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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, 17 Nov 2009 10:43:04 -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/17/t12584801544gmtmunhav86vwj.htm/, Retrieved Tue, 17 Nov 2009 18:49:26 +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/17/t12584801544gmtmunhav86vwj.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 «
15836.8 89.1 17570.4 82.6 18252.1 102.7 16196.7 91.8 16643 94.1 17729 103.1 16446.1 93.2 15993.8 91 16373.5 94.3 17842.2 99.4 22321.5 115.7 22786.7 116.8 18274.1 99.8 22392.9 96 23899.3 115.9 21343.5 109.1 22952.3 117.3 21374.4 109.8 21164.1 112.8 20906.5 110.7 17877.4 100 20664.3 113.3 22160 122.4 19813.6 112.5 17735.4 104.2 19640.2 92.5 20844.4 117.2 19823.1 109.3 18594.6 106.1 21350.6 118.8 18574.1 105.3 18924.2 106 17343.4 102 19961.2 112.9 19932.1 116.5 19464.6 114.8 16165.4 100.5 17574.9 85.4 19795.4 114.6 19439.5 109.9 17170 100.7 21072.4 115.5 17751.8 100.7 17515.5 99 18040.3 102.3 19090.1 108.8 17746.5 105.9 19202.1 113.2 15141.6 95.7 16258.1 80.9 18586.5 113.9 17209.4 98.1 17838.7 102.8 19123.5 104.7 16583.6 95.9 15991.2 94.6 16704.4 101.6 17420.4 103.9 17872 110.3 17823.2 114.1
 
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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
uitvoer[t] = -8033.86813731782 + 255.273412361827indproc[t] + 600.65077261152M1[t] + 5343.71594368815M2[t] + 489.803888705864M3[t] + 1407.01190144279M4[t] + 1138.02594128105M5[t] + 1087.38340364584M6[t] + 1344.43658319079M7[t] + 1480.38463826929M8[t] + 974.791939749771M9[t] + 794.13568831353M10[t] + 182.325658722537M11[t] -36.6871507608812t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-8033.868137317821983.559289-4.05020.0001959.7e-05
indproc255.27341236182717.07562314.949600
M1600.65077261152564.9071591.06330.2932080.146604
M25343.71594368815669.6378287.9800
M3489.803888705864491.1516550.99730.3238580.161929
M41407.01190144279521.9306212.69580.0097760.004888
M51138.02594128105518.307222.19570.0331980.016599
M61087.38340364584493.3848442.20390.0325730.016287
M71344.43658319079534.1166082.51710.015380.00769
M81480.38463826929543.4345562.72410.0090840.004542
M9974.791939749771544.9890621.78860.0802590.040129
M10794.13568831353500.759161.58590.1196220.059811
M11182.325658722537487.8531990.37370.7103220.355161
t-36.68715076088125.873454-6.246300


Multiple Linear Regression - Regression Statistics
Multiple R0.94446092820677
R-squared0.892006444909194
Adjusted R-squared0.86148652716614
F-TEST (value)29.2270265083597
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation771.302682407173
Sum Squared Residuals27365760.082871


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
115836.815274.9565259715561.843474028527
217570.418322.0573659354-751.657365935433
318252.118562.453748665-310.353748664989
416196.716660.4944158971-463.79441589712
51664316941.9501534067-298.950153406699
61772919152.0811762670-1423.08117626705
716446.116845.2404226690-399.140422669041
815993.816382.8998197906-389.099819790635
916373.516683.0222313043-309.522231304264
1017842.217767.573232152574.6267678475399
1122321.521280.03267329841041.46732670164
1222786.721341.82061741301444.87938258705
1318274.117566.1362291125707.963770887464
1422392.921302.47528245331090.42471754666
1523899.321491.81698271052407.48301728947
1621343.520636.4786406261707.021359373852
1722952.322424.0475110705528.252488929496
1821374.420422.1672299607952.232770039286
1921164.121408.3534958303-244.253495830269
2020906.520971.5402341880-65.040234188046
2117877.417697.8348726361179.565127363899
2220664.320875.6278548513-211.327854851277
232216022550.1187269920-390.118726992027
2419813.619803.89913512659.70086487347598
2517735.418249.093434374-513.693434373999
2619640.219968.7725300564-328.572530056371
2720844.421383.4266096503-539.026609650327
2819823.120247.2875139679-424.187513967941
2918594.619124.7394834875-530.139483487471
3021350.622279.3821320866-928.782132086583
3118574.119053.557093986-479.457093985995
3218924.219331.5093869569-407.309386956885
3317343.417768.1358882292-424.735888229181
3419961.220333.2726807760-372.072680775973
3519932.120603.7597849267-671.659784926675
3619464.619950.7821744282-486.18217442815
3716165.416864.3359995047-698.935999504667
3817574.917716.0854931568-141.185493156827
3919795.420279.469928379-484.069928379002
4019439.519960.2057522545-520.705752254463
411717017306.0172476030-136.017247603034
4221072.420996.73406216275.6659378380214
4317751.817439.0535879910312.746412008982
4417515.517104.3496912935411.150308706476
4518040.317404.4721028072635.827897192845
4619090.118846.4058809619243.694119038091
4717746.517457.6158047607288.884195239263
4819202.119102.0989055187100.001094481345
4915141.615198.7778110373-57.1778110373246
5016258.116127.1093283980130.990671601967
5118586.519660.5327305952-1074.03273059515
5217209.416507.7336772543701.666322745671
5317838.717401.8456044323436.854395567707
5419123.517799.53539952371323.96460047632
5516583.615773.4953995237810.104600476323
5615991.215540.9008677709450.299132229090
5716704.416785.5349050233-81.1349050232993
5817420.417155.3203512584265.079648741617
591787218140.5730100222-268.573010022198
6017823.218891.5991675137-1068.39916751372


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.9893878949124990.02122421017500230.0106121050875012
180.9819854601197620.0360290797604770.0180145398802385
190.9825938514366940.03481229712661240.0174061485633062
200.9785539942952680.04289201140946380.0214460057047319
210.9899804938441170.02003901231176590.0100195061558830
220.9937428193858070.01251436122838550.00625718061419276
230.999794791538860.0004104169222790490.000205208461139525
240.9997943426367750.0004113147264505980.000205657363225299
250.9998196701868370.0003606596263254720.000180329813162736
260.999749802524760.0005003949504791340.000250197475239567
270.9997935027057280.0004129945885433460.000206497294271673
280.9994658524745750.001068295050849220.00053414752542461
290.9988749595137170.002250080972566040.00112504048628302
300.9990984810741780.001803037851644020.000901518925822008
310.9986360240974670.002727951805066600.00136397590253330
320.9968866529201940.006226694159611140.00311334707980557
330.998568020351740.002863959296518350.00143197964825917
340.9966960828925730.006607834214853770.00330391710742689
350.9922388065247340.01552238695053280.00776119347526639
360.984933488432780.03013302313444160.0150665115672208
370.9727919055231920.05441618895361590.0272080944768080
380.9581845826884770.08363083462304610.0418154173115231
390.9294079838039770.1411840323920450.0705920161960226
400.8694617151264320.2610765697471360.130538284873568
410.9685392309589260.06292153808214690.0314607690410735
420.9384016658681790.1231966682636430.0615983341318215
430.9191998583710930.1616002832578140.0808001416289071


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level120.444444444444444NOK
5% type I error level200.740740740740741NOK
10% type I error level230.851851851851852NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/10rxio1258479779.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/10rxio1258479779.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/1u3od1258479779.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/1u3od1258479779.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/294qr1258479779.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/294qr1258479779.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/3o6sx1258479779.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/44ovi1258479779.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/44ovi1258479779.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/58vk01258479779.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/6wyxq1258479779.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/7yued1258479779.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/8czua1258479779.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/8czua1258479779.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/930321258479779.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/17/t12584801544gmtmunhav86vwj/930321258479779.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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