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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:12:27 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356081211zj8kb5zd0jef8u2.htm/, Retrieved Fri, 29 Mar 2024 06:43:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203338, Retrieved Fri, 29 Mar 2024 06:43:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:12:27] [c9eeded7548c00546c4c5f04921b1379] [Current]
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Dataseries X:
102.89
102.64
103.33
103.56
103.6
104.24
105.31
105.4
105.89
105.89
105.54
106.15
106.14
105.85
106.27
106.51
106.82
106.53
107.14
107.39
107.33
107.53
107.42
108.25
108.26
108.93
109.43
109.61
109.74
110.12
110.16
110.44
111.23
112.86
112.77
113.04
112.79
113.87
114.28
115.51
116.76
116.91
116.47
116.94
117.24
116.82
117.48
117.11
117.31
117.77
118.37
117.91
118.12
118.02
117.77
117.85
118.68
118.9
118.6
118.21
118.37
117.43
117.5
116.71
116.98
117.74
117.44
117.85
118.54
118.73
118.68
118.19




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=203338&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=203338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203338&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
alpha0.767499072123643
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.767499072123643 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203338&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]0.767499072123643[/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=203338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203338&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
alpha0.767499072123643
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13106.14104.7290095058691.4109904941314
14105.85105.5579107851380.292089214861704
15106.27106.2528123233340.0171876766659409
16106.51106.571534737355-0.0615347373552737
17106.82106.881606583944-0.0616065839443962
18106.53106.572228475694-0.042228475694202
19107.14107.700291421424-0.560291421423827
20107.39107.2812972955740.108702704425653
21107.33107.796273524345-0.466273524344643
22107.53107.3830517059290.146948294070739
23107.42107.0735278851580.346472114841632
24108.25107.9201469597350.329853040264737
25108.26108.517473018442-0.257473018442155
26108.93107.7910086069531.13899139304671
27109.43109.0776606697230.352339330277502
28109.61109.638007745763-0.0280077457633752
29109.74109.978547372105-0.238547372104819
30110.12109.5253104069750.594689593024881
31110.16111.048603784697-0.888603784697182
32110.44110.532302353449-0.0923023534494263
33111.23110.7618965931720.46810340682832
34112.86111.2045468527181.65545314728243
35112.77112.0727826646880.697217335311976
36113.04113.203015178815-0.163015178815272
37112.79113.285984509122-0.495984509122124
38113.87112.6818466848821.18815331511846
39114.28113.8246541480230.455345851976986
40115.51114.3759596886211.13404031137911
41116.76115.5654449932381.19455500676244
42116.91116.3886461039720.521353896027605
43116.47117.541380800453-1.07138080045337
44116.94117.079219131881-0.139219131880651
45117.24117.416661119857-0.176661119857371
46116.82117.644853014419-0.824853014419332
47117.48116.3557335983691.12426640163115
48117.11117.621596959337-0.511596959337268
49117.31117.356855110556-0.0468551105563506
50117.77117.485631866220.284368133780248
51118.37117.7595785940790.610421405921429
52117.91118.591354838963-0.681354838962548
53118.12118.402433431397-0.282433431397251
54118.02117.9296871971820.0903128028175786
55117.77118.381268134087-0.611268134086615
56117.85118.493672986103-0.643672986102828
57118.68118.4373732250550.242626774945336
58118.9118.8358251131960.064174886804409
59118.6118.673224093729-0.0732240937287543
60118.21118.637612646535-0.427612646534698
61118.37118.545805624606-0.175805624605957
62117.43118.652944135305-1.22294413530474
63117.5117.845305290473-0.345305290472666
64116.71117.643400347161-0.93340034716131
65116.98117.351726971213-0.371726971212738
66117.74116.9003382105310.839661789468877
67117.44117.763260376089-0.323260376088825
68117.85118.087730192995-0.237730192994945
69118.54118.549178470324-0.00917847032364705
70118.73118.7129019958680.0170980041318529
71118.68118.4828572711110.197142728889332
72118.19118.572006881252-0.38200688125248

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 106.14 & 104.729009505869 & 1.4109904941314 \tabularnewline
14 & 105.85 & 105.557910785138 & 0.292089214861704 \tabularnewline
15 & 106.27 & 106.252812323334 & 0.0171876766659409 \tabularnewline
16 & 106.51 & 106.571534737355 & -0.0615347373552737 \tabularnewline
17 & 106.82 & 106.881606583944 & -0.0616065839443962 \tabularnewline
18 & 106.53 & 106.572228475694 & -0.042228475694202 \tabularnewline
19 & 107.14 & 107.700291421424 & -0.560291421423827 \tabularnewline
20 & 107.39 & 107.281297295574 & 0.108702704425653 \tabularnewline
21 & 107.33 & 107.796273524345 & -0.466273524344643 \tabularnewline
22 & 107.53 & 107.383051705929 & 0.146948294070739 \tabularnewline
23 & 107.42 & 107.073527885158 & 0.346472114841632 \tabularnewline
24 & 108.25 & 107.920146959735 & 0.329853040264737 \tabularnewline
25 & 108.26 & 108.517473018442 & -0.257473018442155 \tabularnewline
26 & 108.93 & 107.791008606953 & 1.13899139304671 \tabularnewline
27 & 109.43 & 109.077660669723 & 0.352339330277502 \tabularnewline
28 & 109.61 & 109.638007745763 & -0.0280077457633752 \tabularnewline
29 & 109.74 & 109.978547372105 & -0.238547372104819 \tabularnewline
30 & 110.12 & 109.525310406975 & 0.594689593024881 \tabularnewline
31 & 110.16 & 111.048603784697 & -0.888603784697182 \tabularnewline
32 & 110.44 & 110.532302353449 & -0.0923023534494263 \tabularnewline
33 & 111.23 & 110.761896593172 & 0.46810340682832 \tabularnewline
34 & 112.86 & 111.204546852718 & 1.65545314728243 \tabularnewline
35 & 112.77 & 112.072782664688 & 0.697217335311976 \tabularnewline
36 & 113.04 & 113.203015178815 & -0.163015178815272 \tabularnewline
37 & 112.79 & 113.285984509122 & -0.495984509122124 \tabularnewline
38 & 113.87 & 112.681846684882 & 1.18815331511846 \tabularnewline
39 & 114.28 & 113.824654148023 & 0.455345851976986 \tabularnewline
40 & 115.51 & 114.375959688621 & 1.13404031137911 \tabularnewline
41 & 116.76 & 115.565444993238 & 1.19455500676244 \tabularnewline
42 & 116.91 & 116.388646103972 & 0.521353896027605 \tabularnewline
43 & 116.47 & 117.541380800453 & -1.07138080045337 \tabularnewline
44 & 116.94 & 117.079219131881 & -0.139219131880651 \tabularnewline
45 & 117.24 & 117.416661119857 & -0.176661119857371 \tabularnewline
46 & 116.82 & 117.644853014419 & -0.824853014419332 \tabularnewline
47 & 117.48 & 116.355733598369 & 1.12426640163115 \tabularnewline
48 & 117.11 & 117.621596959337 & -0.511596959337268 \tabularnewline
49 & 117.31 & 117.356855110556 & -0.0468551105563506 \tabularnewline
50 & 117.77 & 117.48563186622 & 0.284368133780248 \tabularnewline
51 & 118.37 & 117.759578594079 & 0.610421405921429 \tabularnewline
52 & 117.91 & 118.591354838963 & -0.681354838962548 \tabularnewline
53 & 118.12 & 118.402433431397 & -0.282433431397251 \tabularnewline
54 & 118.02 & 117.929687197182 & 0.0903128028175786 \tabularnewline
55 & 117.77 & 118.381268134087 & -0.611268134086615 \tabularnewline
56 & 117.85 & 118.493672986103 & -0.643672986102828 \tabularnewline
57 & 118.68 & 118.437373225055 & 0.242626774945336 \tabularnewline
58 & 118.9 & 118.835825113196 & 0.064174886804409 \tabularnewline
59 & 118.6 & 118.673224093729 & -0.0732240937287543 \tabularnewline
60 & 118.21 & 118.637612646535 & -0.427612646534698 \tabularnewline
61 & 118.37 & 118.545805624606 & -0.175805624605957 \tabularnewline
62 & 117.43 & 118.652944135305 & -1.22294413530474 \tabularnewline
63 & 117.5 & 117.845305290473 & -0.345305290472666 \tabularnewline
64 & 116.71 & 117.643400347161 & -0.93340034716131 \tabularnewline
65 & 116.98 & 117.351726971213 & -0.371726971212738 \tabularnewline
66 & 117.74 & 116.900338210531 & 0.839661789468877 \tabularnewline
67 & 117.44 & 117.763260376089 & -0.323260376088825 \tabularnewline
68 & 117.85 & 118.087730192995 & -0.237730192994945 \tabularnewline
69 & 118.54 & 118.549178470324 & -0.00917847032364705 \tabularnewline
70 & 118.73 & 118.712901995868 & 0.0170980041318529 \tabularnewline
71 & 118.68 & 118.482857271111 & 0.197142728889332 \tabularnewline
72 & 118.19 & 118.572006881252 & -0.38200688125248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203338&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]106.14[/C][C]104.729009505869[/C][C]1.4109904941314[/C][/ROW]
[ROW][C]14[/C][C]105.85[/C][C]105.557910785138[/C][C]0.292089214861704[/C][/ROW]
[ROW][C]15[/C][C]106.27[/C][C]106.252812323334[/C][C]0.0171876766659409[/C][/ROW]
[ROW][C]16[/C][C]106.51[/C][C]106.571534737355[/C][C]-0.0615347373552737[/C][/ROW]
[ROW][C]17[/C][C]106.82[/C][C]106.881606583944[/C][C]-0.0616065839443962[/C][/ROW]
[ROW][C]18[/C][C]106.53[/C][C]106.572228475694[/C][C]-0.042228475694202[/C][/ROW]
[ROW][C]19[/C][C]107.14[/C][C]107.700291421424[/C][C]-0.560291421423827[/C][/ROW]
[ROW][C]20[/C][C]107.39[/C][C]107.281297295574[/C][C]0.108702704425653[/C][/ROW]
[ROW][C]21[/C][C]107.33[/C][C]107.796273524345[/C][C]-0.466273524344643[/C][/ROW]
[ROW][C]22[/C][C]107.53[/C][C]107.383051705929[/C][C]0.146948294070739[/C][/ROW]
[ROW][C]23[/C][C]107.42[/C][C]107.073527885158[/C][C]0.346472114841632[/C][/ROW]
[ROW][C]24[/C][C]108.25[/C][C]107.920146959735[/C][C]0.329853040264737[/C][/ROW]
[ROW][C]25[/C][C]108.26[/C][C]108.517473018442[/C][C]-0.257473018442155[/C][/ROW]
[ROW][C]26[/C][C]108.93[/C][C]107.791008606953[/C][C]1.13899139304671[/C][/ROW]
[ROW][C]27[/C][C]109.43[/C][C]109.077660669723[/C][C]0.352339330277502[/C][/ROW]
[ROW][C]28[/C][C]109.61[/C][C]109.638007745763[/C][C]-0.0280077457633752[/C][/ROW]
[ROW][C]29[/C][C]109.74[/C][C]109.978547372105[/C][C]-0.238547372104819[/C][/ROW]
[ROW][C]30[/C][C]110.12[/C][C]109.525310406975[/C][C]0.594689593024881[/C][/ROW]
[ROW][C]31[/C][C]110.16[/C][C]111.048603784697[/C][C]-0.888603784697182[/C][/ROW]
[ROW][C]32[/C][C]110.44[/C][C]110.532302353449[/C][C]-0.0923023534494263[/C][/ROW]
[ROW][C]33[/C][C]111.23[/C][C]110.761896593172[/C][C]0.46810340682832[/C][/ROW]
[ROW][C]34[/C][C]112.86[/C][C]111.204546852718[/C][C]1.65545314728243[/C][/ROW]
[ROW][C]35[/C][C]112.77[/C][C]112.072782664688[/C][C]0.697217335311976[/C][/ROW]
[ROW][C]36[/C][C]113.04[/C][C]113.203015178815[/C][C]-0.163015178815272[/C][/ROW]
[ROW][C]37[/C][C]112.79[/C][C]113.285984509122[/C][C]-0.495984509122124[/C][/ROW]
[ROW][C]38[/C][C]113.87[/C][C]112.681846684882[/C][C]1.18815331511846[/C][/ROW]
[ROW][C]39[/C][C]114.28[/C][C]113.824654148023[/C][C]0.455345851976986[/C][/ROW]
[ROW][C]40[/C][C]115.51[/C][C]114.375959688621[/C][C]1.13404031137911[/C][/ROW]
[ROW][C]41[/C][C]116.76[/C][C]115.565444993238[/C][C]1.19455500676244[/C][/ROW]
[ROW][C]42[/C][C]116.91[/C][C]116.388646103972[/C][C]0.521353896027605[/C][/ROW]
[ROW][C]43[/C][C]116.47[/C][C]117.541380800453[/C][C]-1.07138080045337[/C][/ROW]
[ROW][C]44[/C][C]116.94[/C][C]117.079219131881[/C][C]-0.139219131880651[/C][/ROW]
[ROW][C]45[/C][C]117.24[/C][C]117.416661119857[/C][C]-0.176661119857371[/C][/ROW]
[ROW][C]46[/C][C]116.82[/C][C]117.644853014419[/C][C]-0.824853014419332[/C][/ROW]
[ROW][C]47[/C][C]117.48[/C][C]116.355733598369[/C][C]1.12426640163115[/C][/ROW]
[ROW][C]48[/C][C]117.11[/C][C]117.621596959337[/C][C]-0.511596959337268[/C][/ROW]
[ROW][C]49[/C][C]117.31[/C][C]117.356855110556[/C][C]-0.0468551105563506[/C][/ROW]
[ROW][C]50[/C][C]117.77[/C][C]117.48563186622[/C][C]0.284368133780248[/C][/ROW]
[ROW][C]51[/C][C]118.37[/C][C]117.759578594079[/C][C]0.610421405921429[/C][/ROW]
[ROW][C]52[/C][C]117.91[/C][C]118.591354838963[/C][C]-0.681354838962548[/C][/ROW]
[ROW][C]53[/C][C]118.12[/C][C]118.402433431397[/C][C]-0.282433431397251[/C][/ROW]
[ROW][C]54[/C][C]118.02[/C][C]117.929687197182[/C][C]0.0903128028175786[/C][/ROW]
[ROW][C]55[/C][C]117.77[/C][C]118.381268134087[/C][C]-0.611268134086615[/C][/ROW]
[ROW][C]56[/C][C]117.85[/C][C]118.493672986103[/C][C]-0.643672986102828[/C][/ROW]
[ROW][C]57[/C][C]118.68[/C][C]118.437373225055[/C][C]0.242626774945336[/C][/ROW]
[ROW][C]58[/C][C]118.9[/C][C]118.835825113196[/C][C]0.064174886804409[/C][/ROW]
[ROW][C]59[/C][C]118.6[/C][C]118.673224093729[/C][C]-0.0732240937287543[/C][/ROW]
[ROW][C]60[/C][C]118.21[/C][C]118.637612646535[/C][C]-0.427612646534698[/C][/ROW]
[ROW][C]61[/C][C]118.37[/C][C]118.545805624606[/C][C]-0.175805624605957[/C][/ROW]
[ROW][C]62[/C][C]117.43[/C][C]118.652944135305[/C][C]-1.22294413530474[/C][/ROW]
[ROW][C]63[/C][C]117.5[/C][C]117.845305290473[/C][C]-0.345305290472666[/C][/ROW]
[ROW][C]64[/C][C]116.71[/C][C]117.643400347161[/C][C]-0.93340034716131[/C][/ROW]
[ROW][C]65[/C][C]116.98[/C][C]117.351726971213[/C][C]-0.371726971212738[/C][/ROW]
[ROW][C]66[/C][C]117.74[/C][C]116.900338210531[/C][C]0.839661789468877[/C][/ROW]
[ROW][C]67[/C][C]117.44[/C][C]117.763260376089[/C][C]-0.323260376088825[/C][/ROW]
[ROW][C]68[/C][C]117.85[/C][C]118.087730192995[/C][C]-0.237730192994945[/C][/ROW]
[ROW][C]69[/C][C]118.54[/C][C]118.549178470324[/C][C]-0.00917847032364705[/C][/ROW]
[ROW][C]70[/C][C]118.73[/C][C]118.712901995868[/C][C]0.0170980041318529[/C][/ROW]
[ROW][C]71[/C][C]118.68[/C][C]118.482857271111[/C][C]0.197142728889332[/C][/ROW]
[ROW][C]72[/C][C]118.19[/C][C]118.572006881252[/C][C]-0.38200688125248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203338&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203338&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
13106.14104.7290095058691.4109904941314
14105.85105.5579107851380.292089214861704
15106.27106.2528123233340.0171876766659409
16106.51106.571534737355-0.0615347373552737
17106.82106.881606583944-0.0616065839443962
18106.53106.572228475694-0.042228475694202
19107.14107.700291421424-0.560291421423827
20107.39107.2812972955740.108702704425653
21107.33107.796273524345-0.466273524344643
22107.53107.3830517059290.146948294070739
23107.42107.0735278851580.346472114841632
24108.25107.9201469597350.329853040264737
25108.26108.517473018442-0.257473018442155
26108.93107.7910086069531.13899139304671
27109.43109.0776606697230.352339330277502
28109.61109.638007745763-0.0280077457633752
29109.74109.978547372105-0.238547372104819
30110.12109.5253104069750.594689593024881
31110.16111.048603784697-0.888603784697182
32110.44110.532302353449-0.0923023534494263
33111.23110.7618965931720.46810340682832
34112.86111.2045468527181.65545314728243
35112.77112.0727826646880.697217335311976
36113.04113.203015178815-0.163015178815272
37112.79113.285984509122-0.495984509122124
38113.87112.6818466848821.18815331511846
39114.28113.8246541480230.455345851976986
40115.51114.3759596886211.13404031137911
41116.76115.5654449932381.19455500676244
42116.91116.3886461039720.521353896027605
43116.47117.541380800453-1.07138080045337
44116.94117.079219131881-0.139219131880651
45117.24117.416661119857-0.176661119857371
46116.82117.644853014419-0.824853014419332
47117.48116.3557335983691.12426640163115
48117.11117.621596959337-0.511596959337268
49117.31117.356855110556-0.0468551105563506
50117.77117.485631866220.284368133780248
51118.37117.7595785940790.610421405921429
52117.91118.591354838963-0.681354838962548
53118.12118.402433431397-0.282433431397251
54118.02117.9296871971820.0903128028175786
55117.77118.381268134087-0.611268134086615
56117.85118.493672986103-0.643672986102828
57118.68118.4373732250550.242626774945336
58118.9118.8358251131960.064174886804409
59118.6118.673224093729-0.0732240937287543
60118.21118.637612646535-0.427612646534698
61118.37118.545805624606-0.175805624605957
62117.43118.652944135305-1.22294413530474
63117.5117.845305290473-0.345305290472666
64116.71117.643400347161-0.93340034716131
65116.98117.351726971213-0.371726971212738
66117.74116.9003382105310.839661789468877
67117.44117.763260376089-0.323260376088825
68117.85118.087730192995-0.237730192994945
69118.54118.549178470324-0.00917847032364705
70118.73118.7129019958680.0170980041318529
71118.68118.4828572711110.197142728889332
72118.19118.572006881252-0.38200688125248







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73118.573759666385117.351691877291119.795827455479
74118.569761005279117.030202537052120.109319473506
75118.905967829401117.102033852562120.70990180624
76118.827808459811116.79757580992120.858041109702
77119.389446126815117.148175090929121.630717162701
78119.502296567301117.073918449167121.930674685435
79119.446561684426116.847578694436122.045544674417
80120.045734477687117.275150994104122.81631796127
81120.75212948639117.816803944983123.687455027797
82120.928665473425117.84753033321124.009800613641
83120.719969583533117.508427148211123.931512018854
84120.516220549873113.505355716805127.527085382941

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 118.573759666385 & 117.351691877291 & 119.795827455479 \tabularnewline
74 & 118.569761005279 & 117.030202537052 & 120.109319473506 \tabularnewline
75 & 118.905967829401 & 117.102033852562 & 120.70990180624 \tabularnewline
76 & 118.827808459811 & 116.79757580992 & 120.858041109702 \tabularnewline
77 & 119.389446126815 & 117.148175090929 & 121.630717162701 \tabularnewline
78 & 119.502296567301 & 117.073918449167 & 121.930674685435 \tabularnewline
79 & 119.446561684426 & 116.847578694436 & 122.045544674417 \tabularnewline
80 & 120.045734477687 & 117.275150994104 & 122.81631796127 \tabularnewline
81 & 120.75212948639 & 117.816803944983 & 123.687455027797 \tabularnewline
82 & 120.928665473425 & 117.84753033321 & 124.009800613641 \tabularnewline
83 & 120.719969583533 & 117.508427148211 & 123.931512018854 \tabularnewline
84 & 120.516220549873 & 113.505355716805 & 127.527085382941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203338&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]118.573759666385[/C][C]117.351691877291[/C][C]119.795827455479[/C][/ROW]
[ROW][C]74[/C][C]118.569761005279[/C][C]117.030202537052[/C][C]120.109319473506[/C][/ROW]
[ROW][C]75[/C][C]118.905967829401[/C][C]117.102033852562[/C][C]120.70990180624[/C][/ROW]
[ROW][C]76[/C][C]118.827808459811[/C][C]116.79757580992[/C][C]120.858041109702[/C][/ROW]
[ROW][C]77[/C][C]119.389446126815[/C][C]117.148175090929[/C][C]121.630717162701[/C][/ROW]
[ROW][C]78[/C][C]119.502296567301[/C][C]117.073918449167[/C][C]121.930674685435[/C][/ROW]
[ROW][C]79[/C][C]119.446561684426[/C][C]116.847578694436[/C][C]122.045544674417[/C][/ROW]
[ROW][C]80[/C][C]120.045734477687[/C][C]117.275150994104[/C][C]122.81631796127[/C][/ROW]
[ROW][C]81[/C][C]120.75212948639[/C][C]117.816803944983[/C][C]123.687455027797[/C][/ROW]
[ROW][C]82[/C][C]120.928665473425[/C][C]117.84753033321[/C][C]124.009800613641[/C][/ROW]
[ROW][C]83[/C][C]120.719969583533[/C][C]117.508427148211[/C][C]123.931512018854[/C][/ROW]
[ROW][C]84[/C][C]120.516220549873[/C][C]113.505355716805[/C][C]127.527085382941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203338&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203338&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
73118.573759666385117.351691877291119.795827455479
74118.569761005279117.030202537052120.109319473506
75118.905967829401117.102033852562120.70990180624
76118.827808459811116.79757580992120.858041109702
77119.389446126815117.148175090929121.630717162701
78119.502296567301117.073918449167121.930674685435
79119.446561684426116.847578694436122.045544674417
80120.045734477687117.275150994104122.81631796127
81120.75212948639117.816803944983123.687455027797
82120.928665473425117.84753033321124.009800613641
83120.719969583533117.508427148211123.931512018854
84120.516220549873113.505355716805127.527085382941



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')