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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: Wed, 29 Dec 2010 13:51:42 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql.htm/, Retrieved Wed, 29 Dec 2010 14:49:27 +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/2010/Dec/29/t1293630556dp2hp501dar7dql.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
597141 25 593408 24 590072 21 579799 22 574205 20 572775 24 572942 24 619567 24 625809 24 619916 28 587625 27 565742 18 557274 25 560576 27 548854 25 531673 28 525919 28 511038 27 498662 25 555362 24 564591 24 541657 25 527070 18 509846 22 514258 20 516922 23 507561 23 492622 19 490243 17 469357 15 477580 13 528379 15 533590 17 517945 9 506174 4 501866 1 516141 6 528222 2 532638 2 536322 4 536535 7 523597 8 536214 9 586570 15 596594 15 580523 14 564478 16 557560 11 575093 11 580112 11 574761 13 563250 18 551531 13 537034 17 544686 19 600991 22 604378 22 586111 24 563668 26 548604 24
 
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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Werkloos[t] = + 520417.636254683 + 1649.97677557105cv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)520417.63625468311819.64550144.029900
cv1649.97677557105605.0889712.72680.0084440.004222


Multiple Linear Regression - Regression Statistics
Multiple R0.337094357596456
R-squared0.113632605923367
Adjusted R-squared0.0983504094737703
F-TEST (value)7.43562002347922
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.0084443171655817
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation34810.9390710286
Sum Squared Residuals70284485782.3982


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1597141561667.05564395935473.9443560411
2593408560017.07886838833390.9211316119
3590072555067.14854167535004.8514583249
4579799556717.12531724623081.8746827539
5574205553417.17176610420787.8282338960
6572775560017.07886838812757.9211316118
7572942560017.07886838812924.9211316118
8619567560017.07886838859549.9211316118
9625809560017.07886838865791.9211316118
10619916566616.98597067253299.0140293276
11587625564967.00919510122657.9908048987
12565742550117.21821496215624.7817850381
13557274561667.055643959-4393.05564395925
14560576564967.009195101-4391.00919510133
15548854561667.055643959-12813.0556439593
16531673566616.985970672-34943.9859706724
17525919566616.985970672-40697.9859706724
18511038564967.009195101-53929.0091951013
19498662561667.055643959-63005.0556439592
20555362560017.078868388-4655.07886838820
21564591560017.0788683884573.9211316118
22541657561667.055643959-20010.0556439593
23527070550117.218214962-23047.2182149619
24509846556717.125317246-46871.1253172461
25514258553417.171766104-39159.171766104
26516922558367.102092817-41445.1020928172
27507561558367.102092817-50806.1020928172
28492622551767.194990533-59145.194990533
29490243548467.241439391-58224.2414393909
30469357545167.287888249-75810.2878882488
31477580541867.334337107-64287.3343371067
32528379545167.287888249-16788.2878882488
33533590548467.241439391-14877.2414393909
34517945535267.427234823-17322.4272348225
35506174527017.543356967-20843.5433569673
36501866522067.613030254-20201.6130302542
37516141530317.496908109-14176.4969081094
38528222523717.5898058254504.41019417476
39532638523717.5898058258920.41019417476
40536322527017.5433569679304.45664303268
41536535531967.473683684567.52631631954
42523597533617.450459252-10020.4504592515
43536214535267.427234823946.572765177457
44586570545167.28788824941402.7121117512
45596594545167.28788824951426.7121117512
46580523543517.31111267837005.6888873222
47564478546817.2646638217660.7353361801
48557560538567.38078596518992.6192140354
49575093538567.38078596536525.6192140354
50580112538567.38078596541544.6192140354
51574761541867.33433710732893.6656628933
52563250550117.21821496213132.7817850381
53551531541867.3343371079663.66566289328
54537034548467.241439391-11433.2414393909
55544686551767.194990533-7081.19499053298
56600991556717.12531724644273.8746827539
57604378556717.12531724647660.8746827539
58586111560017.07886838826093.9211316118
59563668563317.03241953350.967580469709
60548604560017.078868388-11413.0788683882


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.007620311564060580.01524062312812120.99237968843594
60.01313298471703790.02626596943407590.986867015282962
70.007273796454944260.01454759290988850.992726203545056
80.03205550805300210.06411101610600430.967944491946998
90.06860001121003430.1372000224200690.931399988789966
100.04558270557751440.09116541115502880.954417294422486
110.04127042554312190.08254085108624370.958729574456878
120.02260756709163230.04521513418326460.977392432908368
130.04990860179077740.09981720358155480.950091398209223
140.07365385744806820.1473077148961360.926346142551932
150.1023886121113300.2047772242226610.89761138788867
160.2018009613660070.4036019227320140.798199038633993
170.2803821039631260.5607642079262520.719617896036874
180.4261108637840980.8522217275681960.573889136215902
190.6585312907750790.6829374184498430.341468709224921
200.5918787055114510.8162425889770980.408121294488549
210.517652343768490.964695312463020.48234765623151
220.4681347785101390.9362695570202770.531865221489861
230.512872503802140.974254992395720.48712749619786
240.5961890955087370.8076218089825250.403810904491263
250.6301053827487120.7397892345025750.369894617251288
260.6562390435860230.6875219128279550.343760956413977
270.7311864944395450.5376270111209090.268813505560455
280.8374431434302430.3251137131395140.162556856569757
290.906623100648560.1867537987028810.0933768993514405
300.9810756049570460.03784879008590720.0189243950429536
310.996826541454750.006346917090499190.00317345854524960
320.9967025971750460.006594805649908240.00329740282495412
330.9966930046056660.006613990788668870.00330699539433444
340.9965773160030430.006845367993914510.00342268399695726
350.9964465506318670.007106898736266790.00355344936813339
360.996266374587530.007467250824942030.00373362541247101
370.9960482301942880.007903539611423680.00395176980571184
380.9942205062769740.01155898744605170.00577949372302586
390.9911377551336360.01772448973272830.00886224486636415
400.9862301960390540.0275396079218910.0137698039609455
410.98018217801680.03963564396639810.0198178219831991
420.9841312140184250.03173757196315040.0158687859815752
430.9852508148489230.02949837030215480.0147491851510774
440.9824510369009280.03509792619814480.0175489630990724
450.986653329082260.02669334183548060.0133466709177403
460.9811672279999720.03766554400005520.0188327720000276
470.9662035399626770.06759292007464640.0337964600373232
480.9434643999296160.1130712001407680.0565356000703839
490.9161442437515380.1677115124969240.083855756248462
500.8995970364587270.2008059270825450.100402963541273
510.8766689674171520.2466620651656950.123331032582848
520.7962646833002620.4074706333994760.203735316699738
530.6898213088786660.6203573822426680.310178691121334
540.6089077352257790.7821845295484420.391092264774221
550.8462666927096830.3074666145806330.153733307290317


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level70.137254901960784NOK
5% type I error level210.411764705882353NOK
10% type I error level260.509803921568627NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/106t321293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/106t321293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/1zso81293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/1zso81293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/2zso81293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/2zso81293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/3a1ob1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/3a1ob1293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/4a1ob1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/4a1ob1293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/5a1ob1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/5a1ob1293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/63s5e1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/63s5e1293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/7w2mh1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/7w2mh1293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/8w2mh1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/8w2mh1293630694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/9w2mh1293630694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630556dp2hp501dar7dql/9w2mh1293630694.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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Software written by Ed van Stee & Patrick Wessa


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