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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_boxcoxnorm.wasp

Title produced by software

Box-Cox Normality Plot

Date of computation

Thu, 21 Dec 2017 22:03:12 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/21/t1513890232p3vt2y39wvgb49a.htm/, Retrieved Tue, 14 May 2024 20:45:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310733, Retrieved Tue, 14 May 2024 20:45:16 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Box-Cox Normality Plot] [Box-Cox Normality...] [2017-12-21 21:03:12] [f7fcbef48f036f8c57e773abb9891403] [Current]

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Dataseries X:

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Histogram

Boxplots

83674204.92
1780582985.50
75198229.43
66552858.02
47377292.82
202450191.48
139917216.59
129019740.35
70169361.12
49375016.78
59073785.95
89062635.98
149805035.68
121657356.12
53218003.32
134314180.33
41501724.73
101190684.88
78601349.78
41458023.49
124456725.54
175844207.75
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47068781.84
60350058.62
85555510.86
64400011.97
116681743.38
88648506.56
69194523.37
51115705.16
100175600.31
111989704.69
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5530000.01
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36698020.15
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42195466.42
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15554523.77

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310733&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

5 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310733&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	Big Analytics Cloud Computing Center

Box-Cox Normality Plot
# observations x	589
maximum correlation	0.994239038632349
optimal lambda	0.06
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 589 \tabularnewline
maximum correlation & 0.994239038632349 \tabularnewline
optimal lambda & 0.06 \tabularnewline
transformation formula & for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310733&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]589[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.994239038632349[/C][/ROW]
[ROW][C]optimal lambda[/C][C]0.06[/C][/ROW]
[ROW][C]transformation formula[/C][C]for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310733&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Box-Cox Normality Plot
# observations x	589
maximum correlation	0.994239038632349
optimal lambda	0.06
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

Maximum Likelihood Estimation of Lambda

> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x    0.0597        0.06       0.0023       0.1171
Likelihood ratio tests about transformation parameters
                              LRT df       pval
LR test, lambda = (0)    4.222829  1 0.03988361
LR test, lambda = (1) 1032.519290  1 0.00000000

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x    0.0597        0.06       0.0023       0.1171
Likelihood ratio tests about transformation parameters
                              LRT df       pval
LR test, lambda = (0)    4.222829  1 0.03988361
LR test, lambda = (1) 1032.519290  1 0.00000000
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310733&T=2

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x    0.0597        0.06       0.0023       0.1171
Likelihood ratio tests about transformation parameters
                              LRT df       pval
LR test, lambda = (0)    4.222829  1 0.03988361
LR test, lambda = (1) 1032.519290  1 0.00000000
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310733&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310733&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Maximum Likelihood Estimation of Lambda

> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd
x    0.0597        0.06       0.0023       0.1171
Likelihood ratio tests about transformation parameters
                              LRT df       pval
LR test, lambda = (0)    4.222829  1 0.03988361
LR test, lambda = (1) 1032.519290  1 0.00000000

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = No ;

Parameters (R input):

par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = No ;

R code (references can be found in the software module):

library(car)
par2 <- abs(as.numeric(par2)*100)
par3 <- as.numeric(par3)*100
if(par4=='') par4 <- 0
par4 <- as.numeric(par4)
numlam <- par2 + par3 + 1
x <- x + par4
n <- length(x)
c <- array(NA,dim=c(numlam))
l <- array(NA,dim=c(numlam))
mx <- -1
mxli <- -999
for (i in 1:numlam)
{
l[i] <- (i-par2-1)/100
if (l[i] != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
if (par1 == 'Simple Box-Cox transform') x1 <- x^l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),sort(x1))
if (mx < c[i])
{
mx <- c[i]
mxli <- l[i]
x1.best <- x1
}
}
print(c)
print(mx)
print(mxli)
print(x1.best)
if (mxli != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
if (par1 == 'Simple Box-Cox transform') x1 <- x^mxli
} else {
x1 <- log(x)
}
mypT <- powerTransform(x)
summary(mypT)
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')
mtext(paste('Optimal Lambda =',mxli))
grid()
dev.off()
bitmap(file='test2.png')
hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test3.png')
hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test4.png')
qqPlot(x)
grid()
mtext('Original Data')
dev.off()
bitmap(file='test5.png')
qqPlot(x1)
grid()
mtext('Transformed Data')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Normality 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',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'transformation formula',header=TRUE)
if (par1 == 'Full Box-Cox transform') {
a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')
} else {
a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')
}
a<-table.row.end(a)
if(mx<0) {
a<-table.row.start(a)
a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
if(par5=='Yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Obs.',header=T)
a<-table.element(a,'Original',header=T)
a<-table.element(a,'Transformed',header=T)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i)
a<-table.element(a,x[i])
a<-table.element(a,x1.best[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Maximum Likelihood Estimation of Lambda',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('summary(mypT)'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code