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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 computationSun, 13 Dec 2009 06:15:09 -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/2009/Dec/13/t12607101837r4cze51agjz9f5.htm/, Retrieved Sun, 28 Apr 2024 16:01:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67264, Retrieved Sun, 28 Apr 2024 16:01:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [3/11/2009] [2009-11-02 21:47:57] [b98453cac15ba1066b407e146608df68]
-    D  [Box-Cox Linearity Plot] [WS6 box cox] [2009-11-06 12:23:28] [8b1aef4e7013bd33fbc2a5833375c5f5]
-    D      [Box-Cox Linearity Plot] [PAPER BOX BOX] [2009-12-13 13:15:09] [f0f26816ac6124f58333f11f6c174000] [Current]
- R  D        [Box-Cox Linearity Plot] [Box-Cox_Linearity...] [2009-12-29 13:15:31] [2663058f2a5dda519058ac6b2228468f]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.00
98.04
95.10
92.16
90.20
89.22
94.12
100.00
100.00
98.04
97.06
97.06
97.06
95.10
93.14
92.16
91.18
91.18
97.06
102.94
103.92
103.92
102.94
103.92
105.88
105.88
104.90
103.92
103.92
105.88
111.76
119.61
121.57
121.57
120.59
121.57
122.55
122.55
121.57
120.59
119.61
118.63
123.53
129.41
131.37
129.41
126.47
125.49
124.51
123.53
121.57
118.63
117.65
116.67
122.55
129.41
131.37
130.39
127.45
126.47
127.45
126.47
123.53
121.57
118.63
116.67
120.59
127.45
127.45
123.53
119.61
118.63
117.65
115.69
113.73
111.76
109.80
109.80
115.69
122.55
123.53
121.57
118.63
117.65
117.65
116.67
115.69
112.75
110.78
109.80
113.73
119.61
119.61
114.71
109.80
107.84
106.86
105.88
102.94
100.00
98.04
97.06
100.98
104.90
101.96
99.02
95.10
92.16
87.25
82.35
79.41
81.37
79.41
78.43
85.29
90.20
88.24
87.25
83.33
79.41
73.53
69.61
67.65
69.61
68.63
65.69
68.63
71.57
75.49
82.35
82.35
86.27
89.22
88.24
84.31
77.45
75.49
76.47
90.20
92.16
90.20
85.29
82.35
84.31
88.24
89.22
85.29
80.39
77.45
77.45
89.22
92.16
92.16
89.22
88.24
91.18
97.06
96.08
91.18
81.37
78.43
83.33
101.96
108.82
106.86
98.04
90.20
90.20
93.14
94.12
93.14
89.22
87.25
88.24
99.02
100.98
100.00
94.12
90.20
91.18
92.16
92.16
90.20
88.24
88.24
88.24
96.08
98.04
96.08
91.18
88.24
88.24
89.22
89.22
89.22
90.20
86.27
81.37
82.35
79.41
75.49
77.45
77.45
78.43
77.45
74.51
69.61
66.67
63.73
67.65
80.39
85.29
81.37
77.45
73.53
76.47
81.37
82.35
80.39
75.49
70.59
71.57
79.41
83.33
Dataseries Y:
Download CSV
Histogram 
100.00
100.78
101.24
102.35
102.41
102.67
102.54
102.74
103.07
103.39
103.72
103.91
104.37
104.89
105.61
106.00
106.13
106.20
106.26
106.33
106.98
107.44
107.50
107.57
107.63
108.15
108.35
109.07
109.39
109.78
109.98
110.18
110.31
110.57
110.63
110.70
110.76
111.15
111.48
112.13
112.13
112.20
112.20
112.46
112.85
113.31
113.37
113.37
113.44
113.89
114.16
114.74
114.81
114.22
114.55
114.74
115.26
114.87
114.87
114.94
115.00
115.98
116.44
117.03
117.09
117.16
117.22
117.22
117.29
117.35
117.55
117.68
117.68
118.26
118.66
119.05
119.18
119.44
119.77
119.83
119.90
119.96
120.09
120.29
120.35
121.27
121.72
122.37
122.50
122.57
122.64
122.83
122.90
122.96
122.96
123.03
123.03
123.55
123.94
125.18
125.57
125.90
126.22
126.48
126.68
127.14
127.14
127.14
127.14
127.53
127.85
127.98
127.98
127.98
127.98
128.51
128.96
129.16
129.29
129.48
129.55
130.14
130.46
131.31
131.90
132.35
132.75
132.75
133.07
133.14
133.27
133.40
133.59
133.79
134.18
134.70
134.96
135.09
135.55
135.68
136.01
136.07
136.33
136.40
136.79
136.86
136.92
136.99
137.51
137.90
138.10
138.29
138.42
138.55
138.88
139.20
139.40
139.60
139.79
140.12
140.25
140.83
141.16
141.49
141.68
141.88
142.14
142.27
142.60
142.79
143.05
143.77
144.10
144.16
144.68
144.81
144.94
145.14
145.40
145.53
145.73
146.12
146.84
147.10
147.36
147.62
147.75
148.08
148.27
148.60
148.79
148.99
149.05
149.25
149.38
149.45
149.58
149.77
149.97
150.03
150.16
150.55
150.68
151.14
151.27
151.99
153.36
153.95
154.53
154.66
154.92
155.38
155.84
155.97
156.56
156.69
156.88
157.01
157.27
157.47
157.99
158.45
158.64
159.10

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67264&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67264&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'Gwilym Jenkins' @ 72.249.127.135






Box-Cox Linearity Plot
# observations x224
maximum correlation0.655361185361451
optimal lambda(x)0.13
Residual SD (orginial)12.2975573183441
Residual SD (transformed)12.2602205992437

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 224 \tabularnewline
maximum correlation & 0.655361185361451 \tabularnewline
optimal lambda(x) & 0.13 \tabularnewline
Residual SD (orginial) & 12.2975573183441 \tabularnewline
Residual SD (transformed) & 12.2602205992437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67264&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]224[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.655361185361451[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]0.13[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]12.2975573183441[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]12.2602205992437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67264&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 x224
maximum correlation0.655361185361451
optimal lambda(x)0.13
Residual SD (orginial)12.2975573183441
Residual SD (transformed)12.2602205992437


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')