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With season influences

*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: Sun, 22 Nov 2009 12:19:48 -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/22/t1258917635667wrkkbenonvqb.htm/, Retrieved Sun, 22 Nov 2009 20:20:47 +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/22/t1258917635667wrkkbenonvqb.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 «
17823.2 1.2218 17872 1.249 17420.4 1.2991 16704.4 1.3408 15991.2 1.3119 16583.6 1.3014 19123.5 1.3201 17838.7 1.2938 17209.4 1.2694 18586.5 1.2165 16258.1 1.2037 15141.6 1.2292 19202.1 1.2256 17746.5 1.2015 19090.1 1.1786 18040.3 1.1856 17515.5 1.2103 17751.8 1.1938 21072.4 1.202 17170 1.2271 19439.5 1.277 19795.4 1.265 17574.9 1.2684 16165.4 1.2811 19464.6 1.2727 19932.1 1.2611 19961.2 1.2881 17343.4 1.3213 18924.2 1.2999 18574.1 1.3074 21350.6 1.3242 18594.6 1.3516 19823.1 1.3511 20844.4 1.3419 19640.2 1.3716 17735.4 1.3622 19813.6 1.3896 22160 1.4227 20664.3 1.4684 17877.4 1.457 20906.5 1.4718 21164.1 1.4748 21374.4 1.5527 22952.3 1.5751 21343.5 1.5557 23899.3 1.5553 22392.9 1.577 18274.1 1.4975 22786.7 1.437 22321.5 1.3322 17842.2 1.2732 16373.5 1.3449 15993.8 1.3239 16446.1 1.2785 17729 1.305 16643 1.319 16196.7 1.365 18252.1 1.4016 17570.4 1.4088 15836.8 1.4268
 
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
EUDO[t] = + 0.688170796119973 + 4.03585428287288e-05UITV[t] -0.178658012241435M1[t] -0.202300754539509M2[t] -0.153327146619087M3[t] -0.0551540419778964M4[t] -0.0856662083483208M5[t] -0.107639433978710M6[t] -0.159787456091427M7[t] -0.087122734055486M8[t] -0.0833698761445767M9[t] -0.150402045585577M10[t] -0.076462993523277M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.6881707961199730.10976.273200
UITV4.03585428287288e-056e-066.50200
M1-0.1786580122414350.056103-3.18450.0025740.001287
M2-0.2023007545395090.056526-3.57890.0008140.000407
M3-0.1533271466190870.054512-2.81270.0071470.003574
M4-0.05515404197789640.052647-1.04760.3001730.150086
M5-0.08566620834832080.053056-1.61460.1130810.056541
M6-0.1076394339787100.053289-2.01990.0491130.024556
M7-0.1597874560914270.056814-2.81250.0071520.003576
M8-0.0871227340554860.053959-1.61460.1130910.056545
M9-0.08336987614457670.054202-1.53810.1307190.065359
M10-0.1504020455855770.057166-2.6310.0114770.005739
M11-0.0764629935232770.054028-1.41520.163590.081795


Multiple Linear Regression - Regression Statistics
Multiple R0.709554219020798
R-squared0.503467189730214
Adjusted R-squared0.376692855193248
F-TEST (value)3.97136527333462
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.000309492120214028
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0830072712216853
Sum Squared Residuals0.32383973255651


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.22181.22883116442354-0.0070311644235426
21.2491.207157919015500.0418420809844953
31.29911.237905608994470.0611943910055266
41.34081.307181996970290.0336180030297057
51.31191.247886117854420.0640138821455796
61.30141.249821292995770.0515787070042294
71.32011.300179933813740.019920066186259
81.29381.32099200002333-0.0271920000233316
91.26941.29934722693212-0.0299472269321219
101.21651.28789280682056-0.0713928068205639
111.20371.26786102776045-0.064161027760452
121.22921.29926370821545-0.0700637082154532
131.22561.28448155913007-0.0588815591300718
141.20151.2020929218905-0.000592921890499267
151.17861.30529226795560-0.126692267955602
161.18561.36109697433519-0.175496974335193
171.21031.30940464468825-0.0991046446882518
181.19381.29696814272829-0.103168142728291
191.2021.37883469793265-0.176834697932651
201.22711.29400424243376-0.0669042424337606
211.2771.38935081329447-0.11235081329447
221.2651.33668224924621-0.0716822492462143
231.26841.32100515695732-0.0526051569573221
241.28111.34058278436351-0.0594827843635058
251.27271.29507567662261-0.0223756766226131
261.26111.29030055309697-0.0292005530969688
271.28811.34044859461371-0.0523485946137073
281.32131.33297110583785-0.011671105837852
291.29991.36625772397108-0.0663577239710819
301.30741.33015497249636-0.0227549724963552
311.32421.39006244454760-0.0658624445476028
321.35161.351499022547570.000100977452432218
331.35111.40483235032357-0.0537323503235702
341.34191.37901836067355-0.0371183606735506
351.37161.40435765546150-0.0327576554614957
361.36221.40394569660461-0.0417456966046099
371.38961.309160808069840.0804391919301606
381.42271.380215350665090.0424846493349063
391.46841.368824686076590.0995753139234134
401.4571.354522567708390.102477432291607
411.47181.446260463420470.025539536579529
421.47481.434683598422760.0401164015772375
431.55271.391022977866930.161677022133073
441.57511.527369444632320.0477305553676808
451.55571.466193478840370.0895065211596305
461.55531.502309673161030.0529903268389657
471.5771.515452616306140.0615473836938626
481.49751.425686843626450.071813156373554
491.4371.429150791753930.00784920824606702
501.33221.38673325533193-0.0545332553319334
511.27321.254928842359630.018271157640369
521.34491.293827355148270.0510726448517322
531.32391.247991050065770.0759089499342250
541.27851.244271993356820.0342280066431797
551.3051.243899945839080.0611000541609212
561.3191.272735290363020.0462647096369793
571.3651.258476130609470.106523869390532
581.40161.274396910098640.127203089901363
591.40881.320823543514590.0879764564854073
601.42681.327320967189990.0994790328100148


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.2283705305171950.456741061034390.771629469482805
170.1143556772887040.2287113545774080.885644322711296
180.06162333844330730.1232466768866150.938376661556693
190.04282383473053160.08564766946106310.957176165269468
200.07878400837892080.1575680167578420.92121599162108
210.1599160878158190.3198321756316380.840083912184181
220.1922174149418820.3844348298837630.807782585058118
230.2338950814610730.4677901629221460.766104918538927
240.2396471198224820.4792942396449650.760352880177518
250.2279455815825830.4558911631651660.772054418417417
260.2066255612952560.4132511225905120.793374438704744
270.2130791314747250.426158262949450.786920868525275
280.1941621188061310.3883242376122620.805837881193869
290.1995022626558550.399004525311710.800497737344145
300.1773672952295090.3547345904590180.822632704770491
310.287782947996910.575565895993820.71221705200309
320.2837969134949430.5675938269898850.716203086505057
330.4224695890234440.8449391780468870.577530410976556
340.5731745512322450.853650897535510.426825448767755
350.6998852506278050.600229498744390.300114749372195
360.8543235889683540.2913528220632930.145676411031646
370.8854600797434180.2290798405131640.114539920256582
380.9275510837839060.1448978324321890.0724489162160944
390.964167952574070.07166409485185940.0358320474259297
400.9666894533468320.06662109330633590.0333105466531679
410.9450750692166020.1098498615667950.0549249307833977
420.8934806718602870.2130386562794250.106519328139713
430.9907802532397950.01843949352041050.00921974676020525
440.987459892355210.02508021528957980.0125401076447899


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0689655172413793NOK
10% type I error level50.172413793103448NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/10ka671258917583.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/10ka671258917583.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/11x7f1258917583.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/2fk2b1258917583.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/3d4791258917583.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/3d4791258917583.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/4bexj1258917583.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/5z1ti1258917583.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/6b42g1258917583.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/81mdi1258917583.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/81mdi1258917583.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/9rmji1258917583.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/22/t1258917635667wrkkbenonvqb/9rmji1258917583.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No 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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