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W8-model neutraal

*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: Sun, 28 Nov 2010 14:31:42 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k.htm/, Retrieved Sun, 28 Nov 2010 15:30:56 +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/2010/Nov/28/t1290954656rxzzptxatitv98k.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
465 0 459 0 465 0 468 0 467 0 463 0 460 0 462 0 461 0 476 0 476 0 471 0 453 0 443 0 442 0 444 0 438 0 427 0 424 0 416 0 406 0 431 0 434 0 418 0 412 0 404 0 409 0 412 0 406 0 398 0 397 0 385 0 390 0 413 1 413 1 401 1 397 1 397 1 409 1 419 1 424 1 428 1 430 1 424 1 433 1 456 1 459 1 446 1 441 1 439 1 454 1 460 1 457 1 451 1 444 1 437 1 443 1 471 1 469 1 454 1 444 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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 435.818181818182 + 0.360389610389608X[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)435.8181818181824.37207799.682200
X0.3603896103896086.4531790.05580.9556530.477826


Multiple Linear Regression - Regression Statistics
Multiple R0.00727044638050349
R-squared5.28593905717763e-05
Adjusted R-squared-0.0168953972299271
F-TEST (value)0.00311886890524440
F-TEST (DF numerator)1
F-TEST (DF denominator)59
p-value0.955652519278202
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation25.1156701148520
Sum Squared Residuals37217.0162337662


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1465435.81818181818229.1818181818183
2459435.81818181818223.1818181818182
3465435.81818181818229.1818181818182
4468435.81818181818232.1818181818182
5467435.81818181818231.1818181818182
6463435.81818181818227.1818181818182
7460435.81818181818224.1818181818182
8462435.81818181818226.1818181818182
9461435.81818181818225.1818181818182
10476435.81818181818240.1818181818182
11476435.81818181818240.1818181818182
12471435.81818181818235.1818181818182
13453435.81818181818217.1818181818182
14443435.8181818181827.18181818181818
15442435.8181818181826.18181818181818
16444435.8181818181828.18181818181818
17438435.8181818181822.18181818181818
18427435.818181818182-8.81818181818182
19424435.818181818182-11.8181818181818
20416435.818181818182-19.8181818181818
21406435.818181818182-29.8181818181818
22431435.818181818182-4.81818181818182
23434435.818181818182-1.81818181818182
24418435.818181818182-17.8181818181818
25412435.818181818182-23.8181818181818
26404435.818181818182-31.8181818181818
27409435.818181818182-26.8181818181818
28412435.818181818182-23.8181818181818
29406435.818181818182-29.8181818181818
30398435.818181818182-37.8181818181818
31397435.818181818182-38.8181818181818
32385435.818181818182-50.8181818181818
33390435.818181818182-45.8181818181818
34413436.178571428571-23.1785714285714
35413436.178571428571-23.1785714285714
36401436.178571428571-35.1785714285714
37397436.178571428571-39.1785714285714
38397436.178571428571-39.1785714285714
39409436.178571428571-27.1785714285714
40419436.178571428571-17.1785714285714
41424436.178571428571-12.1785714285714
42428436.178571428571-8.17857142857143
43430436.178571428571-6.17857142857143
44424436.178571428571-12.1785714285714
45433436.178571428571-3.17857142857143
46456436.17857142857119.8214285714286
47459436.17857142857122.8214285714286
48446436.1785714285719.82142857142857
49441436.1785714285714.82142857142857
50439436.1785714285712.82142857142857
51454436.17857142857117.8214285714286
52460436.17857142857123.8214285714286
53457436.17857142857120.8214285714286
54451436.17857142857114.8214285714286
55444436.1785714285717.82142857142857
56437436.1785714285710.821428571428572
57443436.1785714285716.82142857142857
58471436.17857142857134.8214285714286
59469436.17857142857132.8214285714286
60454436.17857142857117.8214285714286
61444436.1785714285717.82142857142857


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.006146448168132940.01229289633626590.993853551831867
60.0009663019164012960.001932603832802590.999033698083599
70.0002645188198491010.0005290376396982030.99973548118015
84.4817575359626e-058.9635150719252e-050.99995518242464
98.77238983586924e-061.75447796717385e-050.999991227610164
109.55615654112471e-050.0001911231308224940.999904438434589
110.0002039836038828820.0004079672077657630.999796016396117
120.0001329516356716520.0002659032713433040.999867048364328
130.0002938311349618620.0005876622699237240.999706168865038
140.002654516252949220.005309032505898430.99734548374705
150.0083740665383980.0167481330767960.991625933461602
160.01412579562612950.0282515912522590.98587420437387
170.03104037584598990.06208075169197970.96895962415401
180.09961161214546920.1992232242909380.90038838785453
190.2047856112945480.4095712225890950.795214388705452
200.3771812133685980.7543624267371960.622818786631402
210.6078289347056720.7843421305886570.392171065294328
220.6187997283682030.7624005432635950.381200271631797
230.6365400956803240.7269198086393520.363459904319676
240.6847815656435240.6304368687129530.315218434356476
250.7394730795427820.5210538409144360.260526920457218
260.8032454539210730.3935090921578540.196754546078927
270.825854044281380.3482919114372410.174145955718620
280.8361701317145990.3276597365708020.163829868285401
290.8514341393748960.2971317212502080.148565860625104
300.8734265347453520.2531469305092970.126573465254648
310.8874421779898670.2251156440202660.112557822010133
320.9138227876964960.1723544246070070.0861772123035036
330.9197836909620220.1604326180759560.0802163090379779
340.9079859865734820.1840280268530350.0920140134265176
350.8973535989692990.2052928020614020.102646401030701
360.9224115648559870.1551768702880250.0775884351440125
370.9605183667966050.0789632664067910.0394816332033955
380.988273898413950.02345220317209860.0117261015860493
390.995134727290090.009730545419820320.00486527270991016
400.9968740746853430.00625185062931460.0031259253146573
410.9975964991371280.004807001725743970.00240350086287199
420.9978393669196540.004321266160692570.00216063308034628
430.9979826860072530.004034627985494540.00201731399274727
440.9992304136531730.001539172693654480.000769586346827238
450.9994063400864270.001187319827145940.000593659913572971
460.9989780198204710.002043960359057270.00102198017952863
470.9984255469646780.003148906070644950.00157445303532247
480.9967329379199480.006534124160103460.00326706208005173
490.994618434617990.01076313076401930.00538156538200963
500.9927897831585980.01442043368280450.00721021684140226
510.9844043814579520.03119123708409570.0155956185420478
520.972051152496610.05589769500678130.0279488475033906
530.9455118865253620.1089762269492770.0544881134746383
540.890196077776560.2196078444468810.109803922223441
550.810411855101660.3791762897966780.189588144898339
560.7709562858825070.4580874282349860.229043714117493


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.365384615384615NOK
5% type I error level260.5NOK
10% type I error level290.557692307692308NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/10ysvr1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/10ysvr1290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/1xdn31290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/1xdn31290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/2k1xi1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/2k1xi1290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/3k1xi1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/3k1xi1290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/4k1xi1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/4k1xi1290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/5dse31290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/5dse31290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/6dse31290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/6dse31290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/76jdo1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/76jdo1290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/86jdo1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/86jdo1290954694.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/9ysvr1290954694.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/28/t1290954656rxzzptxatitv98k/9ysvr1290954694.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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