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Multiple Regression zonder LT-trend

*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, 18 Dec 2009 10:57:07 -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/18/t1261159121tww3jzxwwbzebk3.htm/, Retrieved Fri, 18 Dec 2009 18:58:53 +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/18/t1261159121tww3jzxwwbzebk3.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 «
113 14.3 110 14.2 107 15.9 103 15.3 98 15.5 98 15.1 137 15 148 12.1 147 15.8 139 16.9 130 15.1 128 13.7 127 14.8 123 14.7 118 16 114 15.4 108 15 111 15.5 151 15.1 159 11.7 158 16.3 148 16.7 138 15 137 14.9 136 14.6 133 15.3 126 17.9 120 16.4 114 15.4 116 17.9 153 15.9 162 13.9 161 17.8 149 17.9 139 17.4 135 16.7 130 16 127 16.6 122 19.1 117 17.8 112 17.2 113 18.6 149 16.3 157 15.1 157 19.2 147 17.7 137 19.1 132 18 125 17.5 123 17.8 117 21.1 114 17.2 111 19.4 112 19.8 144 17.6 150 16.2 149 19.5 134 19.9 123 20 116 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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
WK<25j[t] = + 165.733743201702 -2.98888626152753ExpBE[t] -1.75138330574603M1[t] -4.24913691179949M2[t] -2.96911799479788M3[t] -12.4262000472925M4[t] -17.5217309056515M5[t] -13.8261527547884M6[t] + 18.4547647197919M7[t] + 20.0043509103807M8[t] + 30.5861432962875M9[t] + 19.5503901631591M10[t] + 7.7213052731142M11[t] + 0.334641759281152t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)165.73374320170218.8009648.815200
ExpBE-2.988886261527531.403729-2.12920.0386180.019309
M1-1.751383305746034.264698-0.41070.6832210.341611
M2-4.249136911799494.287849-0.9910.3268840.163442
M3-2.969117994797885.61351-0.52890.5994020.299701
M4-12.42620004729254.444025-2.79620.0075220.003761
M5-17.52173090565154.438739-3.94750.0002680.000134
M6-13.82615275478844.891554-2.82650.0069410.003471
M718.45476471979194.2410274.35157.5e-053.7e-05
M820.00435091038075.0626323.95140.0002650.000133
M930.58614329628754.951766.176800
M1019.55039016315914.9635753.93880.0002760.000138
M117.72130527311424.5846881.68420.0989270.049464
t0.3346417592811520.1260682.65450.0108730.005437


Multiple Linear Regression - Regression Statistics
Multiple R0.939979664256332
R-squared0.883561769215446
Adjusted R-squared0.850655312689376
F-TEST (value)26.8507114558341
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.666554877216
Sum Squared Residuals2044.37588082289


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1113121.575928115394-8.57592811539369
2110119.711704894774-9.7117048947742
3107116.245258926460-9.24525892646015
4103108.916150390163-5.91615039016317
598103.557484038780-5.55748403877987
698108.783258453535-10.7832584535351
7137141.697706313549-4.69770631354935
8148152.249704421849-4.24970442184912
9147152.107259399385-5.10725939938521
10139138.1183731378580.881626862142338
11130132.003925277843-2.00392527784344
12128128.801702530149-0.801702530148966
13127124.0971860960042.90281390399620
14123122.2329628753840.767037124615754
15118119.962071411681-1.96207141168123
16114112.6329628753841.36703712461575
17108109.067628280917-1.06762828091747
18111111.603405060298-0.603405060297926
19151145.4145187987705.58548120122961
20159157.4609600378341.53903996216601
21158154.6285173799953.37148262000474
22148142.7318515015375.26814849846299
23138136.318515015371.68148498462995
24137129.2307401276907.76925987231025
25136128.7106644596837.28933554031686
26133124.4553322298428.54466777015844
27126118.2988886261537.70111137384724
28120113.6597777252316.34022227476945
29114111.8877748876802.11222511231972
30116108.4457791440067.55422085599431
31153147.0391109009225.9608890990778
32162154.9011113738477.09888862615275
33161154.1608890990786.83911090092221
34149143.1608890990785.8391109009222
35139133.1608890990785.8391109009222
36135127.8664459683147.13355403168597
37130128.5419248049181.45807519508158
38127124.5854812012302.4145187987704
39122118.7279262236943.27207377630646
40117113.4910380704663.50896192953416
41112110.5234807283051.47651927169544
42113110.3692598723102.63074012768976
43149149.859257507685-0.859257507685013
44157155.3301489713881.66985102861196
45157153.9921494443133.00785055568692
46147147.774367462757-0.774367462757131
47137132.0954835658554.90451643414517
48132127.9965949397024.00340506029793
49125128.074296524001-3.07429652400096
50123125.014518798770-2.01451879877039
51117116.7658548120120.234145187987687
52114119.300070938756-5.30007093875619
53111107.9636320643183.03636793568217
54112110.7982974698511.20170253014896
55144149.989406479073-5.98940647907305
56150156.058075195082-6.05807519508159
57149157.111184677229-8.11118467722866
58134145.214518798770-11.2145187987704
59123133.421187041854-10.4211870418539
60116134.104516434145-18.1045164341452


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.005895578652583690.01179115730516740.994104421347416
180.001112661029640240.002225322059280480.99888733897036
190.003497892064427850.006995784128855710.996502107935572
200.001010013200579030.002020026401158050.998989986799421
210.001672112384841810.003344224769683630.998327887615158
220.002026151775340280.004052303550680560.99797384822466
230.003744224692350830.007488449384701660.99625577530765
240.01336306450716580.02672612901433160.986636935492834
250.006215464247123660.01243092849424730.993784535752876
260.002700447198562790.005400894397125580.997299552801437
270.003078731716396560.006157463432793120.996921268283604
280.009235834672868240.01847166934573650.990764165327132
290.02654226717467580.05308453434935160.973457732825324
300.03101610315224740.06203220630449480.968983896847753
310.07609515744818190.1521903148963640.923904842551818
320.07528066074267730.1505613214853550.924719339257323
330.06976092391166240.1395218478233250.930239076088338
340.1498036500762960.2996073001525920.850196349923704
350.1346259960499970.2692519920999930.865374003950003
360.1387116744728090.2774233489456190.861288325527191
370.2817764399728040.5635528799456090.718223560027196
380.3087224289130630.6174448578261250.691277571086937
390.2458447740738290.4916895481476570.754155225926171
400.3643775028594510.7287550057189030.635622497140549
410.3448114883285740.6896229766571480.655188511671426
420.5131266005021590.9737467989956820.486873399497841
430.6192034622066980.7615930755866040.380796537793302


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level80.296296296296296NOK
5% type I error level120.444444444444444NOK
10% type I error level140.518518518518518NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/10s8i91261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/10s8i91261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/1p6mo1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/1p6mo1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/2w9dt1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/2w9dt1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/33bty1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/33bty1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/4cuni1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/4cuni1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/5t4xu1261159021.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/6r0mh1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/6r0mh1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/7jehp1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/7jehp1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/8aeuq1261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/8aeuq1261159021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/9epo41261159021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/18/t1261159121tww3jzxwwbzebk3/9epo41261159021.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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