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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 09:48:09 -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/t1258735738su7q1cf94qfrguc.htm/, Retrieved Fri, 20 Nov 2009 17:49:10 +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/t1258735738su7q1cf94qfrguc.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 «
29.837 0 29.571 0 30.167 0 30.524 0 30.996 0 31.033 0 31.198 0 30.937 0 31.649 0 33.115 0 34.106 0 33.926 0 33.382 0 32.851 0 32.948 0 36.112 0 36.113 0 35.210 0 35.193 0 34.383 0 35.349 0 37.058 0 38.076 0 36.630 0 36.045 0 35.638 0 35.114 0 35.465 0 35.254 0 35.299 0 35.916 0 36.683 0 37.288 0 38.536 0 38.977 0 36.407 0 34.955 0 34.951 0 32.680 0 34.791 0 34.178 0 35.213 0 34.871 0 35.299 0 35.443 0 37.108 0 36.419 0 34.471 0 33.868 0 34.385 0 33.643 1 34.627 1 32.919 1 35.500 1 36.110 1 37.086 1 37.711 1 40.427 1 39.884 1 38.512 1 38.767 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
saldo_zichtrek[t] = + 34.51236 + 2.32273090909091crisis[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)34.512360.327383105.418800
crisis2.322730909090910.7709483.01280.0038090.001904


Multiple Linear Regression - Regression Statistics
Multiple R0.365151455024568
R-squared0.133335585106559
Adjusted R-squared0.118646357735484
F-TEST (value)9.07709995483573
F-TEST (DF numerator)1
F-TEST (DF denominator)59
p-value0.0038089721258604
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.31495081189860
Sum Squared Residuals316.18083842909


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
129.83734.5123599999999-4.67535999999994
229.57134.51236-4.94136
330.16734.51236-4.34536
430.52434.51236-3.98836
530.99634.51236-3.51636
631.03334.51236-3.47936
731.19834.51236-3.31436
830.93734.51236-3.57536
931.64934.51236-2.86336
1033.11534.51236-1.39736
1134.10634.51236-0.406359999999999
1233.92634.51236-0.586359999999999
1333.38234.51236-1.13036000000000
1432.85134.51236-1.66136000000000
1532.94834.51236-1.56436
1636.11234.512361.59964
1736.11334.512361.60064
1835.2134.512360.69764
1935.19334.512360.680639999999997
2034.38334.51236-0.129359999999998
2135.34934.512360.836639999999996
2237.05834.512362.54564
2338.07634.512363.56364
2436.6334.512362.11764
2536.04534.512361.53264
2635.63834.512361.12564000000000
2735.11434.512360.601639999999996
2835.46534.512360.952640000000003
2935.25434.512360.741639999999997
3035.29934.512360.786639999999999
3135.91634.512361.40364000000000
3236.68334.512362.17064
3337.28834.512362.77564000000000
3438.53634.512364.02364
3538.97734.512364.46464
3636.40734.512361.89464000000000
3734.95534.512360.442639999999997
3834.95134.512360.43864
3932.6834.51236-1.83236
4034.79134.512360.278639999999996
4134.17834.51236-0.334360000000004
4235.21334.512360.70064
4334.87134.512360.358640000000001
4435.29934.512360.786639999999999
4535.44334.512360.930639999999997
4637.10834.512362.59564000000000
4736.41934.512361.90664000000000
4834.47134.51236-0.0413600000000043
4933.86834.51236-0.644359999999999
5034.38534.51236-0.127360000000003
5133.64336.8350909090909-3.19209090909091
5234.62736.8350909090909-2.20809090909091
5332.91936.8350909090909-3.91609090909091
5435.536.8350909090909-1.33509090909091
5536.1136.8350909090909-0.72509090909091
5637.08636.83509090909090.250909090909089
5737.71136.83509090909090.875909090909089
5840.42736.83509090909093.59190909090909
5939.88436.83509090909093.04890909090909
6038.51236.83509090909091.67690909090909
6138.76736.83509090909091.93190909090909


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.04445141809041460.08890283618082920.955548581909585
60.02621345282317430.05242690564634860.973786547176826
70.01769891571934730.03539783143869470.982301084280653
80.00915774183779830.01831548367559660.990842258162202
90.01133002032667380.02266004065334760.988669979673326
100.07876890989871020.1575378197974200.92123109010129
110.2878494692160910.5756989384321820.712150530783909
120.4158165952868590.8316331905737170.584183404713141
130.4448308913708870.8896617827417740.555169108629113
140.4373541270728190.8747082541456370.562645872927181
150.4364579739855270.8729159479710540.563542026014473
160.7346404389339070.5307191221321850.265359561066093
170.8601604459038120.2796791081923760.139839554096188
180.8792166075159130.2415667849681740.120783392484087
190.8867039530042790.2265920939914430.113296046995721
200.8734355343072630.2531289313854740.126564465692737
210.8748826250269380.2502347499461250.125117374973062
220.9261596056705420.1476807886589170.0738403943294585
230.9732014559028880.05359708819422490.0267985440971125
240.9759352237712550.04812955245749080.0240647762287454
250.9722012349645310.0555975300709380.027798765035469
260.964193536560950.07161292687810280.0358064634390514
270.9511241462082420.09775170758351650.0488758537917582
280.9358473972604470.1283052054791050.0641526027395527
290.9150355676948460.1699288646103090.0849644323051545
300.8892270102107090.2215459795785820.110772989789291
310.8649110538140980.2701778923718030.135088946185901
320.8548174426798860.2903651146402290.145182557320114
330.8637317184903160.2725365630193680.136268281509684
340.9217600498458080.1564799003083840.0782399501541919
350.9712031686034950.05759366279301050.0287968313965053
360.9648087970768740.07038240584625230.0351912029231262
370.9465073926060150.1069852147879700.0534926073939852
380.9210943534446430.1578112931107150.0789056465553575
390.9200906488342590.1598187023314820.0799093511657408
400.8855315423863590.2289369152272830.114468457613641
410.847495517310930.305008965378140.15250448268907
420.7938278545193450.412344290961310.206172145480655
430.7294447671673210.5411104656653570.270555232832679
440.6553385333463380.6893229333073240.344661466653662
450.5745011014218030.8509977971563940.425498898578197
460.5644256531952010.8711486936095980.435574346804799
470.5311645303724950.937670939255010.468835469627505
480.4367703539830950.873540707966190.563229646016905
490.3455301425127060.6910602850254120.654469857487294
500.2576471469106810.5152942938213610.74235285308932
510.3008456670934920.6016913341869840.699154332906508
520.3018865927249490.6037731854498980.698113407275051
530.6507930029608370.6984139940783260.349206997039163
540.729664734648440.5406705307031210.270335265351561
550.803036900849810.3939261983003810.196963099150190
560.8096901982058770.3806196035882470.190309801794123


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.0769230769230769NOK
10% type I error level120.230769230769231NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/10888h1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/10888h1258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/1k5zb1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/1k5zb1258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/2m2hg1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/2m2hg1258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/31wr31258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/31wr31258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/4hci91258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/4hci91258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/5mdan1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/5mdan1258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/6yv8u1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/6yv8u1258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/7zs8p1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/7zs8p1258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/88l571258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/88l571258735685.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/9zj0n1258735685.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258735738su7q1cf94qfrguc/9zj0n1258735685.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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