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Multiple Regression - werkloosheid

*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, 21 Nov 2008 08:51:01 -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/Nov/21/t1227282725t1wqu9lxm2mxwvo.htm/, Retrieved Fri, 21 Nov 2008 15:52:05 +0000
 
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/Nov/21/t1227282725t1wqu9lxm2mxwvo.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},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
multiple regression - werkloosheid
 
Dataseries X:
» Textbox « » Textfile « » CSV «
8,4 7,6 9,5 25 6,6 8,4 7,9 9,1 23,6 6,7 8,4 7,9 9 22,3 6,8 8,6 8,1 9,3 21,8 7,2 8,9 8,2 9,9 20,8 7,6 8,8 8 9,8 19,7 7,6 8,3 7,5 9,4 18,3 7,3 7,5 6,8 8,3 17,4 6,4 7,2 6,5 8 17 6,1 7,5 6,6 8,5 18,1 6,3 8,8 7,6 10,4 23,9 7,1 9,3 8 11,1 25,6 7,5 9,3 8 10,9 25,3 7,4 8,7 7,7 9,9 23,6 7,1 8,2 7,5 9,2 21,9 6,8 8,3 7,6 9,2 21,4 6,9 8,5 7,7 9,5 20,6 7,2 8,6 7,9 9,6 20,5 7,4 8,6 7,8 9,5 20,2 7,3 8,2 7,5 9,1 20,6 6,9 8,1 7,5 8,9 19,7 6,9 8 7,1 9 19,3 6,8 8,6 7,5 10,1 22,8 7,1 8,7 7,5 10,3 23,5 7,2 8,8 7,6 10,2 23,8 7,1 8,5 7,7 9,6 22,6 7 8,4 7,7 9,2 22 6,9 8,5 7,9 9,3 21,7 7 8,7 8,1 9,4 20,7 7,4 8,7 8,2 9,4 20,2 7,5 8,6 8,2 9,2 19,1 7,5 8,5 8,1 9 19,5 7,4 8,3 7,9 9 18,7 7,3 8,1 7,3 9 18,6 7 8,2 6,9 9,8 22,2 6,7 8,1 6,6 10 23,2 6,5 8,1 6,7 9,9 23,5 6,5 7,9 6,9 9,3 21,3 6,5 7,9 7 9 20 6,6 7,9 7,1 9 18,7 6,8 8 7,2 9,1 18,9 6,9 8 7,1 9,1 18,3 6,9 7,9 6,9 9,1 18,4 6,8 8 7 9,2 19,9 6,8 7,7 6,8 8,8 19,2 6,5 7,2 6,4 8,3 18,5 6,1 7,5 6,7 8,4 20,9 6 7,3 6,7 8,1 20,5 5,9 7 6,4 7,8 19,4 5,8 7 6,3 7,9 18,1 5,9 7 6,2 7,9 17 5,9 7,2 6,5 8 17 6,2 7,3 6,8 7,9 17,3 6,3 7,1 6,8 7,5 16,7 6,2 6,8 6,5 7,2 15,5 6 6,6 6,3 6,9 15,3 5,8 6,2 5,9 6,6 13,7 5,5 6,2 5,9 6,7 14,1 5,5 6,8 6,4 7,3 17,3 5,7 6,9 6,4 7,5 18,1 5,8 6,8 6,5 7,2 18,1 5,7
 
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
Totaal[t] = + 0.0915442743664928 + 0.465788320786374Mannen[t] + 0.392832052720299Vrouwen[t] + 0.0140978689669122`<25j`[t] + 0.106007892077027`>25j`[t] + 0.0222051691603468M1[t] + 0.00784697233190004M2[t] + 0.0458619353068849M3[t] + 0.0271220437832206M4[t] + 0.0333285255821577M5[t] + 0.0290675940015739M6[t] + 0.0363209336876756M7[t] + 0.0483014035067723M8[t] + 0.0190382857229988M9[t] + 0.0366810978139367M10[t] + 0.0245809750151976M11[t] -0.000376055884064269t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.09154427436649280.1115860.82040.4164140.208207
Mannen0.4657883207863740.0814625.71791e-060
Vrouwen0.3928320527202990.065675.981900
`<25j`0.01409786896691220.0163580.86180.3934640.196732
`>25j`0.1060078920770270.1332130.79580.4304350.215217
M10.02220516916034680.0229030.96950.3375770.168788
M20.007846972331900040.0245430.31970.7506910.375346
M30.04586193530688490.0264331.7350.0897410.04487
M40.02712204378322060.0292730.92650.3592230.179612
M50.03332852558215770.0333360.99980.3228820.161441
M60.02906759400157390.0360310.80670.4241570.212078
M70.03632093368767560.037310.97350.3356330.167817
M80.04830140350677230.0332361.45330.1532350.076618
M90.01903828572299880.0338650.56220.5768450.288423
M100.03668109781393670.0325351.12740.2656690.132834
M110.02458097501519760.0242351.01430.3160020.158001
t-0.0003760558840642690.000519-0.7250.4722840.236142


Multiple Linear Regression - Regression Statistics
Multiple R0.999091516927074
R-squared0.998183859195642
Adjusted R-squared0.997523444357693
F-TEST (value)1511.44977647128
F-TEST (DF numerator)16
F-TEST (DF denominator)44
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0371328161706541
Sum Squared Residuals0.0606692256175981


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.48.43736793834323-0.0373679383432272
28.48.396101133432540.00389886656746406
38.48.386730394802140.0132696051978572
48.68.61397594971513-0.0139759497151340
58.98.93038972720472-0.0303897272047208
68.88.777804214447170.0221957855528353
78.38.34311513259111-0.0431151325911107
87.57.488457279043810.0115427209561911
97.27.16379047811410.0362095218859039
107.57.460761327038760.0392386729612349
118.88.82702832298062-0.0270283229806143
129.39.32973859137467-0.0297385913746721
139.39.258171144209120.041828855790881
148.78.655099597673540.0449004023264599
158.28.26882965883612-0.0688296588361176
168.38.299844398231270.000155601768728534
178.58.490627344490450.0093726555095492
188.68.63822301797382-0.0382230179738217
198.68.544408114527420.0555918854725846
208.28.22237920189437-0.0223792018943709
218.18.10148553561225-0.00148553561225234
2287.955480231982140.044519768017862
238.68.64257954861351-0.0425795486135137
248.78.71665822574285-0.0166582257428535
258.88.739411537308110.0605884626918876
268.58.50803865307406-0.00803865307406344
278.48.369485228489020.0305147715109858
288.58.489181579028220.0108184209717799
298.78.65575816223630.0442418377637036
308.78.70125186157453-0.00125186157453201
318.68.6140550789689-0.0140550789689056
328.58.49555260866030.00444739133969665
338.38.35087668645396-0.0508766864539579
348.18.05545829566920.0445417043307912
358.28.189882391505870.0101176084941286
368.18.096651565466260.00334843453373694
378.18.13000566623923-0.0300056662392272
387.97.9417145343246-0.0417145343246045
397.97.90035621722879-0.000356217228789279
407.97.93069345065812-0.0306934506581173
4188.03580627692474-0.0358062769247431
4287.976131736001310.0238682639986899
437.97.880660353335060.0193396466649388
4487.999273608071130.000726391928870802
457.77.677673073257950.0223269267420489
467.27.25993680968248-0.0599368096824769
477.57.44971442882050.0502855711794979
487.37.290667845310680.00933215468931686
4977.02880240146366-0.0288024014636577
5076.999046081495260.000953918504743992
5176.974598500643940.025401499356064
527.27.166304622367260.033695377632743
537.37.287418489143790.0125815108562111
547.17.10658917000317-0.00658917000317149
556.86.8177613205775-0.0177613205775072
566.66.594337302330390.00566269766961238
576.26.20617422656174-0.00617422656174262
586.26.26836333562741-0.0683633356274111
596.86.79079530807950.00920469192050143
606.96.866283772105530.0337162278944717
616.86.80624131243666-0.00624131243665649


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.9246275087790290.1507449824419420.075372491220971
210.8502793622449450.299441275510110.149720637755055
220.8311555886127940.3376888227744120.168844411387206
230.7814724891733540.4370550216532910.218527510826646
240.752327623443980.4953447531120410.247672376556021
250.8060799208361840.3878401583276320.193920079163816
260.8673765250157720.2652469499684550.132623474984228
270.8243588734919350.3512822530161310.175641126508065
280.7815513286901840.4368973426196310.218448671309816
290.8039540806827770.3920918386344460.196045919317223
300.7248300972695710.5503398054608570.275169902730429
310.6630069713099870.6739860573800270.336993028690013
320.5662932820773330.8674134358453340.433706717922667
330.742149262647160.515701474705680.25785073735284
340.961277751254510.07744449749097930.0387222487454896
350.9287000646017850.1425998707964290.0712999353982145
360.899681752180170.2006364956396610.100318247819830
370.948635206747610.1027295865047780.0513647932523892
380.9436805213650560.1126389572698880.0563194786349438
390.9357466680175110.1285066639649780.064253331982489
400.8665999037032570.2668001925934870.133400096296743
410.7575895147484160.4848209705031680.242410485251584


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 level10.0454545454545455OK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/21/t1227282725t1wqu9lxm2mxwvo/9g40n1227282650.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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