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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 computationMon, 10 Nov 2008 07:09:04 -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/10/t1226326188planyqn4aentcw9.htm/, Retrieved Sun, 19 May 2024 09:26:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23066, Retrieved Sun, 19 May 2024 09:26:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact203

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 q3] [2008-11-10 14:09:04] [4940af498c7c54f3992f17142bd40069] [Current]
- RM D    [Box-Cox Normality Plot] [Hercomputatie fee...] [2008-11-21 20:27:09] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
-    D      [Box-Cox Normality Plot] [Q5] [2008-11-23 13:17:31] [b47fceb71c9525e79a89b5fc6d023d0e]
Feedback Forum
2008-11-16 16:12:47 [Jan Van Riet] [reply] 
Op de box-cox linearity plot zien we al een vrij tot zeer lineaire correlatie. Maar een transformatie zou dit nog kunnen verbeteren (nog meer rechttrekken). Echter, we kunnen nu geen uitspraken doen omdat we geen maximum of minimum kunnen zien op deze grafiek. Je zou dus (als je een conclusie wil trekken) best bvb een lambda-waarden van 0 tot 4 onderzoeken.
2008-11-21 20:20:27 [Kim Wester] [reply] 
De Box-Cox transformatie is bedoeld om tijdreeksen te transformeren die problemen opleveren (geen lineair verband tonen). Het lambda getal transformeert de reeks zodat er een lineair verband = rechte ontstaat. Wanneer er door deze lambda rechte (Box-Cox Linearity Plot) geen max wordt bereikt kunnen er geen besluiten worden genomen. Een oplossing zou het vergroten van de lambda waarden zijn (dit kan door een aanpassing te doen in de R-code).

In dit geval is er visueel geen duidelijk verschil waar te nemen tussen de reeksen voor en na de transformatie. De Box-Cox Linearity Plot weergeeft geen maximum.
2008-11-23 15:37:49 [Nathalie Boden] [reply] 
De box-cox linearity plot is bedoeld om tijdreeksen te transformeren om zo problemen op te lossen. We hebben twee variabelen (x en y) De scatterplot geeft het verband aan dat bestaat tussen x en y, maar we trekken hier een kromme in plaats van een rechte. Alle transformaties van lambda -2 tot +2 worden berekent, dan worden ook de correlaties tussen x en y berekent. We nemen het verband waar de lambda het meest lineair wordt. Als je het maximum niet kan zien kan je ook geen besluit trekken.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110,40
96,40
101,90
106,20
81,00
94,70
101,00
109,40
102,30
90,70
96,20
96,10
106,00
103,10
102,00
104,70
86,00
92,10
106,90
112,60
101,70
92,00
97,40
97,00
105,40
102,70
98,10
104,50
87,40
89,90
109,80
111,70
98,60
96,90
95,10
97,00
112,70
102,90
97,40
111,40
87,40
96,80
114,10
110,30
103,90
101,60
94,60
95,90
104,70
102,80
98,10
113,90
80,90
95,70
113,20
105,90
108,80
102,30
99,00
100,70
115,50
Dataseries Y:
Download CSV
Histogram 
109,20
88,60
94,30
98,30
86,40
80,60
104,10
108,20
93,40
71,90
94,10
94,90
96,40
91,10
84,40
86,40
88,00
75,10
109,70
103,00
82,10
68,00
96,40
94,30
90,00
88,00
76,10
82,50
81,40
66,50
97,20
94,10
80,70
70,50
87,80
89,50
99,60
84,20
75,10
92,00
80,80
73,10
99,80
90,00
83,10
72,40
78,80
87,30
91,00
80,10
73,60
86,40
74,50
71,20
92,40
81,50
85,30
69,90
84,20
90,70
100,30

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23066&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23066&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Box-Cox Linearity Plot
# observations x61
maximum correlation0.574057467611171
optimal lambda(x)2
Residual SD (orginial)8.71926753568429
Residual SD (transformed)8.65481230173688

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 61 \tabularnewline
maximum correlation & 0.574057467611171 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 8.71926753568429 \tabularnewline
Residual SD (transformed) & 8.65481230173688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23066&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]0.574057467611171[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]8.71926753568429[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]8.65481230173688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23066&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 correlation0.574057467611171
optimal lambda(x)2
Residual SD (orginial)8.71926753568429
Residual SD (transformed)8.65481230173688


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')