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Author*The author of this computation has been verified*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationSun, 10 Dec 2017 12:23:39 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/10/t1512905327uxkalw8j70y3efb.htm/, Retrieved Wed, 15 May 2024 21:25:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308899, Retrieved Wed, 15 May 2024 21:25:15 +0000
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Original text written by user:
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User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [] [2017-12-10 11:23:39] [20141777ecd6b11d9726230b5f8289b4] [Current]
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Dataseries X:
62
67,1
75,9
67
74,2
72,2
60,2
65,8
76,2
76,6
76,8
70,6
74,5
73,5
80,2
71,5
76,6
79,6
65,5
69,2
74,8
79,4
75
67,7
72,5
71,2
78,3
76,6
74,9
76,5
69,4
67,4
77,2
82,2
75,1
70,6
75,6
73,5
79,4
77,5
72,9
78
71,5
66,6
81,8
83,5
74,6
79,8
73,9
76,6
88,9
81,7
76,5
88,8
75,5
75,2
89
87,9
85,7
89,2
82,7
81
90,3
86,3
81,5
91,1
73,1
76,4
91
86,9
89,6
90,5
86,3
86,5
98,8
84,3
91,2
95,5
78,1
81,5
94,4
98,5
95,3
91,6
92,8
90,5
102,2
91,5
94,9
102,1
88,8
89,4
97,8
108,8
100,8
95
101
101
102,5
105,6
98,3
105,5
96,4
88
108,1
107,2
92,5
95,7
84,8
85,4
94,6
86
88,6
93,3
83,1
82,6
96,7
96,2
92,6
92,7
89,9
95,4
108,4
96,2
95
109
91,9
92,2
107,1
105,6
105,4
103,9
99,2
102,4
121,8
102,3
110,1
106
91,9
100,1
112
105
103,3
101,8
100,9
104,2
116,8
97,8
100,7
107,2
96,3
95,9
104,6
107,5
102,5
94,9
98,7
96,8
108,3
103,9
102,4
107,3
101,9
92,5
105,4
113,2
105,7
101,7
101,8
102,9
109,2
105,6
103,4
108,8
98,1
90
112,8
112,2
102,2
102,5
101,8
98,8
114,3
105,2
98,3
110,1
96,4
92,1
112,2
111,6
107,6
103,4
103,6
107,7
117,9
110,4
104,4
116,2
98,9
102,1
113,7
109,5
110,3
114,5
107
109,4
124,6
104,8
112
119,2
103
106,5




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308899&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308899&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 Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center







Box-Cox Normality Plot
# observations x212
maximum correlation0.988361624339163
optimal lambda1.95
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 212 \tabularnewline
maximum correlation & 0.988361624339163 \tabularnewline
optimal lambda & 1.95 \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=308899&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]212[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.988361624339163[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.95[/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=308899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308899&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 x212
maximum correlation0.988361624339163
optimal lambda1.95
transformation formulafor 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    1.5913           1       0.6945       2.4882
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 12.346340  1 0.0004418518
LR test, lambda = (1)  1.683412  1 0.1944717163

\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    1.5913           1       0.6945       2.4882
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 12.346340  1 0.0004418518
LR test, lambda = (1)  1.683412  1 0.1944717163
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=308899&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    1.5913           1       0.6945       2.4882
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 12.346340  1 0.0004418518
LR test, lambda = (1)  1.683412  1 0.1944717163
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308899&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    1.5913           1       0.6945       2.4882
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 12.346340  1 0.0004418518
LR test, lambda = (1)  1.683412  1 0.1944717163



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')