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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 computationTue, 11 Nov 2008 15:10:21 -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/11/t1226441502gdkymhwugknf39w.htm/, Retrieved Sun, 19 May 2024 12:13:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24003, Retrieved Sun, 19 May 2024 12:13:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158

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 topic...] [2008-11-11 22:10:21] [382e90e66f02be5ed86892bdc1574692] [Current]
-    D    [Box-Cox Linearity Plot] [Box Cox Linearity...] [2008-11-19 20:17:56] [d32f94eec6fe2d8c421bd223368a5ced]
Feedback Forum
2008-11-21 18:41:26 [Evelien Blockx] [reply] 
Het lijkt dat de maximale lambda 2 is. Dit is echter niet 100% zeker. Verder gaat de correlatie op de y-as van 0,660 tot 0,675. Dat verschil is zeker niet spectaculair. De techniek werkt hier niet goed.
2008-11-22 17:50:34 [Inge Meelberghs] [reply] 
Als we kijken naar de grafiek van de originele data en de grafiek van de getransformeerde data kunnen we inderdaad stellen dat er praktisch geen verschil te zien is.

Op de Box - Cox Linearity Plot kunnen we ziet dat er zich een maximum voordoet. We veronderstellen dus dat er zich een transformatie heeft voorgedaan. Met deze transformatie proberen we een niet lineaire scatterplot toch lineair te maken door een geschikte lambda waarde te kiezen. Hierdoor veranderd de R-code en wordt er een nieuwe variabele gecreëerd. In dit geval bedraagt de optimale lambda waarde 2. Toch zien we na de transformatie weinig tot geen verschil zoals eerder al vermeld is.
2008-11-23 12:39:29 [Pieter Broos] [reply] 
We kunnen alleen maar vermoeden dat er een maximum is bij lambda 2, dit is helemaal niet zeker. Ook het verschil in correlatie op de y-as is minimaal
2008-11-24 21:11:36 [Yara Van Overstraeten] [reply] 
We kunnen inderdaad niet zeker zijn dat het maximum bereikt wordt bij lambda 2 omdat de grafiek niet verder gaat. Het interval van de correaltie is inderdaad zeer klein (0,015).

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
1,249
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
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
Dataseries Y:
Download CSV
Histogram 
24,67
25,59
26,09
28,37
27,34
24,46
27,46
30,23
32,33
29,87
24,87
25,48
27,28
28,24
29,58
26,95
29,08
28,76
29,59
30,7
30,52
32,67
33,19
37,13
35,54
37,75
41,84
42,94
49,14
44,61
40,22
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68

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=24003&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=24003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24003&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 x60
maximum correlation0.677276539764246
optimal lambda(x)2
Residual SD (orginial)11.9845525191782
Residual SD (transformed)11.9631442331643

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.677276539764246 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 11.9845525191782 \tabularnewline
Residual SD (transformed) & 11.9631442331643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24003&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]0.677276539764246[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]11.9845525191782[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]11.9631442331643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24003&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 correlation0.677276539764246
optimal lambda(x)2
Residual SD (orginial)11.9845525191782
Residual SD (transformed)11.9631442331643


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')