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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, 10 Nov 2008 03:58:39 -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/t1226314804lwsepriaqd5ko6z.htm/, Retrieved Sat, 18 May 2024 18:52:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22930, Retrieved Sat, 18 May 2024 18:52:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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...] [2008-11-10 10:58:39] [6aa66640011d9b98524a5838bcf7301d] [Current]
Feedback Forum
2008-11-19 15:23:41 [Mehmet Yilmaz] [reply] 
Met de Box-Cox Linearity Plot kunnen we een tijdreeks transformeren en op die manier interpretatie fouten voorkomen. vb. De scatterplot doet denken dat er een lineair verband bestaat, maar eigenlijk is er geen verband.
Hier worden de correlaties berekend tussen de verschillende waarden en de hoogste hiervan wordt genomen.
Als resultaat bekomen we een maximum correlatie van 0.238960393145301 bij een optimale lambda van 2.

De andere 2 grafieken geven eveneens de correlatie weer. Dankzij de afstand van de puntjes kunnen we de waarde van de correlatie zien. Hoe dichter bij de lijn hoe hoger de correlatie.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,43
4,61
4,54
4,2
4,08
3,95
4,19
4,23
3,89
3,92
4,14
4,24
4,08
4,37
4,43
4,3
4,27
4,06
3,96
4,21
4,31
4,35
4,25
4,06
4
3,87
3,71
3,63
3,48
3,6
3,66
3,45
3,3
3,14
3,21
3,12
3,14
3,4
3,42
3,29
3,49
3,52
3,81
4,03
3,98
4,1
3,96
3,83
3,72
3,82
3,76
3,98
4,14
4
4,13
4,28
4,46
4,63
4,49
4,41
4,5
4,39
4,33
4,45
4,17
4,13
4,33
4,47
4,63
4,9
Dataseries Y:
Download CSV
Histogram 
88,3
88,6
91
91,5
95,4
98,7
99,9
98,6
100,3
100,2
100,4
101,4
103
109,1
111,4
114,1
121,8
127,6
129,9
128
123,5
124
127,4
127,6
128,4
131,4
135,1
134
144,5
147,3
150,9
148,7
141,4
138,9
139,8
145,6
147,9
148,5
151,1
157,5
167,5
172,3
173,5
187,5
205,5
195,1
204,5
204,5
201,7
207
206,6
210,6
211,1
215
223,9
238,2
238,9
229,6
232,2
222,1
221,6
227,3
221
213,6
243,4
253,8
265,3
268,2
268,5
266,9

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22930&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22930&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Box-Cox Linearity Plot
# observations x70
maximum correlation0.238960393145301
optimal lambda(x)2
Residual SD (orginial)52.7476086906614
Residual SD (transformed)52.6230899868048

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 70 \tabularnewline
maximum correlation & 0.238960393145301 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 52.7476086906614 \tabularnewline
Residual SD (transformed) & 52.6230899868048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22930&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]70[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.238960393145301[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]52.7476086906614[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]52.6230899868048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22930&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 x70
maximum correlation0.238960393145301
optimal lambda(x)2
Residual SD (orginial)52.7476086906614
Residual SD (transformed)52.6230899868048


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')