FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 24 Dec 2010 16:06:39 +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/24/t12932066636sefj6us78y9mzi.htm/, Retrieved Tue, 30 Apr 2024 02:37:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115170, Retrieved Tue, 30 Apr 2024 02:37:48 +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)
-     [Multiple Regression] [Multiple Regressi...] [2010-12-17 13:46:43] [1251ac2db27b84d4a3ba43449388906b]
-   PD  [Multiple Regression] [Multiple Regressi...] [2010-12-17 15:41:32] [1251ac2db27b84d4a3ba43449388906b]
-   P     [Multiple Regression] [MR Paper (monthly...] [2010-12-17 16:35:58] [1251ac2db27b84d4a3ba43449388906b]
-   PD      [Multiple Regression] [MR Paper (month)] [2010-12-17 16:45:18] [1251ac2db27b84d4a3ba43449388906b]
-   P         [Multiple Regression] [MR Paper (trend)b] [2010-12-18 12:41:58] [1251ac2db27b84d4a3ba43449388906b]
- RMPD          [Classical Decomposition] [CD] [2010-12-18 14:47:46] [1251ac2db27b84d4a3ba43449388906b]
- RM              [Standard Deviation-Mean Plot] [Mean vs Median Paper] [2010-12-18 18:40:22] [1251ac2db27b84d4a3ba43449388906b]
-   P                 [Standard Deviation-Mean Plot] [] [2010-12-24 16:06:39] [4f70e6cd0867f10d298e58e8e27859b5] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14.458
13.594
17.814
20.235
21.811
21.439
21.393
19.831
20.468
21.080
21.600
17.390
17.848
19.592
21.092
20.899
25.890
24.965
22.225
20.977
22.897
22.785
22.769
19.637
20.203
20.450
23.083
21.738
26.766
25.280
22.574
22.729
21.378
22.902
24.989
21.116
15.169
15.846
20.927
18.273
22.538
15.596
14.034
11.366
14.861
15.149
13.577
13.026
13.190
13.196
15.826
14.733
16.307
15.703
14.589
12.043
15.057
14.053
12.698
10.888
10.045
11.549
13.767
12.434
13.116
14.211
12.266
12.602
15.714
13.742
12.745
10.491
10.057
10.900
11.771
11.992
11.933
14.504
11.727
11.477
13.578
11.555
11.846
11.397
10.066
10.269
14.279
13.870
13.695
14.420
11.424
9.704
12.464
14.301
13.464
9.893
11.572
12.380
16.692
16.052
16.459
14.761
13.654
13.480
18.068
16.560
14.530
10.650
11.651
13.735
13.360
17.818
20.613
16.231
13.862
12.004
17.734
15.034
12.609
12.320
10.833
11.350
13.648
14.890
16.325
18.045
15.616
11.926
16.855
15.083
12.520
12.355

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115170&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115170&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
119.25941666666672.829709797466668.217
221.7982.280371341370848.042
322.76733333333332.023897559989966.563
415.86353.2321882117790811.172
514.02358333333331.653273362334875.419
612.72351.574866430122655.669
711.894751.152184496353064.447
812.320751.921607997343514.716
914.57152.289885805012997.418
1014.74758333333332.801778054227628.962
1114.12052.348985680516757.212

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 19.2594166666667 & 2.82970979746666 & 8.217 \tabularnewline
2 & 21.798 & 2.28037134137084 & 8.042 \tabularnewline
3 & 22.7673333333333 & 2.02389755998996 & 6.563 \tabularnewline
4 & 15.8635 & 3.23218821177908 & 11.172 \tabularnewline
5 & 14.0235833333333 & 1.65327336233487 & 5.419 \tabularnewline
6 & 12.7235 & 1.57486643012265 & 5.669 \tabularnewline
7 & 11.89475 & 1.15218449635306 & 4.447 \tabularnewline
8 & 12.32075 & 1.92160799734351 & 4.716 \tabularnewline
9 & 14.5715 & 2.28988580501299 & 7.418 \tabularnewline
10 & 14.7475833333333 & 2.80177805422762 & 8.962 \tabularnewline
11 & 14.1205 & 2.34898568051675 & 7.212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115170&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]19.2594166666667[/C][C]2.82970979746666[/C][C]8.217[/C][/ROW]
[ROW][C]2[/C][C]21.798[/C][C]2.28037134137084[/C][C]8.042[/C][/ROW]
[ROW][C]3[/C][C]22.7673333333333[/C][C]2.02389755998996[/C][C]6.563[/C][/ROW]
[ROW][C]4[/C][C]15.8635[/C][C]3.23218821177908[/C][C]11.172[/C][/ROW]
[ROW][C]5[/C][C]14.0235833333333[/C][C]1.65327336233487[/C][C]5.419[/C][/ROW]
[ROW][C]6[/C][C]12.7235[/C][C]1.57486643012265[/C][C]5.669[/C][/ROW]
[ROW][C]7[/C][C]11.89475[/C][C]1.15218449635306[/C][C]4.447[/C][/ROW]
[ROW][C]8[/C][C]12.32075[/C][C]1.92160799734351[/C][C]4.716[/C][/ROW]
[ROW][C]9[/C][C]14.5715[/C][C]2.28988580501299[/C][C]7.418[/C][/ROW]
[ROW][C]10[/C][C]14.7475833333333[/C][C]2.80177805422762[/C][C]8.962[/C][/ROW]
[ROW][C]11[/C][C]14.1205[/C][C]2.34898568051675[/C][C]7.212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115170&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
119.25941666666672.829709797466668.217
221.7982.280371341370848.042
322.76733333333332.023897559989966.563
415.86353.2321882117790811.172
514.02358333333331.653273362334875.419
612.72351.574866430122655.669
711.894751.152184496353064.447
812.320751.921607997343514.716
914.57152.289885805012997.418
1014.74758333333332.801778054227628.962
1114.12052.348985680516757.212






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.24784636938976
beta0.0596381976218143
S.D.0.0504583582113365
T-STAT1.18192901505098
p-value0.267519943382429

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.24784636938976 \tabularnewline
beta & 0.0596381976218143 \tabularnewline
S.D. & 0.0504583582113365 \tabularnewline
T-STAT & 1.18192901505098 \tabularnewline
p-value & 0.267519943382429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115170&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.24784636938976[/C][/ROW]
[ROW][C]beta[/C][C]0.0596381976218143[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0504583582113365[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.18192901505098[/C][/ROW]
[ROW][C]p-value[/C][C]0.267519943382429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115170&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115170&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)
alpha1.24784636938976
beta0.0596381976218143
S.D.0.0504583582113365
T-STAT1.18192901505098
p-value0.267519943382429






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.0045249826196
beta0.639372898075873
S.D.0.392326353382875
T-STAT1.62969653341615
p-value0.137604695359158
Lambda0.360627101924127

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.0045249826196 \tabularnewline
beta & 0.639372898075873 \tabularnewline
S.D. & 0.392326353382875 \tabularnewline
T-STAT & 1.62969653341615 \tabularnewline
p-value & 0.137604695359158 \tabularnewline
Lambda & 0.360627101924127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115170&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.0045249826196[/C][/ROW]
[ROW][C]beta[/C][C]0.639372898075873[/C][/ROW]
[ROW][C]S.D.[/C][C]0.392326353382875[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.62969653341615[/C][/ROW]
[ROW][C]p-value[/C][C]0.137604695359158[/C][/ROW]
[ROW][C]Lambda[/C][C]0.360627101924127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115170&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115170&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-1.0045249826196
beta0.639372898075873
S.D.0.392326353382875
T-STAT1.62969653341615
p-value0.137604695359158
Lambda0.360627101924127


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')