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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 computationTue, 06 Dec 2011 04:20:11 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t1323163260kjrxdlrb6czlm1h.htm/, Retrieved Mon, 29 Apr 2024 04:30:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151403, Retrieved Mon, 29 Apr 2024 04:30:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [stand dev mean plot] [2011-12-06 09:20:11] [d14d64ba86ecc27fb5997ae1bd82937b] [Current]
- RMP     [ARIMA Backward Selection] [ARIMA B S] [2011-12-06 09:46:03] [bcad5ea7a7be31884500e96b7abaff18]
- R P       [ARIMA Backward Selection] [] [2011-12-06 19:26:35] [74be16979710d4c4e7c6647856088456]
- R P       [ARIMA Backward Selection] [] [2011-12-06 19:38:29] [74be16979710d4c4e7c6647856088456]
-   P         [ARIMA Backward Selection] [] [2011-12-06 20:04:26] [25b6caf3839c2bdc14961e5bff2d6373]
-               [ARIMA Backward Selection] [] [2011-12-06 20:12:17] [bcad5ea7a7be31884500e96b7abaff18]
- RMP           [ARIMA Forecasting] [] [2011-12-06 20:28:02] [bcad5ea7a7be31884500e96b7abaff18]
- RMP         [ARIMA Forecasting] [] [2011-12-06 20:26:47] [25b6caf3839c2bdc14961e5bff2d6373]
- R P       [ARIMA Backward Selection] [] [2011-12-06 19:31:21] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2851
2672
2755
2721
2946
3036
2282
2212
2922
4301
5764
7132
2541
2475
3031
3266
3776
3230
3028
1759
3595
4474
6838
8357
3113
3006
4047
3523
3937
3986
3260
1573
3528
5211
7614
9254
5375
3088
3718
4514
4520
4539
3663
1643
4739
5428
8314
10651
3633
4292
4154
4121
4647
4753
3965
1723
5048
6922
9858
11331
4016
3957
4510
4276
4968
4677
3523
1821
5222
6873
10803
13916
2639
2899
3370
3740
2927
3986
4217
1738
5221
6424
9842
13076
3934
3162
4286
4676
5010
4874
4633
1659
5951
6981
9851
12670

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' @ yule.wessa.net

\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' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151403&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151403&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' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13466.166666666671513.947269006864920
23864.166666666671900.883757783756598
34337.666666666672119.889119455997681
450162380.616001259879008
55370.583333333332723.367082336049608
65713.53382.1939490648512095
75006.583333333333324.2239957984811338
85640.583333333332995.5727471275611011

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3466.16666666667 & 1513.94726900686 & 4920 \tabularnewline
2 & 3864.16666666667 & 1900.88375778375 & 6598 \tabularnewline
3 & 4337.66666666667 & 2119.88911945599 & 7681 \tabularnewline
4 & 5016 & 2380.61600125987 & 9008 \tabularnewline
5 & 5370.58333333333 & 2723.36708233604 & 9608 \tabularnewline
6 & 5713.5 & 3382.19394906485 & 12095 \tabularnewline
7 & 5006.58333333333 & 3324.22399579848 & 11338 \tabularnewline
8 & 5640.58333333333 & 2995.57274712756 & 11011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151403&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]3466.16666666667[/C][C]1513.94726900686[/C][C]4920[/C][/ROW]
[ROW][C]2[/C][C]3864.16666666667[/C][C]1900.88375778375[/C][C]6598[/C][/ROW]
[ROW][C]3[/C][C]4337.66666666667[/C][C]2119.88911945599[/C][C]7681[/C][/ROW]
[ROW][C]4[/C][C]5016[/C][C]2380.61600125987[/C][C]9008[/C][/ROW]
[ROW][C]5[/C][C]5370.58333333333[/C][C]2723.36708233604[/C][C]9608[/C][/ROW]
[ROW][C]6[/C][C]5713.5[/C][C]3382.19394906485[/C][C]12095[/C][/ROW]
[ROW][C]7[/C][C]5006.58333333333[/C][C]3324.22399579848[/C][C]11338[/C][/ROW]
[ROW][C]8[/C][C]5640.58333333333[/C][C]2995.57274712756[/C][C]11011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151403&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
13466.166666666671513.947269006864920
23864.166666666671900.883757783756598
34337.666666666672119.889119455997681
450162380.616001259879008
55370.583333333332723.367082336049608
65713.53382.1939490648512095
75006.583333333333324.2239957984811338
85640.583333333332995.5727471275611011






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-986.131317649078
beta0.734857757349647
S.D.0.146728218315994
T-STAT5.00829196853641
p-value0.0024321898559722

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -986.131317649078 \tabularnewline
beta & 0.734857757349647 \tabularnewline
S.D. & 0.146728218315994 \tabularnewline
T-STAT & 5.00829196853641 \tabularnewline
p-value & 0.0024321898559722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151403&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-986.131317649078[/C][/ROW]
[ROW][C]beta[/C][C]0.734857757349647[/C][/ROW]
[ROW][C]S.D.[/C][C]0.146728218315994[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.00829196853641[/C][/ROW]
[ROW][C]p-value[/C][C]0.0024321898559722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151403&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-986.131317649078
beta0.734857757349647
S.D.0.146728218315994
T-STAT5.00829196853641
p-value0.0024321898559722






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.42150722561591
beta1.4450033290075
S.D.0.233698131055365
T-STAT6.18320447186275
p-value0.00082324324758908
Lambda-0.445003329007499

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.42150722561591 \tabularnewline
beta & 1.4450033290075 \tabularnewline
S.D. & 0.233698131055365 \tabularnewline
T-STAT & 6.18320447186275 \tabularnewline
p-value & 0.00082324324758908 \tabularnewline
Lambda & -0.445003329007499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151403&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.42150722561591[/C][/ROW]
[ROW][C]beta[/C][C]1.4450033290075[/C][/ROW]
[ROW][C]S.D.[/C][C]0.233698131055365[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.18320447186275[/C][/ROW]
[ROW][C]p-value[/C][C]0.00082324324758908[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.445003329007499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151403&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151403&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-4.42150722561591
beta1.4450033290075
S.D.0.233698131055365
T-STAT6.18320447186275
p-value0.00082324324758908
Lambda-0.445003329007499


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')