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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 computationMon, 24 Nov 2008 13:55:27 -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/24/t1227560172004vvdlltch1msg.htm/, Retrieved Tue, 14 May 2024 11:42:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25531, Retrieved Tue, 14 May 2024 11:42:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Bivariate Kernel Density Estimation] [Q1] [2008-11-11 14:12:08] [491a70d26f8c977398d8a0c1c87d3dd4]
F RMP     [Box-Cox Linearity Plot] [Q3] [2008-11-24 20:55:27] [2ba2a74112fb2c960057a572bf2825d3] [Current]
- RM D      [Box-Cox Normality Plot] [Q4] [2008-11-24 21:10:18] [491a70d26f8c977398d8a0c1c87d3dd4]
- RMP         [Maximum-likelihood Fitting - Normal Distribution] [Q5] [2008-11-24 21:12:21] [491a70d26f8c977398d8a0c1c87d3dd4]
-    D        [Box-Cox Normality Plot] [Q4] [2008-11-24 21:16:12] [491a70d26f8c977398d8a0c1c87d3dd4]
- RMP           [Maximum-likelihood Fitting - Normal Distribution] [Q5] [2008-11-24 21:19:21] [491a70d26f8c977398d8a0c1c87d3dd4]
Feedback Forum
2008-11-24 21:26:36 [Liese Tormans] [reply] 
Aan de hand van de box-cox plot zien we duidelijk een maximum van de functie nl 0,93 (de optimale lambda ). Deze methode wordt vaak gebruikt om tijdreeksen te transformeren. We willen dus met behulp van de lambda parameter de functie recht trekken en zo tot een lineair verband komen.

In de R code wordt er dan een nieuwe variabele gecreëerd. Aan de hand van deze variabele willen we de grafiek lineair maken.

Als we dan de linear fit van de originele data gaan vergelijken met de getransformeerde data zien we geen groot verschil tussen beide grafieken.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109.6
103
111.6
106.3
97.9
108.8
103.9
101.2
122.9
123.9
111.7
120.9
99.6
103.3
119.4
106.5
101.9
124.6
106.5
107.8
127.4
120.1
118.5
127.7
107.7
104.5
118.8
110.3
109.6
119.1
96.5
106.7
126.3
116.2
118.8
115.2
110
111.4
129.6
108.1
117.8
122.9
100.6
111.8
127
128.6
124.8
118.5
114.7
112.6
128.7
111
115.8
126
111.1
113.2
120.1
130.6
124
119.4
116.7
Dataseries Y:
Download CSV
Histogram 
93.4
101.1
114.2
104.8
113.3
118.2
83.6
73.9
99.5
97.7
103
106.3
92.2
101.8
122.8
111.8
106.3
121.5
81.9
85.4
110.9
117.3
106.3
105.6
101.2
105.9
126.3
111.9
108.9
127.2
94.2
85.7
116.2
107.2
110.5
112
104.4
112
132.8
110.8
128.7
136.8
94.8
88.8
123.2
125.3
122.7
125.8
116.3
118.6
142.1
127.9
132
152.4
110.8
99.1
134.9
133.2
131
133.9
119.9

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=25531&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=25531&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25531&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 x61
maximum correlation0.650156074045403
optimal lambda(x)0.34
Residual SD (orginial)12.2241102961156
Residual SD (transformed)12.2201564726320

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 61 \tabularnewline
maximum correlation & 0.650156074045403 \tabularnewline
optimal lambda(x) & 0.34 \tabularnewline
Residual SD (orginial) & 12.2241102961156 \tabularnewline
Residual SD (transformed) & 12.2201564726320 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25531&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]0.650156074045403[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]0.34[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]12.2241102961156[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]12.2201564726320[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25531&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25531&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 correlation0.650156074045403
optimal lambda(x)0.34
Residual SD (orginial)12.2241102961156
Residual SD (transformed)12.2201564726320


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')