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WS7

*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 09:30:09 -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/t12587347755p4r74pktfedjit.htm/, Retrieved Fri, 20 Nov 2009 17:33:07 +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/t12587347755p4r74pktfedjit.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 «
363 14,3 364 14,2 363 15,9 358 15,3 357 15,5 357 15,1 380 15 378 12,1 376 15,8 380 16,9 379 15,1 384 13,7 392 14,8 394 14,7 392 16 396 15,4 392 15 396 15,5 419 15,1 421 11,7 420 16,3 418 16,7 410 15 418 14,9 426 14,6 428 15,3 430 17,9 424 16,4 423 15,4 427 17,9 441 15,9 449 13,9 452 17,8 462 17,9 455 17,4 461 16,7 461 16 463 16,6 462 19,1 456 17,8 455 17,2 456 18,6 472 16,3 472 15,1 471 19,2 465 17,7 459 19,1 465 18 468 17,5 467 17,8 463 21,1 460 17,2 462 19,4 461 19,8 476 17,6 476 16,2 471 19,5 453 19,9 443 20 442 17,3
 
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
WK>25j[t] = + 109.356227758007 + 20.1391918264263ExpBE[t] + 1.69465044197025M1[t] -2.74432326942943M2[t] -49.8616806336816M3[t] -21.2417575479279M4[t] -23.852892894042M5[t] -39.9753817012972M6[t] + 6.41948685569967M7[t] + 51.9229250373091M8[t] -28.2227069222822M9[t] -32.6366261049248M10[t] -28.9670301917116M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)109.35622775800732.2102343.39510.0014030.000702
ExpBE20.13919182642631.89889810.605700
M11.6946504419702514.2370240.1190.9057580.452879
M2-2.7443232694294314.198678-0.19330.8475720.423786
M3-49.861680633681614.620873-3.41030.0013420.000671
M4-21.241757547927914.189787-1.4970.1410860.070543
M5-23.85289289404214.196697-1.68020.099560.04978
M6-39.975381701297214.378808-2.78020.007790.003895
M76.4194868556996714.1808390.45270.6528570.326428
M851.922925037309114.8470023.49720.0010380.000519
M9-28.222706922282214.500221-1.94640.0576030.028801
M10-32.636626104924814.541194-2.24440.0295520.014776
M11-28.967030191711614.360289-2.01720.049410.024705


Multiple Linear Regression - Regression Statistics
Multiple R0.847826266166205
R-squared0.718809377601329
Adjusted R-squared0.647016027201668
F-TEST (value)10.0121999265927
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value2.5348314558471e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation22.4179352962809
Sum Squared Residuals23620.4996785672


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1363399.041321317873-36.0413213178727
2364392.588428423832-28.5884284238318
3363379.707697164505-16.7076971645047
4358396.244105154403-38.2441051544025
5357397.660808173574-40.6608081735736
6357373.482642635748-16.4826426357479
7380417.863592010102-37.8635920101022
8378404.963373895075-26.9633738950752
9376399.332751693261-23.3327516932614
10380417.071943519688-37.0719435196877
11379384.490994145334-5.49099414533349
12384385.263155780048-1.26315578004820
13392409.110917231087-17.1109172310875
14394402.658024337045-8.65802433704512
15392381.72161634714710.2783836528527
16396398.258024337045-2.25802433704512
17392387.5912122603604.40878773963953
18396381.53831936631814.4616806336815
19419419.877511192745-0.877511192744778
20421396.90769716450524.0923028354953
21420409.40234760647510.5976523935254
22418413.0441051544024.95589484559751
23410382.47707496269127.5229250373092
24418409.430185971768.56981402824016
25426405.08307886580220.9169211341978
26428414.74153943290113.2584605670990
27430419.98608081735710.0139191826427
28424418.3972161634715.60278383652856
29423395.64688899093127.353111009069
30427429.872379749742-2.87237974974167
31441435.9888646538865.01113534611412
32449441.2139191826437.78608081735736
33452439.61113534611412.3888646538859
34462437.21113534611424.7888646538859
35455430.81113534611424.1888646538859
36461445.68073125932715.3192687406727
37461433.27794742279927.7220525772009
38463440.92248880725522.0775111927448
39462444.15311100906917.8468889909310
40456446.5920847204689.40791527953162
41455431.89743427849823.1025657215015
42456443.9698140282412.0301859717598
43472444.04454138445627.9554586155436
44472465.3809493743546.61905062564574
45471467.8060039031113.19399609688900
46465433.18329698082931.8167030191712
47459465.047761451039-6.04776145103894
48465471.861680633682-6.86168063368154
49468463.4867351624394.51326483756139
50467465.0895189989671.91048100103314
51463484.431494661922-21.4314946619217
52460434.50856962461325.4914303753875
53462476.203656296636-14.2036562966364
54461468.136844219952-7.13684421995179
55476470.2254907588115.7745092411893
56476487.534060383423-11.5340603834232
57471473.847761451039-2.84776145103891
58453477.489518998967-24.4895189989668
59443483.173034094823-40.1730340948226
60442457.764246355183-15.7642463551831


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.7359729288184820.5280541423630350.264027071181518
170.9817543654115450.03649126917690990.0182456345884550
180.979352320533740.04129535893251890.0206476794662594
190.989544241773010.02091151645397710.0104557582269886
200.9969971576780440.006005684643911950.00300284232195598
210.9970596865985470.00588062680290560.0029403134014528
220.9987066190771930.002586761845614590.00129338092280729
230.998292170128790.003415659742420240.00170782987121012
240.9970866296435250.005826740712950210.00291337035647511
250.9987745492199540.002450901560091490.00122545078004574
260.9988148715657430.002370256868513460.00118512843425673
270.998228967292880.003542065414240460.00177103270712023
280.9987712556651960.002457488669607610.00122874433480381
290.9993687742141360.001262451571727470.000631225785863735
300.9997219771600760.0005560456798483040.000278022839924152
310.999953079314289.38413714405145e-054.69206857202573e-05
320.9999818620532273.62758935469469e-051.81379467734735e-05
330.9999909478659851.81042680293711e-059.05213401468556e-06
340.9999777095254034.45809491942825e-052.22904745971412e-05
350.9999303675668210.0001392648663570636.96324331785316e-05
360.9998397421774510.0003205156450978440.000160257822548922
370.9996189586664540.0007620826670915950.000381041333545797
380.9988665125072340.002266974985531680.00113348749276584
390.9965751135796440.006849772840711610.00342488642035580
400.990735481133130.01852903773374050.00926451886687027
410.9787314807123360.04253703857532850.0212685192876642
420.9517641201384740.0964717597230520.048235879861526
430.9046000935615220.1907998128769550.0953999064384775
440.809934923856130.3801301522877390.190065076143869


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level200.689655172413793NOK
5% type I error level250.862068965517241NOK
10% type I error level260.896551724137931NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/10vzbp1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/10vzbp1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/1jpuq1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/1jpuq1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/2u1ey1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/2u1ey1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/3sz5m1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/3sz5m1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/45k4l1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/45k4l1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/5e05n1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/5e05n1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/6p5ky1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/6p5ky1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/7sxcj1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/7sxcj1258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/833m31258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/833m31258734605.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/90rma1258734605.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t12587347755p4r74pktfedjit/90rma1258734605.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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