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M4

*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 01:28:14 -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/t1258620048qke0co73idelqno.htm/, Retrieved Thu, 19 Nov 2009 09:41:01 +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/t1258620048qke0co73idelqno.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 «
23 2497,84 21 25 19 21 23 2645,64 23 21 25 19 19 2756,76 23 23 21 25 18 2849,27 19 23 23 21 19 2921,44 18 19 23 23 19 2981,85 19 18 19 23 22 3080,58 19 19 18 19 23 3106,22 22 19 19 18 20 3119,31 23 22 19 19 14 3061,26 20 23 22 19 14 3097,31 14 20 23 22 14 3161,69 14 14 20 23 15 3257,16 14 14 14 20 11 3277,01 15 14 14 14 17 3295,32 11 15 14 14 16 3363,99 17 11 15 14 20 3494,17 16 17 11 15 24 3667,03 20 16 17 11 23 3813,06 24 20 16 17 20 3917,96 23 24 20 16 21 3895,51 20 23 24 20 19 3801,06 21 20 23 24 23 3570,12 19 21 20 23 23 3701,61 23 19 21 20 23 3862,27 23 23 19 21 23 3970,1 23 23 23 19 27 4138,52 23 23 23 23 26 4199,75 27 23 23 23 17 4290,89 26 27 23 23 24 4443,91 17 26 27 23 26 4502,64 24 17 26 27 24 4356,98 26 24 17 26 27 4591,27 24 26 24 17 27 4696,96 27 24 26 24 26 4621,4 27 27 24 26 24 4562,84 26 27 27 24 23 4202,52 24 26 27 27 23 4296,49 23 24 26 27 24 4435,23 23 23 24 26 17 4105,18 24 23 23 24 21 4116,68 17 24 23 23 19 3844,49 21 17 24 23 22 3720,98 19 21 1 etc...
 
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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Consvertr[t] = -2.30802815173133 + 0.0038777162416759Aand[t] + 0.405105033674106Y1[t] + 0.0408529815879891Y2[t] + 0.108240589410743Y3[t] -0.0693297363740693Y4[t] + 2.15292212174366M1[t] + 1.04935628306701M2[t] + 1.59721168826427M3[t] -1.18333001580422M4[t] -0.48610405600735M5[t] + 2.64584732173502M6[t] + 2.47449066262075M7[t] + 1.4250603170624M8[t] + 0.806606050478028M9[t] -1.59756470173195M10[t] + 0.569132549626265M11[t] -0.0939253055905727t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-2.308028151731332.604447-0.88620.3809480.190474
Aand0.00387771624167590.0009733.9850.0002860.000143
Y10.4051050336741060.1557592.60080.0130710.006536
Y20.04085298158798910.1614860.2530.8016110.400805
Y30.1082405894107430.164710.65720.5149380.257469
Y4-0.06932973637406930.144338-0.48030.6336770.316839
M12.152922121743661.9789551.08790.2833130.141657
M21.049356283067011.9517730.53760.5938790.296939
M31.597211688264271.9597350.8150.4200140.210007
M4-1.183330015804221.964064-0.60250.5503350.275167
M5-0.486104056007351.968148-0.2470.8062150.403108
M62.645847321735021.9312761.370.1785230.089262
M72.474490662620751.9955881.240.2223920.111196
M81.42506031706242.1026860.67770.5019420.250971
M90.8066060504780282.0770540.38830.6998750.349938
M10-1.597564701731952.050219-0.77920.4405550.220278
M110.5691325496262652.0440530.27840.7821510.391075
t-0.09392530559057270.028977-3.24130.0024380.001219


Multiple Linear Regression - Regression Statistics
Multiple R0.94131041838606
R-squared0.886065303762138
Adjusted R-squared0.8364014618123
F-TEST (value)17.8412557098805
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value2.44582132324922e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.83762272655424
Sum Squared Residuals314.032006792028


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12319.56606038333413.43393961666588
22320.37659684979542.62340315020458
31920.4941839654657-1.49418396546573
41816.85182447494541.14817552505456
51917.02780347753931.97219652246071
61920.2313720822939-1.23137208229387
72220.55886837980321.44113162019679
82320.9078227998982.09217720010201
92020.7045367753906-0.704536775390588
101417.1315989385587-3.13159893855866
111416.6912247883186-2.69122478831864
121415.6386449106067-1.63864491060667
131517.6263929690103-2.62639296901030
141117.3269579440589-6.32695794405887
151716.27232187494220.727678125057794
161616.0395965047024-0.0395965047024457
172016.48541902108693.5145809789131
182422.70007675784401.29992324215603
192324.2606707493043-1.26067074930427
202023.7846865186020-3.78468651860205
212121.8847275463379-0.884727546337865
221918.91736774351410.0826322564858539
232319.06987078281083.93012921718923
242320.77163780626532.22836219373470
252323.3312295249624-0.331229524962437
262323.1234943534262-0.123494353426229
272723.95319047695973.0468095230403
282622.93657616747493.06342383252513
291723.6515987726254-6.65159877262536
302424.0291570570664-0.0291570570664328
312626.0741122337550-0.0741122337550348
322424.5572738049851-0.557273804985117
332725.4065520201421.59344797985799
342724.18307395397352.81692604602647
352625.73026395371450.269736046285519
362424.8984032426914-0.898403242691367
372324.5011290845854-1.50112908458539
382323.0729753492876-0.0729753492876153
392423.8768953762290.123104623770986
401720.1581120380163-3.15811203801632
412118.08045391124522.91954608875479
421921.5056942525665-2.50569425256649
432219.28766355160672.71233644839328
442220.01556352802831.98443647197166
451819.6424179460995-1.64241794609946
461615.76795936395370.232040636046336
471415.5086404751561-1.50864047515611
481211.69131404043670.308685959563333
491412.97518803810771.02481196189226
501612.09997550343193.90002449656813
51810.4034083064033-2.40340830640335
5234.01389081486092-1.01389081486092
5301.75472481750323-1.75472481750323
5452.533699850229242.46630014977076
5513.81868508553076-2.81868508553076
5610.7346533484865060.265346651513494
5731.361765712030081.63823428796992


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.5864798186404230.8270403627191540.413520181359577
220.7037315283759870.5925369432480250.296268471624013
230.5936127225883030.8127745548233940.406387277411697
240.5596457686045050.880708462790990.440354231395495
250.5177667233613450.964466553277310.482233276638655
260.3933472832087450.7866945664174890.606652716791255
270.3722195295020660.7444390590041330.627780470497934
280.4962645743569490.9925291487138980.503735425643051
290.8778053564516220.2443892870967550.122194643548378
300.8259605380411270.3480789239177470.174039461958873
310.747089344237220.5058213115255610.252910655762780
320.6480549073548570.7038901852902870.351945092645143
330.5411702154552340.9176595690895330.458829784544766
340.6603729128260280.6792541743479450.339627087173972
350.6985733972863250.6028532054273490.301426602713675
360.523291160599550.95341767880090.47670883940045


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/10p4031258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/10p4031258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/17beh1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/17beh1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/2zevu1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/2zevu1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/3mhgp1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/3mhgp1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/49e9n1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/49e9n1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/5ztgv1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/5ztgv1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/6ia4c1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/6ia4c1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/7v8le1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/7v8le1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/8kepi1258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/8kepi1258619288.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/9l6h81258619288.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258620048qke0co73idelqno/9l6h81258619288.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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