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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 computationTue, 11 Nov 2008 07:29:04 -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/11/t1226413984s6sjpoe0v2jc0g1.htm/, Retrieved Sun, 19 May 2024 10:20:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23532, Retrieved Sun, 19 May 2024 10:20:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171

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] [Box-Cox] [2008-11-11 14:29:04] [6d5cd2fe15d123a10639b4bf141c23b5] [Current]
- RM D    [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-11-11 14:44:37] [adb6b6905cde49db36d59ca44433140d]
F    D      [Box-Cox Normality Plot] [Box-Cox Normality...] [2008-11-11 23:46:30] [b591abfa820a394aeb0c5ebd9cfa1091]
F RMPD        [Maximum-likelihood Fitting - Normal Distribution] [Normal Distribution ] [2008-11-12 15:48:53] [b478325fa744e3f2fc16a7222294469c]
F    D          [Maximum-likelihood Fitting - Normal Distribution] [Opdracht3_Q5] [2008-11-12 15:58:44] [3f66c6f083b1153972739491b89fa2dd]
F   PD          [Maximum-likelihood Fitting - Normal Distribution] [task 8 maximum li...] [2008-11-12 20:17:58] [1eab65e90adf64584b8e6f0da23ff414]
- RMPD            [Univariate Data Series] [Paper 4.2.1] [2008-12-18 18:27:01] [1eab65e90adf64584b8e6f0da23ff414]
- RMPD            [Histogram] [4.2.1] [2008-12-18 18:38:08] [1eab65e90adf64584b8e6f0da23ff414]
-   PD            [Maximum-likelihood Fitting - Normal Distribution] [4.2.1] [2008-12-18 18:48:23] [1eab65e90adf64584b8e6f0da23ff414]
- RMPD            [Box-Cox Normality Plot] [4.2.1] [2008-12-18 18:51:19] [1eab65e90adf64584b8e6f0da23ff414]
- RMP               [Standard Deviation-Mean Plot] [4.2.2] [2008-12-19 10:25:45] [1eab65e90adf64584b8e6f0da23ff414]
- RMP               [Variance Reduction Matrix] [4.2.2 variantie rdm] [2008-12-19 10:48:41] [1eab65e90adf64584b8e6f0da23ff414]
- RMP               [(Partial) Autocorrelation Function] [4.2.2] [2008-12-19 10:57:29] [1eab65e90adf64584b8e6f0da23ff414]
-   P                 [(Partial) Autocorrelation Function] [4.2.2 D1] [2008-12-19 14:00:41] [1eab65e90adf64584b8e6f0da23ff414]
- RMP                 [Spectral Analysis] [4.2.2 spect] [2008-12-19 14:09:27] [1eab65e90adf64584b8e6f0da23ff414]
- RMP                 [Spectral Analysis] [4.2.2 spec 1] [2008-12-19 14:13:18] [1eab65e90adf64584b8e6f0da23ff414]
- RMP                 [ARIMA Backward Selection] [4.3] [2008-12-19 14:24:21] [1eab65e90adf64584b8e6f0da23ff414]
- RMP                   [(Partial) Autocorrelation Function] [4.2.2] [2008-12-19 17:44:20] [1eab65e90adf64584b8e6f0da23ff414]
- RMP                   [(Partial) Autocorrelation Function] [4.2.2 cor] [2008-12-19 17:50:05] [1eab65e90adf64584b8e6f0da23ff414]
- RMP                   [ARIMA Forecasting] [4.3] [2008-12-19 18:01:56] [1eab65e90adf64584b8e6f0da23ff414]
-   PD                [(Partial) Autocorrelation Function] [4.2.2 pacf] [2008-12-19 16:27:58] [1eab65e90adf64584b8e6f0da23ff414]
F    D        [Box-Cox Normality Plot] [box cox normal plot2] [2008-11-13 08:41:37] [3b5d63cebdc58ed6c519cdb5b6a36d46]
F RMPD    [Maximum-likelihood Fitting - Normal Distribution] [Maximum likehood ...] [2008-11-11 15:10:16] [adb6b6905cde49db36d59ca44433140d]
F    D      [Maximum-likelihood Fitting - Normal Distribution] [Maximum-likelihoo...] [2008-11-11 23:51:03] [b591abfa820a394aeb0c5ebd9cfa1091]
F    D        [Maximum-likelihood Fitting - Normal Distribution] [normal distribution] [2008-11-13 08:47:07] [3b5d63cebdc58ed6c519cdb5b6a36d46]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13812
13031
12574
11964
11451
11346
11353
10702
10646
10556
10463
10407
10625
10872
10805
10653
10574
10431
10383
10296
10872
10635
10297
10570
10662
10709
10413
10846
10371
9924
9828
9897
9721
10171
10738
10812
10511
10244
10368
10457
10186
10166
10827
10997
10940
10756
10893
10236
9960
10018
10063
10002
9728
10002
10177
9948
9394
9308
9155
9103
9732
Dataseries Y:
Download CSV
Histogram 
57.42
56.12
59.15
63.77
63.96
57.81
55.3
51.8
53.26
53.38
45.85
44.23
40.22
44.61
49.14
42.94
41.84
37.75
35.54
37.13
33.19
32.67
30.52
30.7
29.59
28.76
29.08
26.95
29.58
28.24
27.28
25.48
24.87
29.87
32.33
30.23
27.46
24.46
27.34
28.37
26.09
25.59
24.67
25.61
25.97
24.31
20.36
19.82
19.32
19.2
21.74
26.29
25.9
25.36
27.64
28.57
25.38
25.71
27.6
25.85
26.54

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23532&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23532&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Box-Cox Linearity Plot
# observations x61
maximum correlation0.687254195699383
optimal lambda(x)0.47
Residual SD (orginial)8.88942341968068
Residual SD (transformed)8.8818230473357

\begin{tabular}{lllllllll}
\hline
Box-Cox Linearity Plot \tabularnewline
# observations x & 61 \tabularnewline
maximum correlation & 0.687254195699383 \tabularnewline
optimal lambda(x) & 0.47 \tabularnewline
Residual SD (orginial) & 8.88942341968068 \tabularnewline
Residual SD (transformed) & 8.8818230473357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23532&T=1

[TABLE]
[ROW][C]Box-Cox Linearity Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]61[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.687254195699383[/C][/ROW]
[ROW][C]optimal lambda(x)[/C][C]0.47[/C][/ROW]
[ROW][C]Residual SD (orginial)[/C][C]8.88942341968068[/C][/ROW]
[ROW][C]Residual SD (transformed)[/C][C]8.8818230473357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23532&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 x61
maximum correlation0.687254195699383
optimal lambda(x)0.47
Residual SD (orginial)8.88942341968068
Residual SD (transformed)8.8818230473357


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')