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Paper TSA Multiple Regression Model 3

*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: Sat, 18 Dec 2010 15:54:00 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2.htm/, Retrieved Sat, 18 Dec 2010 16:52:39 +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/2010/Dec/18/t1292687556ciehabvu7uabmn2.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
153452 0 169422 174000 80900 35600 36700 173570 0 153452 169422 174000 80900 35600 193036 0 173570 153452 169422 174000 80900 174652 0 193036 173570 153452 169422 174000 105367 0 174652 193036 173570 153452 169422 95963 0 105367 174652 193036 173570 153452 82896 0 95963 105367 174652 193036 173570 121747 0 82896 95963 105367 174652 193036 120196 0 121747 82896 95963 105367 174652 103983 0 120196 121747 82896 95963 105367 81103 0 103983 120196 121747 82896 95963 70944 0 81103 103983 120196 121747 82896 57248 0 70944 81103 103983 120196 121747 47830 0 57248 70944 81103 103983 120196 60095 0 47830 57248 70944 81103 103983 60931 0 60095 47830 57248 70944 81103 82955 0 60931 60095 47830 57248 70944 99559 0 82955 60931 60095 47830 57248 77911 0 99559 82955 60931 60095 47830 70753 0 77911 99559 82955 60931 60095 69287 0 70753 77911 99559 82955 60931 88426 0 69287 70753 77911 99559 82955 91756 1 88426 69287 70753 77911 99559 96933 1 91756 88426 69287 70753 77911 174484 1 96933 91756 88426 6928 etc...
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Multiple Linear Regression - Estimated Regression Equation
Werklozen[t] = + 2988.51888045487 + 23912.3934582369Oliecrisis[t] + 1.49881158651298Y1[t] -0.673512088804689Y2[t] -0.0221308982632136Y3[t] + 0.167146102902263Y4[t] -0.0811341558046364Y5[t] + 659.547249299965t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2988.518880454877674.1708460.38940.6987580.349379
Oliecrisis23912.393458236915252.5988611.56780.1237920.061896
Y11.498811586512980.14360610.436900
Y2-0.6735120888046890.244562-2.75390.0084040.004202
Y3-0.02213089826321360.254812-0.08690.9311660.465583
Y40.1671461029022630.2355550.70960.4815430.240772
Y5-0.08113415580463640.128221-0.63280.530020.26501
t659.547249299965617.2248191.06860.290840.14542


Multiple Linear Regression - Regression Statistics
Multiple R0.992063845653612
R-squared0.984190673853034
Adjusted R-squared0.98178490683067
F-TEST (value)409.096419023047
F-TEST (DF numerator)7
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation25902.3589711847
Sum Squared Residuals30862881212.5171


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1153452141571.00736373711880.9926362627
2173570126978.45132352546591.5486764748
3193036180534.31830300412501.6816969958
4174652188854.661373558-14202.6613735581
5105367146106.349586397-40739.3495863966
69596359530.140005526236432.8599944738
78289694787.4116943797-11891.4116943797
812174779076.863479352442670.1365206476
9120196136886.493688675-16690.4936886754
10103983113393.488485979-9410.48848597948
118110388516.5006790194-7413.5006790194
127094473391.188605654-2447.1886056541
135724871181.6871001941-13933.6871001941
144783056077.9744323401-8247.9744323401
156009549562.088757242610532.9112427574
166093175409.1139755258-14478.1139755258
178295567804.47960527415150.520394726
1899559100176.393063264-617.393063263529
1977911113684.444651707-35773.4446517068
207075369371.93677139411381.06322860586
216928777129.1165641825-7842.1165641825
228842681879.89049006836546.10950993169
2391756131317.837485225-39561.8374852245
2496933124670.483747118-27737.483747118
25174484130758.74216261143725.2578373888
26232595247410.110718477-14815.1107184768
27266197281824.760327151-15627.7603271509
28290435292587.778858616-2152.77885861583
29304296318200.435406401-13904.4354064014
30322310325987.773873417-3677.77387341729
31415555344676.60968889570878.3903111049
32490042473978.45751284116063.5424871586
33545109523429.96514876221679.0348512377
34545720556279.448829298-10559.4488292975
35505944533242.003227274-27298.0032272739
36477930477539.480159391390.519840608818
37466106466148.209074672-42.2090746720397
38424476464468.166101314-39992.166101314
39383018404617.792567814-21599.792567814
40364696369984.354316044-5288.35431604354
41391116372323.0058696118792.9941303902
42435721419839.78450027115881.2154997287
43511435466413.18726976645021.8127302336
44553997550228.2588610363768.7411389639
45555252568601.321888043-13349.3218880429
46544897546112.224847208-1215.2248472075
47540562538500.6961703132061.30382968706
48505282540580.419553465-35298.4195534653
49507626488267.27080685719358.7291931434
50474427514464.855090856-40037.8550908557
51469740464682.9880613555057.01193864499
52491480475080.46047038816399.5395296122
53538974515469.84994413823504.1500558616
54576612567036.2674613739575.7325386268


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.743353116111130.5132937677777380.256646883888869
120.6178258598082650.764348280383470.382174140191735
130.4874480420172970.9748960840345940.512551957982703
140.35341222237760.70682444475520.6465877776224
150.2790155784591930.5580311569183860.720984421540807
160.1849477097128470.3698954194256940.815052290287153
170.2343727473049650.4687454946099290.765627252695035
180.22742667012220.45485334024440.7725733298778
190.1772970331766910.3545940663533810.82270296682331
200.1593420170125470.3186840340250950.840657982987453
210.1123689631258650.224737926251730.887631036874135
220.1044749345292750.2089498690585510.895525065470725
230.09597969245514150.1919593849102830.904020307544859
240.09072071014657610.1814414202931520.909279289853424
250.3621957787101590.7243915574203190.637804221289841
260.3684265339488620.7368530678977240.631573466051138
270.4180439876791060.8360879753582130.581956012320894
280.3946360514179040.7892721028358080.605363948582096
290.4962728947066780.9925457894133570.503727105293322
300.8404422353541370.3191155292917260.159557764645863
310.928231000118180.143537999763640.0717689998818199
320.8971168950047290.2057662099905430.102883104995271
330.8592047477310820.2815905045378360.140795252268918
340.8332683556492970.3334632887014050.166731644350703
350.8637659091276560.2724681817446880.136234090872344
360.8323005173402660.3353989653194680.167699482659734
370.9069853951931570.1860292096136860.093014604806843
380.8781028289937640.2437943420124730.121897171006236
390.8004054261312090.3991891477375820.199594573868791
400.7236104616841440.5527790766317130.276389538315856
410.6346426566685840.7307146866628330.365357343331417
420.5466852504526250.906629499094750.453314749547375
430.4791541876439110.9583083752878230.520845812356089


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/2010/Dec/18/t1292687556ciehabvu7uabmn2/107pxy1292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/107pxy1292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/10pi41292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/10pi41292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/20pi41292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/20pi41292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/3tyz71292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/3tyz71292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/4tyz71292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/4tyz71292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/5tyz71292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/5tyz71292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/6mpya1292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/6mpya1292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/7wgxd1292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/7wgxd1292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/8wgxd1292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/8wgxd1292687632.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/9wgxd1292687632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687556ciehabvu7uabmn2/9wgxd1292687632.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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