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R Software Module: rwasp_boxcoxlin.wasp (opens new window with default values)
Title produced by software: Box-Cox Linearity Plot
Date of computation: Mon, 05 Nov 2007 13:55:26 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971.htm/, Retrieved Mon, 05 Nov 2007 21:52:54 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
106.7 110.2 125.9 100.1 106.4 114.8 81.3 87 104.2 108 105 94.5 92 95.9 108.8 103.4 102.1 110.1 83.2 82.7 106.8 113.7 102.5 96.6 92.1 95.6 102.3 98.6 98.2 104.5 84 73.8 103.9 106 97.2 102.6 89 93.8 116.7 106.8 98.5 118.7 90 91.9 113.3 113.1 104.1 108.7 96.7 101 116.9 105.8 99 129.4 83 88.9 115.9 104.2 113.4 112.2 100.8 107.3 126.6 102.9 117.9 128.8 87.5 93.8 122.7 126.2 124.6 116.7 115.2 111.1 129.9 113.3 118.5 133.5 102.1 102.4
 
Dataseries Y:
» Textbox « » Textfile « » CSV «
124,9 132 151,4 108,9 121,3 123,4 90,3 79,3 117,2 116,9 120,8 96,1 100,8 105,3 116,1 112,8 114,5 117,2 77,1 80,1 120,3 133,4 109,4 93,2 91,2 99,2 108,2 101,5 106,9 104,4 77,9 60 99,5 95 105,6 102,5 93,3 97,3 127 111,7 96,4 133 72,2 95,8 124,1 127,6 110,7 104,6 112,7 115,3 139,4 119 97,4 154 81,5 88,8 127,7 105,1 114,9 106,4 104,5 121,6 141,4 99 126,7 134,1 81,3 88,6 132,7 132,9 134,4 103,7 119,7 115 132,9 108,5 113,9 142,9 95,2 93
 
Text written by user:
 
Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Box-Cox Linearity Plot
# observations x80
maximum correlation0.902849680098257
optimal lambda(x)0.28
Residual SD (orginial)8.12378349779185
Residual SD (transformed)8.06516229039871
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971/16ab81194296123.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971/16ab81194296123.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971/242o31194296123.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971/242o31194296123.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971/3qasg1194296123.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/05/k17ehqpyrj2gydg1194295971/3qasg1194296123.ps (open in new window)


 
Parameters:
 
R code (references can be found in the software module):
n <- length(x)
c <- array(NA,dim=c(401))
l <- array(NA,dim=c(401))
mx <- 0
mxli <- -999
for (i in 1:401)
{
l[i] <- (i-201)/100
if (l[i] != 0)
{
x1 <- (x^l[i] - 1) / l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(x1,y)
if (mx < abs(c[i]))
{
mx <- abs(c[i])
mxli <- l[i]
}
}
c
mx
mxli
if (mxli != 0)
{
x1 <- (x^mxli - 1) / mxli
} else {
x1 <- log(x)
}
r<-lm(y~x)
se <- sqrt(var(r$residuals))
r1 <- lm(y~x1)
se1 <- sqrt(var(r1$residuals))
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Linearity Plot',xlab='Lambda',ylab='correlation')
grid()
dev.off()
bitmap(file='test2.png')
plot(x,y,main='Linear Fit of Original Data',xlab='x',ylab='y')
abline(r)
grid()
mtext(paste('Residual Standard Deviation = ',se))
dev.off()
bitmap(file='test3.png')
plot(x1,y,main='Linear Fit of Transformed Data',xlab='x',ylab='y')
abline(r1)
grid()
mtext(paste('Residual Standard Deviation = ',se1))
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Linearity Plot',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'# observations x',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'maximum correlation',header=TRUE)
a<-table.element(a,mx)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'optimal lambda(x)',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Residual SD (orginial)',header=TRUE)
a<-table.element(a,se)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Residual SD (transformed)',header=TRUE)
a<-table.element(a,se1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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Software written by Ed van Stee & Patrick Wessa


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