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met lineaire trend en seizoenaliteit

*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: Sat, 12 Dec 2009 04:35:34 -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/12/t1260618151s453v4t6ekrgnaf.htm/, Retrieved Sat, 12 Dec 2009 12:42:43 +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/12/t1260618151s453v4t6ekrgnaf.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 «
17192.4 0 15386.1 0 14287.1 0 17526.6 0 14497 0 14398.3 0 16629.6 0 16670.7 0 16614.8 0 16869.2 0 15663.9 0 16359.9 0 18447.7 0 16889 0 16505 0 18320.9 0 15052.1 0 15699.8 0 18135.3 0 16768.7 0 18883 0 19021 0 18101.9 0 17776.1 0 21489.9 0 17065.3 0 18690 0 18953.1 0 16398.9 0 16895.6 0 18553 0 19270 0 19422.1 0 17579.4 0 18637.3 0 18076.7 0 20438.6 0 18075.2 0 19563 0 19899.2 0 19227.5 0 17789.6 0 19220.8 0 21968.9 0 21131.5 0 19484.6 0 22168.7 1 20866.8 1 22176.2 1 23533.8 1 21479.6 1 24347.7 1 22751.6 1 20328.3 1 23650.4 1 23335.7 1 19614.9 1 18042.3 1 17282.5 1 16847.2 1 18159.5 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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Invoer[t] = + 14662.8712459016 + 649.502540983608Dummy[t] + 2134.04735519127M1[t] + 1185.18154644809M2[t] + 1015.16744262295M3[t] + 2634.65333879781M4[t] + 325.499234972678M5[t] -322.674868852462M6[t] + 1807.75102732240M7[t] + 2087.65692349727M8[t] + 1533.04281967213M9[t] + 514.008715846994M10[t] + 470.594103825136M11[t] + 85.0741038251365t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)14662.8712459016874.6959216.763400
Dummy649.502540983608749.6133860.86650.3906450.195323
M12134.04735519127994.8642852.14510.0371470.018573
M21185.181546448091044.1101711.13510.2620840.131042
M31015.167442622951043.0348190.97330.3353960.167698
M42634.653338797811042.2794542.52780.0148990.00745
M5325.4992349726781041.8447740.31240.7560990.378049
M6-322.6748688524621041.731179-0.30970.7581210.379061
M71807.751027322401041.9387741.7350.0892970.044648
M82087.656923497271042.4673682.00260.0510070.025503
M91533.042819672131043.3164731.46940.1483880.074194
M10514.0087158469941044.4853060.49210.6249280.312464
M11470.5941038251361037.1575030.45370.6521080.326054
t85.074103825136518.2926784.65072.7e-051.4e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.796759760684484
R-squared0.634826116245995
Adjusted R-squared0.533820573931058
F-TEST (value)6.28506220249374
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value1.19807218634804e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1639.6349161624
Sum Squared Residuals126354924.940048


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
117192.416881.992704918310.407295082008
215386.116018.201-632.101000000004
314287.115933.261-1646.16100000000
417526.617637.821-111.221000000008
51449715413.741-916.740999999999
614398.314850.641-452.341000000005
716629.617066.141-436.541000000004
816670.717431.121-760.421000000002
916614.816961.581-346.781000000002
1016869.216027.621841.579
1115663.916069.2804918033-405.380491803281
1216359.915683.7604918033676.139508196718
1318447.717902.8819508197544.818049180318
141688917039.0902459016-150.090245901640
151650516954.1502459016-449.15024590164
1618320.918658.7102459016-337.810245901638
1715052.116434.6302459016-1382.53024590164
1815699.815871.5302459016-171.730245901640
1918135.318087.030245901648.2697540983598
2016768.718452.0102459016-1683.31024590164
211888317982.4702459016900.52975409836
221902117048.51024590161972.48975409836
2318101.917090.16973770491011.73026229508
2417776.116704.64973770491071.45026229508
2521489.918923.77119672132566.12880327868
2617065.318059.9794918033-994.679491803278
271869017975.0394918033714.960508196722
2818953.119679.5994918033-726.499491803279
2916398.917455.5194918033-1056.61949180328
3016895.616892.41949180333.18050819672222
311855319107.9194918033-554.919491803277
321927019472.8994918033-202.899491803279
3319422.119003.3594918033418.74050819672
3417579.418069.3994918033-489.999491803277
3518637.318111.0589836066526.241016393441
3618076.717725.5389836066351.161016393443
3720438.619944.6604426230493.93955737704
3818075.219080.8687377049-1005.66873770491
391956318995.9287377049567.071262295085
4019899.220700.4887377049-801.288737704914
4119227.518476.4087377049751.091262295082
4217789.617913.3087377049-123.708737704916
4319220.820128.8087377049-908.008737704917
4421968.920493.78873770491475.11126229509
4521131.520024.24873770491107.25126229508
4619484.619090.2887377049394.311262295082
4722168.719781.45077049182387.2492295082
4820866.819395.93077049181470.86922950820
4922176.221615.0522295082561.147770491796
5023533.820751.26052459022782.53947540984
5121479.620666.3205245902813.279475409836
5224347.722370.88052459021976.81947540984
5322751.620146.80052459022604.79947540983
5420328.319583.7005245902744.599475409839
5523650.421799.20052459021851.19947540984
5623335.722164.18052459021171.51947540984
5719614.921694.6405245902-2079.74052459016
5818042.320760.6805245902-2718.38052459016
5917282.520802.3400163934-3519.84001639344
6016847.220416.8200163934-3569.62001639344
6118159.522635.9414754098-4476.44147540984


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.0301077645545220.0602155291090440.969892235445478
180.006964508820456870.01392901764091370.993035491179543
190.001549118653851870.003098237307703750.998450881346148
200.002044154221582580.004088308443165170.997955845778417
210.001380366280276310.002760732560552620.998619633719724
220.000643318893407120.001286637786814240.999356681106593
230.0003741890227808420.0007483780455616850.99962581097722
240.0001003505088086420.0002007010176172840.999899649491191
250.0001817240369268850.0003634480738537690.999818275963073
260.0003054503945379320.0006109007890758640.999694549605462
270.0001864693380923480.0003729386761846960.999813530661908
280.0001998509848941590.0003997019697883190.999800149015106
290.0002194435810575270.0004388871621150540.999780556418942
300.0001071261559331140.0002142523118662290.999892873844067
310.0001298131011823500.0002596262023647000.999870186898818
320.0003303099781599950.000660619956319990.99966969002184
330.0003013793627126030.0006027587254252060.999698620637287
340.006765271017629890.01353054203525980.99323472898237
350.003582752545871150.00716550509174230.996417247454129
360.002181696849760530.004363393699521050.99781830315024
370.001368667231372290.002737334462744580.998631332768628
380.003242351996319990.006484703992639980.99675764800368
390.001745550972669970.003491101945339950.99825444902733
400.003080569178882910.006161138357765820.996919430821117
410.007015441334736690.01403088266947340.992984558665263
420.005239622438770230.01047924487754050.99476037756123
430.2966072476106900.5932144952213790.70339275238931
440.9425593466087870.1148813067824260.057440653391213


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level210.75NOK
5% type I error level250.892857142857143NOK
10% type I error level260.928571428571429NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/105hu71260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/105hu71260617728.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/17a4l1260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/17a4l1260617728.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/22n681260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/22n681260617728.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/36q311260617728.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/4updx1260617728.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/5sqwa1260617728.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/6m8ts1260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/6m8ts1260617728.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/73kky1260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/73kky1260617728.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/8gej01260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/8gej01260617728.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/9xcvg1260617728.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260618151s453v4t6ekrgnaf/9xcvg1260617728.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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