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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 04:57:18 -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/t1258718293ji7bo351hflmli1.htm/, Retrieved Fri, 20 Nov 2009 12:58:28 +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/t1258718293ji7bo351hflmli1.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 «
8.6 0 8.5 0 8.3 0 7.8 0 7.8 0 8 0 8.6 0 8.9 0 8.9 0 8.6 0 8.3 0 8.3 0 8.3 0 8.4 0 8.5 0 8.4 0 8.6 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.6 0 8.4 0 8.1 0 8 0 8 0 8 0 8 0 7.9 0 7.8 0 7.8 0 7.9 0 8.1 0 8 0 7.6 0 7.3 0 7 0 6.8 0 7 0 7.1 0 7.2 0 7.1 1 6.9 1 6.7 1 6.7 1 6.6 1 6.9 1 7.3 1 7.5 1 7.3 1 7.1 1 6.9 1 7.1 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 8.77083333333333 -0.391666666666667X[t] -0.0127083333333361M1[t] -0.0279166666666659M2[t] -0.0431249999999993M3[t] -0.098333333333333M4[t] -0.0535416666666664M5[t] -0.0687499999999997M6[t] + 0.036041666666667M7[t] + 0.0808333333333339M8[t] + 0.0256250000000003M9[t] -0.00958333333333323M10[t] -0.0647916666666663M11[t] -0.0247916666666667t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)8.770833333333330.22183339.53800
X-0.3916666666666670.182346-2.14790.037020.01851
M1-0.01270833333333610.257051-0.04940.9607830.480392
M2-0.02791666666666590.256295-0.10890.9137370.456868
M3-0.04312499999999930.255609-0.16870.8667610.43338
M4-0.0983333333333330.254994-0.38560.7015490.350774
M5-0.05354166666666640.25445-0.21040.8342690.417134
M6-0.06874999999999970.253978-0.27070.7878380.393919
M70.0360416666666670.2535780.14210.8875960.443798
M80.08083333333333390.253250.31920.7510320.375516
M90.02562500000000030.2529940.10130.9197630.459881
M10-0.009583333333333230.252812-0.03790.9699260.484963
M11-0.06479166666666630.252702-0.25640.7987890.399394
t-0.02479166666666670.004298-5.76831e-060


Multiple Linear Regression - Regression Statistics
Multiple R0.843611399723022
R-squared0.711680193742636
Adjusted R-squared0.630198509365556
F-TEST (value)8.73423517424017
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value1.40547959937010e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.399499233642769
Sum Squared Residuals7.34158333333334


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.68.73333333333334-0.133333333333346
28.58.69333333333333-0.193333333333332
38.38.65333333333333-0.353333333333333
47.88.57333333333333-0.773333333333332
57.88.59333333333333-0.793333333333333
688.55333333333333-0.553333333333332
78.68.63333333333333-0.0333333333333324
88.98.653333333333330.246666666666668
98.98.573333333333330.326666666666667
108.68.513333333333330.0866666666666665
118.38.43333333333333-0.133333333333332
128.38.47333333333333-0.173333333333332
138.38.43583333333333-0.135833333333329
148.48.395833333333330.00416666666666725
158.58.355833333333330.144166666666666
168.48.275833333333330.124166666666667
178.68.295833333333330.304166666666666
188.58.255833333333330.244166666666667
198.58.335833333333330.164166666666667
208.58.355833333333330.144166666666667
218.58.275833333333330.224166666666667
228.58.215833333333330.284166666666667
238.58.135833333333330.364166666666667
248.58.175833333333330.324166666666667
258.58.138333333333330.36166666666667
268.58.098333333333330.401666666666666
278.58.058333333333330.441666666666666
288.57.978333333333330.521666666666667
298.67.998333333333330.601666666666666
308.47.958333333333330.441666666666667
318.18.038333333333330.0616666666666664
3288.05833333333333-0.0583333333333335
3387.978333333333330.0216666666666666
3487.918333333333330.0816666666666668
3587.838333333333330.161666666666666
367.97.878333333333330.0216666666666671
377.87.84083333333333-0.0408333333333306
387.87.80083333333333-0.000833333333334452
397.97.760833333333330.139166666666666
408.17.680833333333330.419166666666666
4187.700833333333330.299166666666666
427.67.66083333333333-0.0608333333333342
437.37.74083333333333-0.440833333333334
4477.76083333333333-0.760833333333334
456.87.68083333333333-0.880833333333334
4677.62083333333333-0.620833333333334
477.17.54083333333333-0.440833333333334
487.27.58083333333333-0.380833333333333
497.17.15166666666666-0.0516666666666639
506.97.11166666666667-0.211666666666667
516.77.07166666666667-0.371666666666667
526.76.99166666666667-0.291666666666667
536.67.01166666666667-0.411666666666667
546.96.97166666666667-0.0716666666666666
557.37.051666666666670.248333333333333
567.57.071666666666670.428333333333333
577.36.991666666666670.308333333333333
587.16.931666666666670.168333333333333
596.96.851666666666670.0483333333333334
607.16.891666666666670.208333333333333


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.7047848115782440.5904303768435130.295215188421756
180.5887189053011020.8225621893977970.411281094698898
190.5173639336220460.965272132755910.482636066377954
200.5557806307752820.8884387384494360.444219369224718
210.5422060038089190.9155879923821620.457793996191081
220.4376263475253950.8752526950507910.562373652474605
230.3353872224811080.6707744449622150.664612777518892
240.2551971114233090.5103942228466180.744802888576691
250.1755042305926470.3510084611852930.824495769407353
260.1158805932909410.2317611865818830.884119406709059
270.07363328162400450.1472665632480090.926366718375995
280.05380587785945680.1076117557189140.946194122140543
290.04111936716319240.08223873432638490.958880632836808
300.02452293006618030.04904586013236050.97547706993382
310.03483935281390290.06967870562780590.965160647186097
320.06742416685497750.1348483337099550.932575833145022
330.08524949671453680.1704989934290740.914750503285463
340.07302561130076720.1460512226015340.926974388699233
350.05154747094417170.1030949418883430.948452529055828
360.03626612713985350.0725322542797070.963733872860146
370.02956503685426590.05913007370853180.970434963145734
380.02510870931297860.05021741862595730.974891290687021
390.02902251762710130.05804503525420250.970977482372899
400.07149552440462030.1429910488092410.92850447559538
410.4134104047683910.8268208095367810.586589595231609
420.6958679054123480.6082641891753050.304132094587652
430.6006233854420890.7987532291158220.399376614557911


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0370370370370370OK
10% type I error level70.259259259259259NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/10wuy1258718233.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/10wuy1258718233.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/10y0w51258718234.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/10y0w51258718234.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/2n7te1258718233.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/2n7te1258718233.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/3h84a1258718233.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/3h84a1258718233.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/4p8le1258718233.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/4p8le1258718233.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/5owdl1258718234.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/5owdl1258718234.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/6j3e31258718234.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/6j3e31258718234.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/708e81258718234.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/708e81258718234.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/89rkn1258718234.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/89rkn1258718234.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/9wxrm1258718234.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718293ji7bo351hflmli1/9wxrm1258718234.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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