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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 computationThu, 01 Nov 2007 04:45:09 -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/Nov/01/k2wdqnjk0izwyzo1193917492.htm/, Retrieved Tue, 10 Feb 2026 09:29:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67, Retrieved Tue, 10 Feb 2026 09:29:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsW6Q3G7
Estimated Impact409

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] [Box-Cox linearity...] [2007-11-01 11:45:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

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

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67&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]1 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=67&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Box-Cox Linearity Plot
# observations x72
maximum correlation0.197714628530170
optimal lambda(x)2
Residual SD (orginial)0.662899423237464
Residual SD (transformed)0.661420230185835

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 72 \tabularnewline
maximum correlation & 0.197714628530170 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 0.662899423237464 \tabularnewline
Residual SD (transformed) & 0.661420230185835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]72[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.197714628530170[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.662899423237464[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.661420230185835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67&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 x72
maximum correlation0.197714628530170
optimal lambda(x)2
Residual SD (orginial)0.662899423237464
Residual SD (transformed)0.661420230185835


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')