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WS7

*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, 23 Nov 2009 01:30:59 -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/23/t12589651132xjd6q97i1845j3.htm/, Retrieved Mon, 23 Nov 2009 09:32:06 +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/23/t12589651132xjd6q97i1845j3.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 «
286602 326011 283042 328282 276687 317480 277915 317539 277128 313737 277103 312276 275037 309391 270150 302950 267140 300316 264993 304035 287259 333476 291186 337698 292300 335932 288186 323931 281477 313927 282656 314485 280190 313218 280408 309664 276836 302963 275216 298989 274352 298423 271311 301631 289802 329765 290726 335083 292300 327616 278506 309119 269826 295916 265861 291413 269034 291542 264176 284678 255198 276475 253353 272566 246057 264981 235372 263290 258556 296806 260993 303598 254663 286994 250643 276427 243422 266424 247105 267153 248541 268381 245039 262522 237080 255542 237085 253158 225554 243803 226839 250741 247934 280445 248333 285257 246969 270976 245098 261076 246263 255603 255765 260376 264319 263903 268347 264291 273046 263276 273963 262572 267430 256167 271993 264221 292710 293860 295881 300713 293299 287224
 
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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = -225475.408018723 + 1.46214500504937X[t] + 16420.7919349884M1[t] + 23028.7163256820M2[t] + 30661.1473651015M3[t] + 31235.5640239155M4[t] + 31993.2453135483M5[t] + 34960.6704055155M6[t] + 37647.041692M7[t] + 39974.3973820299M8[t] + 40611.7071382829M9[t] + 31413.0352303011M10[t] + 7293.95281682754M11[t] + 1278.41807555408t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-225475.40801872324007.470271-9.391900
X1.462145005049370.06722821.749100
M116420.79193498843124.5517655.25544e-062e-06
M223028.71632568203561.6277516.465800
M330661.14736510153864.5929087.933900
M431235.56402391553803.9634068.211300
M531993.24531354833758.6409788.511900
M634960.67040551553842.6772849.09800
M737647.0416924000.4974499.410600
M839974.39738202994096.5825649.75800
M940611.70713828294279.0178399.490900
M1031413.03523030114047.4140217.761300
M117293.952816827543168.8377572.30180.0258260.012913
t1278.4180755540887.51179614.608500


Multiple Linear Regression - Regression Statistics
Multiple R0.970362601330797
R-squared0.941603578061471
Adjusted R-squared0.925451376248687
F-TEST (value)58.2956793739531
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4957.90285228592
Sum Squared Residuals1155297632.55713


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1286602268899.15723296917702.8427670306
2283042280106.0310056852935.968994315
3276687273222.7897761153464.21022388462
4277915275161.8910657812753.10893421868
5277128271638.9151217705489.08487822956
6277103273748.5644369153354.43556308533
7275037273495.0654593861541.93454061418
8270150267683.1632474472466.83675255327
9267140265747.6011359541392.39886404620
10264993263265.0645773051727.93542269529
11287259283471.4113330443787.58866695619
12291186283629.0528030897556.9471969112
13292300298746.114734714-6446.11473471408
14288186289085.254995364-899.254995364174
15281477283368.805479824-1891.80547982388
16282656286037.517127009-3381.51712700947
17280190286221.078770799-6031.07877079874
18280408285270.458590375-4862.45859037459
19276836279437.414273577-2601.41427357734
20275216277232.623789095-2016.62378909508
21274352278320.777548044-3968.77754804426
22271311275091.084891815-3780.08489181489
23289802293386.408125954-3584.40812595447
24290726295146.560521534-4420.56052153358
25292300301927.933779372-9627.9337793724
26278506282768.980087222-4262.98008722176
27269826272375.128700529-2549.12870052852
28265861267643.924477159-1782.92447715923
29269034269868.640547997-834.640547997416
30264176264078.3204008697.6795991401582
31255198256049.134286478-851.134286478446
32253353253939.383227324-586.38322732438
33246057244764.7411958321292.25880416799
34235372234372.000159866999.999840134242
35258556260536.587811181-1980.58781118108
36260993264451.941944203-3458.94194420296
37254663257873.696290906-3210.69629090564
38250643250309.552488797333.447511203453
39243422244594.565118261-1172.56511826129
40247105247513.303561310-408.303561310337
41248541251344.916992698-2803.91699269779
42245039247024.052575635-1985.05257563483
43237080240783.069802429-3703.06980242881
44237085240903.089875975-3818.08987597506
45225554229140.451185545-3586.45118554529
46226839231364.55939815-4525.55939815009
47247934251955.450290217-4021.45029021719
48248333252975.757313241-4642.7573132413
49246969249794.074506674-2825.07450667369
50245098243205.1814229331892.81857706748
51246263244113.7109252712149.28907472906
52255765252945.3637687402819.63623126036
53264319260138.4485667364180.55143326438
54268347264951.6039962163395.39600378393
55273046267432.3161781305613.68382187043
56273963270008.7398601593954.26013984125
57267430262559.4289346254870.57106537536
58271993266415.2909728655577.70902713545
59292710286911.1424396035798.85756039656
60295881290915.6874179334965.31258206665
61293299288892.0234553654406.97654463518


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.04174758449478720.08349516898957450.958252415505213
180.01932127810110570.03864255620221140.980678721898894
190.01858526024489140.03717052048978280.981414739755109
200.009764230464700190.01952846092940040.9902357695353
210.01985911325748780.03971822651497550.980140886742512
220.01354192748729130.02708385497458250.986458072512709
230.00931991265480010.01863982530960020.9906800873452
240.04020919498504020.08041838997008040.95979080501496
250.1219109017024470.2438218034048950.878089098297553
260.678547480696990.6429050386060190.321452519303010
270.8259316574466170.3481366851067650.174068342553383
280.9060511492649260.1878977014701480.0939488507350738
290.9018744627674960.1962510744650080.0981255372325042
300.8638990808571740.2722018382856520.136100919142826
310.869786106972740.2604277860545190.130213893027260
320.840649160304850.3187016793902990.159350839695150
330.8379190477129210.3241619045741580.162080952287079
340.993269102458920.01346179508215910.00673089754107956
350.9965794515974590.006841096805082420.00342054840254121
360.9977469198953840.004506160209232940.00225308010461647
370.9991190488175950.001761902364809890.000880951182404943
380.9978367777886170.004326444422766080.00216322221138304
390.9942002119337120.01159957613257670.00579978806628837
400.9937272158663760.01254556826724850.00627278413362423
410.9861670352305240.02766592953895270.0138329647694764
420.9859861699875990.02802766002480230.0140138300124011
430.9614757926436250.07704841471275090.0385242073563754
440.9374433332725730.1251133334548540.0625566667274269


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.142857142857143NOK
5% type I error level150.535714285714286NOK
10% type I error level180.642857142857143NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/104sjq1258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/104sjq1258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/1ernp1258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/1ernp1258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/22lha1258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/22lha1258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/3ovo11258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/3ovo11258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/4ypof1258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/4ypof1258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/5xbzl1258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/5xbzl1258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/6ool51258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/6ool51258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/7qyo01258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/7qyo01258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/8xrf01258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/8xrf01258965052.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/94a401258965052.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/23/t12589651132xjd6q97i1845j3/94a401258965052.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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