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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, 13 Nov 2008 08:42:40 -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/13/t1226590995zsv2ftvjqyvuft4.htm/, Retrieved Sun, 19 May 2024 10:45:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24654, Retrieved Sun, 19 May 2024 10:45:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124

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] [] [2008-11-13 15:42:40] [1768685c15539a739b6b33586be71b78] [Current]
Feedback Forum
2008-11-18 13:19:46 [Julie Govaerts] [reply] 
er worden 2 variabelen voorgesteld dmv een scatterplot en dan gaan we kijken hoe lineair zij zijn.
Doel: De transformatie vinden van de X-variabele die de correlatie tussen Y en een X-variabele verbetert = meer lineair = zodanig dat de scatterplot tss. x en y zo dicht mogelijk op een rechte ligt

λ (lambda) is de transformatieparameter die schommelt tussen -2 en 2 = wordt toegepast op X --> de optimale waarde van lambda zoeken (!kan ook soms niet de moeite zijn = niet veel verbeterd!)
in dit geval was de transformatie niet de moeite waard = niet meer lineair geworden

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103.0
103.5
103.9
104.4
103.5
104.7
101.6
102.3
101.2
101.4
102.7
101.5
102.1
100.5
101.7
103.6
103.2
101.7
105.6
103.7
104.3
105.9
104.8
106.0
105.6
106.7
103.3
103.0
101.6
101.7
Dataseries Y:
Download CSV
Histogram 
103.2
102.9
102.6
102.3
102.1
101.5
101.1
101.9
101.5
101.5
102.0
101.5
101.6
101.5
101.9
102.0
102.0
102.2
102.2
102.3
102.0
101.8
101.8
101.6
101.9
102.3
102.4
102.1
102.3
102.2

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24654&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24654&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24654&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'George Udny Yule' @ 72.249.76.132






Box-Cox Linearity Plot
# observations x30
maximum correlation0.230476103893843
optimal lambda(x)-2
Residual SD (orginial)0.43468009456807
Residual SD (transformed)0.433620313092990

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 30 \tabularnewline
maximum correlation & 0.230476103893843 \tabularnewline
optimal lambda(x) & -2 \tabularnewline
Residual SD (orginial) & 0.43468009456807 \tabularnewline
Residual SD (transformed) & 0.433620313092990 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24654&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]30[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.230476103893843[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]-2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]0.43468009456807[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]0.433620313092990[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24654&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24654&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 x30
maximum correlation0.230476103893843
optimal lambda(x)-2
Residual SD (orginial)0.43468009456807
Residual SD (transformed)0.433620313092990


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')