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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 computationWed, 12 Nov 2008 08:11:24 -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/12/t1226503147hzteich4c4xvkup.htm/, Retrieved Sun, 19 May 2024 08:51:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24239, Retrieved Sun, 19 May 2024 08:51:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173

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] [Q3 Various EDA To...] [2008-11-12 15:11:24] [56fd94b954e08a6655cb7790b21ee404] [Current]
Feedback Forum
2008-11-22 11:01:33 [Stephanie Vanderlinden] [reply] 
Een box-cox linearity plot probeert de variabelen te lineariseren om zo een lineair verband te ontdekken. Lambda is de transformatieparameter, deze varieert van -2 tot +2. Elke mogelijke transformatie wordt getoond, je moet zoeken naar het maximum van de curve daar het maximum de beste transformatie weergeeft. Als d grafiek een dalende of een stijgende rechte vertoont, wil dit zeggen dat er geen zinnige transformatie bestaat.
2008-11-23 14:55:41 [Alexander Hendrickx] [reply] 
De studente heeft de bewerking goed gedaan, maar er geen of een verkeerde conclusie bijgegeven. De box cox linearity plot probeert de correlatie tussen variabelen te lineariseren dit gebeurd door een transformatie met lamda. We merken op dat bij lamda 2 de correlatie het grootst is, de grafiek blijft stijgen waardoor we kunnen besluiten dat de transformatie het verband verbeterd.
2008-11-24 18:14:00 [Jan De Vleeschauwer] [reply] 
goede keuze, maar geen bewerking
2008-11-24 20:29:20 [94a54c888ac7f7d6874c3108eb0e1808] [reply] 
De berekening van de student zijn juist. Men kan er nog bij vermelden wat Een box-cox linearity plot doet. Deze probeert de variabelen te lineariseren om zo een lineair verband te ontdekken. Lambda is de transformatieparameter, deze varieert van -2 tot +2.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,9059
0,8883
0,8924
0,8833
0,8700
0,8758
0,8858
0,9170
0,9554
0,9922
0,9778
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,2490
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,2020
1,2271
1,2770
1,2650
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
Dataseries Y:
Download CSV
Histogram 
109,86
108,68
113,38
117,12
116,23
114,75
115,81
115,86
117,80
117,11
116,31
118,38
121,57
121,65
124,20
126,12
128,60
128,16
130,12
135,83
138,05
134,99
132,38
128,94
128,12
127,84
132,43
134,13
134,78
133,13
129,08
134,48
132,86
134,08
134,54
134,51
135,97
136,09
139,14
135,63
136,55
138,83
138,84
135,37
132,22
134,75
135,98
136,06
138,05
139,59
140,58
139,81
140,77
140,96
143,59
142,70
145,11
146,70
148,53
148,99
149,65
151,11
154,82
156,56
157,60
155,24
160,68
163,22
164,55
166,76
159,05
159,82
164,95
162,89

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=24239&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=24239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24239&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 x74
maximum correlation0.906918290092313
optimal lambda(x)2
Residual SD (orginial)6.31125742067693
Residual SD (transformed)6.03583515145677

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 74 \tabularnewline
maximum correlation & 0.906918290092313 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 6.31125742067693 \tabularnewline
Residual SD (transformed) & 6.03583515145677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24239&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]74[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.906918290092313[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]6.31125742067693[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]6.03583515145677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24239&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 x74
maximum correlation0.906918290092313
optimal lambda(x)2
Residual SD (orginial)6.31125742067693
Residual SD (transformed)6.03583515145677


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')