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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 06:58:38 -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/t1258984761ifulxwhls059xuj.htm/, Retrieved Mon, 23 Nov 2009 14:59:37 +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/t1258984761ifulxwhls059xuj.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 «
99.9 98.8 98.6 100.5 107.2 110.4 95.7 96.4 93.7 101.9 106.7 106.2 86.7 81 95.3 94.7 99.3 101 101.8 109.4 96 102.3 91.7 90.7 95.3 96.2 96.6 96.1 107.2 106 108 103.1 98.4 102 103.1 104.7 81.1 86 96.6 92.1 103.7 106.9 106.6 112.6 97.6 101.7 87.6 92 99.4 97.4 98.5 97 105.2 105.4 104.6 102.7 97.5 98.1 108.9 104.5 86.8 87.4 88.9 89.9 110.3 109.8 114.8 111.7 94.6 98.6 92 96.9 93.8 95.1 93.8 97 107.6 112.7 101 102.9 95.4 97.4 96.5 111.4 89.2 87.4 87.1 96.8 110.5 114.1 110.8 110.3 104.2 103.9 88.9 101.6 89.8 94.6 90 95.9 93.9 104.7 91.3 102.8 87.8 98.1 99.7 113.9 73.5 80.9 79.2 95.7 96.9 113.2 95.2 105.9 95.6 108.8 89.7 102.3
 
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
TotProd[t] = + 39.1032602682758 + 0.58527352083724ProdMetal[t] + 4.07634027845658M1[t] + 3.5801665171541M2[t] + 6.29025054456396M3[t] + 6.01292972203943M4[t] + 1.82916558241524M5[t] + 5.35126929941585M6[t] -0.19740867179095M7[t] + 0.478414521457085M8[t] + 6.48453488259889M9[t] + 7.76983376921275M10[t] + 3.73879347044081M11[t] -0.158866937034356t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)39.103260268275818.9317422.06550.0445380.022269
ProdMetal0.585273520837240.1981992.9530.0049440.002472
M14.076340278456582.9265561.39290.1703520.085176
M23.58016651715412.930281.22180.2280140.114007
M36.290250544563963.7180931.69180.097450.048725
M46.012929722039433.0985271.94060.0584530.029226
M51.829165582415242.9783240.61420.5421360.271068
M65.351269299415853.7276561.43560.1578930.078947
M7-0.197408671790953.741121-0.05280.9581460.479073
M80.4784145214570852.9508180.16210.8719140.435957
M96.484534882598893.8113011.70140.095620.04781
M107.769833769212753.931921.97610.054160.02708
M113.738793470440813.1671651.18050.2438750.121938
t-0.1588669370343560.036511-4.35127.5e-053.7e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.872950470352862
R-squared0.762042523689282
Adjusted R-squared0.694793671688427
F-TEST (value)11.3316807799127
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value2.42013076245939e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.58625403353776
Sum Squared Residuals967.551398766505


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
199.9100.845757468417-0.945757468416905
298.6101.185681755504-2.58568175550370
3107.2109.531106702168-2.33110670216788
495.7100.901089650888-5.20108965088764
593.799.777462938834-6.07746293883393
6106.7105.6573758584001.04262414159970
786.785.20093822506071.49906177493929
895.393.73614171674461.56385828325542
999.3103.270618322127-3.97061832212663
10101.8109.313347846739-7.51334784673896
1196100.967998612988-4.96799861298823
1291.790.28116536380111.41883463619889
1395.397.4176430698281-2.11764306982815
1496.696.7040750194076-0.104075019407587
15107.2105.0494999660722.15050003392825
16108102.9160189960855.08398100391512
1798.497.92958704650540.470412953494632
18103.1102.8730623327320.226937667267826
1981.186.2209025848346-5.12090258483465
2096.690.30802731815556.29197268184452
21103.7104.817328850654-1.11732885065408
22106.6109.279819869006-2.67981986900584
2397.698.7104312560736-1.11043125607363
2487.689.1356176964772-1.53561769647725
2599.496.21356805042063.18643194957944
2698.595.32441794374883.17558205625117
27105.2102.7919326091572.40806739084287
28104.6100.7755063433383.82449365666229
2997.593.74061707082793.75938292917214
30108.9100.8496043841528.05039561584756
3186.885.13388226959451.66611773040549
3288.987.11402232790131.78597767209873
33110.3104.6082188166705.6917811833302
34114.8106.846670455847.95332954415995
3594.694.989680097066-0.389680097065915
369290.09705470416741.90294529583255
3793.892.96103570808260.838964291917363
3893.893.41801469933660.381985300663441
39107.6105.1580260668572.44197393314328
4010198.98615780309292.01384219690711
4195.491.42452236182953.97547763817048
4296.5102.981588433517-6.48158843351713
4389.283.22747902518225.97252097481777
4487.189.246006377266-2.14600637726596
45110.5105.2184917118585.28150828814235
46110.8104.1208842822566.67911571774436
47104.296.1852265130918.014773486909
4888.990.9414370076902-2.04143700769019
4989.890.7619957032517-0.961995703251743
509090.8678105820033-0.867810582003323
5193.998.5694346557465-4.66943465574652
5291.397.0212272065969-5.72122720659689
5387.889.9278105820033-2.12781058200332
5499.7102.538368991198-2.83836899119795
5573.577.5167978953279-4.01679789532790
5679.286.6958022599327-7.49580225993271
5796.9102.785342298692-5.88534229869186
5895.299.6392775461595-4.43927754615951
5995.697.1466635207812-1.54666352078121
6089.789.4447252278640.255274772136011


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1233224651692630.2466449303385250.876677534830737
180.1137248599178820.2274497198357650.886275140082118
190.550261394685530.899477210628940.44973860531447
200.4529614110716140.9059228221432290.547038588928386
210.3558673344037420.7117346688074850.644132665596258
220.4034990401718520.8069980803437030.596500959828149
230.4034008697239360.8068017394478720.596599130276064
240.464009358110950.92801871622190.53599064188905
250.3749493921599770.7498987843199540.625050607840023
260.2887376336262890.5774752672525770.711262366373711
270.2120109717134620.4240219434269250.787989028286538
280.1436782892452820.2873565784905640.856321710754718
290.1170690003096210.2341380006192410.88293099969038
300.2119322918847650.4238645837695310.788067708115235
310.2514164529807420.5028329059614840.748583547019258
320.339438502990070.678877005980140.66056149700993
330.3099976738152720.6199953476305440.690002326184728
340.4130880996934920.8261761993869840.586911900306508
350.3939797005146260.7879594010292520.606020299485374
360.3267410968329560.6534821936659120.673258903167044
370.3019531858894290.6039063717788580.698046814110571
380.3052085837914020.6104171675828050.694791416208598
390.2590531129001520.5181062258003030.740946887099848
400.1954777046162830.3909554092325670.804522295383717
410.1201111103501020.2402222207002040.879888889649898
420.3789906962434420.7579813924868840.621009303756558
430.2431060615811060.4862121231622120.756893938418894


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/10381h1258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/10381h1258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/1ge3y1258984713.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/1ge3y1258984713.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/2krhg1258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/2krhg1258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/39zc71258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/39zc71258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/4pbqm1258984714.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/5bivu1258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/5bivu1258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/64y581258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/64y581258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/72tbd1258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/72tbd1258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/8olyc1258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/8olyc1258984714.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/9yiqz1258984714.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t1258984761ifulxwhls059xuj/9yiqz1258984714.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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