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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 computationTue, 11 Nov 2008 09:33:36 -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/2008/Nov/11/t1226421244bgs84rapke3tski.htm/, Retrieved Sun, 19 May 2024 12:13:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23692, Retrieved Sun, 19 May 2024 12:13:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Box-Cox Linearity Plot] [Various EDA topic...] [2008-11-11 16:33:36] [db9a5fd0f9c3e1245d8075d8bb09236d] [Current]
Feedback Forum
2008-11-22 16:17:16 [Jens Peeters] [reply] 
Box-cox plot wordt de R-code aangepast. Als de plot geen maximum bereikt, kan je geen besluit vormen. Zoals we op de grafiek kunnen zien, is hier wel een maximum.
2008-11-24 10:16:50 [Stijn Van de Velde] [reply] 
Bij deze methode gaan we kijken of er een lambda bestaat zodanig dat je de x-variabele kan transformeren om een lineair verband te maken van de scatterplot. Deze lambda wordt diegene met de grootste correlatie, dus waar de grafiek een maximum bereikt.

Hier kan je zien dat er een maximum word bereikt, namelijk bij lambda = 1.62

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8638,7
11063,7
11855,7
10684,5
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10478
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12034,1
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11301,2
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12517
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13435
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16216,3
12970
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14235
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12581
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14378,5
13142,8
13714,7
13621,9
15379,8
13306,3
14391,2
14909,9
14025,4
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14344,3
16213,3
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17292,7
17568,5
17930,8
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16979,9
Dataseries Y:
Download CSV
Histogram 
3219,2
3552,3
3787,7
3392,7
3550
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3519,1
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4422,6
5059,2
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4922,6
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6620,4
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Tables (Output of Computation)





Summary of computational 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 computational 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=23692&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]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=23692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23692&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Box-Cox Linearity Plot
# observations x60
maximum correlation0.92208103667245
optimal lambda(x)1.62
Residual SD (orginial)297.410884571646
Residual SD (transformed)294.011652242964

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.92208103667245 \tabularnewline
optimal lambda(x) & 1.62 \tabularnewline
Residual SD (orginial) & 297.410884571646 \tabularnewline
Residual SD (transformed) & 294.011652242964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23692&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]0.92208103667245[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.62[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]297.410884571646[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]294.011652242964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23692&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 correlation0.92208103667245
optimal lambda(x)1.62
Residual SD (orginial)297.410884571646
Residual SD (transformed)294.011652242964


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')