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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, 24 Dec 2010 15:43:44 +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/24/t1293205305dwoagxh1ghh19lj.htm/, Retrieved Fri, 24 Dec 2010 16:41:48 +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/24/t1293205305dwoagxh1ghh19lj.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 «
611 120,9 594 119,6 595 125,9 591 116,1 589 107,5 584 116,7 573 112,5 567 113 569 126,4 621 114,1 629 112,5 628 112,4 612 113,1 595 116,3 597 111,7 593 118,8 590 116,5 580 125,1 574 113,1 573 119,6 573 114,4 620 114 626 117,8 620 117 588 120,9 566 115 557 117,3 561 119,4 549 114,9 532 125,8 526 117,6 511 117,6 499 114,9 555 121,9 565 117 542 106,4 527 110,5 510 113,6 514 114,2 517 125,4 508 124,6 493 120,2 490 120,8 469 111,4 478 124,1 528 120,2 534 125,5 518 116 506 117 502 105,7 516 102 528 106,4 533 96,9 536 107,6 537 98,8 524 101,1 536 105,7 587 104,6 597 103,2 581 101,6
 
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 time6 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Multiple Linear Regression - Estimated Regression Equation
WerkL[t] = + 548.195698689663 + 0.0773540981601292Chem.Nijv.[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)548.19569868966387.3334746.27700
Chem.Nijv.0.07735409816012920.7600620.10180.9192880.459644


Multiple Linear Regression - Regression Statistics
Multiple R0.0133623167258849
R-squared0.000178551508282863
Adjusted R-squared-0.0170597493277811
F-TEST (value)0.0103578368878049
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.919287527063784
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation42.1400252188591
Sum Squared Residuals102995.340075873


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1611557.54780915722353.4521908427768
2594557.44724882961536.5527511703855
3595557.93457964802337.0654203519767
4591557.17650948605433.823490513946
5589556.51126424187732.4887357581231
6584557.2229219449526.7770780550499
7573556.89803473267816.1019652673224
8567556.93671178175810.0632882182424
9569557.97325669710311.0267433028966
10621557.02180128973463.9781987102662
11629556.89803473267872.1019652673224
12628556.89029932286271.1097006771384
13612556.94444719157455.0555528084263
14595557.19198030568637.8080196943139
15597556.83615145414940.1638485458505
16593557.38536555108635.6146344489136
17590557.20745112531832.7925488746819
18580557.87269636949522.1273036305048
19574556.94444719157417.0555528084263
20573557.44724882961515.5527511703855
21573557.04500751918215.9549924808182
22620557.01406587991862.9859341200822
23626557.30801145292668.6919885470737
24620557.24612817439862.7538718256018
25588557.54780915722330.4521908427773
26566557.0914199780788.9085800219221
27557557.269334403846-0.269334403846196
28561557.4317780099833.56822199001753
29549557.083684568262-8.08368456826189
30532557.926844238207-25.9268442382073
31526557.292540633294-31.2925406332942
32511557.292540633294-46.2925406332942
33499557.083684568262-58.0836845682619
34555557.625163255383-2.62516325538279
35565557.2461281743987.75387182560184
36542556.426174733901-14.4261747339008
37527556.743326536357-29.7433265363573
38510556.983124240654-46.9831242406537
39514557.02953669955-43.0295366995498
40517557.895902598943-40.8959025989432
41508557.834019320415-49.8340193204151
42493557.49366128851-64.4936612885106
43490557.540073747407-67.5400737474067
44469556.812945224701-87.8129452247014
45478557.795342271335-79.795342271335
46528557.49366128851-29.4936612885106
47534557.903638008759-23.9036380087593
48518557.168774076238-39.168774076238
49506557.246128174398-51.2461281743982
50502556.372026865189-54.3720268651887
51516556.085816701996-40.0858167019962
52528556.426174733901-28.4261747339008
53533555.69131080138-22.6913108013796
54536556.518999651693-20.5189996516929
55537555.838283587884-18.8382835878838
56524556.016198013652-32.0161980136521
57536556.372026865189-20.3720268651887
58587556.28693735721330.7130626427874
59597556.17864161978840.8213583802116
60581556.05487506273224.9451249372678


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.01225030658160050.0245006131632010.9877496934184
60.004268832504855270.008537665009710530.995731167495145
70.002733190021600240.005466380043200490.9972668099784
80.002100082838340950.00420016567668190.99789991716166
90.003262393850385060.006524787700770110.996737606149615
100.008466810971275140.01693362194255030.991533189028725
110.01866823236651610.03733646473303230.981331767633484
120.02537569142108840.05075138284217690.974624308578912
130.01804524092795140.03609048185590280.981954759072049
140.01045880970912890.02091761941825780.98954119029087
150.006177958136685810.01235591627337160.993822041863314
160.003570647941160740.007141295882321470.99642935205884
170.002107458454718860.004214916909437730.997892541545281
180.001217831250574020.002435662501148040.998782168749426
190.001161070213504530.002322140427009070.998838929786495
200.0008645089019786840.001729017803957370.999135491098021
210.0007446483428073830.001489296685614770.999255351657193
220.001591430180422750.00318286036084550.998408569819577
230.0075294179532130.0150588359064260.992470582046787
240.02596814101550080.05193628203100160.974031858984499
250.03608460283535320.07216920567070650.963915397164647
260.05259886379570020.10519772759140.9474011362043
270.08115287422761690.1623057484552340.918847125772383
280.1106206841915640.2212413683831280.889379315808436
290.1676441864004280.3352883728008570.832355813599572
300.2369627341981130.4739254683962270.763037265801887
310.3565154333016260.7130308666032530.643484566698374
320.5289256791095030.9421486417809940.471074320890497
330.7355725239780370.5288549520439270.264427476021963
340.7613899645677320.4772200708645360.238610035432268
350.8108012701333470.3783974597333060.189198729866653
360.8097460470846820.3805079058306350.190253952915318
370.8099442056478580.3801115887042840.190055794352142
380.8313555883883070.3372888232233860.168644411611693
390.8301691721890430.3396616556219140.169830827810957
400.8244952288063250.351009542387350.175504771193675
410.8109248053727850.378150389254430.189075194627215
420.8179918458635850.3640163082728290.182008154136415
430.8216281356227470.3567437287545060.178371864377253
440.9376844947777820.1246310104444360.0623155052222179
450.953089849137410.09382030172517960.0469101508625898
460.926008761677030.1479824766459410.0739912383229706
470.9000951819015360.1998096361969270.0999048180984637
480.8552172003362760.2895655993274480.144782799663724
490.818317218055910.3633655638881790.181682781944089
500.8587126907314710.2825746185370570.141287309268528
510.8478010289318120.3043979421363770.152198971068188
520.8127998352079160.3744003295841690.187200164792084
530.7232641619146370.5534716761707260.276735838085363
540.6694199620789480.6611600758421030.330580037921051
550.5175463070569860.9649073858860280.482453692943014


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level110.215686274509804NOK
5% type I error level180.352941176470588NOK
10% type I error level220.431372549019608NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/10l6nl1293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/10l6nl1293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/1e4q91293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/1e4q91293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/27w7c1293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/27w7c1293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/37w7c1293205415.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/47w7c1293205415.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/57w7c1293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/57w7c1293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/6i56x1293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/6i56x1293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/7ten01293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/7ten01293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/8ten01293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/8ten01293205415.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/9ten01293205415.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293205305dwoagxh1ghh19lj/9ten01293205415.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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