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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_boxcoxlin.wasp
Title produced by softwareBox-Cox Linearity Plot
Date of computationSat, 07 Nov 2009 08:41:43 -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/2009/Nov/07/t1257608768msiq7c9n2c5qi1o.htm/, Retrieved Mon, 06 May 2024 23:10:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=54437, Retrieved Mon, 06 May 2024 23:10:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235

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] [3/11/2009] [2009-11-02 21:47:57] [b98453cac15ba1066b407e146608df68]
-    D    [Box-Cox Linearity Plot] [WS 6: Box-Cox Lin...] [2009-11-07 15:41:43] [b9056af0304697100f456398102f1287] [Current]
- RM D      [Bagplot] [WS 6: Bag Plot] [2009-11-07 15:52:54] [8cf9233b7464ea02e32be3b30fdac052]
-   P         [Bagplot] [WS 6: Bag Plot] [2009-11-12 17:07:28] [b97b96148b0223bc16666763988dc147]
-   PD        [Bagplot] [Paper: Bivariate ...] [2009-12-17 23:06:13] [8cf9233b7464ea02e32be3b30fdac052]
- RM D      [Bivariate Kernel Density Estimation] [WS 6: Bivariate K...] [2009-11-07 15:57:00] [8cf9233b7464ea02e32be3b30fdac052]
-   P         [Bivariate Kernel Density Estimation] [WS 6: Bivariate K...] [2009-11-12 17:09:08] [b97b96148b0223bc16666763988dc147]
- RM D      [Kendall tau Rank Correlation] [WS 6: Bivariate K...] [2009-11-07 15:59:39] [8cf9233b7464ea02e32be3b30fdac052]
-             [Kendall tau Rank Correlation] [WS 6: Bivariate K...] [2009-11-12 17:11:19] [b97b96148b0223bc16666763988dc147]
-    D      [Box-Cox Linearity Plot] [WS 6: Box-Cox Lin...] [2009-11-12 17:05:09] [b97b96148b0223bc16666763988dc147]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,2
7,4
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
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
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
Dataseries Y:
Download CSV
Histogram 
17
18
23,8
25,5
25,6
23,7
22
21,3
20,7
20,4
20,3
20,4
19,8
19,5
23,1
23,5
23,5
22,9
21,9
21,5
20,5
20,2
19,4
19,2
18,8
18,8
22,6
23,3
23
21,4
19,9
18,8
18,6
18,4
18,6
19,9
19,2
18,4
21,1
20,5
19,1
18,1
17
17,1
17,4
16,8
15,3
14,3
13,4
15,3
22,1
23,7
22,2
19,5
16,6
17,3
19,8
21,2
21,5
20,6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=54437&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=54437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=54437&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 computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Box-Cox Linearity Plot
# observations x60
maximum correlation0.810429105734527
optimal lambda(x)-0.95
Residual SD (orginial)1.55417448188693
Residual SD (transformed)1.54130056330464

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.810429105734527 \tabularnewline
optimal lambda(x) & -0.95 \tabularnewline
Residual SD (orginial) & 1.55417448188693 \tabularnewline
Residual SD (transformed) & 1.54130056330464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=54437&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]0.810429105734527[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]-0.95[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]1.55417448188693[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]1.54130056330464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=54437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=54437&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 x60
maximum correlation0.810429105734527
optimal lambda(x)-0.95
Residual SD (orginial)1.55417448188693
Residual SD (transformed)1.54130056330464


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')