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shw-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: Fri, 20 Nov 2009 05:24:28 -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/t1258720091oudhlwqjrfn36ja.htm/, Retrieved Fri, 20 Nov 2009 13:28:24 +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/t1258720091oudhlwqjrfn36ja.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:
Workshop 7 Model 3
 
Dataseries X:
» Textbox « » Textfile « » CSV «
2529 314 2196 318 3202 320 2718 323 2728 325 2354 327 2697 330 2651 331 2067 332 2641 334 2539 334 2294 334 2712 339 2314 345 3092 346 2677 352 2813 355 2668 358 2939 361 2617 363 2231 364 2481 365 2421 366 2408 370 2560 371 2100 371 3315 372 2801 373 2403 373 3024 374 2507 375 2980 375 2211 376 2471 376 2594 377 2452 377 2232 378 2373 379 3127 380 2802 384 2641 389 2787 390 2619 391 2806 392 2193 393 2323 394 2529 394 2412 395 2262 396 2154 397 3230 398 2295 399 2715 400 2733 400 2317 401 2730 401 1913 406 2390 407 2484 423 1960 427
 
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] = + 1219.03242808287 + 3.60792597062968X[t] + 141.869234895728M1[t] -90.4173137531013M2[t] + 879.025648762825M3[t] + 341.574344531617M4[t] + 343.009381076913M5[t] + 399.130758398712M6[t] + 303.20896533226M7[t] + 449.295098236438M8[t] -183.026694830014M9[t] + 159.537852880037M10[t] + 206.721793066452M11[t] -7.97247368068132t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1219.032428082871238.8751090.9840.3302710.165136
X3.607925970629683.8076620.94750.3483130.174157
M1141.869234895728105.9164841.33940.1870070.093503
M2-90.4173137531013105.36043-0.85820.3952470.197624
M3879.025648762825105.3770428.341700
M4341.574344531617104.7180853.26180.0020890.001045
M5343.009381076913104.460643.28360.0019630.000981
M6399.130758398712104.3933183.82330.0003940.000197
M7303.20896533226104.2654552.9080.0055820.002791
M8449.295098236438104.3658284.3058.7e-054.3e-05
M9-183.026694830014104.250564-1.75560.0858070.042903
M10159.537852880037104.3684331.52860.1332110.066605
M11206.721793066452103.9859341.9880.0527850.026392
t-7.972473680681326.056208-1.31640.1945570.097279


Multiple Linear Regression - Regression Statistics
Multiple R0.88502400689593
R-squared0.783267492782127
Adjusted R-squared0.722017001611859
F-TEST (value)12.7879381506467
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value3.25499627251702e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation164.397756950770
Sum Squared Residuals1243224.63456045


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
125292485.8179440756443.182055924359
221962259.99062562865-63.9906256286457
332023228.67696640515-26.6769664051491
427182694.0769664051523.92303359485
527282694.7553812110233.2446187889761
623542750.1201367934-396.120136793402
726972657.0496479581639.950352041843
826512798.77123315228-147.771233152283
920672162.08489237578-95.084892375779
1026412503.89281834641137.107181653591
1125392543.10428485214-4.10428485214211
1222942328.41001810501-34.4100181050085
1327122480.34640917320231.653590826796
1423142261.7349426674752.2650573325285
1530923226.81335747335-134.813357473346
1626772703.03713538523-26.0371353852344
1728132707.32347616174105.676523838262
1826682766.29615771475-98.2961577147456
1929392673.2256688795265.774331120499
2026172818.55518004426-201.555180044257
2122312181.8688392677549.1311607322468
2224812520.06883926775-39.0688392677533
2324212562.88823174412-141.888231744116
2424082362.625668879545.3743311204986
2525602500.1303560651859.8696439348223
2621002259.87133373567-159.871333735667
2733153224.9497485415490.0502514584587
2828012683.13389660028117.866103399718
2924032676.59645946490-273.596459464896
3030242728.35328907664295.646710923355
3125072628.06694830014-121.066948300141
3229802766.18060752364213.819392476363
3322112129.4942667471381.5057332528665
3424712464.086340776506.9136592234963
3525942506.9057332528787.0942667471334
3624522292.21146650573159.788533494267
3722322429.71615369141-197.716153691409
3823732193.06505733253179.934942667471
3931273158.1434721384-31.1434721384029
4028022627.15139810903174.848601890968
4126412638.653590826802.34640917320456
4227872690.4104204385496.5895795614564
4326192590.1240796620428.8759203379601
4428062731.8456648561774.1543351438341
4521932095.1593240796697.840675920338
4623232433.35932407966-110.359324079662
4725292472.5707905854056.4292094146048
4824122261.48444980889150.515550191108
4922622398.98913699457-136.989136994568
5021542162.33804063569-8.338040635687
5132303127.41645544156102.583544558439
5222952585.6006035003-290.600603500302
5327152582.67109233555132.328907664454
5427332630.81999597666102.180004023336
5523172530.53365520016-213.533655200161
5627302668.6473144236661.352685576343
5719132046.39267752967-133.392677529672
5823902384.592677529675.407322470328
5924842481.530959565482.46904043451999
6019602281.26839670087-321.268396700865


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2071569933909450.4143139867818910.792843006609055
180.2716578183982310.5433156367964630.728342181601769
190.2050386523272960.4100773046545920.794961347672704
200.2721013427884800.5442026855769610.72789865721152
210.1722538503210080.3445077006420170.827746149678992
220.2433787757211280.4867575514422560.756621224278872
230.289262924815790.578525849631580.71073707518421
240.2049076965836170.4098153931672350.795092303416383
250.2075546499555120.4151092999110240.792445350044488
260.2425059235796270.4850118471592530.757494076420373
270.2266667412547220.4533334825094440.773333258745278
280.182988082714420.365976165428840.81701191728558
290.5626671346315990.8746657307368030.437332865368401
300.8567525562013630.2864948875972750.143247443798637
310.8766010594243750.2467978811512500.123398940575625
320.8790614203444760.2418771593110470.120938579655524
330.8173204708766780.3653590582466440.182679529123322
340.756067025702070.487865948595860.24393297429793
350.7070564029456140.5858871941087710.292943597054386
360.6069214115576870.7861571768846260.393078588442313
370.6649268864260220.6701462271479570.335073113573978
380.5761963257615790.8476073484768420.423803674238421
390.5884049602701170.8231900794597660.411595039729883
400.7242148018140220.5515703963719570.275785198185979
410.6753171127767420.6493657744465160.324682887223258
420.5406771831150280.9186456337699440.459322816884972
430.4838893164785530.9677786329571070.516110683521447


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/10hjwu1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/10hjwu1258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/1mz9d1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/1mz9d1258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/2fr071258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/2fr071258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/3ue351258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/3ue351258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/4s5nn1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/4s5nn1258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/5hwzo1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/5hwzo1258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/6qniq1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/6qniq1258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/7p1e01258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/7p1e01258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/86hsq1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/86hsq1258719864.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/9ypep1258719864.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258720091oudhlwqjrfn36ja/9ypep1258719864.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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Software written by Ed van Stee & Patrick Wessa


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