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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 Dec 2011 12:14:36 -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/26/t1324919905rxlqdigj3xy63hl.htm/, Retrieved Fri, 03 May 2024 19:25:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160820, Retrieved Fri, 03 May 2024 19:25:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-26 17:14:36] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
20.89
21.04
21.07
21.12
21.25
21.24
21.24
21.22
21.29
21.25
21.15
21.16
21.16
21.52
21.59
21.6
21.68
21.67
21.67
21.65
21.74
21.72
21.84
21.94
21.94
21.95
21.96
22.1
22.13
22.18
22.18
22.27
22.3
22.04
22.05
22.06
22.06
22.06
21.97
22.03
22.08
22.13
22.13
22.4
22.4
22.12
22.22
22.14
22.14
22.19
22.29
22.24
22.26
22.29
22.29
22.29
22.29
22.35
22.39
22.43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160820&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160820&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.783000905517437
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.783000905517437 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160820&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]0.783000905517437[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160820&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
alpha0.783000905517437
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1321.1620.93214209401710.227857905982901
1421.5221.47375142767740.0462485723225932
1521.5921.58232715529790.00767284470206064
1621.621.59903138659390.000968613406069352
1721.6821.67048619871440.00951380128563883
1821.6721.64571523401560.0242847659843548
1921.6721.7183432813847-0.0483432813847209
2021.6521.6682701685645-0.0182701685645199
2121.7421.72132766364760.0186723363524024
2221.7221.69331117353270.0266888264672929
2321.8421.61532160243680.22467839756316
2421.9421.80444137812540.135558621874619
2521.9421.9632252480193-0.0232252480192692
2621.9522.2688271837818-0.318827183781835
2721.9622.0831773658275-0.123177365827477
2822.121.99597095167130.104029048328737
2922.1322.1499764756912-0.019976475691216
3022.1822.10531988337990.0746801166200797
3122.1822.2016473154175-0.0216473154175141
3222.2722.17900300637360.0909969936264474
3322.322.3256332785104-0.0256332785103695
3422.0422.2646650229343-0.224665022934282
3522.0522.03282871779650.0171712822035168
3622.0622.04013132363220.0198686763677856
3722.0622.0738739054496-0.0138739054495787
3822.0622.3226525985242-0.262652598524244
3921.9722.2234433650254-0.253443365025422
4022.0322.0835421416716-0.0535421416716098
4122.0822.0872601948147-0.00726019481466622
4222.1322.07310085676290.0568991432371213
4322.1322.1346028050146-0.00460280501464538
4422.422.14974807611140.250251923888616
4522.422.39576643940870.00423356059134505
4622.1222.3149942375809-0.194994237580875
4722.2222.15886844347010.061131556529876
4822.1422.2011773160013-0.0611773160012952
4922.1422.1641387027052-0.0241387027052369
5022.1922.35089529911-0.16089529911001
5122.2922.3333605185257-0.0433605185256667
5222.2422.4013327386686-0.16133273866858
5322.2622.3306937973156-0.0706937973155846
5422.2922.28078840932520.0092115906748127
5522.2922.2916050936592-0.00160509365921158
5622.2922.3644008208583-0.0744008208583402
5722.2922.3028300289784-0.0128300289784349
5822.3522.1654647692670.184535230732987
5922.3922.36208995791220.0279100420877718
6022.4322.35184543996610.0781545600338731

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21.16 & 20.9321420940171 & 0.227857905982901 \tabularnewline
14 & 21.52 & 21.4737514276774 & 0.0462485723225932 \tabularnewline
15 & 21.59 & 21.5823271552979 & 0.00767284470206064 \tabularnewline
16 & 21.6 & 21.5990313865939 & 0.000968613406069352 \tabularnewline
17 & 21.68 & 21.6704861987144 & 0.00951380128563883 \tabularnewline
18 & 21.67 & 21.6457152340156 & 0.0242847659843548 \tabularnewline
19 & 21.67 & 21.7183432813847 & -0.0483432813847209 \tabularnewline
20 & 21.65 & 21.6682701685645 & -0.0182701685645199 \tabularnewline
21 & 21.74 & 21.7213276636476 & 0.0186723363524024 \tabularnewline
22 & 21.72 & 21.6933111735327 & 0.0266888264672929 \tabularnewline
23 & 21.84 & 21.6153216024368 & 0.22467839756316 \tabularnewline
24 & 21.94 & 21.8044413781254 & 0.135558621874619 \tabularnewline
25 & 21.94 & 21.9632252480193 & -0.0232252480192692 \tabularnewline
26 & 21.95 & 22.2688271837818 & -0.318827183781835 \tabularnewline
27 & 21.96 & 22.0831773658275 & -0.123177365827477 \tabularnewline
28 & 22.1 & 21.9959709516713 & 0.104029048328737 \tabularnewline
29 & 22.13 & 22.1499764756912 & -0.019976475691216 \tabularnewline
30 & 22.18 & 22.1053198833799 & 0.0746801166200797 \tabularnewline
31 & 22.18 & 22.2016473154175 & -0.0216473154175141 \tabularnewline
32 & 22.27 & 22.1790030063736 & 0.0909969936264474 \tabularnewline
33 & 22.3 & 22.3256332785104 & -0.0256332785103695 \tabularnewline
34 & 22.04 & 22.2646650229343 & -0.224665022934282 \tabularnewline
35 & 22.05 & 22.0328287177965 & 0.0171712822035168 \tabularnewline
36 & 22.06 & 22.0401313236322 & 0.0198686763677856 \tabularnewline
37 & 22.06 & 22.0738739054496 & -0.0138739054495787 \tabularnewline
38 & 22.06 & 22.3226525985242 & -0.262652598524244 \tabularnewline
39 & 21.97 & 22.2234433650254 & -0.253443365025422 \tabularnewline
40 & 22.03 & 22.0835421416716 & -0.0535421416716098 \tabularnewline
41 & 22.08 & 22.0872601948147 & -0.00726019481466622 \tabularnewline
42 & 22.13 & 22.0731008567629 & 0.0568991432371213 \tabularnewline
43 & 22.13 & 22.1346028050146 & -0.00460280501464538 \tabularnewline
44 & 22.4 & 22.1497480761114 & 0.250251923888616 \tabularnewline
45 & 22.4 & 22.3957664394087 & 0.00423356059134505 \tabularnewline
46 & 22.12 & 22.3149942375809 & -0.194994237580875 \tabularnewline
47 & 22.22 & 22.1588684434701 & 0.061131556529876 \tabularnewline
48 & 22.14 & 22.2011773160013 & -0.0611773160012952 \tabularnewline
49 & 22.14 & 22.1641387027052 & -0.0241387027052369 \tabularnewline
50 & 22.19 & 22.35089529911 & -0.16089529911001 \tabularnewline
51 & 22.29 & 22.3333605185257 & -0.0433605185256667 \tabularnewline
52 & 22.24 & 22.4013327386686 & -0.16133273866858 \tabularnewline
53 & 22.26 & 22.3306937973156 & -0.0706937973155846 \tabularnewline
54 & 22.29 & 22.2807884093252 & 0.0092115906748127 \tabularnewline
55 & 22.29 & 22.2916050936592 & -0.00160509365921158 \tabularnewline
56 & 22.29 & 22.3644008208583 & -0.0744008208583402 \tabularnewline
57 & 22.29 & 22.3028300289784 & -0.0128300289784349 \tabularnewline
58 & 22.35 & 22.165464769267 & 0.184535230732987 \tabularnewline
59 & 22.39 & 22.3620899579122 & 0.0279100420877718 \tabularnewline
60 & 22.43 & 22.3518454399661 & 0.0781545600338731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160820&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]21.16[/C][C]20.9321420940171[/C][C]0.227857905982901[/C][/ROW]
[ROW][C]14[/C][C]21.52[/C][C]21.4737514276774[/C][C]0.0462485723225932[/C][/ROW]
[ROW][C]15[/C][C]21.59[/C][C]21.5823271552979[/C][C]0.00767284470206064[/C][/ROW]
[ROW][C]16[/C][C]21.6[/C][C]21.5990313865939[/C][C]0.000968613406069352[/C][/ROW]
[ROW][C]17[/C][C]21.68[/C][C]21.6704861987144[/C][C]0.00951380128563883[/C][/ROW]
[ROW][C]18[/C][C]21.67[/C][C]21.6457152340156[/C][C]0.0242847659843548[/C][/ROW]
[ROW][C]19[/C][C]21.67[/C][C]21.7183432813847[/C][C]-0.0483432813847209[/C][/ROW]
[ROW][C]20[/C][C]21.65[/C][C]21.6682701685645[/C][C]-0.0182701685645199[/C][/ROW]
[ROW][C]21[/C][C]21.74[/C][C]21.7213276636476[/C][C]0.0186723363524024[/C][/ROW]
[ROW][C]22[/C][C]21.72[/C][C]21.6933111735327[/C][C]0.0266888264672929[/C][/ROW]
[ROW][C]23[/C][C]21.84[/C][C]21.6153216024368[/C][C]0.22467839756316[/C][/ROW]
[ROW][C]24[/C][C]21.94[/C][C]21.8044413781254[/C][C]0.135558621874619[/C][/ROW]
[ROW][C]25[/C][C]21.94[/C][C]21.9632252480193[/C][C]-0.0232252480192692[/C][/ROW]
[ROW][C]26[/C][C]21.95[/C][C]22.2688271837818[/C][C]-0.318827183781835[/C][/ROW]
[ROW][C]27[/C][C]21.96[/C][C]22.0831773658275[/C][C]-0.123177365827477[/C][/ROW]
[ROW][C]28[/C][C]22.1[/C][C]21.9959709516713[/C][C]0.104029048328737[/C][/ROW]
[ROW][C]29[/C][C]22.13[/C][C]22.1499764756912[/C][C]-0.019976475691216[/C][/ROW]
[ROW][C]30[/C][C]22.18[/C][C]22.1053198833799[/C][C]0.0746801166200797[/C][/ROW]
[ROW][C]31[/C][C]22.18[/C][C]22.2016473154175[/C][C]-0.0216473154175141[/C][/ROW]
[ROW][C]32[/C][C]22.27[/C][C]22.1790030063736[/C][C]0.0909969936264474[/C][/ROW]
[ROW][C]33[/C][C]22.3[/C][C]22.3256332785104[/C][C]-0.0256332785103695[/C][/ROW]
[ROW][C]34[/C][C]22.04[/C][C]22.2646650229343[/C][C]-0.224665022934282[/C][/ROW]
[ROW][C]35[/C][C]22.05[/C][C]22.0328287177965[/C][C]0.0171712822035168[/C][/ROW]
[ROW][C]36[/C][C]22.06[/C][C]22.0401313236322[/C][C]0.0198686763677856[/C][/ROW]
[ROW][C]37[/C][C]22.06[/C][C]22.0738739054496[/C][C]-0.0138739054495787[/C][/ROW]
[ROW][C]38[/C][C]22.06[/C][C]22.3226525985242[/C][C]-0.262652598524244[/C][/ROW]
[ROW][C]39[/C][C]21.97[/C][C]22.2234433650254[/C][C]-0.253443365025422[/C][/ROW]
[ROW][C]40[/C][C]22.03[/C][C]22.0835421416716[/C][C]-0.0535421416716098[/C][/ROW]
[ROW][C]41[/C][C]22.08[/C][C]22.0872601948147[/C][C]-0.00726019481466622[/C][/ROW]
[ROW][C]42[/C][C]22.13[/C][C]22.0731008567629[/C][C]0.0568991432371213[/C][/ROW]
[ROW][C]43[/C][C]22.13[/C][C]22.1346028050146[/C][C]-0.00460280501464538[/C][/ROW]
[ROW][C]44[/C][C]22.4[/C][C]22.1497480761114[/C][C]0.250251923888616[/C][/ROW]
[ROW][C]45[/C][C]22.4[/C][C]22.3957664394087[/C][C]0.00423356059134505[/C][/ROW]
[ROW][C]46[/C][C]22.12[/C][C]22.3149942375809[/C][C]-0.194994237580875[/C][/ROW]
[ROW][C]47[/C][C]22.22[/C][C]22.1588684434701[/C][C]0.061131556529876[/C][/ROW]
[ROW][C]48[/C][C]22.14[/C][C]22.2011773160013[/C][C]-0.0611773160012952[/C][/ROW]
[ROW][C]49[/C][C]22.14[/C][C]22.1641387027052[/C][C]-0.0241387027052369[/C][/ROW]
[ROW][C]50[/C][C]22.19[/C][C]22.35089529911[/C][C]-0.16089529911001[/C][/ROW]
[ROW][C]51[/C][C]22.29[/C][C]22.3333605185257[/C][C]-0.0433605185256667[/C][/ROW]
[ROW][C]52[/C][C]22.24[/C][C]22.4013327386686[/C][C]-0.16133273866858[/C][/ROW]
[ROW][C]53[/C][C]22.26[/C][C]22.3306937973156[/C][C]-0.0706937973155846[/C][/ROW]
[ROW][C]54[/C][C]22.29[/C][C]22.2807884093252[/C][C]0.0092115906748127[/C][/ROW]
[ROW][C]55[/C][C]22.29[/C][C]22.2916050936592[/C][C]-0.00160509365921158[/C][/ROW]
[ROW][C]56[/C][C]22.29[/C][C]22.3644008208583[/C][C]-0.0744008208583402[/C][/ROW]
[ROW][C]57[/C][C]22.29[/C][C]22.3028300289784[/C][C]-0.0128300289784349[/C][/ROW]
[ROW][C]58[/C][C]22.35[/C][C]22.165464769267[/C][C]0.184535230732987[/C][/ROW]
[ROW][C]59[/C][C]22.39[/C][C]22.3620899579122[/C][C]0.0279100420877718[/C][/ROW]
[ROW][C]60[/C][C]22.43[/C][C]22.3518454399661[/C][C]0.0781545600338731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160820&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160820&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
1321.1620.93214209401710.227857905982901
1421.5221.47375142767740.0462485723225932
1521.5921.58232715529790.00767284470206064
1621.621.59903138659390.000968613406069352
1721.6821.67048619871440.00951380128563883
1821.6721.64571523401560.0242847659843548
1921.6721.7183432813847-0.0483432813847209
2021.6521.6682701685645-0.0182701685645199
2121.7421.72132766364760.0186723363524024
2221.7221.69331117353270.0266888264672929
2321.8421.61532160243680.22467839756316
2421.9421.80444137812540.135558621874619
2521.9421.9632252480193-0.0232252480192692
2621.9522.2688271837818-0.318827183781835
2721.9622.0831773658275-0.123177365827477
2822.121.99597095167130.104029048328737
2922.1322.1499764756912-0.019976475691216
3022.1822.10531988337990.0746801166200797
3122.1822.2016473154175-0.0216473154175141
3222.2722.17900300637360.0909969936264474
3322.322.3256332785104-0.0256332785103695
3422.0422.2646650229343-0.224665022934282
3522.0522.03282871779650.0171712822035168
3622.0622.04013132363220.0198686763677856
3722.0622.0738739054496-0.0138739054495787
3822.0622.3226525985242-0.262652598524244
3921.9722.2234433650254-0.253443365025422
4022.0322.0835421416716-0.0535421416716098
4122.0822.0872601948147-0.00726019481466622
4222.1322.07310085676290.0568991432371213
4322.1322.1346028050146-0.00460280501464538
4422.422.14974807611140.250251923888616
4522.422.39576643940870.00423356059134505
4622.1222.3149942375809-0.194994237580875
4722.2222.15886844347010.061131556529876
4822.1422.2011773160013-0.0611773160012952
4922.1422.1641387027052-0.0241387027052369
5022.1922.35089529911-0.16089529911001
5122.2922.3333605185257-0.0433605185256667
5222.2422.4013327386686-0.16133273866858
5322.2622.3306937973156-0.0706937973155846
5422.2922.28078840932520.0092115906748127
5522.2922.2916050936592-0.00160509365921158
5622.2922.3644008208583-0.0744008208583402
5722.2922.3028300289784-0.0128300289784349
5822.3522.1654647692670.184535230732987
5922.3922.36208995791220.0279100420877718
6022.4322.35184543996610.0781545600338731







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6122.431941157319222.197885915747922.6659963988905
6222.607922322215822.310654619347322.9051900250843
6322.741873647485122.392654062939223.091093232031
6422.818197327952222.423811033448823.2125836224557
6522.893550635264822.458663546063723.328437724466
6622.916337951425222.444413157188323.3882627456621
6722.917594741213822.411334687015123.4238547954125
6822.975850651317122.437440516253723.5142607863805
6922.98589657562522.417150846321823.5546423049283
7022.901405322861222.303862072826223.4989485728962
7122.919551734633522.294536401442323.5445670678247
7222.898356643356622.247026928246223.5496863584671

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 22.4319411573192 & 22.1978859157479 & 22.6659963988905 \tabularnewline
62 & 22.6079223222158 & 22.3106546193473 & 22.9051900250843 \tabularnewline
63 & 22.7418736474851 & 22.3926540629392 & 23.091093232031 \tabularnewline
64 & 22.8181973279522 & 22.4238110334488 & 23.2125836224557 \tabularnewline
65 & 22.8935506352648 & 22.4586635460637 & 23.328437724466 \tabularnewline
66 & 22.9163379514252 & 22.4444131571883 & 23.3882627456621 \tabularnewline
67 & 22.9175947412138 & 22.4113346870151 & 23.4238547954125 \tabularnewline
68 & 22.9758506513171 & 22.4374405162537 & 23.5142607863805 \tabularnewline
69 & 22.985896575625 & 22.4171508463218 & 23.5546423049283 \tabularnewline
70 & 22.9014053228612 & 22.3038620728262 & 23.4989485728962 \tabularnewline
71 & 22.9195517346335 & 22.2945364014423 & 23.5445670678247 \tabularnewline
72 & 22.8983566433566 & 22.2470269282462 & 23.5496863584671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160820&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]61[/C][C]22.4319411573192[/C][C]22.1978859157479[/C][C]22.6659963988905[/C][/ROW]
[ROW][C]62[/C][C]22.6079223222158[/C][C]22.3106546193473[/C][C]22.9051900250843[/C][/ROW]
[ROW][C]63[/C][C]22.7418736474851[/C][C]22.3926540629392[/C][C]23.091093232031[/C][/ROW]
[ROW][C]64[/C][C]22.8181973279522[/C][C]22.4238110334488[/C][C]23.2125836224557[/C][/ROW]
[ROW][C]65[/C][C]22.8935506352648[/C][C]22.4586635460637[/C][C]23.328437724466[/C][/ROW]
[ROW][C]66[/C][C]22.9163379514252[/C][C]22.4444131571883[/C][C]23.3882627456621[/C][/ROW]
[ROW][C]67[/C][C]22.9175947412138[/C][C]22.4113346870151[/C][C]23.4238547954125[/C][/ROW]
[ROW][C]68[/C][C]22.9758506513171[/C][C]22.4374405162537[/C][C]23.5142607863805[/C][/ROW]
[ROW][C]69[/C][C]22.985896575625[/C][C]22.4171508463218[/C][C]23.5546423049283[/C][/ROW]
[ROW][C]70[/C][C]22.9014053228612[/C][C]22.3038620728262[/C][C]23.4989485728962[/C][/ROW]
[ROW][C]71[/C][C]22.9195517346335[/C][C]22.2945364014423[/C][C]23.5445670678247[/C][/ROW]
[ROW][C]72[/C][C]22.8983566433566[/C][C]22.2470269282462[/C][C]23.5496863584671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160820&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160820&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
6122.431941157319222.197885915747922.6659963988905
6222.607922322215822.310654619347322.9051900250843
6322.741873647485122.392654062939223.091093232031
6422.818197327952222.423811033448823.2125836224557
6522.893550635264822.458663546063723.328437724466
6622.916337951425222.444413157188323.3882627456621
6722.917594741213822.411334687015123.4238547954125
6822.975850651317122.437440516253723.5142607863805
6922.98589657562522.417150846321823.5546423049283
7022.901405322861222.303862072826223.4989485728962
7122.919551734633522.294536401442323.5445670678247
7222.898356643356622.247026928246223.5496863584671



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')