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w7

*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: Sun, 22 Nov 2009 06:21:07 -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/22/t1258896131smrtlilx4q3qngx.htm/, Retrieved Sun, 22 Nov 2009 14:22:23 +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/22/t1258896131smrtlilx4q3qngx.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 «
8 0 8,1 0 7,7 0 7,5 0 7,6 0 7,8 0 7,8 0 7,8 0 7,5 0 7,5 0 7,1 0 7,5 0 7,5 0 7,6 0 7,7 0 7,7 0 7,9 0 8,1 0 8,2 0 8,2 0 8,2 0 7,9 0 7,3 0 6,9 0 6,6 0 6,7 0 6,9 0 7 0 7,1 0 7,2 0 7,1 0 6,9 0 7 0 6,8 0 6,4 0 6,7 0 6,6 0 6,4 0 6,3 0 6,2 0 6,5 0 6,8 1 6,8 1 6,4 1 6,1 1 5,8 1 6,1 1 7,2 1 7,3 1 6,9 1 6,1 1 5,8 1 6,2 1 7,1 1 7,7 1 7,9 1 7,7 1 7,4 1 7,5 1 8 1 8,1 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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 7.43134020618557 -0.428350515463918X[t] + 0.0614432989690721M1[t] -0.205670103092784M2[t] -0.405670103092784M3[t] -0.505670103092785M4[t] -0.285670103092784M5[t] + 0.139999999999999M6[t] + 0.259999999999999M7[t] + 0.179999999999999M8[t] + 0.0399999999999992M9[t] -0.180000000000001M10[t] -0.380000000000001M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)7.431340206185570.3056724.311600
X-0.4283505154639180.184438-2.32250.0244950.012247
M10.06144329896907210.4018320.15290.8791120.439556
M2-0.2056701030927840.421122-0.48840.62750.31375
M3-0.4056701030927840.421122-0.96330.3402210.17011
M4-0.5056701030927850.421122-1.20080.2357330.117866
M5-0.2856701030927840.421122-0.67840.5008040.250402
M60.1399999999999990.4195030.33370.7400380.370019
M70.2599999999999990.4195030.61980.5383330.269167
M80.1799999999999990.4195030.42910.6697850.334893
M90.03999999999999920.4195030.09540.9244330.462217
M10-0.1800000000000010.419503-0.42910.6697850.334893
M11-0.3800000000000010.419503-0.90580.3695490.184774


Multiple Linear Regression - Regression Statistics
Multiple R0.446265759861158
R-squared0.199153128424457
Adjusted R-squared-0.00105858946942883
F-TEST (value)0.994712649786114
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.467970416533147
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.663292578485196
Sum Squared Residuals21.1179381443299


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
187.492783505154630.507216494845367
28.17.225670103092780.874329896907217
37.77.025670103092780.674329896907217
47.56.925670103092780.574329896907215
57.67.145670103092780.454329896907216
67.87.571340206185570.228659793814433
77.87.691340206185570.108659793814433
87.87.611340206185570.188659793814433
97.57.471340206185570.0286597938144331
107.57.251340206185570.248659793814433
117.17.051340206185570.0486597938144325
127.57.431340206185570.0686597938144325
137.57.492783505154640.00721649484536001
147.67.225670103092780.374329896907217
157.77.025670103092780.674329896907217
167.76.925670103092780.774329896907217
177.97.145670103092780.754329896907217
188.17.571340206185570.528659793814433
198.27.691340206185570.508659793814433
208.27.611340206185570.588659793814432
218.27.471340206185570.728659793814432
227.97.251340206185570.648659793814433
237.37.051340206185570.248659793814433
246.97.43134020618557-0.531340206185567
256.67.49278350515464-0.89278350515464
266.77.22567010309278-0.525670103092783
276.97.02567010309278-0.125670103092783
2876.925670103092780.0743298969072169
297.17.14567010309278-0.0456701030927837
307.27.57134020618557-0.371340206185567
317.17.69134020618557-0.591340206185567
326.97.61134020618557-0.711340206185567
3377.47134020618557-0.471340206185567
346.87.25134020618557-0.451340206185567
356.47.05134020618557-0.651340206185567
366.77.43134020618557-0.731340206185568
376.67.49278350515464-0.89278350515464
386.47.22567010309278-0.825670103092783
396.37.02567010309278-0.725670103092784
406.26.92567010309278-0.725670103092783
416.57.14567010309278-0.645670103092783
426.87.14298969072165-0.342989690721649
436.87.26298969072165-0.462989690721649
446.47.18298969072165-0.78298969072165
456.17.04298969072165-0.94298969072165
465.86.82298969072165-1.02298969072165
476.16.62298969072165-0.52298969072165
487.27.002989690721650.19701030927835
497.37.064432989690720.235567010309277
506.96.797319587628870.102680412371135
516.16.59731958762887-0.497319587628867
525.86.49731958762887-0.697319587628865
536.26.71731958762887-0.517319587628865
547.17.14298969072165-0.0429896907216496
557.77.262989690721650.437010309278351
567.97.182989690721650.717010309278351
577.77.042989690721650.657010309278351
587.46.822989690721650.577010309278351
597.56.622989690721650.87701030927835
6087.002989690721650.99701030927835
618.17.064432989690721.03556701030928


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.09537936673161050.1907587334632210.90462063326839
170.04835406712064050.0967081342412810.95164593287936
180.02434751703110110.04869503406220230.975652482968899
190.01558920216203590.03117840432407180.984410797837964
200.01099279492386620.02198558984773230.989007205076134
210.01961416557820570.03922833115641130.980385834421794
220.01758424217513860.03516848435027720.982415757824861
230.009769260588840050.01953852117768010.99023073941116
240.00943804319867180.01887608639734360.990561956801328
250.05675964848006930.1135192969601390.943240351519931
260.1197876315322790.2395752630645570.880212368467721
270.1375567169238970.2751134338477930.862443283076103
280.1513200164715790.3026400329431580.84867998352842
290.1567939867898350.3135879735796690.843206013210165
300.1520675056441620.3041350112883230.847932494355838
310.1530919457723260.3061838915446530.846908054227673
320.1730473139563590.3460946279127180.826952686043641
330.1607673581605530.3215347163211070.839232641839447
340.1564761755238850.312952351047770.843523824476115
350.1300286910145540.2600573820291080.869971308985446
360.1055516458663920.2111032917327840.894448354133608
370.1243697433363290.2487394866726580.875630256663671
380.1317758623747260.2635517247494510.868224137625274
390.1211133336004330.2422266672008670.878886666399567
400.1085804110731300.2171608221462610.89141958892687
410.0836789648828280.1673579297656560.916321035117172
420.04811826906314350.0962365381262870.951881730936857
430.03270980886199430.06541961772398860.967290191138006
440.03928985522017620.07857971044035240.960710144779824
450.06126349521808930.1225269904361790.93873650478191


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level70.233333333333333NOK
10% type I error level110.366666666666667NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/10ynkc1258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/10ynkc1258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/1mop11258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/1mop11258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/2o8rz1258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/2o8rz1258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/3paic1258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/3paic1258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/4t0e71258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/4t0e71258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/535fm1258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/535fm1258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/6oez41258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/6oez41258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/74udq1258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/74udq1258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/8ums71258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/8ums71258896063.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/9jymh1258896063.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258896131smrtlilx4q3qngx/9jymh1258896063.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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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Software written by Ed van Stee & Patrick Wessa


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