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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 12:04:16 -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/t1258571184ogwv2uk93mys3wp.htm/, Retrieved Wed, 18 Nov 2009 20:06:36 +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/t1258571184ogwv2uk93mys3wp.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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 25551.4147450011 + 0.113859995860027X[t] -203.055106917519t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)25551.41474500112931.8925368.71500
X0.1138599958600270.00479323.755800
t-203.05510691751911.518337-17.628900


Multiple Linear Regression - Regression Statistics
Multiple R0.98906748563434
R-squared0.978254491139036
Adjusted R-squared0.977491490828125
F-TEST (value)1282.11545545903
F-TEST (DF numerator)2
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1154.56767677021
Sum Squared Residuals75982511.653826


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
19039889337.67731141871060.32268858134
29026989020.7622086411248.23779135899
39039088134.54712656332255.45287343668
48821986679.03206518551539.96793481449
58703285678.95698724781353.04301275220
68717586159.06185549051015.93814450955
79260391762.8665374343840.133462565718
89357193495.431360137275.5686398627849
99411893520.0962449397597.90375506025
109215993089.3211463022-930.321146302176
118952890950.6461097642-1422.64610976420
128995590861.4509987067-906.450998706712
138958790202.955908349-615.955908349086
148948889772.1808097115-284.180809711513
158852188999.8257234939-478.825723493861
168658787544.310662116-957.31066211605
178515986658.0955800384-1499.09558003837
188491586682.760464841-1767.76046484090
199137892400.4251426448-1022.42514264477
209272993108.2500026075-379.250002607462
219219492791.33489983-597.334899829916
228966490766.519859152-1102.51985915197
238628588627.844822614-2342.844822614
248685888652.5097074165-1794.50970741653
258718487994.0146170589-810.014617058907
268662987449.3795225613-820.379522561307
278522086107.7244570435-887.724457043521
288481685221.5093749658-405.509374965843
298483184904.5942721883-73.5942721882968
308495784701.5391652708255.460834729223
319095189849.90386377451101.09613622549
329213490330.00873201711803.99126798285
339179089443.79364993952346.20635006053
348662585597.2186755011027.78132449890
358332482889.243659663434.756340337006
368271981661.44859000521057.55140999477
378361481913.83346652781700.16653347218
388164080344.458409291295.54159071002
397866578205.783372752459.216627247989
407782877319.5682906743508.431709325668
417572875408.6132458564319.386754143586
427218773839.2381886186-1652.23818861858
437935780012.3428498625-655.342849862546
448132980947.8877015453381.112298454708
457730478126.0526898472-822.052689847161
467557676215.0976450292-639.097645029243
477293274076.4226084913-1144.42260849127
487429174328.8074850139-37.8074850138576
497498874467.3323656764520.667634323583
507330273239.537296018762.4627039813413
517048371328.5822512007-845.582251200741
526984870783.9471567031-935.94715670314
536646668189.832136725-1723.83213672506
546761069011.5169925478-1401.51699254778
557509174501.4616786316589.538321368405
567620774981.56654687421225.43345312577
577345472956.7515061963497.248493803711
587200871387.3764489585620.62355104155
597136270728.8813586008633.118641399175
607425072119.86619372372130.13380627632


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.2534296139236060.5068592278472130.746570386076394
70.1504113636034500.3008227272069010.84958863639655
80.0933480988940580.1866961977881160.906651901105942
90.06341807236141530.1268361447228310.936581927638585
100.1329945839505870.2659891679011740.867005416049413
110.2201489565920690.4402979131841370.779851043407931
120.1467000863125880.2934001726251750.853299913687412
130.1047188499197120.2094376998394250.895281150080288
140.1031762804030560.2063525608061130.896823719596944
150.08260530763973390.1652106152794680.917394692360266
160.05792550372261260.1158510074452250.942074496277387
170.04499663750767660.08999327501535320.955003362492323
180.03126669259918150.0625333851983630.968733307400819
190.04310926565581820.08621853131163650.956890734344182
200.1118407632304100.2236815264608190.88815923676959
210.1452773006977790.2905546013955590.85472269930222
220.1351804369804540.2703608739609070.864819563019546
230.1983722247708160.3967444495416310.801627775229184
240.2561585616283880.5123171232567760.743841438371612
250.3482229752266500.6964459504533010.65177702477335
260.434957562097830.869915124195660.56504243790217
270.4897719992957150.979543998591430.510228000704285
280.5422746513771820.9154506972456360.457725348622818
290.5939327707845870.8121344584308250.406067229215413
300.645039036008920.709921927982160.35496096399108
310.8805465867478920.2389068265042170.119453413252108
320.966276797171180.06744640565764020.0337232028288201
330.9875325845848850.02493483083023050.0124674154151153
340.9844856444380850.03102871112382980.0155143555619149
350.9762564817379230.04748703652415410.0237435182620771
360.9687624931926420.06247501361471570.0312375068073579
370.9756279810307350.04874403793853070.0243720189692653
380.9819009724122180.03619805517556360.0180990275877818
390.983570389141110.03285922171778150.0164296108588908
400.9921857953322060.0156284093355880.007814204667794
410.999710952902440.0005780941951193880.000289047097559694
420.999750040335790.0004999193284180390.000249959664209020
430.9996123870538120.0007752258923757390.000387612946187870
440.9990435851709430.00191282965811430.00095641482905715
450.9993521398462140.001295720307572240.000647860153786121
460.9989545640819010.002090871836197960.00104543591809898
470.9987023711464270.002595257707145340.00129762885357267
480.9966383968853670.006723206229265660.00336160311463283
490.9963350507913840.007329898417231750.00366494920861587
500.9977192511147240.004561497770552810.00228074888527640
510.9967169367654470.00656612646910680.0032830632345534
520.995175576862940.009648846274118160.00482442313705908
530.9885329989311820.02293400213763510.0114670010688175
540.9920543874277070.01589122514458610.00794561257229305


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level120.244897959183673NOK
5% type I error level210.428571428571429NOK
10% type I error level260.530612244897959NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/10z54t1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/10z54t1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/1v3ig1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/1v3ig1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/2gfqa1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/2gfqa1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/366in1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/366in1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/4af2u1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/4af2u1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/529xz1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/529xz1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/6g3xu1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/6g3xu1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/7xin91258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/7xin91258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/82all1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/82all1258571048.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/963sf1258571048.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258571184ogwv2uk93mys3wp/963sf1258571048.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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