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Indicator voor het consumentenvertrouwen& Industriële productie

*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: Thu, 19 Nov 2009 02:48:41 -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/19/t1258624171n1m1l1oplu8ky3v.htm/, Retrieved Thu, 19 Nov 2009 10:49:43 +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/19/t1258624171n1m1l1oplu8ky3v.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 «
23 25.7 19 24.7 18 24.2 19 23.6 19 24.4 22 22.5 23 19.4 20 18.1 14 18.1 14 20.7 14 19.1 15 18.3 11 16.9 17 17.9 16 20.2 20 21.2 24 23.8 23 24 20 26.6 21 25.3 19 27.6 23 24.7 23 26.6 23 24.4 23 24.6 27 26 26 24.8 17 24 24 22.7 26 23 24 24.1 27 24 27 22.7 26 22.6 24 23.1 23 24.4 23 23 24 22 17 21.3 21 21.5 19 21.3 22 23.2 22 21.8 18 23.3 16 21 14 22.4 12 20.4 14 19.9 16 21.3 8 18.9 3 15.6 0 12.5 5 7.8 1 5.5 1 4 3 3.3 6 3.7 7 3.1 8 5 14 6.3
 
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
Y[t] = + 0.601780378749309 + 0.921662359123831X[t] -1.95485098721075M1[t] -1.78618604356121M2[t] -4.15945563935701M3[t] -4.15115848233528M4[t] -0.835027561225937M5[t] + 0.0967708880586427M6[t] -0.279264426744397M7[t] -0.129032730277341M8[t] -1.36313350563505M9[t] -1.03686649436496M10[t] -1.76589922464229M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.6017803787493092.5843390.23290.8168840.408442
X0.9216623591238310.08916610.336500
M1-1.954850987210752.815365-0.69440.490880.24544
M2-1.786186043561212.811476-0.63530.5283010.264151
M3-4.159455639357012.805894-1.48240.1449090.072454
M4-4.151158482335282.801721-1.48160.1451080.072554
M5-0.8350275612259372.799145-0.29830.7667770.383389
M60.09677088805864272.7979590.03460.9725560.486278
M7-0.2792644267443972.796978-0.09980.9208920.460446
M8-0.1290327302773412.796622-0.04610.9633950.481698
M9-1.363133505635052.796596-0.48740.6282220.314111
M10-1.036866494364962.796596-0.37080.7124820.356241
M11-1.765899224642292.79664-0.63140.5308150.265407


Multiple Linear Regression - Regression Statistics
Multiple R0.838610587508146
R-squared0.703267717480758
Adjusted R-squared0.627506283646058
F-TEST (value)9.28266113620792
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value8.0980888661486e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.4218030807938
Sum Squared Residuals918.960096809924


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12322.33365202102100.66634797897896
21921.5806546055467-2.58065460554671
31818.746553830189-0.746553830189013
41918.20185357173640.798146428263554
51922.2553143801449-3.25531438014486
62221.43595434709420.564045652905844
72318.20276571900724.79723428099276
82017.15483634861332.84516365138668
91415.9207355732556-1.92073557325561
101418.6433247182477-4.64332471824766
111416.4396322133722-2.43963221337219
121517.4682015507154-2.46820155071542
131114.2230232607313-3.22302326073131
141715.31335056350471.68664943649532
151615.05990439369370.940095606306308
162015.98986390983934.01013609016075
172421.70231696467062.29768303532944
182322.81844788577990.181552114220096
192024.8387347046988-4.83873470469883
202123.7908053343049-2.7908053343049
211924.676527984932-5.676527984932
222322.3299741547430.670025845257014
232323.3520999068009-0.352099906800930
242323.0903419413708-0.090341941370793
252321.31982342598481.68017657401519
262722.77881567240774.22118432759229
272619.29955124566336.70044875433668
281718.570518515386-1.57051851538598
292420.68848836963433.31151163036566
302621.89678552665614.10321447334392
312422.53457880688931.46542119311075
322722.59264426744394.40735573255608
332720.16038242522526.83961757477477
342620.39448320058295.60551679941706
352420.12628164986753.87371835013248
362323.0903419413708-0.090341941370793
372319.84516365138673.15483634861332
382419.09216623591244.90783376408761
391716.07373298872990.926267011270093
402116.26636261757644.7336373824236
411919.3981610668610-0.398161066860982
422222.0811179984808-0.0811179984808388
432220.41475538090441.58524461909556
441821.9474806160572-3.94748061605724
451618.5935564147147-2.59355641471472
461420.2101507287582-6.21015072875817
471217.6377932802332-5.63779328023318
481418.9428613253136-4.94286132531355
491618.2783376408762-2.27833764087617
50816.2350129226285-8.2350129226285
51310.8202575417241-7.82025754172407
5207.97140138546192-7.97140138546192
5356.95571921868926-1.95571921868926
5415.76769424198903-4.76769424198903
5514.00916538850024-3.00916538850024
5633.51423343358061-0.514233433580615
5762.648797601872443.35120239812756
5872.422067197668234.57793280233177
5983.444192949726184.55580705027382
60146.408253241229457.59174675877055


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1803272724691910.3606545449383830.819672727530809
170.1734506449782360.3469012899564720.826549355021764
180.0842964208896240.1685928417792480.915703579110376
190.1433284271351420.2866568542702830.856671572864859
200.08719204134284890.1743840826856980.912807958657151
210.05676269139878180.1135253827975640.943237308601218
220.07054750927616830.1410950185523370.929452490723832
230.05415686927637680.1083137385527540.945843130723623
240.03759552134267980.07519104268535950.96240447865732
250.02636529682594990.05273059365189990.97363470317405
260.02803284217255410.05606568434510810.971967157827446
270.05030104593425240.1006020918685050.949698954065748
280.03571891048723450.07143782097446890.964281089512766
290.0264330946817910.0528661893635820.97356690531821
300.02201658191825190.04403316383650380.977983418081748
310.01254288352697830.02508576705395670.987457116473022
320.01220049688891140.02440099377782290.987799503111089
330.03694048065567520.07388096131135040.963059519344325
340.05019235117100160.1003847023420030.949807648828998
350.04541826828657940.09083653657315880.95458173171342
360.02630173284960610.05260346569921220.973698267150394
370.01923006513812660.03846013027625320.980769934861873
380.03727643743265660.07455287486531320.962723562567343
390.0403655413640920.0807310827281840.959634458635908
400.1339650966066060.2679301932132120.866034903393394
410.09962302398316720.1992460479663340.900376976016833
420.1607337468502790.3214674937005570.839266253149721
430.4935246234656330.9870492469312670.506475376534367
440.6807715933372390.6384568133255230.319228406662761


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.137931034482759NOK
10% type I error level140.482758620689655NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/10atr31258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/10atr31258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/13q8x1258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/13q8x1258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/2gfo51258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/2gfo51258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/3m2ky1258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/3m2ky1258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/4j5be1258624117.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/51z241258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/51z241258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/6b2f61258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/6b2f61258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/788u11258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/788u11258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/89f061258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/89f061258624117.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/9zar21258624117.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258624171n1m1l1oplu8ky3v/9zar21258624117.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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