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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 22:03:09 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/27/t1417125835ae6phb6nwaj7mw9.htm/, Retrieved Sun, 19 May 2024 21:18:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260723, Retrieved Sun, 19 May 2024 21:18:11 +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] [] [2014-11-27 22:03:09] [bdd4dd5e616b71837cf1c04213e8fe07] [Current]
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Dataseries X:
204,12
203,27
203,73
203,7
203,44
203,34
203,34
203,05
202,71
202,51
203,45
203,04
203,04
202,87
202,92
202,87
203,17
203,88
203,88
203,45
203,22
202,11
202,5
202,86
202,86
203,8
203,78
204,53
204,44
204,14
204,14
204,04
204,68
205,01
204,93
204,34
204,34
203,87
202,47
201,95
201,86
200,33
200,33
200,33
200,75
201,86
202,77
202,85
202,85
202,84
202,94
203,05
203,45
204,19
204,18
204,47
204,78
206,05
206,32
206,36
205,21
205,35
205,94
204,57
204,27
204,86
204,66
204,79
205,58
205,63
205,12
204,96




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=260723&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=260723&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260723&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
alpha0.882666398171626
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.882666398171626 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260723&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]0.882666398171626[/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=260723&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260723&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
alpha0.882666398171626
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13203.04203.170456730769-0.130456730769225
14202.87202.83942846160.0305715383995846
15202.92202.8717844347830.0482155652173049
16202.87202.8530475308990.0169524691013123
17203.17203.217549075904-0.0475490759036745
18203.88203.925950607836-0.0459506078358345
19203.88203.147013053820.732986946179892
20203.45203.558950838341-0.1089508383414
21203.22203.1664884311150.0535115688853693
22202.11203.07534279838-0.965342798379652
23202.5203.20238865103-0.702388651029509
24202.86202.1544519604720.705548039528196
25202.86202.7101967193180.149803280681539
26203.8202.6454385718261.15456142817382
27203.78203.6719728898140.108027110185958
28204.53203.7023614152250.827638584774974
29204.44204.7748601554-0.334860155400492
30204.14205.229849405654-1.08984940565421
31204.14203.6208930085240.519106991475496
32204.04203.7452585510120.294741448987565
33204.68203.7281840604140.951815939586396
34205.01204.3103956583770.699604341622603
35204.93205.937887763463-1.00788776346346
36204.34204.785495554739-0.4454955547385
37204.34204.2600452758430.0799547241574317
38203.87204.251526046957-0.381526046957362
39202.47203.799413925028-1.32941392502809
40201.95202.645456155533-0.695456155533151
41201.86202.237170182901-0.377170182900926
42200.33202.5662281855-2.23622818550027
43200.33200.1341864090840.195813590916487
44200.33199.9468661129210.383133887078912
45200.75200.084909573930.665090426070492
46201.86200.3844453004021.47555469959772
47202.77202.4964965143390.273503485661024
48202.85202.5411328076170.308867192382735
49202.85202.7431861514420.106813848557721
50202.84202.70422736810.135772631899925
51202.94202.5974983089530.342501691046778
52203.05202.9936688228480.0563311771521171
53203.45203.2863059069280.163694093071513
54204.19203.8746366604470.315363339552732
55204.18203.9801592064780.199840793521673
56204.47203.8183725517780.651627448221603
57204.78204.2264892336120.553510766388143
58206.05204.522632036131.52736796387023
59206.32206.539376078906-0.219376078906066
60206.36206.1531134932790.206886506720849
61205.21206.241444266015-1.03144426601548
62205.35205.2011811308470.148818869152535
63205.94205.1302238120580.809776187941623
64204.57205.905264405952-1.33526440595233
65204.27204.98218410661-0.712184106610152
66204.86204.8152025033550.0447974966448896
67204.66204.66835099494-0.00835099494025826
68204.79204.3758101996440.414189800356326
69205.58204.5628362643671.0171637356334
70205.63205.3824961358970.247503864103123
71205.12206.064595373571-0.944595373571332
72204.96205.088221009734-0.128221009733949

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 203.04 & 203.170456730769 & -0.130456730769225 \tabularnewline
14 & 202.87 & 202.8394284616 & 0.0305715383995846 \tabularnewline
15 & 202.92 & 202.871784434783 & 0.0482155652173049 \tabularnewline
16 & 202.87 & 202.853047530899 & 0.0169524691013123 \tabularnewline
17 & 203.17 & 203.217549075904 & -0.0475490759036745 \tabularnewline
18 & 203.88 & 203.925950607836 & -0.0459506078358345 \tabularnewline
19 & 203.88 & 203.14701305382 & 0.732986946179892 \tabularnewline
20 & 203.45 & 203.558950838341 & -0.1089508383414 \tabularnewline
21 & 203.22 & 203.166488431115 & 0.0535115688853693 \tabularnewline
22 & 202.11 & 203.07534279838 & -0.965342798379652 \tabularnewline
23 & 202.5 & 203.20238865103 & -0.702388651029509 \tabularnewline
24 & 202.86 & 202.154451960472 & 0.705548039528196 \tabularnewline
25 & 202.86 & 202.710196719318 & 0.149803280681539 \tabularnewline
26 & 203.8 & 202.645438571826 & 1.15456142817382 \tabularnewline
27 & 203.78 & 203.671972889814 & 0.108027110185958 \tabularnewline
28 & 204.53 & 203.702361415225 & 0.827638584774974 \tabularnewline
29 & 204.44 & 204.7748601554 & -0.334860155400492 \tabularnewline
30 & 204.14 & 205.229849405654 & -1.08984940565421 \tabularnewline
31 & 204.14 & 203.620893008524 & 0.519106991475496 \tabularnewline
32 & 204.04 & 203.745258551012 & 0.294741448987565 \tabularnewline
33 & 204.68 & 203.728184060414 & 0.951815939586396 \tabularnewline
34 & 205.01 & 204.310395658377 & 0.699604341622603 \tabularnewline
35 & 204.93 & 205.937887763463 & -1.00788776346346 \tabularnewline
36 & 204.34 & 204.785495554739 & -0.4454955547385 \tabularnewline
37 & 204.34 & 204.260045275843 & 0.0799547241574317 \tabularnewline
38 & 203.87 & 204.251526046957 & -0.381526046957362 \tabularnewline
39 & 202.47 & 203.799413925028 & -1.32941392502809 \tabularnewline
40 & 201.95 & 202.645456155533 & -0.695456155533151 \tabularnewline
41 & 201.86 & 202.237170182901 & -0.377170182900926 \tabularnewline
42 & 200.33 & 202.5662281855 & -2.23622818550027 \tabularnewline
43 & 200.33 & 200.134186409084 & 0.195813590916487 \tabularnewline
44 & 200.33 & 199.946866112921 & 0.383133887078912 \tabularnewline
45 & 200.75 & 200.08490957393 & 0.665090426070492 \tabularnewline
46 & 201.86 & 200.384445300402 & 1.47555469959772 \tabularnewline
47 & 202.77 & 202.496496514339 & 0.273503485661024 \tabularnewline
48 & 202.85 & 202.541132807617 & 0.308867192382735 \tabularnewline
49 & 202.85 & 202.743186151442 & 0.106813848557721 \tabularnewline
50 & 202.84 & 202.7042273681 & 0.135772631899925 \tabularnewline
51 & 202.94 & 202.597498308953 & 0.342501691046778 \tabularnewline
52 & 203.05 & 202.993668822848 & 0.0563311771521171 \tabularnewline
53 & 203.45 & 203.286305906928 & 0.163694093071513 \tabularnewline
54 & 204.19 & 203.874636660447 & 0.315363339552732 \tabularnewline
55 & 204.18 & 203.980159206478 & 0.199840793521673 \tabularnewline
56 & 204.47 & 203.818372551778 & 0.651627448221603 \tabularnewline
57 & 204.78 & 204.226489233612 & 0.553510766388143 \tabularnewline
58 & 206.05 & 204.52263203613 & 1.52736796387023 \tabularnewline
59 & 206.32 & 206.539376078906 & -0.219376078906066 \tabularnewline
60 & 206.36 & 206.153113493279 & 0.206886506720849 \tabularnewline
61 & 205.21 & 206.241444266015 & -1.03144426601548 \tabularnewline
62 & 205.35 & 205.201181130847 & 0.148818869152535 \tabularnewline
63 & 205.94 & 205.130223812058 & 0.809776187941623 \tabularnewline
64 & 204.57 & 205.905264405952 & -1.33526440595233 \tabularnewline
65 & 204.27 & 204.98218410661 & -0.712184106610152 \tabularnewline
66 & 204.86 & 204.815202503355 & 0.0447974966448896 \tabularnewline
67 & 204.66 & 204.66835099494 & -0.00835099494025826 \tabularnewline
68 & 204.79 & 204.375810199644 & 0.414189800356326 \tabularnewline
69 & 205.58 & 204.562836264367 & 1.0171637356334 \tabularnewline
70 & 205.63 & 205.382496135897 & 0.247503864103123 \tabularnewline
71 & 205.12 & 206.064595373571 & -0.944595373571332 \tabularnewline
72 & 204.96 & 205.088221009734 & -0.128221009733949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260723&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]203.04[/C][C]203.170456730769[/C][C]-0.130456730769225[/C][/ROW]
[ROW][C]14[/C][C]202.87[/C][C]202.8394284616[/C][C]0.0305715383995846[/C][/ROW]
[ROW][C]15[/C][C]202.92[/C][C]202.871784434783[/C][C]0.0482155652173049[/C][/ROW]
[ROW][C]16[/C][C]202.87[/C][C]202.853047530899[/C][C]0.0169524691013123[/C][/ROW]
[ROW][C]17[/C][C]203.17[/C][C]203.217549075904[/C][C]-0.0475490759036745[/C][/ROW]
[ROW][C]18[/C][C]203.88[/C][C]203.925950607836[/C][C]-0.0459506078358345[/C][/ROW]
[ROW][C]19[/C][C]203.88[/C][C]203.14701305382[/C][C]0.732986946179892[/C][/ROW]
[ROW][C]20[/C][C]203.45[/C][C]203.558950838341[/C][C]-0.1089508383414[/C][/ROW]
[ROW][C]21[/C][C]203.22[/C][C]203.166488431115[/C][C]0.0535115688853693[/C][/ROW]
[ROW][C]22[/C][C]202.11[/C][C]203.07534279838[/C][C]-0.965342798379652[/C][/ROW]
[ROW][C]23[/C][C]202.5[/C][C]203.20238865103[/C][C]-0.702388651029509[/C][/ROW]
[ROW][C]24[/C][C]202.86[/C][C]202.154451960472[/C][C]0.705548039528196[/C][/ROW]
[ROW][C]25[/C][C]202.86[/C][C]202.710196719318[/C][C]0.149803280681539[/C][/ROW]
[ROW][C]26[/C][C]203.8[/C][C]202.645438571826[/C][C]1.15456142817382[/C][/ROW]
[ROW][C]27[/C][C]203.78[/C][C]203.671972889814[/C][C]0.108027110185958[/C][/ROW]
[ROW][C]28[/C][C]204.53[/C][C]203.702361415225[/C][C]0.827638584774974[/C][/ROW]
[ROW][C]29[/C][C]204.44[/C][C]204.7748601554[/C][C]-0.334860155400492[/C][/ROW]
[ROW][C]30[/C][C]204.14[/C][C]205.229849405654[/C][C]-1.08984940565421[/C][/ROW]
[ROW][C]31[/C][C]204.14[/C][C]203.620893008524[/C][C]0.519106991475496[/C][/ROW]
[ROW][C]32[/C][C]204.04[/C][C]203.745258551012[/C][C]0.294741448987565[/C][/ROW]
[ROW][C]33[/C][C]204.68[/C][C]203.728184060414[/C][C]0.951815939586396[/C][/ROW]
[ROW][C]34[/C][C]205.01[/C][C]204.310395658377[/C][C]0.699604341622603[/C][/ROW]
[ROW][C]35[/C][C]204.93[/C][C]205.937887763463[/C][C]-1.00788776346346[/C][/ROW]
[ROW][C]36[/C][C]204.34[/C][C]204.785495554739[/C][C]-0.4454955547385[/C][/ROW]
[ROW][C]37[/C][C]204.34[/C][C]204.260045275843[/C][C]0.0799547241574317[/C][/ROW]
[ROW][C]38[/C][C]203.87[/C][C]204.251526046957[/C][C]-0.381526046957362[/C][/ROW]
[ROW][C]39[/C][C]202.47[/C][C]203.799413925028[/C][C]-1.32941392502809[/C][/ROW]
[ROW][C]40[/C][C]201.95[/C][C]202.645456155533[/C][C]-0.695456155533151[/C][/ROW]
[ROW][C]41[/C][C]201.86[/C][C]202.237170182901[/C][C]-0.377170182900926[/C][/ROW]
[ROW][C]42[/C][C]200.33[/C][C]202.5662281855[/C][C]-2.23622818550027[/C][/ROW]
[ROW][C]43[/C][C]200.33[/C][C]200.134186409084[/C][C]0.195813590916487[/C][/ROW]
[ROW][C]44[/C][C]200.33[/C][C]199.946866112921[/C][C]0.383133887078912[/C][/ROW]
[ROW][C]45[/C][C]200.75[/C][C]200.08490957393[/C][C]0.665090426070492[/C][/ROW]
[ROW][C]46[/C][C]201.86[/C][C]200.384445300402[/C][C]1.47555469959772[/C][/ROW]
[ROW][C]47[/C][C]202.77[/C][C]202.496496514339[/C][C]0.273503485661024[/C][/ROW]
[ROW][C]48[/C][C]202.85[/C][C]202.541132807617[/C][C]0.308867192382735[/C][/ROW]
[ROW][C]49[/C][C]202.85[/C][C]202.743186151442[/C][C]0.106813848557721[/C][/ROW]
[ROW][C]50[/C][C]202.84[/C][C]202.7042273681[/C][C]0.135772631899925[/C][/ROW]
[ROW][C]51[/C][C]202.94[/C][C]202.597498308953[/C][C]0.342501691046778[/C][/ROW]
[ROW][C]52[/C][C]203.05[/C][C]202.993668822848[/C][C]0.0563311771521171[/C][/ROW]
[ROW][C]53[/C][C]203.45[/C][C]203.286305906928[/C][C]0.163694093071513[/C][/ROW]
[ROW][C]54[/C][C]204.19[/C][C]203.874636660447[/C][C]0.315363339552732[/C][/ROW]
[ROW][C]55[/C][C]204.18[/C][C]203.980159206478[/C][C]0.199840793521673[/C][/ROW]
[ROW][C]56[/C][C]204.47[/C][C]203.818372551778[/C][C]0.651627448221603[/C][/ROW]
[ROW][C]57[/C][C]204.78[/C][C]204.226489233612[/C][C]0.553510766388143[/C][/ROW]
[ROW][C]58[/C][C]206.05[/C][C]204.52263203613[/C][C]1.52736796387023[/C][/ROW]
[ROW][C]59[/C][C]206.32[/C][C]206.539376078906[/C][C]-0.219376078906066[/C][/ROW]
[ROW][C]60[/C][C]206.36[/C][C]206.153113493279[/C][C]0.206886506720849[/C][/ROW]
[ROW][C]61[/C][C]205.21[/C][C]206.241444266015[/C][C]-1.03144426601548[/C][/ROW]
[ROW][C]62[/C][C]205.35[/C][C]205.201181130847[/C][C]0.148818869152535[/C][/ROW]
[ROW][C]63[/C][C]205.94[/C][C]205.130223812058[/C][C]0.809776187941623[/C][/ROW]
[ROW][C]64[/C][C]204.57[/C][C]205.905264405952[/C][C]-1.33526440595233[/C][/ROW]
[ROW][C]65[/C][C]204.27[/C][C]204.98218410661[/C][C]-0.712184106610152[/C][/ROW]
[ROW][C]66[/C][C]204.86[/C][C]204.815202503355[/C][C]0.0447974966448896[/C][/ROW]
[ROW][C]67[/C][C]204.66[/C][C]204.66835099494[/C][C]-0.00835099494025826[/C][/ROW]
[ROW][C]68[/C][C]204.79[/C][C]204.375810199644[/C][C]0.414189800356326[/C][/ROW]
[ROW][C]69[/C][C]205.58[/C][C]204.562836264367[/C][C]1.0171637356334[/C][/ROW]
[ROW][C]70[/C][C]205.63[/C][C]205.382496135897[/C][C]0.247503864103123[/C][/ROW]
[ROW][C]71[/C][C]205.12[/C][C]206.064595373571[/C][C]-0.944595373571332[/C][/ROW]
[ROW][C]72[/C][C]204.96[/C][C]205.088221009734[/C][C]-0.128221009733949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260723&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260723&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
13203.04203.170456730769-0.130456730769225
14202.87202.83942846160.0305715383995846
15202.92202.8717844347830.0482155652173049
16202.87202.8530475308990.0169524691013123
17203.17203.217549075904-0.0475490759036745
18203.88203.925950607836-0.0459506078358345
19203.88203.147013053820.732986946179892
20203.45203.558950838341-0.1089508383414
21203.22203.1664884311150.0535115688853693
22202.11203.07534279838-0.965342798379652
23202.5203.20238865103-0.702388651029509
24202.86202.1544519604720.705548039528196
25202.86202.7101967193180.149803280681539
26203.8202.6454385718261.15456142817382
27203.78203.6719728898140.108027110185958
28204.53203.7023614152250.827638584774974
29204.44204.7748601554-0.334860155400492
30204.14205.229849405654-1.08984940565421
31204.14203.6208930085240.519106991475496
32204.04203.7452585510120.294741448987565
33204.68203.7281840604140.951815939586396
34205.01204.3103956583770.699604341622603
35204.93205.937887763463-1.00788776346346
36204.34204.785495554739-0.4454955547385
37204.34204.2600452758430.0799547241574317
38203.87204.251526046957-0.381526046957362
39202.47203.799413925028-1.32941392502809
40201.95202.645456155533-0.695456155533151
41201.86202.237170182901-0.377170182900926
42200.33202.5662281855-2.23622818550027
43200.33200.1341864090840.195813590916487
44200.33199.9468661129210.383133887078912
45200.75200.084909573930.665090426070492
46201.86200.3844453004021.47555469959772
47202.77202.4964965143390.273503485661024
48202.85202.5411328076170.308867192382735
49202.85202.7431861514420.106813848557721
50202.84202.70422736810.135772631899925
51202.94202.5974983089530.342501691046778
52203.05202.9936688228480.0563311771521171
53203.45203.2863059069280.163694093071513
54204.19203.8746366604470.315363339552732
55204.18203.9801592064780.199840793521673
56204.47203.8183725517780.651627448221603
57204.78204.2264892336120.553510766388143
58206.05204.522632036131.52736796387023
59206.32206.539376078906-0.219376078906066
60206.36206.1531134932790.206886506720849
61205.21206.241444266015-1.03144426601548
62205.35205.2011811308470.148818869152535
63205.94205.1302238120580.809776187941623
64204.57205.905264405952-1.33526440595233
65204.27204.98218410661-0.712184106610152
66204.86204.8152025033550.0447974966448896
67204.66204.66835099494-0.00835099494025826
68204.79204.3758101996440.414189800356326
69205.58204.5628362643671.0171637356334
70205.63205.3824961358970.247503864103123
71205.12206.064595373571-0.944595373571332
72204.96205.088221009734-0.128221009733949







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73204.735465828101203.363037386416206.107894269785
74204.744108412886202.913523469884206.574693355888
75204.61934618175202.424232827149206.814459536352
76204.427939205559201.920748737017206.935129674102
77204.756560185776201.97205206915207.541068302401
78205.307018940765202.270414446012208.343623435518
79205.11439008339201.845070847898208.383709318882
80204.87879866415201.392263181818208.365334146482
81204.770982413268201.079991885569208.461972940966
82204.602519069006200.717819276029208.487218861984
83204.926281665126200.857083477821208.995479852431
84204.879458041958200.633771372694209.125144711222

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 204.735465828101 & 203.363037386416 & 206.107894269785 \tabularnewline
74 & 204.744108412886 & 202.913523469884 & 206.574693355888 \tabularnewline
75 & 204.61934618175 & 202.424232827149 & 206.814459536352 \tabularnewline
76 & 204.427939205559 & 201.920748737017 & 206.935129674102 \tabularnewline
77 & 204.756560185776 & 201.97205206915 & 207.541068302401 \tabularnewline
78 & 205.307018940765 & 202.270414446012 & 208.343623435518 \tabularnewline
79 & 205.11439008339 & 201.845070847898 & 208.383709318882 \tabularnewline
80 & 204.87879866415 & 201.392263181818 & 208.365334146482 \tabularnewline
81 & 204.770982413268 & 201.079991885569 & 208.461972940966 \tabularnewline
82 & 204.602519069006 & 200.717819276029 & 208.487218861984 \tabularnewline
83 & 204.926281665126 & 200.857083477821 & 208.995479852431 \tabularnewline
84 & 204.879458041958 & 200.633771372694 & 209.125144711222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260723&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]204.735465828101[/C][C]203.363037386416[/C][C]206.107894269785[/C][/ROW]
[ROW][C]74[/C][C]204.744108412886[/C][C]202.913523469884[/C][C]206.574693355888[/C][/ROW]
[ROW][C]75[/C][C]204.61934618175[/C][C]202.424232827149[/C][C]206.814459536352[/C][/ROW]
[ROW][C]76[/C][C]204.427939205559[/C][C]201.920748737017[/C][C]206.935129674102[/C][/ROW]
[ROW][C]77[/C][C]204.756560185776[/C][C]201.97205206915[/C][C]207.541068302401[/C][/ROW]
[ROW][C]78[/C][C]205.307018940765[/C][C]202.270414446012[/C][C]208.343623435518[/C][/ROW]
[ROW][C]79[/C][C]205.11439008339[/C][C]201.845070847898[/C][C]208.383709318882[/C][/ROW]
[ROW][C]80[/C][C]204.87879866415[/C][C]201.392263181818[/C][C]208.365334146482[/C][/ROW]
[ROW][C]81[/C][C]204.770982413268[/C][C]201.079991885569[/C][C]208.461972940966[/C][/ROW]
[ROW][C]82[/C][C]204.602519069006[/C][C]200.717819276029[/C][C]208.487218861984[/C][/ROW]
[ROW][C]83[/C][C]204.926281665126[/C][C]200.857083477821[/C][C]208.995479852431[/C][/ROW]
[ROW][C]84[/C][C]204.879458041958[/C][C]200.633771372694[/C][C]209.125144711222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260723&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260723&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
73204.735465828101203.363037386416206.107894269785
74204.744108412886202.913523469884206.574693355888
75204.61934618175202.424232827149206.814459536352
76204.427939205559201.920748737017206.935129674102
77204.756560185776201.97205206915207.541068302401
78205.307018940765202.270414446012208.343623435518
79205.11439008339201.845070847898208.383709318882
80204.87879866415201.392263181818208.365334146482
81204.770982413268201.079991885569208.461972940966
82204.602519069006200.717819276029208.487218861984
83204.926281665126200.857083477821208.995479852431
84204.879458041958200.633771372694209.125144711222



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')