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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, 11 Dec 2016 15:01:05 +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/2016/Dec/11/t14814650134t8of9588n72hgh.htm/, Retrieved Sun, 09 Mar 2025 02:17:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298787, Retrieved Sun, 09 Mar 2025 02:17:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMPD      [Standard Deviation-Mean Plot] [F1:N1809] [2016-12-11 14:01:05] [8d7b5e4c30a3b8052caee801f90adcea] [Current]
- RM D        [Univariate Data Series] [F1:N224] [2016-12-11 15:07:52] [a4c5732063e280fade3b47e7f5057d96]
- RMP           [Notched Boxplots] [F1:N224] [2016-12-17 13:16:40] [a4c5732063e280fade3b47e7f5057d96]
-    D        [Standard Deviation-Mean Plot] [F1:N224] [2016-12-11 15:12:47] [a4c5732063e280fade3b47e7f5057d96]
- RM D        [(Partial) Autocorrelation Function] [F1:N224] [2016-12-11 15:22:31] [a4c5732063e280fade3b47e7f5057d96]
- RMP           [ARIMA Forecasting] [F1:N224] [2016-12-17 13:58:05] [a4c5732063e280fade3b47e7f5057d96]
- RMP         [ARIMA Forecasting] [F1:N1809] [2016-12-17 12:41:42] [a4c5732063e280fade3b47e7f5057d96]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3650
3530
3800
4130
3440
4000
3690
4210
4240
4260
4510
4260
3420
3660
3790
3270
3250
3570
3410
4270
4410
4450
3990
4000
4140
3800
3060
3270
3040
3750
3330
3840
4060
3830
3880
3820
3640
2880
3710
2980
3190
3090
3190
3410
3310
3480
3750
3200
3150
3250
3290
2900
2940
3460
3890
3040
3000
3520
2850
2730
2820
3240
3160
3010
2720
2650
2790
3090
3240
3690
3490
2790
3060
3210
3080
2640
2890
3330
2970
2870
3140
3150
2940
2910
3060
2900
2980
2890
2920
2940
3300
3050
2740
3080
3090
2830
3390
3210
2970
2810
2690
2800
2920
2870
2860
3090
3180
3090

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298787&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298787&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298787&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13976.66666666667343.8375232929681070
23790.83333333333430.9705396666991200
33651.66666666667376.3420430052071100
43319.16666666667283.403289046589870
53168.33333333333332.1783018838291160
63057.5322.916397849351040
73015.83333333333184.216193806641690
82981.66666666667146.339166032718560
92990204.40601307647700

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3976.66666666667 & 343.837523292968 & 1070 \tabularnewline
2 & 3790.83333333333 & 430.970539666699 & 1200 \tabularnewline
3 & 3651.66666666667 & 376.342043005207 & 1100 \tabularnewline
4 & 3319.16666666667 & 283.403289046589 & 870 \tabularnewline
5 & 3168.33333333333 & 332.178301883829 & 1160 \tabularnewline
6 & 3057.5 & 322.91639784935 & 1040 \tabularnewline
7 & 3015.83333333333 & 184.216193806641 & 690 \tabularnewline
8 & 2981.66666666667 & 146.339166032718 & 560 \tabularnewline
9 & 2990 & 204.40601307647 & 700 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298787&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]3976.66666666667[/C][C]343.837523292968[/C][C]1070[/C][/ROW]
[ROW][C]2[/C][C]3790.83333333333[/C][C]430.970539666699[/C][C]1200[/C][/ROW]
[ROW][C]3[/C][C]3651.66666666667[/C][C]376.342043005207[/C][C]1100[/C][/ROW]
[ROW][C]4[/C][C]3319.16666666667[/C][C]283.403289046589[/C][C]870[/C][/ROW]
[ROW][C]5[/C][C]3168.33333333333[/C][C]332.178301883829[/C][C]1160[/C][/ROW]
[ROW][C]6[/C][C]3057.5[/C][C]322.91639784935[/C][C]1040[/C][/ROW]
[ROW][C]7[/C][C]3015.83333333333[/C][C]184.216193806641[/C][C]690[/C][/ROW]
[ROW][C]8[/C][C]2981.66666666667[/C][C]146.339166032718[/C][C]560[/C][/ROW]
[ROW][C]9[/C][C]2990[/C][C]204.40601307647[/C][C]700[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298787&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298787&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
13976.66666666667343.8375232929681070
23790.83333333333430.9705396666991200
33651.66666666667376.3420430052071100
43319.16666666667283.403289046589870
53168.33333333333332.1783018838291160
63057.5322.916397849351040
73015.83333333333184.216193806641690
82981.66666666667146.339166032718560
92990204.40601307647700






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-346.147358033088
beta0.191639942906625
S.D.0.059798696728137
T-STAT3.20475116335526
p-value0.0149667296976845

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -346.147358033088 \tabularnewline
beta & 0.191639942906625 \tabularnewline
S.D. & 0.059798696728137 \tabularnewline
T-STAT & 3.20475116335526 \tabularnewline
p-value & 0.0149667296976845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298787&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-346.147358033088[/C][/ROW]
[ROW][C]beta[/C][C]0.191639942906625[/C][/ROW]
[ROW][C]S.D.[/C][C]0.059798696728137[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.20475116335526[/C][/ROW]
[ROW][C]p-value[/C][C]0.0149667296976845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298787&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298787&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-346.147358033088
beta0.191639942906625
S.D.0.059798696728137
T-STAT3.20475116335526
p-value0.0149667296976845






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-14.2803245618376
beta2.45559798473336
S.D.0.808449635316427
T-STAT3.03741615737415
p-value0.0189156977693289
Lambda-1.45559798473336

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -14.2803245618376 \tabularnewline
beta & 2.45559798473336 \tabularnewline
S.D. & 0.808449635316427 \tabularnewline
T-STAT & 3.03741615737415 \tabularnewline
p-value & 0.0189156977693289 \tabularnewline
Lambda & -1.45559798473336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298787&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.2803245618376[/C][/ROW]
[ROW][C]beta[/C][C]2.45559798473336[/C][/ROW]
[ROW][C]S.D.[/C][C]0.808449635316427[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.03741615737415[/C][/ROW]
[ROW][C]p-value[/C][C]0.0189156977693289[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.45559798473336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298787&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298787&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-14.2803245618376
beta2.45559798473336
S.D.0.808449635316427
T-STAT3.03741615737415
p-value0.0189156977693289
Lambda-1.45559798473336


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
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')