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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_boxcoxlin.wasp
Title produced by softwareBox-Cox Linearity Plot
Date of computationWed, 12 Dec 2007 00:31:26 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/12/t1197443805yqed9v74aksteh2.htm/, Retrieved Tue, 10 Feb 2026 00:32:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3175, Retrieved Tue, 10 Feb 2026 00:32:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact549

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Linearity Plot] [Paper x=tot werkl...] [2007-12-12 07:31:26] [52c41ae5b11545a88aa57081ae5e5ffc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,4
7,2
7
6,6
6,4
6,4
6,8
7,3
7
7
6,7
6,7
6,3
6,2
6
6,3
6,2
6,1
6,2
6,6
6,6
7,8
7,4
7,4
7,5
7,4
7,4
7
6,9
6,9
7,6
7,7
7,6
8,2
8
8,1
8,3
8,2
8,1
7,7
7,6
7,7
8,2
8,4
8,4
8,6
8,4
8,5
8,7
8,7
8,6
7,4
7,3
7,4
9
9,2
9,2
8,5
8,3
8,3
8,6
8,6
8,5
8,1
8,1
8
8,6
8,7
8,7
8,6
8,4
8,4
8,7
8,7
8,5
8,3
8,3
8,3
8,1
8,2
8,1
8,1
7,9
7,7
8,1
8
7,7
7,8
7,6
7,4
7,7
7,9
7,6
Dataseries Y:
Download CSV
Histogram 
6,4
6,3
6
5,3
5,2
5,1
5,4
5,8
5,6
5,6
5,4
5,4
5,5
5,5
5,3
5,7
5,6
5,5
5,6
5,9
6
7
6,6
6,6
6,3
6,3
6,3
6,3
6,2
6,2
6,3
6,4
6,4
7,8
7,7
7,7
7,7
7,7
7,6
7,5
7,4
7,4
7,5
7,6
7,6
8,1
7,8
8
7,9
7,9
7,8
6,7
6,6
6,6
7,7
7,9
8
7,7
7,5
7,6
7,8
7,8
7,7
7,4
7,5
7,2
7,5
7,6
7,6
7,8
7,7
7,7
8,2
8,2
8,1
7,8
7,8
7,7
6,7
6,7
6,7
7,2
6,9
6,8
7,2
7,1
6,9
6,9
6,7
6,5
6,6
6,6
6,5

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3175&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3175&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Box-Cox Linearity Plot
# observations x93
maximum correlation0.934562938813547
optimal lambda(x)1.18
Residual SD (orginial)0.313217564834106
Residual SD (transformed)0.313083058231687

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 93 \tabularnewline
maximum correlation & 0.934562938813547 \tabularnewline
optimal lambda(x) & 1.18 \tabularnewline
Residual SD (orginial) & 0.313217564834106 \tabularnewline
Residual SD (transformed) & 0.313083058231687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3175&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]93[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.934562938813547[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.18[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.313217564834106[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.313083058231687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3175&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Box-Cox Linearity Plot
# observations x93
maximum correlation0.934562938813547
optimal lambda(x)1.18
Residual SD (orginial)0.313217564834106
Residual SD (transformed)0.313083058231687


Figures (Output of Computation)

Input Parameters & R Code

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')