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Consumptiegoederen met seizoenale en lineaire trend

*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: Sat, 20 Dec 2008 07:28:35 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t12297833624x0g9lqd8jzsrm3.htm/, Retrieved Sat, 20 Dec 2008 15:29:32 +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/2008/Dec/20/t12297833624x0g9lqd8jzsrm3.htm/},
    year = {2008},
}
@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 = {2008},
    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 «
98.5 0 97.0 0 103.3 0 99.6 0 100.1 0 102.9 0 95.9 0 94.5 0 107.4 0 116.0 0 102.8 0 99.8 0 109.6 0 103.0 0 111.6 0 106.3 0 97.9 0 108.8 0 103.9 0 101.2 0 122.9 0 123.9 0 111.7 0 120.9 0 99.6 0 103.3 0 119.4 0 106.5 0 101.9 0 124.6 0 106.5 0 107.8 0 127.4 0 120.1 0 118.5 0 127.7 0 107.7 0 104.5 0 118.8 0 110.3 0 109.6 0 119.1 0 96.5 0 106.7 0 126.3 0 116.2 0 118.8 0 115.2 0 110.0 0 111.4 0 129.6 0 108.1 0 117.8 0 122.9 0 100.6 0 111.8 0 127.0 0 128.6 0 124.8 0 118.5 0 114.7 0 112.6 0 128.7 0 111.0 0 115.8 0 126.0 0 111.1 1 113.2 1 120.1 1 130.6 1 124.0 1 119.4 1 116.7 1 116.5 1 119.6 1 126.5 1 111.3 1 123.5 1 114.2 1 103.7 1 129.5 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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 105.892771084337 -3.86265060240966X[t] -7.50534040925615M1[t] -8.99742780646395M2[t] + 2.5390562248996M3[t] -6.69588831516543M4[t] -8.95940428380188M5[t] + 1.24850831899023M6[t] -12.6346289921591M7[t] -11.4552878179384M8[t] + 5.65262478485371M9[t] + 6.20560336584434M10[t] + 0.127801682922166M11[t] + 0.277801682922165t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)105.8927710843372.34301645.195100
X-3.862650602409661.950616-1.98020.0517880.025894
M1-7.505340409256152.778922-2.70080.0087510.004376
M2-8.997427806463952.777607-3.23930.0018660.000933
M32.53905622489962.7766640.91440.3637720.181886
M4-6.695888315165432.776094-2.4120.0186120.009306
M5-8.959404283801882.775896-3.22760.0019340.000967
M61.248508318990232.7760710.44970.654350.327175
M7-12.63462899215912.783763-4.53872.4e-051.2e-05
M8-11.45528781793842.782516-4.11690.0001085.4e-05
M95.652624784853712.7816422.03210.0461090.023055
M106.205603365844342.8811812.15380.0348540.017427
M110.1278016829221662.8806420.04440.9647450.482372
t0.2778016829221650.0321738.634600


Multiple Linear Regression - Regression Statistics
Multiple R0.884495522192808
R-squared0.782332328779128
Adjusted R-squared0.740098303019854
F-TEST (value)18.5237451252760
F-TEST (DF numerator)13
F-TEST (DF denominator)67
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.98910695485532
Sum Squared Residuals1667.70960986804


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
198.598.6652323580039-0.165232358003882
29797.4509466437177-0.450946643717700
3103.3109.265232358003-5.96523235800342
499.6100.308089500861-0.708089500860571
5100.198.32237521514631.77762478485369
6102.9108.808089500861-5.90808950086056
795.995.20275387263340.697246127366638
894.596.6598967297762-2.1598967297762
9107.4114.045611015491-6.6456110154905
10116114.8763912794031.12360872059669
11102.8109.076391279403-6.27639127940332
1299.8109.226391279403-9.42639127940333
13109.6101.9988525530697.60114744693066
14103100.7845668387842.21543316121630
15111.6112.598852553069-0.99885255306941
16106.3103.6417096959272.65829030407345
1797.9101.655995410212-3.75599541021226
18108.8112.141709695927-3.34170969592656
19103.998.53637406769945.36362593230064
20101.299.99351692484221.20648307515778
21122.9117.3792312105565.5207687894435
22123.9118.2100114744695.68998852553071
23111.7112.410011474469-0.710011474469298
24120.9112.5600114744698.33998852553071
2599.6105.332472748135-5.73247274813532
26103.3104.118187033850-0.818187033849684
27119.4115.9324727481353.46752725186462
28106.5106.975329890993-0.475329890992534
29101.9104.989615605278-3.08961560527824
30124.6115.4753298909939.12467010900746
31106.5101.8699942627654.63000573723466
32107.8103.3271371199084.47286288009179
33127.4120.7128514056226.68714859437752
34120.1121.543631669535-1.44363166953529
35118.5115.7436316695352.75636833046472
36127.7115.89363166953511.8063683304647
37107.7108.666092943201-0.966092943201298
38104.5107.451807228916-2.95180722891567
39118.8119.266092943201-0.466092943201378
40110.3110.308950086059-0.00895008605852083
41109.6108.3232358003441.27676419965576
42119.1118.8089500860590.29104991394147
4396.5105.203614457831-8.70361445783133
44106.7106.6607573149740.0392426850258081
45126.3124.0464716006882.25352839931152
46116.2124.877251864601-8.67725186460127
47118.8119.077251864601-0.277251864601271
48115.2119.227251864601-4.02725186460127
49110111.999713138267-1.99971313826729
50111.4110.7854274239820.614572576018355
51129.6122.5997131382677.00028686173263
52108.1113.642570281125-5.54257028112451
53117.8111.6568559954106.14314400458978
54122.9122.1425702811250.757429718875495
55100.6108.537234652897-7.93723465289732
56111.8109.9943775100401.80562248995982
57127127.380091795754-0.380091795754462
58128.6128.2108720596670.389127940332743
59124.8122.4108720596672.38912794033274
60118.5122.560872059667-4.06087205966726
61114.7115.333333333333-0.63333333333327
62112.6114.119047619048-1.51904761904764
63128.7125.9333333333332.76666666666664
64111116.976190476190-5.97619047619049
65115.8114.9904761904760.809523809523795
66126125.4761904761900.523809523809504
67111.1108.0082042455543.09179575444635
68113.2109.4653471026973.7346528973035
69120.1126.851061388411-6.7510613884108
70130.6127.6818416523242.91815834767641
71124121.8818416523242.11815834767642
72119.4122.031841652324-2.63184165232358
73116.7114.8043029259901.89569707401040
74116.5113.5900172117042.90998278829603
75119.6125.404302925990-5.80430292598968
76126.5116.44716006884710.0528399311532
77111.3114.461445783133-3.16144578313253
78123.5124.947160068847-1.44716006884682
79114.2111.3418244406202.85817555938037
80103.7112.798967297762-9.09896729776249
81129.5130.184681583477-0.684681583476776


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.4431979590018830.8863959180037660.556802040998117
180.2936377143803130.5872754287606260.706362285619687
190.1843787340429310.3687574680858620.815621265957069
200.1017370484921510.2034740969843020.89826295150785
210.1930548107427070.3861096214854130.806945189257294
220.1249509596614920.2499019193229840.875049040338508
230.07946265805020580.1589253161004120.920537341949794
240.3033029804846530.6066059609693060.696697019515347
250.7416844596914850.516631080617030.258315540308515
260.7141900365567120.5716199268865770.285809963443288
270.6471684414649330.7056631170701340.352831558535067
280.6074429178115740.7851141643768510.392557082188426
290.6076455137052280.7847089725895440.392354486294772
300.6976991929244410.6046016141511180.302300807075559
310.6472641787795150.7054716424409710.352735821220485
320.5802763694334070.8394472611331870.419723630566593
330.5560448981444870.8879102037110260.443955101855513
340.5681728529195180.8636542941609650.431827147080482
350.4974802314415850.994960462883170.502519768558415
360.722104896051630.5557902078967390.277895103948370
370.7012495750451230.5975008499097540.298750424954877
380.7033802930726970.5932394138546060.296619706927303
390.6457375190891930.7085249618216130.354262480910807
400.5871583120682080.8256833758635850.412841687931792
410.5092672508882220.9814654982235570.490732749111778
420.4394539148288650.878907829657730.560546085171135
430.6519634020534910.6960731958930170.348036597946509
440.5846259555225810.8307480889548390.415374044477419
450.536514453070250.92697109385950.46348554692975
460.6960465887015750.607906822596850.303953411298425
470.6348903476038660.7302193047922680.365109652396134
480.6099389520739740.7801220958520520.390061047926026
490.5550567628140970.8898864743718050.444943237185903
500.4757592749523120.9515185499046240.524240725047688
510.4960159908487970.9920319816975940.503984009151203
520.5608016194637490.8783967610725030.439198380536251
530.5424378998685940.9151242002628110.457562100131406
540.4515048265890420.9030096531780840.548495173410958
550.6188456821585130.7623086356829750.381154317841487
560.547179031013170.9056419379736610.452820968986831
570.4696228571801980.9392457143603960.530377142819802
580.3708373671378370.7416747342756750.629162632862163
590.2817102930130620.5634205860261240.718289706986938
600.2089545834953570.4179091669907150.791045416504643
610.1364052905851840.2728105811703680.863594709414816
620.08715356787897220.1743071357579440.912846432121028
630.09543354196621510.1908670839324300.904566458033785
640.3104357967614890.6208715935229770.689564203238511


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:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297833624x0g9lqd8jzsrm3/9uni61229783308.png (open in new window)
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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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