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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 09:31:50 -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/t1258734791oyod5csklij6oo4.htm/, Retrieved Fri, 20 Nov 2009 17:33:23 +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/t1258734791oyod5csklij6oo4.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 «
111.4 0 87.4 0 96.8 0 114.1 0 110.3 0 103.9 0 101.6 0 94.6 0 95.9 0 104.7 0 102.8 0 98.1 0 113.9 0 80.9 0 95.7 0 113.2 0 105.9 0 108.8 0 102.3 0 99 0 100.7 0 115.5 0 100.7 0 109.9 0 114.6 0 85.4 0 100.5 0 114.8 0 116.5 0 112.9 0 102 0 106 0 105.3 0 118.8 0 106.1 0 109.3 0 117.2 0 92.5 0 104.2 0 112.5 0 122.4 0 113.3 0 100 0 110.7 0 112.8 0 109.8 0 117.3 0 109.1 0 115.9 0 96 0 99.8 0 116.8 1 115.7 1 99.4 1 94.3 1 91 1 93.2 1 103.1 1 94.1 1 91.8 1 102.7 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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 105.300995850622 -8.30497925311204X[t] + 8.69983402489626M1[t] -16.8609958506224M2[t] -5.9009958506224M3[t] + 10.64M4[t] + 10.52M5[t] + 4.02M6[t] -3.59999999999999M7[t] -3.38M8[t] -2.06000000000000M9[t] + 6.74M10[t] + 0.560000000000001M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)105.3009958506222.42429343.435700
X-8.304979253112041.889219-4.3966.1e-053e-05
M18.699834024896263.2430072.68260.0099890.004994
M2-16.86099585062243.407584-4.94811e-055e-06
M3-5.90099585062243.407584-1.73170.0897460.044873
M410.643.3865713.14180.0028750.001437
M510.523.3865713.10640.0031770.001588
M64.023.3865711.1870.2410530.120526
M7-3.599999999999993.386571-1.0630.2930910.146545
M8-3.383.386571-0.99810.3232550.161628
M9-2.060000000000003.386571-0.60830.5458660.272933
M106.743.3865711.99020.0522790.02614
M110.5600000000000013.3865710.16540.8693560.434678


Multiple Linear Regression - Regression Statistics
Multiple R0.855759430330213
R-squared0.73232420259909
Adjusted R-squared0.665405253248862
F-TEST (value)10.9434503934961
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value4.93353691233267e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.35463934521169
Sum Squared Residuals1376.26380082988


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1111.4114.000829875519-2.60082987551872
287.488.44-1.03999999999997
396.899.4-2.60000000000000
4114.1115.940995850622-1.84099585062243
5110.3115.820995850622-5.52099585062241
6103.9109.320995850622-5.4209958506224
7101.6101.700995850622-0.100995850622399
894.6101.920995850622-7.32099585062241
995.9103.240995850622-7.3409958506224
10104.7112.040995850622-7.3409958506224
11102.8105.860995850622-3.06099585062241
1298.1105.300995850622-7.20099585062241
13113.9114.000829875519-0.100829875518659
1480.988.44-7.54
1595.799.4-3.7
16113.2115.940995850622-2.74099585062240
17105.9115.820995850622-9.9209958506224
18108.8109.320995850622-0.52099585062241
19102.3101.7009958506220.599004149377588
2099101.920995850622-2.9209958506224
21100.7103.240995850622-2.54099585062241
22115.5112.0409958506223.45900414937759
23100.7105.860995850622-5.1609958506224
24109.9105.3009958506224.59900414937760
25114.6114.0008298755190.59917012448133
2685.488.44-3.04000000000001
27100.599.41.1
28114.8115.940995850622-1.14099585062240
29116.5115.8209958506220.679004149377588
30112.9109.3209958506223.5790041493776
31102101.7009958506220.299004149377590
32106101.9209958506224.0790041493776
33105.3103.2409958506222.05900414937759
34118.8112.0409958506226.75900414937759
35106.1105.8609958506220.239004149377590
36109.3105.3009958506223.9990041493776
37117.2114.0008298755193.19917012448134
3892.588.444.05999999999999
39104.299.44.8
40112.5115.940995850622-3.4409958506224
41122.4115.8209958506226.5790041493776
42113.3109.3209958506223.97900414937759
43100101.700995850622-1.70099585062241
44110.7101.9209958506228.7790041493776
45112.8103.2409958506229.55900414937759
46109.8112.040995850622-2.24099585062241
47117.3105.86099585062211.4390041493776
48109.1105.3009958506223.79900414937759
49115.9114.0008298755191.89917012448134
509688.447.55999999999999
5199.899.40.399999999999997
52116.8107.6360165975109.16398340248963
53115.7107.5160165975108.18398340248962
5499.4101.016016597510-1.61601659751037
5594.393.39601659751040.903983402489621
569193.6160165975104-2.61601659751037
5793.294.9360165975104-1.73601659751037
58103.1103.736016597510-0.636016597510378
5994.197.5560165975104-3.45601659751038
6091.896.9960165975104-5.19601659751037
61102.7105.695850622407-2.99585062240663


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1850064069147850.3700128138295690.814993593085215
170.1950924613909200.3901849227818410.80490753860908
180.1720381575082240.3440763150164490.827961842491776
190.09221685554237610.1844337110847520.907783144457624
200.08454758980511510.1690951796102300.915452410194885
210.08400938974146790.1680187794829360.915990610258532
220.2314466097642440.4628932195284880.768553390235756
230.2075758296458870.4151516592917740.792424170354113
240.3828688761202260.7657377522404530.617131123879774
250.2957887741514010.5915775483028020.704211225848599
260.278599358302530.557198716605060.72140064169747
270.2343924513511870.4687849027023750.765607548648813
280.1898380473779910.3796760947559830.810161952622009
290.3077943311857890.6155886623715770.692205668814211
300.2958932442583410.5917864885166830.704106755741658
310.2187480270740130.4374960541480250.781251972925987
320.2567184446612320.5134368893224640.743281555338768
330.2542115398826280.5084230797652560.745788460117372
340.3042720393011980.6085440786023950.695727960698802
350.2822982018994280.5645964037988570.717701798100572
360.2366602635747390.4733205271494780.763339736425261
370.1808488587420640.3616977174841280.819151141257936
380.1713704197503680.3427408395007370.828629580249632
390.1485578957464870.2971157914929750.851442104253513
400.4436620122197230.8873240244394460.556337987780277
410.5611352721182020.8777294557635960.438864727881798
420.4506766688847330.9013533377694650.549323331115267
430.5804452842848460.8391094314303070.419554715715154
440.5230904384922510.9538191230154970.476909561507749
450.4596034212680210.9192068425360420.540396578731979


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/10cwzu1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/10cwzu1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/16jlm1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/16jlm1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/2hm6y1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/2hm6y1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/3rxxa1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/3rxxa1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/4f99k1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/4f99k1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/5m6aq1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/5m6aq1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/6g30a1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/6g30a1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/7eopr1258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/7eopr1258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/8s5p61258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/8s5p61258734706.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/9ak641258734706.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258734791oyod5csklij6oo4/9ak641258734706.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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