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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: Fri, 20 Nov 2009 09:39:27 -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/20/t1258735261q6lw5v2ls5ce22b.htm/, Retrieved Fri, 20 Nov 2009 17:41:13 +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/20/t1258735261q6lw5v2ls5ce22b.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 «
2253 14.9 2218 18.6 1855 19.1 2187 18.8 1852 18.2 1570 18 1851 19 1954 20.7 1828 21.2 2251 20.7 2277 19.6 2085 18.6 2282 18.7 2266 23.8 1878 24.9 2267 24.8 2069 23.8 1746 22.3 2299 21.7 2360 20.7 2214 19.7 2825 18.4 2355 17.4 2333 17 3016 18 2155 23.8 2172 25.5 2150 25.6 2533 23.7 2058 22 2160 21.3 2260 20.7 2498 20.4 2695 20.3 2799 20.4 2946 19.8 2930 19.5 2318 23.1 2540 23.5 2570 23.5 2669 22.9 2450 21.9 2842 21.5 3440 20.5 2678 20.2 2981 19.4 2260 19.2 2844 18.8 2546 18.8 2456 22.6 2295 23.3 2379 23 2479 21.4 2057 19.9 2280 18.8 2351 18.6 2276 18.4 2548 18.6 2311 19.9 2201 19.2
 
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
wngb[t] = + 1588.51070846361 + 47.8206258852458`<25`[t] + 157.074438119669M1[t] -376.136315775409M2[t] -552.818466554426M3[t] -384.479991448196M4[t] -320.164477939016M5[t] -607.936139394426M6[t] -280.520714075738M7[t] -83.4001763809834M8[t] -245.166813650820M9[t] + 139.943499291803M10[t] -111.048788048852M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1588.51070846361514.8038783.08570.0033990.0017
`<25`47.820625885245826.447971.80810.0769920.038496
M1157.074438119669205.4794520.76440.4484330.224216
M2-376.136315775409226.837256-1.65820.1039420.051971
M3-552.818466554426237.806522-2.32470.0244610.01223
M4-384.479991448196236.205694-1.62770.1102680.055134
M5-320.164477939016222.686254-1.43770.1571340.078567
M6-607.936139394426212.326307-2.86320.0062470.003123
M7-280.520714075738209.988888-1.33590.188020.09401
M8-83.4001763809834208.761452-0.39950.6913350.345667
M9-245.166813650820207.511926-1.18150.2433640.121682
M10139.943499291803205.7346090.68020.4997060.249853
M11-111.048788048852205.299631-0.54090.5911240.295562


Multiple Linear Regression - Regression Statistics
Multiple R0.563892530113455
R-squared0.317974785517753
Adjusted R-squared0.143840688203137
F-TEST (value)1.82603401873244
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.0710475831667519
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation323.570134071516
Sum Squared Residuals4920788.68816377


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
122532458.11247227345-205.112472273453
222182101.83803415377116.161965846229
318551949.06619631738-94.0661963173776
421872103.0584836580383.9415163419666
518522138.68162163607-286.681621636066
615701841.34583500361-271.345835003607
718512216.58188620754-365.581886207541
819542494.99748790721-540.997487907213
918282357.14116358-529.14116358
1022512718.34116358-467.34116358
1122772414.74618776557-137.746187765574
1220852477.97434992918-392.97434992918
1322822639.83085063737-357.830850637374
1422662350.50528875705-84.505288757049
1518782226.42582645180-348.425826451803
1622672389.98223896951-122.982238969508
1720692406.47712659344-337.477126593442
1817462046.97452631016-300.974526310164
1922992345.69757609770-46.6975760977046
2023602494.99748790721-134.997487907213
2122142285.41022475213-71.4102247521312
2228252608.35372404393216.646275956065
2323552309.5408108180345.459189181967
2423332401.46134851279-68.461348512787
2530162606.35641251770409.643587482298
2621552350.50528875705-195.505288757049
2721722255.11820198295-83.1182019829507
2821502428.23873967770-278.238739677705
2925332401.69506400492131.304935995082
3020582032.6283385445925.3716614554101
3121602326.56932574361-166.569325743606
3222602494.99748790721-234.997487907213
3324982318.88466287180179.115337128197
3426952699.2129132259-4.21291322590157
3527992453.00268847377345.99731152623
3629462535.35910099148410.640899008525
3729302678.08735134557251.912648654429
3823182317.030850637380.969149362623003
3925402159.47695021246380.523049787541
4025702327.81542531869242.184574681312
4126692363.43856329672305.561436703279
4224502027.84627595607422.153724043935
4328422336.13345092066505.866549079345
4434402485.43336273016954.566637269836
4526782309.32053769475368.679462305246
4629812656.17434992918324.82565007082
4722602395.61793741148-135.617937411475
4828442487.53847510623356.46152489377
4925462644.6129132259-98.612913225899
5024562293.12053769475162.879462305246
5122952149.91282503541145.08717496459
5223792303.9051123760775.0948876239345
5324792291.70762446885187.292375531148
5420571932.20502418557124.794975814426
5522802207.0177610304972.982238969508
5623512394.57417354820-43.574173548197
5722762223.2434111013152.7565888986883
5825482617.91784922098-69.917849220984
5923112429.09237553115-118.092375531147
6022012506.66672546033-305.666725460328


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.0002147163872933380.0004294327745866760.999785283612707
170.002327170151665160.004654340303330320.997672829848335
180.001041148170187280.002082296340374560.998958851829813
190.02008089377487020.04016178754974050.97991910622513
200.04921905083138130.09843810166276260.950780949168619
210.07857314975789850.1571462995157970.921426850242101
220.1837921305706130.3675842611412260.816207869429387
230.1200079248425560.2400158496851110.879992075157444
240.09476861630428090.1895372326085620.905231383695719
250.2932179020214640.5864358040429280.706782097978536
260.2312328742426150.4624657484852290.768767125757385
270.211158297069490.422316594138980.78884170293051
280.2137087960758010.4274175921516020.7862912039242
290.2613361845484520.5226723690969030.738663815451548
300.2631480961647720.5262961923295430.736851903835228
310.2927766255080040.5855532510160080.707223374491996
320.5745366409856050.850926718028790.425463359014395
330.608964684518870.782070630962260.39103531548113
340.6335681846904160.7328636306191690.366431815309584
350.6538034884759330.6923930230481350.346196511524067
360.7110787570048130.5778424859903740.288921242995187
370.6625284999089230.6749430001821530.337471500091077
380.5972578650181280.8054842699637430.402742134981872
390.5837997396614980.8324005206770040.416200260338502
400.4921649642236030.9843299284472070.507835035776397
410.4346448896439040.8692897792878080.565355110356096
420.3801741616888510.7603483233777020.619825838311149
430.3552330403641100.7104660807282210.64476695963589
440.5289804490010850.942039101997830.471019550998915


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.103448275862069NOK
5% type I error level40.137931034482759NOK
10% type I error level50.172413793103448NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/10tglf1258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/10tglf1258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/1hrl11258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/1hrl11258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/21xzq1258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/21xzq1258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/3a3mq1258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/3a3mq1258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/47u061258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/47u061258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/58qcr1258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/58qcr1258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/6gki61258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/6gki61258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/7srhb1258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/7srhb1258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/8bqdx1258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/8bqdx1258735161.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/9csq31258735161.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735261q6lw5v2ls5ce22b/9csq31258735161.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; 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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