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*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 10:50:38 -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/t1258740790v3gk7fqrb2la17m.htm/, Retrieved Fri, 20 Nov 2009 19:13:22 +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/t1258740790v3gk7fqrb2la17m.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 «
594 139 595 135 591 130 589 127 584 122 573 117 567 112 569 113 621 149 629 157 628 157 612 147 595 137 597 132 593 125 590 123 580 117 574 114 573 111 573 112 620 144 626 150 620 149 588 134 566 123 557 116 561 117 549 111 532 105 526 102 511 95 499 93 555 124 565 130 542 124 527 115 510 106 514 105 517 105 508 101 493 95 490 93 469 84 478 87 528 116 534 120 518 117 506 109 502 105 516 107 528 109 533 109 536 108 537 107 524 99 536 103 587 131 597 137 581 135 564 124
 
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] = + 295.989857812736 + 2.19348434427469X[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)295.98985781273614.66405320.184700
X2.193484344274690.12230417.934700


Multiple Linear Regression - Regression Statistics
Multiple R0.920450295083232
R-squared0.84722874571881
Adjusted R-squared0.84459475857603
F-TEST (value)321.652574516703
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation16.2389882592519
Sum Squared Residuals15294.874901679


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1594600.884181666918-6.8841816669177
2595592.110244289822.88975571017992
3591581.1428225684479.85717743155344
4589574.56236953562214.4376304643775
5584563.59494781424920.405052185751
6573552.62752609287620.3724739071245
7567541.66010437150225.3398956284979
8569543.85358871577725.1464112842233
9621622.819025109666-1.81902510966577
10629640.366899863863-11.3668998638633
11628640.366899863863-12.3668998638633
12612618.432056421116-6.43205642111638
13595596.49721297837-1.49721297836942
14597585.52979125699611.4702087430040
15593570.17540084707322.8245991529269
16590565.78843215852424.2115678414763
17580552.62752609287627.3724739071245
18574546.04707306005127.9529269399486
19573539.46662002722733.5333799727726
20573541.66010437150231.3398956284979
21620611.8516033882928.1483966117077
22626625.012509453940.987490546059543
23620622.819025109666-2.81902510966577
24588589.916759945545-1.91675994554534
25566565.7884321585240.211567841476303
26557550.4340417486016.56595825139917
27561552.6275260928768.37247390712447
28549539.4666200272279.53337997277264
29532526.3057139615795.69428603842081
30526519.7252609287556.2747390712449
31511504.3708705188326.62912948116776
32499499.983901830283-0.98390183028285
33555567.981916502798-12.9819165027984
34565581.142822568447-16.1428225684466
35542567.981916502798-25.9819165027984
36527548.240557404326-21.2405574043261
37510528.499198305854-18.4991983058539
38514526.305713961579-12.3057139615792
39517526.305713961579-9.30571396157919
40508517.53177658448-9.5317765844804
41493504.370870518832-11.3708705188322
42490499.983901830283-9.98390183028285
43469480.24254273181-11.2425427318106
44478486.822995764635-8.82299576463468
45528550.434041748601-22.4340417486008
46534559.2079791257-25.2079791256996
47518552.627526092876-34.6275260928755
48506535.079651338678-29.079651338678
49502526.305713961579-24.3057139615792
50516530.692682650129-14.6926826501286
51528535.079651338678-7.07965133867797
52533535.079651338678-2.07965133867797
53536532.8861669944033.11383300559673
54537530.6926826501296.30731734987142
55524513.14480789593110.8551921040690
56536521.9187452730314.0812547269702
57587583.3363069127213.66369308727874
58597596.497212978370.502787021630576
59581592.11024428982-11.1102442898200
60564567.981916502798-3.98191650279839


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.001508164975137300.003016329950274600.998491835024863
60.003537975808300730.007075951616601450.9964620241917
70.001360142443866160.002720284887732330.998639857556134
80.0003299248738867480.0006598497477734960.999670075126113
90.0006040936402443190.001208187280488640.999395906359756
100.0001737976362516720.0003475952725033430.999826202363748
114.20460973741466e-058.40921947482933e-050.999957953902626
121.03873661505277e-052.07747323010555e-050.99998961263385
135.38679202537246e-061.07735840507449e-050.999994613207975
141.89827393233831e-063.79654786467663e-060.999998101726068
154.22451908174427e-068.44903816348855e-060.999995775480918
165.4025931050441e-061.08051862100882e-050.999994597406895
174.0188041111402e-068.0376082222804e-060.99999598119589
182.59973881449693e-065.19947762899386e-060.999997400261186
194.20728308965899e-068.41456617931797e-060.99999579271691
207.3606063258039e-061.47212126516078e-050.999992639393674
212.14644127143787e-054.29288254287574e-050.999978535587286
222.14307786120394e-054.28615572240789e-050.999978569221388
239.01847660517522e-061.80369532103504e-050.999990981523395
242.22718507655450e-054.45437015310900e-050.999977728149234
250.0003541567888327830.0007083135776655660.999645843211167
260.001739435898795510.003478871797591020.998260564101205
270.003661972349272030.007323944698544060.996338027650728
280.009983898812709640.01996779762541930.99001610118729
290.03787770105633750.0757554021126750.962122298943662
300.08473176550143760.1694635310028750.915268234498562
310.1587889452626870.3175778905253750.841211054737313
320.2721863886638400.5443727773276790.72781361133616
330.328652936195860.657305872391720.67134706380414
340.3755915169522350.751183033904470.624408483047765
350.5901070579778640.8197858840442720.409892942022136
360.7054182541560910.5891634916878190.294581745843909
370.7685651620191420.4628696759617170.231434837980858
380.7606108424085520.4787783151828960.239389157591448
390.7284667877810280.5430664244379430.271533212218972
400.6913540274968770.6172919450062460.308645972503123
410.6566460937652860.6867078124694280.343353906234714
420.6058050745358180.7883898509283640.394194925464182
430.5558466509886520.8883066980226950.444153349011348
440.4870191286590220.9740382573180450.512980871340978
450.505459158983870.989081682032260.49454084101613
460.5582581500345540.8834836999308920.441741849965446
470.7940632569271840.4118734861456320.205936743072816
480.9227029302838940.1545941394322120.0772970697161058
490.9847941938441740.03041161231165130.0152058061558256
500.995775080708730.008449838582538420.00422491929126921
510.997079504548760.005840990902478950.00292049545123947
520.9960510804557240.007897839088551750.00394891954427587
530.9897107504973690.02057849900526270.0102892495026313
540.9688447357289330.0623105285421330.0311552642710665
550.9135826795783950.172834640843210.086417320421605


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level260.509803921568627NOK
5% type I error level290.568627450980392NOK
10% type I error level310.607843137254902NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/10c63h1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/10c63h1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/1o4km1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/1o4km1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/20i4t1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/20i4t1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/33ypx1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/33ypx1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/4qxbr1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/4qxbr1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/5lxmw1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/5lxmw1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/6908h1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/6908h1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/78kw81258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/78kw81258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/8n0qz1258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/8n0qz1258739434.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/939d01258739434.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258740790v3gk7fqrb2la17m/939d01258739434.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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