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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_boxcoxlin.wasp

Title produced by software

Box-Cox Linearity Plot

Date of computation

Tue, 11 Nov 2008 07:14:49 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/11/t1226413005u56hufpnoe28h4c.htm/, Retrieved Thu, 12 Feb 2026 00:05:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23502, Retrieved Thu, 12 Feb 2026 00:05:25 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

373

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F       [Box-Cox Linearity Plot] [Various EDA Topic...] [2008-11-11 14:14:49] [0f30549460cf4ec26d9cf94b1fcf7789] [Current]

Feedback Forum

2008-11-12 16:12:50 [Veerle Jackers] [reply] 
Ik heb niet vermeld in mijn oplossing welke de optimale lambda is. Het is hier toch vrij duidelijk dat er een maximum bereikt wordt. Wanneer lambda 1,34 is, is er een maximale correlatie.
2008-11-24 18:35:28 [Niels Herremans] [reply] 
Op de Box Cox Linearity plot moet er nagegaan worden waar de lambda een maximum bereikt. Daar is er de beste correlatie. En dat is hier inderdaad bij 1.34

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Dataseries X:

Download CSV

Histogram

Boxplots

0,33
0,33
0,32
0,33
0,34
0,36
0,34
0,33
0,35
0,31
0,28
0,26
0,26
0,26
0,29
0,30
0,30
0,28
0,29
0,29
0,32
0,33
0,29
0,31
0,33
0,36
0,39
0,30
0,27
0,28
0,29
0,30
0,30
0,30
0,31
0,30
0,31
0,29
0,32
0,33
0,35
0,35
0,36
0,40
0,40
0,47
0,43
0,38
0,38
0,40
0,45
0,47
0,45
0,50
0,54
0,55
0,59
0,51
0,50
0,50

Dataseries Y:

Download CSV

Histogram

1,00
1,04
1,02
1,07
1,12
1,08
1,02
1,01
1,04
0,98
0,95
0,94
0,94
0,96
0,97
1,03
1,01
0,99
1,00
1,00
1,02
1,01
0,99
0,98
1,01
1,03
1,03
1,00
0,96
0,97
0,98
1,02
1,04
1,01
1,01
1,00
1,01
1,02
1,03
1,06
1,12
1,12
1,13
1,13
1,13
1,17
1,14
1,08
1,07
1,12
1,14
1,21
1,20
1,23
1,29
1,31
1,37
1,35
1,26
1,26

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	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23502&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23502&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23502&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	'George Udny Yule' @ 72.249.76.132

Box-Cox Linearity Plot
# observations x	60
maximum correlation	0.959183895229564
optimal lambda(x)	1.34
Residual SD (orginial)	0.0299020773169203
Residual SD (transformed)	0.0296903566007326

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.959183895229564 \tabularnewline
optimal lambda(x) & 1.34 \tabularnewline
Residual SD (orginial) & 0.0299020773169203 \tabularnewline
Residual SD (transformed) & 0.0296903566007326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23502&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]60[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.959183895229564[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.34[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.0299020773169203[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.0296903566007326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23502&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23502&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Box-Cox Linearity Plot
# observations x	60
maximum correlation	0.959183895229564
optimal lambda(x)	1.34
Residual SD (orginial)	0.0299020773169203
Residual SD (transformed)	0.0296903566007326

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code