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the Seatbelt Law-Q3 lineair+seasonality

*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, 21 Nov 2008 05:07:32 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6.htm/, Retrieved Fri, 21 Nov 2008 12:09:06 +0000
 
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/2008/Nov/21/t1227269333mezf0ezroikfit6.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
99.29 0 98.69 0 107.92 0 101.03 0 97.55 0 103.02 0 94.08 0 94.12 0 115.08 0 116.48 0 103.42 0 112.51 0 95.55 0 97.53 0 119.26 0 100.94 0 97.73 0 115.25 0 92.8 0 99.2 0 118.69 0 110.12 0 110.26 0 112.9 0 102.17 1 99.38 1 116.1 1 103.77 1 101.81 1 113.74 1 89.67 1 99.5 1 122.89 1 108.61 1 114.37 1 110.5 1 104.08 1 103.64 1 121.61 1 101.14 1 115.97 1 120.12 1 95.97 1 105.01 1 124.68 1 123.89 1 123.61 1 114.76 1 108.75 1 106.09 1 123.17 1 106.16 1 115.18 1 120.6 1 109.48 1 114.44 1 121.44 1 129.48 1 124.32 1 112.59 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'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
omzet[t] = + 102.207166666667 -3.04361111111111dummievariabele[t] -6.93452777777782M1[t] -8.1773888888889M2[t] + 8.02775000000002M3[t] -7.3171111111111M4[t] -4.61797222222222M5[t] + 3.93916666666666M6[t] -14.5476944444444M7[t] -8.83455555555555M8[t] + 8.92658333333334M9[t] + 5.74572222222222M10[t] + 2.88486111111111M11[t] + 0.340861111111111t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)102.2071666666672.27337544.958300
dummievariabele-3.043611111111112.187556-1.39130.1708180.085409
M1-6.934527777777822.71542-2.55380.0140350.007018
M2-8.17738888888892.699956-3.02870.0040190.002009
M38.027750000000022.6858882.98890.0044830.002241
M4-7.31711111111112.673238-2.73720.008780.00439
M5-4.617972222222222.662026-1.73480.089480.04474
M63.939166666666662.6522711.48520.1443110.072155
M7-14.54769444444442.643988-5.50222e-061e-06
M8-8.834555555555552.637192-3.350.0016210.000811
M98.926583333333342.6318953.39170.0014360.000718
M105.745722222222222.6281042.18630.0339220.016961
M112.884861111111112.6258271.09860.2776390.138819
t0.3408611111111110.0631495.39772e-061e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.927865011933247
R-squared0.860933480369885
Adjusted R-squared0.821632072648331
F-TEST (value)21.9059196675472
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.99840144432528e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.15059599061323
Sum Squared Residuals792.462565555554


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
199.2995.61350000000023.67649999999981
298.6994.71153.97850000000001
3107.92111.2575-3.33749999999999
4101.0396.25354.77650000000004
597.5599.2935-1.74350000000002
6103.02108.1915-5.1715
794.0890.04554.0345
894.1296.0995-1.97949999999998
9115.08114.20150.878500000000005
10116.48111.36155.1185
11103.42108.8415-5.4215
12112.51106.29756.21250000000002
1395.5599.7038333333333-4.15383333333329
1497.5398.8018333333333-1.27183333333334
15119.26115.3478333333333.91216666666667
16100.94100.3438333333330.596166666666658
1797.73103.383833333333-5.65383333333332
18115.25112.2818333333332.96816666666667
1992.894.1358333333333-1.33583333333333
2099.2100.189833333333-0.98983333333333
21118.69118.2918333333330.39816666666667
22110.12115.451833333333-5.33183333333332
23110.26112.931833333333-2.67183333333332
24112.9110.3878333333332.51216666666667
25102.17100.7505555555561.41944444444450
2699.3899.8485555555555-0.468555555555560
27116.1116.394555555556-0.294555555555559
28103.77101.3905555555562.37944444444443
29101.81104.430555555556-2.62055555555555
30113.74113.3285555555560.411444444444442
3189.6795.1825555555556-5.51255555555555
3299.5101.236555555556-1.73655555555556
33122.89119.3385555555563.55144444444445
34108.61116.498555555556-7.88855555555555
35114.37113.9785555555560.391444444444453
36110.5111.434555555556-0.934555555555555
37104.08104.840888888889-0.760888888888846
38103.64103.938888888889-0.298888888888893
39121.61120.4848888888891.12511111111111
40101.14105.480888888889-4.3408888888889
41115.97108.5208888888897.44911111111111
42120.12117.4188888888892.70111111111111
4395.9799.2728888888889-3.30288888888889
44105.01105.326888888889-0.316888888888894
45124.68123.4288888888891.25111111111112
46123.89120.5888888888893.30111111111111
47123.61118.0688888888895.5411111111111
48114.76115.524888888889-0.764888888888888
49108.75108.931222222222-0.181222222222181
50106.09108.029222222222-1.93922222222223
51123.17124.575222222222-1.40522222222223
52106.16109.571222222222-3.41122222222224
53115.18112.6112222222222.56877777777778
54120.6121.509222222222-0.909222222222235
55109.48103.3632222222226.11677777777777
56114.44109.4172222222225.02277777777776
57121.44127.519222222222-6.07922222222223
58129.48124.6792222222224.80077777777776
59124.32122.1592222222222.16077777777776
60112.59119.615222222222-7.02522222222223


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.7576275771554880.4847448456890230.242372422844512
180.8584606243141380.2830787513717230.141539375685861
190.7938527874784580.4122944250430840.206147212521542
200.6988033134616760.6023933730766480.301196686538324
210.5864338352279430.8271323295441140.413566164772057
220.662216617480480.675566765039040.33778338251952
230.6690037227455230.6619925545089550.330996277254477
240.5698444332649450.860311133470110.430155566735055
250.4700144816900580.9400289633801160.529985518309942
260.3837635189472940.7675270378945880.616236481052706
270.288350187229680.576700374459360.71164981277032
280.2705645366014020.5411290732028040.729435463398598
290.2414400524630290.4828801049260570.758559947536971
300.1723148198047120.3446296396094240.827685180195288
310.2252771340500880.4505542681001760.774722865949912
320.1733035256866020.3466070513732040.826696474313398
330.1799730123245580.3599460246491160.820026987675442
340.5241092573857550.951781485228490.475890742614245
350.5501475960392590.8997048079214830.449852403960741
360.4827008596721840.9654017193443670.517299140327816
370.3826028294662750.765205658932550.617397170533725
380.2810463408849920.5620926817699840.718953659115008
390.2054016761453150.410803352290630.794598323854685
400.1571460768443210.3142921536886410.84285392315568
410.2346010446961820.4692020893923630.765398955303818
420.1655182051327210.3310364102654430.834481794867279
430.3139634979408480.6279269958816960.686036502059152


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/13xll1227269247.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/3o32u1227269248.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/3o32u1227269248.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/4xehw1227269248.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/5gn511227269248.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/687px1227269248.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/687px1227269248.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/733mk1227269248.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/733mk1227269248.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/8ocuo1227269248.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/8ocuo1227269248.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/9jah81227269248.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227269333mezf0ezroikfit6/9jah81227269248.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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