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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 21 Dec 2009 03:03:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/21/t1261389948vskc4804ohc0ca7.htm/, Retrieved Sun, 05 May 2024 19:24:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70083, Retrieved Sun, 05 May 2024 19:24:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-21 10:03:08] [479db4778e5b462dda1f74ecdd6ccff3] [Current]
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Dataseries X:
43.9
51
51.9
54.3
50.3
57.2
48.8
41.1
58
63
53.8
54.7
55.5
56.1
69.6
69.4
57.2
68
53.3
47.9
60.8
61.7
57.8
51.4
50.5
48.1
58.7
54
56.1
60.4
51.2
50.7
56.4
53.3
52.6
47.7
49.5
48.5
55.3
49.8
57.4
64.6
53
41.5
55.9
58.4
53.5
50.6
58.5
49.1
61.1
52.3
58.4
65.5
61.7
45.1
52.1
59.3
57.9
45
64.9
63.8
69.4
71.1
62.9
73.5
62.7
51.9
73.3
66.7
62.5
70.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70083&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70083&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.319439681255854
beta0.0705399226443017
gamma0.308746635913248

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.319439681255854 \tabularnewline
beta & 0.0705399226443017 \tabularnewline
gamma & 0.308746635913248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70083&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]0.319439681255854[/C][/ROW]
[ROW][C]beta[/C][C]0.0705399226443017[/C][/ROW]
[ROW][C]gamma[/C][C]0.308746635913248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70083&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
alpha0.319439681255854
beta0.0705399226443017
gamma0.308746635913248







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1355.550.50347770493324.99652229506683
1456.152.93090387576463.16909612423542
1569.667.41026604459452.1897339554055
1669.468.82743644835860.572563551641409
1757.257.5918281764854-0.391828176485433
186869.248561695987-1.24856169598704
1953.356.1312008204423-2.83120082044229
2047.946.48142535859551.41857464140452
2160.865.9179045817852-5.11790458178524
2261.768.8827932795695-7.18279327956947
2357.856.45448129207051.34551870792954
2451.457.6349180982275-6.23491809822752
2550.557.3730444907888-6.87304449078883
2648.155.1563646158473-7.05636461584727
2758.764.9441678879978-6.24416788799776
285462.3658765867787-8.36587658677867
2956.148.77616731071497.32383268928515
3060.460.5812181735006-0.181218173500596
3151.248.32804907849132.87195092150872
3250.741.6888856993629.01111430063799
3356.460.7141894843056-4.31418948430564
3453.362.7446818597275-9.44468185972755
3552.651.63334984708260.966650152917438
3647.750.7075133651127-3.00751336511274
3749.550.7747339240367-1.27473392403672
3848.549.9777604796206-1.47776047962063
3955.361.0194842702603-5.71948427026027
4049.857.9313000808969-8.13130008089692
4157.447.80931387306169.5906861269384
4264.658.35075973339086.24924026660916
435348.80961365002954.19038634997052
4441.543.7468642303466-2.24686423034662
4555.955.09293495403460.80706504596536
4658.457.28172549613681.11827450386321
4753.551.77436103636991.72563896363014
4850.650.28391224367320.316087756326816
4958.551.93615741082686.56384258917316
5049.153.8659092798134-4.76590927981338
5161.163.885962510168-2.78596251016796
5252.361.3344169240577-9.03441692405772
5358.454.48801094547293.91198905452712
5465.563.00519359739812.49480640260189
5561.751.453916267640910.2460837323591
5645.146.563595653662-1.46359565366196
5752.160.0928581605871-7.99285816058714
5859.359.6462840826926-0.346284082692634
5957.953.63519644466574.26480355533431
604552.613709154218-7.61370915421795
6164.952.853750913302812.0462490866972
6263.854.05525893787589.74474106212422
6369.470.8485591519473-1.44855915194728
6471.167.31374145614483.78625854385518
6562.967.6864678546306-4.78646785463059
6673.574.8326800239706-1.33268002397057
6762.762.21983220908030.480167790919722
6851.950.81060245389521.08939754610485
6973.365.36712570356427.93287429643581
7066.773.0028707355137-6.30287073551372
7162.565.4940084963394-2.99400849633942
7270.359.032844249352311.2671557506477

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 55.5 & 50.5034777049332 & 4.99652229506683 \tabularnewline
14 & 56.1 & 52.9309038757646 & 3.16909612423542 \tabularnewline
15 & 69.6 & 67.4102660445945 & 2.1897339554055 \tabularnewline
16 & 69.4 & 68.8274364483586 & 0.572563551641409 \tabularnewline
17 & 57.2 & 57.5918281764854 & -0.391828176485433 \tabularnewline
18 & 68 & 69.248561695987 & -1.24856169598704 \tabularnewline
19 & 53.3 & 56.1312008204423 & -2.83120082044229 \tabularnewline
20 & 47.9 & 46.4814253585955 & 1.41857464140452 \tabularnewline
21 & 60.8 & 65.9179045817852 & -5.11790458178524 \tabularnewline
22 & 61.7 & 68.8827932795695 & -7.18279327956947 \tabularnewline
23 & 57.8 & 56.4544812920705 & 1.34551870792954 \tabularnewline
24 & 51.4 & 57.6349180982275 & -6.23491809822752 \tabularnewline
25 & 50.5 & 57.3730444907888 & -6.87304449078883 \tabularnewline
26 & 48.1 & 55.1563646158473 & -7.05636461584727 \tabularnewline
27 & 58.7 & 64.9441678879978 & -6.24416788799776 \tabularnewline
28 & 54 & 62.3658765867787 & -8.36587658677867 \tabularnewline
29 & 56.1 & 48.7761673107149 & 7.32383268928515 \tabularnewline
30 & 60.4 & 60.5812181735006 & -0.181218173500596 \tabularnewline
31 & 51.2 & 48.3280490784913 & 2.87195092150872 \tabularnewline
32 & 50.7 & 41.688885699362 & 9.01111430063799 \tabularnewline
33 & 56.4 & 60.7141894843056 & -4.31418948430564 \tabularnewline
34 & 53.3 & 62.7446818597275 & -9.44468185972755 \tabularnewline
35 & 52.6 & 51.6333498470826 & 0.966650152917438 \tabularnewline
36 & 47.7 & 50.7075133651127 & -3.00751336511274 \tabularnewline
37 & 49.5 & 50.7747339240367 & -1.27473392403672 \tabularnewline
38 & 48.5 & 49.9777604796206 & -1.47776047962063 \tabularnewline
39 & 55.3 & 61.0194842702603 & -5.71948427026027 \tabularnewline
40 & 49.8 & 57.9313000808969 & -8.13130008089692 \tabularnewline
41 & 57.4 & 47.8093138730616 & 9.5906861269384 \tabularnewline
42 & 64.6 & 58.3507597333908 & 6.24924026660916 \tabularnewline
43 & 53 & 48.8096136500295 & 4.19038634997052 \tabularnewline
44 & 41.5 & 43.7468642303466 & -2.24686423034662 \tabularnewline
45 & 55.9 & 55.0929349540346 & 0.80706504596536 \tabularnewline
46 & 58.4 & 57.2817254961368 & 1.11827450386321 \tabularnewline
47 & 53.5 & 51.7743610363699 & 1.72563896363014 \tabularnewline
48 & 50.6 & 50.2839122436732 & 0.316087756326816 \tabularnewline
49 & 58.5 & 51.9361574108268 & 6.56384258917316 \tabularnewline
50 & 49.1 & 53.8659092798134 & -4.76590927981338 \tabularnewline
51 & 61.1 & 63.885962510168 & -2.78596251016796 \tabularnewline
52 & 52.3 & 61.3344169240577 & -9.03441692405772 \tabularnewline
53 & 58.4 & 54.4880109454729 & 3.91198905452712 \tabularnewline
54 & 65.5 & 63.0051935973981 & 2.49480640260189 \tabularnewline
55 & 61.7 & 51.4539162676409 & 10.2460837323591 \tabularnewline
56 & 45.1 & 46.563595653662 & -1.46359565366196 \tabularnewline
57 & 52.1 & 60.0928581605871 & -7.99285816058714 \tabularnewline
58 & 59.3 & 59.6462840826926 & -0.346284082692634 \tabularnewline
59 & 57.9 & 53.6351964446657 & 4.26480355533431 \tabularnewline
60 & 45 & 52.613709154218 & -7.61370915421795 \tabularnewline
61 & 64.9 & 52.8537509133028 & 12.0462490866972 \tabularnewline
62 & 63.8 & 54.0552589378758 & 9.74474106212422 \tabularnewline
63 & 69.4 & 70.8485591519473 & -1.44855915194728 \tabularnewline
64 & 71.1 & 67.3137414561448 & 3.78625854385518 \tabularnewline
65 & 62.9 & 67.6864678546306 & -4.78646785463059 \tabularnewline
66 & 73.5 & 74.8326800239706 & -1.33268002397057 \tabularnewline
67 & 62.7 & 62.2198322090803 & 0.480167790919722 \tabularnewline
68 & 51.9 & 50.8106024538952 & 1.08939754610485 \tabularnewline
69 & 73.3 & 65.3671257035642 & 7.93287429643581 \tabularnewline
70 & 66.7 & 73.0028707355137 & -6.30287073551372 \tabularnewline
71 & 62.5 & 65.4940084963394 & -2.99400849633942 \tabularnewline
72 & 70.3 & 59.0328442493523 & 11.2671557506477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70083&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]55.5[/C][C]50.5034777049332[/C][C]4.99652229506683[/C][/ROW]
[ROW][C]14[/C][C]56.1[/C][C]52.9309038757646[/C][C]3.16909612423542[/C][/ROW]
[ROW][C]15[/C][C]69.6[/C][C]67.4102660445945[/C][C]2.1897339554055[/C][/ROW]
[ROW][C]16[/C][C]69.4[/C][C]68.8274364483586[/C][C]0.572563551641409[/C][/ROW]
[ROW][C]17[/C][C]57.2[/C][C]57.5918281764854[/C][C]-0.391828176485433[/C][/ROW]
[ROW][C]18[/C][C]68[/C][C]69.248561695987[/C][C]-1.24856169598704[/C][/ROW]
[ROW][C]19[/C][C]53.3[/C][C]56.1312008204423[/C][C]-2.83120082044229[/C][/ROW]
[ROW][C]20[/C][C]47.9[/C][C]46.4814253585955[/C][C]1.41857464140452[/C][/ROW]
[ROW][C]21[/C][C]60.8[/C][C]65.9179045817852[/C][C]-5.11790458178524[/C][/ROW]
[ROW][C]22[/C][C]61.7[/C][C]68.8827932795695[/C][C]-7.18279327956947[/C][/ROW]
[ROW][C]23[/C][C]57.8[/C][C]56.4544812920705[/C][C]1.34551870792954[/C][/ROW]
[ROW][C]24[/C][C]51.4[/C][C]57.6349180982275[/C][C]-6.23491809822752[/C][/ROW]
[ROW][C]25[/C][C]50.5[/C][C]57.3730444907888[/C][C]-6.87304449078883[/C][/ROW]
[ROW][C]26[/C][C]48.1[/C][C]55.1563646158473[/C][C]-7.05636461584727[/C][/ROW]
[ROW][C]27[/C][C]58.7[/C][C]64.9441678879978[/C][C]-6.24416788799776[/C][/ROW]
[ROW][C]28[/C][C]54[/C][C]62.3658765867787[/C][C]-8.36587658677867[/C][/ROW]
[ROW][C]29[/C][C]56.1[/C][C]48.7761673107149[/C][C]7.32383268928515[/C][/ROW]
[ROW][C]30[/C][C]60.4[/C][C]60.5812181735006[/C][C]-0.181218173500596[/C][/ROW]
[ROW][C]31[/C][C]51.2[/C][C]48.3280490784913[/C][C]2.87195092150872[/C][/ROW]
[ROW][C]32[/C][C]50.7[/C][C]41.688885699362[/C][C]9.01111430063799[/C][/ROW]
[ROW][C]33[/C][C]56.4[/C][C]60.7141894843056[/C][C]-4.31418948430564[/C][/ROW]
[ROW][C]34[/C][C]53.3[/C][C]62.7446818597275[/C][C]-9.44468185972755[/C][/ROW]
[ROW][C]35[/C][C]52.6[/C][C]51.6333498470826[/C][C]0.966650152917438[/C][/ROW]
[ROW][C]36[/C][C]47.7[/C][C]50.7075133651127[/C][C]-3.00751336511274[/C][/ROW]
[ROW][C]37[/C][C]49.5[/C][C]50.7747339240367[/C][C]-1.27473392403672[/C][/ROW]
[ROW][C]38[/C][C]48.5[/C][C]49.9777604796206[/C][C]-1.47776047962063[/C][/ROW]
[ROW][C]39[/C][C]55.3[/C][C]61.0194842702603[/C][C]-5.71948427026027[/C][/ROW]
[ROW][C]40[/C][C]49.8[/C][C]57.9313000808969[/C][C]-8.13130008089692[/C][/ROW]
[ROW][C]41[/C][C]57.4[/C][C]47.8093138730616[/C][C]9.5906861269384[/C][/ROW]
[ROW][C]42[/C][C]64.6[/C][C]58.3507597333908[/C][C]6.24924026660916[/C][/ROW]
[ROW][C]43[/C][C]53[/C][C]48.8096136500295[/C][C]4.19038634997052[/C][/ROW]
[ROW][C]44[/C][C]41.5[/C][C]43.7468642303466[/C][C]-2.24686423034662[/C][/ROW]
[ROW][C]45[/C][C]55.9[/C][C]55.0929349540346[/C][C]0.80706504596536[/C][/ROW]
[ROW][C]46[/C][C]58.4[/C][C]57.2817254961368[/C][C]1.11827450386321[/C][/ROW]
[ROW][C]47[/C][C]53.5[/C][C]51.7743610363699[/C][C]1.72563896363014[/C][/ROW]
[ROW][C]48[/C][C]50.6[/C][C]50.2839122436732[/C][C]0.316087756326816[/C][/ROW]
[ROW][C]49[/C][C]58.5[/C][C]51.9361574108268[/C][C]6.56384258917316[/C][/ROW]
[ROW][C]50[/C][C]49.1[/C][C]53.8659092798134[/C][C]-4.76590927981338[/C][/ROW]
[ROW][C]51[/C][C]61.1[/C][C]63.885962510168[/C][C]-2.78596251016796[/C][/ROW]
[ROW][C]52[/C][C]52.3[/C][C]61.3344169240577[/C][C]-9.03441692405772[/C][/ROW]
[ROW][C]53[/C][C]58.4[/C][C]54.4880109454729[/C][C]3.91198905452712[/C][/ROW]
[ROW][C]54[/C][C]65.5[/C][C]63.0051935973981[/C][C]2.49480640260189[/C][/ROW]
[ROW][C]55[/C][C]61.7[/C][C]51.4539162676409[/C][C]10.2460837323591[/C][/ROW]
[ROW][C]56[/C][C]45.1[/C][C]46.563595653662[/C][C]-1.46359565366196[/C][/ROW]
[ROW][C]57[/C][C]52.1[/C][C]60.0928581605871[/C][C]-7.99285816058714[/C][/ROW]
[ROW][C]58[/C][C]59.3[/C][C]59.6462840826926[/C][C]-0.346284082692634[/C][/ROW]
[ROW][C]59[/C][C]57.9[/C][C]53.6351964446657[/C][C]4.26480355533431[/C][/ROW]
[ROW][C]60[/C][C]45[/C][C]52.613709154218[/C][C]-7.61370915421795[/C][/ROW]
[ROW][C]61[/C][C]64.9[/C][C]52.8537509133028[/C][C]12.0462490866972[/C][/ROW]
[ROW][C]62[/C][C]63.8[/C][C]54.0552589378758[/C][C]9.74474106212422[/C][/ROW]
[ROW][C]63[/C][C]69.4[/C][C]70.8485591519473[/C][C]-1.44855915194728[/C][/ROW]
[ROW][C]64[/C][C]71.1[/C][C]67.3137414561448[/C][C]3.78625854385518[/C][/ROW]
[ROW][C]65[/C][C]62.9[/C][C]67.6864678546306[/C][C]-4.78646785463059[/C][/ROW]
[ROW][C]66[/C][C]73.5[/C][C]74.8326800239706[/C][C]-1.33268002397057[/C][/ROW]
[ROW][C]67[/C][C]62.7[/C][C]62.2198322090803[/C][C]0.480167790919722[/C][/ROW]
[ROW][C]68[/C][C]51.9[/C][C]50.8106024538952[/C][C]1.08939754610485[/C][/ROW]
[ROW][C]69[/C][C]73.3[/C][C]65.3671257035642[/C][C]7.93287429643581[/C][/ROW]
[ROW][C]70[/C][C]66.7[/C][C]73.0028707355137[/C][C]-6.30287073551372[/C][/ROW]
[ROW][C]71[/C][C]62.5[/C][C]65.4940084963394[/C][C]-2.99400849633942[/C][/ROW]
[ROW][C]72[/C][C]70.3[/C][C]59.0328442493523[/C][C]11.2671557506477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70083&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
1355.550.50347770493324.99652229506683
1456.152.93090387576463.16909612423542
1569.667.41026604459452.1897339554055
1669.468.82743644835860.572563551641409
1757.257.5918281764854-0.391828176485433
186869.248561695987-1.24856169598704
1953.356.1312008204423-2.83120082044229
2047.946.48142535859551.41857464140452
2160.865.9179045817852-5.11790458178524
2261.768.8827932795695-7.18279327956947
2357.856.45448129207051.34551870792954
2451.457.6349180982275-6.23491809822752
2550.557.3730444907888-6.87304449078883
2648.155.1563646158473-7.05636461584727
2758.764.9441678879978-6.24416788799776
285462.3658765867787-8.36587658677867
2956.148.77616731071497.32383268928515
3060.460.5812181735006-0.181218173500596
3151.248.32804907849132.87195092150872
3250.741.6888856993629.01111430063799
3356.460.7141894843056-4.31418948430564
3453.362.7446818597275-9.44468185972755
3552.651.63334984708260.966650152917438
3647.750.7075133651127-3.00751336511274
3749.550.7747339240367-1.27473392403672
3848.549.9777604796206-1.47776047962063
3955.361.0194842702603-5.71948427026027
4049.857.9313000808969-8.13130008089692
4157.447.80931387306169.5906861269384
4264.658.35075973339086.24924026660916
435348.80961365002954.19038634997052
4441.543.7468642303466-2.24686423034662
4555.955.09293495403460.80706504596536
4658.457.28172549613681.11827450386321
4753.551.77436103636991.72563896363014
4850.650.28391224367320.316087756326816
4958.551.93615741082686.56384258917316
5049.153.8659092798134-4.76590927981338
5161.163.885962510168-2.78596251016796
5252.361.3344169240577-9.03441692405772
5358.454.48801094547293.91198905452712
5465.563.00519359739812.49480640260189
5561.751.453916267640910.2460837323591
5645.146.563595653662-1.46359565366196
5752.160.0928581605871-7.99285816058714
5859.359.6462840826926-0.346284082692634
5957.953.63519644466574.26480355533431
604552.613709154218-7.61370915421795
6164.952.853750913302812.0462490866972
6263.854.05525893787589.74474106212422
6369.470.8485591519473-1.44855915194728
6471.167.31374145614483.78625854385518
6562.967.6864678546306-4.78646785463059
6673.574.8326800239706-1.33268002397057
6762.762.21983220908030.480167790919722
6851.950.81060245389521.08939754610485
6973.365.36712570356427.93287429643581
7066.773.0028707355137-6.30287073551372
7162.565.4940084963394-2.99400849633942
7270.359.032844249352311.2671557506477







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7371.938476695521666.137526635427377.7394267556158
7468.389226067725361.601323559508675.177128575942
7581.6361682965673.094881158404990.1774554347152
7679.513368074380470.129547186732988.897188962028
7776.557060984126166.452414624461986.6617073437904
7887.834718811831375.5501329540012100.119304669661
7974.064652377685462.450582064361585.6787226910093
8060.674401006035749.851325655042471.497476357029
8179.256478639721264.681239544758593.8317177346838
8281.610792117473865.654206594893497.567377640054
8376.100353951014760.157834997611192.0428729044182
8473.136065953552756.30187821714289.9702536899635

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 71.9384766955216 & 66.1375266354273 & 77.7394267556158 \tabularnewline
74 & 68.3892260677253 & 61.6013235595086 & 75.177128575942 \tabularnewline
75 & 81.63616829656 & 73.0948811584049 & 90.1774554347152 \tabularnewline
76 & 79.5133680743804 & 70.1295471867329 & 88.897188962028 \tabularnewline
77 & 76.5570609841261 & 66.4524146244619 & 86.6617073437904 \tabularnewline
78 & 87.8347188118313 & 75.5501329540012 & 100.119304669661 \tabularnewline
79 & 74.0646523776854 & 62.4505820643615 & 85.6787226910093 \tabularnewline
80 & 60.6744010060357 & 49.8513256550424 & 71.497476357029 \tabularnewline
81 & 79.2564786397212 & 64.6812395447585 & 93.8317177346838 \tabularnewline
82 & 81.6107921174738 & 65.6542065948934 & 97.567377640054 \tabularnewline
83 & 76.1003539510147 & 60.1578349976111 & 92.0428729044182 \tabularnewline
84 & 73.1360659535527 & 56.301878217142 & 89.9702536899635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70083&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]71.9384766955216[/C][C]66.1375266354273[/C][C]77.7394267556158[/C][/ROW]
[ROW][C]74[/C][C]68.3892260677253[/C][C]61.6013235595086[/C][C]75.177128575942[/C][/ROW]
[ROW][C]75[/C][C]81.63616829656[/C][C]73.0948811584049[/C][C]90.1774554347152[/C][/ROW]
[ROW][C]76[/C][C]79.5133680743804[/C][C]70.1295471867329[/C][C]88.897188962028[/C][/ROW]
[ROW][C]77[/C][C]76.5570609841261[/C][C]66.4524146244619[/C][C]86.6617073437904[/C][/ROW]
[ROW][C]78[/C][C]87.8347188118313[/C][C]75.5501329540012[/C][C]100.119304669661[/C][/ROW]
[ROW][C]79[/C][C]74.0646523776854[/C][C]62.4505820643615[/C][C]85.6787226910093[/C][/ROW]
[ROW][C]80[/C][C]60.6744010060357[/C][C]49.8513256550424[/C][C]71.497476357029[/C][/ROW]
[ROW][C]81[/C][C]79.2564786397212[/C][C]64.6812395447585[/C][C]93.8317177346838[/C][/ROW]
[ROW][C]82[/C][C]81.6107921174738[/C][C]65.6542065948934[/C][C]97.567377640054[/C][/ROW]
[ROW][C]83[/C][C]76.1003539510147[/C][C]60.1578349976111[/C][C]92.0428729044182[/C][/ROW]
[ROW][C]84[/C][C]73.1360659535527[/C][C]56.301878217142[/C][C]89.9702536899635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70083&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70083&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
7371.938476695521666.137526635427377.7394267556158
7468.389226067725361.601323559508675.177128575942
7581.6361682965673.094881158404990.1774554347152
7679.513368074380470.129547186732988.897188962028
7776.557060984126166.452414624461986.6617073437904
7887.834718811831375.5501329540012100.119304669661
7974.064652377685462.450582064361585.6787226910093
8060.674401006035749.851325655042471.497476357029
8179.256478639721264.681239544758593.8317177346838
8281.610792117473865.654206594893497.567377640054
8376.100353951014760.157834997611192.0428729044182
8473.136065953552756.30187821714289.9702536899635



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')