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Multiplelineairregression2

*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: Wed, 18 Nov 2009 08:58:15 -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/18/t1258560311llg1ejfg5nn24df.htm/, Retrieved Wed, 18 Nov 2009 17:05:24 +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/18/t1258560311llg1ejfg5nn24df.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 «
17823.2 0 17872 0 17420.4 0 16704.4 0 15991.2 0 16583.6 0 19123.5 0 17838.7 0 17209.4 0 18586.5 0 16258.1 0 15141.6 0 19202.1 0 17746.5 0 19090.1 0 18040.3 0 17515.5 0 17751.8 0 21072.4 0 17170 0 19439.5 0 19795.4 0 17574.9 0 16165.4 0 19464.6 0 19932.1 0 19961.2 0 17343.4 0 18924.2 0 18574.1 0 21350.6 0 18594.6 0 19823.1 0 20844.4 0 19640.2 0 17735.4 0 19813.6 0 22160 0 20664.3 0 17877.4 0 20906.5 0 21164.1 0 21374.4 0 22952.3 0 21343.5 0 23899.3 0 22392.9 0 18274.1 0 22786.7 0 22321.5 0 17842.2 1 16373.5 1 15993.8 1 16446.1 1 17729 1 16643 1 16196.7 1 18252.1 1 17570.4 1 15836.8 1
 
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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
uitvoer[t] = + 17043.5515 -2064.45750000000dummy[t] + 2774.48850000001M1[t] + 2962.86850000000M2[t] + 2364.98000000000M3[t] + 637.139999999999M4[t] + 1235.58000000000M5[t] + 1473.28000000000M6[t] + 3499.32M7[t] + 2009.06M8[t] + 2171.78M9[t] + 3644.88M10[t] + 2056.64M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)17043.5515794.55617221.450400
dummy-2064.45750000000620.444132-3.32740.0017090.000855
M12774.488500000011116.7994382.48430.01660.0083
M22962.868500000001116.7994382.6530.0108470.005424
M32364.980000000001109.8842052.13080.0383640.019182
M4637.1399999999991109.8842050.57410.5686650.284332
M51235.580000000001109.8842051.11330.2712620.135631
M61473.280000000001109.8842051.32740.1907830.095391
M73499.321109.8842053.15290.0028150.001408
M82009.061109.8842051.81020.0766680.038334
M92171.781109.8842051.95680.0563310.028165
M103644.881109.8842053.2840.0019370.000969
M112056.641109.8842051.8530.0701630.035082


Multiple Linear Regression - Regression Statistics
Multiple R0.65483290912575
R-squared0.428806138874093
Adjusted R-squared0.282969408373862
F-TEST (value)2.94031645802298
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.00403785006313562
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1754.88101308195
Sum Squared Residuals144741546.393550


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
117823.219818.0399999999-1994.83999999995
21787220006.42-2134.42000000001
317420.419408.5315-1988.13150000000
416704.417680.6915-976.291499999998
515991.218279.1315-2287.93150000000
616583.618516.8315-1933.2315
719123.520542.8715-1419.3715
817838.719052.6115-1213.9115
917209.419215.3315-2005.93149999999
1018586.520688.4315-2101.9315
1116258.119100.1915-2842.09150000000
1215141.617043.5515-1901.95150000000
1319202.119818.04-615.940000000015
1417746.520006.42-2259.92000000000
1519090.119408.5315-318.431500000003
1618040.317680.6915359.608499999998
1717515.518279.1315-763.631499999999
1817751.818516.8315-765.0315
1921072.420542.8715529.5285
201717019052.6115-1882.6115
2119439.519215.3315224.168500000000
2219795.420688.4315-893.031499999999
2317574.919100.1915-1525.2915
2416165.417043.5515-878.1515
2519464.619818.04-353.440000000014
2619932.120006.42-74.3199999999988
2719961.219408.5315552.668499999999
2817343.417680.6915-337.291499999999
2918924.218279.1315645.068500000002
3018574.118516.831557.2684999999996
3121350.620542.8715807.728499999997
3218594.619052.6115-458.011500000002
3319823.119215.3315607.768499999998
3420844.420688.4315155.968500000001
3519640.219100.1915540.0085
3617735.417043.5515691.848500000001
3719813.619818.04-4.4400000000139
382216020006.422153.58000000000
3920664.319408.53151255.76850000000
4017877.417680.6915196.708500000001
4120906.518279.13152627.3685
4221164.118516.83152647.2685
4321374.420542.8715831.5285
4422952.319052.61153899.6885
4521343.519215.33152128.1685
4623899.320688.43153210.8685
4722392.919100.19153292.7085
4818274.117043.55151230.54850000000
4922786.719818.042968.65999999999
5022321.520006.422315.08000000000
5117842.217344.074498.126
5216373.515616.234757.266
5315993.816214.674-220.873999999999
5416446.116452.374-6.27400000000014
551772918478.414-749.414000000001
561664316988.154-345.154
5716196.717150.874-954.174
5818252.118623.974-371.874000000001
5917570.417035.734534.666000000001
6015836.814979.094857.706


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.2963902759172560.5927805518345120.703609724082744
170.2546225080273800.5092450160547610.74537749197262
180.1924752556917960.3849505113835920.807524744308204
190.1975747306926070.3951494613852130.802425269307393
200.1624647867616200.3249295735232410.83753521323838
210.1935310199095910.3870620398191820.806468980090409
220.1704468447274220.3408936894548430.829553155272578
230.2034443512081870.4068887024163730.796555648791814
240.1880541734740180.3761083469480360.811945826525982
250.166393420387790.332786840775580.83360657961221
260.2569950074183240.5139900148366490.743004992581676
270.2579786816904630.5159573633809260.742021318309537
280.2056145584553570.4112291169107140.794385441544643
290.2478990884984010.4957981769968030.752100911501599
300.2632769311030870.5265538622061750.736723068896913
310.2154868121786760.4309736243573520.784513187821324
320.309694812507330.619389625014660.69030518749267
330.2804441431083710.5608882862167430.719555856891629
340.3448304324224560.6896608648449110.655169567577544
350.5300496091917910.9399007816164180.469950390808209
360.5527989509203250.894402098159350.447201049079675
370.7016154017885220.5967691964229560.298384598211478
380.7470863386660310.5058273226679380.252913661333969
390.7326670929459120.5346658141081760.267332907054088
400.8945329953664230.2109340092671540.105467004633577
410.868699339909830.2626013201803400.131300660090170
420.821378902085760.3572421958284790.178621097914239
430.7460316720859870.5079366558280260.253968327914013
440.7790185207115780.4419629585768440.220981479288422


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/18/t1258560311llg1ejfg5nn24df/101niy1258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/101niy1258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/1fq711258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/1fq711258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/27o611258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/27o611258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/3qk6y1258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/3qk6y1258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/4w4c11258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/4w4c11258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/5e7x41258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/5e7x41258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/6f1d01258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/6f1d01258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/7a9m71258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/7a9m71258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/81n2i1258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/81n2i1258559889.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/9zxmi1258559889.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258560311llg1ejfg5nn24df/9zxmi1258559889.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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