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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: Wed, 18 Nov 2009 09:30:58 -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/18/t1258561932co23m5pku9rgyev.htm/, Retrieved Wed, 18 Nov 2009 17:32:24 +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/18/t1258561932co23m5pku9rgyev.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 «
521 104.29 501 104.56 518 104.79 547 105.08 629 105.21 572 105.43 582 105.69 574 105.74 461 106.2 576 106.04 460 106.45 455 106.4 444 106.48 488 106.83 513 107.14 468 107.94 488 108.46 536 108.81 486 108.92 460 108.99 376 109.16 503 109.22 369 109.43 353 109.23 359 109.93 400 110.09 374 110.33 430 110.11 433 110.35 418 110.09 438 110.44 389 110.39 368 110.62 386 110.43 261 110.46 294 110.55 263 110.94 293 111.56 303 111.82 326 111.73 314 111.57 332 111.85 347 112.06 290 112.2 340 112.47 371 112.15 340 112.36 376 112.32 322 112.67 364 113.02 379 113.05 343 113.5 358 113.67 433 113.65 344 114 357 114.03 385 114.08 392 114.49 308 114.48 294 114.25
 
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
AvgBouw[t] = + 3066.15011706504 -24.1528003127978Gzhidx[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)3066.15011706504269.39730411.381500
Gzhidx-24.15280031279782.44887-9.862800


Multiple Linear Regression - Regression Statistics
Multiple R0.791498856641332
R-squared0.626470440064537
Adjusted R-squared0.620030275238063
F-TEST (value)97.275528956854
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value5.17363929475323e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation55.4405727636788
Sum Squared Residuals178272.112285156


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1521547.254572443359-26.2545724433594
2501540.733316358902-39.7333163589025
3518535.178172286959-17.1781722869590
4547528.17386019624818.8261398037522
5629525.033996155584103.966003844416
6572519.72038008676852.2796199132316
7582513.44065200544168.5593479945588
8574512.23301198980161.7669880101986
9461501.122723845914-40.1227238459142
10576504.98717189596271.0128281040382
11460495.084523767715-35.0845237677148
12455496.292163783355-41.2921637833546
13444494.359939758331-50.3599397583308
14488485.9064596488522.09354035114829
15513478.41909155188434.5809084481157
16468459.0968513016468.90314869835381
17488446.53739513899141.4626048610086
18536438.08391502951297.916084970488
19486435.42710699510450.5728930048957
20460433.73641097320926.2635890267914
21376429.630434920033-53.6304349200329
22503428.18126690126574.818733098735
23369423.109178835577-54.1091788355773
24353427.939738898137-74.9397388981369
25359411.032778679178-52.0327786791784
26400407.168330629131-7.16833062913084
27374401.371658554059-27.3716585540595
28430406.68527462287523.3147253771250
29433400.88860254780432.1113974521964
30418407.16833062913110.8316693708692
31438398.71485051965239.2851494803483
32389399.922490535292-10.9224905352916
33368394.367346463348-26.367346463348
34386398.956378522780-12.9563785227795
35261398.231794513396-137.231794513396
36294396.058042485244-102.058042485244
37263386.638450363253-123.638450363253
38293371.663714169318-78.6637141693181
39303365.383986087991-62.3839860879909
40326367.557738116142-41.5577381161425
41314371.422186166190-57.4221861661904
42332364.659402078607-32.659402078607
43347359.587314012919-12.5873140129192
44290356.205921969128-66.2059219691275
45340349.684665884672-9.68466588467223
46371357.41356198476713.5864380152326
47340352.34147391908-12.3414739190800
48376353.30758593159222.6924140684080
49322344.854105822113-22.8541058221126
50364336.40062571263427.5993742873665
51379335.67604170325043.3239582967504
52343324.80728156249118.1927184375095
53358320.70130550931537.2986944906852
54433321.184361515571111.815638484429
55344312.73088140609231.2691185939084
56357312.00629739670844.9937026032923
57385310.79865738106874.2013426189322
58392300.89600925282191.1039907471792
59308301.1375372559496.86246274405142
60294306.692681327892-12.6926813278922


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.2917829061706420.5835658123412840.708217093829358
60.1974738856039050.394947771207810.802526114396095
70.1300560516648600.2601121033297210.86994394833514
80.08751944321120660.1750388864224130.912480556788793
90.5265903571953660.9468192856092680.473409642804634
100.4727432480337320.9454864960674630.527256751966268
110.5783375573534680.8433248852930630.421662442646532
120.5900344498898540.8199311002202910.409965550110146
130.5821918288763060.8356163422473870.417808171123694
140.4907493416098230.9814986832196460.509250658390177
150.4445292903497420.8890585806994830.555470709650258
160.3646350205594320.7292700411188640.635364979440568
170.3318506452421810.6637012904843630.668149354757819
180.4782627332695590.9565254665391190.521737266730441
190.4737965118880090.9475930237760190.526203488111991
200.4547364594989010.9094729189978020.545263540501099
210.5378858857486680.9242282285026640.462114114251332
220.6889399859639330.6221200280721340.311060014036067
230.7288458294191620.5423083411616760.271154170580838
240.7750380095201120.4499239809597770.224961990479888
250.7526442125287420.4947115749425160.247355787471258
260.705694764054190.5886104718916210.294305235945810
270.6467763975124410.7064472049751190.353223602487559
280.6601351618137750.679729676372450.339864838186225
290.7097956464359810.5804087071280380.290204353564019
300.7416951034743540.5166097930512920.258304896525646
310.8699918816169560.2600162367660890.130008118383044
320.895978641914450.20804271617110.10402135808555
330.903961581996640.1920768360067180.096038418003359
340.9559431484911540.08811370301769150.0440568515088458
350.9827376393084720.03452472138305640.0172623606915282
360.9824702005099790.03505959898004230.0175297994900212
370.9903589524996120.01928209500077590.00964104750038794
380.98884599580470.02230800839060150.0111540041953008
390.9854464011489560.02910719770208850.0145535988510442
400.9759933309166080.04801333816678320.0240066690833916
410.9661639665337950.06767206693240930.0338360334662047
420.9474924961850510.1050150076298980.052507503814949
430.9204542284959620.1590915430080760.0795457715040379
440.9458386486510540.1083227026978930.0541613513489463
450.924108715574190.1517825688516200.0758912844258101
460.8918093931920580.2163812136158850.108190606807942
470.8551760709375190.2896478581249620.144823929062481
480.8034627261197630.3930745477604750.196537273880237
490.815192996396280.3696140072074380.184807003603719
500.7600983019560110.4798033960879780.239901698043989
510.6867099340495910.6265801319008180.313290065950409
520.6647391712297420.6705216575405160.335260828770258
530.6125851696736650.774829660652670.387414830326335
540.6351102265995860.7297795468008280.364889773400414
550.4736547925765060.9473095851530120.526345207423494


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level60.117647058823529NOK
10% type I error level80.156862745098039NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/10u2661258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/10u2661258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/143mv1258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/143mv1258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/2el571258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/2el571258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/32ju81258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/32ju81258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/4xx0q1258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/4xx0q1258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/50k9a1258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/50k9a1258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/6wvcw1258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/6wvcw1258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/7fock1258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/7fock1258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/8v5us1258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/8v5us1258561853.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/9ury71258561853.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561932co23m5pku9rgyev/9ury71258561853.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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