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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 04 Mar 2014 16:42:30 -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/2014/Mar/04/t1393971100rj7g3hl5vuc00ud.htm/, Retrieved Tue, 14 May 2024 08:06:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234179, Retrieved Tue, 14 May 2024 08:06:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-03-04 21:42:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
23.86
23.97
29.23
24.32
23.89
26.84
29.36
26.3
27.09
29.42
32.43
29.17
28.86
32.1
34.82
30.48
30.87
33.75
35.11
30
29.95
32.63
36.78
32.34
33.63
36.97
39.71
34.96
35.78
38.59
42.96
39.27
40.77
45.31
51.45
45.13
48.13
50.35
56.73
48.83
49.02
50.73
53.74
46.38
46.32
51.65
52.73
47.45
49.01
53.99
55.63
50.04
54.77
56.89
57.82
53.3
54.69
60.88
63.59
59.46
61.59
68.75
71.33
64.88




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=234179&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=234179&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234179&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
alpha0.55695019533657
beta0.393842662498364
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.55695019533657 \tabularnewline
beta & 0.393842662498364 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234179&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]0.55695019533657[/C][/ROW]
[ROW][C]beta[/C][C]0.393842662498364[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234179&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234179&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
alpha0.55695019533657
beta0.393842662498364
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
523.8923.03911434228060.850885657719402
626.8426.7009470635480.139052936451961
729.3630.9707284477937-1.6107284477937
826.324.91736154699381.38263845300624
927.0925.81178327044171.27821672955831
1029.4230.00480213781-0.584802137809994
1132.4333.5801622805004-1.15016228050037
1229.1728.85458124108360.315418758916376
1328.8629.0640254524332-0.204025452433214
1432.131.39465953919840.705340460801644
1534.8235.6015179547765-0.781517954776525
1630.4831.4178370923042-0.937837092304221
1730.8730.40659447396120.463405526038752
1833.7533.54183686279310.208163137206938
1935.1136.6887999373784-1.57879993737841
203031.5008992054316-1.50089920543159
2129.9530.3108457873851-0.360845787385117
2232.6332.10292035443150.527079645568463
2336.7833.87453307260942.90546692739063
2432.3431.41410732594530.925892674054712
2533.6332.8944877174440.73551228255603
2636.9737.1101954228134-0.14019542281337
2739.7140.9165109748282-1.20651097482823
2834.9634.88682371138240.0731762886176099
2935.7835.74527233241350.0347276675865302
3038.5939.0943767777551-0.50437677775507
3142.9641.98937607838370.970623921616294
3239.2737.46536801912721.80463198087283
3340.7739.78262508623430.987374913765734
3445.3144.48170963459190.828290365408073
3551.4550.43070310043941.01929689956062
3645.1346.2658650794649-1.13586507946488
3748.1346.89382612718241.2361738728176
3850.3552.5233127761609-2.17331277616086
3956.7357.1278584404009-0.397858440400945
4048.8349.9377019520681-1.10770195206813
4149.0251.2038550759355-2.18385507593548
4250.7352.1606230511203-1.43062305112034
4353.7456.806996496853-3.06699649685301
4446.3846.4786890022056-0.0986890022056315
4546.3246.4154467793677-0.0954467793677338
4651.6547.79151108737093.85848891262908
4752.7354.7632568353107-2.03325683531071
4847.4546.71228789829060.73771210170942
4949.0147.68501153425251.32498846574753
5053.9952.63646397748241.35353602251762
5155.6356.0209805058781-0.39098050587809
5250.0450.4320241875591-0.392024187559066
5354.7751.47601864467313.29398135532686
5456.8958.7618045275809-1.87180452758093
5557.8259.8473846558804-2.02738465588043
5653.352.86749354596090.4325064540391
5754.6956.1304816075654-1.44048160756537
5860.8857.43636548096953.44363451903054
5963.5961.54865259049232.04134740950772
6059.4658.38667329770411.07332670229585
6161.5962.4141251892121-0.824125189212047
6268.7567.99628754871980.753712451280222
6371.3370.72452826052170.605471739478304
6464.8865.9456489648198-1.06564896481981

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 23.89 & 23.0391143422806 & 0.850885657719402 \tabularnewline
6 & 26.84 & 26.700947063548 & 0.139052936451961 \tabularnewline
7 & 29.36 & 30.9707284477937 & -1.6107284477937 \tabularnewline
8 & 26.3 & 24.9173615469938 & 1.38263845300624 \tabularnewline
9 & 27.09 & 25.8117832704417 & 1.27821672955831 \tabularnewline
10 & 29.42 & 30.00480213781 & -0.584802137809994 \tabularnewline
11 & 32.43 & 33.5801622805004 & -1.15016228050037 \tabularnewline
12 & 29.17 & 28.8545812410836 & 0.315418758916376 \tabularnewline
13 & 28.86 & 29.0640254524332 & -0.204025452433214 \tabularnewline
14 & 32.1 & 31.3946595391984 & 0.705340460801644 \tabularnewline
15 & 34.82 & 35.6015179547765 & -0.781517954776525 \tabularnewline
16 & 30.48 & 31.4178370923042 & -0.937837092304221 \tabularnewline
17 & 30.87 & 30.4065944739612 & 0.463405526038752 \tabularnewline
18 & 33.75 & 33.5418368627931 & 0.208163137206938 \tabularnewline
19 & 35.11 & 36.6887999373784 & -1.57879993737841 \tabularnewline
20 & 30 & 31.5008992054316 & -1.50089920543159 \tabularnewline
21 & 29.95 & 30.3108457873851 & -0.360845787385117 \tabularnewline
22 & 32.63 & 32.1029203544315 & 0.527079645568463 \tabularnewline
23 & 36.78 & 33.8745330726094 & 2.90546692739063 \tabularnewline
24 & 32.34 & 31.4141073259453 & 0.925892674054712 \tabularnewline
25 & 33.63 & 32.894487717444 & 0.73551228255603 \tabularnewline
26 & 36.97 & 37.1101954228134 & -0.14019542281337 \tabularnewline
27 & 39.71 & 40.9165109748282 & -1.20651097482823 \tabularnewline
28 & 34.96 & 34.8868237113824 & 0.0731762886176099 \tabularnewline
29 & 35.78 & 35.7452723324135 & 0.0347276675865302 \tabularnewline
30 & 38.59 & 39.0943767777551 & -0.50437677775507 \tabularnewline
31 & 42.96 & 41.9893760783837 & 0.970623921616294 \tabularnewline
32 & 39.27 & 37.4653680191272 & 1.80463198087283 \tabularnewline
33 & 40.77 & 39.7826250862343 & 0.987374913765734 \tabularnewline
34 & 45.31 & 44.4817096345919 & 0.828290365408073 \tabularnewline
35 & 51.45 & 50.4307031004394 & 1.01929689956062 \tabularnewline
36 & 45.13 & 46.2658650794649 & -1.13586507946488 \tabularnewline
37 & 48.13 & 46.8938261271824 & 1.2361738728176 \tabularnewline
38 & 50.35 & 52.5233127761609 & -2.17331277616086 \tabularnewline
39 & 56.73 & 57.1278584404009 & -0.397858440400945 \tabularnewline
40 & 48.83 & 49.9377019520681 & -1.10770195206813 \tabularnewline
41 & 49.02 & 51.2038550759355 & -2.18385507593548 \tabularnewline
42 & 50.73 & 52.1606230511203 & -1.43062305112034 \tabularnewline
43 & 53.74 & 56.806996496853 & -3.06699649685301 \tabularnewline
44 & 46.38 & 46.4786890022056 & -0.0986890022056315 \tabularnewline
45 & 46.32 & 46.4154467793677 & -0.0954467793677338 \tabularnewline
46 & 51.65 & 47.7915110873709 & 3.85848891262908 \tabularnewline
47 & 52.73 & 54.7632568353107 & -2.03325683531071 \tabularnewline
48 & 47.45 & 46.7122878982906 & 0.73771210170942 \tabularnewline
49 & 49.01 & 47.6850115342525 & 1.32498846574753 \tabularnewline
50 & 53.99 & 52.6364639774824 & 1.35353602251762 \tabularnewline
51 & 55.63 & 56.0209805058781 & -0.39098050587809 \tabularnewline
52 & 50.04 & 50.4320241875591 & -0.392024187559066 \tabularnewline
53 & 54.77 & 51.4760186446731 & 3.29398135532686 \tabularnewline
54 & 56.89 & 58.7618045275809 & -1.87180452758093 \tabularnewline
55 & 57.82 & 59.8473846558804 & -2.02738465588043 \tabularnewline
56 & 53.3 & 52.8674935459609 & 0.4325064540391 \tabularnewline
57 & 54.69 & 56.1304816075654 & -1.44048160756537 \tabularnewline
58 & 60.88 & 57.4363654809695 & 3.44363451903054 \tabularnewline
59 & 63.59 & 61.5486525904923 & 2.04134740950772 \tabularnewline
60 & 59.46 & 58.3866732977041 & 1.07332670229585 \tabularnewline
61 & 61.59 & 62.4141251892121 & -0.824125189212047 \tabularnewline
62 & 68.75 & 67.9962875487198 & 0.753712451280222 \tabularnewline
63 & 71.33 & 70.7245282605217 & 0.605471739478304 \tabularnewline
64 & 64.88 & 65.9456489648198 & -1.06564896481981 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234179&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]5[/C][C]23.89[/C][C]23.0391143422806[/C][C]0.850885657719402[/C][/ROW]
[ROW][C]6[/C][C]26.84[/C][C]26.700947063548[/C][C]0.139052936451961[/C][/ROW]
[ROW][C]7[/C][C]29.36[/C][C]30.9707284477937[/C][C]-1.6107284477937[/C][/ROW]
[ROW][C]8[/C][C]26.3[/C][C]24.9173615469938[/C][C]1.38263845300624[/C][/ROW]
[ROW][C]9[/C][C]27.09[/C][C]25.8117832704417[/C][C]1.27821672955831[/C][/ROW]
[ROW][C]10[/C][C]29.42[/C][C]30.00480213781[/C][C]-0.584802137809994[/C][/ROW]
[ROW][C]11[/C][C]32.43[/C][C]33.5801622805004[/C][C]-1.15016228050037[/C][/ROW]
[ROW][C]12[/C][C]29.17[/C][C]28.8545812410836[/C][C]0.315418758916376[/C][/ROW]
[ROW][C]13[/C][C]28.86[/C][C]29.0640254524332[/C][C]-0.204025452433214[/C][/ROW]
[ROW][C]14[/C][C]32.1[/C][C]31.3946595391984[/C][C]0.705340460801644[/C][/ROW]
[ROW][C]15[/C][C]34.82[/C][C]35.6015179547765[/C][C]-0.781517954776525[/C][/ROW]
[ROW][C]16[/C][C]30.48[/C][C]31.4178370923042[/C][C]-0.937837092304221[/C][/ROW]
[ROW][C]17[/C][C]30.87[/C][C]30.4065944739612[/C][C]0.463405526038752[/C][/ROW]
[ROW][C]18[/C][C]33.75[/C][C]33.5418368627931[/C][C]0.208163137206938[/C][/ROW]
[ROW][C]19[/C][C]35.11[/C][C]36.6887999373784[/C][C]-1.57879993737841[/C][/ROW]
[ROW][C]20[/C][C]30[/C][C]31.5008992054316[/C][C]-1.50089920543159[/C][/ROW]
[ROW][C]21[/C][C]29.95[/C][C]30.3108457873851[/C][C]-0.360845787385117[/C][/ROW]
[ROW][C]22[/C][C]32.63[/C][C]32.1029203544315[/C][C]0.527079645568463[/C][/ROW]
[ROW][C]23[/C][C]36.78[/C][C]33.8745330726094[/C][C]2.90546692739063[/C][/ROW]
[ROW][C]24[/C][C]32.34[/C][C]31.4141073259453[/C][C]0.925892674054712[/C][/ROW]
[ROW][C]25[/C][C]33.63[/C][C]32.894487717444[/C][C]0.73551228255603[/C][/ROW]
[ROW][C]26[/C][C]36.97[/C][C]37.1101954228134[/C][C]-0.14019542281337[/C][/ROW]
[ROW][C]27[/C][C]39.71[/C][C]40.9165109748282[/C][C]-1.20651097482823[/C][/ROW]
[ROW][C]28[/C][C]34.96[/C][C]34.8868237113824[/C][C]0.0731762886176099[/C][/ROW]
[ROW][C]29[/C][C]35.78[/C][C]35.7452723324135[/C][C]0.0347276675865302[/C][/ROW]
[ROW][C]30[/C][C]38.59[/C][C]39.0943767777551[/C][C]-0.50437677775507[/C][/ROW]
[ROW][C]31[/C][C]42.96[/C][C]41.9893760783837[/C][C]0.970623921616294[/C][/ROW]
[ROW][C]32[/C][C]39.27[/C][C]37.4653680191272[/C][C]1.80463198087283[/C][/ROW]
[ROW][C]33[/C][C]40.77[/C][C]39.7826250862343[/C][C]0.987374913765734[/C][/ROW]
[ROW][C]34[/C][C]45.31[/C][C]44.4817096345919[/C][C]0.828290365408073[/C][/ROW]
[ROW][C]35[/C][C]51.45[/C][C]50.4307031004394[/C][C]1.01929689956062[/C][/ROW]
[ROW][C]36[/C][C]45.13[/C][C]46.2658650794649[/C][C]-1.13586507946488[/C][/ROW]
[ROW][C]37[/C][C]48.13[/C][C]46.8938261271824[/C][C]1.2361738728176[/C][/ROW]
[ROW][C]38[/C][C]50.35[/C][C]52.5233127761609[/C][C]-2.17331277616086[/C][/ROW]
[ROW][C]39[/C][C]56.73[/C][C]57.1278584404009[/C][C]-0.397858440400945[/C][/ROW]
[ROW][C]40[/C][C]48.83[/C][C]49.9377019520681[/C][C]-1.10770195206813[/C][/ROW]
[ROW][C]41[/C][C]49.02[/C][C]51.2038550759355[/C][C]-2.18385507593548[/C][/ROW]
[ROW][C]42[/C][C]50.73[/C][C]52.1606230511203[/C][C]-1.43062305112034[/C][/ROW]
[ROW][C]43[/C][C]53.74[/C][C]56.806996496853[/C][C]-3.06699649685301[/C][/ROW]
[ROW][C]44[/C][C]46.38[/C][C]46.4786890022056[/C][C]-0.0986890022056315[/C][/ROW]
[ROW][C]45[/C][C]46.32[/C][C]46.4154467793677[/C][C]-0.0954467793677338[/C][/ROW]
[ROW][C]46[/C][C]51.65[/C][C]47.7915110873709[/C][C]3.85848891262908[/C][/ROW]
[ROW][C]47[/C][C]52.73[/C][C]54.7632568353107[/C][C]-2.03325683531071[/C][/ROW]
[ROW][C]48[/C][C]47.45[/C][C]46.7122878982906[/C][C]0.73771210170942[/C][/ROW]
[ROW][C]49[/C][C]49.01[/C][C]47.6850115342525[/C][C]1.32498846574753[/C][/ROW]
[ROW][C]50[/C][C]53.99[/C][C]52.6364639774824[/C][C]1.35353602251762[/C][/ROW]
[ROW][C]51[/C][C]55.63[/C][C]56.0209805058781[/C][C]-0.39098050587809[/C][/ROW]
[ROW][C]52[/C][C]50.04[/C][C]50.4320241875591[/C][C]-0.392024187559066[/C][/ROW]
[ROW][C]53[/C][C]54.77[/C][C]51.4760186446731[/C][C]3.29398135532686[/C][/ROW]
[ROW][C]54[/C][C]56.89[/C][C]58.7618045275809[/C][C]-1.87180452758093[/C][/ROW]
[ROW][C]55[/C][C]57.82[/C][C]59.8473846558804[/C][C]-2.02738465588043[/C][/ROW]
[ROW][C]56[/C][C]53.3[/C][C]52.8674935459609[/C][C]0.4325064540391[/C][/ROW]
[ROW][C]57[/C][C]54.69[/C][C]56.1304816075654[/C][C]-1.44048160756537[/C][/ROW]
[ROW][C]58[/C][C]60.88[/C][C]57.4363654809695[/C][C]3.44363451903054[/C][/ROW]
[ROW][C]59[/C][C]63.59[/C][C]61.5486525904923[/C][C]2.04134740950772[/C][/ROW]
[ROW][C]60[/C][C]59.46[/C][C]58.3866732977041[/C][C]1.07332670229585[/C][/ROW]
[ROW][C]61[/C][C]61.59[/C][C]62.4141251892121[/C][C]-0.824125189212047[/C][/ROW]
[ROW][C]62[/C][C]68.75[/C][C]67.9962875487198[/C][C]0.753712451280222[/C][/ROW]
[ROW][C]63[/C][C]71.33[/C][C]70.7245282605217[/C][C]0.605471739478304[/C][/ROW]
[ROW][C]64[/C][C]64.88[/C][C]65.9456489648198[/C][C]-1.06564896481981[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234179&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234179&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
523.8923.03911434228060.850885657719402
626.8426.7009470635480.139052936451961
729.3630.9707284477937-1.6107284477937
826.324.91736154699381.38263845300624
927.0925.81178327044171.27821672955831
1029.4230.00480213781-0.584802137809994
1132.4333.5801622805004-1.15016228050037
1229.1728.85458124108360.315418758916376
1328.8629.0640254524332-0.204025452433214
1432.131.39465953919840.705340460801644
1534.8235.6015179547765-0.781517954776525
1630.4831.4178370923042-0.937837092304221
1730.8730.40659447396120.463405526038752
1833.7533.54183686279310.208163137206938
1935.1136.6887999373784-1.57879993737841
203031.5008992054316-1.50089920543159
2129.9530.3108457873851-0.360845787385117
2232.6332.10292035443150.527079645568463
2336.7833.87453307260942.90546692739063
2432.3431.41410732594530.925892674054712
2533.6332.8944877174440.73551228255603
2636.9737.1101954228134-0.14019542281337
2739.7140.9165109748282-1.20651097482823
2834.9634.88682371138240.0731762886176099
2935.7835.74527233241350.0347276675865302
3038.5939.0943767777551-0.50437677775507
3142.9641.98937607838370.970623921616294
3239.2737.46536801912721.80463198087283
3340.7739.78262508623430.987374913765734
3445.3144.48170963459190.828290365408073
3551.4550.43070310043941.01929689956062
3645.1346.2658650794649-1.13586507946488
3748.1346.89382612718241.2361738728176
3850.3552.5233127761609-2.17331277616086
3956.7357.1278584404009-0.397858440400945
4048.8349.9377019520681-1.10770195206813
4149.0251.2038550759355-2.18385507593548
4250.7352.1606230511203-1.43062305112034
4353.7456.806996496853-3.06699649685301
4446.3846.4786890022056-0.0986890022056315
4546.3246.4154467793677-0.0954467793677338
4651.6547.79151108737093.85848891262908
4752.7354.7632568353107-2.03325683531071
4847.4546.71228789829060.73771210170942
4949.0147.68501153425251.32498846574753
5053.9952.63646397748241.35353602251762
5155.6356.0209805058781-0.39098050587809
5250.0450.4320241875591-0.392024187559066
5354.7751.47601864467313.29398135532686
5456.8958.7618045275809-1.87180452758093
5557.8259.8473846558804-2.02738465588043
5653.352.86749354596090.4325064540391
5754.6956.1304816075654-1.44048160756537
5860.8857.43636548096953.44363451903054
5963.5961.54865259049232.04134740950772
6059.4658.38667329770411.07332670229585
6161.5962.4141251892121-0.824125189212047
6268.7567.99628754871980.753712451280222
6371.3370.72452826052170.605471739478304
6464.8865.9456489648198-1.06564896481981







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6567.892719476134765.056163824481670.7292751277878
6675.202120666558571.494661020645778.9095803124714
6777.365044302748772.623697825067582.10639078043
6870.634980324331365.649242219880575.6207184287821

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
65 & 67.8927194761347 & 65.0561638244816 & 70.7292751277878 \tabularnewline
66 & 75.2021206665585 & 71.4946610206457 & 78.9095803124714 \tabularnewline
67 & 77.3650443027487 & 72.6236978250675 & 82.10639078043 \tabularnewline
68 & 70.6349803243313 & 65.6492422198805 & 75.6207184287821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234179&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]65[/C][C]67.8927194761347[/C][C]65.0561638244816[/C][C]70.7292751277878[/C][/ROW]
[ROW][C]66[/C][C]75.2021206665585[/C][C]71.4946610206457[/C][C]78.9095803124714[/C][/ROW]
[ROW][C]67[/C][C]77.3650443027487[/C][C]72.6236978250675[/C][C]82.10639078043[/C][/ROW]
[ROW][C]68[/C][C]70.6349803243313[/C][C]65.6492422198805[/C][C]75.6207184287821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234179&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234179&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
6567.892719476134765.056163824481670.7292751277878
6675.202120666558571.494661020645778.9095803124714
6777.365044302748772.623697825067582.10639078043
6870.634980324331365.649242219880575.6207184287821



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 4 ; 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')