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*The author of this computation has been verified*
R Software Module: /rwasp_boxcoxlin.wasp (opens new window with default values)
Title produced by software: Box-Cox Linearity Plot
Date of computation: Tue, 03 Nov 2009 13:56:05 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn.htm/, Retrieved Tue, 03 Nov 2009 21:56:57 +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/2009/Nov/03/t1257281814bdeap0fvhi4qzdn.htm/},
    year = {2009},
}
@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 = {2009},
    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:
WS6boxcox
 
Dataseries X:
» Textbox « » Textfile « » CSV «
9356 9337 10149 9788 9770 9911 9429 8775 10189 10529 9914 9790 9625 9729 10589 9611 9388 9510 9690 8434 9844 10601 9942 10229 9381 9635 11228 9999 10089 11622 10533 9965 11567 11321 11686 11747 10595 10751 12199 11690 10978 11753 10839 10518 12183 11967 12363 12359 12162 12096 14325 12670 13865 13563 12734 12464 13389 13961 14088 13143 13413 13579 15388 13708 14689 14883 13991 13854 14364 15672 15904 14016
 
Dataseries Y:
» Textbox « » Textfile « » CSV «
14271 14013 15912 14290 14744 14721 13918 13263 15660 15629 15113 14526 15132 14908 16167 14122 13985 14236 13921 12394 15454 16146 15107 14593 14695 14513 17071 15179 15460 17173 15938 15003 18216 17847 18029 17281 16706 16750 18912 17763 16736 18061 16713 16769 19514 19251 19951 19052 19555 19083 22534 18854 19801 20346 18169 19087 20842 21602 22360 20334 21215 20530 23152 20134 21193 21628 20823 20493 22106 24178 24958 21620
 
Output produced by software:


Summary of computational 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 x72
maximum correlation0.98310407362037
optimal lambda(x)0.44
Residual SD (orginial)557.145945954546
Residual SD (transformed)544.085756482833
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn/13o6v1257281763.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn/13o6v1257281763.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn/28wta1257281763.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn/28wta1257281763.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn/3nh661257281763.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/03/t1257281814bdeap0fvhi4qzdn/3nh661257281763.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


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