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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: Mon, 21 Dec 2009 14:53:47 -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/Dec/21/t1261432461mj0jttg90zz8f7k.htm/, Retrieved Mon, 21 Dec 2009 22:54:34 +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/Dec/21/t1261432461mj0jttg90zz8f7k.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 «
120,9 0 0 119,6 0 0 125,9 0 0 116,1 0 0 107,5 0 0 116,7 0 0 112,5 0 0 113 0 0 126,4 0 0 114,1 0 0 112,5 0 0 112,4 0 0 113,1 0 0 116,3 0 0 111,7 0 0 118,8 0 0 116,5 0 0 125,1 0 0 113,1 0 0 119,6 0 0 114,4 0 0 114 0 0 117,8 0 0 117 0 0 120,9 0 0 115 0 0 117,3 0 0 119,4 0 0 114,9 0 0 125,8 0 0 117,6 0 0 117,6 0 0 114,9 0 0 121,9 0 0 117 0 1 106,4 0 1 110,5 0 1 113,6 0 1 114,2 0 1 125,4 0 1 124,6 0 1 120,2 0 1 120,8 0 1 111,4 0 1 124,1 0 1 120,2 0 1 125,5 0 1 116 1 0 117 1 0 105,7 1 0 102 1 0 106,4 1 0 96,9 1 0 107,6 1 0 98,8 1 0 101,1 1 0 105,7 1 0 104,6 1 0 103,2 1 0 101,6 1 0
 
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
ChemischeNijverheid[t] = + 114.045891608392 -14.2594696969697Dummy_1[t] -0.643036130536138Dummy_2[t] + 3.70175990675989M1[t] + 1.19324592074591M2[t] + 1.30473193473193M3[t] + 4.23621794871794M4[t] -0.972296037296041M5[t] + 5.95918997668996M6[t] -0.629324009324017M7[t] -0.717837995338005M8[t] + 3.77364801864801M9[t] + 1.56513403263402M10[t] + 1.86522727272727M11[t] + 0.0685139860139864t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)114.0458916083922.96791138.426300
Dummy_1-14.25946969696973.839393-3.7140.0005610.00028
Dummy_2-0.6430361305361382.802759-0.22940.8195750.409787
M13.701759906759893.3902551.09190.2806960.140348
M21.193245920745913.3820250.35280.7258710.362935
M31.304731934731933.3763650.38640.7009990.350499
M44.236217948717943.3732881.25580.2156650.107833
M5-0.9722960372960413.372802-0.28830.774460.38723
M65.959189976689963.3749081.76570.0842250.042112
M7-0.6293240093240173.3796-0.18620.8531150.426557
M8-0.7178379953380053.386869-0.21190.8331050.416553
M93.773648018648013.3966971.1110.272480.13624
M101.565134032634023.4090620.45910.6483650.324183
M111.865227272727273.3840440.55120.5842350.292117
t0.06851398601398640.0935060.73270.4675290.233765


Multiple Linear Regression - Regression Statistics
Multiple R0.766919546586582
R-squared0.588165590936568
Adjusted R-squared0.460039330339056
F-TEST (value)4.59051554453926
F-TEST (DF numerator)14
F-TEST (DF denominator)45
p-value4.53898964412058e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.30396995837526
Sum Squared Residuals1265.94437937063


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1120.9117.8161655011663.08383449883446
2119.6115.3761655011664.22383449883448
3125.9115.55616550116510.3438344988345
4116.1118.556165501165-2.4561655011655
5107.5113.416165501165-5.9161655011655
6116.7120.416165501165-3.7161655011655
7112.5113.896165501165-1.39616550116549
8113113.876165501165-0.876165501165494
9126.4118.4361655011657.96383449883452
10114.1116.296165501166-2.19616550116550
11112.5116.664772727273-4.16477272727273
12112.4114.868059440559-2.46805944055944
13113.1118.638333333333-5.53833333333334
14116.3116.1983333333330.101666666666667
15111.7116.378333333333-4.67833333333333
16118.8119.378333333333-0.578333333333339
17116.5114.2383333333332.26166666666666
18125.1121.2383333333333.86166666666667
19113.1114.718333333333-1.61833333333334
20119.6114.6983333333334.90166666666666
21114.4119.258333333333-4.85833333333333
22114117.118333333333-3.11833333333333
23117.8117.4869405594410.313059440559436
24117115.6902272727271.30977272727272
25120.9119.4605011655011.43949883449885
26115117.020501165501-2.02050116550116
27117.3117.2005011655010.099498834498827
28119.4120.200501165501-0.800501165501166
29114.9115.060501165501-0.160501165501166
30125.8122.0605011655013.73949883449884
31117.6115.5405011655012.05949883449883
32117.6115.5205011655012.07949883449883
33114.9120.080501165501-5.18050116550117
34121.9117.9405011655013.95949883449884
35117117.666072261072-0.66607226107226
36106.4115.869358974359-9.46935897435897
37110.5119.639632867133-9.13963286713286
38113.6117.199632867133-3.59963286713287
39114.2117.379632867133-3.17963286713287
40125.4120.3796328671335.02036713286714
41124.6115.2396328671339.36036713286713
42120.2122.239632867133-2.03963286713286
43120.8115.7196328671335.08036713286713
44111.4115.699632867133-4.29963286713286
45124.1120.2596328671333.84036713286713
46120.2118.1196328671332.08036713286714
47125.5118.4882400932407.0117599067599
48116103.07509324009312.9249067599068
49117106.84536713286710.1546328671329
50105.7104.4053671328671.29463286713287
51102104.585367132867-2.58536713286713
52106.4107.585367132867-1.18536713286713
5396.9102.445367132867-5.54536713286713
54107.6109.445367132867-1.84536713286713
5598.8102.925367132867-4.12536713286713
56101.1102.905367132867-1.80536713286714
57105.7107.465367132867-1.76536713286713
58104.6105.325367132867-0.725367132867139
59103.2105.693974358974-2.49397435897436
60101.6103.897261072261-2.29726107226108


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
180.8949696615945630.2100606768108740.105030338405437
190.805878860511460.3882422789770780.194121139488539
200.7636357364086020.4727285271827970.236364263591398
210.7821030873587430.4357938252825140.217896912641257
220.6891832176441210.6216335647117570.310816782355879
230.6142766632336580.7714466735326830.385723336766342
240.5220667244682440.9558665510635120.477933275531756
250.4244041517031320.8488083034062640.575595848296868
260.3337628291278850.6675256582557690.666237170872116
270.2443570216840490.4887140433680980.755642978315951
280.1753182354260630.3506364708521260.824681764573937
290.1227589384408500.2455178768817010.87724106155915
300.08980194992376920.1796038998475380.91019805007623
310.05896758228271870.1179351645654370.941032417717281
320.03735097048549060.07470194097098130.96264902951451
330.03308467157652570.06616934315305150.966915328423474
340.02460993025783400.04921986051566790.975390069742166
350.01412921105199840.02825842210399670.985870788948002
360.0821350441424160.1642700882848320.917864955857584
370.4786648006879710.9573296013759430.521335199312029
380.5453203119016810.9093593761966370.454679688098319
390.5026001196861170.9947997606277660.497399880313883
400.4526687380908290.9053374761816580.547331261909171
410.687444369925920.6251112601481590.312555630074080
420.5941101596478310.8117796807043380.405889840352169


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.08NOK
10% type I error level40.16NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/10gt9u1261432421.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/1tf2g1261432421.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/1tf2g1261432421.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/2dgil1261432421.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/2dgil1261432421.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/38oct1261432421.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/4gixx1261432421.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/6guhx1261432421.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/7ey8r1261432421.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/8of6i1261432421.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/8of6i1261432421.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/92ip91261432421.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261432461mj0jttg90zz8f7k/92ip91261432421.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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