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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 10:17:46 -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/t12587376636vbfyqaamgwxfg8.htm/, Retrieved Fri, 20 Nov 2009 18:21:16 +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/t12587376636vbfyqaamgwxfg8.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 «
2253 14.9 2218 18.6 1855 19.1 2187 18.8 1852 18.2 1570 18 1851 19 1954 20.7 1828 21.2 2251 20.7 2277 19.6 2085 18.6 2282 18.7 2266 23.8 1878 24.9 2267 24.8 2069 23.8 1746 22.3 2299 21.7 2360 20.7 2214 19.7 2825 18.4 2355 17.4 2333 17 3016 18 2155 23.8 2172 25.5 2150 25.6 2533 23.7 2058 22 2160 21.3 2260 20.7 2498 20.4 2695 20.3 2799 20.4 2946 19.8 2930 19.5 2318 23.1 2540 23.5 2570 23.5 2669 22.9 2450 21.9 2842 21.5 3440 20.5 2678 20.2 2981 19.4 2260 19.2 2844 18.8 2546 18.8 2456 22.6 2295 23.3 2379 23 2479 21.4 2057 19.9 2280 18.8 2351 18.6 2276 18.4 2548 18.6 2311 19.9 2201 19.2
 
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
wngb[t] = + 1681.39441980409 + 25.6802893156051`<25`[t] + 239.567189564934M1[t] -205.134354973182M2[t] -371.241281120370M3[t] -214.467917951953M4[t] -184.300659681619M5[t] -507.106189838661M6[t] -196.569557234498M7[t] -13.2281651345211M8[t] -189.659561461919M9[t] + 175.472311646427M10[t] -88.4135078262194M11[t] + 8.90827154945574t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1681.39441980409447.0848963.76080.0004770.000239
`<25`25.680289315605123.5782621.08920.281760.14088
M1239.567189564934179.3709451.33560.1882520.094126
M2-205.134354973182201.199127-1.01960.313270.156635
M3-371.241281120370211.048258-1.7590.0852220.042611
M4-214.467917951953209.10242-1.02570.3104160.155208
M5-184.300659681619196.018195-0.94020.3520150.176007
M6-507.106189838661185.82202-2.7290.0089690.004485
M7-196.569557234498183.297603-1.07240.2891320.144566
M8-13.2281651345211181.885959-0.07270.9423380.471169
M9-189.659561461919180.497621-1.05080.2988580.149429
M10175.472311646427178.651980.98220.3311380.165569
M11-88.4135078262194178.147494-0.49630.622050.311025
t8.908271549455742.1944014.05950.0001899.5e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.705597659500331
R-squared0.497868057092345
Adjusted R-squared0.355961203661921
F-TEST (value)3.50841446383311
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.000797409462064635
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation280.638436043883
Sum Squared Residuals3622864.86211721


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
122532312.50619172101-59.506191721009
222181971.72998920007246.270010799925
318551827.3714792601427.628520739855
421871985.34902718334201.650972816664
518522009.01638341376-157.016383413763
615701689.98306694306-119.983066943056
718512035.10826041228-184.108260412278
819542271.01441589824-317.01441589824
918282116.3314357781-288.331435778101
1022512477.5314357781-226.531435778101
1122772194.3055696077482.6944303922565
1220852265.94705966781-180.947059667814
1322822516.99054971376-234.990549713764
1422662212.1667522346953.83324776531
1518782083.21641588412-205.216415884124
1622672246.3300216704420.6699783295644
1720692259.72526217462-190.725262174620
1817461907.30756959363-161.307569593627
1922992211.3443001578887.6556998421186
2023602377.91367449171-17.9136744917094
2122142184.7102603981629.2897396018383
2228252525.36602894568299.633971054322
2323552244.70819170688110.291808293119
2423332331.757855356311.24214464368536
2530162605.91360578631410.08639421369
2621552319.06601082816-164.066010828159
2721722205.52384806696-33.5238480669555
2821502373.77351171639-223.773511716389
2925332364.05649183653168.943508163471
3020582006.5027413924151.4972586075861
3121602307.97144302511-147.971443025108
3222602484.81293308518-224.812933085178
3324982309.58572151255188.414278487446
3426952681.0578372388013.9421627612039
3527992428.64831824717370.351681752835
3629462510.56192403348435.438075966522
3729302751.33329835319178.666701646814
3823182407.98906690070-89.9890669007047
3925402261.06252802921278.937471970786
4025702426.74416274709143.255837252913
4126692450.41151897751218.588481022486
4224502110.83397105432339.166028945678
4328422420.0067594817421.993240518302
4434402586.57613381553853.423866184474
4526782411.3489222429266.651077757098
4629812764.84483544822216.155164551780
4722602504.73122966191-244.731229661908
4828442591.78089331134252.219106688658
4925462840.25635442573-294.256354425731
5024562502.04818083637-46.0481808363711
5122952362.82572875956-67.8257287595621
5223792520.80327668275-141.803276682753
5324792518.79034359757-39.7903435975746
5420572166.37265101658-109.372651016581
5522802457.56923692303-177.569236923033
5623512644.68284270935-293.682842709345
5722762472.02366006828-196.023660068282
5825482851.19986258921-303.199862589206
5923112629.6066907763-318.606690776301
6022012708.95226763105-507.952267631052


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.01227146846400870.02454293692801740.987728531535991
180.004675626087892180.009351252175784350.995324373912108
190.007307772243414250.01461554448682850.992692227756586
200.002383981472755340.004767962945510670.997616018527245
210.0008932019194873990.001786403838974800.999106798080513
220.0002559738403573650.000511947680714730.999744026159643
230.002022145125795580.004044290251591170.997977854874204
240.0009001603102088330.001800320620417670.999099839689791
250.002004394624157340.004008789248314690.997995605375843
260.01168932764505630.02337865529011260.988310672354944
270.006822412702539310.01364482540507860.99317758729746
280.01491919012771350.0298383802554270.985080809872287
290.01342782467625660.02685564935251320.986572175323743
300.008648281092833260.01729656218566650.991351718907167
310.01797971229404920.03595942458809840.98202028770595
320.1483374226365360.2966748452730730.851662577363464
330.1534668593549440.3069337187098880.846533140645056
340.3133359117942540.6266718235885080.686664088205746
350.2499999854977520.4999999709955030.750000014502249
360.2683081608986790.5366163217973580.73169183910132
370.1885217129882260.3770434259764520.811478287011774
380.3169947316096510.6339894632193020.683005268390349
390.2273747267268450.4547494534536910.772625273273154
400.1666818835243000.3333637670486000.8333181164757
410.1567952552714000.3135905105427990.8432047447286
420.1243098534243190.2486197068486380.875690146575681
430.1040586994305300.2081173988610600.89594130056947


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level70.259259259259259NOK
5% type I error level150.555555555555556NOK
10% type I error level150.555555555555556NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/10nbc1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/10nbc1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/10nrmz1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/10nrmz1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/2a9zh1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/2a9zh1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/3f52i1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/3f52i1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/4zav51258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/4zav51258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/56pxt1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/56pxt1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/68zgw1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/68zgw1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/78h6q1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/78h6q1258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/8z6561258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/8z6561258737461.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/94xkn1258737461.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587376636vbfyqaamgwxfg8/94xkn1258737461.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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