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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 05:29:26 -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/t1226406595tifd08tl34yhx9b.htm/, Retrieved Sun, 19 May 2024 12:16:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23386, Retrieved Sun, 19 May 2024 12:16:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

123

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] [2008-11-11 12:29:26] [6fc58909ffe15c247a4f6748c8841ab4] [Current]

Feedback Forum

2008-11-24 11:46:21 [Lindsay Heyndrickx] [reply] 
Hier werd geen uitleg bij gegeven. Deze plot wordt gebruikt om tijdreeksen aan te passen. Hier krijg je een lamda parameter zodanig dat je alle transformaties van -2  tot 2 krijgt. Je kan hier de correlatie berekenen van x en y en zo kan je kijken welke het grootst is of het meest lineair. Als je in de x as niet veel verhoogt zoals hier wilt dit zeggen dat de correlatie niet spectaculair toeneemt. De waarde met de hoogste correlatie is hier de correcte lambda waarde. Normaal zou dit een optimale waarde moeten geven en het midden een maximum.  hier zie je eenrechte lijn dus weet je niet zeker of dit wel de optimale correlatie is.

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Dataseries X:

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Histogram

Boxplots

6.2
6.1
5.9
5.6
5.5
5.5
5.6
5.7
5.6
5.4
5.3
5.3
5.4
5.5
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5.8
5.8
5.7
5.9
6.1
6.4
6.4
6.3
6.2
6.2
6.3
6.5
6.6
6.6
6.7
6.6
6.7
7.0
7.2
7.3
7.5
7.6
7.7
7.8
7.8
7.7
7.6
7.6
7.7
7.8
7.8
7.8
7.7
7.6
7.4
7.1
7.1
7.3
7.6
7.8
7.7
7.6
7.5
7.5
7.5
7.6
7.6
7.7
7.8
7.7
7.6
7.6
7.6
7.7
7.8
7.8
7.9
7.9
7.8
7.8
7.7
7.5
7.1
6.9
7.1
7.1
7.1
7.0
6.9
6.8
6.7
6.8
6.8
6.7
6.8
6.7
6.6
6.4
6.4
6.4
6.5
6.5
6.4
6.3
6.2
6.3

Dataseries Y:

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Histogram

9.0
8.8
8.7
8.7
8.6
8.6
8.5
8.5
8.3
8.2
8.1
7.8
7.5
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7.7
7.7
7.6
7.3
7.2
7.5
8.0
8.1
8.4
8.6
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8.9
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8.8
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9.0
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9.1
9.3
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9.2
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9.9
10.0
9.9
9.6
9.5
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9.5
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9.5
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9.4
9.5
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9.5
9.4
9.3
9.2
9.3
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9.5
9.6
9.5
9.3
9.1
9.0
9.0
8.9
9.0
9.2
9.0
8.7
8.3
8.0
7.7
7.9
7.9
7.8
7.7
7.5
7.3
7.2
7.1
7.1

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=23386&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=23386&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23386&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	102
maximum correlation	0.745881427041808
optimal lambda(x)	2
Residual SD (orginial)	0.49868425919473
Residual SD (transformed)	0.495301469903594

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 102 \tabularnewline
maximum correlation & 0.745881427041808 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 0.49868425919473 \tabularnewline
Residual SD (transformed) & 0.495301469903594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23386&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]102[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.745881427041808[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.49868425919473[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.495301469903594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23386&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23386&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	102
maximum correlation	0.745881427041808
optimal lambda(x)	2
Residual SD (orginial)	0.49868425919473
Residual SD (transformed)	0.495301469903594

Figure 1

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Postscript link

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Figure 2

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Figure 3

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Postscript link

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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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Input Parameters & R Code