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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, 17 Dec 2010 12:34:10 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l.htm/, Retrieved Fri, 17 Dec 2010 13:33:54 +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/2010/Dec/17/t1292589221whfhpo8xpm6l38l.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
2 2,3 2,8 2,4 2,3 2,7 2,7 2,9 3 2,2 2,3 2,8 2,8 2,8 2,2 2,6 2,8 2,5 2,4 2,3 1,9 1,7 2 2,1 1,7 1,8 1,8 1,8 1,3 1,3 1,3 1,2 1,4 2,2 2,9 3,1 3,5 3,6 4,4 4,1 5,1 5,8 5,9 5,4 5,5 4,8 3,2 2,7 2,1 1,9 0,6 0,7 -0,2 -1 -1,7 -0,7 -1 -0,9 0 0,3 0,8
 
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 time19 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
HPC[t] = + 3.11176470588236 -0.176633986928106M1[t] + 0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)3.111764705882360.9155223.39890.001370.000685
M1-0.1766339869281061.067714-0.16540.8692990.434649
M20.02673202614378961.1206790.02390.9810680.490534
M3-0.06794117647058971.119248-0.06070.9518480.475924
M4-0.0826143790849691.117966-0.07390.9413990.4707
M5-0.1172875816993481.116834-0.1050.9167990.4584
M6-0.09196078431372691.115851-0.08240.9346610.46733
M7-0.2066339869281061.115019-0.18530.853760.42688
M8-0.08130718954248551.114338-0.0730.9421380.471069
M9-0.1159803921568641.113808-0.10410.91750.45875
M10-0.2506535947712431.113429-0.22510.8228430.411421
M11-0.1453267973856221.113202-0.13050.8966780.448339
t-0.02532679738562090.012989-1.94990.0570480.028524


Multiple Linear Regression - Regression Statistics
Multiple R0.280701934462105
R-squared0.0787935760107679
Adjusted R-squared-0.15150802998654
F-TEST (value)0.34213211701046
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.976538597787572
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.76000733435786
Sum Squared Residuals148.686039215686


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
122.90980392156862-0.909803921568623
22.33.0878431372549-0.787843137254901
32.82.9678431372549-0.167843137254902
42.42.9278431372549-0.527843137254901
52.32.8678431372549-0.567843137254902
62.72.8678431372549-0.167843137254902
72.72.72784313725490-0.0278431372549023
82.92.82784313725490.0721568627450983
932.76784313725490.232156862745098
102.22.60784313725490-0.407843137254902
112.32.6878431372549-0.387843137254902
122.82.80784313725490-0.00784313725490308
132.82.605882352941180.194117647058822
142.82.783921568627450.0160784313725485
152.22.66392156862745-0.463921568627451
162.62.62392156862745-0.0239215686274506
172.82.563921568627450.236078431372549
182.52.56392156862745-0.0639215686274504
192.42.42392156862745-0.0239215686274508
202.32.52392156862745-0.223921568627451
211.92.46392156862745-0.563921568627451
221.72.30392156862745-0.603921568627451
2322.38392156862745-0.383921568627451
242.12.50392156862745-0.403921568627452
251.72.30196078431373-0.601960784313726
261.82.48-0.68
271.82.36-0.56
281.82.32-0.52
291.32.26-0.96
301.32.26-0.96
311.32.12-0.82
321.22.22-1.02
331.42.16-0.76
342.220.200000000000001
352.92.080.82
363.12.20.899999999999999
373.51.998039215686271.50196078431373
383.62.176078431372551.42392156862745
394.42.056078431372552.34392156862745
404.12.016078431372552.08392156862745
415.11.956078431372553.14392156862745
425.81.956078431372553.84392156862745
435.91.816078431372554.08392156862745
445.41.916078431372553.48392156862745
455.51.856078431372553.64392156862745
464.81.696078431372553.10392156862745
473.21.776078431372551.42392156862745
482.71.896078431372550.80392156862745
492.11.694117647058820.405882352941176
501.91.87215686274510.0278431372549018
510.61.75215686274510-1.15215686274510
520.71.71215686274510-1.01215686274510
53-0.21.6521568627451-1.8521568627451
54-11.65215686274510-2.6521568627451
55-1.71.51215686274510-3.2121568627451
56-0.71.6121568627451-2.3121568627451
57-11.5521568627451-2.5521568627451
58-0.91.3921568627451-2.2921568627451
5901.4721568627451-1.4721568627451
600.31.5921568627451-1.2921568627451
610.81.39019607843137-0.590196078431373


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.01113217501903760.02226435003807520.988867824980962
170.001976030050514370.003952060101028740.998023969949486
180.0004236225071140230.0008472450142280470.999576377492886
199.40906718038906e-050.0001881813436077810.999905909328196
203.28433449934913e-056.56866899869825e-050.999967156655007
212.90369671519759e-055.80739343039517e-050.999970963032848
226.61332579055521e-061.32266515811104e-050.99999338667421
231.22411756558044e-062.44823513116087e-060.999998775882434
243.21460393808537e-076.42920787617074e-070.999999678539606
257.9648074379939e-081.59296148759878e-070.999999920351926
261.95519261053518e-083.91038522107036e-080.999999980448074
274.20133902652341e-098.40267805304683e-090.99999999579866
288.86851316440512e-101.77370263288102e-090.999999999113149
296.60105038255032e-101.32021007651006e-090.999999999339895
305.10036308418355e-101.02007261683671e-090.999999999489964
313.30649947531936e-106.61299895063872e-100.99999999966935
324.71654399629039e-109.43308799258079e-100.999999999528346
335.63848792077113e-101.12769758415423e-090.999999999436151
343.38770359436159e-096.77540718872317e-090.999999996612296
355.57372018510203e-081.11474403702041e-070.999999944262798
366.62492956223794e-071.32498591244759e-060.999999337507044
370.0001327455212411380.0002654910424822750.999867254478759
380.000987026683187470.001974053366374940.999012973316812
390.003739149243676560.007478298487353120.996260850756323
400.00601126050819330.01202252101638660.993988739491807
410.01313096175678970.02626192351357950.98686903824321
420.03888218274808980.07776436549617950.96111781725191
430.1341934154139950.268386830827990.865806584586005
440.1647480199099350.3294960398198710.835251980090065
450.3340787878973950.668157575794790.665921212102605


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level230.766666666666667NOK
5% type I error level260.866666666666667NOK
10% type I error level270.9NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/107prp1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/107prp1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/1i6uv1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/1i6uv1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/2i6uv1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/2i6uv1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/3bxby1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/3bxby1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/4bxby1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/4bxby1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/5bxby1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/5bxby1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/636a11292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/636a11292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/7wgam1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/7wgam1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/8wgam1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/8wgam1292589230.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/9wgam1292589230.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292589221whfhpo8xpm6l38l/9wgam1292589230.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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