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box cox wlh

*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, 25 Dec 2009 12:20:04 -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/Dec/25/t1261768867lp6lpej8p1ek55o.htm/, Retrieved Fri, 25 Dec 2009 20:21:19 +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/Dec/25/t1261768867lp6lpej8p1ek55o.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 «
612613 1 611324 1 594167 1 595454 1 590865 1 589379 1 584428 1 573100 1 567456 1 569028 1 620735 1 628884 1 628232 1 612117 1 595404 1 597141 1 593408 1 590072 1 579799 1 574205 1 572775 1 572942 1 619567 1 625809 1 619916 1 587625 0 565742 0 557274 0 560576 0 548854 0 531673 0 525919 0 511038 0 498662 0 555362 0 564591 0 541657 0 527070 0 509846 0 514258 0 516922 0 507561 0 492622 0 490243 0 469357 0 477580 0 528379 0 533590 0 517945 0 506174 0 501866 0 516141 0 528222 0 532638 0 536322 0 536535 0 523597 0 536214 0 586570 0 596594 0
 
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
wlh[t] = + 529577.685714286 + 67175.1142857143dummies[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)529577.6857142864430.83393119.52100
dummies67175.11428571436864.2184089.786300


Multiple Linear Regression - Regression Statistics
Multiple R0.789186974101873
R-squared0.62281608009207
Adjusted R-squared0.616312909059174
F-TEST (value)95.7711364104749
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value6.87228052242972e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation26213.1670354156
Sum Squared Residuals39853547309.5428


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1612613596752.815860.1999999995
2611324596752.814571.2000000001
3594167596752.8-2585.79999999999
4595454596752.8-1298.79999999998
5590865596752.8-5887.79999999999
6589379596752.8-7373.79999999999
7584428596752.8-12324.8000000000
8573100596752.8-23652.8
9567456596752.8-29296.8
10569028596752.8-27724.8
11620735596752.823982.2
12628884596752.832131.2
13628232596752.831479.2
14612117596752.815364.2
15595404596752.8-1348.79999999998
16597141596752.8388.200000000015
17593408596752.8-3344.79999999999
18590072596752.8-6680.79999999999
19579799596752.8-16953.8
20574205596752.8-22547.8
21572775596752.8-23977.8
22572942596752.8-23810.8
23619567596752.822814.2
24625809596752.829056.2
25619916596752.823163.2
26587625529577.68571428658047.3142857143
27565742529577.68571428636164.3142857143
28557274529577.68571428627696.3142857143
29560576529577.68571428630998.3142857143
30548854529577.68571428619276.3142857143
31531673529577.6857142862095.31428571428
32525919529577.685714286-3658.68571428572
33511038529577.685714286-18539.6857142857
34498662529577.685714286-30915.6857142857
35555362529577.68571428625784.3142857143
36564591529577.68571428635013.3142857143
37541657529577.68571428612079.3142857143
38527070529577.685714286-2507.68571428572
39509846529577.685714286-19731.6857142857
40514258529577.685714286-15319.6857142857
41516922529577.685714286-12655.6857142857
42507561529577.685714286-22016.6857142857
43492622529577.685714286-36955.6857142857
44490243529577.685714286-39334.6857142857
45469357529577.685714286-60220.6857142857
46477580529577.685714286-51997.6857142857
47528379529577.685714286-1198.68571428572
48533590529577.6857142864012.31428571428
49517945529577.685714286-11632.6857142857
50506174529577.685714286-23403.6857142857
51501866529577.685714286-27711.6857142857
52516141529577.685714286-13436.6857142857
53528222529577.685714286-1355.68571428572
54532638529577.6857142863060.31428571428
55536322529577.6857142866744.31428571428
56536535529577.6857142866957.31428571428
57523597529577.685714286-5980.68571428572
58536214529577.6857142866636.31428571428
59586570529577.68571428656992.3142857143
60596594529577.68571428667016.3142857143


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.09682460670594830.1936492134118970.903175393294052
60.05023694560095150.1004738912019030.949763054399049
70.03331037702331120.06662075404662240.966689622976689
80.04769837174465720.09539674348931440.952301628255343
90.06911013958152850.1382202791630570.930889860418471
100.06966194622312170.1393238924462430.930338053776878
110.1069020222572770.2138040445145550.893097977742723
120.1793088998402520.3586177996805030.820691100159748
130.2274347326874260.4548694653748510.772565267312574
140.1804842557868760.3609685115737520.819515744213124
150.1239388228907160.2478776457814310.876061177109284
160.0815976890453790.1631953780907580.918402310954621
170.05240789144347040.1048157828869410.94759210855653
180.03354008237886110.06708016475772220.96645991762114
190.02627995169869920.05255990339739840.97372004830130
200.02495407363180120.04990814726360250.97504592636820
210.02558101139276980.05116202278553950.97441898860723
220.02864900100217180.05729800200434370.971350998997828
230.02760934402279510.05521868804559020.972390655977205
240.03096333722214420.06192667444428840.969036662777856
250.02691420104732960.05382840209465930.97308579895267
260.03324398307978340.06648796615956690.966756016920217
270.03331640676748930.06663281353497850.96668359323251
280.03057822828522810.06115645657045620.969421771714772
290.02752331549125670.05504663098251330.972476684508743
300.02409443624155310.04818887248310610.975905563758447
310.02506478304580690.05012956609161380.974935216954193
320.02546893075657690.05093786151315370.974531069243423
330.03538613886611310.07077227773222620.964613861133887
340.06245073814671380.1249014762934280.937549261853286
350.05641313826266150.1128262765253230.943586861737338
360.06835488344826690.1367097668965340.931645116551733
370.05228745901084350.1045749180216870.947712540989156
380.03894266922663250.0778853384532650.961057330773367
390.03774454389976840.07548908779953670.962255456100232
400.03088350898749070.06176701797498140.96911649101251
410.02293545813868020.04587091627736030.97706454186132
420.02021172368249560.04042344736499130.979788276317504
430.02925973708887720.05851947417775430.970740262911123
440.04381120666849670.08762241333699340.956188793331503
450.1678838503865350.3357677007730690.832116149613465
460.3627124021110180.7254248042220350.637287597888982
470.2816683010404390.5633366020808790.71833169895956
480.2072835634167220.4145671268334450.792716436583278
490.1620848769406440.3241697538812880.837915123059356
500.1658704163726740.3317408327453470.834129583627326
510.2181688814405890.4363377628811790.78183111855941
520.2106721676335470.4213443352670950.789327832366453
530.1624827059671140.3249654119342280.837517294032886
540.1139908842065470.2279817684130930.886009115793453
550.07135881428544320.1427176285708860.928641185714557


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.0784313725490196NOK
10% type I error level250.490196078431373NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/10u0td1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/10u0td1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/195wm1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/195wm1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/217qd1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/217qd1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/3um7k1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/3um7k1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/4gfy61261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/4gfy61261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/5a51b1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/5a51b1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/6ev8w1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/6ev8w1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/72t641261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/72t641261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/8fi0c1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/8fi0c1261768798.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/9qz0d1261768798.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/25/t1261768867lp6lpej8p1ek55o/9qz0d1261768798.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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