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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: Mon, 23 Nov 2009 05:47:54 -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/23/t12589805276kzp4d7aqkdo758.htm/, Retrieved Mon, 23 Nov 2009 13:49:00 +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/23/t12589805276kzp4d7aqkdo758.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 «
5560 543 3922 594 3759 611 4138 613 4634 611 3996 594 4308 595 4143 591 4429 589 5219 584 4929 573 5755 567 5592 569 4163 621 4962 629 5208 628 4755 612 4491 595 5732 597 5731 593 5040 590 6102 580 4904 574 5369 573 5578 573 4619 620 4731 626 5011 620 5299 588 4146 566 4625 557 4736 561 4219 549 5116 532 4205 526 4121 511 5103 499 4300 555 4578 565 3809 542 5526 527 4247 510 3830 514 4394 517 4826 508 4409 493 4569 490 4106 469 4794 478 3914 528 3793 534 4405 518 4022 506 4100 502 4788 516 3163 528 3585 533 3903 536 4178 537 3863 524 4187 536
 
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] = + 2311.02615457282 + 4.07602600150082X[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2311.026154572821048.1948592.20480.0313820.015691
X4.076026001500821.8741762.17480.0336630.016832


Multiple Linear Regression - Regression Statistics
Multiple R0.272429968325699
R-squared0.0742180876419413
Adjusted R-squared0.0585268687884148
F-TEST (value)4.72991220980017
F-TEST (DF numerator)1
F-TEST (DF denominator)59
p-value0.0336631195452499
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation614.560300724891
Sum Squared Residuals22283377.4303971


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
155604524.308273387771035.69172661223
239224732.18559946431-810.185599464307
337594801.47804148982-1042.47804148982
441384809.63009349282-671.630093492824
546344801.47804148982-167.478041489822
639964732.18559946431-736.185599464308
743084736.26162546581-428.261625465809
841434719.9575214598-576.957521459806
944294711.80546945680-282.805469456804
1052194691.4253394493527.5746605507
1149294646.58905343279282.410946567209
1257554622.132897423791132.86710257621
1355924630.28494942679961.715050573212
1441634842.23830150483-679.23830150483
1549624874.8465095168487.1534904831631
1652084870.77048351534337.229516484664
1747554805.55406749132-50.554067491323
1844914736.26162546581-245.261625465809
1957324744.41367746881987.58632253119
2057314728.109573462811002.89042653719
2150404715.88149545830324.118504541695
2261024675.12123544331426.87876455670
2349044650.66507943429253.334920565708
2453694646.58905343279722.410946567209
2555784646.58905343279931.410946567209
2646194838.16227550333-219.162275503330
2747314862.61843151233-131.618431512334
2850114838.16227550333172.837724496670
2952994707.7294434553591.270556544697
3041464618.05687142229-472.056871422285
3146254581.3726374087843.627362591222
3247364597.67674141478138.323258585219
3342194548.76442939677-329.764429396771
3451164479.47198737126636.528012628742
3542054455.01583136225-250.015831362253
3641214393.87544133974-272.875441339740
3751034344.96312932173758.03687067827
3843004573.22058540578-273.220585405776
3945784613.98084542078-35.9808454207845
4038094520.23224738627-711.232247386266
4155264459.091857363751066.90814263625
4242474389.79941533824-142.799415338239
4338304406.10351934424-576.103519344243
4443944418.33159734875-24.3315973487452
4548264381.64736333524444.352636664762
4644094320.5069733127388.4930266872744
4745694308.27889530822260.721104691777
4841064222.68234927671-116.682349276706
4947944259.36658329021534.633416709787
5039144463.16788336525-549.167883365254
5137934487.62403937426-694.624039374259
5244054422.40762335025-17.4076233502460
5340224373.49531133224-351.495311332236
5441004357.19120732623-257.191207326233
5547884414.25557134724373.744428652756
5631634463.16788336525-1300.16788336525
5735854483.54801337276-898.548013372758
5839034495.77609137726-592.776091377261
5941784499.85211737876-321.852117378762
6038634446.86377935925-583.863779359251
6141874495.77609137726-308.776091377261


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.4172611291729570.8345222583459140.582738870827043
60.340940655405660.681881310811320.65905934459434
70.2143700863592020.4287401727184040.785629913640798
80.1495126052429960.2990252104859930.850487394757004
90.0856428828816630.1712857657633260.914357117118337
100.1380295104385160.2760590208770320.861970489561484
110.08441714873874330.1688342974774870.915582851261257
120.1522174795849810.3044349591699630.847782520415019
130.1627064769230380.3254129538460760.837293523076962
140.15906221102750.3181244220550.8409377889725
150.3993296781573930.7986593563147860.600670321842607
160.5714196617867610.8571606764264780.428580338213239
170.507825074453520.984349851092960.49217492554648
180.4421736896912570.8843473793825150.557826310308743
190.5964311853164810.8071376293670380.403568814683519
200.7032258275474370.5935483449051270.296774172452563
210.6396048478989220.7207903042021570.360395152101078
220.8431403784219180.3137192431561630.156859621578082
230.8029859328762420.3940281342475170.197014067123758
240.799465920974250.4010681580515010.200534079025750
250.8467172905570060.3065654188859890.153282709442994
260.7991046096917660.4017907806164680.200895390308234
270.7528449201449890.4943101597100230.247155079855011
280.7372077657283620.5255844685432760.262792234271638
290.7930692790380540.4138614419238910.206930720961946
300.8321585969750720.3356828060498550.167841403024928
310.8243210562352960.3513578875294080.175678943764704
320.8201335497343820.3597329005312350.179866450265618
330.8261357246954870.3477285506090250.173864275304513
340.8623044257056040.2753911485887910.137695574294396
350.8602988997299190.2794022005401630.139701100270081
360.8530807094108680.2938385811782630.146919290589132
370.8682446344183520.2635107311632960.131755365581648
380.842098997143460.3158020057130810.157901002856541
390.8524363269135790.2951273461728420.147563673086421
400.8475289764954830.3049420470090350.152471023504518
410.9871534099948080.02569318001038390.0128465900051919
420.9801345790714090.03973084185718220.0198654209285911
430.9785095034490690.04298099310186290.0214904965509315
440.9685742828144640.06285143437107260.0314257171855363
450.9758066409903860.04838671801922890.0241933590096144
460.959162472932590.08167505413482170.0408375270674108
470.9387826774733760.1224346450532480.0612173225266239
480.9419050414425830.1161899171148350.0580949585574173
490.9096470555742880.1807058888514230.0903529444257117
500.8667610243688220.2664779512623570.133238975631178
510.8144278936772330.3711442126455340.185572106322767
520.7614722199990350.477055560001930.238527780000965
530.6649481387980790.6701037224038420.335051861201921
540.5616350919692880.8767298160614240.438364908030712
550.824010935521170.3519781289576590.175989064478829
560.9083571518143150.1832856963713710.0916428481856853


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.0769230769230769NOK
10% type I error level60.115384615384615NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/10gvzj1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/10gvzj1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/1vyyk1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/1vyyk1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/2it2t1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/2it2t1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/32qgc1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/32qgc1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/4au3e1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/4au3e1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/55hpe1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/55hpe1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/6t8tk1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/6t8tk1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/7uz3l1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/7uz3l1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/8822k1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/8822k1258980468.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/96z8d1258980468.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589805276kzp4d7aqkdo758/96z8d1258980468.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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