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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 14:50:23 -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/t1226613179v1nrovkg26tk0d4.htm/, Retrieved Mon, 20 May 2024 09:48:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24852, Retrieved Mon, 20 May 2024 09:48:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

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] [Box-cox linearity...] [2008-11-13 21:50:23] [6af198e0108e278de39b2b3c538c1a2b] [Current]
Feedback Forum
2008-11-16 13:03:23 [Nicolaj Wuyts] [reply] 
De Box-Cox linearity plot veranderd niets aan de gegevens. De bekomen grafiek is nog steeds hetzelfde. De variantie tov de rechte is nog steeds redelijk groot en alle punten liggen nagenoeg op dezelfde plek. We kunnen dus stellen dat de Box-Cox linearity plot geen nut heeft gehad.
2008-11-16 15:25:52 [Julie Govaerts] [reply] 
box-cox linearity plot --> 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

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 is dat zo

λ is het coördinaat van de variabele op de horizontale as. Het coördinaat van de verticale as is de waarde van de correlatie tussen Y en de getransformeerde X. De waarde van λ die correspondeert met de maximumcorrelatie is de optimale keuze van λ.
2008-11-22 13:13:30 [Gilliam Schoorel] [reply] 
De box cox transformatie zorgt voor een betere fit door lambda toe te voegen. Indien het maximum niet bekomen wordt na de transformatie heeft de transformatie niet veel zin. De lineair fit correlatie grafieken geven dit ook heel duidelijk weer. Er is AMPER iets veranderd in de correlatie op de transformed fit grafiek.
De box cox transformatie zorgt voor een betere fit. Indien het maximum niet bekomen wordt na de transformatie heeft de transformatie niet veel zin.
Je kan op de box-cox plot ook zien dat de lijn eigenlijk al over zijn maximum is gegaan. De fit kan dus niet nog meer verbeterd worden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
108
90
76
81
108
124
114
107
109
74
119
115
99
90
79
86
73
126
123
105
119
81
124
117
101
91
84
79
86
131
127
110
112
77
113
126
99
104
84
95
109
123
109
102
110
71
117
109
109
90
77
113
113
91
109
105
108
82
107
104
Dataseries Y:
Download CSV
Histogram 
93
87
89
91
108
124
104
107
116
70
126
119
102
88
71
76
84
125
122
93
117
71
118
115
101
106
79
77
85
124
115
115
114
75
114
121
113
104
84
113
120
127
92
113
112
75
120
122
116
88
87
107
112
92
112
87
112
75
100
118

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'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24852&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24852&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'George Udny Yule' @ 72.249.76.132






Box-Cox Linearity Plot
# observations x60
maximum correlation0.882971736334535
optimal lambda(x)0.32
Residual SD (orginial)8.0602307159977
Residual SD (transformed)8.01694285063939

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.882971736334535 \tabularnewline
optimal lambda(x) & 0.32 \tabularnewline
Residual SD (orginial) & 8.0602307159977 \tabularnewline
Residual SD (transformed) & 8.01694285063939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24852&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]0.882971736334535[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]0.32[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]8.0602307159977[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]8.01694285063939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24852&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 correlation0.882971736334535
optimal lambda(x)0.32
Residual SD (orginial)8.0602307159977
Residual SD (transformed)8.01694285063939


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')