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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 computationSat, 10 Dec 2016 12:31:58 +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/10/t1481369549y2cbsalb1n1d7tq.htm/, Retrieved Mon, 06 May 2024 06:02:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298660, Retrieved Mon, 06 May 2024 06:02:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Standard Deviation-Mean Plot] [N2527 Standard de...] [2016-12-10 11:31:58] [1eb03b74c4069f30e782d39ada1a3213] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2757.95
2840.2
2835.8
2937.7
2950.95
2946.6
2899.65
2844.6
2820.55
2741.75
2564.55
2184.5
2316.9
2336.85
2297.85
2291.25
2176.1
2202.85
2191.7
2147.5
2307.45
2255.3
2222
2121.1
2232.3
2358.65
2458.4
2687.2
2693.55
3009.05
3111.9
3088.35
3359.7
3516.85
3549
3249.2
3511.85
3555.1
3507.95
3734.15
3847.2
3802.6
3888.2
3841.1
3835.65
4165.3
4275.8
4008.5
4280.35
4191.65
4007.15
3926
4004.4
3983
4062.9
4157.5
4183.6
4294.45
4161.8
3652.45
3797.25
3705.5
3721.6
4009.25
3961.45
3953.35
3968.6
3873.1
3966.25
4058.35
4012.6
4315.6
4129.95
4330.75
4286.85
4671.8
4525.35
4508.6
4552.2
4516.8
4623.7
4851.8
4892.6
4881.75
5312.9
5462.9
5484.45
5947.95
6160.05
6199.8
6103.3
6242.55
6304.15
6383.05
6464.45
6170.15
6649.45
6809.3
7109.2
7465.75
7288.25
7244.7
7206.45
7239.7
7581.95
7682.85
7370.8
6870.65
7459.1
7209.6
7360.35
7632.9
7419.85
7237.45
7262.5
6829.95
6590.75
6664.15
6748.4
6228.4
6619.3
6829.6
6816.1
7302.75
7133.55
6965.8

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298660&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298660&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12777.06666666667215.660714521395766.45
22238.9041666666771.889803482114215.75
32942.84583333333449.9503828496151316.7
43831.11666666667240.698386644642767.85
54075.4375178.125133652263642
63945.24166666667163.625413164745610.1
74564.34583333333239.981534761563762.650000000001
86019.64166666667386.5219115471471151.55
97209.92083333333310.6468694209881033.4
107053.61666666667428.5336755269141404.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2777.06666666667 & 215.660714521395 & 766.45 \tabularnewline
2 & 2238.90416666667 & 71.889803482114 & 215.75 \tabularnewline
3 & 2942.84583333333 & 449.950382849615 & 1316.7 \tabularnewline
4 & 3831.11666666667 & 240.698386644642 & 767.85 \tabularnewline
5 & 4075.4375 & 178.125133652263 & 642 \tabularnewline
6 & 3945.24166666667 & 163.625413164745 & 610.1 \tabularnewline
7 & 4564.34583333333 & 239.981534761563 & 762.650000000001 \tabularnewline
8 & 6019.64166666667 & 386.521911547147 & 1151.55 \tabularnewline
9 & 7209.92083333333 & 310.646869420988 & 1033.4 \tabularnewline
10 & 7053.61666666667 & 428.533675526914 & 1404.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298660&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]2777.06666666667[/C][C]215.660714521395[/C][C]766.45[/C][/ROW]
[ROW][C]2[/C][C]2238.90416666667[/C][C]71.889803482114[/C][C]215.75[/C][/ROW]
[ROW][C]3[/C][C]2942.84583333333[/C][C]449.950382849615[/C][C]1316.7[/C][/ROW]
[ROW][C]4[/C][C]3831.11666666667[/C][C]240.698386644642[/C][C]767.85[/C][/ROW]
[ROW][C]5[/C][C]4075.4375[/C][C]178.125133652263[/C][C]642[/C][/ROW]
[ROW][C]6[/C][C]3945.24166666667[/C][C]163.625413164745[/C][C]610.1[/C][/ROW]
[ROW][C]7[/C][C]4564.34583333333[/C][C]239.981534761563[/C][C]762.650000000001[/C][/ROW]
[ROW][C]8[/C][C]6019.64166666667[/C][C]386.521911547147[/C][C]1151.55[/C][/ROW]
[ROW][C]9[/C][C]7209.92083333333[/C][C]310.646869420988[/C][C]1033.4[/C][/ROW]
[ROW][C]10[/C][C]7053.61666666667[/C][C]428.533675526914[/C][C]1404.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298660&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
12777.06666666667215.660714521395766.45
22238.9041666666771.889803482114215.75
32942.84583333333449.9503828496151316.7
43831.11666666667240.698386644642767.85
54075.4375178.125133652263642
63945.24166666667163.625413164745610.1
74564.34583333333239.981534761563762.650000000001
86019.64166666667386.5219115471471151.55
97209.92083333333310.6468694209881033.4
107053.61666666667428.5336755269141404.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha95.7046988195396
beta0.0387070964922348
S.D.0.0207481965586125
T-STAT1.86556438208445
p-value0.0990800648472477

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 95.7046988195396 \tabularnewline
beta & 0.0387070964922348 \tabularnewline
S.D. & 0.0207481965586125 \tabularnewline
T-STAT & 1.86556438208445 \tabularnewline
p-value & 0.0990800648472477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298660&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]95.7046988195396[/C][/ROW]
[ROW][C]beta[/C][C]0.0387070964922348[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0207481965586125[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.86556438208445[/C][/ROW]
[ROW][C]p-value[/C][C]0.0990800648472477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298660&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)
alpha95.7046988195396
beta0.0387070964922348
S.D.0.0207481965586125
T-STAT1.86556438208445
p-value0.0990800648472477






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.78705837608398
beta0.87140178724372
S.D.0.384442915586562
T-STAT2.26666106179687
p-value0.0531667748505206
Lambda0.12859821275628

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.78705837608398 \tabularnewline
beta & 0.87140178724372 \tabularnewline
S.D. & 0.384442915586562 \tabularnewline
T-STAT & 2.26666106179687 \tabularnewline
p-value & 0.0531667748505206 \tabularnewline
Lambda & 0.12859821275628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298660&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.78705837608398[/C][/ROW]
[ROW][C]beta[/C][C]0.87140178724372[/C][/ROW]
[ROW][C]S.D.[/C][C]0.384442915586562[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.26666106179687[/C][/ROW]
[ROW][C]p-value[/C][C]0.0531667748505206[/C][/ROW]
[ROW][C]Lambda[/C][C]0.12859821275628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298660&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-1.78705837608398
beta0.87140178724372
S.D.0.384442915586562
T-STAT2.26666106179687
p-value0.0531667748505206
Lambda0.12859821275628


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 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')