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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 computationTue, 18 Dec 2012 06:21:45 -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/2012/Dec/18/t1355829717xzspz2cfonz7toc.htm/, Retrieved Thu, 18 Apr 2024 17:55:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201368, Retrieved Thu, 18 Apr 2024 17:55:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-18 11:21:45] [239167cccea8953a8e1721fd6db07280] [Current]
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Dataseries X:
4143
4429
5219
4929
5761
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5657
4248
3830
4736
4839
4411
4570
4104
4801
3953
3828
4440
4026
4109
4785
3224
3552
3940
3913
3681
4309
3830
4143
4087
3818
3380
3430
3458
3970
5260
5024
5634
6549
4676




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201368&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]3 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=201368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201368&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.331578763626859
beta0
gamma0.5487315743831

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.331578763626859 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.5487315743831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201368&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]0.331578763626859[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.5487315743831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201368&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
alpha0.331578763626859
beta0
gamma0.5487315743831







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1357315653.4089209401777.5910790598309
1450404987.087378266752.9126217332951
1561026092.791316558029.20868344197697
1649044891.7122903584112.287709641585
1753695360.820870525918.17912947408604
1855785641.35879942788-63.3587994278796
1946194341.21793697877277.782063021229
2047315149.02547325647-418.025473256471
2150115202.49300693296-191.493006932962
2252994658.57389571434640.426104285655
2341464632.62649483115-486.62649483115
2446255737.51405325704-1112.51405325704
2547365385.99640928179-649.996409281795
2642194469.37064751465-250.370647514646
2751165458.48239616464-342.482396164643
2842054141.9194136553863.0805863446185
2941214626.36287228108-505.36287228108
3051034710.38222308929392.617776910713
3143003686.55846468363613.441535316365
3245784350.45259554648227.547404453525
3338094701.06683313576-892.066833135762
3456574229.986802803111427.01319719689
3542484051.47030043219196.52969956781
3638305153.31250470923-1323.31250470923
3747364901.54256714304-165.542567143045
3848394292.12768180586546.872318194144
3944115511.80316669759-1100.80316669759
4045704092.55106768896477.448932311041
4141044505.89439706453-401.894397064531
4248014953.58648536845-152.586485368453
4339533829.97915724623123.020842753765
4438284189.72047106948-361.720471069481
4544403934.28958859268505.710411407323
4640264777.28388156233-751.283881562334
4741093425.16886790373683.83113209627
4847854131.13632278602653.863677213976
4932244959.60731960524-1735.60731960524
5035524090.8945702875-538.894570287499
5139404346.21207559386-406.212075593863
5239133736.14899303674176.85100696326
5336813727.29151324843-46.2915132484268
5443094384.33607865285-75.3360786528483
5538303387.43165829947442.568341700532
5641433675.33285751985467.667142480148
5740874013.0689222533573.9310777466535
5838184251.84916726029-433.849167260291
5933803531.36575550236-151.365755502357
6034303949.40808091127-519.408080911274
6134583512.42773723679-54.4277372367887
6239703640.09332971917329.906670280832
6352604232.152670768361027.84732923164
6450244311.45134748923712.548652510766
6556344398.374760842131235.62523915787
6665495469.822620927741079.17737907226
6746765045.68931617388-369.689316173875

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5731 & 5653.40892094017 & 77.5910790598309 \tabularnewline
14 & 5040 & 4987.0873782667 & 52.9126217332951 \tabularnewline
15 & 6102 & 6092.79131655802 & 9.20868344197697 \tabularnewline
16 & 4904 & 4891.71229035841 & 12.287709641585 \tabularnewline
17 & 5369 & 5360.82087052591 & 8.17912947408604 \tabularnewline
18 & 5578 & 5641.35879942788 & -63.3587994278796 \tabularnewline
19 & 4619 & 4341.21793697877 & 277.782063021229 \tabularnewline
20 & 4731 & 5149.02547325647 & -418.025473256471 \tabularnewline
21 & 5011 & 5202.49300693296 & -191.493006932962 \tabularnewline
22 & 5299 & 4658.57389571434 & 640.426104285655 \tabularnewline
23 & 4146 & 4632.62649483115 & -486.62649483115 \tabularnewline
24 & 4625 & 5737.51405325704 & -1112.51405325704 \tabularnewline
25 & 4736 & 5385.99640928179 & -649.996409281795 \tabularnewline
26 & 4219 & 4469.37064751465 & -250.370647514646 \tabularnewline
27 & 5116 & 5458.48239616464 & -342.482396164643 \tabularnewline
28 & 4205 & 4141.91941365538 & 63.0805863446185 \tabularnewline
29 & 4121 & 4626.36287228108 & -505.36287228108 \tabularnewline
30 & 5103 & 4710.38222308929 & 392.617776910713 \tabularnewline
31 & 4300 & 3686.55846468363 & 613.441535316365 \tabularnewline
32 & 4578 & 4350.45259554648 & 227.547404453525 \tabularnewline
33 & 3809 & 4701.06683313576 & -892.066833135762 \tabularnewline
34 & 5657 & 4229.98680280311 & 1427.01319719689 \tabularnewline
35 & 4248 & 4051.47030043219 & 196.52969956781 \tabularnewline
36 & 3830 & 5153.31250470923 & -1323.31250470923 \tabularnewline
37 & 4736 & 4901.54256714304 & -165.542567143045 \tabularnewline
38 & 4839 & 4292.12768180586 & 546.872318194144 \tabularnewline
39 & 4411 & 5511.80316669759 & -1100.80316669759 \tabularnewline
40 & 4570 & 4092.55106768896 & 477.448932311041 \tabularnewline
41 & 4104 & 4505.89439706453 & -401.894397064531 \tabularnewline
42 & 4801 & 4953.58648536845 & -152.586485368453 \tabularnewline
43 & 3953 & 3829.97915724623 & 123.020842753765 \tabularnewline
44 & 3828 & 4189.72047106948 & -361.720471069481 \tabularnewline
45 & 4440 & 3934.28958859268 & 505.710411407323 \tabularnewline
46 & 4026 & 4777.28388156233 & -751.283881562334 \tabularnewline
47 & 4109 & 3425.16886790373 & 683.83113209627 \tabularnewline
48 & 4785 & 4131.13632278602 & 653.863677213976 \tabularnewline
49 & 3224 & 4959.60731960524 & -1735.60731960524 \tabularnewline
50 & 3552 & 4090.8945702875 & -538.894570287499 \tabularnewline
51 & 3940 & 4346.21207559386 & -406.212075593863 \tabularnewline
52 & 3913 & 3736.14899303674 & 176.85100696326 \tabularnewline
53 & 3681 & 3727.29151324843 & -46.2915132484268 \tabularnewline
54 & 4309 & 4384.33607865285 & -75.3360786528483 \tabularnewline
55 & 3830 & 3387.43165829947 & 442.568341700532 \tabularnewline
56 & 4143 & 3675.33285751985 & 467.667142480148 \tabularnewline
57 & 4087 & 4013.06892225335 & 73.9310777466535 \tabularnewline
58 & 3818 & 4251.84916726029 & -433.849167260291 \tabularnewline
59 & 3380 & 3531.36575550236 & -151.365755502357 \tabularnewline
60 & 3430 & 3949.40808091127 & -519.408080911274 \tabularnewline
61 & 3458 & 3512.42773723679 & -54.4277372367887 \tabularnewline
62 & 3970 & 3640.09332971917 & 329.906670280832 \tabularnewline
63 & 5260 & 4232.15267076836 & 1027.84732923164 \tabularnewline
64 & 5024 & 4311.45134748923 & 712.548652510766 \tabularnewline
65 & 5634 & 4398.37476084213 & 1235.62523915787 \tabularnewline
66 & 6549 & 5469.82262092774 & 1079.17737907226 \tabularnewline
67 & 4676 & 5045.68931617388 & -369.689316173875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201368&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]5731[/C][C]5653.40892094017[/C][C]77.5910790598309[/C][/ROW]
[ROW][C]14[/C][C]5040[/C][C]4987.0873782667[/C][C]52.9126217332951[/C][/ROW]
[ROW][C]15[/C][C]6102[/C][C]6092.79131655802[/C][C]9.20868344197697[/C][/ROW]
[ROW][C]16[/C][C]4904[/C][C]4891.71229035841[/C][C]12.287709641585[/C][/ROW]
[ROW][C]17[/C][C]5369[/C][C]5360.82087052591[/C][C]8.17912947408604[/C][/ROW]
[ROW][C]18[/C][C]5578[/C][C]5641.35879942788[/C][C]-63.3587994278796[/C][/ROW]
[ROW][C]19[/C][C]4619[/C][C]4341.21793697877[/C][C]277.782063021229[/C][/ROW]
[ROW][C]20[/C][C]4731[/C][C]5149.02547325647[/C][C]-418.025473256471[/C][/ROW]
[ROW][C]21[/C][C]5011[/C][C]5202.49300693296[/C][C]-191.493006932962[/C][/ROW]
[ROW][C]22[/C][C]5299[/C][C]4658.57389571434[/C][C]640.426104285655[/C][/ROW]
[ROW][C]23[/C][C]4146[/C][C]4632.62649483115[/C][C]-486.62649483115[/C][/ROW]
[ROW][C]24[/C][C]4625[/C][C]5737.51405325704[/C][C]-1112.51405325704[/C][/ROW]
[ROW][C]25[/C][C]4736[/C][C]5385.99640928179[/C][C]-649.996409281795[/C][/ROW]
[ROW][C]26[/C][C]4219[/C][C]4469.37064751465[/C][C]-250.370647514646[/C][/ROW]
[ROW][C]27[/C][C]5116[/C][C]5458.48239616464[/C][C]-342.482396164643[/C][/ROW]
[ROW][C]28[/C][C]4205[/C][C]4141.91941365538[/C][C]63.0805863446185[/C][/ROW]
[ROW][C]29[/C][C]4121[/C][C]4626.36287228108[/C][C]-505.36287228108[/C][/ROW]
[ROW][C]30[/C][C]5103[/C][C]4710.38222308929[/C][C]392.617776910713[/C][/ROW]
[ROW][C]31[/C][C]4300[/C][C]3686.55846468363[/C][C]613.441535316365[/C][/ROW]
[ROW][C]32[/C][C]4578[/C][C]4350.45259554648[/C][C]227.547404453525[/C][/ROW]
[ROW][C]33[/C][C]3809[/C][C]4701.06683313576[/C][C]-892.066833135762[/C][/ROW]
[ROW][C]34[/C][C]5657[/C][C]4229.98680280311[/C][C]1427.01319719689[/C][/ROW]
[ROW][C]35[/C][C]4248[/C][C]4051.47030043219[/C][C]196.52969956781[/C][/ROW]
[ROW][C]36[/C][C]3830[/C][C]5153.31250470923[/C][C]-1323.31250470923[/C][/ROW]
[ROW][C]37[/C][C]4736[/C][C]4901.54256714304[/C][C]-165.542567143045[/C][/ROW]
[ROW][C]38[/C][C]4839[/C][C]4292.12768180586[/C][C]546.872318194144[/C][/ROW]
[ROW][C]39[/C][C]4411[/C][C]5511.80316669759[/C][C]-1100.80316669759[/C][/ROW]
[ROW][C]40[/C][C]4570[/C][C]4092.55106768896[/C][C]477.448932311041[/C][/ROW]
[ROW][C]41[/C][C]4104[/C][C]4505.89439706453[/C][C]-401.894397064531[/C][/ROW]
[ROW][C]42[/C][C]4801[/C][C]4953.58648536845[/C][C]-152.586485368453[/C][/ROW]
[ROW][C]43[/C][C]3953[/C][C]3829.97915724623[/C][C]123.020842753765[/C][/ROW]
[ROW][C]44[/C][C]3828[/C][C]4189.72047106948[/C][C]-361.720471069481[/C][/ROW]
[ROW][C]45[/C][C]4440[/C][C]3934.28958859268[/C][C]505.710411407323[/C][/ROW]
[ROW][C]46[/C][C]4026[/C][C]4777.28388156233[/C][C]-751.283881562334[/C][/ROW]
[ROW][C]47[/C][C]4109[/C][C]3425.16886790373[/C][C]683.83113209627[/C][/ROW]
[ROW][C]48[/C][C]4785[/C][C]4131.13632278602[/C][C]653.863677213976[/C][/ROW]
[ROW][C]49[/C][C]3224[/C][C]4959.60731960524[/C][C]-1735.60731960524[/C][/ROW]
[ROW][C]50[/C][C]3552[/C][C]4090.8945702875[/C][C]-538.894570287499[/C][/ROW]
[ROW][C]51[/C][C]3940[/C][C]4346.21207559386[/C][C]-406.212075593863[/C][/ROW]
[ROW][C]52[/C][C]3913[/C][C]3736.14899303674[/C][C]176.85100696326[/C][/ROW]
[ROW][C]53[/C][C]3681[/C][C]3727.29151324843[/C][C]-46.2915132484268[/C][/ROW]
[ROW][C]54[/C][C]4309[/C][C]4384.33607865285[/C][C]-75.3360786528483[/C][/ROW]
[ROW][C]55[/C][C]3830[/C][C]3387.43165829947[/C][C]442.568341700532[/C][/ROW]
[ROW][C]56[/C][C]4143[/C][C]3675.33285751985[/C][C]467.667142480148[/C][/ROW]
[ROW][C]57[/C][C]4087[/C][C]4013.06892225335[/C][C]73.9310777466535[/C][/ROW]
[ROW][C]58[/C][C]3818[/C][C]4251.84916726029[/C][C]-433.849167260291[/C][/ROW]
[ROW][C]59[/C][C]3380[/C][C]3531.36575550236[/C][C]-151.365755502357[/C][/ROW]
[ROW][C]60[/C][C]3430[/C][C]3949.40808091127[/C][C]-519.408080911274[/C][/ROW]
[ROW][C]61[/C][C]3458[/C][C]3512.42773723679[/C][C]-54.4277372367887[/C][/ROW]
[ROW][C]62[/C][C]3970[/C][C]3640.09332971917[/C][C]329.906670280832[/C][/ROW]
[ROW][C]63[/C][C]5260[/C][C]4232.15267076836[/C][C]1027.84732923164[/C][/ROW]
[ROW][C]64[/C][C]5024[/C][C]4311.45134748923[/C][C]712.548652510766[/C][/ROW]
[ROW][C]65[/C][C]5634[/C][C]4398.37476084213[/C][C]1235.62523915787[/C][/ROW]
[ROW][C]66[/C][C]6549[/C][C]5469.82262092774[/C][C]1079.17737907226[/C][/ROW]
[ROW][C]67[/C][C]4676[/C][C]5045.68931617388[/C][C]-369.689316173875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201368&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201368&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
1357315653.4089209401777.5910790598309
1450404987.087378266752.9126217332951
1561026092.791316558029.20868344197697
1649044891.7122903584112.287709641585
1753695360.820870525918.17912947408604
1855785641.35879942788-63.3587994278796
1946194341.21793697877277.782063021229
2047315149.02547325647-418.025473256471
2150115202.49300693296-191.493006932962
2252994658.57389571434640.426104285655
2341464632.62649483115-486.62649483115
2446255737.51405325704-1112.51405325704
2547365385.99640928179-649.996409281795
2642194469.37064751465-250.370647514646
2751165458.48239616464-342.482396164643
2842054141.9194136553863.0805863446185
2941214626.36287228108-505.36287228108
3051034710.38222308929392.617776910713
3143003686.55846468363613.441535316365
3245784350.45259554648227.547404453525
3338094701.06683313576-892.066833135762
3456574229.986802803111427.01319719689
3542484051.47030043219196.52969956781
3638305153.31250470923-1323.31250470923
3747364901.54256714304-165.542567143045
3848394292.12768180586546.872318194144
3944115511.80316669759-1100.80316669759
4045704092.55106768896477.448932311041
4141044505.89439706453-401.894397064531
4248014953.58648536845-152.586485368453
4339533829.97915724623123.020842753765
4438284189.72047106948-361.720471069481
4544403934.28958859268505.710411407323
4640264777.28388156233-751.283881562334
4741093425.16886790373683.83113209627
4847854131.13632278602653.863677213976
4932244959.60731960524-1735.60731960524
5035524090.8945702875-538.894570287499
5139404346.21207559386-406.212075593863
5239133736.14899303674176.85100696326
5336813727.29151324843-46.2915132484268
5443094384.33607865285-75.3360786528483
5538303387.43165829947442.568341700532
5641433675.33285751985467.667142480148
5740874013.0689222533573.9310777466535
5838184251.84916726029-433.849167260291
5933803531.36575550236-151.365755502357
6034303949.40808091127-519.408080911274
6134583512.42773723679-54.4277372367887
6239703640.09332971917329.906670280832
6352604232.152670768361027.84732923164
6450244311.45134748923712.548652510766
6556344398.374760842131235.62523915787
6665495469.822620927741079.17737907226
6746765045.68931617388-369.689316173875







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
685073.468959913553852.392555304746294.54536452237
695111.720507014313825.268862663476398.17215136514
705139.74118985593791.079601237936488.40277847387
714666.723298341183258.59747726766074.84911941475
724999.963317381013534.784633624426465.1420011376
734905.754937754943385.663222530076425.8466529798
745192.435260886143619.346239229756765.52428254252
755931.097909249144306.739784506817555.45603399147
765553.937780775763879.879966727227227.99559482431
775596.451230602423874.127273811027318.77518739382
786200.809455108874431.535575943147970.08333427461
794887.422962924813072.413236543516702.43268930612

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
68 & 5073.46895991355 & 3852.39255530474 & 6294.54536452237 \tabularnewline
69 & 5111.72050701431 & 3825.26886266347 & 6398.17215136514 \tabularnewline
70 & 5139.7411898559 & 3791.07960123793 & 6488.40277847387 \tabularnewline
71 & 4666.72329834118 & 3258.5974772676 & 6074.84911941475 \tabularnewline
72 & 4999.96331738101 & 3534.78463362442 & 6465.1420011376 \tabularnewline
73 & 4905.75493775494 & 3385.66322253007 & 6425.8466529798 \tabularnewline
74 & 5192.43526088614 & 3619.34623922975 & 6765.52428254252 \tabularnewline
75 & 5931.09790924914 & 4306.73978450681 & 7555.45603399147 \tabularnewline
76 & 5553.93778077576 & 3879.87996672722 & 7227.99559482431 \tabularnewline
77 & 5596.45123060242 & 3874.12727381102 & 7318.77518739382 \tabularnewline
78 & 6200.80945510887 & 4431.53557594314 & 7970.08333427461 \tabularnewline
79 & 4887.42296292481 & 3072.41323654351 & 6702.43268930612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201368&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]68[/C][C]5073.46895991355[/C][C]3852.39255530474[/C][C]6294.54536452237[/C][/ROW]
[ROW][C]69[/C][C]5111.72050701431[/C][C]3825.26886266347[/C][C]6398.17215136514[/C][/ROW]
[ROW][C]70[/C][C]5139.7411898559[/C][C]3791.07960123793[/C][C]6488.40277847387[/C][/ROW]
[ROW][C]71[/C][C]4666.72329834118[/C][C]3258.5974772676[/C][C]6074.84911941475[/C][/ROW]
[ROW][C]72[/C][C]4999.96331738101[/C][C]3534.78463362442[/C][C]6465.1420011376[/C][/ROW]
[ROW][C]73[/C][C]4905.75493775494[/C][C]3385.66322253007[/C][C]6425.8466529798[/C][/ROW]
[ROW][C]74[/C][C]5192.43526088614[/C][C]3619.34623922975[/C][C]6765.52428254252[/C][/ROW]
[ROW][C]75[/C][C]5931.09790924914[/C][C]4306.73978450681[/C][C]7555.45603399147[/C][/ROW]
[ROW][C]76[/C][C]5553.93778077576[/C][C]3879.87996672722[/C][C]7227.99559482431[/C][/ROW]
[ROW][C]77[/C][C]5596.45123060242[/C][C]3874.12727381102[/C][C]7318.77518739382[/C][/ROW]
[ROW][C]78[/C][C]6200.80945510887[/C][C]4431.53557594314[/C][C]7970.08333427461[/C][/ROW]
[ROW][C]79[/C][C]4887.42296292481[/C][C]3072.41323654351[/C][C]6702.43268930612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201368&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201368&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
685073.468959913553852.392555304746294.54536452237
695111.720507014313825.268862663476398.17215136514
705139.74118985593791.079601237936488.40277847387
714666.723298341183258.59747726766074.84911941475
724999.963317381013534.784633624426465.1420011376
734905.754937754943385.663222530076425.8466529798
745192.435260886143619.346239229756765.52428254252
755931.097909249144306.739784506817555.45603399147
765553.937780775763879.879966727227227.99559482431
775596.451230602423874.127273811027318.77518739382
786200.809455108874431.535575943147970.08333427461
794887.422962924813072.413236543516702.43268930612



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')