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Workshop 7 data 3

*Unverified author*
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 11:40:21 -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/t12587425281sev99q6hy0vo6x.htm/, Retrieved Fri, 20 Nov 2009 19:42:20 +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/t12587425281sev99q6hy0vo6x.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 «
613 0 611 594 543 611 0 613 611 594 594 0 611 613 611 595 0 594 611 613 591 0 595 594 611 589 0 591 595 594 584 0 589 591 595 573 0 584 589 591 567 0 573 584 589 569 0 567 573 584 621 0 569 567 573 629 0 621 569 567 628 0 629 621 569 612 0 628 629 621 595 0 612 628 629 597 0 595 612 628 593 0 597 595 612 590 0 593 597 595 580 0 590 593 597 574 0 580 590 593 573 0 574 580 590 573 0 573 574 580 620 0 573 573 574 626 0 620 573 573 620 0 626 620 573 588 0 620 626 620 566 0 588 620 626 557 0 566 588 620 561 0 557 566 588 549 0 561 557 566 532 0 549 561 557 526 0 532 549 561 511 0 526 532 549 499 0 511 526 532 555 0 499 511 526 565 0 555 499 511 542 0 565 555 499 527 0 542 565 555 510 0 527 542 565 514 0 510 527 542 517 0 514 510 527 508 0 517 514 510 493 0 508 517 514 490 0 493 508 517 469 1 490 493 508 478 1 469 490 493 528 1 478 469 490 534 1 528 478 469 518 1 534 528 478 506 1 518 534 528 502 1 506 518 534 516 1 502 506 518 528 1 516 502 506 533 1 528 516 502 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] = + 27.2884150780906 + 7.47895824192816X[t] + 1.07957881958415Y1[t] + 0.0219700856362730Y2[t] -0.140078156472438Y3[t] -18.6096792509571M1[t] -17.3675468737958M2[t] -14.4556056693470M3[t] + 3.85191565250290M4[t] + 1.81841815303683M5[t] -6.79023110683807M6[t] -10.5917907190378M7[t] -5.5146948443727M8[t] -13.0312279400098M9[t] + 0.313573448969398M10[t] + 49.1524062059444M11[t] -0.176355958412839t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)27.288415078090632.4546720.84080.4053280.202664
X7.478958241928163.9323941.90190.0642280.032114
Y11.079578819584150.1593326.775700
Y20.02197008563627300.2353540.09330.9260810.46304
Y3-0.1400781564724380.16043-0.87310.387670.193835
M1-18.609679250957112.046999-1.54480.130090.065045
M2-17.367546873795810.959982-1.58460.1207340.060367
M3-14.455605669347011.530624-1.25370.2170630.108532
M43.8519156525029011.5025590.33490.7394270.369713
M51.818418153036839.0830380.20020.8423140.421157
M6-6.790231106838079.113171-0.74510.4604610.23023
M7-10.59179071903789.953327-1.06410.293490.146745
M8-5.514694844372710.450702-0.52770.6005610.300281
M9-13.031227940009810.161493-1.28240.2069010.103451
M100.31357344896939811.0103390.02850.9774180.488709
M1149.15240620594449.5932025.12378e-064e-06
t-0.1763559584128390.13019-1.35460.1829620.091481


Multiple Linear Regression - Regression Statistics
Multiple R0.989562151332385
R-squared0.979233251349577
Adjusted R-squared0.971129154315266
F-TEST (value)120.831876420492
F-TEST (DF numerator)16
F-TEST (DF denominator)41
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.2247844893341
Sum Squared Residuals2140.09794761022


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1613605.1128305380477.88716946195325
2611601.5672700716859.43272992831453
3594599.806309189794-5.80630918979425
4595599.260538136083-4.26053813608336
5591598.036928354917-7.03692835491685
6589587.336906603961.66309339603974
7584580.9718748951623.02812510483808
8573580.99109316811-7.99109316811058
9567561.5931429833995.40685701660145
10569568.7428353368230.257164663176796
11621620.9735089819330.0264910180672184
12629628.6672545460580.332745453941555
13628619.3801380335038.61986196649697
14612612.258032181191-0.258032181190727
15595596.577760976465-1.57776097646458
16597596.1446431932630.85535680673684
17593597.961706422295-4.96170642229492
18590587.2836547569752.71634524302540
19580579.698966072120.301033927880349
20574574.298320161511-0.298320161511326
21573560.32849180301112.6715081969889
22573573.6863194649-0.686319464900039
23620623.167295116661-3.16729511666052
24626624.7188156292311.28118437076930
25620613.442847362276.55715263772948
26588601.579298023127-13.5792980231271
27566568.796071589818-2.7960715898181
28557563.313929120878-6.31392912087777
29561555.3870254098625.61297459013844
30549553.804324141578-4.80432414157761
31532538.220046486752-6.22004648675236
32526523.9439928165492.05600718345097
33511511.081077266847-0.0810772668468236
34499510.305348549865-11.3053485498648
35555546.5237971677088.47620283229231
36565559.4889802195145.51101978048596
37542554.409995879286-12.4099958792862
38527523.0207835415053.97921645849463
39510507.656592959422.3434070405795
40514510.3271647042493.67283529575101
41517514.1633074159772.83669258402338
42508511.086247659018-3.08624765901787
43493496.897720343167-3.89772034316707
44490484.9868127255135.01318727448669
45469482.465297578347-13.4652975783470
46478474.9978498878243.00215011217601
47528533.335398733699-5.33539873369901
48534541.124949605197-7.12494960519685
49518528.654188186894-10.6541881868935
50506505.5746161824910.425383817508676
51502494.1632652845037.83673471549744
52516509.9537248455276.04627515447328
53528524.451032396953.54896760304995
54533529.488866838473.51113316153034
55536529.2113922027996.788607797201
56537535.7797811283161.22021887168424
57524528.531990368397-4.53199036839658
58536527.2676467605888.73235323941201


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.1297580417837720.2595160835675440.870241958216228
210.1451759213855000.2903518427710010.8548240786145
220.07380359005255880.1476071801051180.926196409947441
230.04199307147557450.0839861429511490.958006928524425
240.02096008062155350.04192016124310690.979039919378446
250.04525410400561220.09050820801122450.954745895994388
260.5117502309331910.9764995381336190.488249769066809
270.404776716698050.80955343339610.59522328330195
280.4371751264041280.8743502528082550.562824873595872
290.3703624686090780.7407249372181560.629637531390922
300.3706123933170220.7412247866340450.629387606682978
310.4578108567983400.9156217135966790.54218914320166
320.4730010175665280.9460020351330550.526998982433472
330.4882656846867650.976531369373530.511734315313235
340.6257605189487310.7484789621025370.374239481051269
350.6991427129983170.6017145740033670.300857287001683
360.8366550490405670.3266899019188670.163344950959433
370.7841910662763610.4316178674472780.215808933723639
380.7580153622512130.4839692754975730.241984637748787


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0526315789473684NOK
10% type I error level30.157894736842105NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/105iag1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/105iag1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/1zvjy1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/1zvjy1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/2pt2h1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/2pt2h1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/313qc1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/313qc1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/4824o1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/4824o1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/58jsw1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/58jsw1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/64chy1258742417.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/71sty1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/71sty1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/8kzzl1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/8kzzl1258742417.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/95t9g1258742417.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587425281sev99q6hy0vo6x/95t9g1258742417.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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Software written by Ed van Stee & Patrick Wessa


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