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Model3

*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 15:56:26 -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/21/t12587581278cjlr067uouaqyt.htm/, Retrieved Sat, 21 Nov 2009 00:02:19 +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/21/t12587581278cjlr067uouaqyt.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 «
562 13.9 561 15.9 555 18.2 544 19.7 537 20.1 543 19.9 594 20 611 22.6 613 20.6 611 20.1 594 20.2 595 21.8 591 22 589 19.5 584 17.5 573 18.2 567 18.8 569 19.7 621 18.8 629 18.5 628 18.7 612 18.5 595 19.3 597 18.9 593 21.4 590 22.5 580 25 574 22.9 573 22.9 573 21.3 620 22.3 626 20.9 620 19.9 588 20.2 566 19.8 557 17.7 561 18.1 549 17.6 532 18.2 526 16 511 16.3 499 17.3 555 19 565 18.6 542 18 527 17.9 510 17.8 514 18.5 517 17.4 508 19 493 17.4 490 20.6 469 18.5 478 20 528 18.8 534 18.8 518 19.7 506 15.3 502 10.6 516 6.1 528 0.9
 
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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 582.265639057551 + 1.75858938712907X[t] -3.13436250319707M1[t] -15.9053730581449M2[t] -25.5924034907366M3[t] -31.8332314091302M4[t] -40.0057953604147M5[t] -38.0224822175212M6[t] + 14.4773770150556M7[t] + 25.2475798231175M8[t] + 18.8729362634568M9[t] + 6.74241560961807M10[t] -5.59913577067612M11[t] -1.54606174677481t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)582.26563905755124.04439124.216300
X1.758589387129071.043191.68580.0984670.049234
M1-3.1343625031970715.126943-0.20720.8367460.418373
M2-15.905373058144915.88376-1.00140.321780.16089
M3-25.592403490736615.915677-1.6080.1145330.057267
M4-31.833231409130215.940638-1.9970.0516360.025818
M5-40.005795360414715.912614-2.51410.0154170.007708
M6-38.022482217521215.9634-2.38190.0213260.010663
M714.477377015055615.9917560.90530.3699230.184961
M825.247579823117516.0173041.57630.1216720.060836
M918.872936263456815.9309751.18470.2421040.121052
M106.7424156096180715.7963480.42680.6714490.335725
M11-5.5991357706761215.725664-0.35610.7233960.361698
t-1.546061746774810.200869-7.696900


Multiple Linear Regression - Regression Statistics
Multiple R0.850876194482518
R-squared0.723990298337052
Adjusted R-squared0.647647189366449
F-TEST (value)9.48337457170938
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value3.27576876735236e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation24.8221773982055
Sum Squared Residuals28958.6030670352


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1562602.029607288672-40.0296072886724
2561591.229713761208-30.2297137612081
3555584.041377172239-29.0413771722385
4544578.892371587764-34.8923715877638
5537569.877181644556-32.877181644556
6543569.962715163249-26.9627151632489
7594621.092371587764-27.0923715877637
8611634.888845055586-23.8888450555864
9613623.450960974893-10.4509609748928
10611608.8950838807152.10491611928523
11594595.183329692359-1.18332969235863
12595602.050146735666-7.05014673566647
13591597.72144036312-6.72144036312042
14589579.0078945935759.99210540642488
15584564.25762363995119.7423763600495
16573557.70174654577215.2982534542275
17567549.0382744799917.9617255200094
18569551.05825632452517.9417436754746
19621600.42932336191120.5706766380888
20629609.1258876070619.8741123929404
21628601.5569001780526.4430998219501
22612587.52859990001124.4714000999894
23595575.04785828264519.9521417173552
24597578.39749655169518.6025034483055
25593578.11354576954514.8864542304547
26590565.73092179366524.2690782063354
27580558.89430308212121.1056969178792
28574547.41437570398126.5856242960186
29573537.69575000592235.3042499940779
30573535.31925838263437.6807416173657
31620588.03164525556531.9683547444348
32626594.79376117487231.2062388251283
33620585.11446648130734.8855335186929
34588571.96546089683216.0345391031677
35566557.3744120149128.62558798508829
36557557.734448325842-0.734448325841977
37561553.7574598307227.24254016927827
38549538.56109283543510.4389071645655
39532528.3831542883463.61684571165448
40526516.7273679714939.27263202850682
41511507.5363190895733.46368091042744
42499509.73215987282-10.7321598728203
43555563.675559316742-8.67555931674166
44565572.196264623177-7.19626462317713
45542563.220405684464-21.2204056844642
46527549.367964345138-22.3679643451378
47510535.304492279356-25.3044922793559
48514540.588578874248-26.5885788742476
49517533.973706298434-16.9737062984337
50508522.470377016118-14.4703770161176
51493508.423541817345-15.4235418173446
52490506.264138190989-16.2641381909892
53469492.852474779959-23.8524747799588
54478495.927610256771-17.9276102567711
55528544.771100478018-16.7711004780182
56534553.995241539305-19.9952415393053
57518547.657266681286-29.6572666812860
58506526.242890977305-20.2428909773046
59502504.089907730729-2.08990773072896
60516500.2293295125515.7706704874505
61528486.40424044950641.5957595504935


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
176.29250140119729e-050.0001258500280239460.999937074985988
186.60327958204104e-050.0001320655916408210.99993396720418
198.0168944908761e-061.60337889817522e-050.99999198310551
200.0002494547994328160.0004989095988656320.999750545200567
210.0007581975025070310.001516395005014060.999241802497493
220.01901896518256510.03803793036513030.980981034817435
230.04417704304979850.0883540860995970.955822956950201
240.04487559654274850.0897511930854970.955124403457251
250.05688125607964350.1137625121592870.943118743920357
260.05113679891444670.1022735978288930.948863201085553
270.0525122071180050.105024414236010.947487792881995
280.03414728907914980.06829457815829960.96585271092085
290.0363186938065740.0726373876131480.963681306193426
300.03883932572905560.07767865145811110.961160674270944
310.04724819934595070.09449639869190140.95275180065405
320.0725139975505450.1450279951010900.927486002449455
330.3452381793831690.6904763587663390.65476182061683
340.8885138564232470.2229722871535060.111486143576753
350.993928199317540.01214360136492060.00607180068246028
360.997287480805540.00542503838892170.00271251919446085
370.9990750015920980.001849996815803710.000924998407901855
380.9991031085206280.00179378295874310.00089689147937155
390.9997148580932250.0005702838135497080.000285141906774854
400.9989823973778220.002035205244356370.00101760262217819
410.999585779284940.000828441430120130.000414220715060065
420.9998314678945930.0003370642108133160.000168532105406658
430.9990866229864170.001826754027165510.000913377013582753
440.998987115601890.002025768796220520.00101288439811026


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.5NOK
5% type I error level160.571428571428571NOK
10% type I error level220.785714285714286NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/10yyeo1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/10yyeo1258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/1xkpi1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/1xkpi1258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/2i9g11258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/2i9g11258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/32zkn1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/32zkn1258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/4ryyg1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/4ryyg1258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/5hwzj1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/5hwzj1258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/6a6e71258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/6a6e71258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/7re7u1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/7re7u1258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/897881258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/897881258757781.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/98fao1258757781.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t12587581278cjlr067uouaqyt/98fao1258757781.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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