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Workshop 7 review

*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, 26 Nov 2010 09:37:04 +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/Nov/26/t1290764120j23m7itvv6845w8.htm/, Retrieved Fri, 26 Nov 2010 10:35:23 +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/Nov/26/t1290764120j23m7itvv6845w8.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 «
43071 990633 45552 1047696 36329 835567 37703 867169 50519 1161937 36798 846354 37056 852288 44927 1033321 37635 865605 62924 1447252 8170 187910 27438 631074 27429 630867 33666 774318 27733 637859 33228 764244 25699 591077 303936 6990528 30169 693887 35117 807691 34870 802010 56676 1303548 7054 162242 29722 683606 41629 957467 41117 945691 39341 904843 39486 908178 48138 1107174 45633 1049559 41756 960388 47221 1086083 50530 1162190 68184 1568232 8771 201733 37898 871654 41888 963424 40439 930097 40898 940654 38401 883223 52073 1197679 41547 955581 38529 886167 51321 1180383 41519 954937 69116 1589668 12657 291111 34801 800423 37967 873241 39401 906223 33425 768775 36222 833106 48428 1113844 40891 940493 36432 837936 50669 1165387 39556 909788 68906 1584838
 
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
Verkoopcijfers[t] = -2.16080094974641e-12 + 0.0434782608695652`Totaleuitstootkm/u`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-2.16080094974641e-120-1.98930.0515560.025778
`Totaleuitstootkm/u`0.043478260869565205279036419448320800


Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)2.78682255178618e+33
F-TEST (DF numerator)1
F-TEST (DF denominator)56
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.28579786031869e-12
Sum Squared Residuals1.56462090512838e-21


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
143071430712.2236603765632e-11
245552455523.04672082062726e-11
336329363294.26423361600248e-14
43770337703-2.13385244240005e-13
550519505194.86497751854067e-13
63679836798-3.00659056435213e-13
73705637056-5.38808164607463e-13
84492744927-3.45455282489792e-13
93763537635-5.55874485369407e-13
106292462924-3.58401426601991e-12
1181708170-3.35495697743738e-13
122743827438-4.43717423682596e-12
132742927429-3.25679135312986e-12
143366633666-1.43703305610115e-12
152773327733-2.7549572778756e-12
163322833228-8.52619085953262e-13
172569925699-3.37009792118209e-12
18303936303936-1.8404020615302e-12
193016930169-1.76324649894296e-12
2035117351173.74277331771232e-13
213487034870-6.13054784378416e-13
225667656676-5.41200710054708e-13
2370547054-1.2848435245694e-12
242972229722-1.93645495688464e-12
254162941629-2.60871677557611e-13
264111741117-8.459932444068e-13
273934139341-8.48630114417741e-13
283948639486-3.75031859962197e-13
294813848138-3.41651401952082e-13
304563345633-2.00131334769363e-13
314175641756-3.33293578783459e-13
324722147221-1.47454984751153e-13
3350530505302.28686915795456e-13
346818468184-2.95114455345813e-12
3587718771-1.83540998967634e-12
3637898378985.6460051058624e-14
374188841888-2.80651559699103e-13
384043940439-9.28915592800195e-13
394089840898-5.5356421472793e-13
403840138401-1.08371119844505e-12
4152073520738.52319786951532e-13
424154741547-2.75238036430598e-13
433852938529-1.17934840379857e-12
4451321513211.05158952856091e-12
454151941519-5.87106749390906e-13
466911669116-1.56000611288703e-12
471265712657-5.55082962443998e-12
4834801348013.55637114880694e-14
493796737967-5.92602534017711e-13
503940139401-3.19086172637381e-13
513342533425-6.28760309700135e-13
523622236222-3.53904781871073e-13
5348428484281.21931957432289e-13
544089140891-8.7356001233629e-13
553643236432-4.35175628351609e-13
5650669506698.43353351856457e-13
573955639556-1.04753179377113e-12
586890668906-2.44596156545993e-12


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.6436247806016130.7127504387967740.356375219398387
60.03389929377184420.06779858754368850.966100706228156
71.7533612454129e-053.50672249082579e-050.999982466387546
80.001884253071514250.003768506143028510.998115746928486
91.09350040670322e-092.18700081340644e-090.9999999989065
100.1089472738464990.2178945476929980.891052726153501
110.01319260876323180.02638521752646360.986807391236768
120.6402307148617530.7195385702764930.359769285138247
130.01656231247969770.03312462495939540.983437687520302
140.0001557030031925060.0003114060063850120.999844296996808
151.5621927153799e-083.1243854307598e-080.999999984378073
160.03597121224103090.07194242448206180.96402878775897
174.07618659292687e-078.15237318585373e-070.99999959238134
180.9999999999999251.49815667557007e-137.49078337785034e-14
190.9999999986491472.70170686905424e-091.35085343452712e-09
200.999999768574964.62850081089316e-072.31425040544658e-07
210.999840276515350.0003194469692997840.000159723484649892
220.9999288243625180.0001423512749650287.11756374825139e-05
230.999922756965760.0001544860684812917.72430342406453e-05
240.9999778961461524.42077076953096e-052.21038538476548e-05
250.9988776224573040.002244755085391260.00112237754269563
260.999999999527219.45578953534809e-104.72789476767404e-10
270.01373535998516160.02747071997032310.986264640014838
280.9825920967132310.0348158065735370.0174079032867685
290.999939999919730.0001200001605416836.00000802708417e-05
300.999999997100135.7997410264901e-092.89987051324505e-09
310.9999999999477821.04436260243385e-105.22181301216923e-11
320.9999999998325953.34809765406716e-101.67404882703358e-10
330.999998142678453.71464310169238e-061.85732155084619e-06
349.21861805467312e-061.84372361093462e-050.999990781381945
350.9999987970525682.40589486466529e-061.20294743233265e-06
360.9999999999999911.73178949193526e-148.65894745967632e-15
370.9999975863144484.8273711033365e-062.41368555166825e-06
380.999999551773018.96453980864269e-074.48226990432135e-07
3917.86957129418019e-163.93478564709009e-16
400.9999837515187373.24969625257086e-051.62484812628543e-05
410.4492982409516770.8985964819033540.550701759048323
420.9984214256217580.00315714875648420.0015785743782421
430.003503825499577360.007007650999154710.996496174500423
440.0001940355307491080.0003880710614982160.999805964469251
450.2189864511631510.4379729023263030.781013548836849
460.999959551445038.08971099405522e-054.04485549702761e-05
470.9999963423511227.3152977555781e-063.65764887778905e-06
480.9999496535644210.0001006928711571855.03464355785925e-05
490.9999900026713231.99946573549931e-059.99732867749656e-06
500.992568460363670.01486307927265880.00743153963632939
510.9970319851106870.005936029778625270.00296801488931263
520.9855695550623740.02886088987525130.0144304449376257
530.06562836009682980.131256720193660.93437163990317


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level350.714285714285714NOK
5% type I error level410.836734693877551NOK
10% type I error level430.877551020408163NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/10qlvv1290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/10qlvv1290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/1j2yj1290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/1j2yj1290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/2utf41290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/2utf41290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/3utf41290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/3utf41290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/4utf41290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/4utf41290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/5utf41290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/5utf41290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/6nlwp1290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/6nlwp1290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/7fcwa1290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/7fcwa1290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/8fcwa1290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/8fcwa1290764213.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/9fcwa1290764213.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764120j23m7itvv6845w8/9fcwa1290764213.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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