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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 13:22:41 -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/2009/Dec/04/t1259958211ile6fnt35pvjzur.htm/, Retrieved Sat, 27 Apr 2024 19:30:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64132, Retrieved Sat, 27 Apr 2024 19:30:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [WS9] [2009-12-04 20:22:41] [b8ce264f75295a954feffaf60221d1b0] [Current]
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Dataseries X:
14,3
14,2
15,9
15,3
15,5
15,1
15
12,1
15,8
16,9
15,1
13,7
14,8
14,7
16
15,4
15
15,5
15,1
11,7
16,3
16,7
15
14,9
14,6
15,3
17,9
16,4
15,4
17,9
15,9
13,9
17,8
17,9
17,4
16,7
16
16,6
19,1
17,8
17,2
18,6
16,3
15,1
19,2
17,7
19,1
18
17,5
17,8
21,1
17,2
19,4
19,8
17,6
16,2
19,5
19,9
20
17,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64132&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64132&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.200675449151377
beta0.0641812341628278
gamma0.793209546372447

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.200675449151377 \tabularnewline
beta & 0.0641812341628278 \tabularnewline
gamma & 0.793209546372447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64132&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]0.200675449151377[/C][/ROW]
[ROW][C]beta[/C][C]0.0641812341628278[/C][/ROW]
[ROW][C]gamma[/C][C]0.793209546372447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64132&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
alpha0.200675449151377
beta0.0641812341628278
gamma0.793209546372447







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314.814.75227088571220.0477291142878205
1414.714.68022614674420.0197738532557867
151615.98504639602280.0149536039771938
1615.415.38229857849130.0177014215086970
171515.0053857569075-0.00538575690746335
1815.515.46401047192690.035989528073074
1915.115.09207218224650.00792781775353646
2011.712.1474515255814-0.447451525581389
2116.315.71848999244940.581510007550612
2216.716.9362623346833-0.236262334683264
231515.1112839739173-0.111283973917345
2414.913.69653512823361.20346487176636
2514.615.0868015630430-0.486801563042963
2615.314.89582559234660.40417440765343
2717.916.31285026295401.58714973704605
2816.416.03561755542300.364382444577032
2915.415.7310352789970-0.331035278996975
3017.916.20452058163401.69547941836603
3115.916.1731589235234-0.273158923523402
3213.912.70088402734371.19911597265633
3317.817.76095914976370.0390408502363222
3417.918.4833715355693-0.583371535569281
3517.416.56742250256930.83257749743074
3616.716.17104137046970.528958629530273
371616.4232263059147-0.423226305914714
3816.616.9278212185080-0.327821218507950
3919.119.2134443381708-0.113444338170758
4017.817.73377130718730.0662286928127145
4117.216.88701528357380.312984716426204
4218.618.9695030778725-0.369503077872515
4316.317.1702752957141-0.870275295714109
4415.114.33754048407130.76245951592867
4519.218.80635459694140.393645403058638
4617.719.2234752859687-1.52347528596867
4719.117.95550799550971.14449200449032
481817.38029611893660.619703881063401
4917.517.01554176623490.484458233765114
5017.817.8099268127378-0.00992681273780605
5121.120.47871464220390.62128535779609
5217.219.1746546782697-1.97465467826973
5319.418.02913843885121.37086156114875
5419.820.0044238261271-0.204423826127147
5517.617.7805499364049-0.180549936404915
5616.216.00287086896420.19712913103578
5719.520.4239154419124-0.923915441912413
5819.919.28754390029340.612456099706606
592020.2094019111936-0.209401911193577
6017.318.9532929550498-1.6532929550498

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14.8 & 14.7522708857122 & 0.0477291142878205 \tabularnewline
14 & 14.7 & 14.6802261467442 & 0.0197738532557867 \tabularnewline
15 & 16 & 15.9850463960228 & 0.0149536039771938 \tabularnewline
16 & 15.4 & 15.3822985784913 & 0.0177014215086970 \tabularnewline
17 & 15 & 15.0053857569075 & -0.00538575690746335 \tabularnewline
18 & 15.5 & 15.4640104719269 & 0.035989528073074 \tabularnewline
19 & 15.1 & 15.0920721822465 & 0.00792781775353646 \tabularnewline
20 & 11.7 & 12.1474515255814 & -0.447451525581389 \tabularnewline
21 & 16.3 & 15.7184899924494 & 0.581510007550612 \tabularnewline
22 & 16.7 & 16.9362623346833 & -0.236262334683264 \tabularnewline
23 & 15 & 15.1112839739173 & -0.111283973917345 \tabularnewline
24 & 14.9 & 13.6965351282336 & 1.20346487176636 \tabularnewline
25 & 14.6 & 15.0868015630430 & -0.486801563042963 \tabularnewline
26 & 15.3 & 14.8958255923466 & 0.40417440765343 \tabularnewline
27 & 17.9 & 16.3128502629540 & 1.58714973704605 \tabularnewline
28 & 16.4 & 16.0356175554230 & 0.364382444577032 \tabularnewline
29 & 15.4 & 15.7310352789970 & -0.331035278996975 \tabularnewline
30 & 17.9 & 16.2045205816340 & 1.69547941836603 \tabularnewline
31 & 15.9 & 16.1731589235234 & -0.273158923523402 \tabularnewline
32 & 13.9 & 12.7008840273437 & 1.19911597265633 \tabularnewline
33 & 17.8 & 17.7609591497637 & 0.0390408502363222 \tabularnewline
34 & 17.9 & 18.4833715355693 & -0.583371535569281 \tabularnewline
35 & 17.4 & 16.5674225025693 & 0.83257749743074 \tabularnewline
36 & 16.7 & 16.1710413704697 & 0.528958629530273 \tabularnewline
37 & 16 & 16.4232263059147 & -0.423226305914714 \tabularnewline
38 & 16.6 & 16.9278212185080 & -0.327821218507950 \tabularnewline
39 & 19.1 & 19.2134443381708 & -0.113444338170758 \tabularnewline
40 & 17.8 & 17.7337713071873 & 0.0662286928127145 \tabularnewline
41 & 17.2 & 16.8870152835738 & 0.312984716426204 \tabularnewline
42 & 18.6 & 18.9695030778725 & -0.369503077872515 \tabularnewline
43 & 16.3 & 17.1702752957141 & -0.870275295714109 \tabularnewline
44 & 15.1 & 14.3375404840713 & 0.76245951592867 \tabularnewline
45 & 19.2 & 18.8063545969414 & 0.393645403058638 \tabularnewline
46 & 17.7 & 19.2234752859687 & -1.52347528596867 \tabularnewline
47 & 19.1 & 17.9555079955097 & 1.14449200449032 \tabularnewline
48 & 18 & 17.3802961189366 & 0.619703881063401 \tabularnewline
49 & 17.5 & 17.0155417662349 & 0.484458233765114 \tabularnewline
50 & 17.8 & 17.8099268127378 & -0.00992681273780605 \tabularnewline
51 & 21.1 & 20.4787146422039 & 0.62128535779609 \tabularnewline
52 & 17.2 & 19.1746546782697 & -1.97465467826973 \tabularnewline
53 & 19.4 & 18.0291384388512 & 1.37086156114875 \tabularnewline
54 & 19.8 & 20.0044238261271 & -0.204423826127147 \tabularnewline
55 & 17.6 & 17.7805499364049 & -0.180549936404915 \tabularnewline
56 & 16.2 & 16.0028708689642 & 0.19712913103578 \tabularnewline
57 & 19.5 & 20.4239154419124 & -0.923915441912413 \tabularnewline
58 & 19.9 & 19.2875439002934 & 0.612456099706606 \tabularnewline
59 & 20 & 20.2094019111936 & -0.209401911193577 \tabularnewline
60 & 17.3 & 18.9532929550498 & -1.6532929550498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64132&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]14.8[/C][C]14.7522708857122[/C][C]0.0477291142878205[/C][/ROW]
[ROW][C]14[/C][C]14.7[/C][C]14.6802261467442[/C][C]0.0197738532557867[/C][/ROW]
[ROW][C]15[/C][C]16[/C][C]15.9850463960228[/C][C]0.0149536039771938[/C][/ROW]
[ROW][C]16[/C][C]15.4[/C][C]15.3822985784913[/C][C]0.0177014215086970[/C][/ROW]
[ROW][C]17[/C][C]15[/C][C]15.0053857569075[/C][C]-0.00538575690746335[/C][/ROW]
[ROW][C]18[/C][C]15.5[/C][C]15.4640104719269[/C][C]0.035989528073074[/C][/ROW]
[ROW][C]19[/C][C]15.1[/C][C]15.0920721822465[/C][C]0.00792781775353646[/C][/ROW]
[ROW][C]20[/C][C]11.7[/C][C]12.1474515255814[/C][C]-0.447451525581389[/C][/ROW]
[ROW][C]21[/C][C]16.3[/C][C]15.7184899924494[/C][C]0.581510007550612[/C][/ROW]
[ROW][C]22[/C][C]16.7[/C][C]16.9362623346833[/C][C]-0.236262334683264[/C][/ROW]
[ROW][C]23[/C][C]15[/C][C]15.1112839739173[/C][C]-0.111283973917345[/C][/ROW]
[ROW][C]24[/C][C]14.9[/C][C]13.6965351282336[/C][C]1.20346487176636[/C][/ROW]
[ROW][C]25[/C][C]14.6[/C][C]15.0868015630430[/C][C]-0.486801563042963[/C][/ROW]
[ROW][C]26[/C][C]15.3[/C][C]14.8958255923466[/C][C]0.40417440765343[/C][/ROW]
[ROW][C]27[/C][C]17.9[/C][C]16.3128502629540[/C][C]1.58714973704605[/C][/ROW]
[ROW][C]28[/C][C]16.4[/C][C]16.0356175554230[/C][C]0.364382444577032[/C][/ROW]
[ROW][C]29[/C][C]15.4[/C][C]15.7310352789970[/C][C]-0.331035278996975[/C][/ROW]
[ROW][C]30[/C][C]17.9[/C][C]16.2045205816340[/C][C]1.69547941836603[/C][/ROW]
[ROW][C]31[/C][C]15.9[/C][C]16.1731589235234[/C][C]-0.273158923523402[/C][/ROW]
[ROW][C]32[/C][C]13.9[/C][C]12.7008840273437[/C][C]1.19911597265633[/C][/ROW]
[ROW][C]33[/C][C]17.8[/C][C]17.7609591497637[/C][C]0.0390408502363222[/C][/ROW]
[ROW][C]34[/C][C]17.9[/C][C]18.4833715355693[/C][C]-0.583371535569281[/C][/ROW]
[ROW][C]35[/C][C]17.4[/C][C]16.5674225025693[/C][C]0.83257749743074[/C][/ROW]
[ROW][C]36[/C][C]16.7[/C][C]16.1710413704697[/C][C]0.528958629530273[/C][/ROW]
[ROW][C]37[/C][C]16[/C][C]16.4232263059147[/C][C]-0.423226305914714[/C][/ROW]
[ROW][C]38[/C][C]16.6[/C][C]16.9278212185080[/C][C]-0.327821218507950[/C][/ROW]
[ROW][C]39[/C][C]19.1[/C][C]19.2134443381708[/C][C]-0.113444338170758[/C][/ROW]
[ROW][C]40[/C][C]17.8[/C][C]17.7337713071873[/C][C]0.0662286928127145[/C][/ROW]
[ROW][C]41[/C][C]17.2[/C][C]16.8870152835738[/C][C]0.312984716426204[/C][/ROW]
[ROW][C]42[/C][C]18.6[/C][C]18.9695030778725[/C][C]-0.369503077872515[/C][/ROW]
[ROW][C]43[/C][C]16.3[/C][C]17.1702752957141[/C][C]-0.870275295714109[/C][/ROW]
[ROW][C]44[/C][C]15.1[/C][C]14.3375404840713[/C][C]0.76245951592867[/C][/ROW]
[ROW][C]45[/C][C]19.2[/C][C]18.8063545969414[/C][C]0.393645403058638[/C][/ROW]
[ROW][C]46[/C][C]17.7[/C][C]19.2234752859687[/C][C]-1.52347528596867[/C][/ROW]
[ROW][C]47[/C][C]19.1[/C][C]17.9555079955097[/C][C]1.14449200449032[/C][/ROW]
[ROW][C]48[/C][C]18[/C][C]17.3802961189366[/C][C]0.619703881063401[/C][/ROW]
[ROW][C]49[/C][C]17.5[/C][C]17.0155417662349[/C][C]0.484458233765114[/C][/ROW]
[ROW][C]50[/C][C]17.8[/C][C]17.8099268127378[/C][C]-0.00992681273780605[/C][/ROW]
[ROW][C]51[/C][C]21.1[/C][C]20.4787146422039[/C][C]0.62128535779609[/C][/ROW]
[ROW][C]52[/C][C]17.2[/C][C]19.1746546782697[/C][C]-1.97465467826973[/C][/ROW]
[ROW][C]53[/C][C]19.4[/C][C]18.0291384388512[/C][C]1.37086156114875[/C][/ROW]
[ROW][C]54[/C][C]19.8[/C][C]20.0044238261271[/C][C]-0.204423826127147[/C][/ROW]
[ROW][C]55[/C][C]17.6[/C][C]17.7805499364049[/C][C]-0.180549936404915[/C][/ROW]
[ROW][C]56[/C][C]16.2[/C][C]16.0028708689642[/C][C]0.19712913103578[/C][/ROW]
[ROW][C]57[/C][C]19.5[/C][C]20.4239154419124[/C][C]-0.923915441912413[/C][/ROW]
[ROW][C]58[/C][C]19.9[/C][C]19.2875439002934[/C][C]0.612456099706606[/C][/ROW]
[ROW][C]59[/C][C]20[/C][C]20.2094019111936[/C][C]-0.209401911193577[/C][/ROW]
[ROW][C]60[/C][C]17.3[/C][C]18.9532929550498[/C][C]-1.6532929550498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64132&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
1314.814.75227088571220.0477291142878205
1414.714.68022614674420.0197738532557867
151615.98504639602280.0149536039771938
1615.415.38229857849130.0177014215086970
171515.0053857569075-0.00538575690746335
1815.515.46401047192690.035989528073074
1915.115.09207218224650.00792781775353646
2011.712.1474515255814-0.447451525581389
2116.315.71848999244940.581510007550612
2216.716.9362623346833-0.236262334683264
231515.1112839739173-0.111283973917345
2414.913.69653512823361.20346487176636
2514.615.0868015630430-0.486801563042963
2615.314.89582559234660.40417440765343
2717.916.31285026295401.58714973704605
2816.416.03561755542300.364382444577032
2915.415.7310352789970-0.331035278996975
3017.916.20452058163401.69547941836603
3115.916.1731589235234-0.273158923523402
3213.912.70088402734371.19911597265633
3317.817.76095914976370.0390408502363222
3417.918.4833715355693-0.583371535569281
3517.416.56742250256930.83257749743074
3616.716.17104137046970.528958629530273
371616.4232263059147-0.423226305914714
3816.616.9278212185080-0.327821218507950
3919.119.2134443381708-0.113444338170758
4017.817.73377130718730.0662286928127145
4117.216.88701528357380.312984716426204
4218.618.9695030778725-0.369503077872515
4316.317.1702752957141-0.870275295714109
4415.114.33754048407130.76245951592867
4519.218.80635459694140.393645403058638
4617.719.2234752859687-1.52347528596867
4719.117.95550799550971.14449200449032
481817.38029611893660.619703881063401
4917.517.01554176623490.484458233765114
5017.817.8099268127378-0.00992681273780605
5121.120.47871464220390.62128535779609
5217.219.1746546782697-1.97465467826973
5319.418.02913843885121.37086156114875
5419.820.0044238261271-0.204423826127147
5517.617.7805499364049-0.180549936404915
5616.216.00287086896420.19712913103578
5719.520.4239154419124-0.923915441912413
5819.919.28754390029340.612456099706606
592020.2094019111936-0.209401911193577
6017.318.9532929550498-1.6532929550498







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6117.996883483613716.752990730912219.2407762363153
6218.362135335057317.076843176999519.6474274931151
6321.491332203979520.132946536522422.8497178714365
6418.280409399825216.916625695592619.6441931040579
6519.682664107958018.245435647335821.1198925685803
6620.368655531431218.862457351780421.8748537110819
6718.114656237576216.612792807439319.616519667713
6816.548051866519815.037860049033518.0582436840061
6920.268787522614518.564599328217921.9729757170111
7020.270448277684318.500515280205422.0403812751631
7120.527128811077418.676686918559022.3775707035958
7218.3039957835319-0.15000295718634536.7579945242501

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 17.9968834836137 & 16.7529907309122 & 19.2407762363153 \tabularnewline
62 & 18.3621353350573 & 17.0768431769995 & 19.6474274931151 \tabularnewline
63 & 21.4913322039795 & 20.1329465365224 & 22.8497178714365 \tabularnewline
64 & 18.2804093998252 & 16.9166256955926 & 19.6441931040579 \tabularnewline
65 & 19.6826641079580 & 18.2454356473358 & 21.1198925685803 \tabularnewline
66 & 20.3686555314312 & 18.8624573517804 & 21.8748537110819 \tabularnewline
67 & 18.1146562375762 & 16.6127928074393 & 19.616519667713 \tabularnewline
68 & 16.5480518665198 & 15.0378600490335 & 18.0582436840061 \tabularnewline
69 & 20.2687875226145 & 18.5645993282179 & 21.9729757170111 \tabularnewline
70 & 20.2704482776843 & 18.5005152802054 & 22.0403812751631 \tabularnewline
71 & 20.5271288110774 & 18.6766869185590 & 22.3775707035958 \tabularnewline
72 & 18.3039957835319 & -0.150002957186345 & 36.7579945242501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64132&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]17.9968834836137[/C][C]16.7529907309122[/C][C]19.2407762363153[/C][/ROW]
[ROW][C]62[/C][C]18.3621353350573[/C][C]17.0768431769995[/C][C]19.6474274931151[/C][/ROW]
[ROW][C]63[/C][C]21.4913322039795[/C][C]20.1329465365224[/C][C]22.8497178714365[/C][/ROW]
[ROW][C]64[/C][C]18.2804093998252[/C][C]16.9166256955926[/C][C]19.6441931040579[/C][/ROW]
[ROW][C]65[/C][C]19.6826641079580[/C][C]18.2454356473358[/C][C]21.1198925685803[/C][/ROW]
[ROW][C]66[/C][C]20.3686555314312[/C][C]18.8624573517804[/C][C]21.8748537110819[/C][/ROW]
[ROW][C]67[/C][C]18.1146562375762[/C][C]16.6127928074393[/C][C]19.616519667713[/C][/ROW]
[ROW][C]68[/C][C]16.5480518665198[/C][C]15.0378600490335[/C][C]18.0582436840061[/C][/ROW]
[ROW][C]69[/C][C]20.2687875226145[/C][C]18.5645993282179[/C][C]21.9729757170111[/C][/ROW]
[ROW][C]70[/C][C]20.2704482776843[/C][C]18.5005152802054[/C][C]22.0403812751631[/C][/ROW]
[ROW][C]71[/C][C]20.5271288110774[/C][C]18.6766869185590[/C][C]22.3775707035958[/C][/ROW]
[ROW][C]72[/C][C]18.3039957835319[/C][C]-0.150002957186345[/C][C]36.7579945242501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64132&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64132&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
6117.996883483613716.752990730912219.2407762363153
6218.362135335057317.076843176999519.6474274931151
6321.491332203979520.132946536522422.8497178714365
6418.280409399825216.916625695592619.6441931040579
6519.682664107958018.245435647335821.1198925685803
6620.368655531431218.862457351780421.8748537110819
6718.114656237576216.612792807439319.616519667713
6816.548051866519815.037860049033518.0582436840061
6920.268787522614518.564599328217921.9729757170111
7020.270448277684318.500515280205422.0403812751631
7120.527128811077418.676686918559022.3775707035958
7218.3039957835319-0.15000295718634536.7579945242501



Parameters (Session):
par1 = 0.2 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')