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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: Wed, 09 Dec 2009 12:33:28 -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/Dec/09/t1260387460nhxe5q00zsg88xe.htm/, Retrieved Wed, 09 Dec 2009 20:37:52 +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/Dec/09/t1260387460nhxe5q00zsg88xe.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:
hypothesepaper
 
Dataseries X:
» Textbox « » Textfile « » CSV «
627 0 696 0 825 0 677 0 656 0 785 0 412 0 352 0 839 0 729 0 696 0 641 0 695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 707 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 1 344 1 792 1 852 1 649 1 629 1 685 1 617 1 715 1 715 1 629 1 916 1 531 1 357 1 917 1 828 1 708 1 858 1 775 1 785 1 1006 1 789 1 734 1 906 1 532 1 387 1 991 1 841 1
 
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] = + 653.571428571429 + 56.4285714285714X[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)653.57142857142923.88795827.359900
X56.428571428571437.7701791.4940.1398020.069901


Multiple Linear Regression - Regression Statistics
Multiple R0.178271700568352
R-squared0.0317807992235320
Adjusted R-squared0.0175422815650547
F-TEST (value)2.23203004595145
F-TEST (DF numerator)1
F-TEST (DF denominator)68
p-value0.139802175645581
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation154.811663838692
Sum Squared Residuals1629732.28571429


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1627653.571428571426-26.5714285714261
2696653.57142857142942.4285714285714
3825653.571428571429171.428571428571
4677653.57142857142923.4285714285714
5656653.5714285714292.42857142857136
6785653.571428571429131.428571428571
7412653.571428571429-241.571428571429
8352653.571428571429-301.571428571429
9839653.571428571429185.428571428571
10729653.57142857142975.4285714285714
11696653.57142857142942.4285714285714
12641653.571428571429-12.5714285714286
13695653.57142857142941.4285714285714
14638653.571428571429-15.5714285714286
15762653.571428571429108.428571428571
16635653.571428571429-18.5714285714286
17721653.57142857142967.4285714285714
18854653.571428571429200.428571428571
19418653.571428571429-235.571428571429
20367653.571428571429-286.571428571429
21824653.571428571429170.428571428571
22687653.57142857142933.4285714285714
23601653.571428571429-52.5714285714286
24676653.57142857142922.4285714285714
25740653.57142857142986.4285714285714
26691653.57142857142937.4285714285714
27683653.57142857142929.4285714285714
28594653.571428571429-59.5714285714286
29729653.57142857142975.4285714285714
30731653.57142857142977.4285714285714
31386653.571428571429-267.571428571429
32331653.571428571429-322.571428571429
33707653.57142857142953.4285714285714
34715653.57142857142961.4285714285714
35657653.5714285714293.42857142857136
36653653.571428571429-0.571428571428637
37642653.571428571429-11.5714285714286
38643653.571428571429-10.5714285714286
39718653.57142857142964.4285714285714
40654653.5714285714290.428571428571363
41632653.571428571429-21.5714285714286
42731653.57142857142977.4285714285714
43392710-318
44344710-366
4579271082
46852710142
47649710-61
48629710-81
49685710-25
50617710-93
517157105
527157105
53629710-81
54916710206
55531710-179
56357710-353
57917710207
58828710118
59708710-2
60858710148
6177571065
6278571075
631006710296
6478971079
6573471024
66906710196
67532710-178
68387710-323
69991710281
70841710131


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.1800555135891250.3601110271782510.819944486410875
60.1193837724813480.2387675449626970.880616227518652
70.4831717747761290.9663435495522580.516828225223871
80.7535797516420030.4928404967159950.246420248357997
90.7810111489799960.4379777020400090.218988851020004
100.7096550168287410.5806899663425180.290344983171259
110.6184333406359880.7631333187280240.381566659364012
120.5201380269010990.9597239461978030.479861973098901
130.4267598882577320.8535197765154630.573240111742268
140.3374336165227760.6748672330455510.662566383477224
150.2899090582273840.5798181164547680.710090941772616
160.2198561162700210.4397122325400420.78014388372998
170.1677815755312540.3355631510625080.832218424468746
180.2005408186276210.4010816372552420.799459181372379
190.3135548139667370.6271096279334740.686445186033263
200.5015240234672430.9969519530655150.498475976532757
210.5126008959643770.9747982080712460.487399104035623
220.4383113601196070.8766227202392140.561688639880393
230.3729651539405210.7459303078810430.627034846059479
240.3046733007301260.6093466014602530.695326699269874
250.2599119278278040.5198238556556080.740088072172196
260.2060397956624530.4120795913249050.793960204337547
270.1589126978666230.3178253957332450.841087302133377
280.1244372426623370.2488744853246750.875562757337663
290.09836059663026920.1967211932605380.901639403369731
300.07735275005860760.1547055001172150.922647249941392
310.1449666870618360.2899333741236730.855033312938164
320.3184790178753800.6369580357507610.68152098212462
330.2639264144264310.5278528288528610.73607358557357
340.2164645453753750.432929090750750.783535454624625
350.1683937782952350.3367875565904690.831606221704765
360.1278904124275950.2557808248551890.872109587572405
370.09511948745128580.1902389749025720.904880512548714
380.06913551715206940.1382710343041390.93086448284793
390.05095142442224570.1019028488444910.949048575577754
400.03506562827130190.07013125654260380.964934371728698
410.02431370700442440.04862741400884880.975686292995576
420.01683514782203580.03367029564407160.983164852177964
430.02462157446960110.04924314893920230.9753784255304
440.05623996825630960.1124799365126190.94376003174369
450.09631205865855980.1926241173171200.90368794134144
460.1277585367177860.2555170734355720.872241463282214
470.09915831229121320.1983166245824260.900841687708787
480.07726243746634630.1545248749326930.922737562533654
490.05654738094682120.1130947618936420.943452619053179
500.04397815482860350.0879563096572070.956021845171396
510.030764869242190.061529738484380.96923513075781
520.02067718199043150.0413543639808630.979322818009569
530.01500220840009310.03000441680018620.984997791599907
540.01999998926332910.03999997852665830.98000001073667
550.02337955657692210.04675911315384420.976620443423078
560.1498855871834370.2997711743668740.850114412816563
570.1616635477354410.3233270954708820.838336452264559
580.1258863385305610.2517726770611230.874113661469439
590.0886552278668180.1773104557336360.911344772133182
600.0679127594161550.135825518832310.932087240583845
610.04148336365907270.08296672731814530.958516636340927
620.0235381147571160.0470762295142320.976461885242884
630.04353270274550940.08706540549101880.95646729725449
640.02285628292762450.04571256585524910.977143717072375
650.009569851620077340.01913970324015470.990430148379923


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level100.163934426229508NOK
10% type I error level150.245901639344262NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/10rgs71260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/10rgs71260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/1uyxz1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/1uyxz1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/2d0bw1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/2d0bw1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/3e5te1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/3e5te1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/45tfw1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/45tfw1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/5nhue1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/5nhue1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/69e9n1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/69e9n1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/7l0pz1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/7l0pz1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/8p7hj1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/8p7hj1260387203.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/9u6md1260387203.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/09/t1260387460nhxe5q00zsg88xe/9u6md1260387203.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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