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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 computationSun, 09 Nov 2008 13:18:21 -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/09/t1226261928r62g7z3nwd0uiax.htm/, Retrieved Sun, 19 May 2024 02:24:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22862, Retrieved Sun, 19 May 2024 02:24:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Kendall tau Correlation Matrix] [Hypothesis Testin...] [2008-11-03 18:32:17] [6743688719638b0cb1c0a6e0bf433315]
- RMPD  [Bivariate Kernel Density Estimation] [Various EDA topic...] [2008-11-08 11:46:03] [6743688719638b0cb1c0a6e0bf433315]
F    D    [Bivariate Kernel Density Estimation] [Various EDA topic...] [2008-11-09 08:10:12] [6743688719638b0cb1c0a6e0bf433315]
F RMP         [Box-Cox Linearity Plot] [Verious EDA topic...] [2008-11-09 20:18:21] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
Feedback Forum
2008-11-23 12:55:13 [Pieter Broos] [reply] 
de Box-nox plot geeft een maximum bij lambda 1.23, dit is tevens ook de optimale lambda (correlatie is hier het hoogst). Maar op de y-as zien we dat de correlatie varieert tussen 0.570 en 0.575, een zeer klein verschil dus.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
117,8
113,5
121,2
130,4
115,2
117,9
110,7
107,6
124,3
115,1
112,5
127,9
117,4
119,3
130,4
126
125,4
130,5
115,9
108,7
124
119,4
118,6
131,3
111,1
124,8
132,3
126,7
131,7
130,9
122,1
113,2
133,6
119,2
129,4
131,4
117,1
130,5
132,3
140,8
137,5
128,6
126,7
120,8
139,3
128,6
131,3
136,3
128,8
133,2
136,3
151,1
145
134,4
135,7
128,7
129,2
138,6
132,7
132,5
135,2
Dataseries Y:
Download CSV
Histogram 
77,9
60
99,5
95
105,6
102,5
93,3
97,3
127
111,7
96,4
133
72,2
95,8
124,1
127,6
110,7
104,6
112,7
115,3
139,4
119
97,4
154
81,5
88,8
127,7
105,1
114,9
106,4
104,5
121,6
141,4
99
126,7
134,1
81,3
88,6
132,7
132,9
134,4
103,7
119,7
115
132,9
108,5
113,9
142
97,7
92,2
128,8
134,9
128,2
114,8
117,9
119,1
120,7
129,1
117,6
129,2
99,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22862&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22862&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22862&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Box-Cox Linearity Plot
# observations x61
maximum correlation0.576441326515864
optimal lambda(x)1.23
Residual SD (orginial)15.5204345747642
Residual SD (transformed)15.5198541479929

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 61 \tabularnewline
maximum correlation & 0.576441326515864 \tabularnewline
optimal lambda(x) & 1.23 \tabularnewline
Residual SD (orginial) & 15.5204345747642 \tabularnewline
Residual SD (transformed) & 15.5198541479929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22862&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]61[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.576441326515864[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.23[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]15.5204345747642[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]15.5198541479929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22862&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22862&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 x61
maximum correlation0.576441326515864
optimal lambda(x)1.23
Residual SD (orginial)15.5204345747642
Residual SD (transformed)15.5198541479929


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')