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WorkShop7 (SHW)

*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, 27 Nov 2009 09:41:59 -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/27/t1259340218ifax0o123nf9ps1.htm/, Retrieved Fri, 27 Nov 2009 17:43:50 +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/27/t1259340218ifax0o123nf9ps1.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 «
277051 1 277838 276610 277026 1 277051 277838 274960 1 277026 277051 270073 1 274960 277026 267063 1 270073 274960 264916 1 267063 270073 287182 1 264916 267063 291109 1 287182 264916 292223 1 291109 287182 288109 1 292223 291109 281400 1 288109 292223 282579 1 281400 288109 280113 1 282579 281400 280331 1 280113 282579 276759 1 280331 280113 275139 1 276759 280331 274275 1 275139 276759 271234 1 274275 275139 289725 1 271234 274275 290649 1 289725 271234 292223 1 290649 289725 278429 0 292223 290649 269749 0 278429 292223 265784 0 269749 278429 268957 0 265784 269749 264099 0 268957 265784 255121 0 264099 268957 253276 0 255121 264099 245980 0 253276 255121 235295 0 245980 253276 258479 0 235295 245980 260916 0 258479 235295 254586 0 260916 258479 250566 0 254586 260916 243345 0 250566 254586 247028 0 243345 250566 248464 0 247028 243345 244962 0 248464 247028 237003 0 244962 248464 237008 0 237003 244962 225477 0 237008 237003 226762 0 225477 237008 247857 0 226762 etc...
 
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] = + 9690.06414062205 + 8887.14053601723X[t] + 0.928450603723507Y1[t] + 0.00697821046662423Y2[t] -293.055756716993M1[t] -3225.60445747154M2[t] -6294.3963344095M3[t] -4703.55564690838M4[t] -9394.0620252704M5[t] -6208.55988822182M6[t] + 16596.0512996447M7[t] -1103.97720103963M8[t] -5033.72634393642M9[t] -7293.7916697285M10[t] -7370.59193338102M11[t] + 248.332473555430t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)9690.0641406220510137.937280.95580.3447640.172382
X8887.140536017232265.8322363.92220.0003270.000164
Y10.9284506037235070.1481146.268500
Y20.006978210466624230.1486560.04690.9627870.481394
M1-293.0557567169932607.516637-0.11240.9110640.455532
M2-3225.604457471542570.643895-1.25480.2166630.108331
M3-6294.39633440952420.166044-2.60080.0128770.006438
M4-4703.555646908382348.260993-2.0030.0518190.02591
M5-9394.06202527042394.298419-3.92350.0003260.000163
M6-6208.559888221822375.438718-2.61360.012470.006235
M716596.05129964472418.6890146.861600
M8-1103.977201039634390.783027-0.25140.8027370.401369
M9-5033.726343936422547.754411-1.97580.0549390.02747
M10-7293.79166972852573.647354-2.8340.0071010.003551
M11-7370.591933381022469.135564-2.98510.0047630.002382
t248.33247355543062.8609023.95053e-040.00015


Multiple Linear Regression - Regression Statistics
Multiple R0.98676705339317
R-squared0.97370921766224
Adjusted R-squared0.964090638758182
F-TEST (value)101.232128714086
F-TEST (DF numerator)15
F-TEST (DF denominator)41
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3476.52994540491
Sum Squared Residuals495536678.91318


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1277051278421.583027982-1370.58302798227
2277026275015.2454181062010.75458189406
3274960272166.0828979932793.91710200691
4270073272086.902656495-2013.90265649525
5267063263092.9736684683970.02633153218
6264916263698.0694473141217.93055268632
7287182284736.6252490372445.37475096334
8291109287942.8281465443166.17185345640
9292223288062.8138322744160.18616772568
10288109287112.778385088996.221614911926
11281400283472.438537732-2072.43853773232
12282579284833.679486428-2254.67948642805
13280113285836.782651036-5723.78265103592
14280331280871.234545195-540.234545194788
15276759278235.969106413-1476.96910641328
16275139276760.237960851-1621.23796085119
17274275270789.0479102263485.95208977426
18271234273409.396498257-2175.3964982567
19289725293632.892699912-3907.89269991223
20290649293327.956048206-2678.95604820578
21292223290633.4618264431589.53817355670
22278429281202.417554921-2773.41755492139
23269749268577.8858403371171.11415966330
24265784268041.601571776-2257.6015717765
25268957264255.0007780014701.99922199908
26264099264489.089711916-390.089711916333
27255121257180.359137456-2059.35913745561
28253276250650.0026318362625.99736816436
29245980244432.186989591547.81301041018
30235295241079.171197116-5784.1711971162
31258479254160.7071341884318.29286581208
32260916258159.6477249492756.352275051
33254586256902.64800834-2316.64800834005
34250566249030.8287334411535.17126655924
35243345245425.817444121-2080.81744412143
36247028246312.347635495715.652364505387
37248464249636.718268067-1172.71826806723
38244962248311.457856964-3349.45785696365
39237003242249.585149571-5246.58514957147
40237008236674.782262539333.217737461498
41225477232181.711033647-6704.71103364666
42226762224909.6166237671852.38337623276
43247857249075.153566083-1218.15356608320
44248256251218.090024951-2962.09002495136
45246892248054.330496289-1162.33049628913
46245021244778.97532655242.024673450216
47246186243203.8581778102982.14182219046
48255688251891.3713063013796.62869369917
49264242260676.9152749143565.08472508635
50268270266000.9724678192269.02753218071
51272969266980.0037085675988.99629143345
52273886273210.074488279675.925511720576
53267353269652.08039807-2299.08039806996
54271916267026.7462335464889.25376645381
55292633294270.62135078-1637.62135077999
56295804296085.47805535-281.478055350261
57293222295492.745836653-2270.74583665321


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.08332540088306280.1666508017661260.916674599116937
200.0348487332411470.0696974664822940.965151266758853
210.01371490348469430.02742980696938860.986285096515306
220.004118160343506690.008236320687013380.995881839656493
230.007242740215815040.01448548043163010.992757259784185
240.01396802170119360.02793604340238720.986031978298806
250.01924456536184580.03848913072369160.980755434638154
260.01754811319902190.03509622639804390.982451886800978
270.04641648044425200.09283296088850390.953583519555748
280.02523525318689230.05047050637378460.974764746813108
290.04774268052302140.09548536104604270.952257319476979
300.1913333852153730.3826667704307460.808666614784627
310.4064934447862950.812986889572590.593506555213705
320.4416111102553080.8832222205106150.558388889744692
330.4953784923651080.9907569847302160.504621507634892
340.6165271677098340.7669456645803330.383472832290166
350.5153263436865950.969347312626810.484673656313405
360.5388523019726270.9222953960547450.461147698027373
370.605569615753710.788860768492580.39443038424629
380.9161089673228270.1677820653543470.0838910326771735


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.05NOK
5% type I error level60.3NOK
10% type I error level100.5NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/10uh6f1259340115.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/10uh6f1259340115.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/1p2ma1259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/1p2ma1259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/2xuk01259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/2xuk01259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/3o4z01259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/3o4z01259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/4nq3e1259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/4nq3e1259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/5eskh1259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/5eskh1259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/6coio1259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/6coio1259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/7rof11259340114.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/7rof11259340114.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/81foo1259340115.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/81foo1259340115.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/9ns6x1259340115.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340218ifax0o123nf9ps1/9ns6x1259340115.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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