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M3

*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 00:58:21 -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/t1258618894rzai7tgryny2i3c.htm/, Retrieved Thu, 19 Nov 2009 09:21:46 +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/t1258618894rzai7tgryny2i3c.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 «
21 2472.81 19 2407.6 25 2454.62 21 2448.05 23 2497.84 23 2645.64 19 2756.76 18 2849.27 19 2921.44 19 2981.85 22 3080.58 23 3106.22 20 3119.31 14 3061.26 14 3097.31 14 3161.69 15 3257.16 11 3277.01 17 3295.32 16 3363.99 20 3494.17 24 3667.03 23 3813.06 20 3917.96 21 3895.51 19 3801.06 23 3570.12 23 3701.61 23 3862.27 23 3970.1 27 4138.52 26 4199.75 17 4290.89 24 4443.91 26 4502.64 24 4356.98 27 4591.27 27 4696.96 26 4621.4 24 4562.84 23 4202.52 23 4296.49 24 4435.23 17 4105.18 21 4116.68 19 3844.49 22 3720.98 22 3674.4 18 3857.62 16 3801.06 14 3504.37 12 3032.6 14 3047.03 16 2962.34 8 2197.82 3 2014.45 0 1862.83 5 1905.41 1 1810.99 1 1670.07 3 1864.44
 
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
Consvertr[t] = + 3.55671726525572 + 0.00638085941225368Aand[t] -0.338286051714473M1[t] -2.24724893355562M2[t] + 0.00822180782049912M3[t] -0.964857073231493M4[t] + 0.0778597387859022M5[t] -0.493834744584925M6[t] -0.0836314772970198M7[t] -2.52054447590919M8[t] -3.12456273564482M9[t] -0.332805124311363M10[t] + 0.34971383130199M11[t] -0.191708221875839t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)3.556717265255722.4708071.43950.1566380.078319
Aand0.006380859412253680.00053611.909600
M1-0.3382860517144732.045623-0.16540.8693620.434681
M2-2.247248933555622.150727-1.04490.3014230.150712
M30.008221807820499122.1453920.00380.9969580.498479
M4-0.9648570732314932.142051-0.45040.6544670.327234
M50.07785973878590222.1398060.03640.9711280.485564
M6-0.4938347445849252.138465-0.23090.8183720.409186
M7-0.08363147729701982.136255-0.03910.9689380.484469
M8-2.520544475909192.134929-1.18060.2436930.121847
M9-3.124562735644822.133861-1.46430.1497760.074888
M10-0.3328051243113632.133192-0.1560.8766910.438346
M110.349713831301992.1328260.1640.870460.43523
t-0.1917082218758390.024927-7.690900


Multiple Linear Regression - Regression Statistics
Multiple R0.900153925921666
R-squared0.810277090352189
Adjusted R-squared0.757800540875134
F-TEST (value)15.4407463605527
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value8.77964367873574e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.3718656391664
Sum Squared Residuals534.365460763779


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12118.80537595488052.19462404511954
21916.28860900889042.71139099110961
32518.65239953795486.34760046204518
42117.44569018868853.55430981131151
52318.61440176896624.38559823103384
62318.79409008485064.20590991514943
71919.7216262281523-0.721626228152276
81817.68329831189190.316701688108146
91917.34807845406271.65192154593727
101920.3335955606146-1.33359556061459
112221.45438854412390.545611455876085
122321.07657172627631.92342827372373
132020.6301029023924-0.630102902392358
141418.1590229097940-4.15902290979404
151420.4528154111061-6.45281541110607
161419.6988280371391-5.69882803713913
171521.1590172753685-6.15901727536854
181120.5222746294551-9.52227462945511
191720.8576032107055-3.85760321070554
201618.667155606057-2.66715560605699
212018.70208940273271.29791059726730
222422.40513415019251.59486584980751
232323.8277417839014-0.827741783901411
242023.955671883069-3.95567188306899
252123.2824273156736-2.28242731567359
261920.5790840404692-1.57908404046924
272321.16925088730371.83074911269635
282320.84348298849312.15651701150694
292322.71964045180730.280359548192708
302322.64428581698390.355714183016064
312723.93744520460783.06255479539223
322621.69952400593204.30047599406795
331721.4853490511534-4.48534905115338
342425.0617975478741-1.06179754787406
352625.92735615489320.0726438451067698
362424.4564981197265-0.456498119726525
372725.42147539783311.57852460216687
382723.99519732539723.00480267460277
392625.57682210770760.423177892292376
402424.0383718775982-0.0383718775982237
412322.59022920431650.409770795683464
422322.42643585803930.573564141960659
432423.53021133830750.469788661692517
441718.7955874688052-1.79558746880515
452118.07324087043462.9267591295654
461918.93648413647090.0635158635291115
472218.63919492420103.36080507579905
482217.80055243960034.19944756039965
491818.4396592275232-0.439659227523154
501615.97808671544910.0219132845509014
511416.1487120559278-2.14871205592783
521211.97362690808110.0263730919189082
531412.91671129954151.08328870045853
541611.61291361067104.38708638932896
5586.953114018226931.04688598177307
5633.15443460731396-0.154434607313957
5701.39124222161659-1.39124222161659
5854.262988604847970.737011395152033
5914.15131859288049-3.15131859288049
6012.71070583132787-1.71070583132787
6133.42095920169731-0.420959201697308


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.6477555241614790.7044889516770430.352244475838521
180.8307955788120940.3384088423758120.169204421187906
190.8269861803010220.3460276393979560.173013819698978
200.7568372322354470.4863255355291060.243162767764553
210.7994724771905510.4010550456188970.200527522809449
220.972199710653770.05560057869246050.0278002893462303
230.9735847649787430.05283047004251390.0264152350212570
240.969910116015010.060179767969980.03008988398499
250.9741943286695590.05161134266088270.0258056713304413
260.98057113931980.03885772136040030.0194288606802002
270.983720793734440.03255841253112220.0162792062655611
280.9869516542146380.02609669157072430.0130483457853622
290.982355898076250.03528820384750210.0176441019237511
300.9813674897416750.0372650205166510.0186325102583255
310.9875905119811540.02481897603769230.0124094880188461
320.997018467124860.005963065750279210.00298153287513961
330.9974549656924430.005090068615114110.00254503430755705
340.994839882238230.01032023552353980.00516011776176991
350.9892037873461010.02159242530779740.0107962126538987
360.9837561214320180.03248775713596340.0162438785679817
370.9706789043278170.05864219134436610.0293210956721831
380.962763361769410.07447327646117930.0372366382305896
390.9507985345673160.09840293086536780.0492014654326839
400.9057823736947760.1884352526104470.0942176263052237
410.8447763593457530.3104472813084950.155223640654247
420.813087615717610.3738247685647810.186912384282390
430.7113925675034330.5772148649931330.288607432496567
440.6860739454630680.6278521090738640.313926054536932


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.0714285714285714NOK
5% type I error level110.392857142857143NOK
10% type I error level180.642857142857143NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/1050i21258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/1050i21258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/1kft21258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/1kft21258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/2vkns1258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/2vkns1258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/3uap71258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/3uap71258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/4n1gy1258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/4n1gy1258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/5a51r1258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/5a51r1258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/6yxoy1258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/6yxoy1258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/7at7q1258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/7at7q1258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/81ory1258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/81ory1258617496.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/9wwg41258617496.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258618894rzai7tgryny2i3c/9wwg41258617496.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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