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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, 20 Nov 2009 06:55:26 -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/t12587253580g6zusr971c5fr0.htm/, Retrieved Fri, 20 Nov 2009 14:56:10 +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/t12587253580g6zusr971c5fr0.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:
shwws7
 
Dataseries X:
» Textbox « » Textfile « » CSV «
6539 2605 6699 2682 6962 2755 6981 2760 7024 2735 6940 2659 6774 2654 6671 2670 6965 2785 6969 2845 6822 2723 6878 2746 6691 2767 6837 2940 7018 2977 7167 2993 7076 2892 7171 2824 7093 2771 6971 2686 7142 2738 7047 2723 6999 2731 6650 2632 6475 2606 6437 2605 6639 2646 6422 2627 6272 2535 6232 2456 6003 2404 5673 2319 6050 2519 5977 2504 5796 2382 5752 2394 5609 2381 5839 2501 6069 2532 6006 2515 5809 2429 5797 2389 5502 2261 5568 2272 5864 2439 5764 2373 5615 2327 5615 2364 5681 2388 5915 2553 6334 2663 6494 2694 6620 2679 6578 2611 6495 2580 6538 2627 6737 2732 6651 2707 6530 2633 6563 2683
 
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Voeding-Mannen[t] = -1163.16083712531 + 2.90769983505941`Landbouw-Mannen`[t] -50.7291223751464M1[t] -214.871464759489M2[t] -125.681135126959M3[t] -125.385774599149M4[t] + 6.32547487764123M5[t] + 182.215203958574M6[t] + 168.449455084770M7[t] + 135.077291917911M8[t] + 30.8732529973186M9[t] -3.65280901495669M10[t] + 74.1754192412731M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-1163.16083712531348.945854-3.33340.001680.00084
`Landbouw-Mannen`2.907699835059410.13301621.859800
M1-50.7291223751464104.561894-0.48520.6298180.314909
M2-214.871464759489105.264338-2.04130.0468620.023431
M3-125.681135126959106.451279-1.18060.2436840.121842
M4-125.385774599149106.532305-1.1770.2451320.122566
M56.32547487764123105.2305710.06010.9523220.476161
M6182.215203958574104.5930791.74210.0880260.044013
M7168.449455084770104.6194681.61010.1140690.057035
M8135.077291917911104.7473251.28960.2035160.101758
M930.8732529973186105.068480.29380.7701740.385087
M10-3.65280901495669104.919016-0.03480.9723740.486187
M1174.1754192412731104.5461390.70950.481520.24076


Multiple Linear Regression - Regression Statistics
Multiple R0.957534943039322
R-squared0.916873167141318
Adjusted R-squared0.89564929492208
F-TEST (value)43.2000889220505
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation165.299129084041
Sum Squared Residuals1284218.6975693


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
165396360.66811082931178.331889170690
266996420.41865574453278.581344255468
369626721.8710733364240.1289266636
469816736.70493303951244.295066960493
570246795.72368663981228.276313360188
669406750.62822825623189.37177174377
767746722.3239802071351.6760197928712
866716735.47501440122-64.47501440122
969656965.65645651246-0.656456512459602
1069697105.59238460375-136.592384603749
1168226828.68123298273-6.6812329827309
1268786821.3829099478256.6170900521758
1366916831.71548410893-140.715484108925
1468377170.60521318986-333.60521318986
1570187367.38043671959-349.380436719588
1671677414.19899460835-247.198994608349
1770767252.23256074414-176.232560744139
1871717230.39870104103-59.3987010410319
1970937062.5248609090830.4751390909204
2069716781.99821176217189.001788237830
2171426828.99456426467313.005435735333
2270476750.8530047265296.146995273499
2369996851.94283166321147.057168336794
2466506489.90512875105160.094871248948
2564756363.57581066436111.424189335639
2664376196.52576844496240.474231555042
2766396404.93179131492234.068208685075
2864226349.980854976672.0191450233943
2962726214.1837196279357.8162803720695
3062326160.3651617391771.6348382608299
3160035995.399021442287.60097855772302
3256735714.87237229537-41.872372295368
3360506192.20830038666-142.208300386657
3459776114.06674084849-137.066740848491
3557965837.15558922747-41.155589227473
3657525797.87256800691-45.8725680069128
3756095709.34334777599-100.343347775994
3858395894.12498559878-55.1249855987801
3960696073.45401011815-4.45401011815229
4060066024.31847344995-18.3184734499521
4158095905.96753711163-96.9675371116334
4257975965.54927279019-168.549272790190
4355025579.59794502878-77.5979450287818
4455685578.21048004758-10.2104800475758
4558645959.5923135819-95.5923135819047
4657645733.1580624557130.8419375442915
4756155677.2320982992-62.2320982992057
4856155710.64157295513-95.6415729551306
4956815729.69724662141-48.69724662141
5059156045.32537702187-130.325377021869
5163346454.36268851093-120.362688510935
5264946544.79674392559-50.796743925586
5366206632.89249587649-12.8924958764851
5465786611.05863617338-33.0586361733783
5564956507.15419241273-12.1541924127327
5665386610.44392149367-72.4439214936654
5767376811.54836525431-74.548365254311
5866516704.32980736555-53.3298073655505
5965306566.98824782738-36.9882478273842
6065636638.19782033908-75.1978203390814


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.04767020231190760.09534040462381520.952329797688092
170.01918873451567170.03837746903134330.980811265484328
180.03613029101206390.07226058202412780.963869708987936
190.1575632647614120.3151265295228240.842436735238588
200.358996777506140.717993555012280.64100322249386
210.546080003283050.90783999343390.45391999671695
220.6612861405393820.6774277189212350.338713859460618
230.673849687634060.6523006247318810.326150312365941
240.7218774500158280.5562450999683440.278122549984172
250.7062503618306690.5874992763386630.293749638169331
260.9080855057908420.1838289884183170.0919144942091583
270.9890204711796070.02195905764078590.0109795288203930
280.9986593897491170.002681220501765620.00134061025088281
290.9997943985756350.0004112028487309280.000205601424365464
300.999986711450262.65770994784890e-051.32885497392445e-05
310.9999901005354141.97989291726649e-059.89946458633246e-06
320.9999903369049551.93261900893075e-059.66309504465374e-06
330.9999924778226361.50443547286259e-057.52217736431297e-06
340.9999970078837625.9842324767305e-062.99211623836525e-06
350.999990570550221.88588995606006e-059.4294497803003e-06
360.9999746451721335.0709655734324e-052.5354827867162e-05
370.9999305010152860.0001389979694273316.94989847136657e-05
380.9998361006318090.0003277987363826240.000163899368191312
390.999798268697260.0004034626054811960.000201731302740598
400.9992840823234160.001431835353167070.000715917676583535
410.9982221492865720.003555701426856170.00177785071342809
420.9988919196722550.002216160655490370.00110808032774518
430.9975709447319680.004858110536064960.00242905526803248
440.9901439073628870.01971218527422560.0098560926371128


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level160.551724137931034NOK
5% type I error level190.655172413793103NOK
10% type I error level210.724137931034483NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/102gpx1258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/102gpx1258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/17uq81258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/17uq81258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/2uizp1258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/2uizp1258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/33ngk1258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/33ngk1258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/4v2971258725322.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/5w12z1258725322.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/6df1o1258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/6df1o1258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/7qzk71258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/7qzk71258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/8f0351258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/8f0351258725322.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/9y1to1258725322.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587253580g6zusr971c5fr0/9y1to1258725322.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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