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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 computationFri, 19 Dec 2008 19:01:56 -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/Dec/20/t1229738581qdb7nkd77prse2s.htm/, Retrieved Sat, 18 May 2024 16:27:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35283, Retrieved Sat, 18 May 2024 16:27:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Werkloosheid- Azië] [2008-12-17 14:33:28] [5e74953d94072114d25d7276793b561e]
- RMPD    [Standard Deviation-Mean Plot] [Voeding] [2008-12-20 02:01:56] [5925747fb2a6bb4cfcd8015825ee5e92] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99.2
93.6
104.2
95.3
102.7
103.1
100
107.2
107
119
110.4
101.7
102.4
98.8
105.6
104.4
106.3
107.2
108.5
106.9
114.2
125.9
110.6
110.5
106.7
104.7
107.4
109.8
103.4
114.8
114.3
109.6
118.3
127.3
112.3
114.9
108.2
105.4
122.1
113.5
110
125.3
114.3
115.6
127.1
123
122.2
126.4
112.7
105.8
120.9
116.3
115.7
127.9
108.3
121.1
128.6
123.1
127.7
126.6
118.4
110
129.6
115.8
125.9
128.4
114
125.6
128.5
136.6
133.1
124.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35283&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35283&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1103.6166666666676.8367766638610625.4
2108.4416666666676.803937140072727.1
3111.9583333333336.6228884570972123.9
4117.7583333333337.531202769247121.7
5119.5583333333337.8190278788156922.8
6124.2083333333338.0518160947852326.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.616666666667 & 6.83677666386106 & 25.4 \tabularnewline
2 & 108.441666666667 & 6.8039371400727 & 27.1 \tabularnewline
3 & 111.958333333333 & 6.62288845709721 & 23.9 \tabularnewline
4 & 117.758333333333 & 7.5312027692471 & 21.7 \tabularnewline
5 & 119.558333333333 & 7.81902787881569 & 22.8 \tabularnewline
6 & 124.208333333333 & 8.05181609478523 & 26.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35283&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]103.616666666667[/C][C]6.83677666386106[/C][C]25.4[/C][/ROW]
[ROW][C]2[/C][C]108.441666666667[/C][C]6.8039371400727[/C][C]27.1[/C][/ROW]
[ROW][C]3[/C][C]111.958333333333[/C][C]6.62288845709721[/C][C]23.9[/C][/ROW]
[ROW][C]4[/C][C]117.758333333333[/C][C]7.5312027692471[/C][C]21.7[/C][/ROW]
[ROW][C]5[/C][C]119.558333333333[/C][C]7.81902787881569[/C][C]22.8[/C][/ROW]
[ROW][C]6[/C][C]124.208333333333[/C][C]8.05181609478523[/C][C]26.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35283&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
1103.6166666666676.8367766638610625.4
2108.4416666666676.803937140072727.1
3111.9583333333336.6228884570972123.9
4117.7583333333337.531202769247121.7
5119.5583333333337.8190278788156922.8
6124.2083333333338.0518160947852326.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.717603432313326
beta0.0699757169115793
S.D.0.0179462883370869
T-STAT3.89917489328260
p-value0.0175537172555011

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.717603432313326 \tabularnewline
beta & 0.0699757169115793 \tabularnewline
S.D. & 0.0179462883370869 \tabularnewline
T-STAT & 3.89917489328260 \tabularnewline
p-value & 0.0175537172555011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35283&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.717603432313326[/C][/ROW]
[ROW][C]beta[/C][C]0.0699757169115793[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0179462883370869[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.89917489328260[/C][/ROW]
[ROW][C]p-value[/C][C]0.0175537172555011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35283&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)
alpha-0.717603432313326
beta0.0699757169115793
S.D.0.0179462883370869
T-STAT3.89917489328260
p-value0.0175537172555011






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.09396886526845
beta1.07164951109446
S.D.0.294378429425276
T-STAT3.64038055772861
p-value0.0219572655521118
Lambda-0.0716495110944593

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.09396886526845 \tabularnewline
beta & 1.07164951109446 \tabularnewline
S.D. & 0.294378429425276 \tabularnewline
T-STAT & 3.64038055772861 \tabularnewline
p-value & 0.0219572655521118 \tabularnewline
Lambda & -0.0716495110944593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35283&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.09396886526845[/C][/ROW]
[ROW][C]beta[/C][C]1.07164951109446[/C][/ROW]
[ROW][C]S.D.[/C][C]0.294378429425276[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.64038055772861[/C][/ROW]
[ROW][C]p-value[/C][C]0.0219572655521118[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0716495110944593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35283&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)
alpha-3.09396886526845
beta1.07164951109446
S.D.0.294378429425276
T-STAT3.64038055772861
p-value0.0219572655521118
Lambda-0.0716495110944593


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
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')