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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: Tue, 21 Dec 2010 20:26:33 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz.htm/, Retrieved Tue, 21 Dec 2010 21:24:20 +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/2010/Dec/21/t1292963057xxrvnjd99mwzffz.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
112.3 1 117.3 1 111.1 1 102.2 1 104.3 1 122.9 0 107.6 0 121.3 0 131.5 0 89 0 104.4 0 128.9 0 135.9 0 133.3 0 121.3 0 120.5 0 120.4 0 137.9 0 126.1 0 133.2 0 151.1 0 105 0 119 0 140.4 0 156.6 1 137.1 1 122.7 1 125.8 1 139.3 1 134.9 1 149.2 1 132.3 1 149 1 117.2 1 119.6 1 152 1 149.4 1 127.3 1 114.1 1 102.1 1 107.7 1 104.4 1 102.1 1 96 1 109.3 1 90 1 83.9 1 112 1 114.3 1 103.6 1 91.7 1 80.8 1 87.2 1 109.2 1 102.7 1 95.1 1 117.5 1 85.1 1 92.1 1 113.5 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 time6 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework
error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Multiple Linear Regression - Estimated Regression Equation
Promet[t] = + 143.465911330049 -0.78177339901479Dummy[t] + 0.329540229885031M1[t] -9.27165845648604M2[t] -20.4328571428571M3[t] -25.9540558292282M4[t] -20.0752545155993M5[t] -9.7728078817734M6[t] -13.7140065681445M7[t] -15.2952052545156M8[t] + 1.1835960591133M9[t] -32.8576026272578M10[t] -25.9388013136289M11[t] -0.378801313628899t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)143.4659113300498.23194517.427900
Dummy-0.781773399014796.030553-0.12960.897420.44871
M10.32954022988503110.2925480.0320.9745970.487298
M2-9.2716584564860410.25309-0.90430.3705590.185279
M3-20.432857142857110.216034-2.00010.0514160.025708
M4-25.954055829228210.181407-2.54920.0141980.007099
M5-20.075254515599310.149234-1.9780.0539360.026968
M6-9.77280788177349.968671-0.98040.332040.16602
M7-13.71400656814459.954262-1.37770.1749610.087481
M8-15.29520525451569.942457-1.53840.1308090.065404
M91.18359605911339.9332660.11920.9056720.452836
M10-32.85760262725789.926696-3.310.001820.00091
M11-25.93880131362899.922751-2.61410.0120530.006027
t-0.3788013136288990.161546-2.34490.0234060.011703


Multiple Linear Regression - Regression Statistics
Multiple R0.683211258579278
R-squared0.466777623849482
Adjusted R-squared0.316084343633031
F-TEST (value)3.09753443006229
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.002306270961007
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation15.6871682668679
Sum Squared Residuals11320.0134187192


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1112.3142.634876847291-30.3348768472907
2117.3132.654876847291-15.3548768472906
3111.1121.114876847291-10.0148768472906
4102.2115.214876847291-13.0148768472906
5104.3120.714876847291-16.4148768472906
6122.9131.420295566502-8.52029556650246
7107.6127.100295566502-19.5002955665025
8121.3125.140295566502-3.84029556650247
9131.5141.240295566502-9.74029556650246
1089106.820295566502-17.8202955665025
11104.4113.360295566502-8.96029556650245
12128.9138.920295566502-10.0202955665025
13135.9138.871034482759-2.97103448275858
14133.3128.8910344827594.40896551724139
15121.3117.3510344827593.94896551724137
16120.5111.4510344827599.04896551724137
17120.4116.9510344827593.44896551724137
18137.9126.87467980295611.0253201970443
19126.1122.5546798029563.54532019704433
20133.2120.59467980295612.6053201970443
21151.1136.69467980295614.4053201970443
22105102.2746798029562.72532019704434
23119108.81467980295610.1853201970443
24140.4134.3746798029566.02532019704433
25156.6133.54364532019723.056354679803
26137.1123.56364532019713.536354679803
27122.7112.02364532019710.676354679803
28125.8106.12364532019719.676354679803
29139.3111.62364532019727.676354679803
30134.9121.54729064039413.3527093596059
31149.2117.22729064039431.9727093596059
32132.3115.26729064039417.0327093596059
33149131.36729064039417.6327093596059
34117.296.94729064039420.2527093596059
35119.6103.48729064039416.1127093596059
36152129.04729064039422.9527093596059
37149.4128.9980295566520.4019704433498
38127.3119.018029556658.28197044334975
39114.1107.478029556656.62197044334975
40102.1101.578029556650.521970443349749
41107.7107.078029556650.621970443349752
42104.4117.001674876847-12.6016748768473
43102.1112.681674876847-10.5816748768473
4496110.721674876847-14.7216748768473
45109.3126.821674876847-17.5216748768473
469092.4016748768473-2.40167487684729
4783.998.9416748768473-15.0416748768473
48112124.501674876847-12.5016748768473
49114.3124.452413793103-10.1524137931034
50103.6114.472413793103-10.8724137931035
5191.7102.932413793103-11.2324137931035
5280.897.0324137931034-16.2324137931035
5387.2102.532413793103-15.3324137931035
54109.2112.4560591133-3.2560591133005
55102.7108.1360591133-5.43605911330049
5695.1106.1760591133-11.0760591133005
57117.5122.276059113301-4.7760591133005
5885.187.8560591133005-2.7560591133005
5992.194.3960591133005-2.2960591133005
60113.5119.9560591133-6.4560591133005


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.0814358936240750.162871787248150.918564106375925
180.02605455781351570.05210911562703150.973945442186484
190.009103465940984180.01820693188196840.990896534059016
200.003831748345629020.007663496691258040.99616825165437
210.001663716515092020.003327433030184040.998336283484908
220.0004743335524802040.0009486671049604090.99952566644752
230.000128618887353420.0002572377747068390.999871381112647
245.23033130340177e-050.0001046066260680350.999947696686966
250.0001002241716227670.0002004483432455340.999899775828377
260.0008187188301990150.001637437660398030.9991812811698
270.003187167200166510.006374334400333020.996812832799833
280.00155445213788760.003108904275775210.998445547862112
290.001698824628921490.003397649257842990.998301175371079
300.00206531774229130.004130635484582610.997934682257709
310.009781530881589110.01956306176317820.99021846911841
320.01225501192481490.02451002384962980.987744988075185
330.01079591323863510.02159182647727020.989204086761365
340.006938788410679210.01387757682135840.993061211589321
350.005724158190345540.01144831638069110.994275841809654
360.01152802695972190.02305605391944370.988471973040278
370.0485343482271130.0970686964542260.951465651772887
380.2131931567933890.4263863135867770.786806843206611
390.4582713268387130.9165426536774250.541728673161287
400.7872423061622590.4255153876754820.212757693837741
410.9861316142651080.02773677146978320.0138683857348916
420.9773069822499330.04538603550013420.0226930177500671
430.9440960742161070.1118078515677860.055903925783893


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level110.407407407407407NOK
5% type I error level200.740740740740741NOK
10% type I error level220.814814814814815NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/10uxqg1292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/10uxqg1292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/1net51292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/1net51292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/2yob81292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/2yob81292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/3yob81292963184.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/4yob81292963184.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/5yob81292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/5yob81292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/6qfsa1292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/6qfsa1292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/7169v1292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/7169v1292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/8169v1292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/8169v1292963184.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/9169v1292963184.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292963057xxrvnjd99mwzffz/9169v1292963184.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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