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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Dec 2015 23:14:03 +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/2015/Dec/14/t1450134857g0nvoa2ncdi3vlp.htm/, Retrieved Thu, 16 May 2024 22:20:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286427, Retrieved Thu, 16 May 2024 22:20:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double exponentia...] [2015-12-14 23:14:03] [8d882d7318a4b7284df3ed0f4f96d498] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17.5
19.1
19.7
19.8
20.2
20.6
21.4
22.8
23.2
23.3
23.3
23.3
23.4
23.6
24.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286427&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286427&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286427&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286427&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:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
319.720.7-1
419.820.3-0.499999999999996
520.219.90.299999999999997
620.620.63.5527136788005e-15
721.4210.399999999999995
822.822.20.600000000000005
923.224.2-1
1023.323.6-0.299999999999997
1123.323.4-0.100000000000001
1223.323.30
1323.423.30.0999999999999979
1423.623.50.100000000000005
1524.123.80.299999999999997

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 19.7 & 20.7 & -1 \tabularnewline
4 & 19.8 & 20.3 & -0.499999999999996 \tabularnewline
5 & 20.2 & 19.9 & 0.299999999999997 \tabularnewline
6 & 20.6 & 20.6 & 3.5527136788005e-15 \tabularnewline
7 & 21.4 & 21 & 0.399999999999995 \tabularnewline
8 & 22.8 & 22.2 & 0.600000000000005 \tabularnewline
9 & 23.2 & 24.2 & -1 \tabularnewline
10 & 23.3 & 23.6 & -0.299999999999997 \tabularnewline
11 & 23.3 & 23.4 & -0.100000000000001 \tabularnewline
12 & 23.3 & 23.3 & 0 \tabularnewline
13 & 23.4 & 23.3 & 0.0999999999999979 \tabularnewline
14 & 23.6 & 23.5 & 0.100000000000005 \tabularnewline
15 & 24.1 & 23.8 & 0.299999999999997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286427&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]19.7[/C][C]20.7[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]19.8[/C][C]20.3[/C][C]-0.499999999999996[/C][/ROW]
[ROW][C]5[/C][C]20.2[/C][C]19.9[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]6[/C][C]20.6[/C][C]20.6[/C][C]3.5527136788005e-15[/C][/ROW]
[ROW][C]7[/C][C]21.4[/C][C]21[/C][C]0.399999999999995[/C][/ROW]
[ROW][C]8[/C][C]22.8[/C][C]22.2[/C][C]0.600000000000005[/C][/ROW]
[ROW][C]9[/C][C]23.2[/C][C]24.2[/C][C]-1[/C][/ROW]
[ROW][C]10[/C][C]23.3[/C][C]23.6[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]11[/C][C]23.3[/C][C]23.4[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]12[/C][C]23.3[/C][C]23.3[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]23.4[/C][C]23.3[/C][C]0.0999999999999979[/C][/ROW]
[ROW][C]14[/C][C]23.6[/C][C]23.5[/C][C]0.100000000000005[/C][/ROW]
[ROW][C]15[/C][C]24.1[/C][C]23.8[/C][C]0.299999999999997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286427&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286427&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:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
319.720.7-1
419.820.3-0.499999999999996
520.219.90.299999999999997
620.620.63.5527136788005e-15
721.4210.399999999999995
822.822.20.600000000000005
923.224.2-1
1023.323.6-0.299999999999997
1123.323.4-0.100000000000001
1223.323.30
1323.423.30.0999999999999979
1423.623.50.100000000000005
1524.123.80.299999999999997






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1624.623.623794445639425.5762055543606

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
16 & 24.6 & 23.6237944456394 & 25.5762055543606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286427&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]16[/C][C]24.6[/C][C]23.6237944456394[/C][C]25.5762055543606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286427&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286427&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:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1624.623.623794445639425.5762055543606


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; par2 = 50 ; par3 = 0 ; par4 = 0 ; par5 = 0 ; par6 = Y ; par7 = Y ; par8 = terrain.colors ;
Parameters (R input):
par1 = 1 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
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,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')