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review 7

*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: Tue, 24 Nov 2009 13:46:35 -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/24/t12590956687zhngm0la306rxq.htm/, Retrieved Tue, 24 Nov 2009 21:47:59 +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/24/t12590956687zhngm0la306rxq.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 «
1,6 0 1,4 1,7 0 1,6 2 0 1,7 2 0 2 2,1 0 2 2,5 0 2,1 2,5 0 2,5 2,6 0 2,5 2,7 0 2,6 3,7 0 2,7 4 0 3,7 5 0 4 5,1 0 5 5,1 0 5,1 5 0 5,1 5,1 0 5 4,7 0 5,1 4,5 0 4,7 4,5 0 4,5 4,6 0 4,5 4,6 0 4,6 4,6 0 4,6 4,6 0 4,6 5,3 0 4,6 5,4 0 5,3 5,3 0 5,4 5,2 0 5,3 5 0 5,2 4,2 0 5 4,3 0 4,2 4,3 0 4,3 4,3 0 4,3 4 0 4,3 4 0 4 4,1 0 4 4,4 0 4,1 3,6 0 4,4 3,7 0 3,6 3,8 0 3,7 3,3 0 3,8 3,3 0 3,3 3,3 0 3,3 3,5 0 3,3 3,3 0 3,5 3,3 0 3,3 3,4 0 3,3 3,4 0 3,4 5,2 0 3,4 5,3 0 5,2 4,8 1 5,3 5 1 4,8 4,6 1 5 4,6 1 4,6 3,5 1 4,6 3,5 1 3,5
 
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
IndGez[t] = + 1.42438152443353 -0.167230832567180InvlMex[t] + 0.882141236165582`IndGez-1`[t] -0.982303190498912M1[t] -0.97592854981554M2[t] -0.825357250922293M3[t] -1.09592854981554M4[t] -1.13950030258242M5[t] -1.10542923062600M6[t] -0.924286632839504M7[t] -0.988304098246186M8[t] -1.03830409824619M9[t] -0.719197036437907M10[t] -0.861785876383442M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.424381524433530.2342096.081700
InvlMex-0.1672308325671800.150408-1.11180.2726810.136341
`IndGez-1`0.8821412361655820.04239320.808500
M1-0.9823031904989120.215471-4.55894.6e-052.3e-05
M2-0.975928549815540.217225-4.49275.6e-052.8e-05
M3-0.8253572509222930.217242-3.79920.0004730.000236
M4-1.095928549815540.217225-5.04511e-055e-06
M5-1.139500302582420.217368-5.24235e-063e-06
M6-1.105429230626000.217907-5.07299e-064e-06
M7-0.9242866328395040.218548-4.22920.0001286.4e-05
M8-0.9883040982461860.227301-4.3488.9e-054.4e-05
M9-1.038304098246190.227301-4.5684.4e-052.2e-05
M10-0.7191970364379070.227439-3.16210.0029450.001472
M11-0.8617858763834420.226923-3.79770.0004750.000237


Multiple Linear Regression - Regression Statistics
Multiple R0.962194952626626
R-squared0.925819126860156
Adjusted R-squared0.902298362206059
F-TEST (value)39.3617784317609
F-TEST (DF numerator)13
F-TEST (DF denominator)41
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.320861133855173
Sum Squared Residuals4.22102655597193


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.61.67707606456644-0.0770760645664356
21.71.85987895248292-0.15987895248292
322.09866437499272-0.0986643749927234
422.09273544694915-0.0927354469491545
52.12.049163694182270.0508363058177288
62.52.171448889755260.328551110244742
72.52.70544798200798-0.205447982007984
82.62.64143051660130-0.0414305166013019
92.72.679644640217860.0203553597821408
103.73.08696582564270.613034174357303
1143.826518221862740.173481778137255
1254.952946469095860.0470535309041391
135.14.852784514762530.247215485237469
145.14.947373279062460.15262672093754
1555.09794457795571-0.0979445779557072
165.14.73915915544590.360840844554098
174.74.78380152629558-0.0838015262955758
184.54.465016103785770.0349838962142288
194.54.469730454339150.0302695456608515
204.64.405712988932470.194287011067534
214.64.443927112549020.156072887450976
224.64.7630341743573-0.163034174357303
234.64.62044533441177-0.0204453344117677
245.35.48223121079521-0.18223121079521
255.45.11742688561220.282573114387795
265.35.212015649912130.0879843500878647
275.25.27437282518882-0.0743728251888235
2854.915587402679020.084412597320982
294.24.69558740267902-0.495587402679018
304.34.023945485702980.276054514297019
314.34.293302207106030.00669779289396837
324.34.229284741699350.070715258300651
3344.17928474169935-0.179284741699349
3444.23374943265795-0.233749432657954
354.14.091160592712420.0088394072875814
364.45.04116059271242-0.641160592712419
373.64.32349977306318-0.723499773063182
383.73.624161424814090.0758385751859131
393.83.86294684732389-0.0629468473238928
403.33.68058967204720-0.380589672047203
413.33.195947301197530.104052698802471
423.33.230018373153960.0699816268460437
433.53.411160970940450.0888390290595506
443.33.52357175276688-0.223571752766883
453.33.297143505533770.00285649446623263
463.43.61625056734205-0.216250567342046
473.43.56187585101307-0.161875851013069
485.24.423661727396510.77633827260349
495.35.029212761995650.270787238004353
504.84.9565706937284-0.156570693728398
5154.666071374538850.333928625461147
524.64.571928322878720.0280716771212774
534.64.175500075645610.424499924354394
543.54.20957114760203-0.709571147602033
553.53.420358385606390.0796416143936131


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1788803411660810.3577606823321620.821119658833919
180.1811033077376410.3622066154752830.818896692262359
190.09770504540923380.1954100908184680.902294954590766
200.05130253292715250.1026050658543050.948697467072848
210.02312295804464580.04624591608929160.976877041955354
220.134128888358650.26825777671730.86587111164135
230.08543443861009020.1708688772201800.91456556138991
240.05516981358682720.1103396271736540.944830186413173
250.0384806593616740.0769613187233480.961519340638326
260.02031235299826870.04062470599653750.979687647001731
270.009729703593303640.01945940718660730.990270296406696
280.005289367083390180.01057873416678040.99471063291661
290.01231468042525460.02462936085050920.987685319574745
300.009732793333502350.01946558666700470.990267206666498
310.004497624489575470.008995248979150930.995502375510425
320.002227556361495200.004455112722990390.997772443638505
330.001239480151007820.002478960302015630.998760519848992
340.001113843651772680.002227687303545360.998886156348227
350.0004397941175584880.0008795882351169760.999560205882442
360.02336829835879770.04673659671759550.976631701641202
370.1957035673488310.3914071346976620.804296432651169
380.1152942105923240.2305884211846490.884705789407676


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.227272727272727NOK
5% type I error level120.545454545454545NOK
10% type I error level130.590909090909091NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/10kj2u1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/10kj2u1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/1rnjk1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/1rnjk1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/26f3v1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/26f3v1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/3lsyv1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/3lsyv1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/4nhcb1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/4nhcb1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/5vemt1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/5vemt1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/6gdkz1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/6gdkz1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/7rwgu1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/7rwgu1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/8vwjq1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/8vwjq1259095591.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/9dieg1259095591.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/24/t12590956687zhngm0la306rxq/9dieg1259095591.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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