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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 06:47:46 -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/t1226497732051g137gkz558d6.htm/, Retrieved Sun, 19 May 2024 12:18:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24183, Retrieved Sun, 19 May 2024 12:18:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

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] [] [2008-11-12 13:47:46] [890f958132adb51f538eb267509d2e70] [Current]
Feedback Forum
2008-11-20 17:05:49 [Gert-Jan Geudens] [reply] 
Ook hier is geen conclusie gegeven. De box-cox linearity plot, gaat de data lineair transformeren door een lambda toe te voegen. De optimale lambda die de hoogste correlatie tussen de variabelen geeft, is hier gelijk aan 2. De transformatie heeft hier helemaal geen nut aangezien de correlatie stijgt van -0.18 naar ongeveer -0.08. -0.08 ligt dichter bij nul en dus wordt de negatieve correlatie/verband zelfs nog kleiner in plaats van groter ! Dit kunnen we ook afleiden uit de scatterplots aangezien de gegevens minder goed de regressielijn benaderen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98.1
101.1
111.1
93.3
100
108
70.4
75.4
105.5
112.3
102.5
93.5
86.7
95.2
103.8
97
95.5
101
67.5
64
106.7
100.6
101.2
93.1
84.2
85.8
91.8
92.4
80.3
79.7
62.5
57.1
100.8
100.7
86.2
83.2
71.7
77.5
89.8
80.3
78.7
93.8
57.6
60.6
91
85.3
77.4
77.3
68.3
69.9
81.7
75.1
69.9
84
54.3
60
89.9
77
85.3
77.6
69.2
75.5
85.7
72.2
79.9
85.3
52.2
61.2
82.4
85.4
78.2
70.2
70.2
69.3
77.5
66.1
69
79.2
56.2
63.3
77.8
92
78.1
65.1
71.1
70.9
72
81.9
70.6
72.5
65.1
61.1
Dataseries Y:
Download CSV
Histogram 
98.6
98
106.8
96.7
100.2
107.7
92
98.4
107.4
117.7
105.7
97.5
99.9
98.2
104.5
100.8
101.5
103.9
99.6
98.4
112.7
118.4
108.1
105.4
114.6
106.9
115.9
109.8
101.8
114.2
110.8
108.4
127.5
128.6
116.6
127.4
105
108.3
125
111.6
106.5
130.3
115
116.1
134
126.5
125.8
136.4
114.9
110.9
125.5
116.8
116.8
125.5
104.2
115.1
132.8
123.3
124.8
122
117.4
117.9
137.4
114.6
124.7
129.6
109.4
120.9
134.9
136.3
133.2
127.2
122.7
120.5
137.8
119.1
124.3
134.4
121.1
122.2
127.7
137.4
132.2
129.2
124.9
124.8
128.2
134.4
118.6
132.6
123.2
112.3

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=24183&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=24183&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24183&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 x92
maximum correlation0.175136254626759
optimal lambda(x)2
Residual SD (orginial)11.8142954333158
Residual SD (transformed)11.7542460044452

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 92 \tabularnewline
maximum correlation & 0.175136254626759 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 11.8142954333158 \tabularnewline
Residual SD (transformed) & 11.7542460044452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24183&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]92[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.175136254626759[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]11.8142954333158[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]11.7542460044452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24183&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24183&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 x92
maximum correlation0.175136254626759
optimal lambda(x)2
Residual SD (orginial)11.8142954333158
Residual SD (transformed)11.7542460044452


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')