FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationThu, 13 Nov 2008 02:25:57 -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/13/t1226568430wve6bpb9zjjbiec.htm/, Retrieved Sun, 19 May 2024 12:35:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24514, Retrieved Sun, 19 May 2024 12:35:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210

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] [W3Q3] [2008-11-13 09:25:57] [434228f9e3c7eaa307f0fb12855e2147] [Current]
- RMPD    [Testing Mean with known Variance - Critical Value] [W4Q1] [2008-11-13 09:49:36] [88cf507fbedaeeb6f794e4dc3641d02c]
- RMPD    [Testing Mean with known Variance - p-value] [W4Q2] [2008-11-13 09:56:06] [fefc9cefce013a6daab207c2a2eec05e]
- RMPD    [Testing Mean with known Variance - Type II Error] [W4Q3] [2008-11-13 10:00:09] [fefc9cefce013a6daab207c2a2eec05e]
Feedback Forum
2008-11-22 12:31:46 [Sandra Hofmans] [reply] 
Juiste conclusie, het is goed dat je verwijst naar de tabel, omdat het inderdaad op de grafiek niet duidelijk te zien is. Op de x-as vind je de waarde Lambda (deze varieert van -2 tot 2). De Y-as is de correlatiecoëfficiënt van de getransformeerde X en Y. De waarde van lambda die overeenkomt met de maximale correlatie op de box-cox plot is de optimale keuze van lambda.
2008-11-23 16:02:51 [Peter Van Doninck] [reply] 
De student heeft een correcte box-cox linearity plot getekend. Ze heeft ook een jusite conclusie gemaakt, dat door de variabele x te transformeren, het scatterplot niet lineairder wordt. Hierdoor is de transformatie niet echt zinvol. Wel kan er nog aan toegevoegd worden dat de optimale lambda -1,5 bedraagt.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
118,4
121,4
128,8
131,7
141,7
142,9
139,4
134,7
125,0
113,6
111,5
108,5
112,3
116,6
115,5
120,1
132,9
128,1
129,3
132,5
131,0
124,9
120,8
122,0
122,1
127,4
135,2
137,3
135,0
136,0
138,4
134,7
138,4
133,9
133,6
141,2
151,8
155,4
156,6
161,6
160,7
156,0
159,5
168,7
169,9
169,9
185,9
190,8
195,8
211,9
227,1
251,3
256,7
251,9
251,2
270,3
267,2
243,0
229,9
187,2
Dataseries Y:
Download CSV
Histogram 
111,4
114,1
121,8
127,6
129,9
128,0
123,5
124,0
127,4
127,6
128,4
131,4
135,1
134,0
144,5
147,3
150,9
148,7
141,4
138,9
139,8
145,6
147,9
148,5
151,1
157,5
167,5
172,3
173,5
187,5
205,5
195,1
204,5
204,5
201,7
207,0
206,6
210,6
211,1
215,0
223,9
238,2
238,9
229,6
232,2
222,1
221,6
227,3
221,0
213,6
243,4
253,8
265,3
268,2
268,5
266,9
268,4
250,8
231,2
192,0

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24514&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24514&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'George Udny Yule' @ 72.249.76.132






Box-Cox Linearity Plot
# observations x60
maximum correlation0.879749265233883
optimal lambda(x)-1.5
Residual SD (orginial)26.2263829714733
Residual SD (transformed)23.0901927950382

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.879749265233883 \tabularnewline
optimal lambda(x) & -1.5 \tabularnewline
Residual SD (orginial) & 26.2263829714733 \tabularnewline
Residual SD (transformed) & 23.0901927950382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24514&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]0.879749265233883[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]-1.5[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]26.2263829714733[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]23.0901927950382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24514&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 x60
maximum correlation0.879749265233883
optimal lambda(x)-1.5
Residual SD (orginial)26.2263829714733
Residual SD (transformed)23.0901927950382


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')