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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 27 May 2013 09:15:07 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/27/t1369660544kaajx3pe6zah7hb.htm/, Retrieved Thu, 02 May 2024 07:04:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210749, Retrieved Thu, 02 May 2024 07:04:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-27 13:15:07] [2da1ca6f3ba4ee09ed598073b0ad80d0] [Current]
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Dataseries X:
22,38
22,38
22,38
22,38
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,45
27,45
27,45
27,45
27,45
27,45
27,45
27,45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210749&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]5 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=210749&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210749&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.981970749927385
beta0.0131707953976941
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.981970749927385 \tabularnewline
beta & 0.0131707953976941 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210749&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]0.981970749927385[/C][/ROW]
[ROW][C]beta[/C][C]0.0131707953976941[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210749&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210749&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
alpha0.981970749927385
beta0.0131707953976941
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1322.4122.21389957264960.196100427350427
1422.4122.39455430209360.0154456979063546
1522.4122.39801113578580.0119888642141994
1622.4122.3982285159120.011771484087955
1723.1123.09838467966970.0116153203303249
1823.1123.09853772002380.0114622799762394
1923.1122.90327205807630.206727941923731
2023.1123.1536752465255-0.0436752465255488
2123.1123.1576249615981-0.0476249615981423
2223.1123.1570802223765-0.0470802223764828
2323.1123.128544830143-0.0185448301430391
2423.1123.09987384523770.0101261547623466
2523.1123.10302343748530.00697656251474399
2623.1123.09637783955950.0136221604405051
2723.1123.09962894956320.0103710504367847
2823.1123.09988010183520.0101198981648274
2923.8223.80001661764910.0199833823509188
3023.8223.81009729453380.00990270546623506
3123.8223.61851370257970.20148629742032
3223.8223.8608804088876-0.0408804088875918
3323.8223.8691647500905-0.0491647500904975
3423.8223.868759277966-0.0487592779660417
3523.8223.8407093313069-0.0207093313069464
3623.8223.81202154903490.00797845096506222
3723.8223.81456936032120.00543063967880997
3823.8223.80806951872990.0119304812700776
3923.8223.81112294733410.00887705266594452
4023.8223.81140530017190.008594699828123
4126.124.51170501191641.58829498808362
4226.126.08340663090890.016593369091126
4326.125.92370028157190.176299718428094
4426.126.1584921657275-0.0584921657275217
4526.126.1706324892998-0.0706324892998254
4626.126.1701755589826-0.0701755589825552
4726.126.1423461097606-0.042346109760647
4826.126.1133939668677-0.0133939668677421
4926.126.1150974409454-0.0150974409454072
5026.126.108480002423-0.0084800024230276
5126.126.1110950969052-0.01109509690518
5226.126.1111612008077-0.0111612008077344
5327.0726.83968740619520.23031259380485
5427.0727.05113558986860.0188644101313784
5527.0726.89815025055940.171849749440646
5627.0727.1258932492373-0.0558932492372861
5727.0727.1419543400152-0.0719543400151679
5827.0727.1417781212917-0.0717781212917039
5927.0727.1144265126012-0.0444265126012269
6027.0727.0854763195911-0.0154763195911016
6127.0727.0866001992721-0.016600199272105
6227.0727.0801028952334-0.0101028952333877
6327.0727.0825327105861-0.0125327105861075
6427.0727.082622837293-0.0126228372929624
6527.4527.8154853551908-0.365485355190838
6627.4527.43177747829640.0182225217035636
6727.4527.2746240829010.17537591709895
6827.4527.4954732933487-0.0454732933487172
6927.4527.5153613251369-0.0653613251369123
7027.4527.515632119479-0.0656321194790195
7127.4527.4888580103059-0.0388580103059013
7227.4527.4600190697657-0.010019069765729

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22.41 & 22.2138995726496 & 0.196100427350427 \tabularnewline
14 & 22.41 & 22.3945543020936 & 0.0154456979063546 \tabularnewline
15 & 22.41 & 22.3980111357858 & 0.0119888642141994 \tabularnewline
16 & 22.41 & 22.398228515912 & 0.011771484087955 \tabularnewline
17 & 23.11 & 23.0983846796697 & 0.0116153203303249 \tabularnewline
18 & 23.11 & 23.0985377200238 & 0.0114622799762394 \tabularnewline
19 & 23.11 & 22.9032720580763 & 0.206727941923731 \tabularnewline
20 & 23.11 & 23.1536752465255 & -0.0436752465255488 \tabularnewline
21 & 23.11 & 23.1576249615981 & -0.0476249615981423 \tabularnewline
22 & 23.11 & 23.1570802223765 & -0.0470802223764828 \tabularnewline
23 & 23.11 & 23.128544830143 & -0.0185448301430391 \tabularnewline
24 & 23.11 & 23.0998738452377 & 0.0101261547623466 \tabularnewline
25 & 23.11 & 23.1030234374853 & 0.00697656251474399 \tabularnewline
26 & 23.11 & 23.0963778395595 & 0.0136221604405051 \tabularnewline
27 & 23.11 & 23.0996289495632 & 0.0103710504367847 \tabularnewline
28 & 23.11 & 23.0998801018352 & 0.0101198981648274 \tabularnewline
29 & 23.82 & 23.8000166176491 & 0.0199833823509188 \tabularnewline
30 & 23.82 & 23.8100972945338 & 0.00990270546623506 \tabularnewline
31 & 23.82 & 23.6185137025797 & 0.20148629742032 \tabularnewline
32 & 23.82 & 23.8608804088876 & -0.0408804088875918 \tabularnewline
33 & 23.82 & 23.8691647500905 & -0.0491647500904975 \tabularnewline
34 & 23.82 & 23.868759277966 & -0.0487592779660417 \tabularnewline
35 & 23.82 & 23.8407093313069 & -0.0207093313069464 \tabularnewline
36 & 23.82 & 23.8120215490349 & 0.00797845096506222 \tabularnewline
37 & 23.82 & 23.8145693603212 & 0.00543063967880997 \tabularnewline
38 & 23.82 & 23.8080695187299 & 0.0119304812700776 \tabularnewline
39 & 23.82 & 23.8111229473341 & 0.00887705266594452 \tabularnewline
40 & 23.82 & 23.8114053001719 & 0.008594699828123 \tabularnewline
41 & 26.1 & 24.5117050119164 & 1.58829498808362 \tabularnewline
42 & 26.1 & 26.0834066309089 & 0.016593369091126 \tabularnewline
43 & 26.1 & 25.9237002815719 & 0.176299718428094 \tabularnewline
44 & 26.1 & 26.1584921657275 & -0.0584921657275217 \tabularnewline
45 & 26.1 & 26.1706324892998 & -0.0706324892998254 \tabularnewline
46 & 26.1 & 26.1701755589826 & -0.0701755589825552 \tabularnewline
47 & 26.1 & 26.1423461097606 & -0.042346109760647 \tabularnewline
48 & 26.1 & 26.1133939668677 & -0.0133939668677421 \tabularnewline
49 & 26.1 & 26.1150974409454 & -0.0150974409454072 \tabularnewline
50 & 26.1 & 26.108480002423 & -0.0084800024230276 \tabularnewline
51 & 26.1 & 26.1110950969052 & -0.01109509690518 \tabularnewline
52 & 26.1 & 26.1111612008077 & -0.0111612008077344 \tabularnewline
53 & 27.07 & 26.8396874061952 & 0.23031259380485 \tabularnewline
54 & 27.07 & 27.0511355898686 & 0.0188644101313784 \tabularnewline
55 & 27.07 & 26.8981502505594 & 0.171849749440646 \tabularnewline
56 & 27.07 & 27.1258932492373 & -0.0558932492372861 \tabularnewline
57 & 27.07 & 27.1419543400152 & -0.0719543400151679 \tabularnewline
58 & 27.07 & 27.1417781212917 & -0.0717781212917039 \tabularnewline
59 & 27.07 & 27.1144265126012 & -0.0444265126012269 \tabularnewline
60 & 27.07 & 27.0854763195911 & -0.0154763195911016 \tabularnewline
61 & 27.07 & 27.0866001992721 & -0.016600199272105 \tabularnewline
62 & 27.07 & 27.0801028952334 & -0.0101028952333877 \tabularnewline
63 & 27.07 & 27.0825327105861 & -0.0125327105861075 \tabularnewline
64 & 27.07 & 27.082622837293 & -0.0126228372929624 \tabularnewline
65 & 27.45 & 27.8154853551908 & -0.365485355190838 \tabularnewline
66 & 27.45 & 27.4317774782964 & 0.0182225217035636 \tabularnewline
67 & 27.45 & 27.274624082901 & 0.17537591709895 \tabularnewline
68 & 27.45 & 27.4954732933487 & -0.0454732933487172 \tabularnewline
69 & 27.45 & 27.5153613251369 & -0.0653613251369123 \tabularnewline
70 & 27.45 & 27.515632119479 & -0.0656321194790195 \tabularnewline
71 & 27.45 & 27.4888580103059 & -0.0388580103059013 \tabularnewline
72 & 27.45 & 27.4600190697657 & -0.010019069765729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210749&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]22.41[/C][C]22.2138995726496[/C][C]0.196100427350427[/C][/ROW]
[ROW][C]14[/C][C]22.41[/C][C]22.3945543020936[/C][C]0.0154456979063546[/C][/ROW]
[ROW][C]15[/C][C]22.41[/C][C]22.3980111357858[/C][C]0.0119888642141994[/C][/ROW]
[ROW][C]16[/C][C]22.41[/C][C]22.398228515912[/C][C]0.011771484087955[/C][/ROW]
[ROW][C]17[/C][C]23.11[/C][C]23.0983846796697[/C][C]0.0116153203303249[/C][/ROW]
[ROW][C]18[/C][C]23.11[/C][C]23.0985377200238[/C][C]0.0114622799762394[/C][/ROW]
[ROW][C]19[/C][C]23.11[/C][C]22.9032720580763[/C][C]0.206727941923731[/C][/ROW]
[ROW][C]20[/C][C]23.11[/C][C]23.1536752465255[/C][C]-0.0436752465255488[/C][/ROW]
[ROW][C]21[/C][C]23.11[/C][C]23.1576249615981[/C][C]-0.0476249615981423[/C][/ROW]
[ROW][C]22[/C][C]23.11[/C][C]23.1570802223765[/C][C]-0.0470802223764828[/C][/ROW]
[ROW][C]23[/C][C]23.11[/C][C]23.128544830143[/C][C]-0.0185448301430391[/C][/ROW]
[ROW][C]24[/C][C]23.11[/C][C]23.0998738452377[/C][C]0.0101261547623466[/C][/ROW]
[ROW][C]25[/C][C]23.11[/C][C]23.1030234374853[/C][C]0.00697656251474399[/C][/ROW]
[ROW][C]26[/C][C]23.11[/C][C]23.0963778395595[/C][C]0.0136221604405051[/C][/ROW]
[ROW][C]27[/C][C]23.11[/C][C]23.0996289495632[/C][C]0.0103710504367847[/C][/ROW]
[ROW][C]28[/C][C]23.11[/C][C]23.0998801018352[/C][C]0.0101198981648274[/C][/ROW]
[ROW][C]29[/C][C]23.82[/C][C]23.8000166176491[/C][C]0.0199833823509188[/C][/ROW]
[ROW][C]30[/C][C]23.82[/C][C]23.8100972945338[/C][C]0.00990270546623506[/C][/ROW]
[ROW][C]31[/C][C]23.82[/C][C]23.6185137025797[/C][C]0.20148629742032[/C][/ROW]
[ROW][C]32[/C][C]23.82[/C][C]23.8608804088876[/C][C]-0.0408804088875918[/C][/ROW]
[ROW][C]33[/C][C]23.82[/C][C]23.8691647500905[/C][C]-0.0491647500904975[/C][/ROW]
[ROW][C]34[/C][C]23.82[/C][C]23.868759277966[/C][C]-0.0487592779660417[/C][/ROW]
[ROW][C]35[/C][C]23.82[/C][C]23.8407093313069[/C][C]-0.0207093313069464[/C][/ROW]
[ROW][C]36[/C][C]23.82[/C][C]23.8120215490349[/C][C]0.00797845096506222[/C][/ROW]
[ROW][C]37[/C][C]23.82[/C][C]23.8145693603212[/C][C]0.00543063967880997[/C][/ROW]
[ROW][C]38[/C][C]23.82[/C][C]23.8080695187299[/C][C]0.0119304812700776[/C][/ROW]
[ROW][C]39[/C][C]23.82[/C][C]23.8111229473341[/C][C]0.00887705266594452[/C][/ROW]
[ROW][C]40[/C][C]23.82[/C][C]23.8114053001719[/C][C]0.008594699828123[/C][/ROW]
[ROW][C]41[/C][C]26.1[/C][C]24.5117050119164[/C][C]1.58829498808362[/C][/ROW]
[ROW][C]42[/C][C]26.1[/C][C]26.0834066309089[/C][C]0.016593369091126[/C][/ROW]
[ROW][C]43[/C][C]26.1[/C][C]25.9237002815719[/C][C]0.176299718428094[/C][/ROW]
[ROW][C]44[/C][C]26.1[/C][C]26.1584921657275[/C][C]-0.0584921657275217[/C][/ROW]
[ROW][C]45[/C][C]26.1[/C][C]26.1706324892998[/C][C]-0.0706324892998254[/C][/ROW]
[ROW][C]46[/C][C]26.1[/C][C]26.1701755589826[/C][C]-0.0701755589825552[/C][/ROW]
[ROW][C]47[/C][C]26.1[/C][C]26.1423461097606[/C][C]-0.042346109760647[/C][/ROW]
[ROW][C]48[/C][C]26.1[/C][C]26.1133939668677[/C][C]-0.0133939668677421[/C][/ROW]
[ROW][C]49[/C][C]26.1[/C][C]26.1150974409454[/C][C]-0.0150974409454072[/C][/ROW]
[ROW][C]50[/C][C]26.1[/C][C]26.108480002423[/C][C]-0.0084800024230276[/C][/ROW]
[ROW][C]51[/C][C]26.1[/C][C]26.1110950969052[/C][C]-0.01109509690518[/C][/ROW]
[ROW][C]52[/C][C]26.1[/C][C]26.1111612008077[/C][C]-0.0111612008077344[/C][/ROW]
[ROW][C]53[/C][C]27.07[/C][C]26.8396874061952[/C][C]0.23031259380485[/C][/ROW]
[ROW][C]54[/C][C]27.07[/C][C]27.0511355898686[/C][C]0.0188644101313784[/C][/ROW]
[ROW][C]55[/C][C]27.07[/C][C]26.8981502505594[/C][C]0.171849749440646[/C][/ROW]
[ROW][C]56[/C][C]27.07[/C][C]27.1258932492373[/C][C]-0.0558932492372861[/C][/ROW]
[ROW][C]57[/C][C]27.07[/C][C]27.1419543400152[/C][C]-0.0719543400151679[/C][/ROW]
[ROW][C]58[/C][C]27.07[/C][C]27.1417781212917[/C][C]-0.0717781212917039[/C][/ROW]
[ROW][C]59[/C][C]27.07[/C][C]27.1144265126012[/C][C]-0.0444265126012269[/C][/ROW]
[ROW][C]60[/C][C]27.07[/C][C]27.0854763195911[/C][C]-0.0154763195911016[/C][/ROW]
[ROW][C]61[/C][C]27.07[/C][C]27.0866001992721[/C][C]-0.016600199272105[/C][/ROW]
[ROW][C]62[/C][C]27.07[/C][C]27.0801028952334[/C][C]-0.0101028952333877[/C][/ROW]
[ROW][C]63[/C][C]27.07[/C][C]27.0825327105861[/C][C]-0.0125327105861075[/C][/ROW]
[ROW][C]64[/C][C]27.07[/C][C]27.082622837293[/C][C]-0.0126228372929624[/C][/ROW]
[ROW][C]65[/C][C]27.45[/C][C]27.8154853551908[/C][C]-0.365485355190838[/C][/ROW]
[ROW][C]66[/C][C]27.45[/C][C]27.4317774782964[/C][C]0.0182225217035636[/C][/ROW]
[ROW][C]67[/C][C]27.45[/C][C]27.274624082901[/C][C]0.17537591709895[/C][/ROW]
[ROW][C]68[/C][C]27.45[/C][C]27.4954732933487[/C][C]-0.0454732933487172[/C][/ROW]
[ROW][C]69[/C][C]27.45[/C][C]27.5153613251369[/C][C]-0.0653613251369123[/C][/ROW]
[ROW][C]70[/C][C]27.45[/C][C]27.515632119479[/C][C]-0.0656321194790195[/C][/ROW]
[ROW][C]71[/C][C]27.45[/C][C]27.4888580103059[/C][C]-0.0388580103059013[/C][/ROW]
[ROW][C]72[/C][C]27.45[/C][C]27.4600190697657[/C][C]-0.010019069765729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210749&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210749&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
1322.4122.21389957264960.196100427350427
1422.4122.39455430209360.0154456979063546
1522.4122.39801113578580.0119888642141994
1622.4122.3982285159120.011771484087955
1723.1123.09838467966970.0116153203303249
1823.1123.09853772002380.0114622799762394
1923.1122.90327205807630.206727941923731
2023.1123.1536752465255-0.0436752465255488
2123.1123.1576249615981-0.0476249615981423
2223.1123.1570802223765-0.0470802223764828
2323.1123.128544830143-0.0185448301430391
2423.1123.09987384523770.0101261547623466
2523.1123.10302343748530.00697656251474399
2623.1123.09637783955950.0136221604405051
2723.1123.09962894956320.0103710504367847
2823.1123.09988010183520.0101198981648274
2923.8223.80001661764910.0199833823509188
3023.8223.81009729453380.00990270546623506
3123.8223.61851370257970.20148629742032
3223.8223.8608804088876-0.0408804088875918
3323.8223.8691647500905-0.0491647500904975
3423.8223.868759277966-0.0487592779660417
3523.8223.8407093313069-0.0207093313069464
3623.8223.81202154903490.00797845096506222
3723.8223.81456936032120.00543063967880997
3823.8223.80806951872990.0119304812700776
3923.8223.81112294733410.00887705266594452
4023.8223.81140530017190.008594699828123
4126.124.51170501191641.58829498808362
4226.126.08340663090890.016593369091126
4326.125.92370028157190.176299718428094
4426.126.1584921657275-0.0584921657275217
4526.126.1706324892998-0.0706324892998254
4626.126.1701755589826-0.0701755589825552
4726.126.1423461097606-0.042346109760647
4826.126.1133939668677-0.0133939668677421
4926.126.1150974409454-0.0150974409454072
5026.126.108480002423-0.0084800024230276
5126.126.1110950969052-0.01109509690518
5226.126.1111612008077-0.0111612008077344
5327.0726.83968740619520.23031259380485
5427.0727.05113558986860.0188644101313784
5527.0726.89815025055940.171849749440646
5627.0727.1258932492373-0.0558932492372861
5727.0727.1419543400152-0.0719543400151679
5827.0727.1417781212917-0.0717781212917039
5927.0727.1144265126012-0.0444265126012269
6027.0727.0854763195911-0.0154763195911016
6127.0727.0866001992721-0.016600199272105
6227.0727.0801028952334-0.0101028952333877
6327.0727.0825327105861-0.0125327105861075
6427.0727.082622837293-0.0126228372929624
6527.4527.8154853551908-0.365485355190838
6627.4527.43177747829640.0182225217035636
6727.4527.2746240829010.17537591709895
6827.4527.4954732933487-0.0454732933487172
6927.4527.5153613251369-0.0653613251369123
7027.4527.515632119479-0.0656321194790195
7127.4527.4888580103059-0.0388580103059013
7227.4527.4600190697657-0.010019069765729







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327.460673322712827.023345473127627.898001172298
7427.46500054254426.848099401454428.0819016836336
7527.471844434116226.713667465259628.2300214029728
7627.478938917233326.599100565138128.3587772693285
7728.212697327065727.223515528743829.2018791253876
7828.194392770112127.104442490438929.2843430497852
7928.021532497635526.83717087422129.2058941210499
8028.063271494330126.789416266363629.3371267222965
8128.125128077888626.765701854927129.4845543008501
8228.188095913538926.746300512067129.6298913150107
8328.225621199368526.704117306169229.7471250925679
8428.235330052825926.636360387467529.8342997181844

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27.4606733227128 & 27.0233454731276 & 27.898001172298 \tabularnewline
74 & 27.465000542544 & 26.8480994014544 & 28.0819016836336 \tabularnewline
75 & 27.4718444341162 & 26.7136674652596 & 28.2300214029728 \tabularnewline
76 & 27.4789389172333 & 26.5991005651381 & 28.3587772693285 \tabularnewline
77 & 28.2126973270657 & 27.2235155287438 & 29.2018791253876 \tabularnewline
78 & 28.1943927701121 & 27.1044424904389 & 29.2843430497852 \tabularnewline
79 & 28.0215324976355 & 26.837170874221 & 29.2058941210499 \tabularnewline
80 & 28.0632714943301 & 26.7894162663636 & 29.3371267222965 \tabularnewline
81 & 28.1251280778886 & 26.7657018549271 & 29.4845543008501 \tabularnewline
82 & 28.1880959135389 & 26.7463005120671 & 29.6298913150107 \tabularnewline
83 & 28.2256211993685 & 26.7041173061692 & 29.7471250925679 \tabularnewline
84 & 28.2353300528259 & 26.6363603874675 & 29.8342997181844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210749&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]27.4606733227128[/C][C]27.0233454731276[/C][C]27.898001172298[/C][/ROW]
[ROW][C]74[/C][C]27.465000542544[/C][C]26.8480994014544[/C][C]28.0819016836336[/C][/ROW]
[ROW][C]75[/C][C]27.4718444341162[/C][C]26.7136674652596[/C][C]28.2300214029728[/C][/ROW]
[ROW][C]76[/C][C]27.4789389172333[/C][C]26.5991005651381[/C][C]28.3587772693285[/C][/ROW]
[ROW][C]77[/C][C]28.2126973270657[/C][C]27.2235155287438[/C][C]29.2018791253876[/C][/ROW]
[ROW][C]78[/C][C]28.1943927701121[/C][C]27.1044424904389[/C][C]29.2843430497852[/C][/ROW]
[ROW][C]79[/C][C]28.0215324976355[/C][C]26.837170874221[/C][C]29.2058941210499[/C][/ROW]
[ROW][C]80[/C][C]28.0632714943301[/C][C]26.7894162663636[/C][C]29.3371267222965[/C][/ROW]
[ROW][C]81[/C][C]28.1251280778886[/C][C]26.7657018549271[/C][C]29.4845543008501[/C][/ROW]
[ROW][C]82[/C][C]28.1880959135389[/C][C]26.7463005120671[/C][C]29.6298913150107[/C][/ROW]
[ROW][C]83[/C][C]28.2256211993685[/C][C]26.7041173061692[/C][C]29.7471250925679[/C][/ROW]
[ROW][C]84[/C][C]28.2353300528259[/C][C]26.6363603874675[/C][C]29.8342997181844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210749&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210749&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
7327.460673322712827.023345473127627.898001172298
7427.46500054254426.848099401454428.0819016836336
7527.471844434116226.713667465259628.2300214029728
7627.478938917233326.599100565138128.3587772693285
7728.212697327065727.223515528743829.2018791253876
7828.194392770112127.104442490438929.2843430497852
7928.021532497635526.83717087422129.2058941210499
8028.063271494330126.789416266363629.3371267222965
8128.125128077888626.765701854927129.4845543008501
8228.188095913538926.746300512067129.6298913150107
8328.225621199368526.704117306169229.7471250925679
8428.235330052825926.636360387467529.8342997181844



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')