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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: Sat, 14 Nov 2009 04:27:12 -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/14/t1258198096u19u9nuhqnpgtog.htm/, Retrieved Sat, 14 Nov 2009 12:28:28 +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/14/t1258198096u19u9nuhqnpgtog.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 36.68 3922 36.7 3759 36.71 4138 36.72 4634 36.73 3996 36.73 4308 36.87 4429 37.31 5219 37.39 4929 37.42 5755 37.51 5592 37.67 4163 37.67 4962 37.71 5208 37.78 4755 37.79 4491 37.84 5732 37.88 5731 38.34 5040 38.58 6102 38.72 4904 38.83 5369 38.9 5578 38.92 4619 38.94 4731 39.1 5011 39.14 5299 39.16 4146 39.32 4625 39.34 4736 39.44 4219 39.92 5116 40.19 4205 40.2 4121 40.27 5103 40.28 4300 40.3 4578 40.34 3809 40.4 5526 40.43 4247 40.48 3830 40.48 4394 40.63 4826 40.74 4409 40.77 4569 40.91 4106 40.92 4794 41.03 3914 41 3793 41.04 4405 41.33 4022 41.44 4100 41.46 4788 41.55 3163 41.55 3585 41.81 3903 41.78 4178 41.84 3863 41.84 4187 41.86
 
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] = + 12017.7830247441 -174.383836222070X[t] -719.912886653628M1[t] -823.449856480296M2[t] -765.857775875422M3[t] -449.979957771428M4[t] -864.265695270547M5[t] -588.434180183885M6[t] -686.588928026133M7[t] -679.82747414218M8[t] -132.737858192417M9[t] -513.330989656872M10[t] -419.160565518212M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)12017.78302474411895.3759486.340600
X-174.38383622207046.980391-3.71180.0005440.000272
M1-719.912886653628375.895987-1.91520.0615640.030782
M2-823.449856480296375.542108-2.19270.0333150.016657
M3-765.857775875422375.029626-2.04210.0467720.023386
M4-449.979957771428374.846949-1.20040.2359850.117993
M5-864.265695270547374.568512-2.30740.0254870.012743
M6-588.434180183885374.432193-1.57150.1227660.061383
M7-686.588928026133373.759183-1.8370.072540.03627
M8-679.82747414218372.975923-1.82270.0747120.037356
M9-132.737858192417372.841934-0.3560.7234210.361711
M10-513.330989656872372.781014-1.3770.1750260.087513
M11-419.160565518212372.756004-1.12450.2665150.133258


Multiple Linear Regression - Regression Statistics
Multiple R0.562255368238571
R-squared0.316131099113091
Adjusted R-squared0.141526273354732
F-TEST (value)1.81055190049898
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.0738665033626638
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation589.359817260218
Sum Squared Residuals16325214.7274469


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
155604901.47102546502658.528974534976
239224794.44637891388-872.446378913876
337594850.29462115653-1091.29462115653
441385164.4286008983-1026.42860089830
546344748.39902503696-114.399025036963
639965024.23054012363-1028.23054012363
743084901.66205521029-593.662055210287
844294831.69462115653-402.69462115653
952195364.83353020853-145.833530208527
1049294979.00888365741-50.0088836574102
1157555057.48476253608697.515237463916
1255925448.74391425876143.256085741236
1341634728.83102760514-565.831027605136
1449624618.31870432959343.681295670415
1552084663.70391639891544.296083601085
1647554977.83789614069-222.837896140689
1744914554.83296683046-63.8329668304644
1857324823.68912846824908.310871531756
1957314645.317815963841085.68218403616
2050404610.2271491545429.772850845499
2161025132.90302803317969.096971966826
2249044733.12767458429170.872325415709
2353694815.09123018741553.908769812594
2455785230.76411898118347.235881018824
2546194507.36355560311111.636444396893
2647314375.92517198091355.074828019092
2750114426.5418991369584.458100863101
2852994738.93204051645560.067959483547
2941464296.7448892218-150.744889221801
3046254569.0887275840255.9112724159788
3147364453.49559611957282.504403880433
3242194376.55280861693-157.552808616926
3351164876.55878878673239.441211213269
3442054494.22181896005-289.221818960054
3541214576.18537456317-455.185374563169
3651034993.60210171916109.397898280839
3743004270.2015383410929.7984616589081
3845784159.68921506554418.31078493446
3938094206.81826549709-397.818265497091
4055264517.464568514421008.53543148558
4142474094.4596392042152.540360795800
4238304370.29115429086-540.291154290862
4343944245.9788310153148.021168984697
4448264233.55806291483592.441937085171
4544094775.41616377793-366.416163777929
4645694370.40929524239198.590704757615
4741064462.83588101882-356.835881018823
4847944862.81422455261-68.8142245526083
4939144148.13285298564-234.132852985642
5037934037.62052971009-244.620529710091
5144054044.64129781057360.358702189434
5240224341.33689393013-319.336893930132
5341003923.56347970657176.436520293429
5447884183.70044953325604.299550466753
5531634085.545701691-922.545701690999
5635854046.96735815721-461.967358157214
5739034599.28848919364-696.288489193638
5841784208.23232755586-30.2323275558589
5938634302.40275169452-439.402751694519
6041874718.07564048829-531.07564048829


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.987182754660950.02563449067809780.0128172453390489
170.982538269739660.03492346052068140.0174617302603407
180.9882490518794520.02350189624109540.0117509481205477
190.9854849313116760.02903013737664840.0145150686883242
200.9714871919805220.05702561603895590.0285128080194780
210.9647894186782950.07042116264341070.0352105813217054
220.9596014053510120.08079718929797650.0403985946489882
230.9693199591992030.06136008160159390.0306800408007969
240.9540594588873780.09188108222524390.0459405411126220
250.9494679042098260.1010641915803480.0505320957901738
260.9198645832018950.1602708335962100.0801354167981048
270.8827967645855740.2344064708288520.117203235414426
280.8328669736086450.334266052782710.167133026391355
290.8571938995944490.2856122008111020.142806100405551
300.8313360550608330.3373278898783340.168663944939167
310.7955709897154940.4088580205690120.204429010284506
320.788964524734480.4220709505310390.211035475265520
330.7783654886385180.4432690227229650.221634511361482
340.789231132765680.4215377344686390.210768867234320
350.8235293208928660.3529413582142670.176470679107134
360.7536150428361950.4927699143276110.246384957163806
370.6675220080752060.6649559838495880.332477991924794
380.5861048115959470.8277903768081060.413895188404053
390.6425654356677110.7148691286645770.357434564332289
400.7090380907986750.5819238184026510.290961909201325
410.5995098285051410.8009803429897170.400490171494859
420.948482120157030.1030357596859400.0515178798429699
430.9520041441970510.09599171160589790.0479958558029490
440.9890430951145130.02191380977097380.0109569048854869


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level50.172413793103448NOK
10% type I error level110.379310344827586NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/10wpm01258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/10wpm01258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/1a7nm1258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/1a7nm1258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/2juqt1258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/2juqt1258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/3g8961258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/3g8961258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/4ur981258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/4ur981258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/5flru1258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/5flru1258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/6fwcp1258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/6fwcp1258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/72b331258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/72b331258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/81lim1258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/81lim1258198027.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/9a5mj1258198027.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/14/t1258198096u19u9nuhqnpgtog/9a5mj1258198027.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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