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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: Wed, 29 Dec 2010 18:38:10 +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/29/t1293647748pkdivys4rx6zhc7.htm/, Retrieved Wed, 29 Dec 2010 19:35:56 +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/29/t1293647748pkdivys4rx6zhc7.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 «
597141 25 593408 24 590072 21 579799 22 574205 20 572775 24 572942 24 619567 24 625809 24 619916 28 587625 27 565742 18 557274 25 560576 27 548854 25 531673 28 525919 28 511038 27 498662 25 555362 24 564591 24 541657 25 527070 18 509846 22 514258 20 516922 23 507561 23 492622 19 490243 17 469357 15 477580 13 528379 15 533590 17 517945 9 506174 4 501866 1 516141 6 528222 2 532638 2 536322 4 536535 7 523597 8 536214 9 586570 15 596594 15 580523 14 564478 16 557560 11 575093 11 580112 11 574761 13 563250 18 551531 13 537034 17 544686 19 600991 22 604378 22 586111 24 563668 26 548604 24
 
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' @ www.wessa.org


Multiple Linear Regression - Estimated Regression Equation
werkloos[t] = + 513222.488502579 + 1430.61638726532cv[t] + 12646.9207958182M1[t] + 16464.7501732907M2[t] + 12203.5493831224M3[t] + 107.915818423545M4[t] -3270.71513938551M5[t] -17962.6254266313M6[t] -14468.6727717057M7[t] + 34778.3238312362M8[t] + 40975.9066538026M9[t] + 25737.3825861813M10[t] + 8836.32146073147M11[t] + 48.7706225274404t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)513222.48850257923744.84574821.614100
cv1430.61638726532690.5845122.07160.0439370.021969
M112646.920795818221491.8308790.58850.5591070.279554
M216464.750173290721459.3964560.76730.4468520.223426
M312203.549383122421431.5998710.56940.5718420.285921
M4107.91581842354521422.2445620.0050.9960020.498001
M5-3270.7151393855121382.122604-0.1530.8790950.439547
M6-17962.625426631321393.616404-0.83960.4054610.202731
M7-14468.672771705721377.336001-0.67680.5019080.250954
M834778.323831236221502.9538951.61740.1126350.056318
M940975.906653802621550.1928921.90140.0635220.031761
M1025737.382586181321524.3949111.19570.2379290.118965
M118836.3214607314721393.9156930.4130.6815040.340752
t48.7706225274404296.5108480.16450.8700730.435036


Multiple Linear Regression - Regression Statistics
Multiple R0.584519492891654
R-squared0.341663037570316
Adjusted R-squared0.155611287318449
F-TEST (value)1.83638711867956
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.0655093381447696
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation33687.4434771532
Sum Squared Residuals52202817009.214


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1597141561683.58960255835457.4103974424
2593408564119.57321529229288.4267847075
3590072555615.29388585634456.7061141442
4579799544999.0473309534799.9526690503
5574205538807.95422113735397.0457788626
6572775529887.2801054842887.7198945197
7572942533430.00338293339511.9966170666
8619567582725.77060840336841.2293915973
9625809588972.12405349736836.8759465034
10619916579504.83615746440411.163842536
11587625561221.92926727626403.0707327237
12565742539558.83094368426183.1690563157
13557274562268.837072887-4994.83707288724
14560576568996.669847418-8420.66984741784
15548854561923.006905246-13069.0069052464
16531673554167.993124871-22494.9931248709
17525919550838.132789589-24919.1327895893
18511038534764.376737606-23726.3767376055
19498662535445.867240528-36783.867240528
20555362583311.018078732-27949.018078732
21564591589557.371523826-24966.3715238259
22541657575798.234465997-34141.2344659974
23527070548931.629252218-21861.6292522177
24509846545866.543963075-36020.5439630749
25514258555701.00260689-41443.0026068899
26516922563859.451768686-46937.4517686858
27507561559647.021601045-52086.021601045
28492622541877.693109812-49255.6931098123
29490243535686.6-45443.6
30469357518182.227560751-48825.227560751
31477580518863.718063673-41283.7180636734
32528379571020.718063673-42641.7180636734
33533590580128.304283298-46538.3042832979
34517945553493.619740081-35548.6197400815
35506174529488.247300832-23314.2473008324
36501866516408.847300832-14542.8473008324
37516141536257.620655505-20116.6206555047
38528222534401.755106443-6179.75510644334
39532638530189.3249388032448.67506119748
40536322521003.69477116215318.3052288383
41536535521965.68359767614569.3164023239
42523597508753.16032022314843.839679777
43536214513726.49998494122487.5000150586
44586570571605.96553400314964.0344659973
45596594577852.31897909618741.6810209035
46580523561231.94914673719291.0508532626
47564478547240.89141834617237.1085816544
48557560531300.25864381526259.7413561851
49575093543995.95006216131097.0499378394
50580112547862.5500621632249.4499378395
51574761546511.3526690528249.6473309497
52563250541617.57166320621632.4283367945
53551531531134.62939159720396.3706084027
54537034522213.9552759414820.0447240598
55544686528617.91132792416068.0886720761
56600991582205.52771518918785.4722848108
57604378588451.88116028315926.1188397169
58586111576123.360489729987.63951028013
59563668562132.3027613281535.69723867192
60548604550483.519148593-1879.51914859341


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.01032503929420590.02065007858841180.989674960705794
180.04697423865375150.0939484773075030.953025761346249
190.1181551528388880.2363103056777770.881844847161112
200.07930581831962810.1586116366392560.920694181680372
210.05303959090519340.1060791818103870.946960409094807
220.04753108144271980.09506216288543970.95246891855728
230.06522265472672920.1304453094534580.934777345273271
240.0677799045579810.1355598091159620.932220095442019
250.1497728744264670.2995457488529330.850227125573534
260.1952853461206260.3905706922412510.804714653879374
270.2013541329871710.4027082659743420.798645867012829
280.1649760744548340.3299521489096680.835023925545166
290.1521492160036790.3042984320073580.847850783996321
300.1067408651946550.2134817303893110.893259134805345
310.07716338848028870.1543267769605770.922836611519711
320.05117632460974070.1023526492194810.94882367539026
330.03086981393285260.06173962786570520.969130186067147
340.02512348052864140.05024696105728280.974876519471359
350.02927941285683570.05855882571367150.970720587143164
360.05447043599775650.1089408719955130.945529564002244
370.2786434816588990.5572869633177970.721356518341101
380.6912813114872550.617437377025490.308718688512745
390.9516985578846020.0966028842307960.048301442115398
400.9997039891092360.000592021781528230.000296010890764115
410.9993382097983360.00132358040332820.000661790201664098
420.9989801966570140.002039606685971680.00101980334298584
430.9980539218117450.003892156376510670.00194607818825533


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level40.148148148148148NOK
5% type I error level50.185185185185185NOK
10% type I error level110.407407407407407NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/108wom1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/108wom1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/11drs1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/11drs1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/2cmqd1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/2cmqd1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/3cmqd1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/3cmqd1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/4cmqd1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/4cmqd1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/55vqg1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/55vqg1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/65vqg1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/65vqg1293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/7xn711293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/7xn711293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/8xn711293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/8xn711293647886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/98wom1293647886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293647748pkdivys4rx6zhc7/98wom1293647886.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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