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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 computationMon, 29 Nov 2010 10:52:49 +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/Nov/29/t1291027857lvys8qncifu969u.htm/, Retrieved Sat, 27 Apr 2024 18:18:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102825, Retrieved Sat, 27 Apr 2024 18:18:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact639

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] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP           [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
- RMP             [ARIMA Backward Selection] [Births] [2010-11-29 17:42:52] [b98453cac15ba1066b407e146608df68]
F R PD              [ARIMA Backward Selection] [ARIMA] [2010-12-02 20:40:17] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- R P                 [ARIMA Backward Selection] [] [2011-12-04 15:27:05] [9401a40688cf36283be626153bc5a38b]
- R                     [ARIMA Backward Selection] [WS9.7] [2011-12-06 20:38:53] [246430c28552f7bc561843533d7ec653]
- RMP                 [ARIMA Backward Selection] [WS 9 - ARIMA para...] [2011-12-05 14:17:13] [74be16979710d4c4e7c6647856088456]
- R PD                [ARIMA Backward Selection] [] [2011-12-05 18:48:35] [06c08141d7d783218a8164fd2ea166f2]
- R PD                  [ARIMA Backward Selection] [] [2011-12-20 19:48:55] [06c08141d7d783218a8164fd2ea166f2]
- R PD                [ARIMA Backward Selection] [C9.7] [2011-12-05 19:02:36] [d1ce18d003fa52f731d1c3ce8b58d5f9]
- R P                 [ARIMA Backward Selection] [c9.7] [2011-12-05 19:22:18] [d1ce18d003fa52f731d1c3ce8b58d5f9]
-   PD              [ARIMA Backward Selection] [Model 1: CPI] [2010-12-04 12:17:27] [6bc4f9343b7ea3ef5a59412d1f72bb2b]
-   PD              [ARIMA Backward Selection] [Model 2: CPI] [2010-12-04 12:20:20] [6bc4f9343b7ea3ef5a59412d1f72bb2b]
-   PD              [ARIMA Backward Selection] [Test 5] [2010-12-05 11:00:47] [74be16979710d4c4e7c6647856088456]
-   P                 [ARIMA Backward Selection] [W9 - Blog 8] [2010-12-06 16:09:21] [1aa8d85d6b335d32b1f6be940e33a166]
-    D                  [ARIMA Backward Selection] [Blog 4] [2010-12-10 11:39:46] [1aa8d85d6b335d32b1f6be940e33a166]
-   PD                  [ARIMA Backward Selection] [ARMA parameters] [2010-12-21 13:20:08] [74be16979710d4c4e7c6647856088456]
-                         [ARIMA Backward Selection] [Arima backward] [2010-12-21 19:45:42] [717f3d787904f94c39256c5c1fc72d4c]
-   PD                    [ARIMA Backward Selection] [ARMA parameters] [2010-12-21 20:32:57] [74be16979710d4c4e7c6647856088456]
-                           [ARIMA Backward Selection] [Arima backward] [2010-12-21 20:47:35] [717f3d787904f94c39256c5c1fc72d4c]
-                       [ARIMA Backward Selection] [ws 9] [2011-12-07 11:14:31] [27e29806e0b1d1351a97bc4ee4116294]
F   P                 [ARIMA Backward Selection] [W9 3] [2010-12-06 18:22:48] [1afa3497b02a8d7c9f6727c1b17b89b2]
F   PD              [ARIMA Backward Selection] [W9] [2010-12-06 19:00:10] [5ddc7dfb25e070b079c4c8fcccc4d42e]
-                     [ARIMA Backward Selection] [] [2010-12-15 15:13:49] [2e1e44f0ae3cb9513dc28781dfdb387b]
-                       [ARIMA Backward Selection] [] [2010-12-17 16:50:02] [dc73d270d5d96f29ff77294e1b86f79b]
-   P                 [ARIMA Backward Selection] [ARMA parameters] [2011-12-07 12:53:48] [489eb911c8db04aca1fc54d886fc3144]
-   P                 [ARIMA Backward Selection] [ws9.6] [2011-12-07 13:25:00] [8ae0a4da1b3ee81f40dbba5e42914d07]
-                     [ARIMA Backward Selection] [ARMA parameter] [2011-12-08 08:41:51] [d1852ae60c447c0faaa37b55ffb3cb2b]
- RMP                 [ARIMA Forecasting] [Forecasting] [2011-12-08 08:48:03] [d1852ae60c447c0faaa37b55ffb3cb2b]
-                     [ARIMA Backward Selection] [ARIMA parameters ...] [2011-12-08 14:21:22] [d5821fed422662f85834b1edae505ce2]
-                     [ARIMA Backward Selection] [workshop 9g] [2011-12-08 14:32:47] [bab4e1d4a779bb46523d87231e2a2e96]
-    D                [ARIMA Backward Selection] [workshop 9] [2011-12-08 14:34:12] [b1d8f9e536fbb1cbb331f583f7f5f24b]
-                     [ARIMA Backward Selection] [ARIMA backward] [2011-12-22 13:41:46] [bab4e1d4a779bb46523d87231e2a2e96]
- R                   [ARIMA Backward Selection] [] [2012-11-26 21:01:37] [74be16979710d4c4e7c6647856088456]
F   PD              [ARIMA Backward Selection] [ARIMA] [2010-12-06 20:02:38] [2843717cd92615903379c14ebee3c5df]
-   PD              [ARIMA Backward Selection] [WS 9 ] [2010-12-06 21:01:55] [19f9551d4d95750ef21e9f3cf8fe2131]
F   PD              [ARIMA Backward Selection] [ws 9] [2010-12-07 10:21:33] [bd591a1ebb67d263a02e7adae3fa1a4d]
- RMPD                [ARIMA Forecasting] [] [2010-12-14 12:31:06] [9b13650c94c5192ca5135ec8a1fa39f7]
-                     [ARIMA Backward Selection] [arima] [2010-12-21 10:06:40] [bd591a1ebb67d263a02e7adae3fa1a4d]
-   PD                  [ARIMA Backward Selection] [arima 2] [2010-12-22 18:11:01] [bd591a1ebb67d263a02e7adae3fa1a4d]
-                   [ARIMA Backward Selection] [] [2011-12-04 14:29:55] [50e3859e0b739a5118d466e989dfc0cb]
- R P                 [ARIMA Backward Selection] [] [2011-12-04 14:31:26] [50e3859e0b739a5118d466e989dfc0cb]
- RMPD                [Skewness and Kurtosis Test] [] [2011-12-04 14:59:57] [50e3859e0b739a5118d466e989dfc0cb]
- R                 [ARIMA Backward Selection] [ARIMA- Births] [2011-12-07 13:16:21] [74be16979710d4c4e7c6647856088456]
-   PD              [ARIMA Backward Selection] [paper ARIMA (fout...] [2011-12-09 13:07:59] [7e261c986c934df955dd3ac53e9d45c6]
- R P                 [ARIMA Backward Selection] [paper - ARIMA] [2011-12-11 10:44:54] [7e261c986c934df955dd3ac53e9d45c6]
- R PD              [ARIMA Backward Selection] [ARIMA backward se...] [2011-12-18 12:40:22] [379dab8110dbf77cfcc4b7951c3a599f]
-   P               [ARIMA Backward Selection] [ARIMA model] [2012-11-22 09:40:31] [0dc867bfbaab36a894719867823e3cb9]
- R P               [ARIMA Backward Selection] [WS9-7] [2012-11-29 19:50:13] [f4f48270c576c45d216b84daa061a85b]
- RMP                 [ARIMA Forecasting] [WS9-8] [2012-11-29 20:08:15] [f4f48270c576c45d216b84daa061a85b]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102825&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102825&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102825&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19511438.4640547099921451
29305.91666666667388.9165506035111247
39324441.3024112576521623
49536.75465.0368753707021573
59808.41666666667375.825505528911384
610050.5489.6754955162561482

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9511 & 438.464054709992 & 1451 \tabularnewline
2 & 9305.91666666667 & 388.916550603511 & 1247 \tabularnewline
3 & 9324 & 441.302411257652 & 1623 \tabularnewline
4 & 9536.75 & 465.036875370702 & 1573 \tabularnewline
5 & 9808.41666666667 & 375.82550552891 & 1384 \tabularnewline
6 & 10050.5 & 489.675495516256 & 1482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102825&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]9511[/C][C]438.464054709992[/C][C]1451[/C][/ROW]
[ROW][C]2[/C][C]9305.91666666667[/C][C]388.916550603511[/C][C]1247[/C][/ROW]
[ROW][C]3[/C][C]9324[/C][C]441.302411257652[/C][C]1623[/C][/ROW]
[ROW][C]4[/C][C]9536.75[/C][C]465.036875370702[/C][C]1573[/C][/ROW]
[ROW][C]5[/C][C]9808.41666666667[/C][C]375.82550552891[/C][C]1384[/C][/ROW]
[ROW][C]6[/C][C]10050.5[/C][C]489.675495516256[/C][C]1482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102825&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102825&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
19511438.4640547099921451
29305.91666666667388.9165506035111247
39324441.3024112576521623
49536.75465.0368753707021573
59808.41666666667375.825505528911384
610050.5489.6754955162561482






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-63.9320339299989
beta0.0518420268246785
S.D.0.0707682193515611
T-STAT0.73256084863657
p-value0.50443984674494

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -63.9320339299989 \tabularnewline
beta & 0.0518420268246785 \tabularnewline
S.D. & 0.0707682193515611 \tabularnewline
T-STAT & 0.73256084863657 \tabularnewline
p-value & 0.50443984674494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102825&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-63.9320339299989[/C][/ROW]
[ROW][C]beta[/C][C]0.0518420268246785[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0707682193515611[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.73256084863657[/C][/ROW]
[ROW][C]p-value[/C][C]0.50443984674494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102825&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102825&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-63.9320339299989
beta0.0518420268246785
S.D.0.0707682193515611
T-STAT0.73256084863657
p-value0.50443984674494






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.63608875815898
beta1.05834855630331
S.D.1.61914610202505
T-STAT0.653646113207231
p-value0.5490103780068
Lambda-0.0583485563033119

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.63608875815898 \tabularnewline
beta & 1.05834855630331 \tabularnewline
S.D. & 1.61914610202505 \tabularnewline
T-STAT & 0.653646113207231 \tabularnewline
p-value & 0.5490103780068 \tabularnewline
Lambda & -0.0583485563033119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102825&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.63608875815898[/C][/ROW]
[ROW][C]beta[/C][C]1.05834855630331[/C][/ROW]
[ROW][C]S.D.[/C][C]1.61914610202505[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.653646113207231[/C][/ROW]
[ROW][C]p-value[/C][C]0.5490103780068[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0583485563033119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102825&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102825&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-3.63608875815898
beta1.05834855630331
S.D.1.61914610202505
T-STAT0.653646113207231
p-value0.5490103780068
Lambda-0.0583485563033119


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; 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')