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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 computationTue, 14 Dec 2010 13:28:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292333993fjwu59tjmi2mbxs.htm/, Retrieved Sun, 28 Apr 2024 19:58:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109629, Retrieved Sun, 28 Apr 2024 19:58:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [Spectral Analysis] [Soldiers] [2010-11-29 09:50:20] [b98453cac15ba1066b407e146608df68]
-    D    [Spectral Analysis] [ws 9] [2010-12-14 12:45:12] [20c5a34fea7ed3b9b27ff444f2eb4dfe]
-   P       [Spectral Analysis] [ws 9] [2010-12-14 13:12:01] [20c5a34fea7ed3b9b27ff444f2eb4dfe]
- RM            [Standard Deviation-Mean Plot] [] [2010-12-14 13:28:34] [76f6fcd790878de142f355e7238b5c71] [Current]
- RM              [ARIMA Backward Selection] [] [2010-12-14 13:51:17] [20c5a34fea7ed3b9b27ff444f2eb4dfe]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
921365
987921
1132614
1332224
1418133
1411549
1695920
1636173
1539653
1395314
1127575
1036076
989236
1008380
1207763
1368839
1469798
1498721
1761769
1653214
1599104
1421179
1163995
1037735
1015407
1039210
1258049
1469445
1552346
1549144
1785895
1662335
1629440
1467430
1202209
1076982
1039367
1063449
1335135
1491602
1591972
1641248
1898849
1798580
1762444
1622044
1368955
1262973
1195650
1269530
1479279
1607819
1712466
1721766
1949843
1821326
1757802
1590367
1260647
1149235
1016367
1027885
1262159
1520854
1544144
1564709
1821776
1741365
1623386
1498658
1241822
1136029

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109629&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109629&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11302876.41666667257925.823408225774555
21348311.08333333263644.976474204772533
31392324.33333333263919.094020853770488
41489718.16666667280017.614230648859482
51542977.5268077.320340606800608
61416596.16666667271797.345768977805409

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1302876.41666667 & 257925.823408225 & 774555 \tabularnewline
2 & 1348311.08333333 & 263644.976474204 & 772533 \tabularnewline
3 & 1392324.33333333 & 263919.094020853 & 770488 \tabularnewline
4 & 1489718.16666667 & 280017.614230648 & 859482 \tabularnewline
5 & 1542977.5 & 268077.320340606 & 800608 \tabularnewline
6 & 1416596.16666667 & 271797.345768977 & 805409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109629&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]1302876.41666667[/C][C]257925.823408225[/C][C]774555[/C][/ROW]
[ROW][C]2[/C][C]1348311.08333333[/C][C]263644.976474204[/C][C]772533[/C][/ROW]
[ROW][C]3[/C][C]1392324.33333333[/C][C]263919.094020853[/C][C]770488[/C][/ROW]
[ROW][C]4[/C][C]1489718.16666667[/C][C]280017.614230648[/C][C]859482[/C][/ROW]
[ROW][C]5[/C][C]1542977.5[/C][C]268077.320340606[/C][C]800608[/C][/ROW]
[ROW][C]6[/C][C]1416596.16666667[/C][C]271797.345768977[/C][C]805409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109629&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
11302876.41666667257925.823408225774555
21348311.08333333263644.976474204772533
31392324.33333333263919.094020853770488
41489718.16666667280017.614230648859482
51542977.5268077.320340606800608
61416596.16666667271797.345768977805409






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha180560.567470906
beta0.0614660116855102
S.D.0.0303580921347876
T-STAT2.02469942487182
p-value0.112891846792782

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 180560.567470906 \tabularnewline
beta & 0.0614660116855102 \tabularnewline
S.D. & 0.0303580921347876 \tabularnewline
T-STAT & 2.02469942487182 \tabularnewline
p-value & 0.112891846792782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109629&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]180560.567470906[/C][/ROW]
[ROW][C]beta[/C][C]0.0614660116855102[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0303580921347876[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.02469942487182[/C][/ROW]
[ROW][C]p-value[/C][C]0.112891846792782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109629&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)
alpha180560.567470906
beta0.0614660116855102
S.D.0.0303580921347876
T-STAT2.02469942487182
p-value0.112891846792782






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.79784108787251
beta0.331814097832441
S.D.0.156687452315032
T-STAT2.11768136458881
p-value0.101607063557562
Lambda0.668185902167559

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.79784108787251 \tabularnewline
beta & 0.331814097832441 \tabularnewline
S.D. & 0.156687452315032 \tabularnewline
T-STAT & 2.11768136458881 \tabularnewline
p-value & 0.101607063557562 \tabularnewline
Lambda & 0.668185902167559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109629&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.79784108787251[/C][/ROW]
[ROW][C]beta[/C][C]0.331814097832441[/C][/ROW]
[ROW][C]S.D.[/C][C]0.156687452315032[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.11768136458881[/C][/ROW]
[ROW][C]p-value[/C][C]0.101607063557562[/C][/ROW]
[ROW][C]Lambda[/C][C]0.668185902167559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109629&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109629&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)
alpha7.79784108787251
beta0.331814097832441
S.D.0.156687452315032
T-STAT2.11768136458881
p-value0.101607063557562
Lambda0.668185902167559


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')