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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 Jan 2010 10:45:40 -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/2010/Jan/16/t1263664057ndddk684k49kyxi.htm/, Retrieved Fri, 03 May 2024 07:30:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72247, Retrieved Fri, 03 May 2024 07:30:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 Oef 2] [2010-01-16 17:45:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10,1200
10,1200
10,0500
10,1400
10,1700
10,2000
10,2000
10,3500
10,4300
10,5200
10,5700
10,5700
10,5700
10,6500
10,5700
10,6100
10,6300
10,7100
10,7200
10,7700
10,7900
10,8200
10,9000
10,8300
10,9200
10,9100
10,8800
10,8700
11,0000
10,9900
11,0300
11,0400
10,9900
10,9000
11,0000
10,9900
10,9200
10,9800
11,1500
11,1900
11,3300
11,3800
11,4000
11,4500
11,5600
11,6100
11,8200
11,7700
11,8500
11,8200
11,9200
11,8600
11,8700
11,9400
11,8600
11,9200
11,8300
11,9100
11,9300
11,9900
11,9600
12,1200
11,8500
12,0100
12,1000
12,2100
12,3100
12,3100
12,3900
12,3500
12,4100
12,5100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72247&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72247&T=0

As an alternative you can also use a 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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.770591746725278
beta0
gamma0.461098380461349

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.770591746725278 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.461098380461349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72247&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]0.770591746725278[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.461098380461349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72247&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.770591746725278
beta0
gamma0.461098380461349







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310.5710.32454326923080.245456730769225
1410.6510.59153839361290.0584616063870946
1510.5710.56110328513500.00889671486503829
1610.6110.6174738803228-0.00747388032278806
1710.6310.6424794299699-0.0124794299698952
1810.7110.7252944110378-0.0152944110377877
1910.7210.63844019092760.0815598090724308
2010.7710.8474710334698-0.0774710334698039
2110.7910.8610373546076-0.0710373546075544
2210.8210.8920614155776-0.072061415577636
2310.910.88479634361600.0152036563839708
2410.8310.8931103492188-0.0631103492187588
2510.9210.86454058597070.0554594140292899
2610.9110.9653450441676-0.0553450441676091
2710.8810.84196850702380.0380314929762253
2810.8710.9190584439067-0.0490584439067323
291110.91148978615420.088510213845785
3010.9911.0718287851899-0.0818287851898809
3111.0310.94394894300350.0860510569964781
3211.0411.1396184575375-0.0996184575375167
3310.9911.1367987095738-0.146798709573817
3410.911.1093333707481-0.209333370748146
351111.0055185426698-0.00551854266980811
3610.9910.98958015489010.000419845109865591
3710.9211.0225085178251-0.102508517825051
3810.9810.989863320936-0.0098633209359953
3911.1510.91141197334190.238588026658118
4011.1911.13383676598650.056163234013523
4111.3311.22190304634920.108096953650760
4211.3811.37931700459410.000682995405927755
4311.411.33277835131640.0672216486836206
4411.4511.4942979999135-0.0442979999134909
4511.5611.52911702361990.0308829763800649
4611.6111.6319568232053-0.0219568232052794
4711.8211.69409230265540.125907697344598
4811.7711.7800580520515-0.0100580520515177
4911.8511.79402449493630.0559755050636976
5011.8211.8933057660668-0.0733057660668237
5111.9211.79224732127360.127752678726393
5211.8611.9099664562096-0.0499664562096278
5311.8711.9217436103327-0.0517436103326947
5411.9411.9446235249471-0.00462352494707119
5511.8611.9010341545908-0.0410341545907951
5611.9211.9673362514188-0.047336251418848
5711.8312.0077666502759-0.17776665027594
5811.9111.9442333875419-0.0342333875419012
5911.9312.0125497234098-0.0825497234097785
6011.9911.92349747857930.0665025214206523
6111.9612.0034458822577-0.0434458822576662
6212.1212.01243850922140.107561490778640
6311.8512.0720227966671-0.222022796667057
6412.0111.90140874712020.108591252879819
6512.112.03518117628570.0648188237143454
6612.2112.15286749254020.0571325074598317
6712.3112.15301530289040.156984697109559
6812.3112.3712424581563-0.0612424581562934
6912.3912.38715995075300.00284004924702863
7012.3512.4779836361752-0.127983636175212
7112.4112.4689459131018-0.0589459131018142
7212.5112.41384928246570.0961507175343037

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10.57 & 10.3245432692308 & 0.245456730769225 \tabularnewline
14 & 10.65 & 10.5915383936129 & 0.0584616063870946 \tabularnewline
15 & 10.57 & 10.5611032851350 & 0.00889671486503829 \tabularnewline
16 & 10.61 & 10.6174738803228 & -0.00747388032278806 \tabularnewline
17 & 10.63 & 10.6424794299699 & -0.0124794299698952 \tabularnewline
18 & 10.71 & 10.7252944110378 & -0.0152944110377877 \tabularnewline
19 & 10.72 & 10.6384401909276 & 0.0815598090724308 \tabularnewline
20 & 10.77 & 10.8474710334698 & -0.0774710334698039 \tabularnewline
21 & 10.79 & 10.8610373546076 & -0.0710373546075544 \tabularnewline
22 & 10.82 & 10.8920614155776 & -0.072061415577636 \tabularnewline
23 & 10.9 & 10.8847963436160 & 0.0152036563839708 \tabularnewline
24 & 10.83 & 10.8931103492188 & -0.0631103492187588 \tabularnewline
25 & 10.92 & 10.8645405859707 & 0.0554594140292899 \tabularnewline
26 & 10.91 & 10.9653450441676 & -0.0553450441676091 \tabularnewline
27 & 10.88 & 10.8419685070238 & 0.0380314929762253 \tabularnewline
28 & 10.87 & 10.9190584439067 & -0.0490584439067323 \tabularnewline
29 & 11 & 10.9114897861542 & 0.088510213845785 \tabularnewline
30 & 10.99 & 11.0718287851899 & -0.0818287851898809 \tabularnewline
31 & 11.03 & 10.9439489430035 & 0.0860510569964781 \tabularnewline
32 & 11.04 & 11.1396184575375 & -0.0996184575375167 \tabularnewline
33 & 10.99 & 11.1367987095738 & -0.146798709573817 \tabularnewline
34 & 10.9 & 11.1093333707481 & -0.209333370748146 \tabularnewline
35 & 11 & 11.0055185426698 & -0.00551854266980811 \tabularnewline
36 & 10.99 & 10.9895801548901 & 0.000419845109865591 \tabularnewline
37 & 10.92 & 11.0225085178251 & -0.102508517825051 \tabularnewline
38 & 10.98 & 10.989863320936 & -0.0098633209359953 \tabularnewline
39 & 11.15 & 10.9114119733419 & 0.238588026658118 \tabularnewline
40 & 11.19 & 11.1338367659865 & 0.056163234013523 \tabularnewline
41 & 11.33 & 11.2219030463492 & 0.108096953650760 \tabularnewline
42 & 11.38 & 11.3793170045941 & 0.000682995405927755 \tabularnewline
43 & 11.4 & 11.3327783513164 & 0.0672216486836206 \tabularnewline
44 & 11.45 & 11.4942979999135 & -0.0442979999134909 \tabularnewline
45 & 11.56 & 11.5291170236199 & 0.0308829763800649 \tabularnewline
46 & 11.61 & 11.6319568232053 & -0.0219568232052794 \tabularnewline
47 & 11.82 & 11.6940923026554 & 0.125907697344598 \tabularnewline
48 & 11.77 & 11.7800580520515 & -0.0100580520515177 \tabularnewline
49 & 11.85 & 11.7940244949363 & 0.0559755050636976 \tabularnewline
50 & 11.82 & 11.8933057660668 & -0.0733057660668237 \tabularnewline
51 & 11.92 & 11.7922473212736 & 0.127752678726393 \tabularnewline
52 & 11.86 & 11.9099664562096 & -0.0499664562096278 \tabularnewline
53 & 11.87 & 11.9217436103327 & -0.0517436103326947 \tabularnewline
54 & 11.94 & 11.9446235249471 & -0.00462352494707119 \tabularnewline
55 & 11.86 & 11.9010341545908 & -0.0410341545907951 \tabularnewline
56 & 11.92 & 11.9673362514188 & -0.047336251418848 \tabularnewline
57 & 11.83 & 12.0077666502759 & -0.17776665027594 \tabularnewline
58 & 11.91 & 11.9442333875419 & -0.0342333875419012 \tabularnewline
59 & 11.93 & 12.0125497234098 & -0.0825497234097785 \tabularnewline
60 & 11.99 & 11.9234974785793 & 0.0665025214206523 \tabularnewline
61 & 11.96 & 12.0034458822577 & -0.0434458822576662 \tabularnewline
62 & 12.12 & 12.0124385092214 & 0.107561490778640 \tabularnewline
63 & 11.85 & 12.0720227966671 & -0.222022796667057 \tabularnewline
64 & 12.01 & 11.9014087471202 & 0.108591252879819 \tabularnewline
65 & 12.1 & 12.0351811762857 & 0.0648188237143454 \tabularnewline
66 & 12.21 & 12.1528674925402 & 0.0571325074598317 \tabularnewline
67 & 12.31 & 12.1530153028904 & 0.156984697109559 \tabularnewline
68 & 12.31 & 12.3712424581563 & -0.0612424581562934 \tabularnewline
69 & 12.39 & 12.3871599507530 & 0.00284004924702863 \tabularnewline
70 & 12.35 & 12.4779836361752 & -0.127983636175212 \tabularnewline
71 & 12.41 & 12.4689459131018 & -0.0589459131018142 \tabularnewline
72 & 12.51 & 12.4138492824657 & 0.0961507175343037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72247&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]13[/C][C]10.57[/C][C]10.3245432692308[/C][C]0.245456730769225[/C][/ROW]
[ROW][C]14[/C][C]10.65[/C][C]10.5915383936129[/C][C]0.0584616063870946[/C][/ROW]
[ROW][C]15[/C][C]10.57[/C][C]10.5611032851350[/C][C]0.00889671486503829[/C][/ROW]
[ROW][C]16[/C][C]10.61[/C][C]10.6174738803228[/C][C]-0.00747388032278806[/C][/ROW]
[ROW][C]17[/C][C]10.63[/C][C]10.6424794299699[/C][C]-0.0124794299698952[/C][/ROW]
[ROW][C]18[/C][C]10.71[/C][C]10.7252944110378[/C][C]-0.0152944110377877[/C][/ROW]
[ROW][C]19[/C][C]10.72[/C][C]10.6384401909276[/C][C]0.0815598090724308[/C][/ROW]
[ROW][C]20[/C][C]10.77[/C][C]10.8474710334698[/C][C]-0.0774710334698039[/C][/ROW]
[ROW][C]21[/C][C]10.79[/C][C]10.8610373546076[/C][C]-0.0710373546075544[/C][/ROW]
[ROW][C]22[/C][C]10.82[/C][C]10.8920614155776[/C][C]-0.072061415577636[/C][/ROW]
[ROW][C]23[/C][C]10.9[/C][C]10.8847963436160[/C][C]0.0152036563839708[/C][/ROW]
[ROW][C]24[/C][C]10.83[/C][C]10.8931103492188[/C][C]-0.0631103492187588[/C][/ROW]
[ROW][C]25[/C][C]10.92[/C][C]10.8645405859707[/C][C]0.0554594140292899[/C][/ROW]
[ROW][C]26[/C][C]10.91[/C][C]10.9653450441676[/C][C]-0.0553450441676091[/C][/ROW]
[ROW][C]27[/C][C]10.88[/C][C]10.8419685070238[/C][C]0.0380314929762253[/C][/ROW]
[ROW][C]28[/C][C]10.87[/C][C]10.9190584439067[/C][C]-0.0490584439067323[/C][/ROW]
[ROW][C]29[/C][C]11[/C][C]10.9114897861542[/C][C]0.088510213845785[/C][/ROW]
[ROW][C]30[/C][C]10.99[/C][C]11.0718287851899[/C][C]-0.0818287851898809[/C][/ROW]
[ROW][C]31[/C][C]11.03[/C][C]10.9439489430035[/C][C]0.0860510569964781[/C][/ROW]
[ROW][C]32[/C][C]11.04[/C][C]11.1396184575375[/C][C]-0.0996184575375167[/C][/ROW]
[ROW][C]33[/C][C]10.99[/C][C]11.1367987095738[/C][C]-0.146798709573817[/C][/ROW]
[ROW][C]34[/C][C]10.9[/C][C]11.1093333707481[/C][C]-0.209333370748146[/C][/ROW]
[ROW][C]35[/C][C]11[/C][C]11.0055185426698[/C][C]-0.00551854266980811[/C][/ROW]
[ROW][C]36[/C][C]10.99[/C][C]10.9895801548901[/C][C]0.000419845109865591[/C][/ROW]
[ROW][C]37[/C][C]10.92[/C][C]11.0225085178251[/C][C]-0.102508517825051[/C][/ROW]
[ROW][C]38[/C][C]10.98[/C][C]10.989863320936[/C][C]-0.0098633209359953[/C][/ROW]
[ROW][C]39[/C][C]11.15[/C][C]10.9114119733419[/C][C]0.238588026658118[/C][/ROW]
[ROW][C]40[/C][C]11.19[/C][C]11.1338367659865[/C][C]0.056163234013523[/C][/ROW]
[ROW][C]41[/C][C]11.33[/C][C]11.2219030463492[/C][C]0.108096953650760[/C][/ROW]
[ROW][C]42[/C][C]11.38[/C][C]11.3793170045941[/C][C]0.000682995405927755[/C][/ROW]
[ROW][C]43[/C][C]11.4[/C][C]11.3327783513164[/C][C]0.0672216486836206[/C][/ROW]
[ROW][C]44[/C][C]11.45[/C][C]11.4942979999135[/C][C]-0.0442979999134909[/C][/ROW]
[ROW][C]45[/C][C]11.56[/C][C]11.5291170236199[/C][C]0.0308829763800649[/C][/ROW]
[ROW][C]46[/C][C]11.61[/C][C]11.6319568232053[/C][C]-0.0219568232052794[/C][/ROW]
[ROW][C]47[/C][C]11.82[/C][C]11.6940923026554[/C][C]0.125907697344598[/C][/ROW]
[ROW][C]48[/C][C]11.77[/C][C]11.7800580520515[/C][C]-0.0100580520515177[/C][/ROW]
[ROW][C]49[/C][C]11.85[/C][C]11.7940244949363[/C][C]0.0559755050636976[/C][/ROW]
[ROW][C]50[/C][C]11.82[/C][C]11.8933057660668[/C][C]-0.0733057660668237[/C][/ROW]
[ROW][C]51[/C][C]11.92[/C][C]11.7922473212736[/C][C]0.127752678726393[/C][/ROW]
[ROW][C]52[/C][C]11.86[/C][C]11.9099664562096[/C][C]-0.0499664562096278[/C][/ROW]
[ROW][C]53[/C][C]11.87[/C][C]11.9217436103327[/C][C]-0.0517436103326947[/C][/ROW]
[ROW][C]54[/C][C]11.94[/C][C]11.9446235249471[/C][C]-0.00462352494707119[/C][/ROW]
[ROW][C]55[/C][C]11.86[/C][C]11.9010341545908[/C][C]-0.0410341545907951[/C][/ROW]
[ROW][C]56[/C][C]11.92[/C][C]11.9673362514188[/C][C]-0.047336251418848[/C][/ROW]
[ROW][C]57[/C][C]11.83[/C][C]12.0077666502759[/C][C]-0.17776665027594[/C][/ROW]
[ROW][C]58[/C][C]11.91[/C][C]11.9442333875419[/C][C]-0.0342333875419012[/C][/ROW]
[ROW][C]59[/C][C]11.93[/C][C]12.0125497234098[/C][C]-0.0825497234097785[/C][/ROW]
[ROW][C]60[/C][C]11.99[/C][C]11.9234974785793[/C][C]0.0665025214206523[/C][/ROW]
[ROW][C]61[/C][C]11.96[/C][C]12.0034458822577[/C][C]-0.0434458822576662[/C][/ROW]
[ROW][C]62[/C][C]12.12[/C][C]12.0124385092214[/C][C]0.107561490778640[/C][/ROW]
[ROW][C]63[/C][C]11.85[/C][C]12.0720227966671[/C][C]-0.222022796667057[/C][/ROW]
[ROW][C]64[/C][C]12.01[/C][C]11.9014087471202[/C][C]0.108591252879819[/C][/ROW]
[ROW][C]65[/C][C]12.1[/C][C]12.0351811762857[/C][C]0.0648188237143454[/C][/ROW]
[ROW][C]66[/C][C]12.21[/C][C]12.1528674925402[/C][C]0.0571325074598317[/C][/ROW]
[ROW][C]67[/C][C]12.31[/C][C]12.1530153028904[/C][C]0.156984697109559[/C][/ROW]
[ROW][C]68[/C][C]12.31[/C][C]12.3712424581563[/C][C]-0.0612424581562934[/C][/ROW]
[ROW][C]69[/C][C]12.39[/C][C]12.3871599507530[/C][C]0.00284004924702863[/C][/ROW]
[ROW][C]70[/C][C]12.35[/C][C]12.4779836361752[/C][C]-0.127983636175212[/C][/ROW]
[ROW][C]71[/C][C]12.41[/C][C]12.4689459131018[/C][C]-0.0589459131018142[/C][/ROW]
[ROW][C]72[/C][C]12.51[/C][C]12.4138492824657[/C][C]0.0961507175343037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72247&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72247&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310.5710.32454326923080.245456730769225
1410.6510.59153839361290.0584616063870946
1510.5710.56110328513500.00889671486503829
1610.6110.6174738803228-0.00747388032278806
1710.6310.6424794299699-0.0124794299698952
1810.7110.7252944110378-0.0152944110377877
1910.7210.63844019092760.0815598090724308
2010.7710.8474710334698-0.0774710334698039
2110.7910.8610373546076-0.0710373546075544
2210.8210.8920614155776-0.072061415577636
2310.910.88479634361600.0152036563839708
2410.8310.8931103492188-0.0631103492187588
2510.9210.86454058597070.0554594140292899
2610.9110.9653450441676-0.0553450441676091
2710.8810.84196850702380.0380314929762253
2810.8710.9190584439067-0.0490584439067323
291110.91148978615420.088510213845785
3010.9911.0718287851899-0.0818287851898809
3111.0310.94394894300350.0860510569964781
3211.0411.1396184575375-0.0996184575375167
3310.9911.1367987095738-0.146798709573817
3410.911.1093333707481-0.209333370748146
351111.0055185426698-0.00551854266980811
3610.9910.98958015489010.000419845109865591
3710.9211.0225085178251-0.102508517825051
3810.9810.989863320936-0.0098633209359953
3911.1510.91141197334190.238588026658118
4011.1911.13383676598650.056163234013523
4111.3311.22190304634920.108096953650760
4211.3811.37931700459410.000682995405927755
4311.411.33277835131640.0672216486836206
4411.4511.4942979999135-0.0442979999134909
4511.5611.52911702361990.0308829763800649
4611.6111.6319568232053-0.0219568232052794
4711.8211.69409230265540.125907697344598
4811.7711.7800580520515-0.0100580520515177
4911.8511.79402449493630.0559755050636976
5011.8211.8933057660668-0.0733057660668237
5111.9211.79224732127360.127752678726393
5211.8611.9099664562096-0.0499664562096278
5311.8711.9217436103327-0.0517436103326947
5411.9411.9446235249471-0.00462352494707119
5511.8611.9010341545908-0.0410341545907951
5611.9211.9673362514188-0.047336251418848
5711.8312.0077666502759-0.17776665027594
5811.9111.9442333875419-0.0342333875419012
5911.9312.0125497234098-0.0825497234097785
6011.9911.92349747857930.0665025214206523
6111.9612.0034458822577-0.0434458822576662
6212.1212.01243850922140.107561490778640
6311.8512.0720227966671-0.222022796667057
6412.0111.90140874712020.108591252879819
6512.112.03518117628570.0648188237143454
6612.2112.15286749254020.0571325074598317
6712.3112.15301530289040.156984697109559
6812.3112.3712424581563-0.0612424581562934
6912.3912.38715995075300.00284004924702863
7012.3512.4779836361752-0.127983636175212
7112.4112.4689459131018-0.0589459131018142
7212.5112.41384928246570.0961507175343037







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7312.505014024076312.320631811500212.6893962366524
7412.563459215136512.330683580526512.7962348497465
7512.505294154066512.232581499754912.7780068083781
7612.540741318674712.233235403975012.8482472333744
7712.586203986937712.247459860303912.9249481135716
7812.653128395808912.285793018963013.0204637726548
7912.619812709500412.225956168566813.0136692504339
8012.693984733636012.275283562644413.1126859046275
8112.763873792190712.321721820190913.2060257641905
8212.838670459218612.374250323891813.3030905945454
8312.935558664645312.449890302642413.4212270266482
8412.942291354693112.436266203535413.4483165058508

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 12.5050140240763 & 12.3206318115002 & 12.6893962366524 \tabularnewline
74 & 12.5634592151365 & 12.3306835805265 & 12.7962348497465 \tabularnewline
75 & 12.5052941540665 & 12.2325814997549 & 12.7780068083781 \tabularnewline
76 & 12.5407413186747 & 12.2332354039750 & 12.8482472333744 \tabularnewline
77 & 12.5862039869377 & 12.2474598603039 & 12.9249481135716 \tabularnewline
78 & 12.6531283958089 & 12.2857930189630 & 13.0204637726548 \tabularnewline
79 & 12.6198127095004 & 12.2259561685668 & 13.0136692504339 \tabularnewline
80 & 12.6939847336360 & 12.2752835626444 & 13.1126859046275 \tabularnewline
81 & 12.7638737921907 & 12.3217218201909 & 13.2060257641905 \tabularnewline
82 & 12.8386704592186 & 12.3742503238918 & 13.3030905945454 \tabularnewline
83 & 12.9355586646453 & 12.4498903026424 & 13.4212270266482 \tabularnewline
84 & 12.9422913546931 & 12.4362662035354 & 13.4483165058508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72247&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]73[/C][C]12.5050140240763[/C][C]12.3206318115002[/C][C]12.6893962366524[/C][/ROW]
[ROW][C]74[/C][C]12.5634592151365[/C][C]12.3306835805265[/C][C]12.7962348497465[/C][/ROW]
[ROW][C]75[/C][C]12.5052941540665[/C][C]12.2325814997549[/C][C]12.7780068083781[/C][/ROW]
[ROW][C]76[/C][C]12.5407413186747[/C][C]12.2332354039750[/C][C]12.8482472333744[/C][/ROW]
[ROW][C]77[/C][C]12.5862039869377[/C][C]12.2474598603039[/C][C]12.9249481135716[/C][/ROW]
[ROW][C]78[/C][C]12.6531283958089[/C][C]12.2857930189630[/C][C]13.0204637726548[/C][/ROW]
[ROW][C]79[/C][C]12.6198127095004[/C][C]12.2259561685668[/C][C]13.0136692504339[/C][/ROW]
[ROW][C]80[/C][C]12.6939847336360[/C][C]12.2752835626444[/C][C]13.1126859046275[/C][/ROW]
[ROW][C]81[/C][C]12.7638737921907[/C][C]12.3217218201909[/C][C]13.2060257641905[/C][/ROW]
[ROW][C]82[/C][C]12.8386704592186[/C][C]12.3742503238918[/C][C]13.3030905945454[/C][/ROW]
[ROW][C]83[/C][C]12.9355586646453[/C][C]12.4498903026424[/C][C]13.4212270266482[/C][/ROW]
[ROW][C]84[/C][C]12.9422913546931[/C][C]12.4362662035354[/C][C]13.4483165058508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72247&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72247&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7312.505014024076312.320631811500212.6893962366524
7412.563459215136512.330683580526512.7962348497465
7512.505294154066512.232581499754912.7780068083781
7612.540741318674712.233235403975012.8482472333744
7712.586203986937712.247459860303912.9249481135716
7812.653128395808912.285793018963013.0204637726548
7912.619812709500412.225956168566813.0136692504339
8012.693984733636012.275283562644413.1126859046275
8112.763873792190712.321721820190913.2060257641905
8212.838670459218612.374250323891813.3030905945454
8312.935558664645312.449890302642413.4212270266482
8412.942291354693112.436266203535413.4483165058508



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')