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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 05:44:53 -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/19/t12296907521agdiog1cltkzof.htm/, Retrieved Wed, 15 May 2024 17:01:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35090, Retrieved Wed, 15 May 2024 17:01:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [ARIMA Forecasting] [ARIMA Forecasting] [2008-12-15 12:59:24] [1ce0d16c8f4225c977b42c8fa93bc163]
F       [ARIMA Forecasting] [ARIMA] [2008-12-15 22:45:01] [76963dc1903f0f612b6153510a3818cf]
- RMPD      [Standard Deviation-Mean Plot] [feedback op blog] [2008-12-19 12:44:53] [f4b2017b314c03698059f43b95818e67] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14211
13646.8
12224.6
15916.4
16535.9
15796
14418.6
15044.5
14944.2
16754.8
14254
15454.9
15644.8
14568.3
12520.2
14803
15873.2
14755.3
12875.1
14291.1
14205.3
15859.4
15258.9
15498.6
15106.5
15023.6
12083
15761.3
16943
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22238.5
20682.2
17818.6
21872.1
22117
21865.9
23451.3
20953.7
22497.3

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35090&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35090&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35090&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114933.4751283.521298562534530.2
214679.43333333331090.581008064743353
314955.5751202.948233696924860
415392.3251497.799955161516200.2
517018.01666666671345.174662422785257
618084.53333333331556.779661722085930.8
718958.63333333331413.737344342255185.2
820752.74166666671751.103962677855715.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14933.475 & 1283.52129856253 & 4530.2 \tabularnewline
2 & 14679.4333333333 & 1090.58100806474 & 3353 \tabularnewline
3 & 14955.575 & 1202.94823369692 & 4860 \tabularnewline
4 & 15392.325 & 1497.79995516151 & 6200.2 \tabularnewline
5 & 17018.0166666667 & 1345.17466242278 & 5257 \tabularnewline
6 & 18084.5333333333 & 1556.77966172208 & 5930.8 \tabularnewline
7 & 18958.6333333333 & 1413.73734434225 & 5185.2 \tabularnewline
8 & 20752.7416666667 & 1751.10396267785 & 5715.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35090&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]14933.475[/C][C]1283.52129856253[/C][C]4530.2[/C][/ROW]
[ROW][C]2[/C][C]14679.4333333333[/C][C]1090.58100806474[/C][C]3353[/C][/ROW]
[ROW][C]3[/C][C]14955.575[/C][C]1202.94823369692[/C][C]4860[/C][/ROW]
[ROW][C]4[/C][C]15392.325[/C][C]1497.79995516151[/C][C]6200.2[/C][/ROW]
[ROW][C]5[/C][C]17018.0166666667[/C][C]1345.17466242278[/C][C]5257[/C][/ROW]
[ROW][C]6[/C][C]18084.5333333333[/C][C]1556.77966172208[/C][C]5930.8[/C][/ROW]
[ROW][C]7[/C][C]18958.6333333333[/C][C]1413.73734434225[/C][C]5185.2[/C][/ROW]
[ROW][C]8[/C][C]20752.7416666667[/C][C]1751.10396267785[/C][C]5715.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35090&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35090&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
114933.4751283.521298562534530.2
214679.43333333331090.581008064743353
314955.5751202.948233696924860
415392.3251497.799955161516200.2
517018.01666666671345.174662422785257
618084.53333333331556.779661722085930.8
718958.63333333331413.737344342255185.2
820752.74166666671751.103962677855715.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha100.878982851337
beta0.0766806508032907
S.D.0.0217851126334985
T-STAT3.51986478533880
p-value0.0125206037097887

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 100.878982851337 \tabularnewline
beta & 0.0766806508032907 \tabularnewline
S.D. & 0.0217851126334985 \tabularnewline
T-STAT & 3.51986478533880 \tabularnewline
p-value & 0.0125206037097887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35090&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]100.878982851337[/C][/ROW]
[ROW][C]beta[/C][C]0.0766806508032907[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0217851126334985[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.51986478533880[/C][/ROW]
[ROW][C]p-value[/C][C]0.0125206037097887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35090&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35090&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)
alpha100.878982851337
beta0.0766806508032907
S.D.0.0217851126334985
T-STAT3.51986478533880
p-value0.0125206037097887






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.91202029407689
beta0.94001703253994
S.D.0.277492152692839
T-STAT3.38754456087434
p-value0.0147201356081368
Lambda0.0599829674600605

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.91202029407689 \tabularnewline
beta & 0.94001703253994 \tabularnewline
S.D. & 0.277492152692839 \tabularnewline
T-STAT & 3.38754456087434 \tabularnewline
p-value & 0.0147201356081368 \tabularnewline
Lambda & 0.0599829674600605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35090&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.91202029407689[/C][/ROW]
[ROW][C]beta[/C][C]0.94001703253994[/C][/ROW]
[ROW][C]S.D.[/C][C]0.277492152692839[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.38754456087434[/C][/ROW]
[ROW][C]p-value[/C][C]0.0147201356081368[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0599829674600605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35090&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35090&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-1.91202029407689
beta0.94001703253994
S.D.0.277492152692839
T-STAT3.38754456087434
p-value0.0147201356081368
Lambda0.0599829674600605


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')