.37817880794700
5199.8104.581821192053-4.78182119205298
52116.8107.5285099337759.27149006622517
53115.7107.4085099337758.29149006622516
5499.4100.908509933775-1.50850993377483
5594.393.28850993377481.01149006622516
569193.5085099337748-2.50850993377483
5793.294.8285099337748-1.62850993377483
58103.1103.628509933775-0.528509933774839
5994.197.4485099337748-3.34850993377484
6091.896.8885099337748-5.08850993377484
61102.7106.663410596026-3.96341059602648


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2532787616774220.5065575233548450.746721238322578
180.2981590546067970.5963181092135940.701840945393203
190.182101150420170.364202300840340.81789884957983
200.1621750295122010.3243500590244020.837824970487799
210.1402754986653040.2805509973306080.859724501334696
220.2810991394553180.5621982789106360.718900860544682
230.2421143619285970.4842287238571940.757885638071403
240.3755543730229730.7511087460459470.624445626977027
250.2808540853769170.5617081707538340.719145914623083
260.2333114762387260.4666229524774530.766688523761273
270.1638838735277590.3277677470555190.83611612647224
280.1233892802492980.2467785604985950.876610719750702
290.1554732871513110.3109465743026210.84452671284869
300.1137963451020780.2275926902041560.886203654897922
310.08314097896838910.1662819579367780.916859021031611
320.07433330036788740.1486666007357750.925666699632113
330.05737384751734320.1147476950346860.942626152482657
340.05425659879979160.1085131975995830.945743401200208
350.04383465300738360.08766930601476730.956165346992616
360.02542637187349560.05085274374699110.974573628126504
370.01430433500089360.02860867000178710.985695664999106
380.00983591732181550.0196718346436310.990164082678185
390.004655055442540890.009310110885081780.99534494455746
400.0816514346053670.1633028692107340.918348565394633
410.1161697485683980.2323394971367960.883830251431602
420.06619805687803470.1323961137560690.933801943121965
430.1770836410424440.3541672820848880.822916358957556
440.1260056585454890.2520113170909780.87399434145451


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0357142857142857NOK
5% type I error level30.107142857142857NOK
10% type I error level50.178571428571429NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/101x1b1258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/101x1b1258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/1sstz1258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/1sstz1258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/2m3331258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/2m3331258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/3k9vv1258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/3k9vv1258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/4xw041258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/4xw041258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/5sp801258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/5sp801258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/6ngb61258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/6ngb61258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/7knt41258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/7knt41258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/8v9by1258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/8v9by1258735502.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/9hc891258735502.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735572j9lq8dinp73713p/9hc891258735502.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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Software written by Ed van Stee & Patrick Wessa


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