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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 23 May 2016 15:49:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/May/23/t1464015279k1jbpdz9tedme5i.htm/, Retrieved Wed, 08 May 2024 00:11:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295526, Retrieved Wed, 08 May 2024 00:11:46 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-05-23 14:49:59] [b54f462b245e496e54620f8b97639ccc] [Current]
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Dataseries X:
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17
104,63
105,32
106,16
107,22
107,51
107,87
107,79
108,04
107,74
107,71
111,19
110,82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295526&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295526&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.915824363538186
beta0.0841776073132645
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.915824363538186 \tabularnewline
beta & 0.0841776073132645 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295526&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]0.915824363538186[/C][/ROW]
[ROW][C]beta[/C][C]0.0841776073132645[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295526&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
alpha0.915824363538186
beta0.0841776073132645
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
392.5592.430.120000000000005
492.2492.5191499520616-0.279149952061601
592.4192.22122845211410.188771547885864
692.8392.36639362002180.463606379978174
792.8592.79899952148160.0510004785183895
893.0492.85766260982050.182337390179512
993.0493.0506639782045-0.0106639782045193
1092.8393.0660878848461-0.236087884846086
1192.9692.85686262119180.103137378808213
1292.8392.9662591755887-0.136259175588691
1393.0192.8459060536870.164093946312974
1493.2193.0132739531850.196726046814959
1593.5893.22569311080110.354306889198924
1694.0793.6097428356610.460257164339012
1794.5794.12630650478150.44369349521854
1895.0394.66190593835170.368094061648293
1995.2195.15664664072040.053353359279626
2095.8995.36725325169520.522746748304755
2196.4396.04804130637250.381958693627524
2296.3596.6293381532855-0.279338153285465
2396.7196.5834685262680.12653147373203
2496.3296.9190587442739-0.599058744273876
2597.2396.54395318369560.686046816304412
2697.8897.39866726026960.481332739730348
2798.298.10300605514890.0969939448510928
2898.5698.46283546567510.0971645343248611
2999.3198.83031170511520.479688294884809
3099.6999.58509260791570.104907392084328
3199.77100.004727539505-0.234727539504519
32101.06100.0952209331780.964779066821905
33101.77101.3586283560060.411371643994471
34101.91102.146925201185-0.236925201184519
35102.52102.3232309859640.196769014036391
36102.09102.911893797237-0.821893797237365
37102.22102.504279030296-0.284279030295878
38102.74102.5671093535060.172890646493656
39103.56103.0619552740520.498044725948404
40104.4103.8929804384870.507019561512507
41104.76104.771312079172-0.0113120791723844
42104.86105.174070905208-0.314070905207785
43104.84105.275343498123-0.435343498122762
44104.96105.231990236808-0.271990236808392
45104.83105.317271626942-0.487271626941563
46104.58105.167828377663-0.587828377662831
47104.8104.880975997507-0.0809759975066129
48104.17105.052068782018-0.882068782017683
49104.63104.421500915470.20849908452989
50105.32104.8057752625330.514224737467359
51106.16105.5096831750250.650316824974993
52107.22106.3883616989490.831638301050717
53107.51107.4972114280660.0127885719341236
54107.87107.8571245205360.0128754794638866
55107.79108.218109800262-0.428109800261652
56108.04108.142226217383-0.102226217382935
57107.74108.356913945682-0.616913945681532
58107.71108.052679042334-0.342679042334353
59111.19107.9731773650933.21682263490666
60110.82111.401545026528-0.581545026527792

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 92.55 & 92.43 & 0.120000000000005 \tabularnewline
4 & 92.24 & 92.5191499520616 & -0.279149952061601 \tabularnewline
5 & 92.41 & 92.2212284521141 & 0.188771547885864 \tabularnewline
6 & 92.83 & 92.3663936200218 & 0.463606379978174 \tabularnewline
7 & 92.85 & 92.7989995214816 & 0.0510004785183895 \tabularnewline
8 & 93.04 & 92.8576626098205 & 0.182337390179512 \tabularnewline
9 & 93.04 & 93.0506639782045 & -0.0106639782045193 \tabularnewline
10 & 92.83 & 93.0660878848461 & -0.236087884846086 \tabularnewline
11 & 92.96 & 92.8568626211918 & 0.103137378808213 \tabularnewline
12 & 92.83 & 92.9662591755887 & -0.136259175588691 \tabularnewline
13 & 93.01 & 92.845906053687 & 0.164093946312974 \tabularnewline
14 & 93.21 & 93.013273953185 & 0.196726046814959 \tabularnewline
15 & 93.58 & 93.2256931108011 & 0.354306889198924 \tabularnewline
16 & 94.07 & 93.609742835661 & 0.460257164339012 \tabularnewline
17 & 94.57 & 94.1263065047815 & 0.44369349521854 \tabularnewline
18 & 95.03 & 94.6619059383517 & 0.368094061648293 \tabularnewline
19 & 95.21 & 95.1566466407204 & 0.053353359279626 \tabularnewline
20 & 95.89 & 95.3672532516952 & 0.522746748304755 \tabularnewline
21 & 96.43 & 96.0480413063725 & 0.381958693627524 \tabularnewline
22 & 96.35 & 96.6293381532855 & -0.279338153285465 \tabularnewline
23 & 96.71 & 96.583468526268 & 0.12653147373203 \tabularnewline
24 & 96.32 & 96.9190587442739 & -0.599058744273876 \tabularnewline
25 & 97.23 & 96.5439531836956 & 0.686046816304412 \tabularnewline
26 & 97.88 & 97.3986672602696 & 0.481332739730348 \tabularnewline
27 & 98.2 & 98.1030060551489 & 0.0969939448510928 \tabularnewline
28 & 98.56 & 98.4628354656751 & 0.0971645343248611 \tabularnewline
29 & 99.31 & 98.8303117051152 & 0.479688294884809 \tabularnewline
30 & 99.69 & 99.5850926079157 & 0.104907392084328 \tabularnewline
31 & 99.77 & 100.004727539505 & -0.234727539504519 \tabularnewline
32 & 101.06 & 100.095220933178 & 0.964779066821905 \tabularnewline
33 & 101.77 & 101.358628356006 & 0.411371643994471 \tabularnewline
34 & 101.91 & 102.146925201185 & -0.236925201184519 \tabularnewline
35 & 102.52 & 102.323230985964 & 0.196769014036391 \tabularnewline
36 & 102.09 & 102.911893797237 & -0.821893797237365 \tabularnewline
37 & 102.22 & 102.504279030296 & -0.284279030295878 \tabularnewline
38 & 102.74 & 102.567109353506 & 0.172890646493656 \tabularnewline
39 & 103.56 & 103.061955274052 & 0.498044725948404 \tabularnewline
40 & 104.4 & 103.892980438487 & 0.507019561512507 \tabularnewline
41 & 104.76 & 104.771312079172 & -0.0113120791723844 \tabularnewline
42 & 104.86 & 105.174070905208 & -0.314070905207785 \tabularnewline
43 & 104.84 & 105.275343498123 & -0.435343498122762 \tabularnewline
44 & 104.96 & 105.231990236808 & -0.271990236808392 \tabularnewline
45 & 104.83 & 105.317271626942 & -0.487271626941563 \tabularnewline
46 & 104.58 & 105.167828377663 & -0.587828377662831 \tabularnewline
47 & 104.8 & 104.880975997507 & -0.0809759975066129 \tabularnewline
48 & 104.17 & 105.052068782018 & -0.882068782017683 \tabularnewline
49 & 104.63 & 104.42150091547 & 0.20849908452989 \tabularnewline
50 & 105.32 & 104.805775262533 & 0.514224737467359 \tabularnewline
51 & 106.16 & 105.509683175025 & 0.650316824974993 \tabularnewline
52 & 107.22 & 106.388361698949 & 0.831638301050717 \tabularnewline
53 & 107.51 & 107.497211428066 & 0.0127885719341236 \tabularnewline
54 & 107.87 & 107.857124520536 & 0.0128754794638866 \tabularnewline
55 & 107.79 & 108.218109800262 & -0.428109800261652 \tabularnewline
56 & 108.04 & 108.142226217383 & -0.102226217382935 \tabularnewline
57 & 107.74 & 108.356913945682 & -0.616913945681532 \tabularnewline
58 & 107.71 & 108.052679042334 & -0.342679042334353 \tabularnewline
59 & 111.19 & 107.973177365093 & 3.21682263490666 \tabularnewline
60 & 110.82 & 111.401545026528 & -0.581545026527792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295526&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]3[/C][C]92.55[/C][C]92.43[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]4[/C][C]92.24[/C][C]92.5191499520616[/C][C]-0.279149952061601[/C][/ROW]
[ROW][C]5[/C][C]92.41[/C][C]92.2212284521141[/C][C]0.188771547885864[/C][/ROW]
[ROW][C]6[/C][C]92.83[/C][C]92.3663936200218[/C][C]0.463606379978174[/C][/ROW]
[ROW][C]7[/C][C]92.85[/C][C]92.7989995214816[/C][C]0.0510004785183895[/C][/ROW]
[ROW][C]8[/C][C]93.04[/C][C]92.8576626098205[/C][C]0.182337390179512[/C][/ROW]
[ROW][C]9[/C][C]93.04[/C][C]93.0506639782045[/C][C]-0.0106639782045193[/C][/ROW]
[ROW][C]10[/C][C]92.83[/C][C]93.0660878848461[/C][C]-0.236087884846086[/C][/ROW]
[ROW][C]11[/C][C]92.96[/C][C]92.8568626211918[/C][C]0.103137378808213[/C][/ROW]
[ROW][C]12[/C][C]92.83[/C][C]92.9662591755887[/C][C]-0.136259175588691[/C][/ROW]
[ROW][C]13[/C][C]93.01[/C][C]92.845906053687[/C][C]0.164093946312974[/C][/ROW]
[ROW][C]14[/C][C]93.21[/C][C]93.013273953185[/C][C]0.196726046814959[/C][/ROW]
[ROW][C]15[/C][C]93.58[/C][C]93.2256931108011[/C][C]0.354306889198924[/C][/ROW]
[ROW][C]16[/C][C]94.07[/C][C]93.609742835661[/C][C]0.460257164339012[/C][/ROW]
[ROW][C]17[/C][C]94.57[/C][C]94.1263065047815[/C][C]0.44369349521854[/C][/ROW]
[ROW][C]18[/C][C]95.03[/C][C]94.6619059383517[/C][C]0.368094061648293[/C][/ROW]
[ROW][C]19[/C][C]95.21[/C][C]95.1566466407204[/C][C]0.053353359279626[/C][/ROW]
[ROW][C]20[/C][C]95.89[/C][C]95.3672532516952[/C][C]0.522746748304755[/C][/ROW]
[ROW][C]21[/C][C]96.43[/C][C]96.0480413063725[/C][C]0.381958693627524[/C][/ROW]
[ROW][C]22[/C][C]96.35[/C][C]96.6293381532855[/C][C]-0.279338153285465[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.583468526268[/C][C]0.12653147373203[/C][/ROW]
[ROW][C]24[/C][C]96.32[/C][C]96.9190587442739[/C][C]-0.599058744273876[/C][/ROW]
[ROW][C]25[/C][C]97.23[/C][C]96.5439531836956[/C][C]0.686046816304412[/C][/ROW]
[ROW][C]26[/C][C]97.88[/C][C]97.3986672602696[/C][C]0.481332739730348[/C][/ROW]
[ROW][C]27[/C][C]98.2[/C][C]98.1030060551489[/C][C]0.0969939448510928[/C][/ROW]
[ROW][C]28[/C][C]98.56[/C][C]98.4628354656751[/C][C]0.0971645343248611[/C][/ROW]
[ROW][C]29[/C][C]99.31[/C][C]98.8303117051152[/C][C]0.479688294884809[/C][/ROW]
[ROW][C]30[/C][C]99.69[/C][C]99.5850926079157[/C][C]0.104907392084328[/C][/ROW]
[ROW][C]31[/C][C]99.77[/C][C]100.004727539505[/C][C]-0.234727539504519[/C][/ROW]
[ROW][C]32[/C][C]101.06[/C][C]100.095220933178[/C][C]0.964779066821905[/C][/ROW]
[ROW][C]33[/C][C]101.77[/C][C]101.358628356006[/C][C]0.411371643994471[/C][/ROW]
[ROW][C]34[/C][C]101.91[/C][C]102.146925201185[/C][C]-0.236925201184519[/C][/ROW]
[ROW][C]35[/C][C]102.52[/C][C]102.323230985964[/C][C]0.196769014036391[/C][/ROW]
[ROW][C]36[/C][C]102.09[/C][C]102.911893797237[/C][C]-0.821893797237365[/C][/ROW]
[ROW][C]37[/C][C]102.22[/C][C]102.504279030296[/C][C]-0.284279030295878[/C][/ROW]
[ROW][C]38[/C][C]102.74[/C][C]102.567109353506[/C][C]0.172890646493656[/C][/ROW]
[ROW][C]39[/C][C]103.56[/C][C]103.061955274052[/C][C]0.498044725948404[/C][/ROW]
[ROW][C]40[/C][C]104.4[/C][C]103.892980438487[/C][C]0.507019561512507[/C][/ROW]
[ROW][C]41[/C][C]104.76[/C][C]104.771312079172[/C][C]-0.0113120791723844[/C][/ROW]
[ROW][C]42[/C][C]104.86[/C][C]105.174070905208[/C][C]-0.314070905207785[/C][/ROW]
[ROW][C]43[/C][C]104.84[/C][C]105.275343498123[/C][C]-0.435343498122762[/C][/ROW]
[ROW][C]44[/C][C]104.96[/C][C]105.231990236808[/C][C]-0.271990236808392[/C][/ROW]
[ROW][C]45[/C][C]104.83[/C][C]105.317271626942[/C][C]-0.487271626941563[/C][/ROW]
[ROW][C]46[/C][C]104.58[/C][C]105.167828377663[/C][C]-0.587828377662831[/C][/ROW]
[ROW][C]47[/C][C]104.8[/C][C]104.880975997507[/C][C]-0.0809759975066129[/C][/ROW]
[ROW][C]48[/C][C]104.17[/C][C]105.052068782018[/C][C]-0.882068782017683[/C][/ROW]
[ROW][C]49[/C][C]104.63[/C][C]104.42150091547[/C][C]0.20849908452989[/C][/ROW]
[ROW][C]50[/C][C]105.32[/C][C]104.805775262533[/C][C]0.514224737467359[/C][/ROW]
[ROW][C]51[/C][C]106.16[/C][C]105.509683175025[/C][C]0.650316824974993[/C][/ROW]
[ROW][C]52[/C][C]107.22[/C][C]106.388361698949[/C][C]0.831638301050717[/C][/ROW]
[ROW][C]53[/C][C]107.51[/C][C]107.497211428066[/C][C]0.0127885719341236[/C][/ROW]
[ROW][C]54[/C][C]107.87[/C][C]107.857124520536[/C][C]0.0128754794638866[/C][/ROW]
[ROW][C]55[/C][C]107.79[/C][C]108.218109800262[/C][C]-0.428109800261652[/C][/ROW]
[ROW][C]56[/C][C]108.04[/C][C]108.142226217383[/C][C]-0.102226217382935[/C][/ROW]
[ROW][C]57[/C][C]107.74[/C][C]108.356913945682[/C][C]-0.616913945681532[/C][/ROW]
[ROW][C]58[/C][C]107.71[/C][C]108.052679042334[/C][C]-0.342679042334353[/C][/ROW]
[ROW][C]59[/C][C]111.19[/C][C]107.973177365093[/C][C]3.21682263490666[/C][/ROW]
[ROW][C]60[/C][C]110.82[/C][C]111.401545026528[/C][C]-0.581545026527792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295526&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295526&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
392.5592.430.120000000000005
492.2492.5191499520616-0.279149952061601
592.4192.22122845211410.188771547885864
692.8392.36639362002180.463606379978174
792.8592.79899952148160.0510004785183895
893.0492.85766260982050.182337390179512
993.0493.0506639782045-0.0106639782045193
1092.8393.0660878848461-0.236087884846086
1192.9692.85686262119180.103137378808213
1292.8392.9662591755887-0.136259175588691
1393.0192.8459060536870.164093946312974
1493.2193.0132739531850.196726046814959
1593.5893.22569311080110.354306889198924
1694.0793.6097428356610.460257164339012
1794.5794.12630650478150.44369349521854
1895.0394.66190593835170.368094061648293
1995.2195.15664664072040.053353359279626
2095.8995.36725325169520.522746748304755
2196.4396.04804130637250.381958693627524
2296.3596.6293381532855-0.279338153285465
2396.7196.5834685262680.12653147373203
2496.3296.9190587442739-0.599058744273876
2597.2396.54395318369560.686046816304412
2697.8897.39866726026960.481332739730348
2798.298.10300605514890.0969939448510928
2898.5698.46283546567510.0971645343248611
2999.3198.83031170511520.479688294884809
3099.6999.58509260791570.104907392084328
3199.77100.004727539505-0.234727539504519
32101.06100.0952209331780.964779066821905
33101.77101.3586283560060.411371643994471
34101.91102.146925201185-0.236925201184519
35102.52102.3232309859640.196769014036391
36102.09102.911893797237-0.821893797237365
37102.22102.504279030296-0.284279030295878
38102.74102.5671093535060.172890646493656
39103.56103.0619552740520.498044725948404
40104.4103.8929804384870.507019561512507
41104.76104.771312079172-0.0113120791723844
42104.86105.174070905208-0.314070905207785
43104.84105.275343498123-0.435343498122762
44104.96105.231990236808-0.271990236808392
45104.83105.317271626942-0.487271626941563
46104.58105.167828377663-0.587828377662831
47104.8104.880975997507-0.0809759975066129
48104.17105.052068782018-0.882068782017683
49104.63104.421500915470.20849908452989
50105.32104.8057752625330.514224737467359
51106.16105.5096831750250.650316824974993
52107.22106.3883616989490.831638301050717
53107.51107.4972114280660.0127885719341236
54107.87107.8571245205360.0128754794638866
55107.79108.218109800262-0.428109800261652
56108.04108.142226217383-0.102226217382935
57107.74108.356913945682-0.616913945681532
58107.71108.052679042334-0.342679042334353
59111.19107.9731773650933.21682263490666
60110.82111.401545026528-0.581545026527792







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61111.306442628797110.160824562394112.452060695199
62111.743933334854110.129512879654113.358353790054
63112.181424040911110.154359716735114.208488365088
64112.618914746969110.203143658142115.034685835795
65113.056405453026110.263050115988115.849760790064
66113.493896159083110.327629883895116.660162434271
67113.931386865141110.393198867321117.469574862961
68114.368877571198110.457480035593118.280275106803
69114.806368277255110.518990134235119.093746420275
70115.243858983313110.576727489338119.910990477288
71115.68134968937110.629998790951120.732700587789
72116.118840395427110.678316524791121.559364266064

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 111.306442628797 & 110.160824562394 & 112.452060695199 \tabularnewline
62 & 111.743933334854 & 110.129512879654 & 113.358353790054 \tabularnewline
63 & 112.181424040911 & 110.154359716735 & 114.208488365088 \tabularnewline
64 & 112.618914746969 & 110.203143658142 & 115.034685835795 \tabularnewline
65 & 113.056405453026 & 110.263050115988 & 115.849760790064 \tabularnewline
66 & 113.493896159083 & 110.327629883895 & 116.660162434271 \tabularnewline
67 & 113.931386865141 & 110.393198867321 & 117.469574862961 \tabularnewline
68 & 114.368877571198 & 110.457480035593 & 118.280275106803 \tabularnewline
69 & 114.806368277255 & 110.518990134235 & 119.093746420275 \tabularnewline
70 & 115.243858983313 & 110.576727489338 & 119.910990477288 \tabularnewline
71 & 115.68134968937 & 110.629998790951 & 120.732700587789 \tabularnewline
72 & 116.118840395427 & 110.678316524791 & 121.559364266064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295526&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]111.306442628797[/C][C]110.160824562394[/C][C]112.452060695199[/C][/ROW]
[ROW][C]62[/C][C]111.743933334854[/C][C]110.129512879654[/C][C]113.358353790054[/C][/ROW]
[ROW][C]63[/C][C]112.181424040911[/C][C]110.154359716735[/C][C]114.208488365088[/C][/ROW]
[ROW][C]64[/C][C]112.618914746969[/C][C]110.203143658142[/C][C]115.034685835795[/C][/ROW]
[ROW][C]65[/C][C]113.056405453026[/C][C]110.263050115988[/C][C]115.849760790064[/C][/ROW]
[ROW][C]66[/C][C]113.493896159083[/C][C]110.327629883895[/C][C]116.660162434271[/C][/ROW]
[ROW][C]67[/C][C]113.931386865141[/C][C]110.393198867321[/C][C]117.469574862961[/C][/ROW]
[ROW][C]68[/C][C]114.368877571198[/C][C]110.457480035593[/C][C]118.280275106803[/C][/ROW]
[ROW][C]69[/C][C]114.806368277255[/C][C]110.518990134235[/C][C]119.093746420275[/C][/ROW]
[ROW][C]70[/C][C]115.243858983313[/C][C]110.576727489338[/C][C]119.910990477288[/C][/ROW]
[ROW][C]71[/C][C]115.68134968937[/C][C]110.629998790951[/C][C]120.732700587789[/C][/ROW]
[ROW][C]72[/C][C]116.118840395427[/C][C]110.678316524791[/C][C]121.559364266064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295526&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295526&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
61111.306442628797110.160824562394112.452060695199
62111.743933334854110.129512879654113.358353790054
63112.181424040911110.154359716735114.208488365088
64112.618914746969110.203143658142115.034685835795
65113.056405453026110.263050115988115.849760790064
66113.493896159083110.327629883895116.660162434271
67113.931386865141110.393198867321117.469574862961
68114.368877571198110.457480035593118.280275106803
69114.806368277255110.518990134235119.093746420275
70115.243858983313110.576727489338119.910990477288
71115.68134968937110.629998790951120.732700587789
72116.118840395427110.678316524791121.559364266064



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')