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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: Fri, 20 Nov 2009 07:00:11 -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/t125872574307bpfiu7s1fvuea.htm/, Retrieved Fri, 20 Nov 2009 15:02:39 +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/t125872574307bpfiu7s1fvuea.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 «
1318 1427 1081 831 557 280 1578 934 1318 1081 831 557 1859 709 1578 1318 1081 831 2141 1186 1859 1578 1318 1081 2428 986 2141 1859 1578 1318 2715 1033 2428 2141 1859 1578 3004 1257 2715 2428 2141 1859 3309 1105 3004 2715 2428 2141 269 1179 3309 3004 2715 2428 537 1092 269 3309 3004 2715 813 1092 537 269 3309 3004 1068 1087 813 537 269 3309 1411 2028 1068 813 537 269 1675 2039 1411 1068 813 537 1958 2010 1675 1411 1068 813 2242 754 1958 1675 1411 1068 2524 760 2242 1958 1675 1411 2836 715 2524 2242 1958 1675 3143 855 2836 2524 2242 1958 3522 971 3143 2836 2524 2242 285 815 3522 3143 2836 2524 574 915 285 3522 3143 2836 865 843 574 285 3522 3143 1147 761 865 574 285 3522 1516 1858 1147 865 574 285 1789 2968 1516 1147 865 574 2087 4061 1789 1516 1147 865 2372 3661 2087 1789 1516 1147 2669 3269 2372 2087 1789 1516 2966 2857 2669 2372 2087 1789 3270 2568 2966 2669 2372 2087 3652 2274 3270 2966 2669 2372 329 1987 3652 3270 2966 2669 658 683 329 3652 3270 2966 988 381 658 329 3652 3 etc...
 
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] = + 633.895997338495 + 0.00669906119430542X[t] + 0.656397458381625Y1[t] -0.0466774298093399Y2[t] -0.0549640904534444Y3[t] -0.0357103741220868Y4[t] + 37.8694134566582M1[t] + 156.142482881967M2[t] + 295.305233485109M3[t] + 437.323832062408M4[t] + 588.831879163271M5[t] + 736.098639832787M6[t] + 890.325206224805M7[t] + 1078.14615314873M8[t] -2425.28631966955M9[t] + 83.7658990470096M10[t] + 65.1693704083077M11[t] + 4.86711279747431t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)633.895997338495540.0000711.17390.2477470.123874
X0.006699061194305420.011080.60460.5490360.274518
Y10.6563974583816250.1635114.01440.0002710.000135
Y2-0.04667742980933990.194883-0.23950.8119930.405996
Y3-0.05496409045344440.194595-0.28250.7791280.389564
Y4-0.03571037412208680.15857-0.22520.8230280.411514
M137.8694134566582552.3992220.06860.9457040.472852
M2156.142482881967541.0251960.28860.7744520.387226
M3295.305233485109531.1791770.55590.5815090.290754
M4437.323832062408533.5460230.81970.4175240.208762
M5588.831879163271533.3963651.10390.2765650.138283
M6736.098639832787541.3975551.35960.1819620.090981
M7890.325206224805552.0743841.61270.1150870.057544
M81078.14615314873568.472641.89660.0655060.032753
M9-2425.28631966955586.559103-4.13480.0001899.4e-05
M1083.7658990470096706.0110760.11860.906180.45309
M1165.1693704083077704.1916040.09250.9267510.463376
t4.867112797474311.5344783.17180.0029940.001497


Multiple Linear Regression - Regression Statistics
Multiple R0.998836388403883
R-squared0.997674130799712
Adjusted R-squared0.996633610368004
F-TEST (value)958.82223971542
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation61.0872216019478
Sum Squared Residuals141802.648435728


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
113181316.354889119121.64511088087917
215781555.1373399411622.8626600588374
318591833.7350377646625.2649622353445
421412134.173672415936.82632758406626
524282438.44272337777-10.4427233777739
627152741.38488138103-26.3848813810282
730043051.43430984211-47.4343098421122
833093393.56153591642-84.5615359164223
926956.1797826823087212.820217317691
10537533.6979067863673.30209321363307
11813810.6980507022262.30194929777444
1210681075.21761598108-7.21761598107972
1314111372.5855011686138.4144988313882
1416751684.30048745818-9.3004874581777
1519581961.54274234898-3.54274234898012
1622422245.49324368938-3.49324368937669
1725242548.35658529563-24.3565852956338
1828362847.05431784009-11.0543178400900
1931433173.00299984029-30.0029998402896
2035223527.77719252433-5.77719252433067
21285235.39232300847649.607676991524
22574579.516629467582-5.51662946758245
23865874.304111848152-9.30411184815186
2411471155.35894339907-8.35894339906818
2515161476.6751498646039.3248501353964
2617891809.98406850642-20.9840685064161
2720872097.41694795355-10.4169479535464
2823722394.13446423062-22.1344642306232
2926692692.86466895153-23.8646689515327
3029662997.75727575969-31.7572757596936
3132703309.69531748239-39.6953174823864
3236523659.59369241783-7.59369241783452
33329368.729276295068-39.7292762950684
34658647.55843501031410.4415649896860
35988971.01752946606716.9824705339327
3613031278.8971594058224.1028405941785
3716031624.97282375311-21.9728237531087
3819291911.9174819904817.0825180095211
3922352238.19318371312-3.19318371312122
4025442538.278939291935.72106070806572
4128722849.8969689316622.1030310683432
4231983169.6554605402528.3445394597490
4335443495.6411783829148.3588216170918
4439033867.2375394541935.7624605458114
45332554.698618014147-222.698618014147
46665673.227028735737-8.2270287357366
4710011010.98030798356-9.9803079835553
4813291337.52628121403-8.52628121403101
4916391696.41163609455-57.411636094555
5019751984.66062210376-9.66062210376465
5123042312.11208821970-8.11208821969641
5226402626.9196803721313.0803196278679
5329922955.439053443436.5609465565971
5433303289.1480644789440.8519355210629
5536903621.2261944523068.7738055476964
5640634000.8300396872262.1699603127762


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.6882041933489660.6235916133020680.311795806651034
220.658509719236460.682980561527080.34149028076354
230.5257044411239290.9485911177521420.474295558876071
240.4658828980696050.931765796139210.534117101930395
250.5034153997904670.9931692004190670.496584600209533
260.375371348148420.750742696296840.62462865185158
270.3259854261426050.651970852285210.674014573857395
280.2255908434391610.4511816868783230.774409156560839
290.161773924766590.323547849533180.83822607523341
300.09650170371003770.1930034074200750.903498296289962
310.08721395158371480.1744279031674300.912786048416285
320.2619427912661430.5238855825322870.738057208733857
330.9999864247807772.71504384454100e-051.35752192227050e-05
340.9998723636941890.0002552726116221190.000127636305811059
350.9994419403409650.001116119318069260.000558059659034632


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.2NOK
5% type I error level30.2NOK
10% type I error level30.2NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/10bcky1258725607.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/10bcky1258725607.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/1zxdm1258725607.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/1zxdm1258725607.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/2htco1258725607.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/2htco1258725607.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/34y561258725607.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/34y561258725607.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/42krk1258725607.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/5h3nd1258725607.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/64asl1258725607.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/7ejhd1258725607.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/89jx71258725607.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/89jx71258725607.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/9z6ta1258725607.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t125872574307bpfiu7s1fvuea/9z6ta1258725607.ps (open in new window)


 
Parameters (Session):
 
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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Software written by Ed van Stee & Patrick Wessa


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