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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 10:43:06 -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/t1226425470rxrmqenx7hhdtj6.htm/, Retrieved Sat, 18 May 2024 16:54:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23775, Retrieved Sat, 18 May 2024 16:54:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Box-Cox Linearity Plot] [] [2007-10-30 20:15:08] [d63889a2cb43a84e31f95f02a72561da]
F    D    [Box-Cox Linearity Plot] [Various EDA topic Q5] [2008-11-11 17:43:06] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
Feedback Forum
2008-11-15 15:52:27 [Laura Reussens] [reply
Bij een linearity plot wordt een rechte door de puntenwolk getrokken om zo eventuele wetmatigheden vast te leiden. Een box cox transformatie heeft tot doel de gegevens nog meer lineair te maken. De correlatie wordt afgelezen op de y-as. Aangezien de correlatie door de transformatie weinig verhoogt, heeft deze handeling inderdaad weinig effect.
2008-11-19 14:26:30 [Sam De Cuyper] [reply
Wat gezegd wordt over detransformatie is correct, precieze interpretatie ontbreekt. De box-cox linearity plot geeft de weegave van het verband tussen 2 variabelen die met elkaar in verband staan. Het resultaat is een stijgende of een dalende rechte (bestudeerd wetmatigheid) met geconcentreerde punten. Het is de bedoeling om de variabelen te transformeren (X-variabele) en zo de scatterplot meer lineair te maken. Nu kan echter de vraag gesteld worden of de transfomatie nuttig is. Indien de grafiek een maximum vertoont zal de waarde van het maximum gekozen worden als lambda. Na transformatie is er visueel weinig verschil te merken, waardoor de transformatie onnuttig is. Ze heeft geen of toch zeer weinig effect.
2008-11-24 14:40:36 [Jessica Alves Pires] [reply
Ik ben het eens met de voorgaande opmerkingen. Je berekening klopt en je conclusie ook, er is inderdaad weinig effect. De punten bevinden zich na de transformatie niet op de rechte, of zelfs niet dichterbij. Je had wel meer uitleg mogen geven, bijv. welke reeks je als endogene variabele hebt genomen en welke als exogeen + waarom. Ook had je nog kunnen vermelden dat de optimale waarde voor de transformatie parameter 2 bedraagt.
2008-11-24 15:13:10 [Birgit Van Dyck] [reply
Een box-cox linearity plot transformeert de variabelen, deze transformatie moet nuttig zijj om de scatterplot lineairder te maken. Het is de bedoeling dat de grafiek een maximum vertoont, deze waarde wordt dan gebruitk al lambda. Na de transformatie blijkt er weinig verschil te zijn. De transformatie was onnuttig.

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Dataseries X:
220206
220115
218444
214912
210705
209673
237041
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241878
242621
238545
240337
244752
244576
241572
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236997
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267037
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267366
264777
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254868
277267
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286602
283042
276687
277915
277128
277103
275037
270150
267140
264993
287259
291186
292300
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281477
282656
280190
280408
276836
275216
274352
271311
289802
290726
292300
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269826
265861
269034
264176
255198
253353
246057
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258556
260993
254663
250643
243422
247105
Dataseries Y:
255843
254490
251995
246339
244019
245953
279806
283111
281097
275964
270694
271901
274412
272433
268361
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267153




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23775&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23775&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23775&T=0

As an alternative you can also use a 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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Box-Cox Linearity Plot
# observations x72
maximum correlation0.965744484895852
optimal lambda(x)2
Residual SD (orginial)6654.5188481349
Residual SD (transformed)6217.40958525517

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 72 \tabularnewline
maximum correlation & 0.965744484895852 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 6654.5188481349 \tabularnewline
Residual SD (transformed) & 6217.40958525517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23775&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]72[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.965744484895852[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]6654.5188481349[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]6217.40958525517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23775&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23775&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Box-Cox Linearity Plot
# observations x72
maximum correlation0.965744484895852
optimal lambda(x)2
Residual SD (orginial)6654.5188481349
Residual SD (transformed)6217.40958525517



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')