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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: Mon, 21 Dec 2009 04:47:07 -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/Dec/21/t1261396102grgn1yclaphgf24.htm/, Retrieved Mon, 21 Dec 2009 12:48:34 +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/Dec/21/t1261396102grgn1yclaphgf24.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 «
19169 0 20366 13807 0 22782 29743 0 19169 25591 0 13807 29096 0 29743 26482 0 25591 22405 0 29096 27044 0 26482 17970 0 22405 18730 0 27044 19684 0 17970 19785 0 18730 18479 0 19684 10698 0 19785 31956 0 18479 29506 0 10698 34506 0 31956 27165 0 29506 26736 0 34506 23691 0 27165 18157 0 26736 17328 0 23691 18205 0 18157 20995 0 17328 17382 0 18205 9367 0 20995 31124 0 17382 26551 0 9367 30651 0 31124 25859 0 26551 25100 0 30651 25778 0 25859 20418 0 25100 18688 0 25778 20424 0 20418 24776 0 18688 19814 0 20424 12738 0 24776 31566 0 19814 30111 0 12738 30019 0 31566 31934 1 30111 25826 1 30019 26835 1 31934 20205 1 25826 17789 1 26835 20520 1 20205 22518 1 17789 15572 1 20520 11509 1 22518 25447 1 15572 24090 1 11509 27786 1 25447 26195 1 24090 20516 1 27786 22759 1 26195 19028 1 20516 16971 1 22759
 
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] = + 12622.3004248372 -964.441332928536X[t] + 0.511778704714425Y2[t] -4797.16832219451M1[t] -12461.6239550917M2[t] + 7962.03262905486M3[t] + 8458.52123356123M4[t] + 2300.66498077665M5[t] + 1028.70823520450M6[t] -4052.67073046471M7[t] -1483.48863957148M8[t] -5815.81330573939M9[t] -7647.52117943388M10[t] -2837.64204936683M11[t] + 11.8947607259918t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)12622.30042483722589.1926354.8751.5e-058e-06
X-964.441332928536846.849829-1.13890.2610680.130534
Y20.5117787047144250.1286063.97940.0002610.000131
M1-4797.168322194511205.962828-3.97790.0002620.000131
M2-12461.62395509171291.873158-9.646200
M37962.032629054861185.0902716.718500
M48458.521233561231453.5151655.81941e-060
M52300.664980776651925.1991831.1950.2386260.119313
M61028.708235204501671.0087890.61560.541390.270695
M7-4052.670730464711985.499802-2.04110.0474050.023703
M8-1483.488639571481702.747711-0.87120.3884660.194233
M9-5815.813305739391421.664046-4.09080.0001859.3e-05
M10-7647.521179433881504.749652-5.08238e-064e-06
M11-2837.642049366831255.725187-2.25980.0289580.014479
t11.894760725991822.7638090.52250.6039840.301992


Multiple Linear Regression - Regression Statistics
Multiple R0.965018983561122
R-squared0.93126163863334
Adjusted R-squared0.90888170702559
F-TEST (value)41.6114604349759
F-TEST (DF numerator)14
F-TEST (DF denominator)43
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1765.33289651167
Sum Squared Residuals134005210.126770


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11916918259.9119635826909.08803641736
21380711843.80844200151963.19155799852
32974330430.3033267408-687.303326740833
42559128194.5292772944-2603.52927729443
52909630204.2732235649-1108.27322356492
62648226819.3060567445-337.306056744478
72240523543.6062118253-1138.60621182532
82704424786.89352932102257.10647067896
91797018379.9418447584-409.941844758405
101873018934.2701429601-204.270142960129
111968419112.1640671745571.83593282553
121978522350.6526928503-2565.65269285026
131847918053.6160156793425.383984320706
141069810452.7447926842245.255207315755
153195630219.91314919981736.08685080022
162950626746.14641304922759.85358695081
173450631479.57662580993026.42337419014
182716528965.6568144134-1800.65681441335
192673626455.0661330423280.933866957746
202369125279.1755133529-1588.17551335289
211815720739.1925435885-2582.19254358848
221732817361.0132747646-33.0132747645572
231820519350.6038136680-1145.60381366797
242099521775.8760775525-780.876077552536
251738217439.4324401186-57.4324401185665
26936711214.7341541006-1847.7341541006
273112429801.22903884001322.77096116005
282655126207.7060857862343.293914213805
293065131196.5138721994-545.513872199357
302585927596.0878706941-1737.08787069413
312510024624.8963550800475.103644919953
322577824753.52965370781024.47034629225
332041820044.6597113876373.340288612422
341868818571.8325602155116.167439784537
352042420650.4725937392-226.472593739185
362477622614.63224467612161.36775532395
371981418717.80651459181096.19348540822
381273813292.5065653377-554.506565337742
393156631188.6119774173377.388022582666
403011128075.64922809042035.35077190958
413001931565.457188395-1546.45718839504
423193428596.31585526083337.68414473916
432582623479.74800948392346.25199051610
442683527040.8810806313-205.88108063125
452020519594.5068467936610.493153206382
461778918291.0784468820-502.078446881973
472052019719.7595254184800.240474581624
482251821332.83898492111185.16101507885
491557217945.2330660277-2373.23306602772
501150911315.2060458759193.793954124068
512544728195.9425078021-2748.94250780211
522409026624.9689957798-2534.96899577976
532778627612.1790900308173.820909969170
542619525657.6334028872537.366597112806
552051622479.6832905685-1963.68329056848
562275924246.5202229871-1487.52022298707
571902817019.69905347192008.30094652808
581697116347.8055751779623.194424822123


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
180.9223151657952050.1553696684095890.0776848342047946
190.8514909780424370.2970180439151260.148509021957563
200.911939949859540.1761201002809200.0880600501404602
210.9163221107521240.1673557784957530.0836778892478764
220.8625665046728120.2748669906543760.137433495327188
230.8208086677791930.3583826644416140.179191332220807
240.7894614514530960.4210770970938080.210538548546904
250.7189968842721880.5620062314556240.281003115727812
260.7407434365918430.5185131268163140.259256563408157
270.6797078751663630.6405842496672740.320292124833637
280.5762135950200980.8475728099598030.423786404979902
290.4836511251046010.9673022502092020.516348874895399
300.6100543950579680.7798912098840640.389945604942032
310.5221630051329340.9556739897341310.477836994867066
320.4168606759108890.8337213518217780.583139324089111
330.4260938261458770.8521876522917540.573906173854123
340.4097413597833410.8194827195666830.590258640216659
350.4592750964796410.9185501929592830.540724903520359
360.4886111416772330.9772222833544660.511388858322767
370.3621120188808920.7242240377617830.637887981119108
380.4425169877251390.8850339754502790.557483012274861
390.3643548330211020.7287096660422050.635645166978898
400.2798057653715530.5596115307431070.720194234628447


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/Dec/21/t1261396102grgn1yclaphgf24/10d9qe1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/10d9qe1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/1jq721261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/1jq721261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/27nfb1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/27nfb1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/3m1vu1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/3m1vu1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/49cwx1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/49cwx1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/58bvy1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/58bvy1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/6sig01261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/6sig01261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/796oa1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/796oa1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/8up1d1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/8up1d1261396021.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/9e8zp1261396021.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/21/t1261396102grgn1yclaphgf24/9e8zp1261396021.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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