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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

Wed, 29 Dec 2010 12:05:56 +0000

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/2010/Dec/29/t1293624229fixs5htbxnyyvmd.htm/, Retrieved Fri, 03 May 2024 04:57:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116735, Retrieved Fri, 03 May 2024 04:57:15 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

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

-     [Box-Cox Linearity Plot] [] [2010-12-26 16:47:09] [69c775ce4d55db2aa75a88e773e8d700]
-    D    [Box-Cox Linearity Plot] [] [2010-12-29 12:05:56] [e180d4cd19004beeddc12e67012247dc] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116735&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]7 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=116735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116735&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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Box-Cox Linearity Plot
# observations x	90
maximum correlation	0.705763968525965
optimal lambda(x)	1.43
Residual SD (orginial)	0.107940327298401
Residual SD (transformed)	0.107592485018293

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 90 \tabularnewline
maximum correlation & 0.705763968525965 \tabularnewline
optimal lambda(x) & 1.43 \tabularnewline
Residual SD (orginial) & 0.107940327298401 \tabularnewline
Residual SD (transformed) & 0.107592485018293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116735&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]90[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.705763968525965[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.43[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.107940327298401[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.107592485018293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116735&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	90
maximum correlation	0.705763968525965
optimal lambda(x)	1.43
Residual SD (orginial)	0.107940327298401
Residual SD (transformed)	0.107592485018293

Figure 1

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Figure 2

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Figure 3

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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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