x <- array(list(-15
,-7
,55
,23
,39
,24
,-8
,-2
,19
,4
,-22
,11
,-8
,-7
,-1
,54
,20
,19
,23
,-12
,-3
,18
,6
,-15
,9
,-1
,-6
,0
,52
,20
,14
,19
,-10
,0
,20
,5
,-16
,13
,1
,-6
,-3
,55
,22
,15
,25
,-11
,-4
,21
,4
,-22
,12
,-1
,2
,4
,56
,25
,7
,21
,-13
,-3
,18
,5
,-21
,5
,2
,-4
,2
,54
,22
,12
,19
,-10
,-3
,19
,5
,-11
,13
,2
,-4
,3
,53
,26
,12
,20
,-10
,-3
,19
,4
,-10
,11
,1
,-8
,0
,59
,27
,14
,20
,-11
,-4
,19
,3
,-6
,8
,-1
,-10
,-10
,62
,41
,9
,17
,-11
,-5
,21
,2
,-8
,8
,-2
,-16
,-10
,63
,29
,8
,25
,-11
,-5
,19
,3
,-15
,8
,-2
,-14
,-9
,64
,33
,4
,19
,-10
,-6
,19
,2
,-16
,8
,-1
,-30
,-22
,75
,39
,7
,13
,-13
,-10
,17
,-1
,-24
,0
,-8
,-33
,-16
,77
,27
,3
,15
,-12
,-11
,16
,0
,-27
,3
,-4
,-40
,-18
,79
,27
,5
,15
,-13
,-13
,16
,-2
,-33
,0
,-6
,-38
,-14
,77
,25
,0
,13
,-15
,-12
,17
,1
,-29
,-1
,-3
,-39
,-12
,82
,19
,-2
,11
,-16
,-13
,16
,-2
,-34
,-1
,-3
,-46
,-17
,83
,15
,6
,9
,-18
,-12
,15
,-2
,-37
,-4
,-7
,-50
,-23
,81
,19
,11
,2
,-17
,-15
,16
,-2
,-31
,1
,-9
,-55
,-28
,78
,23
,9
,-2
,-18
,-14
,16
,-6
,-33
,-1
,-11
,-66
,-31
,79
,23
,17
,-4
,-20
,-16
,16
,-4
,-25
,0
,-13
,-63
,-21
,79
,7
,21
,-2
,-22
,-16
,18
,-2
,-27
,-1
,-11
,-56
,-19
,73
,1
,21
,1
,-17
,-12
,19
,0
,-21
,6
,-9
,-66
,-22
,72
,7
,41
,-13
,-19
,-16
,16
,-5
,-32
,0
,-17
,-63
,-22
,67
,4
,57
,-11
,-18
,-15
,16
,-4
,-31
,-3
,-22
,-69
,-25
,67
,-8
,65
,-14
,-26
,-17
,16
,-5
,-32
,-3
,-25
,-69
,-16
,50
,-14
,68
,-4
,-19
,-15
,18
,-1
,-30
,4
,-20
,-72
,-22
,45
,-10
,73
,-9
,-23
,-14
,16
,-2
,-34
,1
,-24
,-69
,-21
,39
,-11
,71
,-5
,-21
,-15
,15
,-4
,-35
,0
,-24
,-67
,-10
,39
,-10
,71
,-4
,-27
,-14
,15
,-1
,-37
,-4
,-22
,-64
,-7
,37
,-8
,70
,-8
,-27
,-16
,16
,1
,-32
,-2
,-19
,-61
,-5
,30
,-8
,69
,-1
,-21
,-11
,18
,1
,-28
,3
,-18
,-58
,-4
,24
,-7
,65
,-2
,-22
,-14
,16
,-2
,-26
,2
,-17
,-47
,7
,27
,-8
,57
,-1
,-24
,-12
,19
,1
,-24
,5
,-11
,-44
,6
,19
,-4
,57
,8
,-21
,-11
,19
,1
,-27
,6
,-11
,-42
,3
,19
,3
,57
,8
,-21
,-13
,18
,3
,-26
,6
,-12
,-34
,10
,25
,-5
,55
,6
,-22
,-12
,17
,3
,-27
,3
,-10
,-38
,0
,16
,-4
,65
,7
,-25
,-12
,19
,1
,-27
,4
,-15
,-41
,-2
,20
,5
,65
,2
,-21
,-10
,22
,1
,-24
,7
,-15
,-38
,-1
,25
,3
,64
,3
,-26
,-12
,19
,0
,-28
,5
,-15
,-37
,2
,34
,6
,60
,0
,-27
,-11
,19
,2
,-23
,6
,-13
,-22
,8
,39
,10
,43
,5
,-22
,-10
,16
,2
,-23
,1
,-8
,-37
,-6
,40
,16
,47
,-1
,-22
,-12
,18
,-1
,-29
,3
,-13
,-36
,-4
,38
,11
,40
,3
,-20
,-12
,20
,1
,-25
,6
,-9
,-25
,4
,42
,10
,31
,4
,-21
,-11
,17
,0
,-24
,0
,-7
,-15
,7
,46
,21
,27
,8
,-16
,-12
,17
,1
,-20
,3
,-4
,-17
,3
,48
,18
,24
,10
,-17
,-9
,17
,1
,-22
,4
,-4
,-19
,3
,51
,20
,23
,14
,-19
,-6
,20
,3
,-24
,7
,-2
,-12
,8
,55
,18
,17
,15
,-20
,-7
,21
,2
,-27
,6
,0
,-17
,3
,52
,23
,16
,9
,-20
,-7
,19
,0
,-25
,6
,-2
,-21
,-3
,55
,28
,15
,8
,-20
,-10
,18
,0
,-26
,6
,-3
,-10
,4
,58
,31
,8
,10
,-19
,-8
,20
,3
,-24
,6
,1
,-19
,-5
,72
,38
,5
,5
,-20
,-11
,17
,-2
,-26
,2
,-2
,-14
,-1
,70
,27
,6
,4
,-25
,-12
,15
,0
,-22
,2
,-1
,-8
,5
,70
,21
,5
,8
,-25
,-11
,17
,1
,-20
,2
,1
,-16
,0
,63
,31
,12
,8
,-22
,-11
,18
,-1
,-26
,3
,-3
,-14
,-6
,66
,31
,8
,10
,-19
,-9
,20
,-2
,-22
,-1
,-4
,-30
,-13
,65
,29
,17
,8
,-20
,-9
,19
,-1
,-29
,-4
,-9
,-33
,-15
,55
,24
,22
,10
,-18
,-12
,20
,-1
,-30
,4
,-9
,-37
,-8
,57
,27
,24
,-8
,-17
,-10
,22
,1
,-26
,5
,-7
,-47
,-20
,60
,36
,36
,-6
,-17
,-10
,20
,-2
,-30
,3
,-14)
,dim=c(13
,60)
,dimnames=list(c('X_1t'
,'X_2t'
,'X_3t'
,'X_4t'
,'X_5t'
,'X_6t'
,'X_7t'
,'X_8t'
,'X_9t'
,'X_10t'
,'X_11t'
,'X_12t'
,'Y_t')
,1:60))
y <- array(NA,dim=c(13,60),dimnames=list(c('X_1t','X_2t','X_3t','X_4t','X_5t','X_6t','X_7t','X_8t','X_9t','X_10t','X_11t','X_12t','Y_t'),1:60))
for (i in 1:dim(x)[1])
{
for (j in 1:dim(x)[2])
{
y[i,j] <- as.numeric(x[i,j])
}
}
par3 = 'Linear Trend'
par2 = 'Do not include Seasonal Dummies'
par1 = '13'
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)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
postscript(file="/var/fisher/rcomp/tmp/1iriw1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
postscript(file="/var/fisher/rcomp/tmp/2kknd1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
postscript(file="/var/fisher/rcomp/tmp/3v1b31352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
postscript(file="/var/fisher/rcomp/tmp/4bjf31352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
postscript(file="/var/fisher/rcomp/tmp/5el4j1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
postscript(file="/var/fisher/rcomp/tmp/6wyho1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
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()
postscript(file="/var/fisher/rcomp/tmp/7a5dw1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
postscript(file="/var/fisher/rcomp/tmp/82nvh1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
postscript(file="/var/fisher/rcomp/tmp/98j5c1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
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) {
postscript(file="/var/fisher/rcomp/tmp/10vvfi1352129298.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
#Note: the /var/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
load(file="/var/fisher/rcomp/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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file="/var/fisher/rcomp/tmp/11b68x1352129298.tab")
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file="/var/fisher/rcomp/tmp/12d3m71352129298.tab")
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$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$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file="/var/fisher/rcomp/tmp/13kdkn1352129298.tab")
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file="/var/fisher/rcomp/tmp/14dlbl1352129298.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="/var/fisher/rcomp/tmp/15o8kt1352129298.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="/var/fisher/rcomp/tmp/16elyu1352129298.tab")
}
try(system("convert tmp/1iriw1352129298.ps tmp/1iriw1352129298.png",intern=TRUE))
try(system("convert tmp/2kknd1352129298.ps tmp/2kknd1352129298.png",intern=TRUE))
try(system("convert tmp/3v1b31352129298.ps tmp/3v1b31352129298.png",intern=TRUE))
try(system("convert tmp/4bjf31352129298.ps tmp/4bjf31352129298.png",intern=TRUE))
try(system("convert tmp/5el4j1352129298.ps tmp/5el4j1352129298.png",intern=TRUE))
try(system("convert tmp/6wyho1352129298.ps tmp/6wyho1352129298.png",intern=TRUE))
try(system("convert tmp/7a5dw1352129298.ps tmp/7a5dw1352129298.png",intern=TRUE))
try(system("convert tmp/82nvh1352129298.ps tmp/82nvh1352129298.png",intern=TRUE))
try(system("convert tmp/98j5c1352129298.ps tmp/98j5c1352129298.png",intern=TRUE))
try(system("convert tmp/10vvfi1352129298.ps tmp/10vvfi1352129298.png",intern=TRUE))