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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, 03 Dec 2010 10:05:27 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara.htm/, Retrieved Fri, 03 Dec 2010 11:03:27 +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/2010/Dec/03/t1291370607ivjxehr2irqkara.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
2284 41 76403 194493 3160 90 108094 530670 4150 136 134759 518365 7285 97 188873 491303 1134 63 146216 527021 4658 114 156608 233773 2384 77 61348 405972 3748 6 50350 652925 5371 47 87720 446211 1285 51 99489 341340 9327 85 87419 387699 5565 43 94355 493408 1528 32 60326 146494 3122 25 94670 414462 7561 77 82425 364304 2675 54 59017 355178 13253 251 90829 357760 880 15 80791 261216 2053 44 100423 397144 1424 73 131116 374943 4036 85 100269 424898 3045 49 27330 202055 5119 38 39039 378525 1431 35 106885 310768 554 9 79285 325738 1975 34 118881 394510 1765 20 77623 247060 1012 29 114768 368078 810 11 74015 236761 1280 52 69465 312378 666 13 117869 339836 1380 29 60982 347385 4677 66 90131 426280 876 33 138971 352850 814 15 39625 301881 514 15 102725 377516 5692 68 64239 357312 3642 100 90262 458343 540 13 103960 354228 2099 45 106611 308636 567 14 103345 386212 2001 36 95551 393343 2949 40 82903 378509 2253 68 63593 452469 6533 29 126910 364839 1889 43 37527 358649 etc...
 
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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 294370.551448375 + 9.09965160204044Costs[t] -180.944089053398Orders[t] + 0.738242849391378Dividends[t] -346.303558627737t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)294370.55144837553080.6364795.54571e-061e-06
Costs9.099651602040447.401321.22950.225150.112575
Orders-180.944089053398474.895146-0.3810.7049430.352472
Dividends0.7382428493913780.4075131.81160.0765830.038291
t-346.303558627737936.761194-0.36970.7133160.356658


Multiple Linear Regression - Regression Statistics
Multiple R0.350414092233016
R-squared0.122790036035489
Adjusted R-squared0.046510908734227
F-TEST (value)1.60974620947790
F-TEST (DF numerator)4
F-TEST (DF denominator)46
p-value0.187896665754246
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation89158.422019695
Sum Squared Residuals365664313983.934


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1194493363793.112919668-169300.112919668
2530670385947.497940873144722.502059127
3518365405971.66695083112393.333049170
4491303481158.86418964610144.1358103537
5527021399501.477428195127519.522571805
6233773429666.01726431-195893.01726431
7405972344997.02342459560974.9765754047
8652925361790.480116336291134.519883664
9446211396382.33873838649828.6612616139
10341340366819.462472095-25479.4624720946
11387699424589.866877107-36890.8668771066
12493408402730.77813522490677.221864776
13146494342517.900116807-196023.900116807
14414462383297.26225470331164.7377452967
15364304404895.435835959-40591.4358359589
16355178346969.1599794368208.84002056363
17357760430717.967048511-72957.9670485114
18261216353073.997512249-91857.9975122487
19397144372647.39031951724496.6096804826
20374943383988.915097027-9045.91509702724
21424898382466.99527911242431.0047208875
22202055325770.228997027-123715.228997027
23378525354931.07336414223593.9266358575
24310768371654.911324157-60886.9113241572
25325738347657.256982726-21919.2569827264
26394510384949.4199887649560.58001123585
27247060354766.983360266-107706.983360266
28368078373362.175984464-5284.17598446397
29236761344349.125563938-107588.125563938
30312378337501.945642350-25123.9456423496
31339836374359.182355092-34523.1823550918
32347385335618.50364213911766.4963578608
33426280380097.86093737246182.1390626277
34352850387190.717342426-34340.717342426
35301881316195.754871797-14314.7548717971
36377516359702.67962915317813.3203708468
37357312368472.321044384-11160.3210443841
38458343362892.81452157795450.1854784235
39354228360173.977992028-5945.97799202815
40308636370180.902225009-61544.9022250092
41386212359092.09802659927119.9019734013
42393343362060.06013796631282.9398620343
43378509360279.15438275718229.8456172434
44452469334277.589393866118191.410606134
45364839426677.936659968-61838.9366599678
46358649315553.27320756743095.7267924328
47376641344942.31411278531698.6858872151
48429112362012.33983549667099.6601645036
49330546338100.650623410-7554.65062341034
50403560393023.86695239910536.1330476012
51317892341720.270997787-23828.2709977874


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.9999961593426387.68131472472353e-063.84065736236176e-06
90.9999942851988861.14296022270545e-055.71480111352725e-06
100.9999907764782151.84470435705724e-059.22352178528618e-06
110.9999791402327834.1719534434222e-052.0859767217111e-05
120.9999903733672971.92532654051587e-059.62663270257937e-06
130.9999997338460745.32307851399562e-072.66153925699781e-07
140.999999742339835.15320340034468e-072.57660170017234e-07
150.9999993130223371.37395532618426e-066.86977663092131e-07
160.999998746019372.50796125806381e-061.25398062903190e-06
170.9999997178220245.6435595116163e-072.82177975580815e-07
180.9999992067016931.58659661321778e-067.93298306608889e-07
190.9999991041891531.79162169421509e-068.95810847107547e-07
200.999997833059484.33388104127622e-062.16694052063811e-06
210.99999596311678.07376659947206e-064.03688329973603e-06
220.9999986076147062.78477058867004e-061.39238529433502e-06
230.9999994604263161.07914736875013e-065.39573684375067e-07
240.9999985804305462.83913890789466e-061.41956945394733e-06
250.9999974041983525.19160329527971e-062.59580164763985e-06
260.9999965897411986.82051760401477e-063.41025880200738e-06
270.9999941962065821.16075868362915e-055.80379341814576e-06
280.9999862085141852.75829716298629e-051.37914858149315e-05
290.9999844533551633.10932896743656e-051.55466448371828e-05
300.999980140152953.97196940991508e-051.98598470495754e-05
310.9999393212552080.0001213574895834476.06787447917233e-05
320.9998489791395030.0003020417209942720.000151020860497136
330.9998197581724480.0003604836551044200.000180241827552210
340.99968071149110.000638577017801510.000319288508900755
350.999095732128420.001808535743158410.000904267871579207
360.9980496304238370.003900739152326050.00195036957616302
370.9948888068320020.01022238633599670.00511119316799836
380.9897256036159880.02054879276802460.0102743963840123
390.975427356918840.04914528616232180.0245726430811609
400.9984602803512070.00307943929758520.0015397196487926
410.9939608549265690.01207829014686290.00603914507343144
420.9839273775838530.03214524483229380.0160726224161469
430.9701533824284670.05969323514306660.0298466175715333


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level300.833333333333333NOK
5% type I error level350.972222222222222NOK
10% type I error level361NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/10s77x1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/10s77x1291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/1exao1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/1exao1291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/2exao1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/2exao1291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/3exao1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/3exao1291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/47or91291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/47or91291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/57or91291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/57or91291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/67or91291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/67or91291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/7hxqb1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/7hxqb1291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/8s77x1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/8s77x1291370719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/9s77x1291370719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291370607ivjxehr2irqkara/9s77x1291370719.ps (open in new window)


 
Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 4 ; 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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