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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 11:36:19 +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/30/t14173477360m3q25vpr1fphq3.htm/, Retrieved Sun, 19 May 2024 20:16:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261355, Retrieved Sun, 19 May 2024 20:16:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 11:36:19] [23e6dab13f5783a368d8e0aa48b4f84f] [Current]
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Dataseries X:
105.86
105.97
106.08
106.04
106.65
106.85
106.85
106.95
107.29
107.65
107.87
107.98
107.98
107.83
108.69
108.91
109.67
109.72
109.72
109.72
109.74
109.78
110.49
110.37
110.37
110.41
110.64
110.88
110.91
110.99
110.99
110.99
111.28
112.37
112.35
112.24
112.24
112.21
112.35
112.71
113.08
113.26
113.26
113.27
113.85
114.92
115.24
115.21
115.21
115.18
115.24
116.24
116.68
116.77
116.77
116.84
116.94
117.83
118.16
118.27
113.62
113.72
113.53
113.69
114.61
114.46
114.68
114.72
115.62
115.4
115.43
115.44




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261355&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261355&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.909252465308063
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.909252465308063 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261355&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]0.909252465308063[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261355&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
alpha0.909252465308063
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107.98106.6069711538461.37302884615379
14107.83107.6919365649360.138063435063842
15108.69108.6815066314220.00849336857760363
16108.91108.939931462193-0.0299314621925504
17109.67109.696335087523-0.0263350875225683
18109.72109.735175392054-0.015175392054104
19109.72109.4333293438690.286670656130909
20109.72109.84968755914-0.129687559139782
21109.74110.107054374058-0.367054374057716
22109.78110.126511493996-0.34651149399582
23110.49110.0075639449410.482436055058585
24110.37110.532338998476-0.162338998475789
25110.37110.3671007450150.00289925498509547
26110.41110.2062724475430.203727552456797
27110.64111.255547774651-0.615547774651247
28110.88110.946561657487-0.0665616574869006
29110.91111.669659187441-0.759659187440818
30110.99111.041722746252-0.0517227462518832
31110.99110.7066459261620.283354073837941
32110.99111.119988530806-0.129988530806486
33111.28111.377081686494-0.0970816864944766
34112.37111.6420121381650.727987861834706
35112.35112.500055777372-0.150055777371733
36112.24112.449736072982-0.209736072981642
37112.24112.241401912678-0.00140191267793455
38112.21112.0766627679050.133337232095101
39112.35113.06193552269-0.711935522690254
40112.71112.6653086079960.0446913920040544
41113.08113.489563247473-0.409563247472548
42113.26113.1799524027940.0800475972059189
43113.26112.9646880923480.295311907652248
44113.27113.388903386868-0.118903386867572
45113.85113.656075737010.193924262989682
46114.92114.1856040656690.734395934331076
47115.24115.0494742605910.190525739409452
48115.21115.308829139972-0.0988291399721106
49115.21115.2013373819270.00866261807293256
50115.18115.0457494365510.134250563448575
51115.24116.031852640122-0.79185264012159
52116.24115.5625608893830.67743911061747
53116.68116.962142951926-0.282142951926417
54116.77116.7683893251040.00161067489642619
55116.77116.4818060496760.288193950323844
56116.84116.899549323947-0.0595493239471665
57116.94117.220689502126-0.28068950212635
58117.83117.3186740947840.511325905215941
59118.16117.9797173157960.18028268420359
60118.27118.229758671980.040241328020258
61113.62118.248717079808-4.6287170798083
62113.72113.876580211565-0.156580211564602
63113.53114.598244815967-1.06824481596657
64113.69113.877642797949-0.187642797948598
65114.61114.4906470024350.119352997564604
66114.46114.661954557498-0.201954557498453
67114.68114.1902790926650.489720907335041
68114.72114.791261249424-0.0712612494244524
69115.62115.101752330490.518247669510103
70115.4115.926172516084-0.526172516084316
71115.43115.643867739776-0.213867739776177
72115.44115.535526851254-0.0955268512536946

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 107.98 & 106.606971153846 & 1.37302884615379 \tabularnewline
14 & 107.83 & 107.691936564936 & 0.138063435063842 \tabularnewline
15 & 108.69 & 108.681506631422 & 0.00849336857760363 \tabularnewline
16 & 108.91 & 108.939931462193 & -0.0299314621925504 \tabularnewline
17 & 109.67 & 109.696335087523 & -0.0263350875225683 \tabularnewline
18 & 109.72 & 109.735175392054 & -0.015175392054104 \tabularnewline
19 & 109.72 & 109.433329343869 & 0.286670656130909 \tabularnewline
20 & 109.72 & 109.84968755914 & -0.129687559139782 \tabularnewline
21 & 109.74 & 110.107054374058 & -0.367054374057716 \tabularnewline
22 & 109.78 & 110.126511493996 & -0.34651149399582 \tabularnewline
23 & 110.49 & 110.007563944941 & 0.482436055058585 \tabularnewline
24 & 110.37 & 110.532338998476 & -0.162338998475789 \tabularnewline
25 & 110.37 & 110.367100745015 & 0.00289925498509547 \tabularnewline
26 & 110.41 & 110.206272447543 & 0.203727552456797 \tabularnewline
27 & 110.64 & 111.255547774651 & -0.615547774651247 \tabularnewline
28 & 110.88 & 110.946561657487 & -0.0665616574869006 \tabularnewline
29 & 110.91 & 111.669659187441 & -0.759659187440818 \tabularnewline
30 & 110.99 & 111.041722746252 & -0.0517227462518832 \tabularnewline
31 & 110.99 & 110.706645926162 & 0.283354073837941 \tabularnewline
32 & 110.99 & 111.119988530806 & -0.129988530806486 \tabularnewline
33 & 111.28 & 111.377081686494 & -0.0970816864944766 \tabularnewline
34 & 112.37 & 111.642012138165 & 0.727987861834706 \tabularnewline
35 & 112.35 & 112.500055777372 & -0.150055777371733 \tabularnewline
36 & 112.24 & 112.449736072982 & -0.209736072981642 \tabularnewline
37 & 112.24 & 112.241401912678 & -0.00140191267793455 \tabularnewline
38 & 112.21 & 112.076662767905 & 0.133337232095101 \tabularnewline
39 & 112.35 & 113.06193552269 & -0.711935522690254 \tabularnewline
40 & 112.71 & 112.665308607996 & 0.0446913920040544 \tabularnewline
41 & 113.08 & 113.489563247473 & -0.409563247472548 \tabularnewline
42 & 113.26 & 113.179952402794 & 0.0800475972059189 \tabularnewline
43 & 113.26 & 112.964688092348 & 0.295311907652248 \tabularnewline
44 & 113.27 & 113.388903386868 & -0.118903386867572 \tabularnewline
45 & 113.85 & 113.65607573701 & 0.193924262989682 \tabularnewline
46 & 114.92 & 114.185604065669 & 0.734395934331076 \tabularnewline
47 & 115.24 & 115.049474260591 & 0.190525739409452 \tabularnewline
48 & 115.21 & 115.308829139972 & -0.0988291399721106 \tabularnewline
49 & 115.21 & 115.201337381927 & 0.00866261807293256 \tabularnewline
50 & 115.18 & 115.045749436551 & 0.134250563448575 \tabularnewline
51 & 115.24 & 116.031852640122 & -0.79185264012159 \tabularnewline
52 & 116.24 & 115.562560889383 & 0.67743911061747 \tabularnewline
53 & 116.68 & 116.962142951926 & -0.282142951926417 \tabularnewline
54 & 116.77 & 116.768389325104 & 0.00161067489642619 \tabularnewline
55 & 116.77 & 116.481806049676 & 0.288193950323844 \tabularnewline
56 & 116.84 & 116.899549323947 & -0.0595493239471665 \tabularnewline
57 & 116.94 & 117.220689502126 & -0.28068950212635 \tabularnewline
58 & 117.83 & 117.318674094784 & 0.511325905215941 \tabularnewline
59 & 118.16 & 117.979717315796 & 0.18028268420359 \tabularnewline
60 & 118.27 & 118.22975867198 & 0.040241328020258 \tabularnewline
61 & 113.62 & 118.248717079808 & -4.6287170798083 \tabularnewline
62 & 113.72 & 113.876580211565 & -0.156580211564602 \tabularnewline
63 & 113.53 & 114.598244815967 & -1.06824481596657 \tabularnewline
64 & 113.69 & 113.877642797949 & -0.187642797948598 \tabularnewline
65 & 114.61 & 114.490647002435 & 0.119352997564604 \tabularnewline
66 & 114.46 & 114.661954557498 & -0.201954557498453 \tabularnewline
67 & 114.68 & 114.190279092665 & 0.489720907335041 \tabularnewline
68 & 114.72 & 114.791261249424 & -0.0712612494244524 \tabularnewline
69 & 115.62 & 115.10175233049 & 0.518247669510103 \tabularnewline
70 & 115.4 & 115.926172516084 & -0.526172516084316 \tabularnewline
71 & 115.43 & 115.643867739776 & -0.213867739776177 \tabularnewline
72 & 115.44 & 115.535526851254 & -0.0955268512536946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261355&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]107.98[/C][C]106.606971153846[/C][C]1.37302884615379[/C][/ROW]
[ROW][C]14[/C][C]107.83[/C][C]107.691936564936[/C][C]0.138063435063842[/C][/ROW]
[ROW][C]15[/C][C]108.69[/C][C]108.681506631422[/C][C]0.00849336857760363[/C][/ROW]
[ROW][C]16[/C][C]108.91[/C][C]108.939931462193[/C][C]-0.0299314621925504[/C][/ROW]
[ROW][C]17[/C][C]109.67[/C][C]109.696335087523[/C][C]-0.0263350875225683[/C][/ROW]
[ROW][C]18[/C][C]109.72[/C][C]109.735175392054[/C][C]-0.015175392054104[/C][/ROW]
[ROW][C]19[/C][C]109.72[/C][C]109.433329343869[/C][C]0.286670656130909[/C][/ROW]
[ROW][C]20[/C][C]109.72[/C][C]109.84968755914[/C][C]-0.129687559139782[/C][/ROW]
[ROW][C]21[/C][C]109.74[/C][C]110.107054374058[/C][C]-0.367054374057716[/C][/ROW]
[ROW][C]22[/C][C]109.78[/C][C]110.126511493996[/C][C]-0.34651149399582[/C][/ROW]
[ROW][C]23[/C][C]110.49[/C][C]110.007563944941[/C][C]0.482436055058585[/C][/ROW]
[ROW][C]24[/C][C]110.37[/C][C]110.532338998476[/C][C]-0.162338998475789[/C][/ROW]
[ROW][C]25[/C][C]110.37[/C][C]110.367100745015[/C][C]0.00289925498509547[/C][/ROW]
[ROW][C]26[/C][C]110.41[/C][C]110.206272447543[/C][C]0.203727552456797[/C][/ROW]
[ROW][C]27[/C][C]110.64[/C][C]111.255547774651[/C][C]-0.615547774651247[/C][/ROW]
[ROW][C]28[/C][C]110.88[/C][C]110.946561657487[/C][C]-0.0665616574869006[/C][/ROW]
[ROW][C]29[/C][C]110.91[/C][C]111.669659187441[/C][C]-0.759659187440818[/C][/ROW]
[ROW][C]30[/C][C]110.99[/C][C]111.041722746252[/C][C]-0.0517227462518832[/C][/ROW]
[ROW][C]31[/C][C]110.99[/C][C]110.706645926162[/C][C]0.283354073837941[/C][/ROW]
[ROW][C]32[/C][C]110.99[/C][C]111.119988530806[/C][C]-0.129988530806486[/C][/ROW]
[ROW][C]33[/C][C]111.28[/C][C]111.377081686494[/C][C]-0.0970816864944766[/C][/ROW]
[ROW][C]34[/C][C]112.37[/C][C]111.642012138165[/C][C]0.727987861834706[/C][/ROW]
[ROW][C]35[/C][C]112.35[/C][C]112.500055777372[/C][C]-0.150055777371733[/C][/ROW]
[ROW][C]36[/C][C]112.24[/C][C]112.449736072982[/C][C]-0.209736072981642[/C][/ROW]
[ROW][C]37[/C][C]112.24[/C][C]112.241401912678[/C][C]-0.00140191267793455[/C][/ROW]
[ROW][C]38[/C][C]112.21[/C][C]112.076662767905[/C][C]0.133337232095101[/C][/ROW]
[ROW][C]39[/C][C]112.35[/C][C]113.06193552269[/C][C]-0.711935522690254[/C][/ROW]
[ROW][C]40[/C][C]112.71[/C][C]112.665308607996[/C][C]0.0446913920040544[/C][/ROW]
[ROW][C]41[/C][C]113.08[/C][C]113.489563247473[/C][C]-0.409563247472548[/C][/ROW]
[ROW][C]42[/C][C]113.26[/C][C]113.179952402794[/C][C]0.0800475972059189[/C][/ROW]
[ROW][C]43[/C][C]113.26[/C][C]112.964688092348[/C][C]0.295311907652248[/C][/ROW]
[ROW][C]44[/C][C]113.27[/C][C]113.388903386868[/C][C]-0.118903386867572[/C][/ROW]
[ROW][C]45[/C][C]113.85[/C][C]113.65607573701[/C][C]0.193924262989682[/C][/ROW]
[ROW][C]46[/C][C]114.92[/C][C]114.185604065669[/C][C]0.734395934331076[/C][/ROW]
[ROW][C]47[/C][C]115.24[/C][C]115.049474260591[/C][C]0.190525739409452[/C][/ROW]
[ROW][C]48[/C][C]115.21[/C][C]115.308829139972[/C][C]-0.0988291399721106[/C][/ROW]
[ROW][C]49[/C][C]115.21[/C][C]115.201337381927[/C][C]0.00866261807293256[/C][/ROW]
[ROW][C]50[/C][C]115.18[/C][C]115.045749436551[/C][C]0.134250563448575[/C][/ROW]
[ROW][C]51[/C][C]115.24[/C][C]116.031852640122[/C][C]-0.79185264012159[/C][/ROW]
[ROW][C]52[/C][C]116.24[/C][C]115.562560889383[/C][C]0.67743911061747[/C][/ROW]
[ROW][C]53[/C][C]116.68[/C][C]116.962142951926[/C][C]-0.282142951926417[/C][/ROW]
[ROW][C]54[/C][C]116.77[/C][C]116.768389325104[/C][C]0.00161067489642619[/C][/ROW]
[ROW][C]55[/C][C]116.77[/C][C]116.481806049676[/C][C]0.288193950323844[/C][/ROW]
[ROW][C]56[/C][C]116.84[/C][C]116.899549323947[/C][C]-0.0595493239471665[/C][/ROW]
[ROW][C]57[/C][C]116.94[/C][C]117.220689502126[/C][C]-0.28068950212635[/C][/ROW]
[ROW][C]58[/C][C]117.83[/C][C]117.318674094784[/C][C]0.511325905215941[/C][/ROW]
[ROW][C]59[/C][C]118.16[/C][C]117.979717315796[/C][C]0.18028268420359[/C][/ROW]
[ROW][C]60[/C][C]118.27[/C][C]118.22975867198[/C][C]0.040241328020258[/C][/ROW]
[ROW][C]61[/C][C]113.62[/C][C]118.248717079808[/C][C]-4.6287170798083[/C][/ROW]
[ROW][C]62[/C][C]113.72[/C][C]113.876580211565[/C][C]-0.156580211564602[/C][/ROW]
[ROW][C]63[/C][C]113.53[/C][C]114.598244815967[/C][C]-1.06824481596657[/C][/ROW]
[ROW][C]64[/C][C]113.69[/C][C]113.877642797949[/C][C]-0.187642797948598[/C][/ROW]
[ROW][C]65[/C][C]114.61[/C][C]114.490647002435[/C][C]0.119352997564604[/C][/ROW]
[ROW][C]66[/C][C]114.46[/C][C]114.661954557498[/C][C]-0.201954557498453[/C][/ROW]
[ROW][C]67[/C][C]114.68[/C][C]114.190279092665[/C][C]0.489720907335041[/C][/ROW]
[ROW][C]68[/C][C]114.72[/C][C]114.791261249424[/C][C]-0.0712612494244524[/C][/ROW]
[ROW][C]69[/C][C]115.62[/C][C]115.10175233049[/C][C]0.518247669510103[/C][/ROW]
[ROW][C]70[/C][C]115.4[/C][C]115.926172516084[/C][C]-0.526172516084316[/C][/ROW]
[ROW][C]71[/C][C]115.43[/C][C]115.643867739776[/C][C]-0.213867739776177[/C][/ROW]
[ROW][C]72[/C][C]115.44[/C][C]115.535526851254[/C][C]-0.0955268512536946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261355&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
13107.98106.6069711538461.37302884615379
14107.83107.6919365649360.138063435063842
15108.69108.6815066314220.00849336857760363
16108.91108.939931462193-0.0299314621925504
17109.67109.696335087523-0.0263350875225683
18109.72109.735175392054-0.015175392054104
19109.72109.4333293438690.286670656130909
20109.72109.84968755914-0.129687559139782
21109.74110.107054374058-0.367054374057716
22109.78110.126511493996-0.34651149399582
23110.49110.0075639449410.482436055058585
24110.37110.532338998476-0.162338998475789
25110.37110.3671007450150.00289925498509547
26110.41110.2062724475430.203727552456797
27110.64111.255547774651-0.615547774651247
28110.88110.946561657487-0.0665616574869006
29110.91111.669659187441-0.759659187440818
30110.99111.041722746252-0.0517227462518832
31110.99110.7066459261620.283354073837941
32110.99111.119988530806-0.129988530806486
33111.28111.377081686494-0.0970816864944766
34112.37111.6420121381650.727987861834706
35112.35112.500055777372-0.150055777371733
36112.24112.449736072982-0.209736072981642
37112.24112.241401912678-0.00140191267793455
38112.21112.0766627679050.133337232095101
39112.35113.06193552269-0.711935522690254
40112.71112.6653086079960.0446913920040544
41113.08113.489563247473-0.409563247472548
42113.26113.1799524027940.0800475972059189
43113.26112.9646880923480.295311907652248
44113.27113.388903386868-0.118903386867572
45113.85113.656075737010.193924262989682
46114.92114.1856040656690.734395934331076
47115.24115.0494742605910.190525739409452
48115.21115.308829139972-0.0988291399721106
49115.21115.2013373819270.00866261807293256
50115.18115.0457494365510.134250563448575
51115.24116.031852640122-0.79185264012159
52116.24115.5625608893830.67743911061747
53116.68116.962142951926-0.282142951926417
54116.77116.7683893251040.00161067489642619
55116.77116.4818060496760.288193950323844
56116.84116.899549323947-0.0595493239471665
57116.94117.220689502126-0.28068950212635
58117.83117.3186740947840.511325905215941
59118.16117.9797173157960.18028268420359
60118.27118.229758671980.040241328020258
61113.62118.248717079808-4.6287170798083
62113.72113.876580211565-0.156580211564602
63113.53114.598244815967-1.06824481596657
64113.69113.877642797949-0.187642797948598
65114.61114.4906470024350.119352997564604
66114.46114.661954557498-0.201954557498453
67114.68114.1902790926650.489720907335041
68114.72114.791261249424-0.0712612494244524
69115.62115.101752330490.518247669510103
70115.4115.926172516084-0.526172516084316
71115.43115.643867739776-0.213867739776177
72115.44115.535526851254-0.0955268512536946







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73115.431037707367114.023684883308116.838390531426
74115.267573255153113.365438137642117.169708372663
75116.131608802938113.839100561046118.424117044831
76116.38231101739113.756845330503119.007776704278
77117.165929898509114.245220034982120.086639762036
78117.228715446295114.039981819793120.417449072796
79116.940667660747113.504754656223120.376580665271
80117.096369875199113.429903700728120.76283604967
81117.471655422985113.588299883967121.355010962002
82117.824857637437113.736101558102121.913613716771
83118.020976518556113.73665599948122.305297037632
84118.107095399675113.635755740909122.578435058441

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 115.431037707367 & 114.023684883308 & 116.838390531426 \tabularnewline
74 & 115.267573255153 & 113.365438137642 & 117.169708372663 \tabularnewline
75 & 116.131608802938 & 113.839100561046 & 118.424117044831 \tabularnewline
76 & 116.38231101739 & 113.756845330503 & 119.007776704278 \tabularnewline
77 & 117.165929898509 & 114.245220034982 & 120.086639762036 \tabularnewline
78 & 117.228715446295 & 114.039981819793 & 120.417449072796 \tabularnewline
79 & 116.940667660747 & 113.504754656223 & 120.376580665271 \tabularnewline
80 & 117.096369875199 & 113.429903700728 & 120.76283604967 \tabularnewline
81 & 117.471655422985 & 113.588299883967 & 121.355010962002 \tabularnewline
82 & 117.824857637437 & 113.736101558102 & 121.913613716771 \tabularnewline
83 & 118.020976518556 & 113.73665599948 & 122.305297037632 \tabularnewline
84 & 118.107095399675 & 113.635755740909 & 122.578435058441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261355&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]115.431037707367[/C][C]114.023684883308[/C][C]116.838390531426[/C][/ROW]
[ROW][C]74[/C][C]115.267573255153[/C][C]113.365438137642[/C][C]117.169708372663[/C][/ROW]
[ROW][C]75[/C][C]116.131608802938[/C][C]113.839100561046[/C][C]118.424117044831[/C][/ROW]
[ROW][C]76[/C][C]116.38231101739[/C][C]113.756845330503[/C][C]119.007776704278[/C][/ROW]
[ROW][C]77[/C][C]117.165929898509[/C][C]114.245220034982[/C][C]120.086639762036[/C][/ROW]
[ROW][C]78[/C][C]117.228715446295[/C][C]114.039981819793[/C][C]120.417449072796[/C][/ROW]
[ROW][C]79[/C][C]116.940667660747[/C][C]113.504754656223[/C][C]120.376580665271[/C][/ROW]
[ROW][C]80[/C][C]117.096369875199[/C][C]113.429903700728[/C][C]120.76283604967[/C][/ROW]
[ROW][C]81[/C][C]117.471655422985[/C][C]113.588299883967[/C][C]121.355010962002[/C][/ROW]
[ROW][C]82[/C][C]117.824857637437[/C][C]113.736101558102[/C][C]121.913613716771[/C][/ROW]
[ROW][C]83[/C][C]118.020976518556[/C][C]113.73665599948[/C][C]122.305297037632[/C][/ROW]
[ROW][C]84[/C][C]118.107095399675[/C][C]113.635755740909[/C][C]122.578435058441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261355&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
73115.431037707367114.023684883308116.838390531426
74115.267573255153113.365438137642117.169708372663
75116.131608802938113.839100561046118.424117044831
76116.38231101739113.756845330503119.007776704278
77117.165929898509114.245220034982120.086639762036
78117.228715446295114.039981819793120.417449072796
79116.940667660747113.504754656223120.376580665271
80117.096369875199113.429903700728120.76283604967
81117.471655422985113.588299883967121.355010962002
82117.824857637437113.736101558102121.913613716771
83118.020976518556113.73665599948122.305297037632
84118.107095399675113.635755740909122.578435058441



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')