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 23:32:13 +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/t1493678058azeht1r25rc82hl.htm/, Retrieved Sun, 19 Apr 2026 15:46:44 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 Apr 2026 15:46:44 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
88,05
93,25
92,96
93,08
90,67
92,17
94,28
95,01
93,27
95,59
97,4
97,05
97,38
96,23
96,65
96,46
97,87
98,59
99,54
97,39
97,09
97,83
97,58
96,81
97,52
98,19
96,18
97,41
99,23
96,93
98,82
102,47
95,95
101,17
100,55
99,5
99,89
100,43
100,63
99,36
100
99,55
100,12
101,31
96,59
98,79
100,93
102,4
106,99
105,27
107,27
109,21
108,57
110,17
108,1
107,58
106,91
103
106,12
109,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.65149213465126
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.65149213465126 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \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]0.65149213465126[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/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
alpha0.65149213465126
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
293.2588.055.2
392.9691.43775910018661.52224089981344
493.0892.42948707345950.650512926540543
590.6792.8532911285896-2.18329112858959
692.1791.43089413065960.739105869340406
794.2891.91241579120952.36758420879055
895.0193.4548782813611.55512171863897
993.2794.4680278494797-1.19802784947969
1095.5993.68752212845051.90247787154951
1197.494.92697149811312.47302850188694
1297.0596.53813011586080.511869884139202
1397.3896.87160931934230.508390680657655
1496.2397.2028218491208-0.972821849120791
1596.6596.56903606600170.080963933998305
1696.4696.621783432192-0.161783432192024
1797.8796.5163827986021.35361720139798
1898.5997.39825375864151.19174624135854
1999.5498.17466706138671.36533293861326
2097.3999.0641707320736-1.67417073207356
2197.0997.9734616680643-0.883461668064285
2297.8397.39789334005450.432106659945475
2397.5897.6794074303394-0.0994074303394257
2496.8197.6146442713474-0.804644271347399
2597.5297.09042485737240.429575142627627
2698.1997.3702896840360.819710315964045
2796.1897.904324507579-1.72432450757901
2897.4196.78094065330490.629059346695101
2999.2397.19076786990562.03923213009439
3096.9398.5193115633902-1.58931156339023
3198.8297.48388758033121.33611241966879
32102.4798.35435431275534.11564568724472
3395.95101.035665107007-5.08566510700659
34101.1797.72239429032143.44760570967856
35100.5599.96848229355580.581517706444188
3699.5100.347336505465-0.847336505464639
3799.8999.79530343675160.0946965632484478
38100.4399.85699750288640.573002497113578
39100.63100.2303041228910.399695877108542
4099.36100.49070284308-1.13070284308021
4110099.75405883418560.245941165814358
4299.5599.9142875693007-0.364287569300657
43100.1299.67695708315010.443042916849947
44101.3199.96559605879071.34440394120926
4596.59100.841464652283-4.25146465228272
4698.7998.07166887057270.718331129427327
47100.9398.53965595146972.39034404853027
48102.4100.0969462981982.30305370180236
49106.99101.5973676706015.39263232939865
50105.27105.1106252182710.15937478172934
51107.27105.2144566350292.05554336497092
52109.21106.5536269697422.65637303025778
53108.57108.2842331056550.285766894345102
54110.17108.4704079896641.69959201033556
55108.1109.577678816514-1.47767881651419
56107.58108.614982690014-1.03498269001442
57106.91107.94069960797-1.03069960796982
58103107.269206920189-4.26920692018935
59106.12104.4878521904871.63214780951274
60109.69105.5511836509734.1388163490269

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 93.25 & 88.05 & 5.2 \tabularnewline
3 & 92.96 & 91.4377591001866 & 1.52224089981344 \tabularnewline
4 & 93.08 & 92.4294870734595 & 0.650512926540543 \tabularnewline
5 & 90.67 & 92.8532911285896 & -2.18329112858959 \tabularnewline
6 & 92.17 & 91.4308941306596 & 0.739105869340406 \tabularnewline
7 & 94.28 & 91.9124157912095 & 2.36758420879055 \tabularnewline
8 & 95.01 & 93.454878281361 & 1.55512171863897 \tabularnewline
9 & 93.27 & 94.4680278494797 & -1.19802784947969 \tabularnewline
10 & 95.59 & 93.6875221284505 & 1.90247787154951 \tabularnewline
11 & 97.4 & 94.9269714981131 & 2.47302850188694 \tabularnewline
12 & 97.05 & 96.5381301158608 & 0.511869884139202 \tabularnewline
13 & 97.38 & 96.8716093193423 & 0.508390680657655 \tabularnewline
14 & 96.23 & 97.2028218491208 & -0.972821849120791 \tabularnewline
15 & 96.65 & 96.5690360660017 & 0.080963933998305 \tabularnewline
16 & 96.46 & 96.621783432192 & -0.161783432192024 \tabularnewline
17 & 97.87 & 96.516382798602 & 1.35361720139798 \tabularnewline
18 & 98.59 & 97.3982537586415 & 1.19174624135854 \tabularnewline
19 & 99.54 & 98.1746670613867 & 1.36533293861326 \tabularnewline
20 & 97.39 & 99.0641707320736 & -1.67417073207356 \tabularnewline
21 & 97.09 & 97.9734616680643 & -0.883461668064285 \tabularnewline
22 & 97.83 & 97.3978933400545 & 0.432106659945475 \tabularnewline
23 & 97.58 & 97.6794074303394 & -0.0994074303394257 \tabularnewline
24 & 96.81 & 97.6146442713474 & -0.804644271347399 \tabularnewline
25 & 97.52 & 97.0904248573724 & 0.429575142627627 \tabularnewline
26 & 98.19 & 97.370289684036 & 0.819710315964045 \tabularnewline
27 & 96.18 & 97.904324507579 & -1.72432450757901 \tabularnewline
28 & 97.41 & 96.7809406533049 & 0.629059346695101 \tabularnewline
29 & 99.23 & 97.1907678699056 & 2.03923213009439 \tabularnewline
30 & 96.93 & 98.5193115633902 & -1.58931156339023 \tabularnewline
31 & 98.82 & 97.4838875803312 & 1.33611241966879 \tabularnewline
32 & 102.47 & 98.3543543127553 & 4.11564568724472 \tabularnewline
33 & 95.95 & 101.035665107007 & -5.08566510700659 \tabularnewline
34 & 101.17 & 97.7223942903214 & 3.44760570967856 \tabularnewline
35 & 100.55 & 99.9684822935558 & 0.581517706444188 \tabularnewline
36 & 99.5 & 100.347336505465 & -0.847336505464639 \tabularnewline
37 & 99.89 & 99.7953034367516 & 0.0946965632484478 \tabularnewline
38 & 100.43 & 99.8569975028864 & 0.573002497113578 \tabularnewline
39 & 100.63 & 100.230304122891 & 0.399695877108542 \tabularnewline
40 & 99.36 & 100.49070284308 & -1.13070284308021 \tabularnewline
41 & 100 & 99.7540588341856 & 0.245941165814358 \tabularnewline
42 & 99.55 & 99.9142875693007 & -0.364287569300657 \tabularnewline
43 & 100.12 & 99.6769570831501 & 0.443042916849947 \tabularnewline
44 & 101.31 & 99.9655960587907 & 1.34440394120926 \tabularnewline
45 & 96.59 & 100.841464652283 & -4.25146465228272 \tabularnewline
46 & 98.79 & 98.0716688705727 & 0.718331129427327 \tabularnewline
47 & 100.93 & 98.5396559514697 & 2.39034404853027 \tabularnewline
48 & 102.4 & 100.096946298198 & 2.30305370180236 \tabularnewline
49 & 106.99 & 101.597367670601 & 5.39263232939865 \tabularnewline
50 & 105.27 & 105.110625218271 & 0.15937478172934 \tabularnewline
51 & 107.27 & 105.214456635029 & 2.05554336497092 \tabularnewline
52 & 109.21 & 106.553626969742 & 2.65637303025778 \tabularnewline
53 & 108.57 & 108.284233105655 & 0.285766894345102 \tabularnewline
54 & 110.17 & 108.470407989664 & 1.69959201033556 \tabularnewline
55 & 108.1 & 109.577678816514 & -1.47767881651419 \tabularnewline
56 & 107.58 & 108.614982690014 & -1.03498269001442 \tabularnewline
57 & 106.91 & 107.94069960797 & -1.03069960796982 \tabularnewline
58 & 103 & 107.269206920189 & -4.26920692018935 \tabularnewline
59 & 106.12 & 104.487852190487 & 1.63214780951274 \tabularnewline
60 & 109.69 & 105.551183650973 & 4.1388163490269 \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]2[/C][C]93.25[/C][C]88.05[/C][C]5.2[/C][/ROW]
[ROW][C]3[/C][C]92.96[/C][C]91.4377591001866[/C][C]1.52224089981344[/C][/ROW]
[ROW][C]4[/C][C]93.08[/C][C]92.4294870734595[/C][C]0.650512926540543[/C][/ROW]
[ROW][C]5[/C][C]90.67[/C][C]92.8532911285896[/C][C]-2.18329112858959[/C][/ROW]
[ROW][C]6[/C][C]92.17[/C][C]91.4308941306596[/C][C]0.739105869340406[/C][/ROW]
[ROW][C]7[/C][C]94.28[/C][C]91.9124157912095[/C][C]2.36758420879055[/C][/ROW]
[ROW][C]8[/C][C]95.01[/C][C]93.454878281361[/C][C]1.55512171863897[/C][/ROW]
[ROW][C]9[/C][C]93.27[/C][C]94.4680278494797[/C][C]-1.19802784947969[/C][/ROW]
[ROW][C]10[/C][C]95.59[/C][C]93.6875221284505[/C][C]1.90247787154951[/C][/ROW]
[ROW][C]11[/C][C]97.4[/C][C]94.9269714981131[/C][C]2.47302850188694[/C][/ROW]
[ROW][C]12[/C][C]97.05[/C][C]96.5381301158608[/C][C]0.511869884139202[/C][/ROW]
[ROW][C]13[/C][C]97.38[/C][C]96.8716093193423[/C][C]0.508390680657655[/C][/ROW]
[ROW][C]14[/C][C]96.23[/C][C]97.2028218491208[/C][C]-0.972821849120791[/C][/ROW]
[ROW][C]15[/C][C]96.65[/C][C]96.5690360660017[/C][C]0.080963933998305[/C][/ROW]
[ROW][C]16[/C][C]96.46[/C][C]96.621783432192[/C][C]-0.161783432192024[/C][/ROW]
[ROW][C]17[/C][C]97.87[/C][C]96.516382798602[/C][C]1.35361720139798[/C][/ROW]
[ROW][C]18[/C][C]98.59[/C][C]97.3982537586415[/C][C]1.19174624135854[/C][/ROW]
[ROW][C]19[/C][C]99.54[/C][C]98.1746670613867[/C][C]1.36533293861326[/C][/ROW]
[ROW][C]20[/C][C]97.39[/C][C]99.0641707320736[/C][C]-1.67417073207356[/C][/ROW]
[ROW][C]21[/C][C]97.09[/C][C]97.9734616680643[/C][C]-0.883461668064285[/C][/ROW]
[ROW][C]22[/C][C]97.83[/C][C]97.3978933400545[/C][C]0.432106659945475[/C][/ROW]
[ROW][C]23[/C][C]97.58[/C][C]97.6794074303394[/C][C]-0.0994074303394257[/C][/ROW]
[ROW][C]24[/C][C]96.81[/C][C]97.6146442713474[/C][C]-0.804644271347399[/C][/ROW]
[ROW][C]25[/C][C]97.52[/C][C]97.0904248573724[/C][C]0.429575142627627[/C][/ROW]
[ROW][C]26[/C][C]98.19[/C][C]97.370289684036[/C][C]0.819710315964045[/C][/ROW]
[ROW][C]27[/C][C]96.18[/C][C]97.904324507579[/C][C]-1.72432450757901[/C][/ROW]
[ROW][C]28[/C][C]97.41[/C][C]96.7809406533049[/C][C]0.629059346695101[/C][/ROW]
[ROW][C]29[/C][C]99.23[/C][C]97.1907678699056[/C][C]2.03923213009439[/C][/ROW]
[ROW][C]30[/C][C]96.93[/C][C]98.5193115633902[/C][C]-1.58931156339023[/C][/ROW]
[ROW][C]31[/C][C]98.82[/C][C]97.4838875803312[/C][C]1.33611241966879[/C][/ROW]
[ROW][C]32[/C][C]102.47[/C][C]98.3543543127553[/C][C]4.11564568724472[/C][/ROW]
[ROW][C]33[/C][C]95.95[/C][C]101.035665107007[/C][C]-5.08566510700659[/C][/ROW]
[ROW][C]34[/C][C]101.17[/C][C]97.7223942903214[/C][C]3.44760570967856[/C][/ROW]
[ROW][C]35[/C][C]100.55[/C][C]99.9684822935558[/C][C]0.581517706444188[/C][/ROW]
[ROW][C]36[/C][C]99.5[/C][C]100.347336505465[/C][C]-0.847336505464639[/C][/ROW]
[ROW][C]37[/C][C]99.89[/C][C]99.7953034367516[/C][C]0.0946965632484478[/C][/ROW]
[ROW][C]38[/C][C]100.43[/C][C]99.8569975028864[/C][C]0.573002497113578[/C][/ROW]
[ROW][C]39[/C][C]100.63[/C][C]100.230304122891[/C][C]0.399695877108542[/C][/ROW]
[ROW][C]40[/C][C]99.36[/C][C]100.49070284308[/C][C]-1.13070284308021[/C][/ROW]
[ROW][C]41[/C][C]100[/C][C]99.7540588341856[/C][C]0.245941165814358[/C][/ROW]
[ROW][C]42[/C][C]99.55[/C][C]99.9142875693007[/C][C]-0.364287569300657[/C][/ROW]
[ROW][C]43[/C][C]100.12[/C][C]99.6769570831501[/C][C]0.443042916849947[/C][/ROW]
[ROW][C]44[/C][C]101.31[/C][C]99.9655960587907[/C][C]1.34440394120926[/C][/ROW]
[ROW][C]45[/C][C]96.59[/C][C]100.841464652283[/C][C]-4.25146465228272[/C][/ROW]
[ROW][C]46[/C][C]98.79[/C][C]98.0716688705727[/C][C]0.718331129427327[/C][/ROW]
[ROW][C]47[/C][C]100.93[/C][C]98.5396559514697[/C][C]2.39034404853027[/C][/ROW]
[ROW][C]48[/C][C]102.4[/C][C]100.096946298198[/C][C]2.30305370180236[/C][/ROW]
[ROW][C]49[/C][C]106.99[/C][C]101.597367670601[/C][C]5.39263232939865[/C][/ROW]
[ROW][C]50[/C][C]105.27[/C][C]105.110625218271[/C][C]0.15937478172934[/C][/ROW]
[ROW][C]51[/C][C]107.27[/C][C]105.214456635029[/C][C]2.05554336497092[/C][/ROW]
[ROW][C]52[/C][C]109.21[/C][C]106.553626969742[/C][C]2.65637303025778[/C][/ROW]
[ROW][C]53[/C][C]108.57[/C][C]108.284233105655[/C][C]0.285766894345102[/C][/ROW]
[ROW][C]54[/C][C]110.17[/C][C]108.470407989664[/C][C]1.69959201033556[/C][/ROW]
[ROW][C]55[/C][C]108.1[/C][C]109.577678816514[/C][C]-1.47767881651419[/C][/ROW]
[ROW][C]56[/C][C]107.58[/C][C]108.614982690014[/C][C]-1.03498269001442[/C][/ROW]
[ROW][C]57[/C][C]106.91[/C][C]107.94069960797[/C][C]-1.03069960796982[/C][/ROW]
[ROW][C]58[/C][C]103[/C][C]107.269206920189[/C][C]-4.26920692018935[/C][/ROW]
[ROW][C]59[/C][C]106.12[/C][C]104.487852190487[/C][C]1.63214780951274[/C][/ROW]
[ROW][C]60[/C][C]109.69[/C][C]105.551183650973[/C][C]4.1388163490269[/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
293.2588.055.2
392.9691.43775910018661.52224089981344
493.0892.42948707345950.650512926540543
590.6792.8532911285896-2.18329112858959
692.1791.43089413065960.739105869340406
794.2891.91241579120952.36758420879055
895.0193.4548782813611.55512171863897
993.2794.4680278494797-1.19802784947969
1095.5993.68752212845051.90247787154951
1197.494.92697149811312.47302850188694
1297.0596.53813011586080.511869884139202
1397.3896.87160931934230.508390680657655
1496.2397.2028218491208-0.972821849120791
1596.6596.56903606600170.080963933998305
1696.4696.621783432192-0.161783432192024
1797.8796.5163827986021.35361720139798
1898.5997.39825375864151.19174624135854
1999.5498.17466706138671.36533293861326
2097.3999.0641707320736-1.67417073207356
2197.0997.9734616680643-0.883461668064285
2297.8397.39789334005450.432106659945475
2397.5897.6794074303394-0.0994074303394257
2496.8197.6146442713474-0.804644271347399
2597.5297.09042485737240.429575142627627
2698.1997.3702896840360.819710315964045
2796.1897.904324507579-1.72432450757901
2897.4196.78094065330490.629059346695101
2999.2397.19076786990562.03923213009439
3096.9398.5193115633902-1.58931156339023
3198.8297.48388758033121.33611241966879
32102.4798.35435431275534.11564568724472
3395.95101.035665107007-5.08566510700659
34101.1797.72239429032143.44760570967856
35100.5599.96848229355580.581517706444188
3699.5100.347336505465-0.847336505464639
3799.8999.79530343675160.0946965632484478
38100.4399.85699750288640.573002497113578
39100.63100.2303041228910.399695877108542
4099.36100.49070284308-1.13070284308021
4110099.75405883418560.245941165814358
4299.5599.9142875693007-0.364287569300657
43100.1299.67695708315010.443042916849947
44101.3199.96559605879071.34440394120926
4596.59100.841464652283-4.25146465228272
4698.7998.07166887057270.718331129427327
47100.9398.53965595146972.39034404853027
48102.4100.0969462981982.30305370180236
49106.99101.5973676706015.39263232939865
50105.27105.1106252182710.15937478172934
51107.27105.2144566350292.05554336497092
52109.21106.5536269697422.65637303025778
53108.57108.2842331056550.285766894345102
54110.17108.4704079896641.69959201033556
55108.1109.577678816514-1.47767881651419
56107.58108.614982690014-1.03498269001442
57106.91107.94069960797-1.03069960796982
58103107.269206920189-4.26920692018935
59106.12104.4878521904871.63214780951274
60109.69105.5511836509734.1388163490269







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61108.24758994913104.287680266374112.207499631887
62108.24758994913103.521438154988112.973741743272
63108.24758994913102.863155265066113.632024633194
64108.24758994913102.277015190145114.218164708116
65108.24758994913101.74348439661114.75169550165
66108.24758994913101.250518052687115.244661845574
67108.24758994913100.790067491257115.705112407003
68108.24758994913100.356438746969116.138741151291
69108.2475899491399.9454279788331116.549751919427
70108.2475899491399.5538266979985116.941353200262
71108.2475899491399.1791200918494117.316059806411
72108.2475899491398.8192936216863117.675886276574

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 108.24758994913 & 104.287680266374 & 112.207499631887 \tabularnewline
62 & 108.24758994913 & 103.521438154988 & 112.973741743272 \tabularnewline
63 & 108.24758994913 & 102.863155265066 & 113.632024633194 \tabularnewline
64 & 108.24758994913 & 102.277015190145 & 114.218164708116 \tabularnewline
65 & 108.24758994913 & 101.74348439661 & 114.75169550165 \tabularnewline
66 & 108.24758994913 & 101.250518052687 & 115.244661845574 \tabularnewline
67 & 108.24758994913 & 100.790067491257 & 115.705112407003 \tabularnewline
68 & 108.24758994913 & 100.356438746969 & 116.138741151291 \tabularnewline
69 & 108.24758994913 & 99.9454279788331 & 116.549751919427 \tabularnewline
70 & 108.24758994913 & 99.5538266979985 & 116.941353200262 \tabularnewline
71 & 108.24758994913 & 99.1791200918494 & 117.316059806411 \tabularnewline
72 & 108.24758994913 & 98.8192936216863 & 117.675886276574 \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]61[/C][C]108.24758994913[/C][C]104.287680266374[/C][C]112.207499631887[/C][/ROW]
[ROW][C]62[/C][C]108.24758994913[/C][C]103.521438154988[/C][C]112.973741743272[/C][/ROW]
[ROW][C]63[/C][C]108.24758994913[/C][C]102.863155265066[/C][C]113.632024633194[/C][/ROW]
[ROW][C]64[/C][C]108.24758994913[/C][C]102.277015190145[/C][C]114.218164708116[/C][/ROW]
[ROW][C]65[/C][C]108.24758994913[/C][C]101.74348439661[/C][C]114.75169550165[/C][/ROW]
[ROW][C]66[/C][C]108.24758994913[/C][C]101.250518052687[/C][C]115.244661845574[/C][/ROW]
[ROW][C]67[/C][C]108.24758994913[/C][C]100.790067491257[/C][C]115.705112407003[/C][/ROW]
[ROW][C]68[/C][C]108.24758994913[/C][C]100.356438746969[/C][C]116.138741151291[/C][/ROW]
[ROW][C]69[/C][C]108.24758994913[/C][C]99.9454279788331[/C][C]116.549751919427[/C][/ROW]
[ROW][C]70[/C][C]108.24758994913[/C][C]99.5538266979985[/C][C]116.941353200262[/C][/ROW]
[ROW][C]71[/C][C]108.24758994913[/C][C]99.1791200918494[/C][C]117.316059806411[/C][/ROW]
[ROW][C]72[/C][C]108.24758994913[/C][C]98.8192936216863[/C][C]117.675886276574[/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
61108.24758994913104.287680266374112.207499631887
62108.24758994913103.521438154988112.973741743272
63108.24758994913102.863155265066113.632024633194
64108.24758994913102.277015190145114.218164708116
65108.24758994913101.74348439661114.75169550165
66108.24758994913101.250518052687115.244661845574
67108.24758994913100.790067491257115.705112407003
68108.24758994913100.356438746969116.138741151291
69108.2475899491399.9454279788331116.549751919427
70108.2475899491399.5538266979985116.941353200262
71108.2475899491399.1791200918494117.316059806411
72108.2475899491398.8192936216863117.675886276574



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')