Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 May 2017 13:51:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/01/t14936431735ky8kil8ll3iqzk.htm/, Retrieved Sat, 29 Aug 2026 08:32:00 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 29 Aug 2026 08:32:00 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92,94
92,97
93,37
92,6
92,84
92,55
92,93
92,44
93,36
93,24
92,65
92,06
92,88
91,69
91,66
90,26
91,11
92,33
91,82
92,24
93,35
93,53
93,34
92,59
92,42
92,64
94,44
93,59
93,39
93,33
93,72
95,43
97,06
97,7
97,59
96,97
97,75
99,27
100,63
99,8
99,5
99,72
99,77
100,18
101,11
100,67
101,13
100,46
101,6
102,3
103,26
104,56
104,61
104,62
105,03
104,93
104,73
104,33
104,6
104,41
104,63
105,55
106,12
106,62
106,72
106,52
106,79
106,95
106,92
106,74
108,13
107,86




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.784250816244739
beta0.0432366119661203
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.784250816244739 \tabularnewline
beta & 0.0432366119661203 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.784250816244739[/C][/ROW]
[ROW][C]beta[/C][C]0.0432366119661203[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.784250816244739
beta0.0432366119661203
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.8893.5361030982906-0.656103098290615
1491.6991.7994593076144-0.109459307614401
1591.6691.60197643831860.0580235616813667
1690.2690.14739296244320.112607037556771
1791.1190.96026827405210.149731725947916
1892.3392.16733580833850.16266419166152
1991.8292.2054779801382-0.385477980138248
2092.2491.38191828470190.858081715298141
2193.3593.04146742906930.308532570930709
2293.5393.28466070492080.245339295079162
2393.3493.01744698618910.322553013810932
2492.5992.7333920959783-0.143392095978342
2592.4293.321670142718-0.90167014271799
2692.6491.53335219340271.10664780659732
2794.4492.38994684167362.05005315832643
2893.5992.64114720481860.948852795181381
2993.3994.2779709294967-0.887970929496689
3093.3394.7989350690104-1.46893506901037
3193.7293.50883371765740.211166282342617
3295.4393.51132173770111.9186782622989
3397.0696.00987486385311.05012513614695
3497.796.97197004897940.728029951020602
3597.5997.26727414316840.322725856831653
3696.9797.0501418641611-0.0801418641611065
3797.7597.69388513410850.0561148658914874
3899.2797.29193977238661.97806022761335
39100.6399.26696336805011.36303663194991
4099.898.94997589483680.850024105163214
4199.5100.317837316488-0.817837316487825
4299.72100.975676772421-1.25567677242074
4399.77100.429750658064-0.659750658064496
44100.18100.302531066394-0.122531066394004
45101.11101.128575839411-0.0185758394106728
46100.67101.262513111057-0.592513111057002
47101.13100.469422241640.660577758360034
48100.46100.476474248345-0.0164742483451619
49101.6101.2478470780770.352152921923093
50102.3101.5510670097650.74893299023455
51103.26102.4461171164260.813882883573513
52104.56101.58581382632.97418617369972
53104.61104.3297786632130.280221336786752
54104.62105.86160868373-1.24160868373004
55105.03105.563063752516-0.533063752515545
56104.93105.763176602391-0.833176602390907
57104.73106.142301916872-1.4123019168715
58104.33105.100099555358-0.770099555358286
59104.6104.4727857198930.127214280106642
60104.41103.9320841066660.477915893333517
61104.63105.204088313782-0.574088313781843
62105.55104.868474959970.681525040030451
63106.12105.7243547046580.395645295342462
64106.62104.9876316618251.63236833817454
65106.72106.0380549706640.681945029336205
66106.52107.510226246401-0.990226246401306
67106.79107.523842856812-0.733842856812473
68106.95107.457084009476-0.507084009475562
69106.92107.933397735037-1.01339773503726
70106.74107.322512963747-0.582512963746737
71108.13107.0221915696281.10780843037193
72107.86107.3457184100470.514281589952958

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.88 & 93.5361030982906 & -0.656103098290615 \tabularnewline
14 & 91.69 & 91.7994593076144 & -0.109459307614401 \tabularnewline
15 & 91.66 & 91.6019764383186 & 0.0580235616813667 \tabularnewline
16 & 90.26 & 90.1473929624432 & 0.112607037556771 \tabularnewline
17 & 91.11 & 90.9602682740521 & 0.149731725947916 \tabularnewline
18 & 92.33 & 92.1673358083385 & 0.16266419166152 \tabularnewline
19 & 91.82 & 92.2054779801382 & -0.385477980138248 \tabularnewline
20 & 92.24 & 91.3819182847019 & 0.858081715298141 \tabularnewline
21 & 93.35 & 93.0414674290693 & 0.308532570930709 \tabularnewline
22 & 93.53 & 93.2846607049208 & 0.245339295079162 \tabularnewline
23 & 93.34 & 93.0174469861891 & 0.322553013810932 \tabularnewline
24 & 92.59 & 92.7333920959783 & -0.143392095978342 \tabularnewline
25 & 92.42 & 93.321670142718 & -0.90167014271799 \tabularnewline
26 & 92.64 & 91.5333521934027 & 1.10664780659732 \tabularnewline
27 & 94.44 & 92.3899468416736 & 2.05005315832643 \tabularnewline
28 & 93.59 & 92.6411472048186 & 0.948852795181381 \tabularnewline
29 & 93.39 & 94.2779709294967 & -0.887970929496689 \tabularnewline
30 & 93.33 & 94.7989350690104 & -1.46893506901037 \tabularnewline
31 & 93.72 & 93.5088337176574 & 0.211166282342617 \tabularnewline
32 & 95.43 & 93.5113217377011 & 1.9186782622989 \tabularnewline
33 & 97.06 & 96.0098748638531 & 1.05012513614695 \tabularnewline
34 & 97.7 & 96.9719700489794 & 0.728029951020602 \tabularnewline
35 & 97.59 & 97.2672741431684 & 0.322725856831653 \tabularnewline
36 & 96.97 & 97.0501418641611 & -0.0801418641611065 \tabularnewline
37 & 97.75 & 97.6938851341085 & 0.0561148658914874 \tabularnewline
38 & 99.27 & 97.2919397723866 & 1.97806022761335 \tabularnewline
39 & 100.63 & 99.2669633680501 & 1.36303663194991 \tabularnewline
40 & 99.8 & 98.9499758948368 & 0.850024105163214 \tabularnewline
41 & 99.5 & 100.317837316488 & -0.817837316487825 \tabularnewline
42 & 99.72 & 100.975676772421 & -1.25567677242074 \tabularnewline
43 & 99.77 & 100.429750658064 & -0.659750658064496 \tabularnewline
44 & 100.18 & 100.302531066394 & -0.122531066394004 \tabularnewline
45 & 101.11 & 101.128575839411 & -0.0185758394106728 \tabularnewline
46 & 100.67 & 101.262513111057 & -0.592513111057002 \tabularnewline
47 & 101.13 & 100.46942224164 & 0.660577758360034 \tabularnewline
48 & 100.46 & 100.476474248345 & -0.0164742483451619 \tabularnewline
49 & 101.6 & 101.247847078077 & 0.352152921923093 \tabularnewline
50 & 102.3 & 101.551067009765 & 0.74893299023455 \tabularnewline
51 & 103.26 & 102.446117116426 & 0.813882883573513 \tabularnewline
52 & 104.56 & 101.5858138263 & 2.97418617369972 \tabularnewline
53 & 104.61 & 104.329778663213 & 0.280221336786752 \tabularnewline
54 & 104.62 & 105.86160868373 & -1.24160868373004 \tabularnewline
55 & 105.03 & 105.563063752516 & -0.533063752515545 \tabularnewline
56 & 104.93 & 105.763176602391 & -0.833176602390907 \tabularnewline
57 & 104.73 & 106.142301916872 & -1.4123019168715 \tabularnewline
58 & 104.33 & 105.100099555358 & -0.770099555358286 \tabularnewline
59 & 104.6 & 104.472785719893 & 0.127214280106642 \tabularnewline
60 & 104.41 & 103.932084106666 & 0.477915893333517 \tabularnewline
61 & 104.63 & 105.204088313782 & -0.574088313781843 \tabularnewline
62 & 105.55 & 104.86847495997 & 0.681525040030451 \tabularnewline
63 & 106.12 & 105.724354704658 & 0.395645295342462 \tabularnewline
64 & 106.62 & 104.987631661825 & 1.63236833817454 \tabularnewline
65 & 106.72 & 106.038054970664 & 0.681945029336205 \tabularnewline
66 & 106.52 & 107.510226246401 & -0.990226246401306 \tabularnewline
67 & 106.79 & 107.523842856812 & -0.733842856812473 \tabularnewline
68 & 106.95 & 107.457084009476 & -0.507084009475562 \tabularnewline
69 & 106.92 & 107.933397735037 & -1.01339773503726 \tabularnewline
70 & 106.74 & 107.322512963747 & -0.582512963746737 \tabularnewline
71 & 108.13 & 107.022191569628 & 1.10780843037193 \tabularnewline
72 & 107.86 & 107.345718410047 & 0.514281589952958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]92.88[/C][C]93.5361030982906[/C][C]-0.656103098290615[/C][/ROW]
[ROW][C]14[/C][C]91.69[/C][C]91.7994593076144[/C][C]-0.109459307614401[/C][/ROW]
[ROW][C]15[/C][C]91.66[/C][C]91.6019764383186[/C][C]0.0580235616813667[/C][/ROW]
[ROW][C]16[/C][C]90.26[/C][C]90.1473929624432[/C][C]0.112607037556771[/C][/ROW]
[ROW][C]17[/C][C]91.11[/C][C]90.9602682740521[/C][C]0.149731725947916[/C][/ROW]
[ROW][C]18[/C][C]92.33[/C][C]92.1673358083385[/C][C]0.16266419166152[/C][/ROW]
[ROW][C]19[/C][C]91.82[/C][C]92.2054779801382[/C][C]-0.385477980138248[/C][/ROW]
[ROW][C]20[/C][C]92.24[/C][C]91.3819182847019[/C][C]0.858081715298141[/C][/ROW]
[ROW][C]21[/C][C]93.35[/C][C]93.0414674290693[/C][C]0.308532570930709[/C][/ROW]
[ROW][C]22[/C][C]93.53[/C][C]93.2846607049208[/C][C]0.245339295079162[/C][/ROW]
[ROW][C]23[/C][C]93.34[/C][C]93.0174469861891[/C][C]0.322553013810932[/C][/ROW]
[ROW][C]24[/C][C]92.59[/C][C]92.7333920959783[/C][C]-0.143392095978342[/C][/ROW]
[ROW][C]25[/C][C]92.42[/C][C]93.321670142718[/C][C]-0.90167014271799[/C][/ROW]
[ROW][C]26[/C][C]92.64[/C][C]91.5333521934027[/C][C]1.10664780659732[/C][/ROW]
[ROW][C]27[/C][C]94.44[/C][C]92.3899468416736[/C][C]2.05005315832643[/C][/ROW]
[ROW][C]28[/C][C]93.59[/C][C]92.6411472048186[/C][C]0.948852795181381[/C][/ROW]
[ROW][C]29[/C][C]93.39[/C][C]94.2779709294967[/C][C]-0.887970929496689[/C][/ROW]
[ROW][C]30[/C][C]93.33[/C][C]94.7989350690104[/C][C]-1.46893506901037[/C][/ROW]
[ROW][C]31[/C][C]93.72[/C][C]93.5088337176574[/C][C]0.211166282342617[/C][/ROW]
[ROW][C]32[/C][C]95.43[/C][C]93.5113217377011[/C][C]1.9186782622989[/C][/ROW]
[ROW][C]33[/C][C]97.06[/C][C]96.0098748638531[/C][C]1.05012513614695[/C][/ROW]
[ROW][C]34[/C][C]97.7[/C][C]96.9719700489794[/C][C]0.728029951020602[/C][/ROW]
[ROW][C]35[/C][C]97.59[/C][C]97.2672741431684[/C][C]0.322725856831653[/C][/ROW]
[ROW][C]36[/C][C]96.97[/C][C]97.0501418641611[/C][C]-0.0801418641611065[/C][/ROW]
[ROW][C]37[/C][C]97.75[/C][C]97.6938851341085[/C][C]0.0561148658914874[/C][/ROW]
[ROW][C]38[/C][C]99.27[/C][C]97.2919397723866[/C][C]1.97806022761335[/C][/ROW]
[ROW][C]39[/C][C]100.63[/C][C]99.2669633680501[/C][C]1.36303663194991[/C][/ROW]
[ROW][C]40[/C][C]99.8[/C][C]98.9499758948368[/C][C]0.850024105163214[/C][/ROW]
[ROW][C]41[/C][C]99.5[/C][C]100.317837316488[/C][C]-0.817837316487825[/C][/ROW]
[ROW][C]42[/C][C]99.72[/C][C]100.975676772421[/C][C]-1.25567677242074[/C][/ROW]
[ROW][C]43[/C][C]99.77[/C][C]100.429750658064[/C][C]-0.659750658064496[/C][/ROW]
[ROW][C]44[/C][C]100.18[/C][C]100.302531066394[/C][C]-0.122531066394004[/C][/ROW]
[ROW][C]45[/C][C]101.11[/C][C]101.128575839411[/C][C]-0.0185758394106728[/C][/ROW]
[ROW][C]46[/C][C]100.67[/C][C]101.262513111057[/C][C]-0.592513111057002[/C][/ROW]
[ROW][C]47[/C][C]101.13[/C][C]100.46942224164[/C][C]0.660577758360034[/C][/ROW]
[ROW][C]48[/C][C]100.46[/C][C]100.476474248345[/C][C]-0.0164742483451619[/C][/ROW]
[ROW][C]49[/C][C]101.6[/C][C]101.247847078077[/C][C]0.352152921923093[/C][/ROW]
[ROW][C]50[/C][C]102.3[/C][C]101.551067009765[/C][C]0.74893299023455[/C][/ROW]
[ROW][C]51[/C][C]103.26[/C][C]102.446117116426[/C][C]0.813882883573513[/C][/ROW]
[ROW][C]52[/C][C]104.56[/C][C]101.5858138263[/C][C]2.97418617369972[/C][/ROW]
[ROW][C]53[/C][C]104.61[/C][C]104.329778663213[/C][C]0.280221336786752[/C][/ROW]
[ROW][C]54[/C][C]104.62[/C][C]105.86160868373[/C][C]-1.24160868373004[/C][/ROW]
[ROW][C]55[/C][C]105.03[/C][C]105.563063752516[/C][C]-0.533063752515545[/C][/ROW]
[ROW][C]56[/C][C]104.93[/C][C]105.763176602391[/C][C]-0.833176602390907[/C][/ROW]
[ROW][C]57[/C][C]104.73[/C][C]106.142301916872[/C][C]-1.4123019168715[/C][/ROW]
[ROW][C]58[/C][C]104.33[/C][C]105.100099555358[/C][C]-0.770099555358286[/C][/ROW]
[ROW][C]59[/C][C]104.6[/C][C]104.472785719893[/C][C]0.127214280106642[/C][/ROW]
[ROW][C]60[/C][C]104.41[/C][C]103.932084106666[/C][C]0.477915893333517[/C][/ROW]
[ROW][C]61[/C][C]104.63[/C][C]105.204088313782[/C][C]-0.574088313781843[/C][/ROW]
[ROW][C]62[/C][C]105.55[/C][C]104.86847495997[/C][C]0.681525040030451[/C][/ROW]
[ROW][C]63[/C][C]106.12[/C][C]105.724354704658[/C][C]0.395645295342462[/C][/ROW]
[ROW][C]64[/C][C]106.62[/C][C]104.987631661825[/C][C]1.63236833817454[/C][/ROW]
[ROW][C]65[/C][C]106.72[/C][C]106.038054970664[/C][C]0.681945029336205[/C][/ROW]
[ROW][C]66[/C][C]106.52[/C][C]107.510226246401[/C][C]-0.990226246401306[/C][/ROW]
[ROW][C]67[/C][C]106.79[/C][C]107.523842856812[/C][C]-0.733842856812473[/C][/ROW]
[ROW][C]68[/C][C]106.95[/C][C]107.457084009476[/C][C]-0.507084009475562[/C][/ROW]
[ROW][C]69[/C][C]106.92[/C][C]107.933397735037[/C][C]-1.01339773503726[/C][/ROW]
[ROW][C]70[/C][C]106.74[/C][C]107.322512963747[/C][C]-0.582512963746737[/C][/ROW]
[ROW][C]71[/C][C]108.13[/C][C]107.022191569628[/C][C]1.10780843037193[/C][/ROW]
[ROW][C]72[/C][C]107.86[/C][C]107.345718410047[/C][C]0.514281589952958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1392.8893.5361030982906-0.656103098290615
1491.6991.7994593076144-0.109459307614401
1591.6691.60197643831860.0580235616813667
1690.2690.14739296244320.112607037556771
1791.1190.96026827405210.149731725947916
1892.3392.16733580833850.16266419166152
1991.8292.2054779801382-0.385477980138248
2092.2491.38191828470190.858081715298141
2193.3593.04146742906930.308532570930709
2293.5393.28466070492080.245339295079162
2393.3493.01744698618910.322553013810932
2492.5992.7333920959783-0.143392095978342
2592.4293.321670142718-0.90167014271799
2692.6491.53335219340271.10664780659732
2794.4492.38994684167362.05005315832643
2893.5992.64114720481860.948852795181381
2993.3994.2779709294967-0.887970929496689
3093.3394.7989350690104-1.46893506901037
3193.7293.50883371765740.211166282342617
3295.4393.51132173770111.9186782622989
3397.0696.00987486385311.05012513614695
3497.796.97197004897940.728029951020602
3597.5997.26727414316840.322725856831653
3696.9797.0501418641611-0.0801418641611065
3797.7597.69388513410850.0561148658914874
3899.2797.29193977238661.97806022761335
39100.6399.26696336805011.36303663194991
4099.898.94997589483680.850024105163214
4199.5100.317837316488-0.817837316487825
4299.72100.975676772421-1.25567677242074
4399.77100.429750658064-0.659750658064496
44100.18100.302531066394-0.122531066394004
45101.11101.128575839411-0.0185758394106728
46100.67101.262513111057-0.592513111057002
47101.13100.469422241640.660577758360034
48100.46100.476474248345-0.0164742483451619
49101.6101.2478470780770.352152921923093
50102.3101.5510670097650.74893299023455
51103.26102.4461171164260.813882883573513
52104.56101.58581382632.97418617369972
53104.61104.3297786632130.280221336786752
54104.62105.86160868373-1.24160868373004
55105.03105.563063752516-0.533063752515545
56104.93105.763176602391-0.833176602390907
57104.73106.142301916872-1.4123019168715
58104.33105.100099555358-0.770099555358286
59104.6104.4727857198930.127214280106642
60104.41103.9320841066660.477915893333517
61104.63105.204088313782-0.574088313781843
62105.55104.868474959970.681525040030451
63106.12105.7243547046580.395645295342462
64106.62104.9876316618251.63236833817454
65106.72106.0380549706640.681945029336205
66106.52107.510226246401-0.990226246401306
67106.79107.523842856812-0.733842856812473
68106.95107.457084009476-0.507084009475562
69106.92107.933397735037-1.01339773503726
70106.74107.322512963747-0.582512963746737
71108.13107.0221915696281.10780843037193
72107.86107.3457184100470.514281589952958







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73108.440039600232106.631881927213110.24819727325
74108.865785622558106.529561647586111.20200959753
75109.142623679621106.344121591129111.941125768112
76108.366145002425105.141557146735111.590732858116
77107.87968566692104.251391385172111.507979948669
78108.381504389788104.364193119622112.398815659954
79109.185831166484104.789435322981113.582227009988
80109.727205531198104.958499486212114.495911576184
81110.492851229633105.356403929412115.629298529854
82110.804937837767105.303718407445116.306157268089
83111.381140565268105.516922916193117.245358214343
84110.725253247806104.498897222983116.951609272629

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 108.440039600232 & 106.631881927213 & 110.24819727325 \tabularnewline
74 & 108.865785622558 & 106.529561647586 & 111.20200959753 \tabularnewline
75 & 109.142623679621 & 106.344121591129 & 111.941125768112 \tabularnewline
76 & 108.366145002425 & 105.141557146735 & 111.590732858116 \tabularnewline
77 & 107.87968566692 & 104.251391385172 & 111.507979948669 \tabularnewline
78 & 108.381504389788 & 104.364193119622 & 112.398815659954 \tabularnewline
79 & 109.185831166484 & 104.789435322981 & 113.582227009988 \tabularnewline
80 & 109.727205531198 & 104.958499486212 & 114.495911576184 \tabularnewline
81 & 110.492851229633 & 105.356403929412 & 115.629298529854 \tabularnewline
82 & 110.804937837767 & 105.303718407445 & 116.306157268089 \tabularnewline
83 & 111.381140565268 & 105.516922916193 & 117.245358214343 \tabularnewline
84 & 110.725253247806 & 104.498897222983 & 116.951609272629 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]108.440039600232[/C][C]106.631881927213[/C][C]110.24819727325[/C][/ROW]
[ROW][C]74[/C][C]108.865785622558[/C][C]106.529561647586[/C][C]111.20200959753[/C][/ROW]
[ROW][C]75[/C][C]109.142623679621[/C][C]106.344121591129[/C][C]111.941125768112[/C][/ROW]
[ROW][C]76[/C][C]108.366145002425[/C][C]105.141557146735[/C][C]111.590732858116[/C][/ROW]
[ROW][C]77[/C][C]107.87968566692[/C][C]104.251391385172[/C][C]111.507979948669[/C][/ROW]
[ROW][C]78[/C][C]108.381504389788[/C][C]104.364193119622[/C][C]112.398815659954[/C][/ROW]
[ROW][C]79[/C][C]109.185831166484[/C][C]104.789435322981[/C][C]113.582227009988[/C][/ROW]
[ROW][C]80[/C][C]109.727205531198[/C][C]104.958499486212[/C][C]114.495911576184[/C][/ROW]
[ROW][C]81[/C][C]110.492851229633[/C][C]105.356403929412[/C][C]115.629298529854[/C][/ROW]
[ROW][C]82[/C][C]110.804937837767[/C][C]105.303718407445[/C][C]116.306157268089[/C][/ROW]
[ROW][C]83[/C][C]111.381140565268[/C][C]105.516922916193[/C][C]117.245358214343[/C][/ROW]
[ROW][C]84[/C][C]110.725253247806[/C][C]104.498897222983[/C][C]116.951609272629[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73108.440039600232106.631881927213110.24819727325
74108.865785622558106.529561647586111.20200959753
75109.142623679621106.344121591129111.941125768112
76108.366145002425105.141557146735111.590732858116
77107.87968566692104.251391385172111.507979948669
78108.381504389788104.364193119622112.398815659954
79109.185831166484104.789435322981113.582227009988
80109.727205531198104.958499486212114.495911576184
81110.492851229633105.356403929412115.629298529854
82110.804937837767105.303718407445116.306157268089
83111.381140565268105.516922916193117.245358214343
84110.725253247806104.498897222983116.951609272629



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