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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 11:56:39 -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/t1226429841tnswyk5l8c22rqq.htm/, Retrieved Sat, 18 May 2024 16:48:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23831, Retrieved Sat, 18 May 2024 16:48:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

170

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

F     [Pearson Partial Correlation] [Workshop 4] [2007-10-30 14:41:06] [c8ea599e5a03d5b991b7fa762eaf839d]
F RMPD    [Box-Cox Linearity Plot] [Q3 Box-Cox Linear...] [2008-11-11 18:56:39] [35348cd8592af0baf5f138bd59921307] [Current]

Feedback Forum

2008-11-22 20:54:06 [Nilay Erdogdu] [reply] 
Het doel van de box cox linearity plot is het zoeken van de transformatie van de variabele x dat de correlatie tussen de y- en de x- variabele maximaliseert. Yt wordt de endogene dataset die we zullen proberen te voorspellen. De optimale lamda is hier -2, dus verschillend van 1. Wanneer we de oorspronkelijke residuals gaan vergelijken met de getransformeerde, merken we nauwelijks verschil op. Dit wil zeggen dat de transformatie geen meerwaarde biedt.
2008-11-24 09:09:09 [Stéphanie Claes] [reply] 
De box-cox transformation heeft tot doel met een bepaalde parameter de waarde gaan transformeren. 
We hebben 2 variabelen, scatterplot kan doen vermoeden dat er een verband is, maar het is niet lineair => kromme lijn. 
Het lijkt alsof er links een maximum bereikt wordt (als we kijken naar box-cox-plot), dan moet je -2 gebruiken om te lineairiseren. 
Als je het maximum niet zou kunnen zien dan kan je geen besluit nemen.

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Dataseries X:

Download CSV

Histogram

Boxplots

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

Dataseries Y:

Download CSV

Histogram

9,0
9,1
8,7
8,2
7,9
7,9
9,1
9,4
9,5
9,1
9,0
9,3
9,9
9,8
9,4
8,3
8,0
8,5
10,4
11,1
10,9
9,9
9,2
9,2
9,5
9,6
9,5
9,1
8,9
9,0
10,1
10,3
10,2
9,6
9,2
9,3
9,4
9,4
9,2
9,0
9,0
9,0
9,8
10,0
9,9
9,3
9,0
9,0
9,1
9,1
9,1
9,2
8,8
8,3
8,4
8,1
7,8
7,9
7,9
8,0
7,9
7,5
7,2
6,9
6,6
6,7
7,3
7,5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23831&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23831&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Box-Cox Linearity Plot
# observations x	68
maximum correlation	0.73128174085834
optimal lambda(x)	-2
Residual SD (orginial)	0.669431016696626
Residual SD (transformed)	0.64534809608437

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 68 \tabularnewline
maximum correlation & 0.73128174085834 \tabularnewline
optimal lambda(x) & -2 \tabularnewline
Residual SD (orginial) & 0.669431016696626 \tabularnewline
Residual SD (transformed) & 0.64534809608437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23831&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]68[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.73128174085834[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]-2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.669431016696626[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.64534809608437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23831&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	68
maximum correlation	0.73128174085834
optimal lambda(x)	-2
Residual SD (orginial)	0.669431016696626
Residual SD (transformed)	0.64534809608437

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):

par1 = ward ; par2 = ALL ; par3 = FALSE ; par4 = FALSE ;

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