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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 02:51:03 -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/t1226569970umssj337rubnzks.htm/, Retrieved Sun, 19 May 2024 08:45:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24525, Retrieved Sun, 19 May 2024 08:45:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Box-Cox Linearity Plot] [hierarched] [2008-11-12 18:46:21] [762cc4d66bc29c3c2c407be34c6d0239]
F    D    [Box-Cox Linearity Plot] [box linearity plot] [2008-11-13 09:51:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-11-16 15:35:46 [074508d5a5a3592082de3e836d27af7d] [reply] 
Een goede conclusie. Alleen had je misschien nog kunnen vermelden dat de transformatie bijna niet geholpen heeft. De correlatie schommelt namelijk tussen -0.32 en -0.20, dus de transformatie heeft bijna geen effect gehad.
2008-11-18 09:50:22 [72e979bcc364082694890d2eccc1a66f] [reply] 
We kunnen een negatief verband waarnemen. De transformatie heeft niet veel invloed gehad maar er is toch een heel lichte verbetering waarneembaar.
2008-11-24 11:30:34 [Anna Hayan] [reply] 
Een kleine theorieaanvulling De box-cox linearity plot geeft de weegave van het verband tussen 2 variabelen die met elkaar in verband staan. Het resultaat is een stijgende of een dalende rechte (staat in voor de wetmatigheid) met geconcentreerde punten. Het is de bedoeling om de variabelen te transformeren (X-variabele) en zo de scatterplot meer lineair te maken. Nu kan echter de vraag gesteld worden of de transfomatie nuttig is. Indien de grafiek een maximum vertoont zal de waarde van het maximum gekozen worden als lambda. Na transformatie is er visueel weinig verschil te merken, waardoor de transformatie onnuttig is. Ze heeft geen of toch zeer weinig effect.
2008-11-24 20:26:19 [Erik Geysen] [reply] 
Een stijgende of dalende lijn komt zeer vaak voor. Maar de punten kunnen geconcentreerd zijn boven of onder de lijn. Is er dan wel een lineair verband? Daarom gebruiken we de Box-cox linearity plot om deze gegevens meer lineair te maken. Er is een negatief verband. Na de transformatie is dit licht verbeterd, maar we kunnen toch zeggen dat deze transformatie weinig of geen effect had. Het verschil is verwaarloosbaar.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
200,7
146,5
143,6
141,5
137,5
138,7
135,5
136,4
112,1
109
123,8
151,2
139,2
115,7
147,6
126,1
122,8
137,3
142
137,4
89,4
108
117,7
127,3
121
104,1
119,5
116,7
96,1
125
118,8
114,9
79,3
90,5
87,8
109,4
88,9
97,4
112
86,8
82,9
105,2
89,1
85,5
87,1
85,2
88,2
104
96,4
82,3
114,1
88,9
93,6
101,8
96,6
93,7
68,4
68,7
81,2
85,1
75,4
71,6
83
72,3
90,2
89
84,9
90,9
46,6
55,4
88,7
76
76,9
72,1
90
92,3
78
93,9
84,5
80,4
60,5
75,3
91,5
105,2
92,7
Dataseries Y:
Download CSV
Histogram 
43.5
37.7
36.8
24.4
31.3
43.9
53.6
48.9
30.9
31.8
41.3
43.7
54.1
47.8
36.7
30.8
31.9
61.7
73
64.7
24.2
33.9
32.4
63.2
71.8
60.4
48
44.5
44.9
70.9
72.7
59.5
35.9
40
43.6
57.2
75.8
57.7
47.7
42.3
43
68
70.6
54.2
38.6
40.3
49.2
68.5
75.9
63.2
49.8
37
48.8
74.9
75.3
66.9
44.1
39.8
56.6
77.1
78.5
70.6
54.2
47.2
55.1
74.5
88
80.8
54.4
55.2
73.8
85.3
98.7
86.1
62.5
58.6
67
88.4
96.5
87.1
61.2
62.5
85.2
101.7
113.7

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=24525&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=24525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24525&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 x85
maximum correlation0.316346694797905
optimal lambda(x)1.69
Residual SD (orginial)18.3729678518831
Residual SD (transformed)18.3433496259242

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 85 \tabularnewline
maximum correlation & 0.316346694797905 \tabularnewline
optimal lambda(x) & 1.69 \tabularnewline
Residual SD (orginial) & 18.3729678518831 \tabularnewline
Residual SD (transformed) & 18.3433496259242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24525&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]85[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.316346694797905[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]1.69[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]18.3729678518831[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]18.3433496259242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24525&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 x85
maximum correlation0.316346694797905
optimal lambda(x)1.69
Residual SD (orginial)18.3729678518831
Residual SD (transformed)18.3433496259242


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')