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Box cox linearity plot

R Software Module: rwasp_boxcoxlin.wasp (opens new window with default values)
Title produced by software: Box-Cox Linearity Plot
Date of computation: Fri, 02 Nov 2007 06:15:31 -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/02/bgqytzwdyfbpkgu1194009688.htm/, Retrieved Fri, 02 Nov 2007 14:21:28 +0100
 
User-defined keywords:
W6Q3G7
 
Dataseries X:
» Textbox « » Textfile « » CSV «
87 75 74 91 101 103 106 102 105 105 100 95 96 98 99 92 84 81 72 89 96 91 88 90 98 87 100 100 104 107 105 102 98 106 97 101 100 93 94 96 96 98 102 95 85 84 82 87 77 90 90 94 97 96 93 93 93 97 100 95 97 103 102 93 99 100 97 104 102 103 100 90 90
 
Dataseries Y:
» Textbox « » Textfile « » CSV «
96 86 82 92 99 101 102 100 101 100 99 97 97 97 96 92 91 87 82 89 91 90 87 89 95 85 94 94 97 99 97 96 94 100 96 98 98 94 93 94 94 97 98 95 89 89 89 90 86 92 91 95 99 98 95 96 94 98 98 98 98 102 101 92 99 101 99 102 102 101 99 98 98
 
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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Box-Cox Linearity Plot
# observations x73
maximum correlation0.878368609753348
optimal lambda(x)0.7
Residual SD (orginial)2.34740756948175
Residual SD (transformed)2.34613971653057
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/02/bgqytzwdyfbpkgu1194009688/1yg391194009325.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/02/bgqytzwdyfbpkgu1194009688/1yg391194009325.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/02/bgqytzwdyfbpkgu1194009688/218e11194009325.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/02/bgqytzwdyfbpkgu1194009688/218e11194009325.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/02/bgqytzwdyfbpkgu1194009688/3m2cq1194009326.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/02/bgqytzwdyfbpkgu1194009688/3m2cq1194009326.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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