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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 computationWed, 12 Nov 2008 03:46:20 -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/t1226486814xrxzlv7r3ywnfll.htm/, Retrieved Sun, 19 May 2024 09:37:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24087, Retrieved Sun, 19 May 2024 09:37:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Box-Cox Linearity Plot] [Q3] [2008-11-12 10:46:20] [7596afe9a05f2a2719ece78b1b0e12e6] [Current]
Feedback Forum
2008-11-15 16:35:56 [Laura Reussens] [reply
Bij een box cox linearity plot wordt een rechte door de puntenwolk getrokken om wetmatigheden af te leiden. Het doel van een box cox transformatie is om de gegevens meer lineair te maken. De correlatie wordt weergegeven op de y-as.
Aangezien bij deze gegevens de transformatie de correlatie slechts matig verhoogd, heeft deze handeling zeer weinig effect.
In het box cox linearity plot zien we echter wel een parabool waarvan het maximum zich bevindt rond (0,3;0,847).
  2008-11-22 13:31:31 [Sandra Hofmans] [reply
Ik kan hier nog bij aanvullen dat op de X-as de waarde van lambda komt, deze varieert van -2 tot 2. De waarde van lambda die overeenkomt met de maximale correlatie op de box-cox plot is de optimale keuze van lambda. Op de tekening is niet duidelijk te zien dat er een transformatie heeft plaatsgevonden, maar in de tabel zie je dit wel (correlatie bedraagt nu 0,84.)

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Dataseries X:
1784
1429
1744
1551
1679
1639
1393
1405
1750
1263
1357
1593
1821
1419
1524
1637
1540
1623
1523
1335
1700
1615
1493
1577
1607
1765
1504
1936
1862
2570
2082
1781
1869
1785
1682
1556
2080
2027
1887
1935
1798
1589
1592
1387
1849
1470
1437
1500
2081
1552
1586
1914
1639
1633
1693
1224
1417
1577
1225
1510
Dataseries Y:
3269
2934
3098
2956
3429
2887
2587
2865
3645
2557
3120
2827
3530
2606
3015
3481
3011
3179
2899
2768
3498
3417
3317
2951
3911
3674
3505
4263
3729
4384
4110
3360
3450
3708
3515
2877
3810
3953
3226
3818
3295
2884
3190
2652
3388
3071
2545
2686
4085
2869
2719
3599
2912
3509
3533
2365
2606
2712
2551
2646




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24087&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]4 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=24087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24087&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Box-Cox Linearity Plot
# observations x60
maximum correlation0.847240424348005
optimal lambda(x)0.21
Residual SD (orginial)259.035399198157
Residual SD (transformed)256.008457476857

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.847240424348005 \tabularnewline
optimal lambda(x) & 0.21 \tabularnewline
Residual SD (orginial) & 259.035399198157 \tabularnewline
Residual SD (transformed) & 256.008457476857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24087&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]0.847240424348005[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]0.21[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]259.035399198157[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]256.008457476857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24087&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 x60
maximum correlation0.847240424348005
optimal lambda(x)0.21
Residual SD (orginial)259.035399198157
Residual SD (transformed)256.008457476857



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')