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Model 3

*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, 20 Dec 2009 03:57:13 -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/Dec/20/t12613067278prnpeifnrl3fyd.htm/, Retrieved Sun, 20 Dec 2009 11:58:59 +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/20/t12613067278prnpeifnrl3fyd.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 «
100.0 100.0 95.3 100.6 90.7 114.2 88.4 91.5 86.0 94.7 86.0 110.6 95.3 71.3 95.3 104.1 88.4 112.3 86.0 110.2 81.4 112.9 83.7 95.1 95.3 103.1 88.4 101.9 86.0 100.4 83.7 106.9 76.7 100.7 79.1 114.3 86.0 73.3 86.0 105.9 79.1 113.9 76.7 112.1 69.8 117.5 69.8 97.5 76.7 112.3 69.8 106.9 67.4 120.9 65.1 92.7 58.1 110.9 60.5 116.5 65.1 77.1 62.8 113.1 55.8 115.9 51.2 123.5 48.8 123.6 48.8 101.5 53.5 121.0 48.8 112.2 46.5 126.0 44.2 101.8 39.5 117.9 41.9 122.2 48.8 82.7 46.5 120.5 41.9 120.3 39.5 134.2 37.2 128.2 37.2 100.5 41.9 126.0 39.5 122.9 39.5 106.1 34.9 130.4 34.9 121.3 34.9 126.1 41.9 88.7 41.9 118.7 39.5 129.3 39.5 136.2 41.9 123.0 46.5 103.5
 
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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Werkloosheid[t] = + 122.578682792808 -0.282440508201765Productie[t] + 8.53269735149619M1[t] + 3.43605920340464M2[t] + 3.43543322256755M3[t] -0.79249080882931M4[t] -2.72395608114270M5[t] + 2.24731688263167M6[t] -0.883745028590917M7[t] + 8.78854064022755M8[t] + 5.9237896997247M9[t] + 5.98224706118411M10[t] + 3.63537681441102M11[t] -1.03449887127078t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)122.57868279280812.400939.884600
Productie-0.2824405082017650.141067-2.00220.0511830.025591
M18.532697351496194.3324841.96950.0549390.027469
M23.436059203404644.0402410.85050.3994750.199738
M33.435433222567554.3438560.79090.4330780.216539
M4-0.792490808829313.756521-0.2110.8338470.416924
M5-2.723956081142703.966113-0.68680.4956520.247826
M62.247316882631674.6088810.48760.6281450.314073
M7-0.8837450285909174.461179-0.19810.8438420.421921
M88.788540640227554.1016212.14270.0374620.018731
M95.92378969972474.5339971.30650.1978680.098934
M105.982247061184114.9518281.20810.2331880.116594
M113.635376814411024.7039970.77280.4435780.221789
t-1.034498871270780.070302-14.715100


Multiple Linear Regression - Regression Statistics
Multiple R0.971426418637605
R-squared0.943669286827083
Adjusted R-squared0.927749737452129
F-TEST (value)59.2773868531544
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.62474753413341
Sum Squared Residuals1455.33810184603


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1100101.832830452856-1.83283045285648
295.395.5322291285732-0.232229128573165
390.790.65591336492140.0440866350786144
488.491.8048899984338-3.40488999843381
58687.935116228604-1.93511622860400
68687.3810862406995-1.38108624069954
795.394.31543743053550.984562569464472
895.393.68917555906541.61082444093464
988.487.47391358003730.926086419962743
108687.0909971374496-1.09099713744960
1181.482.947038647261-1.54703864726096
1283.783.30460400757060.395395992429427
1395.388.54327842218196.75672157781813
1488.482.75107001266175.64892998733833
158682.13960592285643.86039407714355
1683.775.04131971687748.65868028312265
1776.773.82648672414412.87351327585588
1879.173.92206990510375.17793009489627
198681.33656995888274.66343004111732
208680.76679618905295.23320381094713
2179.174.60802231166514.49197768833486
2276.774.1403737166172.55962628338305
2369.869.23382585428360.566174145716451
2469.870.212760332637-0.412760332637047
2576.773.53083929147643.16916070852364
2669.868.92488101640350.87511898359645
2767.463.9355890494713.46441095052902
2865.166.6379884780931-1.53798847809310
2958.158.5316070852368-0.431607085236823
3060.560.8867143318105-0.386714331810541
3165.167.8493095724667-2.74930957246669
3262.866.3192380747509-3.51923807475087
3355.861.6291548400123-5.8291548400123
3451.258.5065654678675-7.30656546786754
3548.855.0969522990035-6.29695229900349
3648.856.6690118445807-7.86901184458068
3753.558.6596204148717-5.15962041487171
3848.855.0139598676849-6.2139598676849
3946.550.0811560023927-3.58115600239269
4044.251.6537933982077-7.45379339820773
4139.544.1405370725752-4.64053707257518
4241.946.8628169798112-4.96281697981119
4348.853.8536562712875-5.0536562712875
4446.551.8151918588085-5.31519185880851
4541.947.9724301486752-6.07243014867524
4639.543.0704655748594-3.57046557485937
4737.241.3837395060261-4.18373950602606
4837.244.5374658975332-7.33746589753315
4941.944.8334314186136-2.93343141861359
5039.539.5778599746767-0.0778599746767222
5139.543.2877356603585-3.78773566035850
5234.931.1620084083883.737991591612
5334.930.76625288943994.13374711056012
5434.933.3473125425751.55268745742499
5541.939.74502676682762.15497323317240
5641.939.90959831832241.99040168167761
5739.533.01647911961016.48352088038994
5839.530.09159810320659.40840189679346
5941.930.438443693425911.4615563065741
6046.531.276157917678615.2238420823214


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.02259397556677500.04518795113354990.977406024433225
180.005289273550104810.01057854710020960.994710726449895
190.002951889556026260.005903779112052510.997048110443974
200.001483562961124360.002967125922248720.998516437038876
210.0007068303077423830.001413660615484770.999293169692258
220.0002917446939912660.0005834893879825320.99970825530601
230.0002887593392902640.0005775186785805280.99971124066071
240.0007101365534111080.001420273106822220.999289863446589
250.004758370538170520.009516741076341040.99524162946183
260.01475257362111440.02950514724222890.985247426378886
270.02446749434286430.04893498868572860.975532505657136
280.04030101670889860.08060203341779720.959698983291101
290.05270628575760430.1054125715152090.947293714242396
300.0865498091163710.1730996182327420.913450190883629
310.1764874147910290.3529748295820590.82351258520897
320.3636471452066180.7272942904132360.636352854793382
330.4934834563287860.9869669126575710.506516543671214
340.533123022772940.933753954454120.46687697722706
350.4874780688192390.9749561376384780.512521931180761
360.4403277681636930.8806555363273860.559672231836307
370.4934635319204190.9869270638408370.506536468079581
380.4752264044303850.950452808860770.524773595569615
390.5862432213668370.8275135572663260.413756778633163
400.4919712502040120.9839425004080230.508028749795988
410.3810449289589240.7620898579178470.618955071041076
420.342195013012040.684390026024080.65780498698796
430.3228347676896650.645669535379330.677165232310335


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level70.259259259259259NOK
5% type I error level110.407407407407407NOK
10% type I error level120.444444444444444NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/10ttt11261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/10ttt11261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/1yhyk1261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/1yhyk1261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/2rcyv1261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/2rcyv1261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/3vgig1261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/3vgig1261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/4va8x1261306627.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/5lms11261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/5lms11261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/6pssi1261306627.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/75r741261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/75r741261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/8j13v1261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/8j13v1261306627.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/94hvf1261306627.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12613067278prnpeifnrl3fyd/94hvf1261306627.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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