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SHW WS7

*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 04:20:18 -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/t1258716079w93fq2xga4vo18o.htm/, Retrieved Fri, 20 Nov 2009 12:21:32 +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/t1258716079w93fq2xga4vo18o.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 «
8.6 0 8.5 0 8.3 0 7.8 0 7.8 0 8 0 8.6 0 8.9 0 8.9 0 8.6 0 8.3 0 8.3 0 8.3 0 8.4 0 8.5 0 8.4 0 8.6 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.5 0 8.6 0 8.4 0 8.1 0 8 0 8 0 8 0 8 0 7.9 0 7.8 0 7.8 0 7.9 0 8.1 0 8 0 7.6 0 7.3 0 7 0 6.8 0 7 0 7.1 0 7.2 0 7.1 1 6.9 1 6.7 1 6.7 1 6.6 1 6.9 1 7.3 1 7.5 1 7.3 1 7.1 1 6.9 1 7.1 1
 
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
Y[t] = + 8.02708333333333 -1.13541666666667X[t] + 0.259999999999997M1[t] + 0.220000000000001M2[t] + 0.18M3[t] + 0.0999999999999998M4[t] + 0.12M5[t] + 0.0799999999999999M6[t] + 0.16M7[t] + 0.18M8[t] + 0.1M9[t] + 0.0399999999999998M10[t] -0.0399999999999999M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)8.027083333333330.23443534.240100
X-1.135416666666670.167454-6.780500
M10.2599999999999970.3281410.79230.4321420.216071
M20.2200000000000010.3281410.67040.5058560.252928
M30.180.3281410.54850.5859140.292957
M40.09999999999999980.3281410.30470.7619040.380952
M50.120.3281410.36570.7162320.358116
M60.07999999999999990.3281410.24380.8084480.404224
M70.160.3281410.48760.6281030.314051
M80.180.3281410.54850.5859140.292957
M90.10.3281410.30470.7619040.380952
M100.03999999999999980.3281410.12190.9034990.451749
M11-0.03999999999999990.328141-0.12190.9034990.451749


Multiple Linear Regression - Regression Statistics
Multiple R0.709316796716717
R-squared0.503130318104464
Adjusted R-squared0.37626997379071
F-TEST (value)3.96601728322691
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.000313507766686705
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.518835814913426
Sum Squared Residuals12.6519583333333


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.68.287083333333350.312916666666653
28.58.247083333333330.252916666666669
38.38.207083333333330.0929166666666671
47.88.12708333333333-0.327083333333333
57.88.14708333333333-0.347083333333333
688.10708333333333-0.107083333333333
78.68.187083333333330.412916666666667
88.98.207083333333330.692916666666668
98.98.127083333333330.772916666666667
108.68.067083333333330.532916666666666
118.37.987083333333330.312916666666667
128.38.027083333333330.272916666666667
138.38.287083333333330.0129166666666705
148.48.247083333333330.152916666666666
158.58.207083333333330.292916666666666
168.48.127083333333330.272916666666667
178.68.147083333333330.452916666666666
188.58.107083333333330.392916666666667
198.58.187083333333330.312916666666667
208.58.207083333333330.292916666666667
218.58.127083333333330.372916666666667
228.58.067083333333330.432916666666667
238.57.987083333333330.512916666666667
248.58.027083333333330.472916666666667
258.58.287083333333330.21291666666667
268.58.247083333333330.252916666666666
278.58.207083333333330.292916666666666
288.58.127083333333330.372916666666667
298.68.147083333333330.452916666666666
308.48.107083333333330.292916666666667
318.18.18708333333333-0.0870833333333334
3288.20708333333333-0.207083333333333
3388.12708333333333-0.127083333333333
3488.06708333333333-0.0670833333333332
3587.987083333333330.0129166666666665
367.98.02708333333333-0.127083333333333
377.88.28708333333333-0.48708333333333
387.88.24708333333333-0.447083333333334
397.98.20708333333333-0.307083333333333
408.18.12708333333333-0.0270833333333337
4188.14708333333333-0.147083333333333
427.68.10708333333333-0.507083333333334
437.38.18708333333333-0.887083333333333
4478.20708333333333-1.20708333333333
456.88.12708333333333-1.32708333333333
4678.06708333333333-1.06708333333333
477.17.98708333333333-0.887083333333334
487.28.02708333333333-0.827083333333333
497.17.15166666666666-0.051666666666664
506.97.11166666666667-0.211666666666667
516.77.07166666666667-0.371666666666667
526.76.99166666666667-0.291666666666667
536.67.01166666666667-0.411666666666667
546.96.97166666666667-0.0716666666666665
557.37.051666666666670.248333333333333
567.57.071666666666670.428333333333333
577.36.991666666666670.308333333333333
587.16.931666666666670.168333333333333
596.96.851666666666670.0483333333333333
607.16.891666666666670.208333333333333


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1520180315712610.3040360631425230.847981968428739
170.2307882190190740.4615764380381490.769211780980926
180.1812434368131800.3624868736263590.81875656318682
190.1053698333059290.2107396666118570.894630166694071
200.07711748283965370.1542349656793070.922882517160346
210.06060016968879620.1212003393775920.939399830311204
220.03835492507361420.07670985014722840.961645074926386
230.02677758265759410.05355516531518820.973222417342406
240.01867723222368410.03735446444736830.981322767776316
250.01066320828641030.02132641657282050.98933679171359
260.006528822840217410.01305764568043480.993471177159783
270.004442002674487360.008884005348974720.995557997325513
280.004920576821530770.009841153643061530.99507942317847
290.007282366903602360.01456473380720470.992717633096398
300.006518899793926550.01303779958785310.993481100206073
310.007090901300862080.01418180260172420.992909098699138
320.0140116424779360.0280232849558720.985988357522064
330.02747959129444550.0549591825888910.972520408705555
340.03729817505624110.07459635011248220.962701824943759
350.04624774765952750.0924954953190550.953752252340473
360.04838112934576190.09676225869152370.951618870654238
370.0509218482124330.1018436964248660.949078151787567
380.056907253955330.113814507910660.94309274604467
390.07875747767414980.1575149553483000.92124252232585
400.1680444578696020.3360889157392040.831955542130398
410.6345158659501730.7309682680996550.365484134049827
420.8776988653584470.2446022692831060.122301134641553
430.8434661682350850.3130676635298290.156533831764915
440.8699826355959880.2600347288080230.130017364404012


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.0689655172413793NOK
5% type I error level90.310344827586207NOK
10% type I error level150.517241379310345NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/10p9kk1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/10p9kk1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/1wcdu1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/1wcdu1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/2v88g1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/2v88g1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/32bq91258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/32bq91258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/4zk3o1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/4zk3o1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/5vkrm1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/5vkrm1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/609fc1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/609fc1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/7mvnm1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/7mvnm1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/8b7zw1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/8b7zw1258716014.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/923yv1258716014.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258716079w93fq2xga4vo18o/923yv1258716014.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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