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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 08:37:17 -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/t1258731716deyxzjsv6jmj4g0.htm/, Retrieved Fri, 20 Nov 2009 16:42:07 +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/t1258731716deyxzjsv6jmj4g0.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 «
101.6 595454 594167 611324 612613 610763 94.6 590865 595454 594167 611324 612613 95.9 589379 590865 595454 594167 611324 104.7 584428 589379 590865 595454 594167 102.8 573100 584428 589379 590865 595454 98.1 567456 573100 584428 589379 590865 113.9 569028 567456 573100 584428 589379 80.9 620735 569028 567456 573100 584428 95.7 628884 620735 569028 567456 573100 113.2 628232 628884 620735 569028 567456 105.9 612117 628232 628884 620735 569028 108.8 595404 612117 628232 628884 620735 102.3 597141 595404 612117 628232 628884 99 593408 597141 595404 612117 628232 100.7 590072 593408 597141 595404 612117 115.5 579799 590072 593408 597141 595404 100.7 574205 579799 590072 593408 597141 109.9 572775 574205 579799 590072 593408 114.6 572942 572775 574205 579799 590072 85.4 619567 572942 572775 574205 579799 100.5 625809 619567 572942 572775 574205 114.8 619916 625809 619567 572942 572775 116.5 587625 619916 625809 619567 572942 112.9 565742 587625 619916 625809 619567 102 557274 565742 587625 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Niet_werkende_werkzoekenden[t] = + 68970.6356205958 -418.292868757629X[t] + 0.930452455967116y1[t] + 0.0330128831486056y2[t] + 0.187881114683878y3[t] -0.219786393126637y4[t] + 17114.8877611796M1[t] + 18207.1937484543M2[t] + 12179.1884528439M3[t] + 7221.81459494864M4[t] + 8205.4763419188M5[t] + 3015.34139103115M6[t] + 20206.3648793463M7[t] + 58365.2100442902M8[t] + 23794.5572772682M9[t] + 7833.16211110014M10[t] -10011.4779756030M11[t] -53.8205884163031t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)68970.635620595842530.5998971.62170.1129320.056466
X-418.292868757629205.895392-2.03160.049050.024525
y10.9304524559671160.1621675.73761e-061e-06
y20.03301288314860560.2110660.15640.8765170.438258
y30.1878811146838780.2203740.85260.3991120.199556
y4-0.2197863931266370.143742-1.5290.1343280.067164
M117114.88776117965565.0022893.07550.003830.001915
M218207.19374845436728.2465882.70610.0100460.005023
M312179.18845284397006.0314811.73840.0900330.045017
M47221.814594948645854.4950091.23360.2247530.112377
M58205.47634191885106.2334841.6070.1161320.058066
M63015.341391031155469.5092610.55130.5845730.292286
M720206.36487934635608.5390993.60280.000880.00044
M858365.21004429027108.1725928.21100
M923794.557277268212273.1066611.93880.0597920.029896
M107833.1621111001412856.1674140.60930.5458640.272932
M11-10011.47797560308789.739214-1.1390.2616530.130826
t-53.8205884163031112.933153-0.47660.6363280.318164


Multiple Linear Regression - Regression Statistics
Multiple R0.990937737242827
R-squared0.981957599091935
Adjusted R-squared0.974092962798675
F-TEST (value)124.857343998675
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6734.34761480654
Sum Squared Residuals1768706074.08497


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1595454597419.875994766-1965.87599476635
2590865601368.718165465-10503.7181654651
3589379587575.5811883411803.41881165846
4584428581361.9391680993066.06083190139
5573100577285.758000202-4185.75800020164
6567456564033.5751600323422.42483996780
7569028568332.710313161695.289686839065
8620735620477.591272211257.408727789035
9628884629254.524102224-370.524102223715
10628232616744.26087211211487.7391278883
11612117610930.9697093741186.0302906255
12595404594826.360223601577.639776398962
13597141596610.138730408530.861269592154
14593408597209.038761307-3801.03876130654
15590072587401.880015822670.11998418011
16579799576972.3641105272826.63588947326
17574205573341.141502384863.858497616324
18572775558898.490390213876.5096097998
19572942571357.6004428951584.39955710515
20619567622991.812585438-3424.81258543762
21625809626399.790911864-590.79091186413
22619916612095.767729327820.23227068054
23587625596932.371915395-9307.37191539508
24565742569081.311792408-3339.31179240771
25557274566795.571056221-9521.57105622053
26560576552787.7248014167788.27519858387
27548854552777.224828446-3923.22482844574
28531673534539.929866863-2866.92986686344
29525919526890.544414083-971.544414082744
30511038511458.956821315-420.956821314821
31498662510603.977599991-11941.9775999914
32555362549729.3738120675632.62618793326
33564591561027.7527420923563.24725790764
34541657552945.107008256-11288.1070082559
35527070523244.1618097763825.83819022427
36509846511950.723182472-2104.72318247165
37514258511730.1393753192527.86062468074
38516922514129.3927349192792.60726508106
39507561509763.489806872-2202.48980687243
40492622501999.687160432-9377.6871604319
41490243485114.08668755128.91331250016
42469357478249.14075206-8892.14075206053
43477580472280.6489538645299.35104613632
44528379528507.72484173-128.724841729892
45533590536430.044701778-2840.04470177786
46517945525964.864390313-8019.86439031294
47506174501878.4965654554295.5034345453
48501866496999.604801524866.3951984804
49516141507712.2748432868428.725156714
50528222524498.1255368933723.8744631067
51532638530985.824160521652.1758394796
52536322529970.0796940796351.9203059207
53536535537370.469395832-835.469395832101
54523597531582.836876392-7985.83687639227
55536214531851.0626900894362.93730991082
56586570588906.497488555-2336.49748855479
57596594596355.887542042238.112457958066


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.004328684122104980.008657368244209970.995671315877895
220.1369288824899330.2738577649798650.863071117510067
230.2706149693847680.5412299387695350.729385030615233
240.1871144061696650.3742288123393290.812885593830335
250.2437007944242930.4874015888485850.756299205575707
260.3889667221354730.7779334442709470.611033277864527
270.3020345872793040.6040691745586090.697965412720696
280.2392721772525400.4785443545050810.76072782274746
290.3435858233144650.687171646628930.656414176685535
300.420327385282740.840654770565480.57967261471726
310.5469244841126960.9061510317746080.453075515887304
320.76458077381510.47083845236980.2354192261849
330.8852269678370380.2295460643259230.114773032162962
340.9141835313781260.1716329372437490.0858164686218744
350.8798533137706790.2402933724586420.120146686229321
360.7677515013302140.4644969973395730.232248498669786


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0625NOK
5% type I error level10.0625NOK
10% type I error level10.0625OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/10hu6a1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/10hu6a1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/1pwh31258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/1pwh31258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/23r791258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/23r791258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/3tj1g1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/3tj1g1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/4vopj1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/4vopj1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/5fimt1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/5fimt1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/69yzh1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/69yzh1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/7kbxq1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/7kbxq1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/89zjc1258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/89zjc1258731432.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/99zx01258731432.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731716deyxzjsv6jmj4g0/99zx01258731432.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 2 ; 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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