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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: Wed, 18 Nov 2009 11:37:15 -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/18/t1258569513c4yozh6xbbjxmqj.htm/, Retrieved Wed, 18 Nov 2009 19:38:45 +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/18/t1258569513c4yozh6xbbjxmqj.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 «
90398 562000 90269 561000 90390 555000 88219 544000 87032 537000 87175 543000 92603 594000 93571 611000 94118 613000 92159 611000 89528 594000 89955 595000 89587 591000 89488 589000 88521 584000 86587 573000 85159 567000 84915 569000 91378 621000 92729 629000 92194 628000 89664 612000 86285 595000 86858 597000 87184 593000 86629 590000 85220 580000 84816 574000 84831 573000 84957 573000 90951 620000 92134 626000 91790 620000 86625 588000 83324 566000 82719 557000 83614 561000 81640 549000 78665 532000 77828 526000 75728 511000 72187 499000 79357 555000 81329 565000 77304 542000 75576 527000 72932 510000 74291 514000 74988 517000 73302 508000 70483 493000 69848 490000 66466 469000 67610 478000 75091 528000 76207 534000 73454 518000 72008 506000 71362 502000 74250 516000
 
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
Y[t] = -20578.3075841541 + 0.183866332465193X[t] + 1884.80300781325M1[t] + 1989.08120312530M2[t] + 2328.26432725635M3[t] + 2492.67518749878M4[t] + 2714.93851215070M5[t] + 2056.67217968551M6[t] -850.08404253236M7[t] -1260.42756770517M8[t] -1064.40384201148M9[t] -798.462322047506M10[t] -487.120802083538M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-20578.30758415415588.045948-3.68260.0005950.000298
X0.1838663324651930.00979818.765200
M11884.803007813251773.5587841.06270.2933370.146669
M21989.081203125301771.7162721.12270.2672730.133637
M32328.264327256351772.6924681.31340.1954220.097711
M42492.675187498781776.9755231.40280.1672590.08363
M52714.938512150701787.4261161.51890.1354840.067742
M62056.672179685511786.1419481.15150.2553670.127683
M7-850.084042532361792.186141-0.47430.6374620.318731
M8-1260.427567705171808.477395-0.6970.4892640.244632
M9-1064.403842011481793.089085-0.59360.5556160.277808
M10-798.4623220475061775.938974-0.44960.6550660.327533
M11-487.1208020835381771.521186-0.2750.7845420.392271


Multiple Linear Regression - Regression Statistics
Multiple R0.945772715791592
R-squared0.894486029935803
Adjusted R-squared0.867546292898136
F-TEST (value)33.2032205320018
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2800.77414274199
Sum Squared Residuals368683782.536650


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
19039884639.37426909755758.62573090246
29026984559.78613194435709.21386805568
39039083795.77126128426594.2287387158
48821981937.65246440956281.3475355905
58703280872.85146180516159.14853819492
68717581317.7831241315857.21687586895
79260387788.2098576384814.79014236200
89357190503.59398437353067.40601562653
99411891067.35037499753050.64962500245
109215990965.55923003111193.44076996886
118952888151.17309808681376.82690191317
128995588822.16023263561132.83976736444
138958789971.497910588-384.49791058803
148948889708.0434409697-220.043440969703
158852189127.8949027748-606.894902774786
168658787269.7761059001-682.776105900093
178515986388.8414357609-1229.84143576086
188491586098.307768226-1183.30776822606
199137892752.6008341982-1374.60083419821
209272993813.187968747-1084.18796874694
219219493825.3453619754-1631.34536197544
228966491149.4255624963-1485.42556249633
238628588335.039430552-2050.03943055202
248685889189.892897566-2331.89289756594
258718490339.2305755184-3155.23057551842
268662989891.9097734349-3262.90977343490
278522088392.429572914-3172.42957291401
288481687453.6424383653-2637.64243836529
298483187492.039430552-2661.03943055202
308495786833.7730980868-1876.77309808683
319095192568.734501733-1617.73450173302
329213493261.5889713514-1127.58897135136
339179092354.4147022539-564.414702253901
348662586736.6335833317-111.633583331701
358332483002.9157890614321.08421093857
368271981835.2395989582883.760401041769
378361484455.5079366322-841.507936632245
388164082353.390142362-713.390142361991
397866579566.8456145848-901.845614584762
407782878628.058480036-800.058480036032
417572876092.32681771-364.326817710067
427218773227.6644956626-1040.66449566256
437935780617.4228914955-1260.42289149548
448132982045.7426909746-716.742690974601
457730478012.8407699689-708.840769968862
467557675520.78730295555.2126970450593
477293272706.4011710106225.598828989367
487429173928.987302955362.012697045059
497498876365.3893081638-1377.38930816376
507330274814.8705112891-1512.87051128909
517048372396.0586484422-1913.05864844224
526984872008.8705112891-2160.87051128909
536646668369.940854172-1903.94085417197
546761069366.4715138935-1756.47151389351
557509175653.0319149353-562.03191493528
567620776345.8863845536-138.886384553624
577345473600.0487908042-146.048790804236
587200871659.5943211859348.405678814108
597136271235.4705112891126.529488710910
607425074296.7199678853-46.7199678853268


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1313980662333270.2627961324666530.868601933766673
170.07845247358441080.1569049471688220.921547526415589
180.1053512484555180.2107024969110350.894648751544482
190.0529028869943510.1058057739887020.94709711300565
200.0236860692320980.0473721384641960.976313930767902
210.04250234091727390.08500468183454770.957497659082726
220.3339497086078580.6678994172157160.666050291392142
230.7969401046015330.4061197907969350.203059895398467
240.9623289562328640.07534208753427280.0376710437671364
250.9831160408919410.03376791821611720.0168839591080586
260.9962742527047320.007451494590536650.00372574729526832
270.9996871389828580.000625722034283540.00031286101714177
280.9996673882721310.0006652234557377060.000332611727868853
290.9998035877337170.0003928245325665220.000196412266283261
300.9995784542833960.0008430914332074040.000421545716603702
310.9993799406153180.001240118769364550.000620059384682276
320.999336309905780.001327380188440490.000663690094220245
330.999134058228390.001731883543220950.000865941771610474
340.9999619703107987.60593784031995e-053.80296892015998e-05
350.9999888135214172.23729571668393e-051.11864785834197e-05
360.999990673956641.86520867192285e-059.32604335961424e-06
370.9999833361781723.33276436558205e-051.66638218279103e-05
380.999971870725495.62585490195347e-052.81292745097674e-05
390.9999544659477759.10681044495212e-054.55340522247606e-05
400.9999331849755650.0001336300488696886.6815024434844e-05
410.999989146157012.17076859795375e-051.08538429897688e-05
420.9999988889185172.2221629659937e-061.11108148299685e-06
430.9999840407752143.19184495716426e-051.59592247858213e-05
440.9996871764935190.0006256470129627820.000312823506481391


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.655172413793103NOK
5% type I error level210.724137931034483NOK
10% type I error level230.793103448275862NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/1010z01258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/1010z01258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/1t24u1258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/1t24u1258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/23bdo1258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/23bdo1258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/3077n1258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/3077n1258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/4rri61258569430.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/50s1g1258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/50s1g1258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/6ga4u1258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/6ga4u1258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/7mro71258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/7mro71258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/85r7x1258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/85r7x1258569430.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/95hd51258569430.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258569513c4yozh6xbbjxmqj/95hd51258569430.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = 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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