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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, 18 Nov 2009 09:38:41 -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/18/t1258562408six2zg3mbchp0he.htm/, Retrieved Wed, 18 Nov 2009 17:40:21 +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/18/t1258562408six2zg3mbchp0he.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:
ws7multipleregressionlineairtrendwmanecogr
 
Dataseries X:
» Textbox « » Textfile « » CSV «
8,00 96,80 8,10 114,10 7,70 110,30 7,50 103,90 7,60 101,60 7,80 94,60 7,80 95,90 7,80 104,70 7,50 102,80 7,50 98,10 7,10 113,90 7,50 80,90 7,50 95,70 7,60 113,20 7,70 105,90 7,70 108,80 7,90 102,30 8,10 99,00 8,20 100,70 8,20 115,50 8,20 100,70 7,90 109,90 7,30 114,60 6,90 85,40 6,60 100,50 6,70 114,80 6,90 116,50 7,00 112,90 7,10 102,00 7,20 106,00 7,10 105,30 6,90 118,80 7,00 106,10 6,80 109,30 6,40 117,20 6,70 92,50 6,60 104,20 6,40 112,50 6,30 122,40 6,20 113,30 6,50 100,00 6,80 110,70 6,80 112,80 6,40 109,80 6,10 117,30 5,80 109,10 6,10 115,90 7,20 96,00 7,30 99,80 6,90 116,80 6,10 115,70 5,80 99,40 6,20 94,30 7,10 91,00 7,70 93,20 7,90 103,10 7,70 94,10 7,40 91,80 7,50 102,70 8,00 82,60
 
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
Wman[t] = + 11.8416227316364 -0.0442772635382484Ecogr[t] + 0.251375956642180M1[t] + 0.869895185794386M2[t] + 0.684255461872863M3[t] + 0.316126796577316M4[t] + 0.218407596118930M5[t] + 0.587822141800411M6[t] + 0.785941677373967M7[t] + 1.11525514421362M8[t] + 0.721295203250312M9[t] + 0.49617348337196M10[t] + 0.724083400897677M11[t] -0.0196735477030671t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)11.84162273163641.05038911.273600
Ecogr-0.04427726353824840.011625-3.80880.0004120.000206
M10.2513759566421800.3563350.70540.4840880.242044
M20.8698951857943860.4524071.92280.0607070.030354
M30.6842554618728630.451091.51690.1361360.068068
M40.3161267965773160.4024540.78550.4361890.218094
M50.2184075961189300.3576880.61060.5444630.272232
M60.5878221418004110.3584441.63990.1078420.053921
M70.7859416773739670.3648312.15430.0364920.018246
M81.115255144213620.4207022.65090.0109720.005486
M90.7212952032503120.3791381.90250.0633820.031691
M100.496173483371960.3757141.32060.1931620.096581
M110.7240834008976770.4391651.64880.1060080.053004
t-0.01967354770306710.003912-5.02888e-064e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.723465284054046
R-squared0.523402017231401
Adjusted R-squared0.38871128297071
F-TEST (value)3.88595414602439
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.000308225772254089
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.514224918714163
Sum Squared Residuals12.1636542832230


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
187.787286030073060.212713969926935
28.17.62013505231050.479864947689505
37.77.583075382131250.116924617868750
47.57.478647655777430.0213523442225741
57.67.463092613753940.136907386246056
67.88.1227744565001-0.322774456500098
77.88.24366000177086-0.443660001770861
87.88.16366000177086-0.363660001770861
97.57.83415331382716-0.334153313827159
107.57.7974611848755-0.297461184875506
117.17.30611679079383-0.206116790793833
127.58.02350953895529-0.523509538955286
137.57.59990844752832-0.0999084475283223
147.67.423902017058110.176097982941885
157.77.541812769262740.158187230737263
167.77.02560649200320.674393507996798
177.97.196015956840360.703984043159636
188.17.6918719244950.408128075505002
198.27.795046564350460.404953435649535
208.27.449382983120970.750617016879025
218.27.691052994820670.508947005179325
227.97.038906902687370.86109309731263
237.37.039040133880250.260959866119747
246.97.58817928059636-0.688179280596362
256.67.15129501010792-0.551295010107925
266.77.11697582296011-0.416975822960111
276.96.83639120332050.0636087966795017
2876.607987139059580.392012860940422
297.16.973216563465030.126783436534967
307.27.145848507290450.0541514927095463
317.17.35528857963772-0.255288579637716
326.97.06718544100795-0.167185441007948
3377.21587319927733-0.215873199277328
346.86.82939068837351-0.0293906883735145
356.46.687836676244-0.287836676244001
366.77.037728137038-0.337728137037993
376.66.7513865625796-0.1513865625796
386.46.98273095666128-0.582730956661276
396.36.33907277600803-0.0390727760080276
406.26.35419366120747-0.154193661207474
416.56.82568851810472-0.325688518104725
426.86.701662796223880.0983372037761192
436.86.787126530664050.0128734693359522
446.47.22959824041538-0.829598240415378
456.16.48388527521214-0.383885275212141
465.86.60216356864436-0.802163568644359
476.16.50931454640692-0.409314546406919
487.26.646675142217320.553324857782682
497.36.710123949711090.589876050288912
506.96.556256151010.343743848989997
516.16.39964786927749-0.299647869277487
525.86.73356505195232-0.93356505195232
536.26.84198634783593-0.641986347835935
547.17.33784231549057-0.237842315490569
557.77.418878323576910.281121676423090
567.97.290173333684840.609826666315162
577.77.27503521686270.424964783137302
587.47.132077655419250.26792234458075
597.56.857691852674990.642308147325008
6087.003907901193040.996092098806958


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.1474296209561530.2948592419123060.852570379043847
180.0637525270249130.1275050540498260.936247472975087
190.02631988783136640.05263977566273270.973680112168634
200.01285378858819230.02570757717638450.987146211411808
210.03930575331493380.07861150662986770.960694246685066
220.03074172081466870.06148344162933750.969258279185331
230.01683625596045420.03367251192090840.983163744039546
240.04347805198262840.08695610396525680.956521948017372
250.2267052080653350.4534104161306710.773294791934665
260.2844548587845020.5689097175690050.715545141215498
270.2682491752931950.5364983505863890.731750824706805
280.3185599015510830.6371198031021660.681440098448917
290.3346006651799040.6692013303598080.665399334820096
300.3130285632591820.6260571265183640.686971436740818
310.2610395084013980.5220790168027950.738960491598602
320.2536048234624810.5072096469249620.746395176537519
330.2016041510941040.4032083021882090.798395848905896
340.2379484501827790.4758969003655580.762051549817221
350.1866303215277150.3732606430554300.813369678472285
360.1293855085823330.2587710171646670.870614491417667
370.0840214299824980.1680428599649960.915978570017502
380.0626703838755960.1253407677511920.937329616124404
390.05189402261785940.1037880452357190.94810597738214
400.1296162295736610.2592324591473220.870383770426339
410.3815921538856100.7631843077712190.61840784611439
420.6413063969531610.7173872060936790.358693603046839
430.6399637952396190.7200724095207630.360036204760381


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0740740740740741NOK
10% type I error level60.222222222222222NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/1054l71258562316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/1054l71258562316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/1exho1258562316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/1exho1258562316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/2hgi21258562316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/31krw1258562316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/47bz31258562316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/5xejj1258562316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/6wz5q1258562316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/7wnjk1258562316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/8m7sf1258562316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/8m7sf1258562316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/9rhm81258562316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258562408six2zg3mbchp0he/9rhm81258562316.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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Software written by Ed van Stee & Patrick Wessa


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