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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:13:54 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356081330vf1mb22sn44i2zy.htm/, Retrieved Sat, 20 Apr 2024 13:07:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203342, Retrieved Sat, 20 Apr 2024 13:07:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:13:54] [626ef45870361663d1821a5d69b931ae] [Current]
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Dataseries X:
23.9
24.06
24.33
24.39
24.39
24.49
24.83
25.08
25.11
25.13
25.17
25.11
25.35
25.36
25.35
25.34
25.39
25.58
25.71
25.66
25.74
25.73
25.72
25.55
25.71
25.92
25.93
26
26.02
26.08
26.17
26.18
26.21
26.28
26.34
26.17
26.38
26.36
26.27
26.26
26.49
26.99
27.14
27.1
27.01
26.93
26.97
26.35
26.93
26.92
27.05
27.01
26.9
26.93
26.95
26.89
26.7
26.55
26.48
25.71
26.17
26.31
26.58
26.49
26.57
26.6
26.69
26.59
26.75
26.79
26.8
26.62




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203342&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203342&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.874592242584807
beta0.0335201586784274
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.874592242584807 \tabularnewline
beta & 0.0335201586784274 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203342&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]0.874592242584807[/C][/ROW]
[ROW][C]beta[/C][C]0.0335201586784274[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203342&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
alpha0.874592242584807
beta0.0335201586784274
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325.3524.82148452543520.528515474564795
1425.3625.32021548710960.0397845128904137
1525.3525.3828895904979-0.0328895904978879
1625.3425.3800982759491-0.0400982759491306
1725.3925.4331617440996-0.0431617440996419
1825.5825.6292095794622-0.0492095794621612
1925.7125.7187633832763-0.00876338327631032
2025.6625.9341999146569-0.274199914656915
2125.7425.70118067283540.0388193271645711
2225.7325.7478570394352-0.0178570394352207
2325.7225.7658478322993-0.0458478322993408
2425.5525.6499903247036-0.0999903247036293
2525.7125.862470486768-0.152470486767964
2625.9225.68259244726710.237407552732872
2725.9325.89331779790580.0366822020941839
282625.93690735957590.0630926404240704
2926.0226.0707526889101-0.0507526889100554
3026.0826.2536990701944-0.173699070194395
3126.1726.227466589048-0.0574665890479835
3226.1826.354051274782-0.174051274782038
3326.2126.2356140795416-0.0256140795416009
3426.2826.20404187107120.0759581289287716
3526.3426.28888785201420.0511121479858119
3626.1726.2394362877906-0.0694362877906443
3726.3826.4704183814213-0.0904183814212907
3826.3626.3865816382685-0.0265816382685458
3926.2726.3267464372922-0.0567464372922188
4026.2626.2755557892662-0.0155557892662479
4126.4926.30834679065120.181653209348802
4226.9926.67024711433050.319752885669494
4327.1427.09583480820810.0441651917918975
4427.127.3063498390033-0.206349839003344
4527.0127.1832695384262-0.173269538426162
4626.9327.0344866366711-0.104486636671112
4726.9726.95292993841860.0170700615814248
4826.3526.8492187360235-0.499218736023487
4926.9326.68581581341090.244184186589099
5026.9226.89337631580260.0266236841974283
5127.0526.86763224013070.182367759869326
5227.0127.0296339225862-0.019633922586241
5326.927.0841864026099-0.184186402609889
5426.9327.1351651078699-0.205165107869924
5526.9527.0412061851579-0.0912061851578692
5626.8927.0714306312138-0.181430631213793
5726.726.9450793027355-0.245079302735522
5826.5526.7114255247806-0.161425524780604
5926.4826.5629732784842-0.0829732784841859
6025.7126.27491968591-0.564919685910013
6126.1726.10230406108670.0676959389133316
6226.3126.08782922058540.222170779414569
6326.5826.21746611052260.362533889477358
6426.4926.48161813588870.00838186411131048
6526.5726.50922666932810.0607733306718821
6626.626.7459046932843-0.145904693284344
6726.6926.6953336733872-0.00533367338718094
6826.5926.7690792776431-0.17907927764308
6926.7526.61717522864030.132824771359694
7026.7926.71589991675610.0741000832438594
7126.826.78146076098650.0185392390134744
7226.6226.51815519782670.101844802173275

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 25.35 & 24.8214845254352 & 0.528515474564795 \tabularnewline
14 & 25.36 & 25.3202154871096 & 0.0397845128904137 \tabularnewline
15 & 25.35 & 25.3828895904979 & -0.0328895904978879 \tabularnewline
16 & 25.34 & 25.3800982759491 & -0.0400982759491306 \tabularnewline
17 & 25.39 & 25.4331617440996 & -0.0431617440996419 \tabularnewline
18 & 25.58 & 25.6292095794622 & -0.0492095794621612 \tabularnewline
19 & 25.71 & 25.7187633832763 & -0.00876338327631032 \tabularnewline
20 & 25.66 & 25.9341999146569 & -0.274199914656915 \tabularnewline
21 & 25.74 & 25.7011806728354 & 0.0388193271645711 \tabularnewline
22 & 25.73 & 25.7478570394352 & -0.0178570394352207 \tabularnewline
23 & 25.72 & 25.7658478322993 & -0.0458478322993408 \tabularnewline
24 & 25.55 & 25.6499903247036 & -0.0999903247036293 \tabularnewline
25 & 25.71 & 25.862470486768 & -0.152470486767964 \tabularnewline
26 & 25.92 & 25.6825924472671 & 0.237407552732872 \tabularnewline
27 & 25.93 & 25.8933177979058 & 0.0366822020941839 \tabularnewline
28 & 26 & 25.9369073595759 & 0.0630926404240704 \tabularnewline
29 & 26.02 & 26.0707526889101 & -0.0507526889100554 \tabularnewline
30 & 26.08 & 26.2536990701944 & -0.173699070194395 \tabularnewline
31 & 26.17 & 26.227466589048 & -0.0574665890479835 \tabularnewline
32 & 26.18 & 26.354051274782 & -0.174051274782038 \tabularnewline
33 & 26.21 & 26.2356140795416 & -0.0256140795416009 \tabularnewline
34 & 26.28 & 26.2040418710712 & 0.0759581289287716 \tabularnewline
35 & 26.34 & 26.2888878520142 & 0.0511121479858119 \tabularnewline
36 & 26.17 & 26.2394362877906 & -0.0694362877906443 \tabularnewline
37 & 26.38 & 26.4704183814213 & -0.0904183814212907 \tabularnewline
38 & 26.36 & 26.3865816382685 & -0.0265816382685458 \tabularnewline
39 & 26.27 & 26.3267464372922 & -0.0567464372922188 \tabularnewline
40 & 26.26 & 26.2755557892662 & -0.0155557892662479 \tabularnewline
41 & 26.49 & 26.3083467906512 & 0.181653209348802 \tabularnewline
42 & 26.99 & 26.6702471143305 & 0.319752885669494 \tabularnewline
43 & 27.14 & 27.0958348082081 & 0.0441651917918975 \tabularnewline
44 & 27.1 & 27.3063498390033 & -0.206349839003344 \tabularnewline
45 & 27.01 & 27.1832695384262 & -0.173269538426162 \tabularnewline
46 & 26.93 & 27.0344866366711 & -0.104486636671112 \tabularnewline
47 & 26.97 & 26.9529299384186 & 0.0170700615814248 \tabularnewline
48 & 26.35 & 26.8492187360235 & -0.499218736023487 \tabularnewline
49 & 26.93 & 26.6858158134109 & 0.244184186589099 \tabularnewline
50 & 26.92 & 26.8933763158026 & 0.0266236841974283 \tabularnewline
51 & 27.05 & 26.8676322401307 & 0.182367759869326 \tabularnewline
52 & 27.01 & 27.0296339225862 & -0.019633922586241 \tabularnewline
53 & 26.9 & 27.0841864026099 & -0.184186402609889 \tabularnewline
54 & 26.93 & 27.1351651078699 & -0.205165107869924 \tabularnewline
55 & 26.95 & 27.0412061851579 & -0.0912061851578692 \tabularnewline
56 & 26.89 & 27.0714306312138 & -0.181430631213793 \tabularnewline
57 & 26.7 & 26.9450793027355 & -0.245079302735522 \tabularnewline
58 & 26.55 & 26.7114255247806 & -0.161425524780604 \tabularnewline
59 & 26.48 & 26.5629732784842 & -0.0829732784841859 \tabularnewline
60 & 25.71 & 26.27491968591 & -0.564919685910013 \tabularnewline
61 & 26.17 & 26.1023040610867 & 0.0676959389133316 \tabularnewline
62 & 26.31 & 26.0878292205854 & 0.222170779414569 \tabularnewline
63 & 26.58 & 26.2174661105226 & 0.362533889477358 \tabularnewline
64 & 26.49 & 26.4816181358887 & 0.00838186411131048 \tabularnewline
65 & 26.57 & 26.5092266693281 & 0.0607733306718821 \tabularnewline
66 & 26.6 & 26.7459046932843 & -0.145904693284344 \tabularnewline
67 & 26.69 & 26.6953336733872 & -0.00533367338718094 \tabularnewline
68 & 26.59 & 26.7690792776431 & -0.17907927764308 \tabularnewline
69 & 26.75 & 26.6171752286403 & 0.132824771359694 \tabularnewline
70 & 26.79 & 26.7158999167561 & 0.0741000832438594 \tabularnewline
71 & 26.8 & 26.7814607609865 & 0.0185392390134744 \tabularnewline
72 & 26.62 & 26.5181551978267 & 0.101844802173275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203342&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]25.35[/C][C]24.8214845254352[/C][C]0.528515474564795[/C][/ROW]
[ROW][C]14[/C][C]25.36[/C][C]25.3202154871096[/C][C]0.0397845128904137[/C][/ROW]
[ROW][C]15[/C][C]25.35[/C][C]25.3828895904979[/C][C]-0.0328895904978879[/C][/ROW]
[ROW][C]16[/C][C]25.34[/C][C]25.3800982759491[/C][C]-0.0400982759491306[/C][/ROW]
[ROW][C]17[/C][C]25.39[/C][C]25.4331617440996[/C][C]-0.0431617440996419[/C][/ROW]
[ROW][C]18[/C][C]25.58[/C][C]25.6292095794622[/C][C]-0.0492095794621612[/C][/ROW]
[ROW][C]19[/C][C]25.71[/C][C]25.7187633832763[/C][C]-0.00876338327631032[/C][/ROW]
[ROW][C]20[/C][C]25.66[/C][C]25.9341999146569[/C][C]-0.274199914656915[/C][/ROW]
[ROW][C]21[/C][C]25.74[/C][C]25.7011806728354[/C][C]0.0388193271645711[/C][/ROW]
[ROW][C]22[/C][C]25.73[/C][C]25.7478570394352[/C][C]-0.0178570394352207[/C][/ROW]
[ROW][C]23[/C][C]25.72[/C][C]25.7658478322993[/C][C]-0.0458478322993408[/C][/ROW]
[ROW][C]24[/C][C]25.55[/C][C]25.6499903247036[/C][C]-0.0999903247036293[/C][/ROW]
[ROW][C]25[/C][C]25.71[/C][C]25.862470486768[/C][C]-0.152470486767964[/C][/ROW]
[ROW][C]26[/C][C]25.92[/C][C]25.6825924472671[/C][C]0.237407552732872[/C][/ROW]
[ROW][C]27[/C][C]25.93[/C][C]25.8933177979058[/C][C]0.0366822020941839[/C][/ROW]
[ROW][C]28[/C][C]26[/C][C]25.9369073595759[/C][C]0.0630926404240704[/C][/ROW]
[ROW][C]29[/C][C]26.02[/C][C]26.0707526889101[/C][C]-0.0507526889100554[/C][/ROW]
[ROW][C]30[/C][C]26.08[/C][C]26.2536990701944[/C][C]-0.173699070194395[/C][/ROW]
[ROW][C]31[/C][C]26.17[/C][C]26.227466589048[/C][C]-0.0574665890479835[/C][/ROW]
[ROW][C]32[/C][C]26.18[/C][C]26.354051274782[/C][C]-0.174051274782038[/C][/ROW]
[ROW][C]33[/C][C]26.21[/C][C]26.2356140795416[/C][C]-0.0256140795416009[/C][/ROW]
[ROW][C]34[/C][C]26.28[/C][C]26.2040418710712[/C][C]0.0759581289287716[/C][/ROW]
[ROW][C]35[/C][C]26.34[/C][C]26.2888878520142[/C][C]0.0511121479858119[/C][/ROW]
[ROW][C]36[/C][C]26.17[/C][C]26.2394362877906[/C][C]-0.0694362877906443[/C][/ROW]
[ROW][C]37[/C][C]26.38[/C][C]26.4704183814213[/C][C]-0.0904183814212907[/C][/ROW]
[ROW][C]38[/C][C]26.36[/C][C]26.3865816382685[/C][C]-0.0265816382685458[/C][/ROW]
[ROW][C]39[/C][C]26.27[/C][C]26.3267464372922[/C][C]-0.0567464372922188[/C][/ROW]
[ROW][C]40[/C][C]26.26[/C][C]26.2755557892662[/C][C]-0.0155557892662479[/C][/ROW]
[ROW][C]41[/C][C]26.49[/C][C]26.3083467906512[/C][C]0.181653209348802[/C][/ROW]
[ROW][C]42[/C][C]26.99[/C][C]26.6702471143305[/C][C]0.319752885669494[/C][/ROW]
[ROW][C]43[/C][C]27.14[/C][C]27.0958348082081[/C][C]0.0441651917918975[/C][/ROW]
[ROW][C]44[/C][C]27.1[/C][C]27.3063498390033[/C][C]-0.206349839003344[/C][/ROW]
[ROW][C]45[/C][C]27.01[/C][C]27.1832695384262[/C][C]-0.173269538426162[/C][/ROW]
[ROW][C]46[/C][C]26.93[/C][C]27.0344866366711[/C][C]-0.104486636671112[/C][/ROW]
[ROW][C]47[/C][C]26.97[/C][C]26.9529299384186[/C][C]0.0170700615814248[/C][/ROW]
[ROW][C]48[/C][C]26.35[/C][C]26.8492187360235[/C][C]-0.499218736023487[/C][/ROW]
[ROW][C]49[/C][C]26.93[/C][C]26.6858158134109[/C][C]0.244184186589099[/C][/ROW]
[ROW][C]50[/C][C]26.92[/C][C]26.8933763158026[/C][C]0.0266236841974283[/C][/ROW]
[ROW][C]51[/C][C]27.05[/C][C]26.8676322401307[/C][C]0.182367759869326[/C][/ROW]
[ROW][C]52[/C][C]27.01[/C][C]27.0296339225862[/C][C]-0.019633922586241[/C][/ROW]
[ROW][C]53[/C][C]26.9[/C][C]27.0841864026099[/C][C]-0.184186402609889[/C][/ROW]
[ROW][C]54[/C][C]26.93[/C][C]27.1351651078699[/C][C]-0.205165107869924[/C][/ROW]
[ROW][C]55[/C][C]26.95[/C][C]27.0412061851579[/C][C]-0.0912061851578692[/C][/ROW]
[ROW][C]56[/C][C]26.89[/C][C]27.0714306312138[/C][C]-0.181430631213793[/C][/ROW]
[ROW][C]57[/C][C]26.7[/C][C]26.9450793027355[/C][C]-0.245079302735522[/C][/ROW]
[ROW][C]58[/C][C]26.55[/C][C]26.7114255247806[/C][C]-0.161425524780604[/C][/ROW]
[ROW][C]59[/C][C]26.48[/C][C]26.5629732784842[/C][C]-0.0829732784841859[/C][/ROW]
[ROW][C]60[/C][C]25.71[/C][C]26.27491968591[/C][C]-0.564919685910013[/C][/ROW]
[ROW][C]61[/C][C]26.17[/C][C]26.1023040610867[/C][C]0.0676959389133316[/C][/ROW]
[ROW][C]62[/C][C]26.31[/C][C]26.0878292205854[/C][C]0.222170779414569[/C][/ROW]
[ROW][C]63[/C][C]26.58[/C][C]26.2174661105226[/C][C]0.362533889477358[/C][/ROW]
[ROW][C]64[/C][C]26.49[/C][C]26.4816181358887[/C][C]0.00838186411131048[/C][/ROW]
[ROW][C]65[/C][C]26.57[/C][C]26.5092266693281[/C][C]0.0607733306718821[/C][/ROW]
[ROW][C]66[/C][C]26.6[/C][C]26.7459046932843[/C][C]-0.145904693284344[/C][/ROW]
[ROW][C]67[/C][C]26.69[/C][C]26.6953336733872[/C][C]-0.00533367338718094[/C][/ROW]
[ROW][C]68[/C][C]26.59[/C][C]26.7690792776431[/C][C]-0.17907927764308[/C][/ROW]
[ROW][C]69[/C][C]26.75[/C][C]26.6171752286403[/C][C]0.132824771359694[/C][/ROW]
[ROW][C]70[/C][C]26.79[/C][C]26.7158999167561[/C][C]0.0741000832438594[/C][/ROW]
[ROW][C]71[/C][C]26.8[/C][C]26.7814607609865[/C][C]0.0185392390134744[/C][/ROW]
[ROW][C]72[/C][C]26.62[/C][C]26.5181551978267[/C][C]0.101844802173275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203342&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
1325.3524.82148452543520.528515474564795
1425.3625.32021548710960.0397845128904137
1525.3525.3828895904979-0.0328895904978879
1625.3425.3800982759491-0.0400982759491306
1725.3925.4331617440996-0.0431617440996419
1825.5825.6292095794622-0.0492095794621612
1925.7125.7187633832763-0.00876338327631032
2025.6625.9341999146569-0.274199914656915
2125.7425.70118067283540.0388193271645711
2225.7325.7478570394352-0.0178570394352207
2325.7225.7658478322993-0.0458478322993408
2425.5525.6499903247036-0.0999903247036293
2525.7125.862470486768-0.152470486767964
2625.9225.68259244726710.237407552732872
2725.9325.89331779790580.0366822020941839
282625.93690735957590.0630926404240704
2926.0226.0707526889101-0.0507526889100554
3026.0826.2536990701944-0.173699070194395
3126.1726.227466589048-0.0574665890479835
3226.1826.354051274782-0.174051274782038
3326.2126.2356140795416-0.0256140795416009
3426.2826.20404187107120.0759581289287716
3526.3426.28888785201420.0511121479858119
3626.1726.2394362877906-0.0694362877906443
3726.3826.4704183814213-0.0904183814212907
3826.3626.3865816382685-0.0265816382685458
3926.2726.3267464372922-0.0567464372922188
4026.2626.2755557892662-0.0155557892662479
4126.4926.30834679065120.181653209348802
4226.9926.67024711433050.319752885669494
4327.1427.09583480820810.0441651917918975
4427.127.3063498390033-0.206349839003344
4527.0127.1832695384262-0.173269538426162
4626.9327.0344866366711-0.104486636671112
4726.9726.95292993841860.0170700615814248
4826.3526.8492187360235-0.499218736023487
4926.9326.68581581341090.244184186589099
5026.9226.89337631580260.0266236841974283
5127.0526.86763224013070.182367759869326
5227.0127.0296339225862-0.019633922586241
5326.927.0841864026099-0.184186402609889
5426.9327.1351651078699-0.205165107869924
5526.9527.0412061851579-0.0912061851578692
5626.8927.0714306312138-0.181430631213793
5726.726.9450793027355-0.245079302735522
5826.5526.7114255247806-0.161425524780604
5926.4826.5629732784842-0.0829732784841859
6025.7126.27491968591-0.564919685910013
6126.1726.10230406108670.0676959389133316
6226.3126.08782922058540.222170779414569
6326.5826.21746611052260.362533889477358
6426.4926.48161813588870.00838186411131048
6526.5726.50922666932810.0607733306718821
6626.626.7459046932843-0.145904693284344
6726.6926.6953336733872-0.00533367338718094
6826.5926.7690792776431-0.17907927764308
6926.7526.61717522864030.132824771359694
7026.7926.71589991675610.0741000832438594
7126.826.78146076098650.0185392390134744
7226.6226.51815519782670.101844802173275







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327.042883494448726.691996898243227.3937700906543
7427.005360746985426.532906141490527.4778153524803
7526.968654906246226.394738268111427.5425715443809
7626.871464945700826.207889342704827.5350405486967
7726.900005333586126.150933826397327.6490768407748
7827.059052208998726.22561267534427.8924917426534
7927.159132756427726.24581125378728.0724542590684
8027.220552284470126.230649932161528.2104546367787
8127.274505720387326.209859014713128.3391524260615
8227.25444747426226.119019730739128.3898752177849
8327.251223846318626.045384901690728.4570627909465
8426.980109598948415.465814501215138.4944046966817

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27.0428834944487 & 26.6919968982432 & 27.3937700906543 \tabularnewline
74 & 27.0053607469854 & 26.5329061414905 & 27.4778153524803 \tabularnewline
75 & 26.9686549062462 & 26.3947382681114 & 27.5425715443809 \tabularnewline
76 & 26.8714649457008 & 26.2078893427048 & 27.5350405486967 \tabularnewline
77 & 26.9000053335861 & 26.1509338263973 & 27.6490768407748 \tabularnewline
78 & 27.0590522089987 & 26.225612675344 & 27.8924917426534 \tabularnewline
79 & 27.1591327564277 & 26.245811253787 & 28.0724542590684 \tabularnewline
80 & 27.2205522844701 & 26.2306499321615 & 28.2104546367787 \tabularnewline
81 & 27.2745057203873 & 26.2098590147131 & 28.3391524260615 \tabularnewline
82 & 27.254447474262 & 26.1190197307391 & 28.3898752177849 \tabularnewline
83 & 27.2512238463186 & 26.0453849016907 & 28.4570627909465 \tabularnewline
84 & 26.9801095989484 & 15.4658145012151 & 38.4944046966817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203342&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]27.0428834944487[/C][C]26.6919968982432[/C][C]27.3937700906543[/C][/ROW]
[ROW][C]74[/C][C]27.0053607469854[/C][C]26.5329061414905[/C][C]27.4778153524803[/C][/ROW]
[ROW][C]75[/C][C]26.9686549062462[/C][C]26.3947382681114[/C][C]27.5425715443809[/C][/ROW]
[ROW][C]76[/C][C]26.8714649457008[/C][C]26.2078893427048[/C][C]27.5350405486967[/C][/ROW]
[ROW][C]77[/C][C]26.9000053335861[/C][C]26.1509338263973[/C][C]27.6490768407748[/C][/ROW]
[ROW][C]78[/C][C]27.0590522089987[/C][C]26.225612675344[/C][C]27.8924917426534[/C][/ROW]
[ROW][C]79[/C][C]27.1591327564277[/C][C]26.245811253787[/C][C]28.0724542590684[/C][/ROW]
[ROW][C]80[/C][C]27.2205522844701[/C][C]26.2306499321615[/C][C]28.2104546367787[/C][/ROW]
[ROW][C]81[/C][C]27.2745057203873[/C][C]26.2098590147131[/C][C]28.3391524260615[/C][/ROW]
[ROW][C]82[/C][C]27.254447474262[/C][C]26.1190197307391[/C][C]28.3898752177849[/C][/ROW]
[ROW][C]83[/C][C]27.2512238463186[/C][C]26.0453849016907[/C][C]28.4570627909465[/C][/ROW]
[ROW][C]84[/C][C]26.9801095989484[/C][C]15.4658145012151[/C][C]38.4944046966817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203342&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
7327.042883494448726.691996898243227.3937700906543
7427.005360746985426.532906141490527.4778153524803
7526.968654906246226.394738268111427.5425715443809
7626.871464945700826.207889342704827.5350405486967
7726.900005333586126.150933826397327.6490768407748
7827.059052208998726.22561267534427.8924917426534
7927.159132756427726.24581125378728.0724542590684
8027.220552284470126.230649932161528.2104546367787
8127.274505720387326.209859014713128.3391524260615
8227.25444747426226.119019730739128.3898752177849
8327.251223846318626.045384901690728.4570627909465
8426.980109598948415.465814501215138.4944046966817



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')