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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 21:10:03 -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/26/t1369617119bt8zu6nmaw3di7b.htm/, Retrieved Mon, 29 Apr 2024 09:41:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210726, Retrieved Mon, 29 Apr 2024 09:41:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Inschrijvingen ni...] [2012-03-09 13:44:23] [dd1db122e2fe6bd517fcf7008a48ce3e]
- RMP   [(Partial) Autocorrelation Function] [] [2013-05-26 23:17:52] [f974b105a61ab974a820d469d59cfaf7]
-    D    [(Partial) Autocorrelation Function] [] [2013-05-26 23:26:36] [f974b105a61ab974a820d469d59cfaf7]
- RMPD      [Classical Decomposition] [] [2013-05-27 00:48:49] [f974b105a61ab974a820d469d59cfaf7]
- RM D          [Exponential Smoothing] [] [2013-05-27 01:10:03] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
20,5
20,2
19,4
19,2
18,8
18,8
22,6
23,3
23
21,4
19,9
18,8
18,6
18,4
18,6
19,9
19,2
18,4
21,1
20,5
19,1
18,1
17
17,1
17,4
16,8
15,3
14,3
13,4
15,3
22,1
23,7
22,2
19,5
16,6
17,3
19,8
21,2
21,5
20,6
19,1
19,6
23,4
24,3
24,1
22,8
22,5
23,8
24,9
25,2
24,3
22,8
20,7
19,8
22,5
22,6
22,5
21,8
21,2
20,6
19,9
18,7
17,6
16,4
15,9
16,8
22,8
24
22,2
17,9
16
16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210726&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210726&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210726&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210726&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[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210726&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210726&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
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1318.618.7376335470085-0.137633547008548
1418.418.4535110722611-0.0535110722610703
1518.618.7535110722611-0.153511072261079
1619.920.0743444055944-0.174344405594404
1719.219.3326777389277-0.13267773892774
1818.418.4660110722611-0.0660110722610696
1921.120.96601107226110.133988927738926
2020.521.8285110722611-1.32851107226108
2119.120.1826777389277-1.08267773892774
2218.117.37851107226110.721488927738928
231716.42851107226110.571488927738926
2417.115.77434440559441.32565559440559
2517.416.85351107226110.54648892773892
2616.817.2535110722611-0.453511072261065
2715.317.1535110722611-1.85351107226108
2814.316.7743444055944-2.4743444055944
2913.413.7326777389277-0.332677738927739
3015.312.66601107226112.63398892773893
3122.117.86601107226114.23398892773893
3223.722.82851107226110.871488927738923
3322.223.3826777389277-1.18267773892774
3419.520.4785110722611-0.978511072261071
3516.617.8285110722611-1.22851107226107
3617.315.37434440559441.92565559440559
3719.817.05351107226112.74648892773892
3821.219.65351107226111.54648892773893
3921.521.5535110722611-0.053511072261081
4020.622.9743444055944-2.3743444055944
4119.120.0326777389277-0.93267773892774
4219.618.36601107226111.23398892773893
4323.422.16601107226111.23398892773892
4424.324.12851107226110.171488927738928
4524.123.98267773892770.11732226107226
4622.822.37851107226110.421488927738928
4722.521.12851107226111.37148892773893
4823.821.27434440559442.52565559440559
4924.923.55351107226111.34648892773892
5025.224.75351107226110.446488927738933
5124.325.5535110722611-1.25351107226108
5222.825.7743444055944-2.9743444055944
5320.722.2326777389277-1.53267773892774
5419.819.9660110722611-0.166011072261067
5522.522.36601107226110.133988927738923
5622.623.2285110722611-0.628511072261073
5722.522.28267773892770.217322261072258
5821.820.77851107226111.02148892773893
5921.220.12851107226111.07148892773893
6020.619.97434440559440.625655594405593
6119.920.3535110722611-0.45351107226108
6218.719.7535110722611-1.05351107226107
6317.619.0535110722611-1.45351107226108
6416.419.0743444055944-2.6743444055944
6515.915.83267773892770.0673222610722615
6616.815.16601107226111.63398892773893
6722.819.36601107226113.43398892773892
682423.52851107226110.471488927738925
6922.223.6826777389277-1.48267773892774
7017.920.4785110722611-2.57851107226107
711616.2285110722611-0.228511072261071
721614.77434440559441.22565559440559

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 18.6 & 18.7376335470085 & -0.137633547008548 \tabularnewline
14 & 18.4 & 18.4535110722611 & -0.0535110722610703 \tabularnewline
15 & 18.6 & 18.7535110722611 & -0.153511072261079 \tabularnewline
16 & 19.9 & 20.0743444055944 & -0.174344405594404 \tabularnewline
17 & 19.2 & 19.3326777389277 & -0.13267773892774 \tabularnewline
18 & 18.4 & 18.4660110722611 & -0.0660110722610696 \tabularnewline
19 & 21.1 & 20.9660110722611 & 0.133988927738926 \tabularnewline
20 & 20.5 & 21.8285110722611 & -1.32851107226108 \tabularnewline
21 & 19.1 & 20.1826777389277 & -1.08267773892774 \tabularnewline
22 & 18.1 & 17.3785110722611 & 0.721488927738928 \tabularnewline
23 & 17 & 16.4285110722611 & 0.571488927738926 \tabularnewline
24 & 17.1 & 15.7743444055944 & 1.32565559440559 \tabularnewline
25 & 17.4 & 16.8535110722611 & 0.54648892773892 \tabularnewline
26 & 16.8 & 17.2535110722611 & -0.453511072261065 \tabularnewline
27 & 15.3 & 17.1535110722611 & -1.85351107226108 \tabularnewline
28 & 14.3 & 16.7743444055944 & -2.4743444055944 \tabularnewline
29 & 13.4 & 13.7326777389277 & -0.332677738927739 \tabularnewline
30 & 15.3 & 12.6660110722611 & 2.63398892773893 \tabularnewline
31 & 22.1 & 17.8660110722611 & 4.23398892773893 \tabularnewline
32 & 23.7 & 22.8285110722611 & 0.871488927738923 \tabularnewline
33 & 22.2 & 23.3826777389277 & -1.18267773892774 \tabularnewline
34 & 19.5 & 20.4785110722611 & -0.978511072261071 \tabularnewline
35 & 16.6 & 17.8285110722611 & -1.22851107226107 \tabularnewline
36 & 17.3 & 15.3743444055944 & 1.92565559440559 \tabularnewline
37 & 19.8 & 17.0535110722611 & 2.74648892773892 \tabularnewline
38 & 21.2 & 19.6535110722611 & 1.54648892773893 \tabularnewline
39 & 21.5 & 21.5535110722611 & -0.053511072261081 \tabularnewline
40 & 20.6 & 22.9743444055944 & -2.3743444055944 \tabularnewline
41 & 19.1 & 20.0326777389277 & -0.93267773892774 \tabularnewline
42 & 19.6 & 18.3660110722611 & 1.23398892773893 \tabularnewline
43 & 23.4 & 22.1660110722611 & 1.23398892773892 \tabularnewline
44 & 24.3 & 24.1285110722611 & 0.171488927738928 \tabularnewline
45 & 24.1 & 23.9826777389277 & 0.11732226107226 \tabularnewline
46 & 22.8 & 22.3785110722611 & 0.421488927738928 \tabularnewline
47 & 22.5 & 21.1285110722611 & 1.37148892773893 \tabularnewline
48 & 23.8 & 21.2743444055944 & 2.52565559440559 \tabularnewline
49 & 24.9 & 23.5535110722611 & 1.34648892773892 \tabularnewline
50 & 25.2 & 24.7535110722611 & 0.446488927738933 \tabularnewline
51 & 24.3 & 25.5535110722611 & -1.25351107226108 \tabularnewline
52 & 22.8 & 25.7743444055944 & -2.9743444055944 \tabularnewline
53 & 20.7 & 22.2326777389277 & -1.53267773892774 \tabularnewline
54 & 19.8 & 19.9660110722611 & -0.166011072261067 \tabularnewline
55 & 22.5 & 22.3660110722611 & 0.133988927738923 \tabularnewline
56 & 22.6 & 23.2285110722611 & -0.628511072261073 \tabularnewline
57 & 22.5 & 22.2826777389277 & 0.217322261072258 \tabularnewline
58 & 21.8 & 20.7785110722611 & 1.02148892773893 \tabularnewline
59 & 21.2 & 20.1285110722611 & 1.07148892773893 \tabularnewline
60 & 20.6 & 19.9743444055944 & 0.625655594405593 \tabularnewline
61 & 19.9 & 20.3535110722611 & -0.45351107226108 \tabularnewline
62 & 18.7 & 19.7535110722611 & -1.05351107226107 \tabularnewline
63 & 17.6 & 19.0535110722611 & -1.45351107226108 \tabularnewline
64 & 16.4 & 19.0743444055944 & -2.6743444055944 \tabularnewline
65 & 15.9 & 15.8326777389277 & 0.0673222610722615 \tabularnewline
66 & 16.8 & 15.1660110722611 & 1.63398892773893 \tabularnewline
67 & 22.8 & 19.3660110722611 & 3.43398892773892 \tabularnewline
68 & 24 & 23.5285110722611 & 0.471488927738925 \tabularnewline
69 & 22.2 & 23.6826777389277 & -1.48267773892774 \tabularnewline
70 & 17.9 & 20.4785110722611 & -2.57851107226107 \tabularnewline
71 & 16 & 16.2285110722611 & -0.228511072261071 \tabularnewline
72 & 16 & 14.7743444055944 & 1.22565559440559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210726&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]18.6[/C][C]18.7376335470085[/C][C]-0.137633547008548[/C][/ROW]
[ROW][C]14[/C][C]18.4[/C][C]18.4535110722611[/C][C]-0.0535110722610703[/C][/ROW]
[ROW][C]15[/C][C]18.6[/C][C]18.7535110722611[/C][C]-0.153511072261079[/C][/ROW]
[ROW][C]16[/C][C]19.9[/C][C]20.0743444055944[/C][C]-0.174344405594404[/C][/ROW]
[ROW][C]17[/C][C]19.2[/C][C]19.3326777389277[/C][C]-0.13267773892774[/C][/ROW]
[ROW][C]18[/C][C]18.4[/C][C]18.4660110722611[/C][C]-0.0660110722610696[/C][/ROW]
[ROW][C]19[/C][C]21.1[/C][C]20.9660110722611[/C][C]0.133988927738926[/C][/ROW]
[ROW][C]20[/C][C]20.5[/C][C]21.8285110722611[/C][C]-1.32851107226108[/C][/ROW]
[ROW][C]21[/C][C]19.1[/C][C]20.1826777389277[/C][C]-1.08267773892774[/C][/ROW]
[ROW][C]22[/C][C]18.1[/C][C]17.3785110722611[/C][C]0.721488927738928[/C][/ROW]
[ROW][C]23[/C][C]17[/C][C]16.4285110722611[/C][C]0.571488927738926[/C][/ROW]
[ROW][C]24[/C][C]17.1[/C][C]15.7743444055944[/C][C]1.32565559440559[/C][/ROW]
[ROW][C]25[/C][C]17.4[/C][C]16.8535110722611[/C][C]0.54648892773892[/C][/ROW]
[ROW][C]26[/C][C]16.8[/C][C]17.2535110722611[/C][C]-0.453511072261065[/C][/ROW]
[ROW][C]27[/C][C]15.3[/C][C]17.1535110722611[/C][C]-1.85351107226108[/C][/ROW]
[ROW][C]28[/C][C]14.3[/C][C]16.7743444055944[/C][C]-2.4743444055944[/C][/ROW]
[ROW][C]29[/C][C]13.4[/C][C]13.7326777389277[/C][C]-0.332677738927739[/C][/ROW]
[ROW][C]30[/C][C]15.3[/C][C]12.6660110722611[/C][C]2.63398892773893[/C][/ROW]
[ROW][C]31[/C][C]22.1[/C][C]17.8660110722611[/C][C]4.23398892773893[/C][/ROW]
[ROW][C]32[/C][C]23.7[/C][C]22.8285110722611[/C][C]0.871488927738923[/C][/ROW]
[ROW][C]33[/C][C]22.2[/C][C]23.3826777389277[/C][C]-1.18267773892774[/C][/ROW]
[ROW][C]34[/C][C]19.5[/C][C]20.4785110722611[/C][C]-0.978511072261071[/C][/ROW]
[ROW][C]35[/C][C]16.6[/C][C]17.8285110722611[/C][C]-1.22851107226107[/C][/ROW]
[ROW][C]36[/C][C]17.3[/C][C]15.3743444055944[/C][C]1.92565559440559[/C][/ROW]
[ROW][C]37[/C][C]19.8[/C][C]17.0535110722611[/C][C]2.74648892773892[/C][/ROW]
[ROW][C]38[/C][C]21.2[/C][C]19.6535110722611[/C][C]1.54648892773893[/C][/ROW]
[ROW][C]39[/C][C]21.5[/C][C]21.5535110722611[/C][C]-0.053511072261081[/C][/ROW]
[ROW][C]40[/C][C]20.6[/C][C]22.9743444055944[/C][C]-2.3743444055944[/C][/ROW]
[ROW][C]41[/C][C]19.1[/C][C]20.0326777389277[/C][C]-0.93267773892774[/C][/ROW]
[ROW][C]42[/C][C]19.6[/C][C]18.3660110722611[/C][C]1.23398892773893[/C][/ROW]
[ROW][C]43[/C][C]23.4[/C][C]22.1660110722611[/C][C]1.23398892773892[/C][/ROW]
[ROW][C]44[/C][C]24.3[/C][C]24.1285110722611[/C][C]0.171488927738928[/C][/ROW]
[ROW][C]45[/C][C]24.1[/C][C]23.9826777389277[/C][C]0.11732226107226[/C][/ROW]
[ROW][C]46[/C][C]22.8[/C][C]22.3785110722611[/C][C]0.421488927738928[/C][/ROW]
[ROW][C]47[/C][C]22.5[/C][C]21.1285110722611[/C][C]1.37148892773893[/C][/ROW]
[ROW][C]48[/C][C]23.8[/C][C]21.2743444055944[/C][C]2.52565559440559[/C][/ROW]
[ROW][C]49[/C][C]24.9[/C][C]23.5535110722611[/C][C]1.34648892773892[/C][/ROW]
[ROW][C]50[/C][C]25.2[/C][C]24.7535110722611[/C][C]0.446488927738933[/C][/ROW]
[ROW][C]51[/C][C]24.3[/C][C]25.5535110722611[/C][C]-1.25351107226108[/C][/ROW]
[ROW][C]52[/C][C]22.8[/C][C]25.7743444055944[/C][C]-2.9743444055944[/C][/ROW]
[ROW][C]53[/C][C]20.7[/C][C]22.2326777389277[/C][C]-1.53267773892774[/C][/ROW]
[ROW][C]54[/C][C]19.8[/C][C]19.9660110722611[/C][C]-0.166011072261067[/C][/ROW]
[ROW][C]55[/C][C]22.5[/C][C]22.3660110722611[/C][C]0.133988927738923[/C][/ROW]
[ROW][C]56[/C][C]22.6[/C][C]23.2285110722611[/C][C]-0.628511072261073[/C][/ROW]
[ROW][C]57[/C][C]22.5[/C][C]22.2826777389277[/C][C]0.217322261072258[/C][/ROW]
[ROW][C]58[/C][C]21.8[/C][C]20.7785110722611[/C][C]1.02148892773893[/C][/ROW]
[ROW][C]59[/C][C]21.2[/C][C]20.1285110722611[/C][C]1.07148892773893[/C][/ROW]
[ROW][C]60[/C][C]20.6[/C][C]19.9743444055944[/C][C]0.625655594405593[/C][/ROW]
[ROW][C]61[/C][C]19.9[/C][C]20.3535110722611[/C][C]-0.45351107226108[/C][/ROW]
[ROW][C]62[/C][C]18.7[/C][C]19.7535110722611[/C][C]-1.05351107226107[/C][/ROW]
[ROW][C]63[/C][C]17.6[/C][C]19.0535110722611[/C][C]-1.45351107226108[/C][/ROW]
[ROW][C]64[/C][C]16.4[/C][C]19.0743444055944[/C][C]-2.6743444055944[/C][/ROW]
[ROW][C]65[/C][C]15.9[/C][C]15.8326777389277[/C][C]0.0673222610722615[/C][/ROW]
[ROW][C]66[/C][C]16.8[/C][C]15.1660110722611[/C][C]1.63398892773893[/C][/ROW]
[ROW][C]67[/C][C]22.8[/C][C]19.3660110722611[/C][C]3.43398892773892[/C][/ROW]
[ROW][C]68[/C][C]24[/C][C]23.5285110722611[/C][C]0.471488927738925[/C][/ROW]
[ROW][C]69[/C][C]22.2[/C][C]23.6826777389277[/C][C]-1.48267773892774[/C][/ROW]
[ROW][C]70[/C][C]17.9[/C][C]20.4785110722611[/C][C]-2.57851107226107[/C][/ROW]
[ROW][C]71[/C][C]16[/C][C]16.2285110722611[/C][C]-0.228511072261071[/C][/ROW]
[ROW][C]72[/C][C]16[/C][C]14.7743444055944[/C][C]1.22565559440559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210726&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210726&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
1318.618.7376335470085-0.137633547008548
1418.418.4535110722611-0.0535110722610703
1518.618.7535110722611-0.153511072261079
1619.920.0743444055944-0.174344405594404
1719.219.3326777389277-0.13267773892774
1818.418.4660110722611-0.0660110722610696
1921.120.96601107226110.133988927738926
2020.521.8285110722611-1.32851107226108
2119.120.1826777389277-1.08267773892774
2218.117.37851107226110.721488927738928
231716.42851107226110.571488927738926
2417.115.77434440559441.32565559440559
2517.416.85351107226110.54648892773892
2616.817.2535110722611-0.453511072261065
2715.317.1535110722611-1.85351107226108
2814.316.7743444055944-2.4743444055944
2913.413.7326777389277-0.332677738927739
3015.312.66601107226112.63398892773893
3122.117.86601107226114.23398892773893
3223.722.82851107226110.871488927738923
3322.223.3826777389277-1.18267773892774
3419.520.4785110722611-0.978511072261071
3516.617.8285110722611-1.22851107226107
3617.315.37434440559441.92565559440559
3719.817.05351107226112.74648892773892
3821.219.65351107226111.54648892773893
3921.521.5535110722611-0.053511072261081
4020.622.9743444055944-2.3743444055944
4119.120.0326777389277-0.93267773892774
4219.618.36601107226111.23398892773893
4323.422.16601107226111.23398892773892
4424.324.12851107226110.171488927738928
4524.123.98267773892770.11732226107226
4622.822.37851107226110.421488927738928
4722.521.12851107226111.37148892773893
4823.821.27434440559442.52565559440559
4924.923.55351107226111.34648892773892
5025.224.75351107226110.446488927738933
5124.325.5535110722611-1.25351107226108
5222.825.7743444055944-2.9743444055944
5320.722.2326777389277-1.53267773892774
5419.819.9660110722611-0.166011072261067
5522.522.36601107226110.133988927738923
5622.623.2285110722611-0.628511072261073
5722.522.28267773892770.217322261072258
5821.820.77851107226111.02148892773893
5921.220.12851107226111.07148892773893
6020.619.97434440559440.625655594405593
6119.920.3535110722611-0.45351107226108
6218.719.7535110722611-1.05351107226107
6317.619.0535110722611-1.45351107226108
6416.419.0743444055944-2.6743444055944
6515.915.83267773892770.0673222610722615
6616.815.16601107226111.63398892773893
6722.819.36601107226113.43398892773892
682423.52851107226110.471488927738925
6922.223.6826777389277-1.48267773892774
7017.920.4785110722611-2.57851107226107
711616.2285110722611-0.228511072261071
721614.77434440559441.22565559440559







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7315.753511072261112.842224321965918.6647978225563
7415.607022144522111.489840938297519.7242033507467
7515.960533216783210.918036649869821.0030297836966
7617.434877622377611.612304121787223.2574511229681
7716.867555361305410.357720285650823.3773904369599
7816.13356643356649.0023994004177123.2647334667151
7918.699577505827510.99703676934926.4021182423061
8019.428088578088611.193726165639427.6624509905378
8119.110766317016310.376906066130727.844626567902
8217.38927738927748.1829803364746126.5955744420802
8315.71778846153856.0621426536761225.3734342694008
8414.49213286713294.4071397333060524.5771260009597

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 15.7535110722611 & 12.8422243219659 & 18.6647978225563 \tabularnewline
74 & 15.6070221445221 & 11.4898409382975 & 19.7242033507467 \tabularnewline
75 & 15.9605332167832 & 10.9180366498698 & 21.0030297836966 \tabularnewline
76 & 17.4348776223776 & 11.6123041217872 & 23.2574511229681 \tabularnewline
77 & 16.8675553613054 & 10.3577202856508 & 23.3773904369599 \tabularnewline
78 & 16.1335664335664 & 9.00239940041771 & 23.2647334667151 \tabularnewline
79 & 18.6995775058275 & 10.997036769349 & 26.4021182423061 \tabularnewline
80 & 19.4280885780886 & 11.1937261656394 & 27.6624509905378 \tabularnewline
81 & 19.1107663170163 & 10.3769060661307 & 27.844626567902 \tabularnewline
82 & 17.3892773892774 & 8.18298033647461 & 26.5955744420802 \tabularnewline
83 & 15.7177884615385 & 6.06214265367612 & 25.3734342694008 \tabularnewline
84 & 14.4921328671329 & 4.40713973330605 & 24.5771260009597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210726&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]15.7535110722611[/C][C]12.8422243219659[/C][C]18.6647978225563[/C][/ROW]
[ROW][C]74[/C][C]15.6070221445221[/C][C]11.4898409382975[/C][C]19.7242033507467[/C][/ROW]
[ROW][C]75[/C][C]15.9605332167832[/C][C]10.9180366498698[/C][C]21.0030297836966[/C][/ROW]
[ROW][C]76[/C][C]17.4348776223776[/C][C]11.6123041217872[/C][C]23.2574511229681[/C][/ROW]
[ROW][C]77[/C][C]16.8675553613054[/C][C]10.3577202856508[/C][C]23.3773904369599[/C][/ROW]
[ROW][C]78[/C][C]16.1335664335664[/C][C]9.00239940041771[/C][C]23.2647334667151[/C][/ROW]
[ROW][C]79[/C][C]18.6995775058275[/C][C]10.997036769349[/C][C]26.4021182423061[/C][/ROW]
[ROW][C]80[/C][C]19.4280885780886[/C][C]11.1937261656394[/C][C]27.6624509905378[/C][/ROW]
[ROW][C]81[/C][C]19.1107663170163[/C][C]10.3769060661307[/C][C]27.844626567902[/C][/ROW]
[ROW][C]82[/C][C]17.3892773892774[/C][C]8.18298033647461[/C][C]26.5955744420802[/C][/ROW]
[ROW][C]83[/C][C]15.7177884615385[/C][C]6.06214265367612[/C][C]25.3734342694008[/C][/ROW]
[ROW][C]84[/C][C]14.4921328671329[/C][C]4.40713973330605[/C][C]24.5771260009597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210726&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210726&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
7315.753511072261112.842224321965918.6647978225563
7415.607022144522111.489840938297519.7242033507467
7515.960533216783210.918036649869821.0030297836966
7617.434877622377611.612304121787223.2574511229681
7716.867555361305410.357720285650823.3773904369599
7816.13356643356649.0023994004177123.2647334667151
7918.699577505827510.99703676934926.4021182423061
8019.428088578088611.193726165639427.6624509905378
8119.110766317016310.376906066130727.844626567902
8217.38927738927748.1829803364746126.5955744420802
8315.71778846153856.0621426536761225.3734342694008
8414.49213286713294.4071397333060524.5771260009597



Parameters (Session):
par1 = 200 ; par2 = 5 ; par3 = 0 ;
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')