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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: Fri, 13 Nov 2009 06:56:54 -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/13/t1258120697h0gy44l6qglu51y.htm/, Retrieved Fri, 13 Nov 2009 14:58:24 +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/13/t1258120697h0gy44l6qglu51y.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

100 96,66958808 91,06047327 89,04469763 82,90972831 84,04907975 91,76161262 90,09640666 85,97721297 99,82471516 70,90271691 83,87379492 99,21121823 92,81332165 95,3549518 89,65819457 86,76599474 88,25591586 101,2269939 88,25591586 96,3190184 100,4382121 74,84662577 88,08063103 100,6134969 102,1034181 98,94829097 89,39526731 92,90096407 92,28746713 104,1191937 92,98860649 95,79316389 102,716915 81,06923751 91,32340053 98,5977213 107,2743208 99,29886065 87,64241893 97,02015776 98,86064855 96,23137599 102,8045574 95,61787905 101,5775635 84,13672217 87,46713409 102,3663453 101,4022787 87,11656442 82,64680105 79,75460123 81,68273444 90,35933392 82,47151621 80,45574058 90,00876424 72,39263804 78,08939527

Dataseries Y:

» Textbox « » Textfile « » CSV «

100 111,8629088 94,1225572 67,79436315 146,0424236 125,6555043 142,8655602 130,0304429 110,0117843 132,789944 88,23529412 91,96700383 96,65128155 97,14720613 90,7345576 52,52872434 156,9085731 144,8787194 169,4294412 133,3840715 131,2776196 116,32623 89,15349111 85,08298144 89,38917804 103,0884808 85,34812923 45,9933222 152,823333 130,3692429 150,5008347 126,971423 123,2446234 126,5737013 100,2553275 91,76077777 100,2847884 121,6537366 97,28960031 62,54541884 154,9936168 147,8493568 147,3976235 156,8005499 126,8093882 131,7637239 99,20946676 87,34655799 100,7561622 110,5666307 76,46076795 56,51085142 124,9484435 118,2853776 136,4332711 128,6212315 100,7365217 111,7499754 93,43022685 83,3300599

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Box-Cox Linearity Plot
# observations x	60
maximum correlation	0.314273923905249
optimal lambda(x)	2
Residual SD (orginial)	26.8436170040198
Residual SD (transformed)	26.8348500573646

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/13/t1258120697h0gy44l6qglu51y/10k0r1258120611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/13/t1258120697h0gy44l6qglu51y/10k0r1258120611.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/13/t1258120697h0gy44l6qglu51y/2qez31258120611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/13/t1258120697h0gy44l6qglu51y/2qez31258120611.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/13/t1258120697h0gy44l6qglu51y/3png01258120611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/13/t1258120697h0gy44l6qglu51y/3png01258120611.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')

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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