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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 24 Dec 2017 11:23:03 +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/24/t15141109959b6f96my9lczpx8.htm/, Retrieved Mon, 13 May 2024 21:08:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310897, Retrieved Mon, 13 May 2024 21:08:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2017-12-24 10:23:03] [ec772448347bb766a411d58621b503be] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
66,6
89,1
96,2
78,9
107,5
96,2
36,9
100,3
102,1
101,1
90,6
71,8
69
85,7
95,8
83
100,2
102
42,9
99,9
91,3
107,5
89,7
65,5
74
78
97,1
95,2
95,5
98,1
46,8
88,5
103
104,9
91
61,3
69,8
80,2
99,3
93,9
89,5
101,6
53,6
86,4
109,4
108
86
68,4
74,8
86,9
110,6
96,3
91,1
110,7
48
97
109,9
105,2
91,4
80,6
69,2
83,9
91,5
107,1
95,9
116,9
46,2
103,3
115,9
103
99,8
80,7
77,3
85,1
111,1
93,8
107
114,3
47,3
101
114,8
108,9
103,9
76,9
82,9
93,1
110,9
95,3
102,3
114,2
51,5
105
106
117,9
102,7
74,5
93,9
104,5
92,3
118,3
106,4
113,7
61,3
97,6
118,7
112,1
94,5
77
77,6
93,8
115,6
101,8
102,3
117,6
59,3
104,1
123,4
121,3
91,8
74,1
73,4
84,2
128,3
110,3
102,3
127,7
59
107,2
124,2
120,3
100,3
63
83,4
109,6
130,1
103,1
127
113,6
54,3
113,5
129,8
117,9
114,4
85,6
97,9
96,2
136
111,3
125
128,7
69,4
124,2
125,9
134
123
82,8
76,4
98,2
112,1
117,9
117,6
128,8
69,8
109,5
129,8
130,7
111
88,5
104,8
108,3
122,4
109,5
108,5
118
68
103
128,2
128,7
103,9
80,5
92,2
98,4
119,2
105,2
100,5
123,7
65,3
104,2
122,3
125,4
97,4
76,9
92,6
102,8
107,2
115,7
105,3
124,7
59,7
110
127,1
118,1
98,6
90,6
83,6
107,7
133,1
98,7
121
124
60,3
110,4
121,4

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310897&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310897&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310897&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
186.441666666666720.067361938020570.6
286.041666666666718.651953752566564.6
386.116666666666717.777761047971958.1
487.17516.96430075187355.8
591.87518.14733263645662.7
692.783333333333320.332769490443670.7
795.116666666666720.207191939025267.5
896.358333333333318.877377434057966.4
999.191666666666717.139134290926857.4
1098.558333333333320.202405722331664.1
11100.01666666666724.746747567135369.3
12106.85833333333322.41502979266575.8
13112.86666666666721.486288792171866.6
14107.52520.38890629729860.9
15106.98333333333317.945312547410360.7
16102.55833333333318.701067462645760.1
17104.36666666666718.20770732576267.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 86.4416666666667 & 20.0673619380205 & 70.6 \tabularnewline
2 & 86.0416666666667 & 18.6519537525665 & 64.6 \tabularnewline
3 & 86.1166666666667 & 17.7777610479719 & 58.1 \tabularnewline
4 & 87.175 & 16.964300751873 & 55.8 \tabularnewline
5 & 91.875 & 18.147332636456 & 62.7 \tabularnewline
6 & 92.7833333333333 & 20.3327694904436 & 70.7 \tabularnewline
7 & 95.1166666666667 & 20.2071919390252 & 67.5 \tabularnewline
8 & 96.3583333333333 & 18.8773774340579 & 66.4 \tabularnewline
9 & 99.1916666666667 & 17.1391342909268 & 57.4 \tabularnewline
10 & 98.5583333333333 & 20.2024057223316 & 64.1 \tabularnewline
11 & 100.016666666667 & 24.7467475671353 & 69.3 \tabularnewline
12 & 106.858333333333 & 22.415029792665 & 75.8 \tabularnewline
13 & 112.866666666667 & 21.4862887921718 & 66.6 \tabularnewline
14 & 107.525 & 20.388906297298 & 60.9 \tabularnewline
15 & 106.983333333333 & 17.9453125474103 & 60.7 \tabularnewline
16 & 102.558333333333 & 18.7010674626457 & 60.1 \tabularnewline
17 & 104.366666666667 & 18.207707325762 & 67.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310897&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]86.4416666666667[/C][C]20.0673619380205[/C][C]70.6[/C][/ROW]
[ROW][C]2[/C][C]86.0416666666667[/C][C]18.6519537525665[/C][C]64.6[/C][/ROW]
[ROW][C]3[/C][C]86.1166666666667[/C][C]17.7777610479719[/C][C]58.1[/C][/ROW]
[ROW][C]4[/C][C]87.175[/C][C]16.964300751873[/C][C]55.8[/C][/ROW]
[ROW][C]5[/C][C]91.875[/C][C]18.147332636456[/C][C]62.7[/C][/ROW]
[ROW][C]6[/C][C]92.7833333333333[/C][C]20.3327694904436[/C][C]70.7[/C][/ROW]
[ROW][C]7[/C][C]95.1166666666667[/C][C]20.2071919390252[/C][C]67.5[/C][/ROW]
[ROW][C]8[/C][C]96.3583333333333[/C][C]18.8773774340579[/C][C]66.4[/C][/ROW]
[ROW][C]9[/C][C]99.1916666666667[/C][C]17.1391342909268[/C][C]57.4[/C][/ROW]
[ROW][C]10[/C][C]98.5583333333333[/C][C]20.2024057223316[/C][C]64.1[/C][/ROW]
[ROW][C]11[/C][C]100.016666666667[/C][C]24.7467475671353[/C][C]69.3[/C][/ROW]
[ROW][C]12[/C][C]106.858333333333[/C][C]22.415029792665[/C][C]75.8[/C][/ROW]
[ROW][C]13[/C][C]112.866666666667[/C][C]21.4862887921718[/C][C]66.6[/C][/ROW]
[ROW][C]14[/C][C]107.525[/C][C]20.388906297298[/C][C]60.9[/C][/ROW]
[ROW][C]15[/C][C]106.983333333333[/C][C]17.9453125474103[/C][C]60.7[/C][/ROW]
[ROW][C]16[/C][C]102.558333333333[/C][C]18.7010674626457[/C][C]60.1[/C][/ROW]
[ROW][C]17[/C][C]104.366666666667[/C][C]18.207707325762[/C][C]67.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310897&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310897&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:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
186.441666666666720.067361938020570.6
286.041666666666718.651953752566564.6
386.116666666666717.777761047971958.1
487.17516.96430075187355.8
591.87518.14733263645662.7
692.783333333333320.332769490443670.7
795.116666666666720.207191939025267.5
896.358333333333318.877377434057966.4
999.191666666666717.139134290926857.4
1098.558333333333320.202405722331664.1
11100.01666666666724.746747567135369.3
12106.85833333333322.41502979266575.8
13112.86666666666721.486288792171866.6
14107.52520.38890629729860.9
15106.98333333333317.945312547410360.7
16102.55833333333318.701067462645760.1
17104.36666666666718.20770732576267.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha10.9607158802363
beta0.087863409227142
S.D.0.0573068332322344
T-STAT1.53320999035277
p-value0.146042419380283

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 10.9607158802363 \tabularnewline
beta & 0.087863409227142 \tabularnewline
S.D. & 0.0573068332322344 \tabularnewline
T-STAT & 1.53320999035277 \tabularnewline
p-value & 0.146042419380283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310897&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.9607158802363[/C][/ROW]
[ROW][C]beta[/C][C]0.087863409227142[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0573068332322344[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.53320999035277[/C][/ROW]
[ROW][C]p-value[/C][C]0.146042419380283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310897&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310897&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha10.9607158802363
beta0.087863409227142
S.D.0.0573068332322344
T-STAT1.53320999035277
p-value0.146042419380283






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.00542655849803
beta0.428649817357855
S.D.0.274196297724871
T-STAT1.56329542344136
p-value0.138831284527447
Lambda0.571350182642145

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.00542655849803 \tabularnewline
beta & 0.428649817357855 \tabularnewline
S.D. & 0.274196297724871 \tabularnewline
T-STAT & 1.56329542344136 \tabularnewline
p-value & 0.138831284527447 \tabularnewline
Lambda & 0.571350182642145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310897&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.00542655849803[/C][/ROW]
[ROW][C]beta[/C][C]0.428649817357855[/C][/ROW]
[ROW][C]S.D.[/C][C]0.274196297724871[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.56329542344136[/C][/ROW]
[ROW][C]p-value[/C][C]0.138831284527447[/C][/ROW]
[ROW][C]Lambda[/C][C]0.571350182642145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310897&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310897&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.00542655849803
beta0.428649817357855
S.D.0.274196297724871
T-STAT1.56329542344136
p-value0.138831284527447
Lambda0.571350182642145


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = First and Seasonal Differences (s) ; par4 = 2 ; par5 = 1 ; par6 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- '12'
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')