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M2

*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: Thu, 19 Nov 2009 00:34:35 -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/19/t1258617097gziup5lodpwmvvx.htm/, Retrieved Thu, 19 Nov 2009 08:51:50 +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/19/t1258617097gziup5lodpwmvvx.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 «
21 2472,81 19 2407,6 25 2454,62 21 2448,05 23 2497,84 23 2645,64 19 2756,76 18 2849,27 19 2921,44 19 2981,85 22 3080,58 23 3106,22 20 3119,31 14 3061,26 14 3097,31 14 3161,69 15 3257,16 11 3277,01 17 3295,32 16 3363,99 20 3494,17 24 3667,03 23 3813,06 20 3917,96 21 3895,51 19 3801,06 23 3570,12 23 3701,61 23 3862,27 23 3970,1 27 4138,52 26 4199,75 17 4290,89 24 4443,91 26 4502,64 24 4356,98 27 4591,27 27 4696,96 26 4621,4 24 4562,84 23 4202,52 23 4296,49 24 4435,23 17 4105,18 21 4116,68 19 3844,49 22 3720,98 22 3674,4 18 3857,62 16 3801,06 14 3504,37 12 3032,6 14 3047,03 16 2962,34 8 2197,82 3 2014,45 0 1862,83 5 1905,41 1 1810,99 1 1670,07 3 1864,44
 
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
Consvertr[t] = -2.54623902332245 + 0.0061421420368986Aand[t] + 0.609520892164507M1[t] -0.280403213295958M2[t] + 1.75852696995038M3[t] + 0.577457909719086M4[t] + 1.42655819316205M5[t] + 0.676750919876607M6[t] + 0.879589447508637M7[t] -1.76292560165979M8[t] -2.55132966649962M9[t] + 0.0562001706321281M10[t] + 0.551095836096717M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-2.546239023322453.479677-0.73170.4678810.233941
Aand0.00614214203689860.0007957.72200
M10.6095208921645073.0365130.20070.8417570.420879
M2-0.2804032132959583.175646-0.08830.9300070.465004
M31.758526969950383.1724020.55430.5819330.290967
M40.5774579097190863.1714450.18210.8562860.428143
M51.426558193162053.1713940.44980.6548650.327432
M60.6767509198766073.1720380.21330.8319580.415979
M70.8795894475086373.1713530.27740.7826990.391349
M8-1.762925601659793.171463-0.55590.5808810.29044
M9-2.551329666499623.171321-0.80450.4250750.212537
M100.05620017063212813.1713690.01770.9859350.492967
M110.5510958360967173.1714780.17380.862780.43139


Multiple Linear Regression - Regression Statistics
Multiple R0.755982426459113
R-squared0.571509429115009
Adjusted R-squared0.464386786393761
F-TEST (value)5.33509456634839
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value1.24190173838024e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.01428849726404
Sum Squared Residuals1206.86827842214


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12113.25163211910537.74836788089471
21911.96117893141877.03882106858135
32514.288912633240010.7110873667600
42113.06748969982627.93251030017375
52314.22240723528648.7775927647136
62314.38040855505468.61959144494545
71915.26576190582683.73423809417324
81813.19145641649184.80854358350818
91912.84633074245506.15366925754504
101915.82490738003583.17509261996425
112216.92621672880335.07378327119665
122316.53260541453276.4673945854673
132017.22252694596022.77747305403978
141415.9760514952578-1.97605149525779
151418.2364058989343-4.23640589893432
161417.4507679430386-3.45076794303856
171518.8862585267442-3.88625852674423
181118.2583727728912-7.25837277289122
191718.5736739212189-1.57367392121887
201616.3529397657243-0.352939765724267
212016.36411975124793.6358802487521
222420.03338026087793.96661973912206
232321.42521292799081.57478707200917
242021.5184277915648-1.51842779156477
252121.9900575950009-0.990057595000907
261920.5200081741554-1.52000817415537
272321.14047207540031.85952792459965
282320.76703327160092.23296672839915
292322.60293009469190.397069905308057
302322.51542999724530.484570002754728
312723.75272808673183.24727191326823
322621.48629639448264.51370360551736
331721.2576871548858-4.25768715488575
342424.8050875665037-0.805087566503718
352625.66071123379540.339288766204634
362424.214950988604-0.214950988603991
372726.26351433859350.736485661406522
382726.02275322501280.97724677498718
392627.5975831559511-1.59758315595110
402426.0568302580390-2.05683025803903
412324.6927939227467-1.69279392274669
422324.5201637366686-1.52016373666860
432425.5751630504999-1.57516305049995
441720.9054340220531-3.90543402205314
452120.18766459063760.812335409362354
461921.1233647867460-2.12336478674596
472220.85964448923321.14035551076679
482220.02244767705781.97755232294225
491821.7573318332228-3.75733183322282
501620.5200081741554-4.52000817415537
511420.7366262364743-6.73662623647426
521216.6578788274953-4.65787882749532
531417.5956102205307-3.59561022053073
541616.3256249381403-0.325624938140343
55811.8326730357227-3.83267303572266
5638.06387340124813-5.06387340124813
5706.34419776077374-6.34419776077374
5859.21326000583663-4.21326000583663
5919.12821462017726-8.12821462017726
6017.71156812824078-6.71156812824078
6139.51493716811727-6.51493716811727


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.6038016587010310.7923966825979380.396198341298969
170.4400811883895550.880162376779110.559918811610445
180.5837742389330110.8324515221339780.416225761066989
190.5329312156388960.9341375687222080.467068784361104
200.4651764758115770.9303529516231530.534823524188423
210.651035669253670.6979286614926580.348964330746329
220.9141561024322670.1716877951354660.085843897567733
230.9189126354584320.1621747290831350.0810873645415675
240.879735598266930.2405288034661420.120264401733071
250.890126981814460.2197460363710810.109873018185540
260.9018919235063150.1962161529873700.0981080764936852
270.9559274264966770.08814514700664670.0440725735033233
280.982987817080920.03402436583816010.0170121829190800
290.9812708092279240.03745838154415190.0187291907720759
300.9791283385456420.04174332290871590.0208716614543579
310.9888569757023360.02228604859532710.0111430242976635
320.9976648268763920.004670346247215920.00233517312360796
330.9982718358455450.00345632830891010.00172816415445505
340.9963382957959950.007323408408009580.00366170420400479
350.9922435729284880.01551285414302490.00775642707151247
360.9860806285137960.02783874297240740.0139193714862037
370.9786250333431560.04274993331368770.0213749666568438
380.9779911249533340.04401775009333150.0220088750466658
390.9661984035595230.06760319288095410.0338015964404771
400.934986409737380.1300271805252390.0650135902626197
410.8818387971313660.2363224057372680.118161202868634
420.8650824625833030.2698350748333940.134917537416697
430.8140251586194570.3719496827610870.185974841380543
440.8248187926782780.3503624146434450.175181207321723
450.6770847008254070.6458305983491870.322915299174593


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.1NOK
5% type I error level110.366666666666667NOK
10% type I error level130.433333333333333NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/103lw1258616066.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/103lw1258616066.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/10h6001258616066.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/10h6001258616066.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/2ulic1258616066.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/2ulic1258616066.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/3g2y51258616066.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/488tg1258616066.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/5oobi1258616066.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/6xvap1258616066.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/709fw1258616066.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/8xd1e1258616066.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/8xd1e1258616066.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/9qxiy1258616066.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258617097gziup5lodpwmvvx/9qxiy1258616066.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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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Software written by Ed van Stee & Patrick Wessa


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