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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: Tue, 15 Dec 2009 12:02:02 -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/15/t1260904285tcfendpy3xdn1o1.htm/, Retrieved Tue, 15 Dec 2009 20:11:39 +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/Dec/15/t1260904285tcfendpy3xdn1o1.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 «
564 -0.9 581 -1 597 -0.7 587 -1.7 536 -1 524 -0.2 537 0.7 536 0.6 533 1.9 528 2.1 516 2.7 502 3.2 506 4.8 518 5.5 534 5.4 528 5.9 478 5.8 469 5.1 490 4.1 493 4.4 508 3.6 517 3.5 514 3.1 510 2.9 527 2.2 542 1.4 565 1.2 555 1.3 499 1.3 511 1.3 526 1.8 532 1.8 549 1.8 561 1.7 557 2.1 566 2 588 1.7 620 1.9 626 2.3 620 2.4 573 2.5 573 2.8 574 2.6 580 2.2 590 2.8 593 2.8 597 2.8 595 2.3 612 2.2 628 3 629 2.9 621 2.7 569 2.7 567 2.3 573 2.4 584 2.8 589 2.3 591 2 595 1.9 594 2.3
 
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
BouwV[t] = + 518.747264117247 -11.3910198062011X[t] + 19.2778823073052M1[t] + 37.7341697487835M2[t] + 49.0513552096416M3[t] + 38.1459775015075M4[t] -13.2255554531384M5[t] -17.1918311806524M6[t] -7.0746457197943M7[t] -3.38528065506023M8[t] + 5.01536599416992M9[t] + 6.76562907828386M10[t] + 3.93845533138997M11[t] + 1.76627572751399t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)518.74726411724710.65718948.675800
X-11.39101980620111.612509-7.064200
M119.277882307305212.3868121.55630.1264850.063243
M237.734169748783512.3593883.05310.0037580.001879
M349.051355209641612.3407713.97470.0002470.000123
M438.145977501507512.3315433.09340.003360.00168
M5-13.225555453138412.312201-1.07420.2883430.144172
M6-17.191831180652412.301295-1.39760.1689490.084474
M7-7.074645719794312.290025-0.57560.5676630.283832
M8-3.3852806550602312.281387-0.27560.7840570.392028
M95.0153659941699212.2737450.40860.6847110.342355
M106.7656290782838612.2701250.55140.5840350.292017
M113.9384553313899712.2666330.32110.7496110.374806
t1.766275727513990.14968911.799700


Multiple Linear Regression - Regression Statistics
Multiple R0.909497131849277
R-squared0.82718503284206
Adjusted R-squared0.778346020384382
F-TEST (value)16.9369729488052
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value2.36588526547621e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation19.3938442355615
Sum Squared Residuals17301.5749347282


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1564550.04333997764813.9566600223522
2581571.405005127269.59499487274032
3597581.07116037377115.9288396262285
4587583.3230781993523.6769218006476
5536525.7441071078810.2558928921202
6524514.4312912629199.56870873708105
7537516.0628346257120.9371653742900
8536522.65757739857813.3424226014218
9533518.01617402726114.9838259727391
10528519.2545088776498.7454911223514
11516511.3589989745484.64100102545195
12502503.491309467572-1.49130946757155
13506506.309835812469-0.309835812468962
14518518.55868511712-0.55868511712047
15534532.7812482861131.21875171388738
16528517.94663640239210.0533635976080
17478469.480481155888.51951884411976
18469475.254195020221-6.25419502022099
19490498.528676014794-8.52867601479417
20493500.567010865182-7.56701086518187
21508519.846749086887-11.8467490868869
22517524.502389879135-7.50238987913494
23514527.997899782235-13.9978997822355
24510528.1039241396-18.1039241395997
25527557.12179603876-30.1217960387597
26542586.457175052713-44.4571750527128
27565601.818840202325-36.8188402023251
28555591.540636241085-36.5406362410849
29499541.935379013953-42.935379013953
30511539.735379013953-28.7353790139531
31526545.923330299225-19.9233302992246
32532551.378971091473-19.3789710914726
33549561.545893468217-12.5458934682168
34561566.201534260465-5.20153426046479
35557560.584228318604-3.58422831860446
36566559.5511506953496.4488493046514
37588584.0126146720283.98738532797186
38620601.9569738797818.0430261202198
39626610.48402714567215.5159728543282
40620600.20582318443219.7941768155684
41573549.4614639766823.5385360233204
42573543.84415803481929.1558419651807
43574558.00582318443215.9941768155684
44580568.0178718991611.9821281008399
45590571.35018239218418.6498176078165
46593574.86672120381118.1332787961885
47597573.80582318443223.1941768155684
48595577.32915348365617.6708465163439
49612599.51241349909512.4875865009045
50628610.62216082312717.3778391768732
51629624.8447239921194.15527600788097
52621617.9838259727393.01617402726085
53569568.3785687456070.621431254392733
54567570.734976668088-3.73497666808771
55573581.47933587584-8.47933587583966
56584582.3785687456071.62143125439271
57589598.241001025452-9.24100102545196
58591605.17484577894-14.1748457789402
59595605.25304974018-10.2530497401804
60594598.524462213824-4.52446221382403


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.002418959017233110.004837918034466210.997581040982767
180.0007255558813377320.001451111762675460.999274444118662
190.0002174012744920830.0004348025489841670.999782598725508
200.0001161462455523120.0002322924911046240.999883853754448
210.0001572079537109940.0003144159074219880.99984279204629
220.0005665519758261480.001133103951652300.999433448024174
230.000525689411550960.001051378823101920.99947431058845
240.0009604939074498710.001920987814899740.99903950609255
250.00277364802855690.00554729605711380.997226351971443
260.005840700664533060.01168140132906610.994159299335467
270.002644914197892700.005289828395785390.997355085802107
280.001435218127839540.002870436255679080.99856478187216
290.002432479528491150.00486495905698230.997567520471509
300.007697618012550420.01539523602510080.99230238198745
310.02195334991753370.04390669983506730.978046650082466
320.09517933495196920.1903586699039380.904820665048031
330.2864842867170760.5729685734341520.713515713282924
340.5220789305094510.9558421389810990.477921069490549
350.9379553411276960.1240893177446070.0620446588723037
360.9988933395864270.002213320827146790.00110666041357340
370.9999998475156633.04968674122329e-071.52484337061164e-07
380.9999998824844082.35031184252051e-071.17515592126026e-07
390.9999994096711681.18065766486405e-065.90328832432025e-07
400.9999960289552687.9420894632852e-063.9710447316426e-06
410.999991982461261.60350774780667e-058.01753873903334e-06
420.9999957630992048.47380159274221e-064.23690079637111e-06
430.9999122512874060.0001754974251884438.77487125942217e-05


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level200.740740740740741NOK
5% type I error level230.851851851851852NOK
10% type I error level230.851851851851852NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/107v891260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/107v891260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/1k7uw1260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/1k7uw1260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/2xwam1260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/2xwam1260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/3030x1260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/3030x1260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/4twxs1260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/4twxs1260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/52qk31260903717.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/6eh071260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/6eh071260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/7hdnw1260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/7hdnw1260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/8ct061260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/8ct061260903717.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/9seeo1260903717.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/15/t1260904285tcfendpy3xdn1o1/9seeo1260903717.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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