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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 04:59:11 -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/17/t135573842920oyzkqeqlt2j1n.htm/, Retrieved Thu, 25 Apr 2024 08:03:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200728, Retrieved Thu, 25 Apr 2024 08:03:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-17 09:59:11] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
79,49
79,69
79,86
79,87
79,83
79,83
79,83
79,37
79,53
79,78
79,94
79,97
79,97
79,98
80,25
80,38
80,13
80,15
80,15
80,18
80,47
80,83
80,62
80,66
80,66
80,67
80,8
81,04
81,24
81,26
81,26
81,47
81,94
82,83
82,29
82,32
82,32
82,3
82,54
82,54
82,62
82,63
82,63
82,63
82,71
83,25
83,14
83,34
83,34
83,37
83,33
83,26
83,66
83,64
83,64
83,71
83,87
84,17
84,35
84,44
84,44
84,45
84,67
84,95
84,89
84,93
84,93
84,93
85,45
85,77
85,79
85,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200728&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200728&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.74609464521476
beta0.0285617541446278
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.74609464521476 \tabularnewline
beta & 0.0285617541446278 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200728&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]0.74609464521476[/C][/ROW]
[ROW][C]beta[/C][C]0.0285617541446278[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200728&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
alpha0.74609464521476
beta0.0285617541446278
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1379.9779.7887141606670.181285839333043
1479.9879.93682918869520.043170811304833
1580.2580.21688788926570.0331121107342511
1680.3880.34012911994690.0398708800531153
1780.1380.10025080562560.0297491943743893
1880.1580.13840112217150.0115988778284617
1980.1580.3970072819908-0.247007281990776
2080.1879.7662042901530.413795709847051
2180.4780.2645462853610.205453714638978
2280.8380.69395698511080.136043014889154
2380.6280.9875078084567-0.367507808456736
2480.6680.7738861281105-0.113886128110536
2580.6680.7624260594944-0.102426059494391
2680.6780.66496923033150.00503076966855076
2780.880.9167007550875-0.116700755087535
2881.0480.92804857500360.111951424996391
2981.2480.73618382368840.503816176311545
3081.2681.13236836212920.127631637870806
3181.2681.4254459503386-0.165445950338608
3281.4781.03179658168360.438203418316363
3381.9481.51067200885710.429327991142856
3482.8382.1117435996780.718256400321962
3582.2982.7428702284517-0.452870228451644
3682.3282.5610074910535-0.241007491053509
3782.3282.4849281794536-0.164928179453639
3882.382.392677025697-0.0926770256970144
3982.5482.5674329709407-0.02743297094068
4082.5482.7311362521813-0.191136252181266
4182.6282.4265835538320.193416446168044
4282.6382.50562147888730.124378521112689
4382.6382.7349406665972-0.104940666597244
4482.6382.54962751995580.0803724800442325
4582.7182.7657557965501-0.0557557965501445
4683.2583.07514445245210.174855547547907
4783.1482.98555847423850.154441525761541
4883.3483.3085044813670.0314955186330366
4983.3483.4581333228188-0.118133322818835
5083.3783.4223781505626-0.0523781505625465
5183.3383.650684738237-0.320684738236992
5283.2683.552892915403-0.292892915402973
5383.6683.26474313651410.395256863485926
5483.6483.47538409757220.164615902427798
5583.6483.677707978853-0.0377079788530068
5683.7183.59057982052010.119420179479846
5783.8783.80532508958760.0646749104124495
5884.1784.2737382826334-0.103738282633401
5984.3583.96773114717050.382268852829498
6084.4484.43568997339080.00431002660918978
6184.4484.5314911880881-0.0914911880880709
6284.4584.5371265735377-0.0871265735377449
6384.6784.6769727990631-0.00697279906312076
6484.9584.8322489751660.117751024833979
6584.8985.0452944866619-0.155294486661901
6684.9384.7911691112160.138830888784
6784.9384.92949537865350.000504621346522072
6884.9384.91742409912190.0125759008780619
6985.4585.04490218498970.405097815010279
7085.7785.74292261053550.0270773894644947
7185.7985.6700375901170.119962409883001
7285.985.85666378497330.0433362150266703

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 79.97 & 79.788714160667 & 0.181285839333043 \tabularnewline
14 & 79.98 & 79.9368291886952 & 0.043170811304833 \tabularnewline
15 & 80.25 & 80.2168878892657 & 0.0331121107342511 \tabularnewline
16 & 80.38 & 80.3401291199469 & 0.0398708800531153 \tabularnewline
17 & 80.13 & 80.1002508056256 & 0.0297491943743893 \tabularnewline
18 & 80.15 & 80.1384011221715 & 0.0115988778284617 \tabularnewline
19 & 80.15 & 80.3970072819908 & -0.247007281990776 \tabularnewline
20 & 80.18 & 79.766204290153 & 0.413795709847051 \tabularnewline
21 & 80.47 & 80.264546285361 & 0.205453714638978 \tabularnewline
22 & 80.83 & 80.6939569851108 & 0.136043014889154 \tabularnewline
23 & 80.62 & 80.9875078084567 & -0.367507808456736 \tabularnewline
24 & 80.66 & 80.7738861281105 & -0.113886128110536 \tabularnewline
25 & 80.66 & 80.7624260594944 & -0.102426059494391 \tabularnewline
26 & 80.67 & 80.6649692303315 & 0.00503076966855076 \tabularnewline
27 & 80.8 & 80.9167007550875 & -0.116700755087535 \tabularnewline
28 & 81.04 & 80.9280485750036 & 0.111951424996391 \tabularnewline
29 & 81.24 & 80.7361838236884 & 0.503816176311545 \tabularnewline
30 & 81.26 & 81.1323683621292 & 0.127631637870806 \tabularnewline
31 & 81.26 & 81.4254459503386 & -0.165445950338608 \tabularnewline
32 & 81.47 & 81.0317965816836 & 0.438203418316363 \tabularnewline
33 & 81.94 & 81.5106720088571 & 0.429327991142856 \tabularnewline
34 & 82.83 & 82.111743599678 & 0.718256400321962 \tabularnewline
35 & 82.29 & 82.7428702284517 & -0.452870228451644 \tabularnewline
36 & 82.32 & 82.5610074910535 & -0.241007491053509 \tabularnewline
37 & 82.32 & 82.4849281794536 & -0.164928179453639 \tabularnewline
38 & 82.3 & 82.392677025697 & -0.0926770256970144 \tabularnewline
39 & 82.54 & 82.5674329709407 & -0.02743297094068 \tabularnewline
40 & 82.54 & 82.7311362521813 & -0.191136252181266 \tabularnewline
41 & 82.62 & 82.426583553832 & 0.193416446168044 \tabularnewline
42 & 82.63 & 82.5056214788873 & 0.124378521112689 \tabularnewline
43 & 82.63 & 82.7349406665972 & -0.104940666597244 \tabularnewline
44 & 82.63 & 82.5496275199558 & 0.0803724800442325 \tabularnewline
45 & 82.71 & 82.7657557965501 & -0.0557557965501445 \tabularnewline
46 & 83.25 & 83.0751444524521 & 0.174855547547907 \tabularnewline
47 & 83.14 & 82.9855584742385 & 0.154441525761541 \tabularnewline
48 & 83.34 & 83.308504481367 & 0.0314955186330366 \tabularnewline
49 & 83.34 & 83.4581333228188 & -0.118133322818835 \tabularnewline
50 & 83.37 & 83.4223781505626 & -0.0523781505625465 \tabularnewline
51 & 83.33 & 83.650684738237 & -0.320684738236992 \tabularnewline
52 & 83.26 & 83.552892915403 & -0.292892915402973 \tabularnewline
53 & 83.66 & 83.2647431365141 & 0.395256863485926 \tabularnewline
54 & 83.64 & 83.4753840975722 & 0.164615902427798 \tabularnewline
55 & 83.64 & 83.677707978853 & -0.0377079788530068 \tabularnewline
56 & 83.71 & 83.5905798205201 & 0.119420179479846 \tabularnewline
57 & 83.87 & 83.8053250895876 & 0.0646749104124495 \tabularnewline
58 & 84.17 & 84.2737382826334 & -0.103738282633401 \tabularnewline
59 & 84.35 & 83.9677311471705 & 0.382268852829498 \tabularnewline
60 & 84.44 & 84.4356899733908 & 0.00431002660918978 \tabularnewline
61 & 84.44 & 84.5314911880881 & -0.0914911880880709 \tabularnewline
62 & 84.45 & 84.5371265735377 & -0.0871265735377449 \tabularnewline
63 & 84.67 & 84.6769727990631 & -0.00697279906312076 \tabularnewline
64 & 84.95 & 84.832248975166 & 0.117751024833979 \tabularnewline
65 & 84.89 & 85.0452944866619 & -0.155294486661901 \tabularnewline
66 & 84.93 & 84.791169111216 & 0.138830888784 \tabularnewline
67 & 84.93 & 84.9294953786535 & 0.000504621346522072 \tabularnewline
68 & 84.93 & 84.9174240991219 & 0.0125759008780619 \tabularnewline
69 & 85.45 & 85.0449021849897 & 0.405097815010279 \tabularnewline
70 & 85.77 & 85.7429226105355 & 0.0270773894644947 \tabularnewline
71 & 85.79 & 85.670037590117 & 0.119962409883001 \tabularnewline
72 & 85.9 & 85.8566637849733 & 0.0433362150266703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200728&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]79.97[/C][C]79.788714160667[/C][C]0.181285839333043[/C][/ROW]
[ROW][C]14[/C][C]79.98[/C][C]79.9368291886952[/C][C]0.043170811304833[/C][/ROW]
[ROW][C]15[/C][C]80.25[/C][C]80.2168878892657[/C][C]0.0331121107342511[/C][/ROW]
[ROW][C]16[/C][C]80.38[/C][C]80.3401291199469[/C][C]0.0398708800531153[/C][/ROW]
[ROW][C]17[/C][C]80.13[/C][C]80.1002508056256[/C][C]0.0297491943743893[/C][/ROW]
[ROW][C]18[/C][C]80.15[/C][C]80.1384011221715[/C][C]0.0115988778284617[/C][/ROW]
[ROW][C]19[/C][C]80.15[/C][C]80.3970072819908[/C][C]-0.247007281990776[/C][/ROW]
[ROW][C]20[/C][C]80.18[/C][C]79.766204290153[/C][C]0.413795709847051[/C][/ROW]
[ROW][C]21[/C][C]80.47[/C][C]80.264546285361[/C][C]0.205453714638978[/C][/ROW]
[ROW][C]22[/C][C]80.83[/C][C]80.6939569851108[/C][C]0.136043014889154[/C][/ROW]
[ROW][C]23[/C][C]80.62[/C][C]80.9875078084567[/C][C]-0.367507808456736[/C][/ROW]
[ROW][C]24[/C][C]80.66[/C][C]80.7738861281105[/C][C]-0.113886128110536[/C][/ROW]
[ROW][C]25[/C][C]80.66[/C][C]80.7624260594944[/C][C]-0.102426059494391[/C][/ROW]
[ROW][C]26[/C][C]80.67[/C][C]80.6649692303315[/C][C]0.00503076966855076[/C][/ROW]
[ROW][C]27[/C][C]80.8[/C][C]80.9167007550875[/C][C]-0.116700755087535[/C][/ROW]
[ROW][C]28[/C][C]81.04[/C][C]80.9280485750036[/C][C]0.111951424996391[/C][/ROW]
[ROW][C]29[/C][C]81.24[/C][C]80.7361838236884[/C][C]0.503816176311545[/C][/ROW]
[ROW][C]30[/C][C]81.26[/C][C]81.1323683621292[/C][C]0.127631637870806[/C][/ROW]
[ROW][C]31[/C][C]81.26[/C][C]81.4254459503386[/C][C]-0.165445950338608[/C][/ROW]
[ROW][C]32[/C][C]81.47[/C][C]81.0317965816836[/C][C]0.438203418316363[/C][/ROW]
[ROW][C]33[/C][C]81.94[/C][C]81.5106720088571[/C][C]0.429327991142856[/C][/ROW]
[ROW][C]34[/C][C]82.83[/C][C]82.111743599678[/C][C]0.718256400321962[/C][/ROW]
[ROW][C]35[/C][C]82.29[/C][C]82.7428702284517[/C][C]-0.452870228451644[/C][/ROW]
[ROW][C]36[/C][C]82.32[/C][C]82.5610074910535[/C][C]-0.241007491053509[/C][/ROW]
[ROW][C]37[/C][C]82.32[/C][C]82.4849281794536[/C][C]-0.164928179453639[/C][/ROW]
[ROW][C]38[/C][C]82.3[/C][C]82.392677025697[/C][C]-0.0926770256970144[/C][/ROW]
[ROW][C]39[/C][C]82.54[/C][C]82.5674329709407[/C][C]-0.02743297094068[/C][/ROW]
[ROW][C]40[/C][C]82.54[/C][C]82.7311362521813[/C][C]-0.191136252181266[/C][/ROW]
[ROW][C]41[/C][C]82.62[/C][C]82.426583553832[/C][C]0.193416446168044[/C][/ROW]
[ROW][C]42[/C][C]82.63[/C][C]82.5056214788873[/C][C]0.124378521112689[/C][/ROW]
[ROW][C]43[/C][C]82.63[/C][C]82.7349406665972[/C][C]-0.104940666597244[/C][/ROW]
[ROW][C]44[/C][C]82.63[/C][C]82.5496275199558[/C][C]0.0803724800442325[/C][/ROW]
[ROW][C]45[/C][C]82.71[/C][C]82.7657557965501[/C][C]-0.0557557965501445[/C][/ROW]
[ROW][C]46[/C][C]83.25[/C][C]83.0751444524521[/C][C]0.174855547547907[/C][/ROW]
[ROW][C]47[/C][C]83.14[/C][C]82.9855584742385[/C][C]0.154441525761541[/C][/ROW]
[ROW][C]48[/C][C]83.34[/C][C]83.308504481367[/C][C]0.0314955186330366[/C][/ROW]
[ROW][C]49[/C][C]83.34[/C][C]83.4581333228188[/C][C]-0.118133322818835[/C][/ROW]
[ROW][C]50[/C][C]83.37[/C][C]83.4223781505626[/C][C]-0.0523781505625465[/C][/ROW]
[ROW][C]51[/C][C]83.33[/C][C]83.650684738237[/C][C]-0.320684738236992[/C][/ROW]
[ROW][C]52[/C][C]83.26[/C][C]83.552892915403[/C][C]-0.292892915402973[/C][/ROW]
[ROW][C]53[/C][C]83.66[/C][C]83.2647431365141[/C][C]0.395256863485926[/C][/ROW]
[ROW][C]54[/C][C]83.64[/C][C]83.4753840975722[/C][C]0.164615902427798[/C][/ROW]
[ROW][C]55[/C][C]83.64[/C][C]83.677707978853[/C][C]-0.0377079788530068[/C][/ROW]
[ROW][C]56[/C][C]83.71[/C][C]83.5905798205201[/C][C]0.119420179479846[/C][/ROW]
[ROW][C]57[/C][C]83.87[/C][C]83.8053250895876[/C][C]0.0646749104124495[/C][/ROW]
[ROW][C]58[/C][C]84.17[/C][C]84.2737382826334[/C][C]-0.103738282633401[/C][/ROW]
[ROW][C]59[/C][C]84.35[/C][C]83.9677311471705[/C][C]0.382268852829498[/C][/ROW]
[ROW][C]60[/C][C]84.44[/C][C]84.4356899733908[/C][C]0.00431002660918978[/C][/ROW]
[ROW][C]61[/C][C]84.44[/C][C]84.5314911880881[/C][C]-0.0914911880880709[/C][/ROW]
[ROW][C]62[/C][C]84.45[/C][C]84.5371265735377[/C][C]-0.0871265735377449[/C][/ROW]
[ROW][C]63[/C][C]84.67[/C][C]84.6769727990631[/C][C]-0.00697279906312076[/C][/ROW]
[ROW][C]64[/C][C]84.95[/C][C]84.832248975166[/C][C]0.117751024833979[/C][/ROW]
[ROW][C]65[/C][C]84.89[/C][C]85.0452944866619[/C][C]-0.155294486661901[/C][/ROW]
[ROW][C]66[/C][C]84.93[/C][C]84.791169111216[/C][C]0.138830888784[/C][/ROW]
[ROW][C]67[/C][C]84.93[/C][C]84.9294953786535[/C][C]0.000504621346522072[/C][/ROW]
[ROW][C]68[/C][C]84.93[/C][C]84.9174240991219[/C][C]0.0125759008780619[/C][/ROW]
[ROW][C]69[/C][C]85.45[/C][C]85.0449021849897[/C][C]0.405097815010279[/C][/ROW]
[ROW][C]70[/C][C]85.77[/C][C]85.7429226105355[/C][C]0.0270773894644947[/C][/ROW]
[ROW][C]71[/C][C]85.79[/C][C]85.670037590117[/C][C]0.119962409883001[/C][/ROW]
[ROW][C]72[/C][C]85.9[/C][C]85.8566637849733[/C][C]0.0433362150266703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200728&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200728&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
1379.9779.7887141606670.181285839333043
1479.9879.93682918869520.043170811304833
1580.2580.21688788926570.0331121107342511
1680.3880.34012911994690.0398708800531153
1780.1380.10025080562560.0297491943743893
1880.1580.13840112217150.0115988778284617
1980.1580.3970072819908-0.247007281990776
2080.1879.7662042901530.413795709847051
2180.4780.2645462853610.205453714638978
2280.8380.69395698511080.136043014889154
2380.6280.9875078084567-0.367507808456736
2480.6680.7738861281105-0.113886128110536
2580.6680.7624260594944-0.102426059494391
2680.6780.66496923033150.00503076966855076
2780.880.9167007550875-0.116700755087535
2881.0480.92804857500360.111951424996391
2981.2480.73618382368840.503816176311545
3081.2681.13236836212920.127631637870806
3181.2681.4254459503386-0.165445950338608
3281.4781.03179658168360.438203418316363
3381.9481.51067200885710.429327991142856
3482.8382.1117435996780.718256400321962
3582.2982.7428702284517-0.452870228451644
3682.3282.5610074910535-0.241007491053509
3782.3282.4849281794536-0.164928179453639
3882.382.392677025697-0.0926770256970144
3982.5482.5674329709407-0.02743297094068
4082.5482.7311362521813-0.191136252181266
4182.6282.4265835538320.193416446168044
4282.6382.50562147888730.124378521112689
4382.6382.7349406665972-0.104940666597244
4482.6382.54962751995580.0803724800442325
4582.7182.7657557965501-0.0557557965501445
4683.2583.07514445245210.174855547547907
4783.1482.98555847423850.154441525761541
4883.3483.3085044813670.0314955186330366
4983.3483.4581333228188-0.118133322818835
5083.3783.4223781505626-0.0523781505625465
5183.3383.650684738237-0.320684738236992
5283.2683.552892915403-0.292892915402973
5383.6683.26474313651410.395256863485926
5483.6483.47538409757220.164615902427798
5583.6483.677707978853-0.0377079788530068
5683.7183.59057982052010.119420179479846
5783.8783.80532508958760.0646749104124495
5884.1784.2737382826334-0.103738282633401
5984.3583.96773114717050.382268852829498
6084.4484.43568997339080.00431002660918978
6184.4484.5314911880881-0.0914911880880709
6284.4584.5371265735377-0.0871265735377449
6384.6784.6769727990631-0.00697279906312076
6484.9584.8322489751660.117751024833979
6584.8985.0452944866619-0.155294486661901
6684.9384.7911691112160.138830888784
6784.9384.92949537865350.000504621346522072
6884.9384.91742409912190.0125759008780619
6985.4585.04490218498970.405097815010279
7085.7785.74292261053550.0270773894644947
7185.7985.6700375901170.119962409883001
7285.985.85666378497330.0433362150266703







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7385.968086867596285.534380513066586.4017932221259
7486.0560090713185.509339661079186.6026784815409
7586.298906449901585.653445512330886.9443673874721
7686.508280625507685.772767104084987.2437941469302
7786.576192531302585.757216491429887.3951685711753
7886.525599541500785.628154762006987.4230443209945
7986.536573292178885.563179996475987.5099665878818
8086.538335179961285.491388413323987.5852819465985
8186.770911213074285.649667224162987.8921552019854
8287.077936093646285.88273678448988.2731354028034
8387.009365201326985.745894068344388.2728363343094
8487.087662000602382.5261298344291.6491941667845

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 85.9680868675962 & 85.5343805130665 & 86.4017932221259 \tabularnewline
74 & 86.05600907131 & 85.5093396610791 & 86.6026784815409 \tabularnewline
75 & 86.2989064499015 & 85.6534455123308 & 86.9443673874721 \tabularnewline
76 & 86.5082806255076 & 85.7727671040849 & 87.2437941469302 \tabularnewline
77 & 86.5761925313025 & 85.7572164914298 & 87.3951685711753 \tabularnewline
78 & 86.5255995415007 & 85.6281547620069 & 87.4230443209945 \tabularnewline
79 & 86.5365732921788 & 85.5631799964759 & 87.5099665878818 \tabularnewline
80 & 86.5383351799612 & 85.4913884133239 & 87.5852819465985 \tabularnewline
81 & 86.7709112130742 & 85.6496672241629 & 87.8921552019854 \tabularnewline
82 & 87.0779360936462 & 85.882736784489 & 88.2731354028034 \tabularnewline
83 & 87.0093652013269 & 85.7458940683443 & 88.2728363343094 \tabularnewline
84 & 87.0876620006023 & 82.52612983442 & 91.6491941667845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200728&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]85.9680868675962[/C][C]85.5343805130665[/C][C]86.4017932221259[/C][/ROW]
[ROW][C]74[/C][C]86.05600907131[/C][C]85.5093396610791[/C][C]86.6026784815409[/C][/ROW]
[ROW][C]75[/C][C]86.2989064499015[/C][C]85.6534455123308[/C][C]86.9443673874721[/C][/ROW]
[ROW][C]76[/C][C]86.5082806255076[/C][C]85.7727671040849[/C][C]87.2437941469302[/C][/ROW]
[ROW][C]77[/C][C]86.5761925313025[/C][C]85.7572164914298[/C][C]87.3951685711753[/C][/ROW]
[ROW][C]78[/C][C]86.5255995415007[/C][C]85.6281547620069[/C][C]87.4230443209945[/C][/ROW]
[ROW][C]79[/C][C]86.5365732921788[/C][C]85.5631799964759[/C][C]87.5099665878818[/C][/ROW]
[ROW][C]80[/C][C]86.5383351799612[/C][C]85.4913884133239[/C][C]87.5852819465985[/C][/ROW]
[ROW][C]81[/C][C]86.7709112130742[/C][C]85.6496672241629[/C][C]87.8921552019854[/C][/ROW]
[ROW][C]82[/C][C]87.0779360936462[/C][C]85.882736784489[/C][C]88.2731354028034[/C][/ROW]
[ROW][C]83[/C][C]87.0093652013269[/C][C]85.7458940683443[/C][C]88.2728363343094[/C][/ROW]
[ROW][C]84[/C][C]87.0876620006023[/C][C]82.52612983442[/C][C]91.6491941667845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200728&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200728&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
7385.968086867596285.534380513066586.4017932221259
7486.0560090713185.509339661079186.6026784815409
7586.298906449901585.653445512330886.9443673874721
7686.508280625507685.772767104084987.2437941469302
7786.576192531302585.757216491429887.3951685711753
7886.525599541500785.628154762006987.4230443209945
7986.536573292178885.563179996475987.5099665878818
8086.538335179961285.491388413323987.5852819465985
8186.770911213074285.649667224162987.8921552019854
8287.077936093646285.88273678448988.2731354028034
8387.009365201326985.745894068344388.2728363343094
8487.087662000602382.5261298344291.6491941667845



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=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')