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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 22 Apr 2016 12:56:12 +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/Apr/22/t1461326189cbz1ml938mz03rb.htm/, Retrieved Sun, 05 May 2024 22:59:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294591, Retrieved Sun, 05 May 2024 22:59:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-22 11:56:12] [62731d77c8be8d15fdc4807de050d219] [Current]
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Dataseries X:
91.16
91.17
91.17
91.38
92.68
92.72
92.79
92.81
92.81
92.81
92.81
92.81
92.81
92.82
92.82
92.88
93.38
93.89
94.1
94.18
94.3
94.31
94.36
94.38
94.38
94.5
94.57
94.89
96.71
97.57
97.88
97.97
98.4
98.51
98.46
98.46
98.48
98.6
98.6
98.71
99.13
99.2
99.3
100.18
101.37
101.77
102.28
102.38
102.35
103.23
105.37
106.62
107
107.24
107.31
107.35
107.42
107.58
107.64
107.64
107.68
108.51
110.37
111.31
111.57
111.66
111.69
111.9
111.95
112.04
112.13
112.14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294591&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294591&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0541420482110748
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0541420482110748 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294591&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0541420482110748[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294591&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
alpha1
beta0.0541420482110748
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.8192.18007596640510.629924033594932
1492.8292.8551642943423-0.0351642943422661
1592.8292.8457516015936-0.0257516015936545
1692.8892.8989519536668-0.0189519536668428
1793.3893.3955008106465-0.0155008106465431
1893.8993.9017961046046-0.0117961046045707
1994.194.2299499200011-0.129949920001138
2094.1894.11494600442880.065053995571219
2194.394.1780998267250.121900173275037
2294.3194.3108706490452-0.000870649045225491
2394.3694.3610145421191-0.00101454211906571
2494.3894.4248329440268-0.0448329440268367
2594.3894.4165278864331-0.0365278864330634
2694.594.41623460224070.083765397759251
2794.5794.52282856819740.0471714318026386
2894.8994.6509166386680.239083361331964
2996.7195.43078385224721.27921614775283
3097.5797.33299697487430.237003025125716
3197.8898.0190622111509-0.139062211150872
3297.9797.9908639781276-0.0208639781276077
3398.498.05840333969030.341596660309662
3498.5198.5127410180747-0.00274101807474381
3598.4698.6643327280454-0.204332728045443
3698.4698.6177711217295-0.15777112172951
3798.4898.5821566935531-0.102156693553127
3898.698.59827315660520.00172684339474927
3998.698.6995557446231-0.099555744623089
4098.7198.7521128106627-0.0421128106626583
4199.1399.325111108135-0.195111108134981
4299.299.7419110293188-0.541911029318797
4399.399.5892723918805-0.289272391880459
44100.1899.3377867607040.842213239295958
45101.37100.2406158461091.12938415389074
46101.77101.4966582145280.273341785472297
47102.28101.9541492060950.325850793905232
48102.38102.496256567732-0.116256567731966
49102.35102.561667337823-0.211667337822831
50103.23102.5219222879450.708077712054603
51105.37103.4196321251051.95036787489477
52106.62105.724287726990.895712273010176
53107107.525531734564-0.525531734563913
54107.24107.885643638464-0.645643638464023
55107.31107.882857762998-0.572857762997657
56107.35107.558584247284-0.20858424728354
57107.42107.563818380472-0.143818380472112
58107.58107.632876082195-0.0528760821954961
59107.64107.835454125174-0.195454125173811
60107.64107.90053813128-0.260538131280001
61107.68107.856743035168-0.176743035168187
62108.51107.8888680761120.6211319238882
63110.37108.7308915831961.63910841680449
64111.31110.7419844415320.568015558467721
65111.57112.237782246744-0.667782246743755
66111.66112.469915684727-0.809915684726562
67111.69112.29895586471-0.608955864709884
68111.9111.917849964262-0.0178499642619272
69111.95112.102232612239-0.152232612239416
70112.04112.151186752429-0.111186752429447
71112.13112.282623214086-0.152623214085892
72112.14112.38066991517-0.240669915169889

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.81 & 92.1800759664051 & 0.629924033594932 \tabularnewline
14 & 92.82 & 92.8551642943423 & -0.0351642943422661 \tabularnewline
15 & 92.82 & 92.8457516015936 & -0.0257516015936545 \tabularnewline
16 & 92.88 & 92.8989519536668 & -0.0189519536668428 \tabularnewline
17 & 93.38 & 93.3955008106465 & -0.0155008106465431 \tabularnewline
18 & 93.89 & 93.9017961046046 & -0.0117961046045707 \tabularnewline
19 & 94.1 & 94.2299499200011 & -0.129949920001138 \tabularnewline
20 & 94.18 & 94.1149460044288 & 0.065053995571219 \tabularnewline
21 & 94.3 & 94.178099826725 & 0.121900173275037 \tabularnewline
22 & 94.31 & 94.3108706490452 & -0.000870649045225491 \tabularnewline
23 & 94.36 & 94.3610145421191 & -0.00101454211906571 \tabularnewline
24 & 94.38 & 94.4248329440268 & -0.0448329440268367 \tabularnewline
25 & 94.38 & 94.4165278864331 & -0.0365278864330634 \tabularnewline
26 & 94.5 & 94.4162346022407 & 0.083765397759251 \tabularnewline
27 & 94.57 & 94.5228285681974 & 0.0471714318026386 \tabularnewline
28 & 94.89 & 94.650916638668 & 0.239083361331964 \tabularnewline
29 & 96.71 & 95.4307838522472 & 1.27921614775283 \tabularnewline
30 & 97.57 & 97.3329969748743 & 0.237003025125716 \tabularnewline
31 & 97.88 & 98.0190622111509 & -0.139062211150872 \tabularnewline
32 & 97.97 & 97.9908639781276 & -0.0208639781276077 \tabularnewline
33 & 98.4 & 98.0584033396903 & 0.341596660309662 \tabularnewline
34 & 98.51 & 98.5127410180747 & -0.00274101807474381 \tabularnewline
35 & 98.46 & 98.6643327280454 & -0.204332728045443 \tabularnewline
36 & 98.46 & 98.6177711217295 & -0.15777112172951 \tabularnewline
37 & 98.48 & 98.5821566935531 & -0.102156693553127 \tabularnewline
38 & 98.6 & 98.5982731566052 & 0.00172684339474927 \tabularnewline
39 & 98.6 & 98.6995557446231 & -0.099555744623089 \tabularnewline
40 & 98.71 & 98.7521128106627 & -0.0421128106626583 \tabularnewline
41 & 99.13 & 99.325111108135 & -0.195111108134981 \tabularnewline
42 & 99.2 & 99.7419110293188 & -0.541911029318797 \tabularnewline
43 & 99.3 & 99.5892723918805 & -0.289272391880459 \tabularnewline
44 & 100.18 & 99.337786760704 & 0.842213239295958 \tabularnewline
45 & 101.37 & 100.240615846109 & 1.12938415389074 \tabularnewline
46 & 101.77 & 101.496658214528 & 0.273341785472297 \tabularnewline
47 & 102.28 & 101.954149206095 & 0.325850793905232 \tabularnewline
48 & 102.38 & 102.496256567732 & -0.116256567731966 \tabularnewline
49 & 102.35 & 102.561667337823 & -0.211667337822831 \tabularnewline
50 & 103.23 & 102.521922287945 & 0.708077712054603 \tabularnewline
51 & 105.37 & 103.419632125105 & 1.95036787489477 \tabularnewline
52 & 106.62 & 105.72428772699 & 0.895712273010176 \tabularnewline
53 & 107 & 107.525531734564 & -0.525531734563913 \tabularnewline
54 & 107.24 & 107.885643638464 & -0.645643638464023 \tabularnewline
55 & 107.31 & 107.882857762998 & -0.572857762997657 \tabularnewline
56 & 107.35 & 107.558584247284 & -0.20858424728354 \tabularnewline
57 & 107.42 & 107.563818380472 & -0.143818380472112 \tabularnewline
58 & 107.58 & 107.632876082195 & -0.0528760821954961 \tabularnewline
59 & 107.64 & 107.835454125174 & -0.195454125173811 \tabularnewline
60 & 107.64 & 107.90053813128 & -0.260538131280001 \tabularnewline
61 & 107.68 & 107.856743035168 & -0.176743035168187 \tabularnewline
62 & 108.51 & 107.888868076112 & 0.6211319238882 \tabularnewline
63 & 110.37 & 108.730891583196 & 1.63910841680449 \tabularnewline
64 & 111.31 & 110.741984441532 & 0.568015558467721 \tabularnewline
65 & 111.57 & 112.237782246744 & -0.667782246743755 \tabularnewline
66 & 111.66 & 112.469915684727 & -0.809915684726562 \tabularnewline
67 & 111.69 & 112.29895586471 & -0.608955864709884 \tabularnewline
68 & 111.9 & 111.917849964262 & -0.0178499642619272 \tabularnewline
69 & 111.95 & 112.102232612239 & -0.152232612239416 \tabularnewline
70 & 112.04 & 112.151186752429 & -0.111186752429447 \tabularnewline
71 & 112.13 & 112.282623214086 & -0.152623214085892 \tabularnewline
72 & 112.14 & 112.38066991517 & -0.240669915169889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294591&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]92.81[/C][C]92.1800759664051[/C][C]0.629924033594932[/C][/ROW]
[ROW][C]14[/C][C]92.82[/C][C]92.8551642943423[/C][C]-0.0351642943422661[/C][/ROW]
[ROW][C]15[/C][C]92.82[/C][C]92.8457516015936[/C][C]-0.0257516015936545[/C][/ROW]
[ROW][C]16[/C][C]92.88[/C][C]92.8989519536668[/C][C]-0.0189519536668428[/C][/ROW]
[ROW][C]17[/C][C]93.38[/C][C]93.3955008106465[/C][C]-0.0155008106465431[/C][/ROW]
[ROW][C]18[/C][C]93.89[/C][C]93.9017961046046[/C][C]-0.0117961046045707[/C][/ROW]
[ROW][C]19[/C][C]94.1[/C][C]94.2299499200011[/C][C]-0.129949920001138[/C][/ROW]
[ROW][C]20[/C][C]94.18[/C][C]94.1149460044288[/C][C]0.065053995571219[/C][/ROW]
[ROW][C]21[/C][C]94.3[/C][C]94.178099826725[/C][C]0.121900173275037[/C][/ROW]
[ROW][C]22[/C][C]94.31[/C][C]94.3108706490452[/C][C]-0.000870649045225491[/C][/ROW]
[ROW][C]23[/C][C]94.36[/C][C]94.3610145421191[/C][C]-0.00101454211906571[/C][/ROW]
[ROW][C]24[/C][C]94.38[/C][C]94.4248329440268[/C][C]-0.0448329440268367[/C][/ROW]
[ROW][C]25[/C][C]94.38[/C][C]94.4165278864331[/C][C]-0.0365278864330634[/C][/ROW]
[ROW][C]26[/C][C]94.5[/C][C]94.4162346022407[/C][C]0.083765397759251[/C][/ROW]
[ROW][C]27[/C][C]94.57[/C][C]94.5228285681974[/C][C]0.0471714318026386[/C][/ROW]
[ROW][C]28[/C][C]94.89[/C][C]94.650916638668[/C][C]0.239083361331964[/C][/ROW]
[ROW][C]29[/C][C]96.71[/C][C]95.4307838522472[/C][C]1.27921614775283[/C][/ROW]
[ROW][C]30[/C][C]97.57[/C][C]97.3329969748743[/C][C]0.237003025125716[/C][/ROW]
[ROW][C]31[/C][C]97.88[/C][C]98.0190622111509[/C][C]-0.139062211150872[/C][/ROW]
[ROW][C]32[/C][C]97.97[/C][C]97.9908639781276[/C][C]-0.0208639781276077[/C][/ROW]
[ROW][C]33[/C][C]98.4[/C][C]98.0584033396903[/C][C]0.341596660309662[/C][/ROW]
[ROW][C]34[/C][C]98.51[/C][C]98.5127410180747[/C][C]-0.00274101807474381[/C][/ROW]
[ROW][C]35[/C][C]98.46[/C][C]98.6643327280454[/C][C]-0.204332728045443[/C][/ROW]
[ROW][C]36[/C][C]98.46[/C][C]98.6177711217295[/C][C]-0.15777112172951[/C][/ROW]
[ROW][C]37[/C][C]98.48[/C][C]98.5821566935531[/C][C]-0.102156693553127[/C][/ROW]
[ROW][C]38[/C][C]98.6[/C][C]98.5982731566052[/C][C]0.00172684339474927[/C][/ROW]
[ROW][C]39[/C][C]98.6[/C][C]98.6995557446231[/C][C]-0.099555744623089[/C][/ROW]
[ROW][C]40[/C][C]98.71[/C][C]98.7521128106627[/C][C]-0.0421128106626583[/C][/ROW]
[ROW][C]41[/C][C]99.13[/C][C]99.325111108135[/C][C]-0.195111108134981[/C][/ROW]
[ROW][C]42[/C][C]99.2[/C][C]99.7419110293188[/C][C]-0.541911029318797[/C][/ROW]
[ROW][C]43[/C][C]99.3[/C][C]99.5892723918805[/C][C]-0.289272391880459[/C][/ROW]
[ROW][C]44[/C][C]100.18[/C][C]99.337786760704[/C][C]0.842213239295958[/C][/ROW]
[ROW][C]45[/C][C]101.37[/C][C]100.240615846109[/C][C]1.12938415389074[/C][/ROW]
[ROW][C]46[/C][C]101.77[/C][C]101.496658214528[/C][C]0.273341785472297[/C][/ROW]
[ROW][C]47[/C][C]102.28[/C][C]101.954149206095[/C][C]0.325850793905232[/C][/ROW]
[ROW][C]48[/C][C]102.38[/C][C]102.496256567732[/C][C]-0.116256567731966[/C][/ROW]
[ROW][C]49[/C][C]102.35[/C][C]102.561667337823[/C][C]-0.211667337822831[/C][/ROW]
[ROW][C]50[/C][C]103.23[/C][C]102.521922287945[/C][C]0.708077712054603[/C][/ROW]
[ROW][C]51[/C][C]105.37[/C][C]103.419632125105[/C][C]1.95036787489477[/C][/ROW]
[ROW][C]52[/C][C]106.62[/C][C]105.72428772699[/C][C]0.895712273010176[/C][/ROW]
[ROW][C]53[/C][C]107[/C][C]107.525531734564[/C][C]-0.525531734563913[/C][/ROW]
[ROW][C]54[/C][C]107.24[/C][C]107.885643638464[/C][C]-0.645643638464023[/C][/ROW]
[ROW][C]55[/C][C]107.31[/C][C]107.882857762998[/C][C]-0.572857762997657[/C][/ROW]
[ROW][C]56[/C][C]107.35[/C][C]107.558584247284[/C][C]-0.20858424728354[/C][/ROW]
[ROW][C]57[/C][C]107.42[/C][C]107.563818380472[/C][C]-0.143818380472112[/C][/ROW]
[ROW][C]58[/C][C]107.58[/C][C]107.632876082195[/C][C]-0.0528760821954961[/C][/ROW]
[ROW][C]59[/C][C]107.64[/C][C]107.835454125174[/C][C]-0.195454125173811[/C][/ROW]
[ROW][C]60[/C][C]107.64[/C][C]107.90053813128[/C][C]-0.260538131280001[/C][/ROW]
[ROW][C]61[/C][C]107.68[/C][C]107.856743035168[/C][C]-0.176743035168187[/C][/ROW]
[ROW][C]62[/C][C]108.51[/C][C]107.888868076112[/C][C]0.6211319238882[/C][/ROW]
[ROW][C]63[/C][C]110.37[/C][C]108.730891583196[/C][C]1.63910841680449[/C][/ROW]
[ROW][C]64[/C][C]111.31[/C][C]110.741984441532[/C][C]0.568015558467721[/C][/ROW]
[ROW][C]65[/C][C]111.57[/C][C]112.237782246744[/C][C]-0.667782246743755[/C][/ROW]
[ROW][C]66[/C][C]111.66[/C][C]112.469915684727[/C][C]-0.809915684726562[/C][/ROW]
[ROW][C]67[/C][C]111.69[/C][C]112.29895586471[/C][C]-0.608955864709884[/C][/ROW]
[ROW][C]68[/C][C]111.9[/C][C]111.917849964262[/C][C]-0.0178499642619272[/C][/ROW]
[ROW][C]69[/C][C]111.95[/C][C]112.102232612239[/C][C]-0.152232612239416[/C][/ROW]
[ROW][C]70[/C][C]112.04[/C][C]112.151186752429[/C][C]-0.111186752429447[/C][/ROW]
[ROW][C]71[/C][C]112.13[/C][C]112.282623214086[/C][C]-0.152623214085892[/C][/ROW]
[ROW][C]72[/C][C]112.14[/C][C]112.38066991517[/C][C]-0.240669915169889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294591&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294591&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
1392.8192.18007596640510.629924033594932
1492.8292.8551642943423-0.0351642943422661
1592.8292.8457516015936-0.0257516015936545
1692.8892.8989519536668-0.0189519536668428
1793.3893.3955008106465-0.0155008106465431
1893.8993.9017961046046-0.0117961046045707
1994.194.2299499200011-0.129949920001138
2094.1894.11494600442880.065053995571219
2194.394.1780998267250.121900173275037
2294.3194.3108706490452-0.000870649045225491
2394.3694.3610145421191-0.00101454211906571
2494.3894.4248329440268-0.0448329440268367
2594.3894.4165278864331-0.0365278864330634
2694.594.41623460224070.083765397759251
2794.5794.52282856819740.0471714318026386
2894.8994.6509166386680.239083361331964
2996.7195.43078385224721.27921614775283
3097.5797.33299697487430.237003025125716
3197.8898.0190622111509-0.139062211150872
3297.9797.9908639781276-0.0208639781276077
3398.498.05840333969030.341596660309662
3498.5198.5127410180747-0.00274101807474381
3598.4698.6643327280454-0.204332728045443
3698.4698.6177711217295-0.15777112172951
3798.4898.5821566935531-0.102156693553127
3898.698.59827315660520.00172684339474927
3998.698.6995557446231-0.099555744623089
4098.7198.7521128106627-0.0421128106626583
4199.1399.325111108135-0.195111108134981
4299.299.7419110293188-0.541911029318797
4399.399.5892723918805-0.289272391880459
44100.1899.3377867607040.842213239295958
45101.37100.2406158461091.12938415389074
46101.77101.4966582145280.273341785472297
47102.28101.9541492060950.325850793905232
48102.38102.496256567732-0.116256567731966
49102.35102.561667337823-0.211667337822831
50103.23102.5219222879450.708077712054603
51105.37103.4196321251051.95036787489477
52106.62105.724287726990.895712273010176
53107107.525531734564-0.525531734563913
54107.24107.885643638464-0.645643638464023
55107.31107.882857762998-0.572857762997657
56107.35107.558584247284-0.20858424728354
57107.42107.563818380472-0.143818380472112
58107.58107.632876082195-0.0528760821954961
59107.64107.835454125174-0.195454125173811
60107.64107.90053813128-0.260538131280001
61107.68107.856743035168-0.176743035168187
62108.51107.8888680761120.6211319238882
63110.37108.7308915831961.63910841680449
64111.31110.7419844415320.568015558467721
65111.57112.237782246744-0.667782246743755
66111.66112.469915684727-0.809915684726562
67111.69112.29895586471-0.608955864709884
68111.9111.917849964262-0.0178499642619272
69111.95112.102232612239-0.152232612239416
70112.04112.151186752429-0.111186752429447
71112.13112.282623214086-0.152623214085892
72112.14112.38066991517-0.240669915169889







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73112.346722182146111.322492493764113.370951870527
74112.555039251525111.067686036162114.042392466888
75112.741711754395110.87242675462114.61099675417
76112.994349721319110.779515221941115.209184220696
77113.77983481532111.230295961074116.329373669565
78114.575367814086111.702224731241117.44851089693
79115.150812755985111.966028192218118.335597319752
80115.337615302029111.855982187365118.819248416694
81115.499117156826111.724552984506119.273681329146
82115.667935190614111.602089150129119.733781231098
83115.885671172706111.527709739284120.243632606128
84116.120160941632110.635135854617121.605186028646

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 112.346722182146 & 111.322492493764 & 113.370951870527 \tabularnewline
74 & 112.555039251525 & 111.067686036162 & 114.042392466888 \tabularnewline
75 & 112.741711754395 & 110.87242675462 & 114.61099675417 \tabularnewline
76 & 112.994349721319 & 110.779515221941 & 115.209184220696 \tabularnewline
77 & 113.77983481532 & 111.230295961074 & 116.329373669565 \tabularnewline
78 & 114.575367814086 & 111.702224731241 & 117.44851089693 \tabularnewline
79 & 115.150812755985 & 111.966028192218 & 118.335597319752 \tabularnewline
80 & 115.337615302029 & 111.855982187365 & 118.819248416694 \tabularnewline
81 & 115.499117156826 & 111.724552984506 & 119.273681329146 \tabularnewline
82 & 115.667935190614 & 111.602089150129 & 119.733781231098 \tabularnewline
83 & 115.885671172706 & 111.527709739284 & 120.243632606128 \tabularnewline
84 & 116.120160941632 & 110.635135854617 & 121.605186028646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294591&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]112.346722182146[/C][C]111.322492493764[/C][C]113.370951870527[/C][/ROW]
[ROW][C]74[/C][C]112.555039251525[/C][C]111.067686036162[/C][C]114.042392466888[/C][/ROW]
[ROW][C]75[/C][C]112.741711754395[/C][C]110.87242675462[/C][C]114.61099675417[/C][/ROW]
[ROW][C]76[/C][C]112.994349721319[/C][C]110.779515221941[/C][C]115.209184220696[/C][/ROW]
[ROW][C]77[/C][C]113.77983481532[/C][C]111.230295961074[/C][C]116.329373669565[/C][/ROW]
[ROW][C]78[/C][C]114.575367814086[/C][C]111.702224731241[/C][C]117.44851089693[/C][/ROW]
[ROW][C]79[/C][C]115.150812755985[/C][C]111.966028192218[/C][C]118.335597319752[/C][/ROW]
[ROW][C]80[/C][C]115.337615302029[/C][C]111.855982187365[/C][C]118.819248416694[/C][/ROW]
[ROW][C]81[/C][C]115.499117156826[/C][C]111.724552984506[/C][C]119.273681329146[/C][/ROW]
[ROW][C]82[/C][C]115.667935190614[/C][C]111.602089150129[/C][C]119.733781231098[/C][/ROW]
[ROW][C]83[/C][C]115.885671172706[/C][C]111.527709739284[/C][C]120.243632606128[/C][/ROW]
[ROW][C]84[/C][C]116.120160941632[/C][C]110.635135854617[/C][C]121.605186028646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294591&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294591&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
73112.346722182146111.322492493764113.370951870527
74112.555039251525111.067686036162114.042392466888
75112.741711754395110.87242675462114.61099675417
76112.994349721319110.779515221941115.209184220696
77113.77983481532111.230295961074116.329373669565
78114.575367814086111.702224731241117.44851089693
79115.150812755985111.966028192218118.335597319752
80115.337615302029111.855982187365118.819248416694
81115.499117156826111.724552984506119.273681329146
82115.667935190614111.602089150129119.733781231098
83115.885671172706111.527709739284120.243632606128
84116.120160941632110.635135854617121.605186028646



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')