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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 05:15:31 -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/t12587194252shp7opct0rwr77.htm/, Retrieved Fri, 20 Nov 2009 13:17:18 +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/t12587194252shp7opct0rwr77.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:
WS7,MR2
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1.3 2 1.2 2.1 1.1 2.1 1.4 2.5 1.2 2.2 1.5 2.3 1.1 2.3 1.3 2.2 1.5 2.2 1.1 1.6 1.4 1.8 1.3 1.7 1.5 1.9 1.6 1.8 1.7 1.9 1.1 1.5 1.6 1 1.3 0.8 1.7 1.1 1.6 1.5 1.7 1.7 1.9 2.3 1.8 2.4 1.9 3 1.6 3 1.5 3.2 1.6 3.2 1.6 3.2 1.7 3.5 2 4 2 4.3 1.9 4.1 1.7 4 1.8 4.1 1.9 4.2 1.7 4.5 2 5.6 2.1 6.5 2.4 7.6 2.5 8.5 2.5 8.7 2.6 8.3 2.2 8.3 2.5 8.5 2.8 8.7 2.8 8.7 2.9 8.5 3 7.9 3.1 7 2.9 5.8 2.7 4.5 2.2 3.7 2.5 3.1 2.3 2.7 2.6 2.3 2.3 1.8 2.2 1.5 1.8 1.2 1.8 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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
inflatie[t] = + 1.26580173511677 + 0.165894330966839inflatie_levensmiddelen[t] -0.0127896258874350M1[t] -0.0494717392680991M2[t] -0.00615385264876214M3[t] -0.149471739268099M4[t] + 0.0203892403059319M5[t] + 0.073660786783279M6[t] + 0.0470250135446055M7[t] + 0.0536607867832790M8[t] + 0.113660786783279M9[t] + 0.0202965600219525M10[t] + 0.100296560021952M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.265801735116770.217355.82381e-060
inflatie_levensmiddelen0.1658943309668390.0210027.89900
M1-0.01278962588743500.26568-0.04810.9618140.480907
M2-0.04947173926809910.265693-0.18620.8531070.426554
M3-0.006153852648762140.265706-0.02320.9816230.490811
M4-0.1494717392680990.265693-0.56260.5764570.288229
M50.02038924030593190.2658380.07670.9391960.469598
M60.0736607867832790.2659190.2770.7830180.391509
M70.04702501354460550.2658770.17690.8603890.430195
M80.05366078678327900.2659190.20180.8409680.420484
M90.1136607867832790.2659190.42740.6710640.335532
M100.02029656002195250.2659640.07630.9395010.46975
M110.1002965600219520.2659640.37710.7078290.353915


Multiple Linear Regression - Regression Statistics
Multiple R0.76178189947505
R-squared0.580311662367816
Adjusted R-squared0.470827748202899
F-TEST (value)5.30042853138848
F-TEST (DF numerator)12
F-TEST (DF denominator)46
p-value1.6074668327537e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.395878426184873
Sum Squared Residuals7.20910750265615


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.31.58480077116300-0.284800771163005
21.21.56470809087903-0.364708090879029
31.11.60802597749836-0.508025977498364
41.41.53106582326576-0.131065823265763
51.21.65115850354974-0.451158503549743
61.51.72101948312377-0.221019483123773
71.11.6943837098851-0.5943837098851
81.31.68443005002709-0.384430050027089
91.51.74443005002709-0.244430050027089
101.11.55152922468566-0.451529224685660
111.41.66470809087903-0.264708090879027
121.31.54782209776039-0.247822097760391
131.51.56821133806632-0.0682113380663236
141.61.514939791588980.0850602084110244
151.71.574847111305000.125152888695004
161.11.36517149229892-0.265171492298924
171.61.452085306389540.147914693610464
181.31.47217798667352-0.172177986673515
191.71.495310512724890.204689487275107
201.61.568304018350300.0316959816496978
211.71.661482884543670.0385171154563299
221.91.667655256362450.232344743637553
231.81.764244689459130.0357553105408696
241.91.763484728017280.136515271982719
251.61.75069510212985-0.150695102129846
261.51.74719185494255-0.247191854942550
271.61.79050974156189-0.190509741561886
281.61.64719185494255-0.0471918549425498
291.71.86682113380663-0.166821133806632
3022.0030398457674-0.00303984576739860
3122.02617237181878-0.0261723718187767
321.91.99962927886408-0.0996292788640825
331.72.0430398457674-0.343039845767399
341.81.96626505210276-0.166265052102756
351.92.06285448519944-0.16285448519944
361.72.01232622446754-0.312326224467539
3722.18202036264363-0.182020362643626
382.12.29464314713312-0.194643147133117
392.42.52044479781598-0.120444797815976
402.52.52643180906679-0.0264318090667941
412.52.72947165483419-0.229471654834193
422.62.71638546892480-0.116385468924804
432.22.68974969568613-0.489749695686131
442.52.72956433511817-0.229564335118172
452.82.82274320131154-0.02274320131154
462.82.729378974550210.0706210254497865
472.92.776200108356850.123799891643154
4832.576366949754790.42363305024521
493.12.41427242599720.6857275740028
502.92.178517115456330.72148288454367
512.72.006172371818780.693827628181223
522.21.730139020425970.469860979574031
532.51.800463401419900.699536598580103
542.31.787377215510510.512622784489492
552.61.69438370988510.9056162901149
562.31.618072317640350.681927682359646
572.21.628304018350300.571695981649698
581.81.485171492298920.314828507701076
591.81.531992626105560.268007373894444


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.4409287685466860.8818575370933710.559071231453314
170.3182198804215050.6364397608430090.681780119578495
180.250123874436360.500247748872720.74987612556364
190.2368139244046550.473627848809310.763186075595345
200.1579403243201930.3158806486403850.842059675679807
210.09530230131853870.1906046026370770.904697698681461
220.2064866688894320.4129733377788640.793513331110568
230.1713230138361420.3426460276722840.828676986163858
240.1679245074259480.3358490148518970.832075492574052
250.1304455438629620.2608910877259240.869554456137038
260.1057779655216260.2115559310432520.894222034478374
270.08831318032121590.1766263606424320.911686819678784
280.07059013007970840.1411802601594170.929409869920292
290.05648285637732120.1129657127546420.943517143622679
300.04215699505154620.08431399010309240.957843004948454
310.02833299217098570.05666598434197150.971667007829014
320.01876532156099160.03753064312198330.981234678439008
330.02101496154798330.04202992309596660.978985038452017
340.01440547608870020.02881095217740030.9855945239113
350.009418249959075870.01883649991815170.990581750040924
360.02259492673784780.04518985347569550.977405073262152
370.05737890287434820.1147578057486960.942621097125652
380.1163368354184570.2326736708369130.883663164581543
390.1187660312773490.2375320625546980.88123396872265
400.07129383480589310.1425876696117860.928706165194107
410.05676078070662430.1135215614132490.943239219293376
420.02867007932371570.05734015864743130.971329920676284
430.2806125858744570.5612251717489140.719387414125543


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level50.178571428571429NOK
10% type I error level80.285714285714286NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/10qz9b1258719325.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/10qz9b1258719325.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/15eff1258719324.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/15eff1258719324.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/2pm5j1258719324.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/2pm5j1258719324.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/3h1ve1258719324.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/4azn21258719325.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/5ou651258719325.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/5ou651258719325.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/6925d1258719325.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/754d41258719325.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/754d41258719325.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/8agg31258719325.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/8agg31258719325.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/9usio1258719325.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587194252shp7opct0rwr77/9usio1258719325.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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