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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_boxcoxlin.wasp
Title produced by softwareBox-Cox Linearity Plot
Date of computationThu, 13 Nov 2008 13:11:25 -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/t1226607265ll8ja4clb3nynwf.htm/, Retrieved Sun, 19 May 2024 08:52:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24820, Retrieved Sun, 19 May 2024 08:52:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [question 3 box-co...] [2008-11-12 15:13:33] [31c9f333c18b3396ccf9d2485dd39c8a]
F    D    [Box-Cox Linearity Plot] [Taak 2 Part 1 Oef 3] [2008-11-13 20:11:25] [dcb9dbe132bac62365bf3d43fe342148] [Current]
Feedback Forum
2008-11-20 16:01:29 [Marie-Lien Loos] [reply] 
Methode juist. Er valt inderdaad niet veel over te vertellen. De transformatie zorgt hier niet voor een verbetering.
Bij de transformatie zoeken we x-waarden die de correlatie trussen X- en Y-variabelen verbeteren (= meer lineair maken)
2008-11-24 20:36:43 [Marlies Polfliet] [reply] 
De student heeft de juiste berekeningsmethode gebruikt, maar is zijn box cox linearity plot vergeten toe te voegen evenals zijn conclusie. Het doel van een scatterplot is om een verband te zoeken tussen twee variabelen; om het gemakkelijker te benaderen en de correlatie tussen x- en y variabelen te verbeteren = om het meer lineair te maken, passen we de box-cox transformatie toe. De transformatie zorgt in dit geval voor niet veel verbetering.
2008-11-24 21:22:08 [Erik Geysen] [reply] 
De student heeft de juiste methode gebruikt. Het doel van de transformaties is om het verband tussen de variabelen meer lineair te maken. Het is hier juist om de box-cox transformatie toe te passen. Hier heeft deze transformatie echter niet veel verbetering gebracht.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,9059
0,8883
0,8924
0,8833
0,87
0,8758
0,8858
0,917
0,9554
0,9922
0,9778
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
Dataseries Y:
Download CSV
Histogram 
109,86
108,68
113,38
117,12
116,23
114,75
115,81
115,86
117,8
117,11
116,31
118,38
121,57
121,65
124,2
126,12
128,6
128,16
130,12
135,83
138,05
134,99
132,38
128,94
128,12
127,84
132,43
134,13
134,78
133,13
129,08
134,48
132,86
134,08
134,54
134,51
135,97
136,09
139,14
135,63
136,55
138,83
138,84
135,37
132,22
134,75
135,98
136,06
138,05
139,59
140,58
139,81
140,77
140,96
143,59
142,7
145,11
146,7
148,53
148,99
149,65
151,11
154,82
156,56
157,6
155,24
160,68
163,22
164,55
166,76
159,05
159,82
164,95
162,89

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=24820&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=24820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24820&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 x74
maximum correlation0.906918290092313
optimal lambda(x)2
Residual SD (orginial)6.31125742067692
Residual SD (transformed)6.03583515145677

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 74 \tabularnewline
maximum correlation & 0.906918290092313 \tabularnewline
optimal lambda(x) & 2 \tabularnewline
Residual SD (orginial) & 6.31125742067692 \tabularnewline
Residual SD (transformed) & 6.03583515145677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24820&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]74[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.906918290092313[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]2[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]6.31125742067692[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]6.03583515145677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24820&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 x74
maximum correlation0.906918290092313
optimal lambda(x)2
Residual SD (orginial)6.31125742067692
Residual SD (transformed)6.03583515145677


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')