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Model 2

*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: Sat, 19 Dec 2009 18:00:02 -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/Dec/20/t12612708496t4ifxlqkvwvbj6.htm/, Retrieved Sun, 20 Dec 2009 02:01:01 +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/Dec/20/t12612708496t4ifxlqkvwvbj6.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 «
3016 0 2155 0 2172 0 2150 0 2533 0 2058 0 2160 0 2260 0 2498 0 2695 0 2799 0 2946 0 2930 0 2318 0 2540 0 2570 0 2669 0 2450 0 2842 0 3440 0 2678 0 2981 0 2260 0 2844 0 2546 0 2456 0 2295 0 2379 0 2479 0 2057 0 2280 0 2351 0 2276 0 2548 1 2311 1 2201 1 2725 1 2408 1 2139 1 1898 1 2537 1 2068 1 2063 1 2520 1 2434 1 2190 1 2794 1 2070 1 2615 1 2265 1 2139 1 2428 1 2137 1 1823 1 2063 1 1806 1 1758 1 2243 1 1993 1 1932 1 2465 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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 2589.64081632653 -318.401360544218x[t] + 285.726530612245M1[t] -141.880272108844M2[t] -205.280272108843M3[t] -177.280272108844M4[t] + 8.71972789115645M5[t] -371.080272108844M6[t] -180.680272108843M7[t] + 13.1197278911563M8[t] -133.480272108844M9[t] + 132.800000000000M10[t] + 32.7999999999998M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2589.64081632653131.78103419.651100
x-318.40136054421872.543072-4.38916.2e-053.1e-05
M1285.726530612245168.5748651.6950.0965630.048282
M2-141.880272108844176.504911-0.80380.4254570.212729
M3-205.280272108843176.504911-1.1630.2505670.125284
M4-177.280272108844176.504911-1.00440.3202260.160113
M58.71972789115645176.5049110.04940.9608040.480402
M6-371.080272108844176.504911-2.10240.0407910.020395
M7-180.680272108843176.504911-1.02370.3111290.155565
M813.1197278911563176.5049110.07430.9410560.470528
M9-133.480272108844176.504911-0.75620.45320.2266
M10132.800000000000175.90760.75490.4539720.226986
M1132.7999999999998175.90760.18650.8528690.426434


Multiple Linear Regression - Regression Statistics
Multiple R0.668376440301656
R-squared0.446727065950313
Adjusted R-squared0.308408832437891
F-TEST (value)3.22970482348008
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.00186216208043333
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation278.134337495171
Sum Squared Residuals3713218.06530612


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
130162875.36734693877140.632653061227
221552447.76054421769-292.760544217687
321722384.36054421769-212.360544217686
421502412.36054421769-262.360544217687
525332598.36054421769-65.3605442176871
620582218.56054421769-160.560544217687
721602408.96054421769-248.960544217687
822602602.76054421769-342.760544217687
924982456.1605442176941.8394557823126
1026952722.44081632653-27.4408163265305
1127992622.44081632653176.559183673469
1229462589.64081632653356.359183673469
1329302875.3673469387854.6326530612238
1423182447.76054421769-129.760544217687
1525402384.36054421769155.639455782313
1625702412.36054421769157.639455782313
1726692598.3605442176970.6394557823127
1824502218.56054421769231.439455782313
1928422408.96054421769433.039455782313
2034402602.76054421769837.239455782313
2126782456.16054421769221.839455782313
2229812722.44081632653258.559183673469
2322602622.44081632653-362.440816326531
2428442589.64081632653254.359183673469
2525462875.36734693878-329.367346938776
2624562447.760544217698.23945578231283
2722952384.36054421769-89.3605442176873
2823792412.36054421769-33.3605442176871
2924792598.36054421769-119.360544217687
3020572218.56054421769-161.560544217687
3122802408.96054421769-128.960544217687
3223512602.76054421769-251.760544217687
3322762456.16054421769-180.160544217687
3425482404.03945578231143.960544217687
3523112304.039455782316.96054421768714
3622012271.23945578231-70.239455782313
3727252556.96598639456168.034013605442
3824082129.35918367347278.640816326531
3921392065.9591836734773.0408163265305
4018982093.95918367347-195.959183673469
4125372279.95918367347257.040816326531
4220681900.15918367347167.840816326531
4320632090.55918367347-27.5591836734693
4425202284.35918367347235.640816326531
4524342137.75918367347296.240816326531
4621902404.03945578231-214.039455782313
4727942304.03945578231489.960544217687
4820702271.23945578231-201.239455782313
4926152556.9659863945658.0340136054416
5022652129.35918367347135.640816326531
5121392065.9591836734773.0408163265305
5224282093.95918367347334.040816326531
5321372279.95918367347-142.959183673469
5418231900.15918367347-77.1591836734694
5520632090.55918367347-27.5591836734693
5618062284.35918367347-478.359183673469
5717582137.75918367347-379.759183673469
5822432404.03945578231-161.039455782313
5919932304.03945578231-311.039455782313
6019322271.23945578231-339.239455782313
6124652556.96598639456-91.9659863945585


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.4050712790188840.8101425580377690.594928720981116
170.2571287815948000.5142575631895990.7428712184052
180.2615867756691380.5231735513382760.738413224330862
190.4895012918439670.9790025836879340.510498708156033
200.9646476633588680.07070467328226450.0353523366411322
210.9516937506546950.09661249869060910.0483062493453046
220.949309254193210.1013814916135800.0506907458067902
230.9536884529976320.09262309400473520.0463115470023676
240.9663628321170880.06727433576582420.0336371678829121
250.9642103954918950.07157920901620930.0357896045081047
260.9449812432237330.1100375135525340.0550187567762668
270.9121414727899580.1757170544200840.0878585272100422
280.8665591258264770.2668817483470470.133440874173523
290.8102612251704780.3794775496590440.189738774829522
300.7496624023318940.5006751953362130.250337597668106
310.6810618255014750.637876348997050.318938174498525
320.664212738323090.6715745233538220.335787261676911
330.5982903041300070.8034193917399850.401709695869993
340.5496814249488080.9006371501023840.450318575051192
350.4532379613032980.9064759226065950.546762038696702
360.406826032154760.813652064309520.59317396784524
370.3419172191043400.6838344382086810.65808278089566
380.2891542465471230.5783084930942470.710845753452877
390.2042762113290970.4085524226581950.795723788670903
400.2088098956617520.4176197913235040.791190104338248
410.1817506023058410.3635012046116830.818249397694159
420.126332261340030.252664522680060.87366773865997
430.07318348079067370.1463669615813470.926816519209326
440.1157643486010260.2315286972020510.884235651398974
450.1965246798524740.3930493597049490.803475320147526


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level50.166666666666667NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/10ewfb1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/10ewfb1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/1z7av1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/1z7av1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/2rkcq1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/2rkcq1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/3wa2f1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/3wa2f1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/41o4y1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/41o4y1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/56znt1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/56znt1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/6argw1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/6argw1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/7s9gi1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/7s9gi1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/8dsev1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/8dsev1261270796.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/92xnx1261270796.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t12612708496t4ifxlqkvwvbj6/92xnx1261270796.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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