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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 computationMon, 10 Nov 2008 10:37:05 -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/10/t1226338813zl4lsiy0904pavg.htm/, Retrieved Sun, 19 May 2024 12:19:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23152, Retrieved Sun, 19 May 2024 12:19:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171

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] [Opdracht 6 Box-Cox] [2008-11-10 17:37:05] [8a1195ff8db4df756ce44b463a631c76] [Current]
Feedback Forum
2008-11-14 13:04:21 [Ken Van den Heuvel] [reply] 
Deze transformatie gaat na of er een lambda-waarde bestaat om van het niet lineaire verband een lineair verband te maken. Deze waarde duidt dus niet op de Tukey-lambda waarde en zegt dus in principe niet rechtsstreeks iets over de verdeling.
Er is inderdaad een gering verschil tussen voor en na de transformatie. Kijk naar de box-cox linearity plot, de waarden op de y-as varieren niet al te sterk bij het testen van verschillende lambda-waarden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
89.3
87.5
106.7
102.5
109.2
123.7
83.1
97
119.1
125.1
113.6
122.4
92.8
97.2
115.6
111.3
114.6
137.5
83.7
106
123.4
126.5
120
141.6
90.5
96.5
113.5
120.1
123.9
144.4
90.8
114.2
138.1
135
131.3
144.6
101.7
108.7
135.3
124.3
138.3
158.2
93.5
124.8
154.4
152.8
148.9
170.3
124.8
134.4
154
147.9
168.1
175.7
116.7
140.8
164.2
173.8
167.8
166.6
135.1
158.1
151.8
168.7
166.9
Dataseries Y:
Download CSV
Histogram 
74.8
93.1
103.9
83.9
77.7
141.5
58.9
75.3
108.4
91
84.6
179.8
85.6
76.4
109.7
99.1
86.7
111.4
78.4
76.7
114.2
99.7
94.2
173.5
83.1
88.9
132
122.1
105.1
133.7
63.6
112.7
120.5
112
126.2
209.2
91
116.7
137.6
108.1
136.6
152.3
114.3
120.7
131.8
129.4
187.5
189.5
109.2
158.1
176.2
125.5
155
170.3
99.4
139.2
169.6
136.1
168.2
318.6
154.1
161.4
183.4
167.2
205.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23152&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]3 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=23152&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23152&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Box-Cox Linearity Plot
# observations x65
maximum correlation0.780300947314252
optimal lambda(x)1.42
Residual SD (orginial)27.6487677767624
Residual SD (transformed)27.6043820617930

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 65 \tabularnewline
maximum correlation & 0.780300947314252 \tabularnewline
optimal lambda(x) & 1.42 \tabularnewline
Residual SD (orginial) & 27.6487677767624 \tabularnewline
Residual SD (transformed) & 27.6043820617930 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23152&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]65[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.780300947314252[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.42[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]27.6487677767624[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]27.6043820617930[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23152&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23152&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 x65
maximum correlation0.780300947314252
optimal lambda(x)1.42
Residual SD (orginial)27.6487677767624
Residual SD (transformed)27.6043820617930


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')