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Model5

*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 16:08:43 -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/21/t1258758673oioerow0h5yem4a.htm/, Retrieved Sat, 21 Nov 2009 00:11:25 +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/21/t1258758673oioerow0h5yem4a.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 «
561 15,9 562 555 18,2 561 544 19,7 555 537 20,1 544 543 19,9 537 594 20 543 611 22,6 594 613 20,6 611 611 20,1 613 594 20,2 611 595 21,8 594 591 22 595 589 19,5 591 584 17,5 589 573 18,2 584 567 18,8 573 569 19,7 567 621 18,8 569 629 18,5 621 628 18,7 629 612 18,5 628 595 19,3 612 597 18,9 595 593 21,4 597 590 22,5 593 580 25 590 574 22,9 580 573 22,9 574 573 21,3 573 620 22,3 573 626 20,9 620 620 19,9 626 588 20,2 620 566 19,8 588 557 17,7 566 561 18,1 557 549 17,6 561 532 18,2 549 526 16 532 511 16,3 526 499 17,3 511 555 19 499 565 18,6 555 542 18 565 527 17,9 542 510 17,8 527 514 18,5 510 517 17,4 514 508 19 517 493 17,4 508 490 20,6 493 469 18,5 490 478 20 469 528 18,8 478 534 18,8 528 518 19,7 534 506 15,3 518 502 10,6 506 516 6,1 502 528 0,9 516
 
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] = + 49.328366603281 -0.651288616346723X[t] + 0.947192748369779Y1[t] -7.46602476253019M1[t] -12.5116219686066M2[t] -9.5229972894487M3[t] -12.4128790792859M4[t] -1.52744118751515M5[t] + 49.0216445212456M6[t] + 10.1956027171895M7[t] -7.6285553748178M8[t] -15.1264239823416M9[t] -16.2946658166632M10[t] + 0.284989259707416M11[t] -0.205098050841956t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)49.32836660328123.8527122.0680.0444130.022207
X-0.6512886163467230.296327-2.19790.0331450.016572
Y10.9471927483697790.039823.798900
M1-7.466024762530194.301168-1.73580.089440.04472
M2-12.51162196860664.341435-2.88190.0060380.003019
M3-9.52299728944874.431793-2.14880.0370680.018534
M4-12.41287907928594.484485-2.7680.008160.00408
M5-1.527441187515154.623348-0.33040.7426490.371325
M649.02164452124564.60015610.656500
M710.19560271718954.3376392.35050.0231920.011596
M8-7.62855537481784.387332-1.73880.0889140.044457
M9-15.12642398234164.302066-3.51610.0010120.000506
M10-16.29466581666324.218318-3.86280.0003560.000178
M110.2849892597074164.1986950.06790.9461850.473093
t-0.2050980508419560.083122-2.46740.0174780.008739


Multiple Linear Regression - Regression Statistics
Multiple R0.99054160865246
R-squared0.981172678471802
Adjusted R-squared0.975315289551918
F-TEST (value)167.510249343534
F-TEST (DF numerator)14
F-TEST (DF denominator)45
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.62519234950304
Sum Squared Residuals1975.19281505611


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1561563.624079373812-2.62407937381185
2555555.928227550926-0.928227550926121
3544552.051664764503-8.05166476450334
4537538.277049245218-1.27704924521792
5543542.4572975708280.542702429172447
6594598.41931285733-4.41931285733032
7611606.001652766794.99834723321046
8613605.377250578927.62274942108004
9611599.89431372546711.1056862745328
10594596.561459481929-2.56145948192933
11595595.791677999017-0.791677999017001
12591596.118525713568-5.11852571356806
13589586.2868534475842.71314655241640
14584580.4443499266193.55565007338085
15573578.036010781643-5.03601078164348
16567564.1311375390892.86886246091123
17569568.5421611350870.457838864913215
18621621.366694044457-0.366694044457154
19629631.784963689692-2.78496368969167
20628621.2029918105316.79700818946873
21612612.683090127065-0.68309012706509
22595595.633635374908-0.633635374907683
23597596.1664311246890.833568875311195
24593595.942507770012-2.94250777001218
25590583.766196485186.23380351482047
26580574.0457014422855.95429855771496
27574568.7250066812315.2749933187687
28573559.94687035033313.0531296496665
29573570.7220792290472.27792077095277
30620620.414778270619-0.414778270619278
31626626.813501651986-0.813501651986298
32620615.1186906157024.88130938429759
33588601.537180882214-13.5371808822140
34566570.114188495756-4.11418849575617
35557567.018211151478-10.0182111514778
36561557.7428736590623.25712634093825
37549554.186166147342-5.18616614734208
38532537.178384740178-5.17838474017835
39526525.2924696021710.707530397829175
40511516.318946686369-5.31894668636903
41499512.140106685404-13.1401066854044
42555550.0105907150964.98940928490363
43565564.2827602154450.717239784555338
44542556.116204726101-14.1162047261012
45527526.6929337168650.307066283134788
46510511.17683146779-1.17683146778963
47514510.9932097395893.00679026041063
48517515.00831090051.99168909949949
49508509.136704546083-1.13670454608293
50493496.403336339991-3.40333633999134
51490482.8948481704517.10515182954894
52469478.325996178991-9.32599617899074
53478468.1383553796349.86164462036595
54528527.7886241124970.211375887503119
55534536.117121676088-2.11712167608783
56518523.184862268745-5.18486226874515
57506503.1924815483892.80751845161147
58502493.5138851796178.4861148203828
59516509.0304699852276.96953001477299
60528525.1877819568582.8122180431425


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
180.007766343283125920.01553268656625180.992233656716874
190.03833887436876020.07667774873752040.96166112563124
200.01486399513887740.02972799027775470.985136004861123
210.02025612209302350.0405122441860470.979743877906976
220.02898158804805470.05796317609610940.971018411951945
230.01880050256603380.03760100513206750.981199497433966
240.008362648872560250.01672529774512050.99163735112744
250.004582215270312710.009164430540625420.995417784729687
260.003215283108374000.006430566216747990.996784716891626
270.003225164988883340.006450329977766680.996774835011117
280.01377587281200990.02755174562401980.98622412718799
290.009799724381599180.01959944876319840.9902002756184
300.005934108639613320.01186821727922660.994065891360387
310.004526871171659170.009053742343318340.99547312882834
320.07342982867070380.1468596573414080.926570171329296
330.3358667062988410.6717334125976820.664133293701159
340.3133595177001080.6267190354002170.686640482299892
350.2406864196979960.4813728393959920.759313580302004
360.4716727849479650.943345569895930.528327215052035
370.4199438804723160.8398877609446330.580056119527684
380.6739892085751940.6520215828496130.326010791424807
390.6095678275224050.780864344955190.390432172477595
400.9434354867509270.1131290264981450.0565645132490726
410.9265028878048660.1469942243902680.0734971121951342
420.8513994579111130.2972010841777730.148600542088887


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.16NOK
5% type I error level120.48NOK
10% type I error level140.56NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/102nhj1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/102nhj1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/1454w1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/1454w1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/2j7ux1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/2j7ux1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/36sci1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/36sci1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/477ep1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/477ep1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/59f1i1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/59f1i1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/67i2x1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/67i2x1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/792na1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/792na1258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/8rdo61258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/8rdo61258758519.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/9r1ub1258758519.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258758673oioerow0h5yem4a/9r1ub1258758519.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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