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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 01:47:59 -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/t1226393358try52f0e4f8pc0j.htm/, Retrieved Sat, 14 Feb 2026 06:14:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23233, Retrieved Sat, 14 Feb 2026 06:14:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

460

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

F       [Box-Cox Linearity Plot] [Box-Cox Linearity...] [2008-11-11 08:47:59] [8a2d94dac8ebd598299eaec920908ca6] [Current]

Feedback Forum

2008-11-14 17:48:24 [Kevin Neelen] [reply] 
Door gebruik te maken van de Box-Cox-transformatie, kunnen met een formule tijdreeksen simepl aangepast worden. Hierdoor kunnen sommige problemen opgelost worden, zoals het ontdekken van niet-lineaire verbanden tussen reeksen. Door deze transformatie wordt deze niet-lineaire verbanden lineair gemaakt waardoor we ze kunnen bestuderen. Bij de gekozen Lambda-waarde waarbij de correlatiewaarde het hoogste is, is het verband tussen de reeksen het sterkst. Deze grafiek loopt over Lambda-waarden tussen -2 en 2 aangezien deze waarden het meest voorkomen. Als we geen maximum kunnen zien, kan er geen conclusie getrokken worden.  
 
In deze Box-Cox Linearity Plot kunnen we een maximum van de grafiek zien. De optimale Lambda-waarde bedraagt hier 0,64. 
 
De conclusie van de student klopt.
2008-11-21 11:28:01 [Stijn Van de Velde] [reply] 
Correct antwoord. 
In tegenstelling tot de vorige grafiek kunnen we hier wel een maximum vinden. Visueel is dit nogal moeilijk vast te stellen, gelukkig geeft de tabel ons een uitkomst, namelijk: Lambda 0,64.
2008-11-23 16:19:45 [Karen Van den Broeck] [reply] 
Hier kunnen we nu wel het maximum zien en kunnen we dus wel een beluist trekken. De lambda-waarde bedraagt hier dus 0,64.  
De student zijn antwoord is juist.

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Dataseries X:

Download CSV

Histogram

Boxplots

2,2
2,3
2,1
2,8
3,1
2,9
2,6
2,7
2,3
2,3
2,1
2,2
2,9
2,6
2,7
1,8
1,3
0,9
1,3
1,3
1,3
1,3
1,1
1,4
1,2
1,7
1,8
1,5
1
1,6
1,5
1,8
1,8
1,6
1,9
1,7
1,6
1,3
1,1
1,9
2,6
2,3
2,4
2,2
2
2,9
2,6
2,3
2,3
2,6
3,1
2,8
2,5
2,9
3,1
3,1
3,2
2,5
2,6
2,9

Dataseries Y:

Download CSV

Histogram

2,1
2,2
2,2
2,7
3,1
3,2
3,1
3,1
2,8
3
2,8
2,7
3,2
3,1
3
2
1,7
1,2
1,4
1,3
1,3
1,1
0,9
1,2
0,9
1,3
1,4
1,5
1,1
1,6
1,5
1,6
1,7
1,6
1,7
1,6
1,6
1,3
1,1
1,6
1,9
1,6
1,7
1,6
1,4
2,1
1,9
1,7
1,8
2
2,5
2,1
2,1
2,3
2,4
2,4
2,3
1,7
2
2,3

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=23233&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=23233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23233&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	0.783734838729467
optimal lambda(x)	0.64
Residual SD (orginial)	0.400277622762867
Residual SD (transformed)	0.399159823389136

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.783734838729467 \tabularnewline
optimal lambda(x) & 0.64 \tabularnewline
Residual SD (orginial) & 0.400277622762867 \tabularnewline
Residual SD (transformed) & 0.399159823389136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23233&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]0.783734838729467[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]0.64[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.400277622762867[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.399159823389136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23233&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	0.783734838729467
optimal lambda(x)	0.64
Residual SD (orginial)	0.400277622762867
Residual SD (transformed)	0.399159823389136

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