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WS 7 Model 2

*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 11:37:24 -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/t1258742295l1p80n1oha15tte.htm/, Retrieved Fri, 20 Nov 2009 19:38:27 +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/t1258742295l1p80n1oha15tte.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:
WS 7 Model 2
 
Dataseries X:
» Textbox « » Textfile « » CSV «
286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 0 280190 0 280408 0 276836 0 275216 0 274352 0 271311 0 289802 0 290726 0 292300 0 278506 0 269826 0 265861 0 269034 0 264176 0 255198 0 253353 0 246057 0 235372 0 258556 0 260993 0 254663 0 250643 0 243422 0 247105 0 248541 0 245039 0 237080 0 237085 0 225554 0 226839 1 247934 1 248333 1 246969 1 245098 1 246263 1 255765 1 264319 1 268347 1 273046 1 273963 1 267430 1 271993 1 292710 1 295881 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
nwwmb[t] = + 280315.607407407 -7229.51851851852dummy_variable[t] -4302.90370370365M1[t] -9774.70370370372M2[t] -15334.7037037037M3[t] -13009.3037037037M4[t] -11027.3037037037M5[t] -11855.1037037037M6[t] -15430.3037037037M7[t] -16916.3037037037M8[t] -22763.1037037037M9[t] -23322.2M10[t] -2171.60000000001M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)280315.6074074078458.08424333.141700
dummy_variable-7229.518518518525553.004354-1.30190.1992920.099646
M1-4302.9037037036511595.0135-0.37110.7122310.356115
M2-9774.7037037037211595.0135-0.8430.4034930.201747
M3-15334.703703703711595.0135-1.32250.1923930.096196
M4-13009.303703703711595.0135-1.1220.2675730.133786
M5-11027.303703703711595.0135-0.9510.346450.173225
M6-11855.103703703711595.0135-1.02240.3118110.155905
M7-15430.303703703711595.0135-1.33080.1896850.094842
M8-16916.303703703711595.0135-1.45890.1512360.075618
M9-22763.103703703711595.0135-1.96320.0555580.027779
M10-23322.211541.702811-2.02070.049030.024515
M11-2171.6000000000111541.702811-0.18820.8515670.425784


Multiple Linear Regression - Regression Statistics
Multiple R0.423309059985496
R-squared0.179190560265804
Adjusted R-squared-0.0303778073259051
F-TEST (value)0.855045836950505
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.595817608029634
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation18249.0344800242
Sum Squared Residuals15652281194.2963


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1286602276012.70370370310589.2962962966
2283042270540.90370370412501.0962962963
3276687264980.90370370411706.0962962963
4277915267306.30370370410608.6962962963
5277128269288.3037037047839.69629629632
6277103268460.5037037048642.4962962963
7275037264885.30370370410151.6962962963
8270150263399.3037037046750.69629629628
9267140257552.5037037049587.49629629633
10264993256993.4074074077999.5925925926
11287259278144.0074074079114.99259259259
12291186280315.60740740710870.3925925926
13292300276012.70370370416287.2962962962
14288186270540.90370370417645.0962962963
15281477264980.90370370416496.0962962963
16282656267306.30370370415349.6962962963
17280190269288.30370370410901.6962962963
18280408268460.50370370411947.4962962963
19276836264885.30370370411950.6962962963
20275216263399.30370370411816.6962962963
21274352257552.50370370416799.4962962963
22271311256993.40740740714317.5925925926
23289802278144.00740740711657.9925925926
24290726280315.60740740710410.3925925926
25292300276012.70370370416287.2962962962
26278506270540.9037037047965.0962962963
27269826264980.9037037044845.09629629629
28265861267306.303703704-1445.30370370371
29269034269288.303703704-254.303703703708
30264176268460.503703704-4284.5037037037
31255198264885.303703704-9687.3037037037
32253353263399.303703704-10046.3037037037
33246057257552.503703704-11495.5037037037
34235372256993.407407407-21621.4074074074
35258556278144.007407407-19588.0074074074
36260993280315.607407407-19322.6074074074
37254663276012.703703704-21349.7037037038
38250643270540.903703704-19897.9037037037
39243422264980.903703704-21558.9037037037
40247105267306.303703704-20201.3037037037
41248541269288.303703704-20747.3037037037
42245039268460.503703704-23421.5037037037
43237080264885.303703704-27805.3037037037
44237085263399.303703704-26314.3037037037
45225554257552.503703704-31998.5037037037
46226839249763.888888889-22924.8888888889
47247934270914.488888889-22980.4888888889
48248333273086.088888889-24753.0888888889
49246969268783.185185185-21814.1851851852
50245098263311.385185185-18213.3851851852
51246263257751.385185185-11488.3851851852
52255765260076.785185185-4311.78518518518
53264319262058.7851851852260.21481481482
54268347261230.9851851857116.01481481482
55273046257655.78518518515390.2148148148
56273963256169.78518518517793.2148148148
57267430250322.98518518517107.0148148148
58271993249763.88888888922229.1111111111
59292710270914.48888888921795.5111111111
60295881273086.08888888922794.9111111111


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.01320034024509380.02640068049018770.986799659754906
170.002762821085192640.005525642170385270.997237178914807
180.0005905518063446120.001181103612689220.999409448193655
190.0001070981336186310.0002141962672372610.999892901866381
203.19451423826744e-056.38902847653488e-050.999968054857617
211.85074315587043e-053.70148631174086e-050.999981492568441
228.629697499727e-061.7259394999454e-050.9999913703025
232.22681911124678e-064.45363822249355e-060.999997773180889
245.21299249819169e-071.04259849963834e-060.99999947870075
253.11468622378155e-076.22937244756309e-070.999999688531378
264.89464989846093e-079.78929979692187e-070.99999951053501
271.33583296998494e-062.67166593996987e-060.99999866416703
281.11248061855685e-052.22496123711369e-050.999988875193814
291.27486690731494e-052.54973381462989e-050.999987251330927
303.48197090339416e-056.96394180678833e-050.999965180290966
310.0002077858565615760.0004155717131231520.999792214143438
320.0004529761794929560.0009059523589859120.999547023820507
330.001502464908984930.003004929817969860.998497535091015
340.006990953350796040.01398190670159210.993009046649204
350.01295848715566060.02591697431132130.98704151284434
360.0184999509668820.0369999019337640.981500049033118
370.04523921813421640.09047843626843290.954760781865784
380.07409043186145390.1481808637229080.925909568138546
390.0941116758838650.188223351767730.905888324116135
400.09439153401383840.1887830680276770.905608465986162
410.08149561297036320.1629912259407260.918504387029637
420.06414405607262510.1282881121452500.935855943927375
430.04441487391755660.08882974783511330.955585126082443
440.02528704383854580.05057408767709160.974712956161454


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level170.586206896551724NOK
5% type I error level210.724137931034483NOK
10% type I error level240.827586206896552NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/108bvo1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/108bvo1258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/1hje01258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/1hje01258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/2l78t1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/2l78t1258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/3vo3s1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/3vo3s1258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/4j86l1258742239.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/5u8co1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/5u8co1258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/6vwoe1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/6vwoe1258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/72vv71258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/72vv71258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/8pvzj1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/8pvzj1258742239.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/9n0ki1258742239.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258742295l1p80n1oha15tte/9n0ki1258742239.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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