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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 04:16:54 -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/t1356081448pmenmrx38pvfeqd.htm/, Retrieved Fri, 26 Apr 2024 04:46:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203348, Retrieved Fri, 26 Apr 2024 04:46:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:16:54] [b7ec516ed4ac617af0f7d8ff855a58b9] [Current]
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Dataseries X:
15,58
15,66
15,73
15,74
15,77
15,78
15,8
15,81
15,82
15,88
15,85
15,89
15,92
16,02
16,1
16,13
16,21
16,25
16,27
16,21
16,21
16,24
16,32
16,32
16,36
16,48
16,54
16,58
16,56
16,55
16,58
16,53
16,6
16,46
16,48
16,48
16,49
16,54
16,67
16,72
16,79
16,86
16,84
16,86
16,96
17,01
17,02
17,04
17,04
17,39
17,54
17,57
17,58
17,56
17,63
17,67
17,71
17,75
17,82
17,86
17,89
17,96
18
18,08
18
18,02
18,01
18,02
17,95
17,96
18
18,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203348&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203348&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.875400024974026
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.875400024974026 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203348&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]0.875400024974026[/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=203348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203348&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
alpha0.875400024974026
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.9215.71131771409690.208682285903068
1416.0215.99225363514870.0277463648512963
1516.116.09822864662650.00177135337345646
1616.1316.1331456193546-0.00314561935457291
1716.2116.2104184985029-0.000418498502913422
1816.2516.24714568330910.00285431669093583
1916.2716.20993097959660.0600690204033683
2016.2116.2773936674675-0.0673936674675026
2116.2116.2320554895922-0.0220554895921765
2216.2416.2763933413951-0.0363933413950939
2316.3216.2130805667670.106919433233038
2416.3216.3434474441589-0.023447444158883
2516.3616.3748842060348-0.0148842060348287
2616.4816.43870113474490.0412988652550759
2716.5416.5545459289014-0.0145459289013772
2816.5816.57451298415370.00548701584634159
2916.5616.6609523904799-0.100952390479915
3016.5516.6101405751483-0.0601405751483313
3116.5816.52361224361820.0563877563817634
3216.5316.5712769388902-0.0412769388902348
3316.616.55414164063470.0458583593653117
3416.4616.6567819810659-0.196781981065872
3516.4816.47012005181710.0098799481828955
3616.4816.4991555437033-0.019155543703345
3716.4916.5355992630508-0.0455992630507929
3816.5416.5799256240661-0.0399256240661288
3916.6716.61785684123060.0521431587694359
4016.7216.69870322779310.0212967722069131
4116.7916.78593098176860.00406901823141226
4216.8616.83222500094060.0277749990593783
4316.8416.83615546318460.00384453681535746
4416.8616.82488539207120.0351146079287759
4516.9616.88537373928010.0746262607198638
4617.0116.98265467626170.0273453237383343
4717.0217.01717461016820.00282538983181979
4817.0417.03583492752510.0041650724749438
4917.0417.0899081166026-0.0499081166025626
5017.3917.13285705778730.257142942212674
5117.5417.44475072375950.0952492762404802
5217.5717.5593138655230.0106861344769982
5317.5817.6367143109081-0.0567143109081343
5417.5617.6332647738813-0.0732647738812595
5517.6317.54332254632660.0866774536734027
5617.6717.60635586655790.0636441334420539
5717.7117.6967094767330.0132905232669991
5817.7517.7340262905360.0159737094639993
5917.8217.75436612112830.0656338788716511
6017.8617.82733343680350.0326665631964858
6117.8917.9000436508077-0.0100436508077024
6217.9618.0202200991569-0.0602200991568935
631818.0351230629853-0.0351230629853418
6418.0818.02464896181850.0553510381814846
651818.1334435102797-0.133443510279744
6618.0218.0609616630024-0.0409616630024274
6718.0118.0181043168846-0.00810431688463353
6818.0217.99418314254030.0258168574597484
6917.9518.0450257744868-0.0950257744867855
7017.9617.9877338065294-0.0277338065293975
711817.97570884708640.0242911529136229
7218.0118.00814137294280.00185862705722784

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.92 & 15.7113177140969 & 0.208682285903068 \tabularnewline
14 & 16.02 & 15.9922536351487 & 0.0277463648512963 \tabularnewline
15 & 16.1 & 16.0982286466265 & 0.00177135337345646 \tabularnewline
16 & 16.13 & 16.1331456193546 & -0.00314561935457291 \tabularnewline
17 & 16.21 & 16.2104184985029 & -0.000418498502913422 \tabularnewline
18 & 16.25 & 16.2471456833091 & 0.00285431669093583 \tabularnewline
19 & 16.27 & 16.2099309795966 & 0.0600690204033683 \tabularnewline
20 & 16.21 & 16.2773936674675 & -0.0673936674675026 \tabularnewline
21 & 16.21 & 16.2320554895922 & -0.0220554895921765 \tabularnewline
22 & 16.24 & 16.2763933413951 & -0.0363933413950939 \tabularnewline
23 & 16.32 & 16.213080566767 & 0.106919433233038 \tabularnewline
24 & 16.32 & 16.3434474441589 & -0.023447444158883 \tabularnewline
25 & 16.36 & 16.3748842060348 & -0.0148842060348287 \tabularnewline
26 & 16.48 & 16.4387011347449 & 0.0412988652550759 \tabularnewline
27 & 16.54 & 16.5545459289014 & -0.0145459289013772 \tabularnewline
28 & 16.58 & 16.5745129841537 & 0.00548701584634159 \tabularnewline
29 & 16.56 & 16.6609523904799 & -0.100952390479915 \tabularnewline
30 & 16.55 & 16.6101405751483 & -0.0601405751483313 \tabularnewline
31 & 16.58 & 16.5236122436182 & 0.0563877563817634 \tabularnewline
32 & 16.53 & 16.5712769388902 & -0.0412769388902348 \tabularnewline
33 & 16.6 & 16.5541416406347 & 0.0458583593653117 \tabularnewline
34 & 16.46 & 16.6567819810659 & -0.196781981065872 \tabularnewline
35 & 16.48 & 16.4701200518171 & 0.0098799481828955 \tabularnewline
36 & 16.48 & 16.4991555437033 & -0.019155543703345 \tabularnewline
37 & 16.49 & 16.5355992630508 & -0.0455992630507929 \tabularnewline
38 & 16.54 & 16.5799256240661 & -0.0399256240661288 \tabularnewline
39 & 16.67 & 16.6178568412306 & 0.0521431587694359 \tabularnewline
40 & 16.72 & 16.6987032277931 & 0.0212967722069131 \tabularnewline
41 & 16.79 & 16.7859309817686 & 0.00406901823141226 \tabularnewline
42 & 16.86 & 16.8322250009406 & 0.0277749990593783 \tabularnewline
43 & 16.84 & 16.8361554631846 & 0.00384453681535746 \tabularnewline
44 & 16.86 & 16.8248853920712 & 0.0351146079287759 \tabularnewline
45 & 16.96 & 16.8853737392801 & 0.0746262607198638 \tabularnewline
46 & 17.01 & 16.9826546762617 & 0.0273453237383343 \tabularnewline
47 & 17.02 & 17.0171746101682 & 0.00282538983181979 \tabularnewline
48 & 17.04 & 17.0358349275251 & 0.0041650724749438 \tabularnewline
49 & 17.04 & 17.0899081166026 & -0.0499081166025626 \tabularnewline
50 & 17.39 & 17.1328570577873 & 0.257142942212674 \tabularnewline
51 & 17.54 & 17.4447507237595 & 0.0952492762404802 \tabularnewline
52 & 17.57 & 17.559313865523 & 0.0106861344769982 \tabularnewline
53 & 17.58 & 17.6367143109081 & -0.0567143109081343 \tabularnewline
54 & 17.56 & 17.6332647738813 & -0.0732647738812595 \tabularnewline
55 & 17.63 & 17.5433225463266 & 0.0866774536734027 \tabularnewline
56 & 17.67 & 17.6063558665579 & 0.0636441334420539 \tabularnewline
57 & 17.71 & 17.696709476733 & 0.0132905232669991 \tabularnewline
58 & 17.75 & 17.734026290536 & 0.0159737094639993 \tabularnewline
59 & 17.82 & 17.7543661211283 & 0.0656338788716511 \tabularnewline
60 & 17.86 & 17.8273334368035 & 0.0326665631964858 \tabularnewline
61 & 17.89 & 17.9000436508077 & -0.0100436508077024 \tabularnewline
62 & 17.96 & 18.0202200991569 & -0.0602200991568935 \tabularnewline
63 & 18 & 18.0351230629853 & -0.0351230629853418 \tabularnewline
64 & 18.08 & 18.0246489618185 & 0.0553510381814846 \tabularnewline
65 & 18 & 18.1334435102797 & -0.133443510279744 \tabularnewline
66 & 18.02 & 18.0609616630024 & -0.0409616630024274 \tabularnewline
67 & 18.01 & 18.0181043168846 & -0.00810431688463353 \tabularnewline
68 & 18.02 & 17.9941831425403 & 0.0258168574597484 \tabularnewline
69 & 17.95 & 18.0450257744868 & -0.0950257744867855 \tabularnewline
70 & 17.96 & 17.9877338065294 & -0.0277338065293975 \tabularnewline
71 & 18 & 17.9757088470864 & 0.0242911529136229 \tabularnewline
72 & 18.01 & 18.0081413729428 & 0.00185862705722784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203348&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]15.92[/C][C]15.7113177140969[/C][C]0.208682285903068[/C][/ROW]
[ROW][C]14[/C][C]16.02[/C][C]15.9922536351487[/C][C]0.0277463648512963[/C][/ROW]
[ROW][C]15[/C][C]16.1[/C][C]16.0982286466265[/C][C]0.00177135337345646[/C][/ROW]
[ROW][C]16[/C][C]16.13[/C][C]16.1331456193546[/C][C]-0.00314561935457291[/C][/ROW]
[ROW][C]17[/C][C]16.21[/C][C]16.2104184985029[/C][C]-0.000418498502913422[/C][/ROW]
[ROW][C]18[/C][C]16.25[/C][C]16.2471456833091[/C][C]0.00285431669093583[/C][/ROW]
[ROW][C]19[/C][C]16.27[/C][C]16.2099309795966[/C][C]0.0600690204033683[/C][/ROW]
[ROW][C]20[/C][C]16.21[/C][C]16.2773936674675[/C][C]-0.0673936674675026[/C][/ROW]
[ROW][C]21[/C][C]16.21[/C][C]16.2320554895922[/C][C]-0.0220554895921765[/C][/ROW]
[ROW][C]22[/C][C]16.24[/C][C]16.2763933413951[/C][C]-0.0363933413950939[/C][/ROW]
[ROW][C]23[/C][C]16.32[/C][C]16.213080566767[/C][C]0.106919433233038[/C][/ROW]
[ROW][C]24[/C][C]16.32[/C][C]16.3434474441589[/C][C]-0.023447444158883[/C][/ROW]
[ROW][C]25[/C][C]16.36[/C][C]16.3748842060348[/C][C]-0.0148842060348287[/C][/ROW]
[ROW][C]26[/C][C]16.48[/C][C]16.4387011347449[/C][C]0.0412988652550759[/C][/ROW]
[ROW][C]27[/C][C]16.54[/C][C]16.5545459289014[/C][C]-0.0145459289013772[/C][/ROW]
[ROW][C]28[/C][C]16.58[/C][C]16.5745129841537[/C][C]0.00548701584634159[/C][/ROW]
[ROW][C]29[/C][C]16.56[/C][C]16.6609523904799[/C][C]-0.100952390479915[/C][/ROW]
[ROW][C]30[/C][C]16.55[/C][C]16.6101405751483[/C][C]-0.0601405751483313[/C][/ROW]
[ROW][C]31[/C][C]16.58[/C][C]16.5236122436182[/C][C]0.0563877563817634[/C][/ROW]
[ROW][C]32[/C][C]16.53[/C][C]16.5712769388902[/C][C]-0.0412769388902348[/C][/ROW]
[ROW][C]33[/C][C]16.6[/C][C]16.5541416406347[/C][C]0.0458583593653117[/C][/ROW]
[ROW][C]34[/C][C]16.46[/C][C]16.6567819810659[/C][C]-0.196781981065872[/C][/ROW]
[ROW][C]35[/C][C]16.48[/C][C]16.4701200518171[/C][C]0.0098799481828955[/C][/ROW]
[ROW][C]36[/C][C]16.48[/C][C]16.4991555437033[/C][C]-0.019155543703345[/C][/ROW]
[ROW][C]37[/C][C]16.49[/C][C]16.5355992630508[/C][C]-0.0455992630507929[/C][/ROW]
[ROW][C]38[/C][C]16.54[/C][C]16.5799256240661[/C][C]-0.0399256240661288[/C][/ROW]
[ROW][C]39[/C][C]16.67[/C][C]16.6178568412306[/C][C]0.0521431587694359[/C][/ROW]
[ROW][C]40[/C][C]16.72[/C][C]16.6987032277931[/C][C]0.0212967722069131[/C][/ROW]
[ROW][C]41[/C][C]16.79[/C][C]16.7859309817686[/C][C]0.00406901823141226[/C][/ROW]
[ROW][C]42[/C][C]16.86[/C][C]16.8322250009406[/C][C]0.0277749990593783[/C][/ROW]
[ROW][C]43[/C][C]16.84[/C][C]16.8361554631846[/C][C]0.00384453681535746[/C][/ROW]
[ROW][C]44[/C][C]16.86[/C][C]16.8248853920712[/C][C]0.0351146079287759[/C][/ROW]
[ROW][C]45[/C][C]16.96[/C][C]16.8853737392801[/C][C]0.0746262607198638[/C][/ROW]
[ROW][C]46[/C][C]17.01[/C][C]16.9826546762617[/C][C]0.0273453237383343[/C][/ROW]
[ROW][C]47[/C][C]17.02[/C][C]17.0171746101682[/C][C]0.00282538983181979[/C][/ROW]
[ROW][C]48[/C][C]17.04[/C][C]17.0358349275251[/C][C]0.0041650724749438[/C][/ROW]
[ROW][C]49[/C][C]17.04[/C][C]17.0899081166026[/C][C]-0.0499081166025626[/C][/ROW]
[ROW][C]50[/C][C]17.39[/C][C]17.1328570577873[/C][C]0.257142942212674[/C][/ROW]
[ROW][C]51[/C][C]17.54[/C][C]17.4447507237595[/C][C]0.0952492762404802[/C][/ROW]
[ROW][C]52[/C][C]17.57[/C][C]17.559313865523[/C][C]0.0106861344769982[/C][/ROW]
[ROW][C]53[/C][C]17.58[/C][C]17.6367143109081[/C][C]-0.0567143109081343[/C][/ROW]
[ROW][C]54[/C][C]17.56[/C][C]17.6332647738813[/C][C]-0.0732647738812595[/C][/ROW]
[ROW][C]55[/C][C]17.63[/C][C]17.5433225463266[/C][C]0.0866774536734027[/C][/ROW]
[ROW][C]56[/C][C]17.67[/C][C]17.6063558665579[/C][C]0.0636441334420539[/C][/ROW]
[ROW][C]57[/C][C]17.71[/C][C]17.696709476733[/C][C]0.0132905232669991[/C][/ROW]
[ROW][C]58[/C][C]17.75[/C][C]17.734026290536[/C][C]0.0159737094639993[/C][/ROW]
[ROW][C]59[/C][C]17.82[/C][C]17.7543661211283[/C][C]0.0656338788716511[/C][/ROW]
[ROW][C]60[/C][C]17.86[/C][C]17.8273334368035[/C][C]0.0326665631964858[/C][/ROW]
[ROW][C]61[/C][C]17.89[/C][C]17.9000436508077[/C][C]-0.0100436508077024[/C][/ROW]
[ROW][C]62[/C][C]17.96[/C][C]18.0202200991569[/C][C]-0.0602200991568935[/C][/ROW]
[ROW][C]63[/C][C]18[/C][C]18.0351230629853[/C][C]-0.0351230629853418[/C][/ROW]
[ROW][C]64[/C][C]18.08[/C][C]18.0246489618185[/C][C]0.0553510381814846[/C][/ROW]
[ROW][C]65[/C][C]18[/C][C]18.1334435102797[/C][C]-0.133443510279744[/C][/ROW]
[ROW][C]66[/C][C]18.02[/C][C]18.0609616630024[/C][C]-0.0409616630024274[/C][/ROW]
[ROW][C]67[/C][C]18.01[/C][C]18.0181043168846[/C][C]-0.00810431688463353[/C][/ROW]
[ROW][C]68[/C][C]18.02[/C][C]17.9941831425403[/C][C]0.0258168574597484[/C][/ROW]
[ROW][C]69[/C][C]17.95[/C][C]18.0450257744868[/C][C]-0.0950257744867855[/C][/ROW]
[ROW][C]70[/C][C]17.96[/C][C]17.9877338065294[/C][C]-0.0277338065293975[/C][/ROW]
[ROW][C]71[/C][C]18[/C][C]17.9757088470864[/C][C]0.0242911529136229[/C][/ROW]
[ROW][C]72[/C][C]18.01[/C][C]18.0081413729428[/C][C]0.00185862705722784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203348&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
1315.9215.71131771409690.208682285903068
1416.0215.99225363514870.0277463648512963
1516.116.09822864662650.00177135337345646
1616.1316.1331456193546-0.00314561935457291
1716.2116.2104184985029-0.000418498502913422
1816.2516.24714568330910.00285431669093583
1916.2716.20993097959660.0600690204033683
2016.2116.2773936674675-0.0673936674675026
2116.2116.2320554895922-0.0220554895921765
2216.2416.2763933413951-0.0363933413950939
2316.3216.2130805667670.106919433233038
2416.3216.3434474441589-0.023447444158883
2516.3616.3748842060348-0.0148842060348287
2616.4816.43870113474490.0412988652550759
2716.5416.5545459289014-0.0145459289013772
2816.5816.57451298415370.00548701584634159
2916.5616.6609523904799-0.100952390479915
3016.5516.6101405751483-0.0601405751483313
3116.5816.52361224361820.0563877563817634
3216.5316.5712769388902-0.0412769388902348
3316.616.55414164063470.0458583593653117
3416.4616.6567819810659-0.196781981065872
3516.4816.47012005181710.0098799481828955
3616.4816.4991555437033-0.019155543703345
3716.4916.5355992630508-0.0455992630507929
3816.5416.5799256240661-0.0399256240661288
3916.6716.61785684123060.0521431587694359
4016.7216.69870322779310.0212967722069131
4116.7916.78593098176860.00406901823141226
4216.8616.83222500094060.0277749990593783
4316.8416.83615546318460.00384453681535746
4416.8616.82488539207120.0351146079287759
4516.9616.88537373928010.0746262607198638
4617.0116.98265467626170.0273453237383343
4717.0217.01717461016820.00282538983181979
4817.0417.03583492752510.0041650724749438
4917.0417.0899081166026-0.0499081166025626
5017.3917.13285705778730.257142942212674
5117.5417.44475072375950.0952492762404802
5217.5717.5593138655230.0106861344769982
5317.5817.6367143109081-0.0567143109081343
5417.5617.6332647738813-0.0732647738812595
5517.6317.54332254632660.0866774536734027
5617.6717.60635586655790.0636441334420539
5717.7117.6967094767330.0132905232669991
5817.7517.7340262905360.0159737094639993
5917.8217.75436612112830.0656338788716511
6017.8617.82733343680350.0326665631964858
6117.8917.9000436508077-0.0100436508077024
6217.9618.0202200991569-0.0602200991568935
631818.0351230629853-0.0351230629853418
6418.0818.02464896181850.0553510381814846
651818.1334435102797-0.133443510279744
6618.0218.0609616630024-0.0409616630024274
6718.0118.0181043168846-0.00810431688463353
6818.0217.99418314254030.0258168574597484
6917.9518.0450257744868-0.0950257744867855
7017.9617.9877338065294-0.0277338065293975
711817.97570884708640.0242911529136229
7218.0118.00814137294280.00185862705722784







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318.048596197878617.912464199022818.1847281967345
7418.172071416089317.99076081767218.3533820145066
7518.243236039350418.026004301451518.4604677772492
7618.274720246567418.026978540049318.5224619530855
7718.311450381722718.036513982984218.5863867804611
7818.367663049469518.067732034560318.6675940643786
7918.364031991119218.041846879606418.686217102632
8018.35050014718.007740645696818.6932596483031
8118.363238041514318.000723596864218.7257524861643
8218.397505204497218.015910785906218.7790996230882
8318.415852590009318.016393563746718.8153116162719
8418.423622641929214.486248000088522.3609972837699

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18.0485961978786 & 17.9124641990228 & 18.1847281967345 \tabularnewline
74 & 18.1720714160893 & 17.990760817672 & 18.3533820145066 \tabularnewline
75 & 18.2432360393504 & 18.0260043014515 & 18.4604677772492 \tabularnewline
76 & 18.2747202465674 & 18.0269785400493 & 18.5224619530855 \tabularnewline
77 & 18.3114503817227 & 18.0365139829842 & 18.5863867804611 \tabularnewline
78 & 18.3676630494695 & 18.0677320345603 & 18.6675940643786 \tabularnewline
79 & 18.3640319911192 & 18.0418468796064 & 18.686217102632 \tabularnewline
80 & 18.350500147 & 18.0077406456968 & 18.6932596483031 \tabularnewline
81 & 18.3632380415143 & 18.0007235968642 & 18.7257524861643 \tabularnewline
82 & 18.3975052044972 & 18.0159107859062 & 18.7790996230882 \tabularnewline
83 & 18.4158525900093 & 18.0163935637467 & 18.8153116162719 \tabularnewline
84 & 18.4236226419292 & 14.4862480000885 & 22.3609972837699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203348&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]18.0485961978786[/C][C]17.9124641990228[/C][C]18.1847281967345[/C][/ROW]
[ROW][C]74[/C][C]18.1720714160893[/C][C]17.990760817672[/C][C]18.3533820145066[/C][/ROW]
[ROW][C]75[/C][C]18.2432360393504[/C][C]18.0260043014515[/C][C]18.4604677772492[/C][/ROW]
[ROW][C]76[/C][C]18.2747202465674[/C][C]18.0269785400493[/C][C]18.5224619530855[/C][/ROW]
[ROW][C]77[/C][C]18.3114503817227[/C][C]18.0365139829842[/C][C]18.5863867804611[/C][/ROW]
[ROW][C]78[/C][C]18.3676630494695[/C][C]18.0677320345603[/C][C]18.6675940643786[/C][/ROW]
[ROW][C]79[/C][C]18.3640319911192[/C][C]18.0418468796064[/C][C]18.686217102632[/C][/ROW]
[ROW][C]80[/C][C]18.350500147[/C][C]18.0077406456968[/C][C]18.6932596483031[/C][/ROW]
[ROW][C]81[/C][C]18.3632380415143[/C][C]18.0007235968642[/C][C]18.7257524861643[/C][/ROW]
[ROW][C]82[/C][C]18.3975052044972[/C][C]18.0159107859062[/C][C]18.7790996230882[/C][/ROW]
[ROW][C]83[/C][C]18.4158525900093[/C][C]18.0163935637467[/C][C]18.8153116162719[/C][/ROW]
[ROW][C]84[/C][C]18.4236226419292[/C][C]14.4862480000885[/C][C]22.3609972837699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203348&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203348&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
7318.048596197878617.912464199022818.1847281967345
7418.172071416089317.99076081767218.3533820145066
7518.243236039350418.026004301451518.4604677772492
7618.274720246567418.026978540049318.5224619530855
7718.311450381722718.036513982984218.5863867804611
7818.367663049469518.067732034560318.6675940643786
7918.364031991119218.041846879606418.686217102632
8018.35050014718.007740645696818.6932596483031
8118.363238041514318.000723596864218.7257524861643
8218.397505204497218.015910785906218.7790996230882
8318.415852590009318.016393563746718.8153116162719
8418.423622641929214.486248000088522.3609972837699



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')