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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 09:18:24 -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/t1258561138loaimgvmc0dtmha.htm/, Retrieved Wed, 18 Nov 2009 17:19:10 +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/t1258561138loaimgvmc0dtmha.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 «
23 25,7 19 24,7 18 24,2 19 23,6 19 24,4 22 22,5 23 19,4 20 18,1 14 18,1 14 20,7 14 19,1 15 18,3 11 16,9 17 17,9 16 20,2 20 21,2 24 23,8 23 24 20 26,6 21 25,3 19 27,6 23 24,7 23 26,6 23 24,4 23 24,6 27 26 26 24,8 17 24 24 22,7 26 23 24 24,1 27 24 27 22,7 26 22,6 24 23,1 23 24,4 23 23 24 22 17 21,3 21 21,5 19 21,3 22 23,2 22 21,8 18 23,3 16 21 14 22,4 12 20,4 14 19,9 16 21,3 8 18,9 3 15,6 0 12,5 5 7,8 1 5,5 1 4 3 3,3 6 3,7 7 3,1 8 5 14 6,3
 
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
Icons[t] = -0.38093323978063 + 0.898293762592767Inprod[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-0.380933239780631.746297-0.21810.8280870.414044
Inprod0.8982937625927670.08350210.757700


Multiple Linear Regression - Regression Statistics
Multiple R0.816177622465578
R-squared0.666145911413564
Adjusted R-squared0.660389806437936
F-TEST (value)115.728589772785
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value1.99840144432528e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.22211716668176
Sum Squared Residuals1033.92385541295


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12322.70521645885350.294783541146501
21921.8069226962607-2.80692269626071
31821.3577758149643-3.35777581496433
41920.8187995574087-1.81879955740868
51921.5374345674829-2.53743456748289
62219.83067641855662.16932358144337
72317.04596575451915.95403424548095
82015.87818386314854.12181613685154
91415.8781838631485-1.87818386314846
101418.2137476458897-4.21374764588965
111416.7764776257412-2.77647762574122
121516.057842615667-1.05784261566701
131114.8002313480371-3.80023134803714
141715.69852511062991.30147488937010
151617.7646007645933-1.76460076459327
162018.66289452718601.33710547281397
172420.99845830992723.00154169007277
182321.17811706244581.82188293755422
192023.5136808451870-3.51368084518698
202122.3458989538164-1.34589895381638
211924.4119746077797-5.41197460777974
222321.80692269626071.19307730373928
232323.5136808451870-0.513680845186977
242321.53743456748291.46256543251711
252321.71709332000141.28290667999856
262722.97470458763134.02529541236868
272621.896752072524.10324792748000
281721.1781170624458-4.17811706244578
292420.01033517107523.98966482892482
302620.2798232998535.72017670014699
312421.26794643870512.73205356129494
322721.17811706244585.82188293755422
332720.01033517107526.98966482892482
342619.92050579481596.07949420518409
352420.36965267611233.63034732388771
362321.53743456748291.46256543251711
372320.2798232998532.72017670014699
382419.38152953726024.61847046273975
391718.7527239034453-1.75272390344531
402118.93238265596392.06761734403614
411918.75272390344530.247276096554688
422220.45948205237161.54051794762843
432219.20187078474172.79812921525830
441820.5493114286308-2.54931142863085
451618.4832357746675-2.48323577466748
461419.7408470422974-5.74084704229735
471217.9442595171118-5.94425951711182
481417.4951126358154-3.49511263581544
491618.7527239034453-2.75272390344531
50816.5968188732227-8.59681887322267
51313.6324494566665-10.6324494566665
52010.8477387926290-10.8477387926290
5356.62575810844296-1.62575810844296
5414.55968245447959-3.55968245447959
5513.21224181059044-2.21224181059044
5632.583436176775510.416563823224494
5762.942753681812613.05724631818739
5872.403777424256954.59622257574305
5984.110535573183213.88946442681679
60145.278317464553818.72168253544619


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.02964079617923420.05928159235846830.970359203820766
60.09665762949453980.1933152589890800.90334237050546
70.05713890140061560.1142778028012310.942861098599384
80.0352371268173470.0704742536346940.964762873182653
90.1297536643297050.259507328659410.870246335670295
100.1826905739424090.3653811478848180.817309426057591
110.1724315039468130.3448630078936270.827568496053187
120.1207157632418770.2414315264837540.879284236758123
130.1293290517528360.2586581035056720.870670948247164
140.0888450685439990.1776901370879980.911154931456001
150.05823336232054080.1164667246410820.94176663767946
160.04080952656800140.08161905313600270.959190473431999
170.04189925113265450.0837985022653090.958100748867345
180.03067231529921990.06134463059843990.96932768470078
190.02422104142335130.04844208284670260.975778958576649
200.01434298946573670.02868597893147350.985657010534263
210.01607616283847990.03215232567695990.98392383716152
220.01150673573937630.02301347147875260.988493264260624
230.006846884076788590.01369376815357720.993153115923211
240.004718120938524920.009436241877049850.995281879061475
250.003048581655290980.006097163310581960.99695141834471
260.00418492108150380.00836984216300760.995815078918496
270.004945184110185610.009890368220371210.995054815889814
280.005135534258474820.01027106851694960.994864465741525
290.005349727931664370.01069945586332870.994650272068336
300.00943710706336790.01887421412673580.990562892936632
310.007083616677063430.01416723335412690.992916383322937
320.01204696856251210.02409393712502430.987953031437488
330.02858159499936970.05716318999873950.97141840500063
340.0478312636102260.0956625272204520.952168736389774
350.04712829772387430.09425659544774850.952871702276126
360.03605669425507270.07211338851014550.963943305744927
370.03301165760859020.06602331521718030.96698834239141
380.04891739971706480.09783479943412960.951082600282935
390.03587738767980680.07175477535961360.964122612320193
400.03427586595947880.06855173191895750.965724134040521
410.02721061498258810.05442122996517630.972789385017412
420.03153418712491070.06306837424982140.96846581287509
430.06090770128317760.1218154025663550.939092298716822
440.0620102411778790.1240204823557580.93798975882212
450.06133959411320320.1226791882264060.938660405886797
460.0643588507774920.1287177015549840.935641149222508
470.06136267641533790.1227253528306760.938637323584662
480.06071803252526680.1214360650505340.939281967474733
490.1686401683280730.3372803366561460.831359831671927
500.2356237533356690.4712475066713380.764376246664331
510.2211273180542590.4422546361085170.778872681945741
520.2770699772196610.5541399544393220.722930022780339
530.2736654654693950.5473309309387890.726334534530605
540.6054218516835680.7891562966328650.394578148316432
550.825098681553290.349802636893420.17490131844671


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.0784313725490196NOK
5% type I error level140.274509803921569NOK
10% type I error level290.568627450980392NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/10b4i01258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/10b4i01258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/15ty51258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/15ty51258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/21ca81258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/21ca81258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/301st1258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/301st1258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/4ebsa1258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/4ebsa1258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/5atvx1258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/5atvx1258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/6222p1258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/6222p1258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/7uue31258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/7uue31258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/8vd4m1258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/8vd4m1258561099.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/9e8jp1258561099.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561138loaimgvmc0dtmha/9e8jp1258561099.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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