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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 May 2012 05:44:53 -0400
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/May/14/t13369886980zwtq5dyslenx7w.htm/, Retrieved Sun, 05 May 2024 16:42:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166433, Retrieved Sun, 05 May 2024 16:42:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-14 09:44:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
65
65,3
62,9
63,5
62,1
59,3
61,6
61,5
60,1
59,5
62,7
65,5
63,8
63,8
62,7
62,3
62,4
64,8
66,4
65,1
67,4
68,8
68,6
71,5
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166433&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166433&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0533214777581741
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0533214777581741 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166433&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0533214777581741[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166433&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
alpha1
beta0.0533214777581741
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
362.965.6-2.7
463.563.05603201005290.443967989947076
562.163.6797050393542-1.57970503935423
659.362.1954728322338-2.89547283223384
761.659.24108194201052.35891805798953
861.561.6668629387729-0.166862938772923
960.161.5579655602945-1.45796556029448
1059.560.0802246820991-0.58022468209905
1162.759.44928624461783.25071375538224
1265.562.82261910582362.67738089417643
1363.865.7653810116226-1.96538101162255
1463.863.960583991725-0.160583991724984
1562.763.9520214159819-1.2520214159819
1662.362.7852617838969-0.485261783896874
1762.462.35938690847990.0406130915200862
1864.862.46155245853612.3384475414639
1966.464.98624193710691.41375806289309
2065.166.6616256062129-1.56162560621293
2167.465.27835742118462.12164257881537
2268.867.69148653876171.10851346123826
2368.669.1505941146298-0.550594114629789
2471.568.92123562279282.57876437720724
257571.95873915017563.0412608498244
2684.375.62090367293638.67909632706368
278485.3836859147009-1.38368591470089
2879.185.0099057369759-5.90990573697587
2978.879.7947808296688-0.994780829668798
3082.779.44173764578543.25826235421464
3185.383.51547300943591.78452699056407
3284.586.2106266256721-1.71062662567213
3380.885.3194134860988-4.51941348609883
3470.181.3784316804198-11.2784316804198
3568.270.0770490364252-1.87704903642521
3668.168.07696200797850.0230379920215142
3772.367.97819042775764.32180957224236
3873.172.4086357007390.691364299260968
3971.573.2455002668449-1.74550026684486
4074.171.55242761318942.54757238681059
4180.374.28826793755016.01173206244994
4280.680.8088223750061-0.208822375006093
4381.481.09768765738180.302312342618208
4487.481.91380739823475.48619260176527
4589.388.20633929502681.09366070497317
4693.290.1646548999823.03534510001796
4792.894.226503986221-1.42650398622104
4896.893.75044068564783.04955931435221
49100.397.91304769480032.38695230519974
5095.6101.540323519052-5.94032351905179
518996.5235766906543-7.52357669065431
5287.489.5224084634817-2.12240846348166
5386.787.8092385078024-1.10923850780237
5492.887.05009227138015.74990772861992
5598.693.45668584844325.14331415155675
56100.899.53093495957881.26906504042122
57105.5101.7986033829053.70139661709473
58107.8106.6959673202981.10403267970213
59113.7109.0548359742734.6451640257271
60120.3115.2025229845545.09747701544622

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 62.9 & 65.6 & -2.7 \tabularnewline
4 & 63.5 & 63.0560320100529 & 0.443967989947076 \tabularnewline
5 & 62.1 & 63.6797050393542 & -1.57970503935423 \tabularnewline
6 & 59.3 & 62.1954728322338 & -2.89547283223384 \tabularnewline
7 & 61.6 & 59.2410819420105 & 2.35891805798953 \tabularnewline
8 & 61.5 & 61.6668629387729 & -0.166862938772923 \tabularnewline
9 & 60.1 & 61.5579655602945 & -1.45796556029448 \tabularnewline
10 & 59.5 & 60.0802246820991 & -0.58022468209905 \tabularnewline
11 & 62.7 & 59.4492862446178 & 3.25071375538224 \tabularnewline
12 & 65.5 & 62.8226191058236 & 2.67738089417643 \tabularnewline
13 & 63.8 & 65.7653810116226 & -1.96538101162255 \tabularnewline
14 & 63.8 & 63.960583991725 & -0.160583991724984 \tabularnewline
15 & 62.7 & 63.9520214159819 & -1.2520214159819 \tabularnewline
16 & 62.3 & 62.7852617838969 & -0.485261783896874 \tabularnewline
17 & 62.4 & 62.3593869084799 & 0.0406130915200862 \tabularnewline
18 & 64.8 & 62.4615524585361 & 2.3384475414639 \tabularnewline
19 & 66.4 & 64.9862419371069 & 1.41375806289309 \tabularnewline
20 & 65.1 & 66.6616256062129 & -1.56162560621293 \tabularnewline
21 & 67.4 & 65.2783574211846 & 2.12164257881537 \tabularnewline
22 & 68.8 & 67.6914865387617 & 1.10851346123826 \tabularnewline
23 & 68.6 & 69.1505941146298 & -0.550594114629789 \tabularnewline
24 & 71.5 & 68.9212356227928 & 2.57876437720724 \tabularnewline
25 & 75 & 71.9587391501756 & 3.0412608498244 \tabularnewline
26 & 84.3 & 75.6209036729363 & 8.67909632706368 \tabularnewline
27 & 84 & 85.3836859147009 & -1.38368591470089 \tabularnewline
28 & 79.1 & 85.0099057369759 & -5.90990573697587 \tabularnewline
29 & 78.8 & 79.7947808296688 & -0.994780829668798 \tabularnewline
30 & 82.7 & 79.4417376457854 & 3.25826235421464 \tabularnewline
31 & 85.3 & 83.5154730094359 & 1.78452699056407 \tabularnewline
32 & 84.5 & 86.2106266256721 & -1.71062662567213 \tabularnewline
33 & 80.8 & 85.3194134860988 & -4.51941348609883 \tabularnewline
34 & 70.1 & 81.3784316804198 & -11.2784316804198 \tabularnewline
35 & 68.2 & 70.0770490364252 & -1.87704903642521 \tabularnewline
36 & 68.1 & 68.0769620079785 & 0.0230379920215142 \tabularnewline
37 & 72.3 & 67.9781904277576 & 4.32180957224236 \tabularnewline
38 & 73.1 & 72.408635700739 & 0.691364299260968 \tabularnewline
39 & 71.5 & 73.2455002668449 & -1.74550026684486 \tabularnewline
40 & 74.1 & 71.5524276131894 & 2.54757238681059 \tabularnewline
41 & 80.3 & 74.2882679375501 & 6.01173206244994 \tabularnewline
42 & 80.6 & 80.8088223750061 & -0.208822375006093 \tabularnewline
43 & 81.4 & 81.0976876573818 & 0.302312342618208 \tabularnewline
44 & 87.4 & 81.9138073982347 & 5.48619260176527 \tabularnewline
45 & 89.3 & 88.2063392950268 & 1.09366070497317 \tabularnewline
46 & 93.2 & 90.164654899982 & 3.03534510001796 \tabularnewline
47 & 92.8 & 94.226503986221 & -1.42650398622104 \tabularnewline
48 & 96.8 & 93.7504406856478 & 3.04955931435221 \tabularnewline
49 & 100.3 & 97.9130476948003 & 2.38695230519974 \tabularnewline
50 & 95.6 & 101.540323519052 & -5.94032351905179 \tabularnewline
51 & 89 & 96.5235766906543 & -7.52357669065431 \tabularnewline
52 & 87.4 & 89.5224084634817 & -2.12240846348166 \tabularnewline
53 & 86.7 & 87.8092385078024 & -1.10923850780237 \tabularnewline
54 & 92.8 & 87.0500922713801 & 5.74990772861992 \tabularnewline
55 & 98.6 & 93.4566858484432 & 5.14331415155675 \tabularnewline
56 & 100.8 & 99.5309349595788 & 1.26906504042122 \tabularnewline
57 & 105.5 & 101.798603382905 & 3.70139661709473 \tabularnewline
58 & 107.8 & 106.695967320298 & 1.10403267970213 \tabularnewline
59 & 113.7 & 109.054835974273 & 4.6451640257271 \tabularnewline
60 & 120.3 & 115.202522984554 & 5.09747701544622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166433&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]3[/C][C]62.9[/C][C]65.6[/C][C]-2.7[/C][/ROW]
[ROW][C]4[/C][C]63.5[/C][C]63.0560320100529[/C][C]0.443967989947076[/C][/ROW]
[ROW][C]5[/C][C]62.1[/C][C]63.6797050393542[/C][C]-1.57970503935423[/C][/ROW]
[ROW][C]6[/C][C]59.3[/C][C]62.1954728322338[/C][C]-2.89547283223384[/C][/ROW]
[ROW][C]7[/C][C]61.6[/C][C]59.2410819420105[/C][C]2.35891805798953[/C][/ROW]
[ROW][C]8[/C][C]61.5[/C][C]61.6668629387729[/C][C]-0.166862938772923[/C][/ROW]
[ROW][C]9[/C][C]60.1[/C][C]61.5579655602945[/C][C]-1.45796556029448[/C][/ROW]
[ROW][C]10[/C][C]59.5[/C][C]60.0802246820991[/C][C]-0.58022468209905[/C][/ROW]
[ROW][C]11[/C][C]62.7[/C][C]59.4492862446178[/C][C]3.25071375538224[/C][/ROW]
[ROW][C]12[/C][C]65.5[/C][C]62.8226191058236[/C][C]2.67738089417643[/C][/ROW]
[ROW][C]13[/C][C]63.8[/C][C]65.7653810116226[/C][C]-1.96538101162255[/C][/ROW]
[ROW][C]14[/C][C]63.8[/C][C]63.960583991725[/C][C]-0.160583991724984[/C][/ROW]
[ROW][C]15[/C][C]62.7[/C][C]63.9520214159819[/C][C]-1.2520214159819[/C][/ROW]
[ROW][C]16[/C][C]62.3[/C][C]62.7852617838969[/C][C]-0.485261783896874[/C][/ROW]
[ROW][C]17[/C][C]62.4[/C][C]62.3593869084799[/C][C]0.0406130915200862[/C][/ROW]
[ROW][C]18[/C][C]64.8[/C][C]62.4615524585361[/C][C]2.3384475414639[/C][/ROW]
[ROW][C]19[/C][C]66.4[/C][C]64.9862419371069[/C][C]1.41375806289309[/C][/ROW]
[ROW][C]20[/C][C]65.1[/C][C]66.6616256062129[/C][C]-1.56162560621293[/C][/ROW]
[ROW][C]21[/C][C]67.4[/C][C]65.2783574211846[/C][C]2.12164257881537[/C][/ROW]
[ROW][C]22[/C][C]68.8[/C][C]67.6914865387617[/C][C]1.10851346123826[/C][/ROW]
[ROW][C]23[/C][C]68.6[/C][C]69.1505941146298[/C][C]-0.550594114629789[/C][/ROW]
[ROW][C]24[/C][C]71.5[/C][C]68.9212356227928[/C][C]2.57876437720724[/C][/ROW]
[ROW][C]25[/C][C]75[/C][C]71.9587391501756[/C][C]3.0412608498244[/C][/ROW]
[ROW][C]26[/C][C]84.3[/C][C]75.6209036729363[/C][C]8.67909632706368[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]85.3836859147009[/C][C]-1.38368591470089[/C][/ROW]
[ROW][C]28[/C][C]79.1[/C][C]85.0099057369759[/C][C]-5.90990573697587[/C][/ROW]
[ROW][C]29[/C][C]78.8[/C][C]79.7947808296688[/C][C]-0.994780829668798[/C][/ROW]
[ROW][C]30[/C][C]82.7[/C][C]79.4417376457854[/C][C]3.25826235421464[/C][/ROW]
[ROW][C]31[/C][C]85.3[/C][C]83.5154730094359[/C][C]1.78452699056407[/C][/ROW]
[ROW][C]32[/C][C]84.5[/C][C]86.2106266256721[/C][C]-1.71062662567213[/C][/ROW]
[ROW][C]33[/C][C]80.8[/C][C]85.3194134860988[/C][C]-4.51941348609883[/C][/ROW]
[ROW][C]34[/C][C]70.1[/C][C]81.3784316804198[/C][C]-11.2784316804198[/C][/ROW]
[ROW][C]35[/C][C]68.2[/C][C]70.0770490364252[/C][C]-1.87704903642521[/C][/ROW]
[ROW][C]36[/C][C]68.1[/C][C]68.0769620079785[/C][C]0.0230379920215142[/C][/ROW]
[ROW][C]37[/C][C]72.3[/C][C]67.9781904277576[/C][C]4.32180957224236[/C][/ROW]
[ROW][C]38[/C][C]73.1[/C][C]72.408635700739[/C][C]0.691364299260968[/C][/ROW]
[ROW][C]39[/C][C]71.5[/C][C]73.2455002668449[/C][C]-1.74550026684486[/C][/ROW]
[ROW][C]40[/C][C]74.1[/C][C]71.5524276131894[/C][C]2.54757238681059[/C][/ROW]
[ROW][C]41[/C][C]80.3[/C][C]74.2882679375501[/C][C]6.01173206244994[/C][/ROW]
[ROW][C]42[/C][C]80.6[/C][C]80.8088223750061[/C][C]-0.208822375006093[/C][/ROW]
[ROW][C]43[/C][C]81.4[/C][C]81.0976876573818[/C][C]0.302312342618208[/C][/ROW]
[ROW][C]44[/C][C]87.4[/C][C]81.9138073982347[/C][C]5.48619260176527[/C][/ROW]
[ROW][C]45[/C][C]89.3[/C][C]88.2063392950268[/C][C]1.09366070497317[/C][/ROW]
[ROW][C]46[/C][C]93.2[/C][C]90.164654899982[/C][C]3.03534510001796[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]94.226503986221[/C][C]-1.42650398622104[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]93.7504406856478[/C][C]3.04955931435221[/C][/ROW]
[ROW][C]49[/C][C]100.3[/C][C]97.9130476948003[/C][C]2.38695230519974[/C][/ROW]
[ROW][C]50[/C][C]95.6[/C][C]101.540323519052[/C][C]-5.94032351905179[/C][/ROW]
[ROW][C]51[/C][C]89[/C][C]96.5235766906543[/C][C]-7.52357669065431[/C][/ROW]
[ROW][C]52[/C][C]87.4[/C][C]89.5224084634817[/C][C]-2.12240846348166[/C][/ROW]
[ROW][C]53[/C][C]86.7[/C][C]87.8092385078024[/C][C]-1.10923850780237[/C][/ROW]
[ROW][C]54[/C][C]92.8[/C][C]87.0500922713801[/C][C]5.74990772861992[/C][/ROW]
[ROW][C]55[/C][C]98.6[/C][C]93.4566858484432[/C][C]5.14331415155675[/C][/ROW]
[ROW][C]56[/C][C]100.8[/C][C]99.5309349595788[/C][C]1.26906504042122[/C][/ROW]
[ROW][C]57[/C][C]105.5[/C][C]101.798603382905[/C][C]3.70139661709473[/C][/ROW]
[ROW][C]58[/C][C]107.8[/C][C]106.695967320298[/C][C]1.10403267970213[/C][/ROW]
[ROW][C]59[/C][C]113.7[/C][C]109.054835974273[/C][C]4.6451640257271[/C][/ROW]
[ROW][C]60[/C][C]120.3[/C][C]115.202522984554[/C][C]5.09747701544622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166433&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166433&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
362.965.6-2.7
463.563.05603201005290.443967989947076
562.163.6797050393542-1.57970503935423
659.362.1954728322338-2.89547283223384
761.659.24108194201052.35891805798953
861.561.6668629387729-0.166862938772923
960.161.5579655602945-1.45796556029448
1059.560.0802246820991-0.58022468209905
1162.759.44928624461783.25071375538224
1265.562.82261910582362.67738089417643
1363.865.7653810116226-1.96538101162255
1463.863.960583991725-0.160583991724984
1562.763.9520214159819-1.2520214159819
1662.362.7852617838969-0.485261783896874
1762.462.35938690847990.0406130915200862
1864.862.46155245853612.3384475414639
1966.464.98624193710691.41375806289309
2065.166.6616256062129-1.56162560621293
2167.465.27835742118462.12164257881537
2268.867.69148653876171.10851346123826
2368.669.1505941146298-0.550594114629789
2471.568.92123562279282.57876437720724
257571.95873915017563.0412608498244
2684.375.62090367293638.67909632706368
278485.3836859147009-1.38368591470089
2879.185.0099057369759-5.90990573697587
2978.879.7947808296688-0.994780829668798
3082.779.44173764578543.25826235421464
3185.383.51547300943591.78452699056407
3284.586.2106266256721-1.71062662567213
3380.885.3194134860988-4.51941348609883
3470.181.3784316804198-11.2784316804198
3568.270.0770490364252-1.87704903642521
3668.168.07696200797850.0230379920215142
3772.367.97819042775764.32180957224236
3873.172.4086357007390.691364299260968
3971.573.2455002668449-1.74550026684486
4074.171.55242761318942.54757238681059
4180.374.28826793755016.01173206244994
4280.680.8088223750061-0.208822375006093
4381.481.09768765738180.302312342618208
4487.481.91380739823475.48619260176527
4589.388.20633929502681.09366070497317
4693.290.1646548999823.03534510001796
4792.894.226503986221-1.42650398622104
4896.893.75044068564783.04955931435221
49100.397.91304769480032.38695230519974
5095.6101.540323519052-5.94032351905179
518996.5235766906543-7.52357669065431
5287.489.5224084634817-2.12240846348166
5386.787.8092385078024-1.10923850780237
5492.887.05009227138015.74990772861992
5598.693.45668584844325.14331415155675
56100.899.53093495957881.26906504042122
57105.5101.7986033829053.70139661709473
58107.8106.6959673202981.10403267970213
59113.7109.0548359742734.6451640257271
60120.3115.2025229845545.09747701544622







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61122.074327991856115.238882110821128.909773872891
62123.848655983711113.920806439478133.776505527945
63125.622983975567113.141705428864138.10426252227
64127.397311967423112.6105151955142.184108739345
65129.171639959279112.217908333662146.125371584895
66130.945967951134111.909503690208149.982432212061
67132.72029594299111.653997953888153.786593932092
68134.494623934846111.431655351486157.557592518206
69136.268951926701111.229233799075161.308670054327
70138.043279918557111.037438167435165.049121669679
71139.817607910413110.849518228431168.785697592394
72141.591935902268110.660441225479172.523430579058

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 122.074327991856 & 115.238882110821 & 128.909773872891 \tabularnewline
62 & 123.848655983711 & 113.920806439478 & 133.776505527945 \tabularnewline
63 & 125.622983975567 & 113.141705428864 & 138.10426252227 \tabularnewline
64 & 127.397311967423 & 112.6105151955 & 142.184108739345 \tabularnewline
65 & 129.171639959279 & 112.217908333662 & 146.125371584895 \tabularnewline
66 & 130.945967951134 & 111.909503690208 & 149.982432212061 \tabularnewline
67 & 132.72029594299 & 111.653997953888 & 153.786593932092 \tabularnewline
68 & 134.494623934846 & 111.431655351486 & 157.557592518206 \tabularnewline
69 & 136.268951926701 & 111.229233799075 & 161.308670054327 \tabularnewline
70 & 138.043279918557 & 111.037438167435 & 165.049121669679 \tabularnewline
71 & 139.817607910413 & 110.849518228431 & 168.785697592394 \tabularnewline
72 & 141.591935902268 & 110.660441225479 & 172.523430579058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166433&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]122.074327991856[/C][C]115.238882110821[/C][C]128.909773872891[/C][/ROW]
[ROW][C]62[/C][C]123.848655983711[/C][C]113.920806439478[/C][C]133.776505527945[/C][/ROW]
[ROW][C]63[/C][C]125.622983975567[/C][C]113.141705428864[/C][C]138.10426252227[/C][/ROW]
[ROW][C]64[/C][C]127.397311967423[/C][C]112.6105151955[/C][C]142.184108739345[/C][/ROW]
[ROW][C]65[/C][C]129.171639959279[/C][C]112.217908333662[/C][C]146.125371584895[/C][/ROW]
[ROW][C]66[/C][C]130.945967951134[/C][C]111.909503690208[/C][C]149.982432212061[/C][/ROW]
[ROW][C]67[/C][C]132.72029594299[/C][C]111.653997953888[/C][C]153.786593932092[/C][/ROW]
[ROW][C]68[/C][C]134.494623934846[/C][C]111.431655351486[/C][C]157.557592518206[/C][/ROW]
[ROW][C]69[/C][C]136.268951926701[/C][C]111.229233799075[/C][C]161.308670054327[/C][/ROW]
[ROW][C]70[/C][C]138.043279918557[/C][C]111.037438167435[/C][C]165.049121669679[/C][/ROW]
[ROW][C]71[/C][C]139.817607910413[/C][C]110.849518228431[/C][C]168.785697592394[/C][/ROW]
[ROW][C]72[/C][C]141.591935902268[/C][C]110.660441225479[/C][C]172.523430579058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166433&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166433&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
61122.074327991856115.238882110821128.909773872891
62123.848655983711113.920806439478133.776505527945
63125.622983975567113.141705428864138.10426252227
64127.397311967423112.6105151955142.184108739345
65129.171639959279112.217908333662146.125371584895
66130.945967951134111.909503690208149.982432212061
67132.72029594299111.653997953888153.786593932092
68134.494623934846111.431655351486157.557592518206
69136.268951926701111.229233799075161.308670054327
70138.043279918557111.037438167435165.049121669679
71139.817607910413110.849518228431168.785697592394
72141.591935902268110.660441225479172.523430579058



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')