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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 08:13:33 -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/t1226503207txv24ozc9kbji46.htm/, Retrieved Tue, 28 May 2024 12:26:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24242, Retrieved Tue, 28 May 2024 12:26:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178

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] [question 3 box-co...] [2008-11-12 15:13:33] [f7fbcd402030df685d3fe4ce577d7846] [Current]
F RMPD    [Maximum-likelihood Fitting - Normal Distribution] [question 5] [2008-11-12 15:49:20] [31c9f333c18b3396ccf9d2485dd39c8a]
- R  D      [Maximum-likelihood Fitting - Normal Distribution] [q5] [2008-11-13 14:11:05] [379d6c32f73e3218fd773d79e4063d07]
- R  D      [Maximum-likelihood Fitting - Normal Distribution] [q5] [2008-11-13 14:11:05] [379d6c32f73e3218fd773d79e4063d07]
- R  D      [Maximum-likelihood Fitting - Normal Distribution] [question 5] [2008-11-13 14:14:05] [379d6c32f73e3218fd773d79e4063d07]
F RMPD      [Testing Mean with known Variance - Critical Value] [question 1] [2008-11-13 14:31:27] [379d6c32f73e3218fd773d79e4063d07]
F RMPD      [Testing Mean with known Variance - Type II Error] [question 2] [2008-11-13 14:42:18] [379d6c32f73e3218fd773d79e4063d07]
F RMPD      [Testing Mean with known Variance - Critical Value] [question 3] [2008-11-13 14:49:41] [379d6c32f73e3218fd773d79e4063d07]
F RMPD      [Testing Population Mean with known Variance - Confidence Interval] [question 5] [2008-11-13 14:56:36] [379d6c32f73e3218fd773d79e4063d07]
F RMPD      [Testing Sample Mean with known Variance - Confidence Interval] [question 6] [2008-11-13 15:02:49] [379d6c32f73e3218fd773d79e4063d07]
- RMPD      [Testing Variance - p-value (probability)] [question 1] [2008-11-13 15:10:29] [db2695c9827accc799f4506094970dce]
- RMPD      [Testing Variance - Confidence Intervals for Sample Variance] [question 2] [2008-11-13 15:13:57] [379d6c32f73e3218fd773d79e4063d07]
F    D    [Box-Cox Linearity Plot] [Taak 2 Part 1 Oef 3] [2008-11-13 20:11:25] [17bef6922a2795858ae28bf8ba596537]
F RM D    [Box-Cox Normality Plot] [Vincent Dolhain T...] [2008-11-13 20:20:28] [17bef6922a2795858ae28bf8ba596537]
F RMPD      [Maximum-likelihood Fitting - Normal Distribution] [Taak 2 Part 1 Oef5] [2008-11-13 20:29:43] [17bef6922a2795858ae28bf8ba596537]
Feedback Forum
2008-11-19 17:31:56 [Steven Vercammen] [reply] 
Er wordt geen interpretatie gegeven.In het e-hanboek vinden we dat het doel van de Box-cox transformatie is om de X variabele te transformeren zodat de correlatie met de Y variabele maximaal wordt. “Transformations can often significantly improve a fit. The Box-Cox linearity plot provides a convenient way to find a suitable transformation without engaging in a lot of trial and error fitting.” De formule die wordt toegepast is T(X) = (X^lambda -1) / lambda. Waarbij X de variabele is die getransformeerd wordt en lambda de transformatieparameter. Als lambda echter 0 is dan wordt ipv deze formule de natuurlijke logaritme van data gebruikt. De box-coxlinearity plot geeft aan welke waarde van lambda nodig is opdat de transformatie een optimaal effect heeft. Men moet echter ook kijken naar het verschil in correlatie voor en na transformatie. Dit kunnen we nagaan door de scatterplots voor en na transformatie te vergelijken. Hier is de optimale lambda 2, het verschil in correlatie is klein.
2008-11-19 19:13:33 [Toon Wouters] [reply] 
In de scatterplot worden 2 variabelen met elkaar in verband gebracht. Doormiddel van deze scatterplot te transformeren en lineair te maken bekomen we de box-cox lineairity plot. We hopen een maximum vast te stellen. En dat is hier ook het geval bij een lambda gelijk aan 2. Dat wil zeggen dat bij de lambda gelijk aan 2 de correlatie optimaal is.
2008-11-23 17:14:55 [c00776cbed2786c9c4960950021bd861] [reply] 
De box-cox linearity plot is een plot van de correlatie van y en de getransformeerde x-variabelen voor verschillende waarden van lambda.
De optimal lambda (de lambda met de hoogste correlatie) is hier 2.
we zien ook dat een transformatie hier geen nut heeft omdat er bijna geen verbetering is. The residual standard deviation is hier ook niet veel gedaald, waaruit we kunnen besluiten dat de transformatie geen echte verbetering is, en dus zinloos is.

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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 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=24242&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=24242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24242&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 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=24242&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=24242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24242&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')