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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 07:21:30 -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/t1226413444tpsh2m96ijtvu62.htm/, Retrieved Sun, 19 May 2024 09:21:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23518, Retrieved Sun, 19 May 2024 09:21:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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 14:21:30] [620b6ad5c4696049e39cb73ce029682c] [Current]
Feedback Forum
2008-11-14 10:26:32 [Ciska Tanghe] [reply] 
Bij de Box-Cox linearity plot gaan we een variabele transformeren met een bepaalde parameter. We zijn op zoek naar een lambda-waarde waardoor x transformeert en zo een lineair verloop van de grafiek weergeeft. Op deze grafiek zien we niet duidelijk waar een maximum bereikt wordt, maar we hebben een vermoeden dat dit in het punt 2 zal zijn. Daarom zullen we de lambda toepassen en zien of deze lambda-waarde optimaal is.
2008-11-24 18:03:14 [Jan Cavents] [reply] 
Bij BCL-plot moeten we op zoek gaan naar de optimale lambda waarden. hiermee gaan we x laten transformeren om een lineair verloop te bekomen. in dit geval is de optimale lambdawaarde in het punt 2 te vinden. dit moet opnieuw berekend worden om de geldigheid te testen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1045,9
1401,9
1027,6
1703,8
1481,3
1422,7
1304,7
1246,1
1417,8
1459,1
1156,4
1304,5
1336,9
1372,3
975,5
1180,8
1361,3
1428,1
1355,9
1781,2
1697
1852
1844,1
1967,2
1747,1
1863,9
1559,3
1675
2237,5
1965,2
1871,5
1752,2
1360,7
1444,3
1621,6
1368
1553,9
1695,3
1397,1
1848,4
1809,2
1551,1
1546,6
1467,9
1662,4
1972,3
1673,5
1762
2019,8
1754,3
1400,4
1453,6
1740,9
1694,6
1541,2
1482,3
1632,1
1837,3
1797
2066,2
1983,8
1601,7
1660,3
1954
1991,9
1881,4
2345,5
1773,1
1719,2
2240,9
1816,4
2171,3
1823,3
2022,5
1991
1920
2168,4
2013,5
1790,8
1855,7
2074
2535,8
1837,2
1805,1
1785,7
2250
1959,7
1890,8
2405,7
2090,3
1666,5
1803,5
1793,8
1488,8
1545
1369,9
1451,6
Dataseries Y:
Download CSV
Histogram 
1593
1477,9
1733,7
1569,7
1843,7
1950,3
1657,5
1772,1
1568,3
1809,8
1646,7
1808,5
1763,9
1625,5
1538,8
1342,4
1645,1
1619,9
1338,1
1505,5
1529,1
1511,9
1656,7
1694,4
1662,3
1588,7
1483,3
1585,6
1658,9
1584,4
1470,6
1618,7
1407,6
1473,9
1515,3
1485,4
1496,1
1493,5
1298,4
1375,3
1507,9
1455,3
1363,3
1392,8
1348,8
1880,3
1669,2
1543,6
1701,2
1516,5
1466,8
1484,1
1577,2
1684,5
1414,7
1674,5
1598,7
1739,1
1674,6
1671,8
1802
1526,8
1580,9
1634,8
1610,3
1712
1678,8
1708,1
1680,6
2056
1624
2021,4
1861,1
1750,8
1767,5
1710,3
2151,5
2047,9
1915,4
1984,7
1896,5
2170,8
2139,9
2330,5
2121,8
2226,8
1857,9
2155,9
2341,7
2290,2
2006,5
2111,9
1731,3
1762,2
1863,2
1943,5
1975,2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23518&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23518&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132






Box-Cox Linearity Plot
# observations x97
maximum correlation0.498176776421004
optimal lambda(x)2
Residual SD (orginial)212.381142536152
Residual SD (transformed)209.108619045711

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 97 \tabularnewline
maximum correlation & 0.498176776421004 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 212.381142536152 \tabularnewline
Residual SD (transformed) & 209.108619045711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23518&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]97[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.498176776421004[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]212.381142536152[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]209.108619045711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23518&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 x97
maximum correlation0.498176776421004
optimal lambda(x)2
Residual SD (orginial)212.381142536152
Residual SD (transformed)209.108619045711


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')