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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

Sun, 21 Dec 2008 14:49:45 -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/Dec/21/t122989627134e4q7plejyeywu.htm/, Retrieved Fri, 17 May 2024 07:00:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35854, Retrieved Fri, 17 May 2024 07:00:04 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

153

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...] [2008-12-21 21:47:51] [c5e27150943bc3d623392efb0d98f8d3]
-    D    [Box-Cox Linearity Plot] [Box cox linearity...] [2008-12-21 21:49:45] [25d75405d700c34901b109463a9659f5] [Current]
-    D      [Box-Cox Linearity Plot] [Box cox linearity...] [2008-12-21 21:52:43] [c5e27150943bc3d623392efb0d98f8d3] 
- RMPD      [Standard Deviation Plot] [standard deviatio...] [2008-12-21 21:54:49] [c5e27150943bc3d623392efb0d98f8d3] 
- RMPD      [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-21 21:56:51] [c5e27150943bc3d623392efb0d98f8d3] 
-    D        [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-21 21:58:39] [c5e27150943bc3d623392efb0d98f8d3] 
-    D          [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-21 22:00:36] [c5e27150943bc3d623392efb0d98f8d3] 
- RMPD          [Box-Cox Normality Plot] [box cox normality...] [2008-12-21 22:02:22] [c5e27150943bc3d623392efb0d98f8d3] 
-    D            [Box-Cox Normality Plot] [box cox normality...] [2008-12-21 22:04:17] [c5e27150943bc3d623392efb0d98f8d3] 
-    D              [Box-Cox Normality Plot] [box cox normality...] [2008-12-21 22:05:43] [c5e27150943bc3d623392efb0d98f8d3] 
- RM D              [Variance Reduction Matrix] [variance reductio...] [2008-12-21 22:07:14] [c5e27150943bc3d623392efb0d98f8d3] 
-    D                [Variance Reduction Matrix] [variance reductio...] [2008-12-21 22:08:53] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                  [Variance Reduction Matrix] [variance reductio...] [2008-12-21 22:10:18] [4ddbf81f78ea7c738951638c7e93f6ee] 

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Dataseries X:

Download CSV

Histogram

Boxplots

7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8
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
7.1
7.2
7.1
6.9
7
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

Dataseries Y:

Download CSV

Histogram

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

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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35854&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35854&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35854&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	'George Udny Yule' @ 72.249.76.132

Box-Cox Linearity Plot
# observations x	60
maximum correlation	0.933350482720162
optimal lambda(x)	-2
Residual SD (orginial)	0.288827773680498
Residual SD (transformed)	0.259946078222710

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.933350482720162 \tabularnewline
optimal lambda(x) & -2 \tabularnewline
Residual SD (orginial) & 0.288827773680498 \tabularnewline
Residual SD (transformed) & 0.259946078222710 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35854&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]60[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.933350482720162[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]-2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.288827773680498[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.259946078222710[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35854&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35854&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	60
maximum correlation	0.933350482720162
optimal lambda(x)	-2
Residual SD (orginial)	0.288827773680498
Residual SD (transformed)	0.259946078222710

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):

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code