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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 07:54:32 -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/t1258728982w3v19bc33za40be.htm/, Retrieved Fri, 20 Nov 2009 15:56:34 +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/t1258728982w3v19bc33za40be.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 «
20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 0 29506 0 34506 0 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 0 12738 0 31566 0 30111 0 30019 0 31934 1 25826 1 26835 1 20205 1 17789 1 20520 1 22518 1 15572 1 11509 1 25447 1 24090 1 27786 1 26195 1 20516 1 22759 1 19028 1 16971 1 20036 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] = + 22527.8181455235 -1760.41995763605X[t] + 22.9871244635193t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)22527.81814552351750.22961712.871400
X-1760.419957636052651.69407-0.66390.5093940.254697
t22.987124463519368.6883710.33470.739090.369545


Multiple Linear Regression - Regression Statistics
Multiple R0.0957486084587364
R-squared0.00916779602178442
Adjusted R-squared-0.0249988317016023
F-TEST (value)0.268326043061872
F-TEST (DF numerator)2
F-TEST (DF denominator)58
p-value0.76560241245108
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5790.43373566096
Sum Squared Residuals1944689125.13067


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12036622550.8052699870-2184.80526998704
22278222573.7923944505208.207605549456
31916922596.7795189141-3427.77951891406
41380722619.7666433776-8812.76664337758
52974322642.75376784117100.2462321589
62559122665.74089230462925.25910769538
72909622688.72801676816407.27198323186
82648222711.71514123173770.28485876834
92240522734.7022656952-329.702265695178
102704422757.68939015874286.3106098413
111797022780.6765146222-4810.67651462222
121873022803.6636390857-4073.66363908574
131968422826.6507635493-3142.65076354926
141978522849.6378880128-3064.63788801278
151847922872.6250124763-4393.62501247629
161069822895.6121369398-12197.6121369398
173195622918.59926140339037.40073859667
182950622941.58638586696564.41361413315
193450622964.573510330411541.4264896696
202716522987.56063479394177.43936520611
212673623010.54775925743725.45224074259
222369123033.5348837209657.46511627907
231815723056.5220081844-4899.52200818445
241732823079.5091326480-5751.50913264797
251820523102.4962571115-4897.49625711149
262099523125.483381575-2130.48338157501
271738223148.4705060385-5766.47050603853
28936723171.4576305020-13804.4576305020
293112423194.44475496567929.55524503443
302655123217.43187942913333.56812057092
313065123240.41900389267410.5809961074
322585923263.40612835612595.59387164388
332510023286.39325281961813.60674718036
342577823309.38037728322468.61962271684
352041823332.3675017467-2914.36750174668
361868823355.3546262102-4667.3546262102
372042423378.3417506737-2954.34175067372
382477623401.32887513721374.67112486276
391981423424.3159996008-3610.31599960076
401273823447.3031240643-10709.3031240643
413156623470.29024852788095.7097514722
423011123493.27737299136617.72262700868
433001923516.26449745486502.73550254516
443193421778.831664282310155.1683357177
452582621801.81878874584024.18121125417
462683521824.80591320935010.19408679065
472020521847.7930376729-1642.79303767287
481778921870.7801621364-4081.78016213639
492052021893.7672865999-1373.76728659990
502251821916.7544110634601.245588936576
511557221939.7415355269-6367.74153552694
521150921962.7286599905-10453.7286599905
532544721985.7157844543461.28421554602
542409022008.70290891752081.2970910825
552778622031.6900333815754.30996661898
562619522054.67715784454140.32284215546
572051622077.6642823081-1561.66428230806
582275922100.6514067716658.348593228421
591902822123.6385312351-3095.6385312351
601697122146.6256556986-5175.62565569862
612003622169.6127801621-2133.61278016214


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.6902282965408620.6195434069182750.309771703459138
70.5607304143101350.8785391713797290.439269585689865
80.4302175144657910.8604350289315820.569782485534209
90.4052909168356290.8105818336712580.594709083164371
100.2952236164141780.5904472328283560.704776383585822
110.4084833463609860.8169666927219710.591516653639014
120.3896969104846160.7793938209692330.610303089515384
130.3208151217832830.6416302435665660.679184878216717
140.2497811637120510.4995623274241020.750218836287949
150.2001895983350370.4003791966700740.799810401664963
160.3734325804846720.7468651609693430.626567419515328
170.613810893758750.7723782124825010.386189106241251
180.6414608474209190.7170783051581620.358539152579081
190.7895203957004540.4209592085990920.210479604299546
200.7429771866453080.5140456267093840.257022813354692
210.6908717909959190.6182564180081620.309128209004081
220.627127072373950.7457458552521010.372872927626050
230.6290677413094130.7418645173811740.370932258690587
240.6342711341434150.731457731713170.365728865856585
250.6108928190485450.778214361902910.389107180951455
260.5440320768298430.9119358463403140.455967923170157
270.5393416141755350.921316771648930.460658385824465
280.8499099193993490.3001801612013020.150090080600651
290.8816152984539140.2367694030921710.118384701546086
300.8519106558025690.2961786883948630.148089344197431
310.8642586987581910.2714826024836180.135741301241809
320.8226864310159210.3546271379681570.177313568984079
330.769792458818890.4604150823622190.230207541181109
340.7132944888304080.5734110223391850.286705511169592
350.66684616324080.6663076735183990.333153836759199
360.6538921290595860.6922157418808270.346107870940414
370.6143238018776040.7713523962447930.385676198122396
380.5387256950344720.9225486099310570.461274304965528
390.5221122925226920.9557754149546170.477887707477308
400.8882999305752950.223400138849410.111700069424705
410.8742939045755430.2514121908489140.125706095424457
420.842110468286110.3157790634277790.157889531713889
430.7988433089801310.4023133820397370.201156691019869
440.8520551895715980.2958896208568040.147944810428402
450.8256695949588420.3486608100823160.174330405041158
460.8352352000168110.3295295999663780.164764799983189
470.78330110488810.4333977902238010.216698895111901
480.737109031091390.5257819378172210.262890968908610
490.6482443489925520.7035113020148970.351755651007448
500.5529841462239020.8940317075521950.447015853776098
510.554213652410740.8915726951785210.445786347589260
520.9845303935890520.03093921282189520.0154696064109476
530.9664841518611370.06703169627772660.0335158481388633
540.9510625796783920.09787484064321650.0489374203216082
550.8926352054068530.2147295891862940.107364794593147


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.02OK
10% type I error level30.06OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/10nn8b1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/10nn8b1258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/1gv2b1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/1gv2b1258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/2x35h1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/2x35h1258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/3eoc51258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/3eoc51258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/4vzn81258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/4vzn81258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/5qfys1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/5qfys1258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/6pzyv1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/6pzyv1258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/7mcy81258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/7mcy81258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/80ztv1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/80ztv1258728868.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/9z3uz1258728868.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258728982w3v19bc33za40be/9z3uz1258728868.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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