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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 01:23:13 -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/t12587054728lysygpi6xijj3t.htm/, Retrieved Fri, 20 Nov 2009 09:24:44 +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/t12587054728lysygpi6xijj3t.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 «
56.6 0 56 0 54.8 0 52.7 0 50.9 0 50.6 0 52.1 0 53.3 0 53.9 0 54.3 0 54.2 0 54.2 0 53.5 0 51.4 0 50.5 0 50.3 0 49.8 0 50.7 0 52.8 0 55.3 0 57.3 0 57.5 0 56.8 0 56.4 0 56.3 0 56.4 0 57 0 57.9 0 58.9 0 58.8 0 56.5 1 51.9 1 47.4 1 44.9 1 43.9 1 43.4 1 42.9 1 42.6 1 42.2 1 41.2 1 40.2 1 39.3 1 38.5 1 38.3 1 37.9 1 37.6 1 37.3 1 36 1 34.5 1 33.5 1 32.9 1 32.9 1 32.8 1 31.9 1 30.5 1 29.2 1 28.7 1 28.4 1 28 1 27.4 1 26.9 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 59.5323076923077 -7.21057692307693X[t] -0.712996794871812M1[t] -0.199326923076930M2[t] -0.373605769230770M3[t] -0.527884615384615M4[t] -0.682163461538468M5[t] -0.616442307692312M6[t] + 0.97139423076923M7[t] + 0.817115384615381M8[t] + 0.582836538461533M9[t] + 0.408557692307688M10[t] + 0.234278846153841M11[t] -0.325721153846153t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)59.53230769230772.82315321.087200
X-7.210576923076932.725502-2.64560.0110560.005528
M1-0.7129967948718123.168376-0.2250.8229270.411464
M2-0.1993269230769303.327191-0.05990.9524830.476241
M3-0.3736057692307703.321148-0.11250.9109120.455456
M4-0.5278846153846153.316887-0.15920.8742320.437116
M5-0.6821634615384683.314416-0.20580.8378230.418911
M6-0.6164423076923123.313739-0.1860.8532250.426612
M70.971394230769233.3249470.29220.7714550.385728
M80.8171153846153813.3168870.24640.8064840.403242
M90.5828365384615333.3106060.17610.861010.430505
M100.4085576923076883.3061110.12360.9021780.451089
M110.2342788461538413.3034120.07090.9437620.471881
t-0.3257211538461530.07712-4.22350.0001095.5e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.890912068408306
R-squared0.793724313635566
Adjusted R-squared0.736669336556041
F-TEST (value)13.9115701077095
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value5.62927482405939e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.22172889694719
Sum Squared Residuals1281.52327564103


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
156.658.4935897435898-1.8935897435898
25658.6815384615385-2.68153846153848
354.858.1815384615385-3.38153846153846
452.757.7015384615385-5.00153846153845
550.957.2215384615385-6.32153846153846
650.656.9615384615385-6.36153846153846
752.158.2236538461538-6.12365384615384
853.357.7436538461538-4.44365384615384
953.957.1836538461538-3.28365384615384
1054.356.6836538461538-2.38365384615385
1154.256.1836538461538-1.98365384615384
1254.255.6236538461539-1.42365384615385
1353.554.5849358974359-1.08493589743588
1451.454.7728846153846-3.3728846153846
1550.554.2728846153846-3.77288461538461
1650.353.7928846153846-3.49288461538462
1749.853.3128846153846-3.51288461538461
1850.753.0528846153846-2.35288461538461
1952.854.315-1.51500000000000
2055.353.8351.46500000000000
2157.353.2754.025
2257.552.7754.725
2356.852.2754.525
2456.451.7154.68499999999999
2556.350.6762820512825.62371794871796
2656.450.86423076923085.53576923076923
275750.36423076923086.63576923076923
2857.949.88423076923088.01576923076922
2958.949.40423076923089.49576923076923
3058.849.14423076923089.65576923076923
3156.543.195769230769213.3042307692308
3251.942.71576923076929.18423076923077
3347.442.15576923076925.24423076923077
3444.941.65576923076923.24423076923077
3543.941.15576923076922.74423076923077
3643.440.59576923076922.80423076923077
3742.939.55705128205133.34294871794873
3842.639.7452.85500000000000
3942.239.2452.95500000000000
4041.238.7652.435
4140.238.2851.91500000000001
4239.338.0251.27500000000000
4338.539.2871153846154-0.787115384615385
4438.338.8071153846154-0.507115384615387
4537.938.2471153846154-0.347115384615384
4637.637.7471153846154-0.147115384615383
4737.337.24711538461540.0528846153846132
483636.6871153846154-0.68711538461539
4934.535.6483974358974-1.14839743589742
5033.535.8363461538462-2.33634615384615
5132.935.3363461538462-2.43634615384616
5232.934.8563461538462-1.95634615384616
5332.834.3763461538462-1.57634615384616
5431.934.1163461538462-2.21634615384616
5530.535.3784615384615-4.87846153846154
5629.234.8984615384615-5.69846153846154
5728.734.3384615384615-5.63846153846154
5828.433.8384615384615-5.43846153846155
592833.3384615384615-5.33846153846154
6027.432.7784615384615-5.37846153846155
6126.931.7397435897436-4.83974358974358


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.04834885593453090.09669771186906180.95165114406547
180.08810755504566060.1762151100913210.91189244495434
190.1812953698327390.3625907396654770.818704630167261
200.3509195079874950.7018390159749910.649080492012505
210.5297344982769830.9405310034460350.470265501723017
220.5957489854594070.8085020290811870.404251014540593
230.6160853706678710.7678292586642580.383914629332129
240.6226652144689010.7546695710621970.377334785531099
250.6108223011666070.7783553976667860.389177698833393
260.6106323124695510.7787353750608990.389367687530449
270.6564473642751270.6871052714497450.343552635724873
280.749478330174480.501043339651040.25052166982552
290.8498647627062420.3002704745875160.150135237293758
300.8680673909729180.2638652180541630.131932609027082
310.9976341033066550.004731793386689610.00236589669334480
320.9999990922621641.81547567208814e-069.0773783604407e-07
330.9999998991035572.01792885263215e-071.00896442631608e-07
340.9999998684529732.63094055117641e-071.31547027558821e-07
350.9999998925623852.14875230803867e-071.07437615401934e-07
360.9999998057743923.88451216032274e-071.94225608016137e-07
370.9999994390892181.12182156397282e-065.60910781986408e-07
380.9999977484903394.50301932283994e-062.25150966141997e-06
390.9999923796494041.52407011921703e-057.62035059608513e-06
400.999957448906518.51021869808447e-054.25510934904223e-05
410.999887809534770.0002243809304606710.000112190465230336
420.9997853194171240.0004293611657525090.000214680582876255
430.9993209219712020.001358156057595610.000679078028797807
440.9957803062274280.008439387545143360.00421969377257168


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.5NOK
5% type I error level140.5NOK
10% type I error level150.535714285714286NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/10ic0e1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/10ic0e1258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/1g5cn1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/1g5cn1258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/2ivih1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/2ivih1258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/35awt1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/35awt1258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/4dkct1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/4dkct1258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/57l661258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/57l661258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/6s7m21258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/6s7m21258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/73k071258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/73k071258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/8ci7m1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/8ci7m1258705389.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/93bpd1258705389.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587054728lysygpi6xijj3t/93bpd1258705389.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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