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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: Thu, 19 Nov 2009 02:58:07 -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/19/t12586247617rng5o4w12ni3kr.htm/, Retrieved Thu, 19 Nov 2009 10:59:34 +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/19/t12586247617rng5o4w12ni3kr.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 «
3499 1 4164 3186 4145 1 3499 3902 3796 1 4145 4164 3711 1 3796 3499 3949 1 3711 4145 3740 1 3949 3796 3243 1 3740 3711 4407 1 3243 3949 4814 1 4407 3740 3908 1 4814 3243 5250 1 3908 4407 3937 1 5250 4814 4004 1 3937 3908 5560 1 4004 5250 3922 1 5560 3937 3759 1 3922 4004 4138 1 3759 5560 4634 1 4138 3922 3996 1 4634 3759 4308 1 3996 4138 4143 0 4308 4634 4429 0 4143 3996 5219 0 4429 4308 4929 0 5219 4143 5755 0 4929 4429 5592 0 5755 5219 4163 0 5592 4929 4962 0 4163 5755 5208 0 4962 5592 4755 0 5208 4163 4491 0 4755 4962 5732 0 4491 5208 5731 0 5732 4755 5040 0 5731 4491 6102 0 5040 5732 4904 0 6102 5731 5369 0 4904 5040 5578 0 5369 6102 4619 0 5578 4904 4731 0 4619 5369 5011 0 4731 5578 5299 0 5011 4619 4146 0 5299 4731 4625 0 4146 5011 4736 0 4625 5299 4219 0 4736 4146 5116 0 4219 4625 4205 0 5116 4736 4121 0 4205 4219 5103 1 4121 5116 4300 1 5103 4205 4578 1 4300 4121 3809 1 4578 5103 5526 1 3809 4300 4247 1 5526 4578 3830 1 4247 3809 4394 1 3830 5526
 
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] = + 873.552019317555 -166.509677507681X[t] + 0.336497568874567Y1[t] + 0.386622532227597Y3[t] + 679.099448674866M1[t] + 947.051054819987M2[t] -37.8228504198242M3[t] + 453.097384497474M4[t] + 216.144363232371M5[t] + 960.49461647157M6[t] -0.897572909612111M7[t] + 785.141475967574M8[t] + 607.148401348361M9[t] + 435.889731644429M10[t] + 1304.84169438637M11[t] -1.33397701611762t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)873.552019317555990.0459260.88230.382740.19137
X-166.509677507681175.658568-0.94790.3487260.174363
Y10.3364975688745670.1378512.4410.0190510.009526
Y30.3866225322275970.1446512.67280.0107470.005373
M1679.099448674866322.0126882.10890.0411040.020552
M2947.051054819987317.2346692.98530.004760.00238
M3-37.8228504198242294.395804-0.12850.89840.4492
M4453.097384497474326.2728941.38870.172420.08621
M5216.144363232371329.5252120.65590.5155360.257768
M6960.49461647157318.8982823.01190.0044330.002216
M7-0.897572909612111302.394262-0.0030.9976460.498823
M8785.141475967574338.213862.32140.0253120.012656
M9607.148401348361310.3111051.95660.0572310.028616
M10435.889731644429336.8808681.29390.2029420.101471
M111304.84169438637336.3070553.87990.0003710.000186
t-1.333977016117624.302301-0.31010.7580850.379042


Multiple Linear Regression - Regression Statistics
Multiple R0.833103487567017
R-squared0.694061420996326
Adjusted R-squared0.582132672580348
F-TEST (value)6.20092184375079
F-TEST (DF numerator)15
F-TEST (DF denominator)41
p-value1.60352825517851e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation432.709464877265
Sum Squared Residuals7676736.72076912


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
134994017.76307793944-518.763077939445
241454337.43155684182-192.431556841816
337963669.89620752249126.103792477511
437113784.9408299551-73.9408299550955
539493767.80969413856181.190305861437
637404455.98112800636-715.981128006359
732433390.06405447493-147.064054474930
844074099.54599727551307.454002724493
948144231.09800657461582.901993425395
1039084003.30847186939-95.3084718693893
1152505016.08828770778233.911712292218
1239374318.84772435159-381.847724351590
1340044204.51187387983-200.511873879830
1455605012.52227837286547.477721627136
1539224042.26922847093-120.269228470927
1637594006.57617821482-247.576178214815
1741384315.02473635318-177.024736353180
1846344552.2858833909281.7141166090809
1939963693.44303840231302.556961597694
2043084409.99260103566-101.992601035661
2141434693.92724438177-550.927244381765
2244294219.14732323621209.852676763795
2352195303.62984371517-84.6298437151687
2449294199.49453390603729.505466093969
2557554890.24975480825864.750245191752
2655925740.24617628745-148.246176287446
2741634587.06865595896-424.068655958959
2849624915.1500995583846.8499004416228
2952084882.70518605484325.294813945162
3047555156.01626566783-401.016265667827
3144914349.7681038202141.231896179802
3257325140.74696042637591.25303957363
3357315203.87338466528527.126615334724
3450404928.87589186827111.124108131734
3561026043.7726199962258.2273800037847
3649045094.57074420629-190.570744206286
3753695102.05595858403266.944041415966
3855785935.73808646542-357.738086465419
3946194556.6844024956162.3155975043864
4047314903.34896933192-172.348969331916
4150114783.55380800021227.446191999785
4252995250.0183951019148.9816048980898
4341464427.50525214998-281.505252149977
4446254932.4829361224-307.482936122397
4547365025.68550925953-289.685509259532
4642194444.66831302614-225.66831302614
4751165323.50924858083-207.509248580835
4842054362.08699753609-157.086997536093
4941214533.41933478844-412.419334788443
5051034952.06190203246150.938097967544
5143003944.08150555201355.918494447989
5245784130.9839229398447.016077060204
5338094365.90657545320-556.906575453204
5455264539.69832783298986.301672167016
5542474262.21955115259-15.2195511525879
5638304319.23150514006-489.231505140064
5743944663.41585511882-269.415855118822


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.6216029541288690.7567940917422620.378397045871131
200.5804285455051220.8391429089897560.419571454494878
210.5006035440216450.998792911956710.499396455978355
220.5733219671800180.8533560656399640.426678032819982
230.4961340464059570.9922680928119130.503865953594043
240.5314902101435210.9370195797129580.468509789856479
250.7911492771177470.4177014457645070.208850722882253
260.715392938265480.5692141234690390.284607061734520
270.7494803540357190.5010392919285620.250519645964281
280.7065689482120760.5868621035758470.293431051787924
290.6141123236998290.7717753526003420.385887676300171
300.8724650515343450.255069896931310.127534948465655
310.9450837651795270.1098324696409450.0549162348204727
320.9123284586862170.1753430826275660.0876715413137831
330.873502925512730.2529941489745410.126497074487271
340.7899136814114120.4201726371771750.210086318588588
350.6765581855951680.6468836288096630.323441814404832
360.6062704432190570.7874591135618860.393729556780943
370.4490041353218660.8980082706437330.550995864678134
380.3395777609290350.6791555218580690.660422239070965


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/19/t12586247617rng5o4w12ni3kr/102rqd1258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/102rqd1258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/1iekg1258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/1iekg1258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/256xl1258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/256xl1258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/3qv851258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/3qv851258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/4hlu81258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/4hlu81258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/55c681258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/55c681258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/652lb1258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/652lb1258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/76j4d1258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/76j4d1258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/8dc1w1258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/8dc1w1258624682.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/9vnz11258624682.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586247617rng5o4w12ni3kr/9vnz11258624682.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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