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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Jun 2009 06:15:59 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/04/t1244117791xncdt7g7os52zql.htm/, Retrieved Tue, 14 May 2024 01:47:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41622, Retrieved Tue, 14 May 2024 01:47:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef 2] [2009-06-04 12:15:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
65
65,05
65,84
66,6
67,55
68,07
69,06
69,06
69,11
69,29
69,38
69,28
69,75
69,9
70,21
70,48
71,55
72,18
72,64
72,77
72,74
73,13
73,44
73,34
73,34
73,81
74,26
74,72
75,11
75,26
75,89
75,91
76,43
76,56
76,76
76,76
76,56
76,82
77,09
77,51
77,76
77,86
77,89
77,94
77,99
78,17
78,91
78,87
78,88
79,08
79,41
79,51
79,73
80,38
80,56
80,46
80,45
80,58
80,68
80,52
81,49
81,66
81,95
82,3
82,4
83,14
83,17
83,11
83,21
83,33
83,88
83,8
83,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41622&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41622&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.942505883717753
beta0.0229525145944379
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.942505883717753 \tabularnewline
beta & 0.0229525145944379 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41622&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]0.942505883717753[/C][/ROW]
[ROW][C]beta[/C][C]0.0229525145944379[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41622&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
alpha0.942505883717753
beta0.0229525145944379
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1369.7567.67580128205132.07419871794869
1469.969.8517967397160.0482032602840547
1570.2170.2772390001607-0.0672390001606828
1670.4870.5470050110147-0.0670050110146718
1771.5571.5976253799827-0.0476253799827333
1872.1872.2163142244234-0.0363142244234069
1972.6473.1361283182693-0.496128318269299
2072.7772.62891557218320.141084427816793
2172.7472.7911649843006-0.0511649843005983
2273.1372.94152801505450.188471984945451
2373.4473.24724415778920.192755842210772
2473.3473.3615843918819-0.0215843918818877
2573.3473.9801949839464-0.64019498394643
2673.8173.4628418179170.347158182083007
2774.2674.15134708584050.108652914159478
2874.7274.57864424798610.141355752013865
2975.1175.8230060543459-0.713006054345882
3075.2675.7970719004046-0.537071900404555
3175.8976.1895013798266-0.299501379826623
3275.9175.87951931729940.0304806827006274
3376.4375.8993508147360.530649185264039
3476.5676.5973211313606-0.0373211313605708
3576.7676.67105396671040.0889460332896022
3676.7676.65356557426860.106434425731393
3776.5677.3383736330767-0.778373633076654
3876.8276.72566952006490.0943304799351381
3977.0977.1348173952727-0.044817395272716
4077.5177.3886749575030.121325042497062
4177.7678.5339304522478-0.773930452247839
4277.8678.4282654303364-0.568265430336425
4377.8978.7718544823174-0.881854482317436
4477.9477.88627599746990.0537240025300889
4577.9977.91157680270450.0784231972955212
4678.1778.09568915897050.0743108410295434
4778.9178.22933297072530.68066702927473
4878.8778.73078877408670.1392112259133
4978.8879.3565651549811-0.476565154981145
5079.0879.0459688991750.0340311008250183
5179.4179.35645586052510.0535441394748659
5279.5179.6808715937616-0.170871593761618
5379.7380.461236694468-0.731236694468009
5480.3880.3705374864430.00946251355694017
5580.5681.2160090859209-0.656009085920886
5680.4680.5773672471657-0.117367247165660
5780.4580.41941817778170.0305818222182666
5880.5880.53375295003080.0462470499691676
5980.6880.65075091592940.0292490840706279
6080.5280.46796143312670.052038566873307
6181.4980.9351382383230.55486176167696
6281.6681.60730162255990.0526983774401231
6381.9581.9181857357850.0318142642149297
6482.382.19042951860850.109570481391501
6582.483.1901731678355-0.790173167835505
6683.1483.07251480654080.0674851934592482
6783.1783.9216705926155-0.75167059261554
6883.1183.2090246944902-0.0990246944901827
6983.2183.06245532918920.147544670810802
7083.3383.2760447153780.0539552846220204
7183.8883.38761298861660.492387011383414
7283.883.64094552953670.159054470463289
7383.7384.2385114320388-0.508511432038773

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 69.75 & 67.6758012820513 & 2.07419871794869 \tabularnewline
14 & 69.9 & 69.851796739716 & 0.0482032602840547 \tabularnewline
15 & 70.21 & 70.2772390001607 & -0.0672390001606828 \tabularnewline
16 & 70.48 & 70.5470050110147 & -0.0670050110146718 \tabularnewline
17 & 71.55 & 71.5976253799827 & -0.0476253799827333 \tabularnewline
18 & 72.18 & 72.2163142244234 & -0.0363142244234069 \tabularnewline
19 & 72.64 & 73.1361283182693 & -0.496128318269299 \tabularnewline
20 & 72.77 & 72.6289155721832 & 0.141084427816793 \tabularnewline
21 & 72.74 & 72.7911649843006 & -0.0511649843005983 \tabularnewline
22 & 73.13 & 72.9415280150545 & 0.188471984945451 \tabularnewline
23 & 73.44 & 73.2472441577892 & 0.192755842210772 \tabularnewline
24 & 73.34 & 73.3615843918819 & -0.0215843918818877 \tabularnewline
25 & 73.34 & 73.9801949839464 & -0.64019498394643 \tabularnewline
26 & 73.81 & 73.462841817917 & 0.347158182083007 \tabularnewline
27 & 74.26 & 74.1513470858405 & 0.108652914159478 \tabularnewline
28 & 74.72 & 74.5786442479861 & 0.141355752013865 \tabularnewline
29 & 75.11 & 75.8230060543459 & -0.713006054345882 \tabularnewline
30 & 75.26 & 75.7970719004046 & -0.537071900404555 \tabularnewline
31 & 75.89 & 76.1895013798266 & -0.299501379826623 \tabularnewline
32 & 75.91 & 75.8795193172994 & 0.0304806827006274 \tabularnewline
33 & 76.43 & 75.899350814736 & 0.530649185264039 \tabularnewline
34 & 76.56 & 76.5973211313606 & -0.0373211313605708 \tabularnewline
35 & 76.76 & 76.6710539667104 & 0.0889460332896022 \tabularnewline
36 & 76.76 & 76.6535655742686 & 0.106434425731393 \tabularnewline
37 & 76.56 & 77.3383736330767 & -0.778373633076654 \tabularnewline
38 & 76.82 & 76.7256695200649 & 0.0943304799351381 \tabularnewline
39 & 77.09 & 77.1348173952727 & -0.044817395272716 \tabularnewline
40 & 77.51 & 77.388674957503 & 0.121325042497062 \tabularnewline
41 & 77.76 & 78.5339304522478 & -0.773930452247839 \tabularnewline
42 & 77.86 & 78.4282654303364 & -0.568265430336425 \tabularnewline
43 & 77.89 & 78.7718544823174 & -0.881854482317436 \tabularnewline
44 & 77.94 & 77.8862759974699 & 0.0537240025300889 \tabularnewline
45 & 77.99 & 77.9115768027045 & 0.0784231972955212 \tabularnewline
46 & 78.17 & 78.0956891589705 & 0.0743108410295434 \tabularnewline
47 & 78.91 & 78.2293329707253 & 0.68066702927473 \tabularnewline
48 & 78.87 & 78.7307887740867 & 0.1392112259133 \tabularnewline
49 & 78.88 & 79.3565651549811 & -0.476565154981145 \tabularnewline
50 & 79.08 & 79.045968899175 & 0.0340311008250183 \tabularnewline
51 & 79.41 & 79.3564558605251 & 0.0535441394748659 \tabularnewline
52 & 79.51 & 79.6808715937616 & -0.170871593761618 \tabularnewline
53 & 79.73 & 80.461236694468 & -0.731236694468009 \tabularnewline
54 & 80.38 & 80.370537486443 & 0.00946251355694017 \tabularnewline
55 & 80.56 & 81.2160090859209 & -0.656009085920886 \tabularnewline
56 & 80.46 & 80.5773672471657 & -0.117367247165660 \tabularnewline
57 & 80.45 & 80.4194181777817 & 0.0305818222182666 \tabularnewline
58 & 80.58 & 80.5337529500308 & 0.0462470499691676 \tabularnewline
59 & 80.68 & 80.6507509159294 & 0.0292490840706279 \tabularnewline
60 & 80.52 & 80.4679614331267 & 0.052038566873307 \tabularnewline
61 & 81.49 & 80.935138238323 & 0.55486176167696 \tabularnewline
62 & 81.66 & 81.6073016225599 & 0.0526983774401231 \tabularnewline
63 & 81.95 & 81.918185735785 & 0.0318142642149297 \tabularnewline
64 & 82.3 & 82.1904295186085 & 0.109570481391501 \tabularnewline
65 & 82.4 & 83.1901731678355 & -0.790173167835505 \tabularnewline
66 & 83.14 & 83.0725148065408 & 0.0674851934592482 \tabularnewline
67 & 83.17 & 83.9216705926155 & -0.75167059261554 \tabularnewline
68 & 83.11 & 83.2090246944902 & -0.0990246944901827 \tabularnewline
69 & 83.21 & 83.0624553291892 & 0.147544670810802 \tabularnewline
70 & 83.33 & 83.276044715378 & 0.0539552846220204 \tabularnewline
71 & 83.88 & 83.3876129886166 & 0.492387011383414 \tabularnewline
72 & 83.8 & 83.6409455295367 & 0.159054470463289 \tabularnewline
73 & 83.73 & 84.2385114320388 & -0.508511432038773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41622&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]69.75[/C][C]67.6758012820513[/C][C]2.07419871794869[/C][/ROW]
[ROW][C]14[/C][C]69.9[/C][C]69.851796739716[/C][C]0.0482032602840547[/C][/ROW]
[ROW][C]15[/C][C]70.21[/C][C]70.2772390001607[/C][C]-0.0672390001606828[/C][/ROW]
[ROW][C]16[/C][C]70.48[/C][C]70.5470050110147[/C][C]-0.0670050110146718[/C][/ROW]
[ROW][C]17[/C][C]71.55[/C][C]71.5976253799827[/C][C]-0.0476253799827333[/C][/ROW]
[ROW][C]18[/C][C]72.18[/C][C]72.2163142244234[/C][C]-0.0363142244234069[/C][/ROW]
[ROW][C]19[/C][C]72.64[/C][C]73.1361283182693[/C][C]-0.496128318269299[/C][/ROW]
[ROW][C]20[/C][C]72.77[/C][C]72.6289155721832[/C][C]0.141084427816793[/C][/ROW]
[ROW][C]21[/C][C]72.74[/C][C]72.7911649843006[/C][C]-0.0511649843005983[/C][/ROW]
[ROW][C]22[/C][C]73.13[/C][C]72.9415280150545[/C][C]0.188471984945451[/C][/ROW]
[ROW][C]23[/C][C]73.44[/C][C]73.2472441577892[/C][C]0.192755842210772[/C][/ROW]
[ROW][C]24[/C][C]73.34[/C][C]73.3615843918819[/C][C]-0.0215843918818877[/C][/ROW]
[ROW][C]25[/C][C]73.34[/C][C]73.9801949839464[/C][C]-0.64019498394643[/C][/ROW]
[ROW][C]26[/C][C]73.81[/C][C]73.462841817917[/C][C]0.347158182083007[/C][/ROW]
[ROW][C]27[/C][C]74.26[/C][C]74.1513470858405[/C][C]0.108652914159478[/C][/ROW]
[ROW][C]28[/C][C]74.72[/C][C]74.5786442479861[/C][C]0.141355752013865[/C][/ROW]
[ROW][C]29[/C][C]75.11[/C][C]75.8230060543459[/C][C]-0.713006054345882[/C][/ROW]
[ROW][C]30[/C][C]75.26[/C][C]75.7970719004046[/C][C]-0.537071900404555[/C][/ROW]
[ROW][C]31[/C][C]75.89[/C][C]76.1895013798266[/C][C]-0.299501379826623[/C][/ROW]
[ROW][C]32[/C][C]75.91[/C][C]75.8795193172994[/C][C]0.0304806827006274[/C][/ROW]
[ROW][C]33[/C][C]76.43[/C][C]75.899350814736[/C][C]0.530649185264039[/C][/ROW]
[ROW][C]34[/C][C]76.56[/C][C]76.5973211313606[/C][C]-0.0373211313605708[/C][/ROW]
[ROW][C]35[/C][C]76.76[/C][C]76.6710539667104[/C][C]0.0889460332896022[/C][/ROW]
[ROW][C]36[/C][C]76.76[/C][C]76.6535655742686[/C][C]0.106434425731393[/C][/ROW]
[ROW][C]37[/C][C]76.56[/C][C]77.3383736330767[/C][C]-0.778373633076654[/C][/ROW]
[ROW][C]38[/C][C]76.82[/C][C]76.7256695200649[/C][C]0.0943304799351381[/C][/ROW]
[ROW][C]39[/C][C]77.09[/C][C]77.1348173952727[/C][C]-0.044817395272716[/C][/ROW]
[ROW][C]40[/C][C]77.51[/C][C]77.388674957503[/C][C]0.121325042497062[/C][/ROW]
[ROW][C]41[/C][C]77.76[/C][C]78.5339304522478[/C][C]-0.773930452247839[/C][/ROW]
[ROW][C]42[/C][C]77.86[/C][C]78.4282654303364[/C][C]-0.568265430336425[/C][/ROW]
[ROW][C]43[/C][C]77.89[/C][C]78.7718544823174[/C][C]-0.881854482317436[/C][/ROW]
[ROW][C]44[/C][C]77.94[/C][C]77.8862759974699[/C][C]0.0537240025300889[/C][/ROW]
[ROW][C]45[/C][C]77.99[/C][C]77.9115768027045[/C][C]0.0784231972955212[/C][/ROW]
[ROW][C]46[/C][C]78.17[/C][C]78.0956891589705[/C][C]0.0743108410295434[/C][/ROW]
[ROW][C]47[/C][C]78.91[/C][C]78.2293329707253[/C][C]0.68066702927473[/C][/ROW]
[ROW][C]48[/C][C]78.87[/C][C]78.7307887740867[/C][C]0.1392112259133[/C][/ROW]
[ROW][C]49[/C][C]78.88[/C][C]79.3565651549811[/C][C]-0.476565154981145[/C][/ROW]
[ROW][C]50[/C][C]79.08[/C][C]79.045968899175[/C][C]0.0340311008250183[/C][/ROW]
[ROW][C]51[/C][C]79.41[/C][C]79.3564558605251[/C][C]0.0535441394748659[/C][/ROW]
[ROW][C]52[/C][C]79.51[/C][C]79.6808715937616[/C][C]-0.170871593761618[/C][/ROW]
[ROW][C]53[/C][C]79.73[/C][C]80.461236694468[/C][C]-0.731236694468009[/C][/ROW]
[ROW][C]54[/C][C]80.38[/C][C]80.370537486443[/C][C]0.00946251355694017[/C][/ROW]
[ROW][C]55[/C][C]80.56[/C][C]81.2160090859209[/C][C]-0.656009085920886[/C][/ROW]
[ROW][C]56[/C][C]80.46[/C][C]80.5773672471657[/C][C]-0.117367247165660[/C][/ROW]
[ROW][C]57[/C][C]80.45[/C][C]80.4194181777817[/C][C]0.0305818222182666[/C][/ROW]
[ROW][C]58[/C][C]80.58[/C][C]80.5337529500308[/C][C]0.0462470499691676[/C][/ROW]
[ROW][C]59[/C][C]80.68[/C][C]80.6507509159294[/C][C]0.0292490840706279[/C][/ROW]
[ROW][C]60[/C][C]80.52[/C][C]80.4679614331267[/C][C]0.052038566873307[/C][/ROW]
[ROW][C]61[/C][C]81.49[/C][C]80.935138238323[/C][C]0.55486176167696[/C][/ROW]
[ROW][C]62[/C][C]81.66[/C][C]81.6073016225599[/C][C]0.0526983774401231[/C][/ROW]
[ROW][C]63[/C][C]81.95[/C][C]81.918185735785[/C][C]0.0318142642149297[/C][/ROW]
[ROW][C]64[/C][C]82.3[/C][C]82.1904295186085[/C][C]0.109570481391501[/C][/ROW]
[ROW][C]65[/C][C]82.4[/C][C]83.1901731678355[/C][C]-0.790173167835505[/C][/ROW]
[ROW][C]66[/C][C]83.14[/C][C]83.0725148065408[/C][C]0.0674851934592482[/C][/ROW]
[ROW][C]67[/C][C]83.17[/C][C]83.9216705926155[/C][C]-0.75167059261554[/C][/ROW]
[ROW][C]68[/C][C]83.11[/C][C]83.2090246944902[/C][C]-0.0990246944901827[/C][/ROW]
[ROW][C]69[/C][C]83.21[/C][C]83.0624553291892[/C][C]0.147544670810802[/C][/ROW]
[ROW][C]70[/C][C]83.33[/C][C]83.276044715378[/C][C]0.0539552846220204[/C][/ROW]
[ROW][C]71[/C][C]83.88[/C][C]83.3876129886166[/C][C]0.492387011383414[/C][/ROW]
[ROW][C]72[/C][C]83.8[/C][C]83.6409455295367[/C][C]0.159054470463289[/C][/ROW]
[ROW][C]73[/C][C]83.73[/C][C]84.2385114320388[/C][C]-0.508511432038773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41622&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41622&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
1369.7567.67580128205132.07419871794869
1469.969.8517967397160.0482032602840547
1570.2170.2772390001607-0.0672390001606828
1670.4870.5470050110147-0.0670050110146718
1771.5571.5976253799827-0.0476253799827333
1872.1872.2163142244234-0.0363142244234069
1972.6473.1361283182693-0.496128318269299
2072.7772.62891557218320.141084427816793
2172.7472.7911649843006-0.0511649843005983
2273.1372.94152801505450.188471984945451
2373.4473.24724415778920.192755842210772
2473.3473.3615843918819-0.0215843918818877
2573.3473.9801949839464-0.64019498394643
2673.8173.4628418179170.347158182083007
2774.2674.15134708584050.108652914159478
2874.7274.57864424798610.141355752013865
2975.1175.8230060543459-0.713006054345882
3075.2675.7970719004046-0.537071900404555
3175.8976.1895013798266-0.299501379826623
3275.9175.87951931729940.0304806827006274
3376.4375.8993508147360.530649185264039
3476.5676.5973211313606-0.0373211313605708
3576.7676.67105396671040.0889460332896022
3676.7676.65356557426860.106434425731393
3776.5677.3383736330767-0.778373633076654
3876.8276.72566952006490.0943304799351381
3977.0977.1348173952727-0.044817395272716
4077.5177.3886749575030.121325042497062
4177.7678.5339304522478-0.773930452247839
4277.8678.4282654303364-0.568265430336425
4377.8978.7718544823174-0.881854482317436
4477.9477.88627599746990.0537240025300889
4577.9977.91157680270450.0784231972955212
4678.1778.09568915897050.0743108410295434
4778.9178.22933297072530.68066702927473
4878.8778.73078877408670.1392112259133
4978.8879.3565651549811-0.476565154981145
5079.0879.0459688991750.0340311008250183
5179.4179.35645586052510.0535441394748659
5279.5179.6808715937616-0.170871593761618
5379.7380.461236694468-0.731236694468009
5480.3880.3705374864430.00946251355694017
5580.5681.2160090859209-0.656009085920886
5680.4680.5773672471657-0.117367247165660
5780.4580.41941817778170.0305818222182666
5880.5880.53375295003080.0462470499691676
5980.6880.65075091592940.0292490840706279
6080.5280.46796143312670.052038566873307
6181.4980.9351382383230.55486176167696
6281.6681.60730162255990.0526983774401231
6381.9581.9181857357850.0318142642149297
6482.382.19042951860850.109570481391501
6582.483.1901731678355-0.790173167835505
6683.1483.07251480654080.0674851934592482
6783.1783.9216705926155-0.75167059261554
6883.1183.2090246944902-0.0990246944901827
6983.2183.06245532918920.147544670810802
7083.3383.2760447153780.0539552846220204
7183.8883.38761298861660.492387011383414
7283.883.64094552953670.159054470463289
7383.7384.2385114320388-0.508511432038773







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7483.857180663144782.966319370951684.7480419553377
7584.093668292797782.856184176521885.3311524090737
7684.316181996104582.798757454950485.8336065372587
7785.134339057564483.371384845446986.8972932696819
7885.801241788643883.814183486096187.7883000911915
7986.528743768684884.332269438966888.7252180984027
8086.567383949526684.17217065712688.9625972419271
8186.535773242165783.949891339490989.1216551448405
8286.609179265775483.838898090788489.3794604407623
8386.698193599103583.748480519883889.6479066783233
8486.460724064327483.335571842404289.5858762862506
8586.858998514147683.561649869886490.1563471584088

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 83.8571806631447 & 82.9663193709516 & 84.7480419553377 \tabularnewline
75 & 84.0936682927977 & 82.8561841765218 & 85.3311524090737 \tabularnewline
76 & 84.3161819961045 & 82.7987574549504 & 85.8336065372587 \tabularnewline
77 & 85.1343390575644 & 83.3713848454469 & 86.8972932696819 \tabularnewline
78 & 85.8012417886438 & 83.8141834860961 & 87.7883000911915 \tabularnewline
79 & 86.5287437686848 & 84.3322694389668 & 88.7252180984027 \tabularnewline
80 & 86.5673839495266 & 84.172170657126 & 88.9625972419271 \tabularnewline
81 & 86.5357732421657 & 83.9498913394909 & 89.1216551448405 \tabularnewline
82 & 86.6091792657754 & 83.8388980907884 & 89.3794604407623 \tabularnewline
83 & 86.6981935991035 & 83.7484805198838 & 89.6479066783233 \tabularnewline
84 & 86.4607240643274 & 83.3355718424042 & 89.5858762862506 \tabularnewline
85 & 86.8589985141476 & 83.5616498698864 & 90.1563471584088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41622&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]74[/C][C]83.8571806631447[/C][C]82.9663193709516[/C][C]84.7480419553377[/C][/ROW]
[ROW][C]75[/C][C]84.0936682927977[/C][C]82.8561841765218[/C][C]85.3311524090737[/C][/ROW]
[ROW][C]76[/C][C]84.3161819961045[/C][C]82.7987574549504[/C][C]85.8336065372587[/C][/ROW]
[ROW][C]77[/C][C]85.1343390575644[/C][C]83.3713848454469[/C][C]86.8972932696819[/C][/ROW]
[ROW][C]78[/C][C]85.8012417886438[/C][C]83.8141834860961[/C][C]87.7883000911915[/C][/ROW]
[ROW][C]79[/C][C]86.5287437686848[/C][C]84.3322694389668[/C][C]88.7252180984027[/C][/ROW]
[ROW][C]80[/C][C]86.5673839495266[/C][C]84.172170657126[/C][C]88.9625972419271[/C][/ROW]
[ROW][C]81[/C][C]86.5357732421657[/C][C]83.9498913394909[/C][C]89.1216551448405[/C][/ROW]
[ROW][C]82[/C][C]86.6091792657754[/C][C]83.8388980907884[/C][C]89.3794604407623[/C][/ROW]
[ROW][C]83[/C][C]86.6981935991035[/C][C]83.7484805198838[/C][C]89.6479066783233[/C][/ROW]
[ROW][C]84[/C][C]86.4607240643274[/C][C]83.3355718424042[/C][C]89.5858762862506[/C][/ROW]
[ROW][C]85[/C][C]86.8589985141476[/C][C]83.5616498698864[/C][C]90.1563471584088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41622&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41622&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
7483.857180663144782.966319370951684.7480419553377
7584.093668292797782.856184176521885.3311524090737
7684.316181996104582.798757454950485.8336065372587
7785.134339057564483.371384845446986.8972932696819
7885.801241788643883.814183486096187.7883000911915
7986.528743768684884.332269438966888.7252180984027
8086.567383949526684.17217065712688.9625972419271
8186.535773242165783.949891339490989.1216551448405
8286.609179265775483.838898090788489.3794604407623
8386.698193599103583.748480519883889.6479066783233
8486.460724064327483.335571842404289.5858762862506
8586.858998514147683.561649869886490.1563471584088



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')