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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 22 Dec 2013 05:29:11 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/22/t1387708197ja2gk0kz9uq9lle.htm/, Retrieved Sun, 05 Dec 2021 17:09:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232502, Retrieved Sun, 05 Dec 2021 17:09:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-22 10:29:11] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
51.02
51.06
50.9
51.23
51.29
51.3
51.3
51.3
51.46
51.47
51.77
51.82
51.82
51.84
51.9
51.94
52.22
52.27
52.27
52.28
52.53
52.73
52.72
52.67
52.67
52.65
52.69
52.73
52.84
52.83
52.83
52.84
52.82
53.09
53.4
53.43
53.43
53.42
53.6
53.69
54.05
54.04
54.04
54.08
54.05
54.39
54.38
54.46
54.46
54.69
54.91
55.52
56.01
56.07
56.07
56.09
56.29
56.45
56.87
56.87
56.87
56.87
56.8
56.89
57.01
57.03
57.03
57.03
57.06
57.25
57.24
57.31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 6 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232502&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232502&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232502&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 time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917860981142453
beta0.00174783084819955
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917860981142453 \tabularnewline
beta & 0.00174783084819955 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232502&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]0.917860981142453[/C][/ROW]
[ROW][C]beta[/C][C]0.00174783084819955[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232502&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232502&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
alpha0.917860981142453
beta0.00174783084819955
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1351.8251.37343750.446562500000006
1451.8451.80272938112790.0372706188721281
1551.951.89224133998030.00775866001972503
1651.9451.92301120361070.0169887963892563
1752.2252.20728030380940.0127196961906151
1852.2752.2747347026172-0.00473470261723463
1952.2752.25157746075550.0184225392444617
2052.2852.2834549022781-0.00345490227807943
2152.5352.44691301794520.0830869820548372
2252.7352.54285451274120.187145487258825
2352.7253.0275241469797-0.307524146979674
2452.6752.796829141609-0.126829141608951
2552.6752.7167971024509-0.0467971024508742
2652.6552.6594325684718-0.0094325684717731
2752.6952.7033764334951-0.0133764334950754
2852.7352.7151944903680.0148055096319979
2952.8452.9967945911348-0.156794591134819
3052.8352.9066384206996-0.076638420699588
3152.8352.81868399009760.0113160099023872
3252.8452.841528548643-0.00152854864302299
3352.8253.013153259599-0.193153259599022
3453.0952.86293872090810.227061279091878
3553.453.34252470235110.0574752976488782
3653.4353.4611869896648-0.031186989664846
3753.4353.4751647723974-0.045164772397392
3853.4253.42202006463-0.00202006463003102
3953.653.47210801211090.12789198788915
4053.6953.61579668969820.0742033103017761
4154.0553.93780695170950.112193048290536
4254.0454.1015458183178-0.0615458183177537
4354.0454.03511083093510.00488916906488157
4454.0854.0514331350020.0285668649980195
4554.0554.2354213985394-0.185421398539376
4654.3954.127312059740.262687940259994
4754.3854.6262183082572-0.246218308257227
4854.4654.45891181697850.00108818302152969
4954.4654.5014797437545-0.0414797437545147
5054.6954.45538129945740.234618700542555
5154.9154.73384127161040.176158728389638
5255.5254.917999291330.602000708669955
5356.0155.72899847798020.281001522019842
5456.0756.03510397644390.0348960235561151
5556.0756.06449547626450.00550452373551735
5656.0956.08517781919450.00482218080548336
5756.2956.23160725091340.0583927490865577
5856.4556.3862960823090.063703917691015
5956.8756.66264579345470.207354206545283
6056.8756.9345811717864-0.0645811717864362
6156.8756.9158837648952-0.0458837648952226
6256.8756.8909209240433-0.0209209240433523
6356.856.9321186747215-0.132118674721497
6456.8956.86989405215430.0201059478457211
6557.0157.1210895855878-0.111089585587791
6657.0357.0471274739372-0.0171274739371867
6757.0357.02630336962450.00369663037555057
6857.0357.0452162937375-0.0152162937374811
6957.0657.1775673013669-0.117567301366883
7057.2557.17081711160630.0791828883937029
7157.2457.4728300813725-0.232830081372477
7257.3157.3173512211716-0.00735122117164622

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 51.82 & 51.3734375 & 0.446562500000006 \tabularnewline
14 & 51.84 & 51.8027293811279 & 0.0372706188721281 \tabularnewline
15 & 51.9 & 51.8922413399803 & 0.00775866001972503 \tabularnewline
16 & 51.94 & 51.9230112036107 & 0.0169887963892563 \tabularnewline
17 & 52.22 & 52.2072803038094 & 0.0127196961906151 \tabularnewline
18 & 52.27 & 52.2747347026172 & -0.00473470261723463 \tabularnewline
19 & 52.27 & 52.2515774607555 & 0.0184225392444617 \tabularnewline
20 & 52.28 & 52.2834549022781 & -0.00345490227807943 \tabularnewline
21 & 52.53 & 52.4469130179452 & 0.0830869820548372 \tabularnewline
22 & 52.73 & 52.5428545127412 & 0.187145487258825 \tabularnewline
23 & 52.72 & 53.0275241469797 & -0.307524146979674 \tabularnewline
24 & 52.67 & 52.796829141609 & -0.126829141608951 \tabularnewline
25 & 52.67 & 52.7167971024509 & -0.0467971024508742 \tabularnewline
26 & 52.65 & 52.6594325684718 & -0.0094325684717731 \tabularnewline
27 & 52.69 & 52.7033764334951 & -0.0133764334950754 \tabularnewline
28 & 52.73 & 52.715194490368 & 0.0148055096319979 \tabularnewline
29 & 52.84 & 52.9967945911348 & -0.156794591134819 \tabularnewline
30 & 52.83 & 52.9066384206996 & -0.076638420699588 \tabularnewline
31 & 52.83 & 52.8186839900976 & 0.0113160099023872 \tabularnewline
32 & 52.84 & 52.841528548643 & -0.00152854864302299 \tabularnewline
33 & 52.82 & 53.013153259599 & -0.193153259599022 \tabularnewline
34 & 53.09 & 52.8629387209081 & 0.227061279091878 \tabularnewline
35 & 53.4 & 53.3425247023511 & 0.0574752976488782 \tabularnewline
36 & 53.43 & 53.4611869896648 & -0.031186989664846 \tabularnewline
37 & 53.43 & 53.4751647723974 & -0.045164772397392 \tabularnewline
38 & 53.42 & 53.42202006463 & -0.00202006463003102 \tabularnewline
39 & 53.6 & 53.4721080121109 & 0.12789198788915 \tabularnewline
40 & 53.69 & 53.6157966896982 & 0.0742033103017761 \tabularnewline
41 & 54.05 & 53.9378069517095 & 0.112193048290536 \tabularnewline
42 & 54.04 & 54.1015458183178 & -0.0615458183177537 \tabularnewline
43 & 54.04 & 54.0351108309351 & 0.00488916906488157 \tabularnewline
44 & 54.08 & 54.051433135002 & 0.0285668649980195 \tabularnewline
45 & 54.05 & 54.2354213985394 & -0.185421398539376 \tabularnewline
46 & 54.39 & 54.12731205974 & 0.262687940259994 \tabularnewline
47 & 54.38 & 54.6262183082572 & -0.246218308257227 \tabularnewline
48 & 54.46 & 54.4589118169785 & 0.00108818302152969 \tabularnewline
49 & 54.46 & 54.5014797437545 & -0.0414797437545147 \tabularnewline
50 & 54.69 & 54.4553812994574 & 0.234618700542555 \tabularnewline
51 & 54.91 & 54.7338412716104 & 0.176158728389638 \tabularnewline
52 & 55.52 & 54.91799929133 & 0.602000708669955 \tabularnewline
53 & 56.01 & 55.7289984779802 & 0.281001522019842 \tabularnewline
54 & 56.07 & 56.0351039764439 & 0.0348960235561151 \tabularnewline
55 & 56.07 & 56.0644954762645 & 0.00550452373551735 \tabularnewline
56 & 56.09 & 56.0851778191945 & 0.00482218080548336 \tabularnewline
57 & 56.29 & 56.2316072509134 & 0.0583927490865577 \tabularnewline
58 & 56.45 & 56.386296082309 & 0.063703917691015 \tabularnewline
59 & 56.87 & 56.6626457934547 & 0.207354206545283 \tabularnewline
60 & 56.87 & 56.9345811717864 & -0.0645811717864362 \tabularnewline
61 & 56.87 & 56.9158837648952 & -0.0458837648952226 \tabularnewline
62 & 56.87 & 56.8909209240433 & -0.0209209240433523 \tabularnewline
63 & 56.8 & 56.9321186747215 & -0.132118674721497 \tabularnewline
64 & 56.89 & 56.8698940521543 & 0.0201059478457211 \tabularnewline
65 & 57.01 & 57.1210895855878 & -0.111089585587791 \tabularnewline
66 & 57.03 & 57.0471274739372 & -0.0171274739371867 \tabularnewline
67 & 57.03 & 57.0263033696245 & 0.00369663037555057 \tabularnewline
68 & 57.03 & 57.0452162937375 & -0.0152162937374811 \tabularnewline
69 & 57.06 & 57.1775673013669 & -0.117567301366883 \tabularnewline
70 & 57.25 & 57.1708171116063 & 0.0791828883937029 \tabularnewline
71 & 57.24 & 57.4728300813725 & -0.232830081372477 \tabularnewline
72 & 57.31 & 57.3173512211716 & -0.00735122117164622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232502&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]51.82[/C][C]51.3734375[/C][C]0.446562500000006[/C][/ROW]
[ROW][C]14[/C][C]51.84[/C][C]51.8027293811279[/C][C]0.0372706188721281[/C][/ROW]
[ROW][C]15[/C][C]51.9[/C][C]51.8922413399803[/C][C]0.00775866001972503[/C][/ROW]
[ROW][C]16[/C][C]51.94[/C][C]51.9230112036107[/C][C]0.0169887963892563[/C][/ROW]
[ROW][C]17[/C][C]52.22[/C][C]52.2072803038094[/C][C]0.0127196961906151[/C][/ROW]
[ROW][C]18[/C][C]52.27[/C][C]52.2747347026172[/C][C]-0.00473470261723463[/C][/ROW]
[ROW][C]19[/C][C]52.27[/C][C]52.2515774607555[/C][C]0.0184225392444617[/C][/ROW]
[ROW][C]20[/C][C]52.28[/C][C]52.2834549022781[/C][C]-0.00345490227807943[/C][/ROW]
[ROW][C]21[/C][C]52.53[/C][C]52.4469130179452[/C][C]0.0830869820548372[/C][/ROW]
[ROW][C]22[/C][C]52.73[/C][C]52.5428545127412[/C][C]0.187145487258825[/C][/ROW]
[ROW][C]23[/C][C]52.72[/C][C]53.0275241469797[/C][C]-0.307524146979674[/C][/ROW]
[ROW][C]24[/C][C]52.67[/C][C]52.796829141609[/C][C]-0.126829141608951[/C][/ROW]
[ROW][C]25[/C][C]52.67[/C][C]52.7167971024509[/C][C]-0.0467971024508742[/C][/ROW]
[ROW][C]26[/C][C]52.65[/C][C]52.6594325684718[/C][C]-0.0094325684717731[/C][/ROW]
[ROW][C]27[/C][C]52.69[/C][C]52.7033764334951[/C][C]-0.0133764334950754[/C][/ROW]
[ROW][C]28[/C][C]52.73[/C][C]52.715194490368[/C][C]0.0148055096319979[/C][/ROW]
[ROW][C]29[/C][C]52.84[/C][C]52.9967945911348[/C][C]-0.156794591134819[/C][/ROW]
[ROW][C]30[/C][C]52.83[/C][C]52.9066384206996[/C][C]-0.076638420699588[/C][/ROW]
[ROW][C]31[/C][C]52.83[/C][C]52.8186839900976[/C][C]0.0113160099023872[/C][/ROW]
[ROW][C]32[/C][C]52.84[/C][C]52.841528548643[/C][C]-0.00152854864302299[/C][/ROW]
[ROW][C]33[/C][C]52.82[/C][C]53.013153259599[/C][C]-0.193153259599022[/C][/ROW]
[ROW][C]34[/C][C]53.09[/C][C]52.8629387209081[/C][C]0.227061279091878[/C][/ROW]
[ROW][C]35[/C][C]53.4[/C][C]53.3425247023511[/C][C]0.0574752976488782[/C][/ROW]
[ROW][C]36[/C][C]53.43[/C][C]53.4611869896648[/C][C]-0.031186989664846[/C][/ROW]
[ROW][C]37[/C][C]53.43[/C][C]53.4751647723974[/C][C]-0.045164772397392[/C][/ROW]
[ROW][C]38[/C][C]53.42[/C][C]53.42202006463[/C][C]-0.00202006463003102[/C][/ROW]
[ROW][C]39[/C][C]53.6[/C][C]53.4721080121109[/C][C]0.12789198788915[/C][/ROW]
[ROW][C]40[/C][C]53.69[/C][C]53.6157966896982[/C][C]0.0742033103017761[/C][/ROW]
[ROW][C]41[/C][C]54.05[/C][C]53.9378069517095[/C][C]0.112193048290536[/C][/ROW]
[ROW][C]42[/C][C]54.04[/C][C]54.1015458183178[/C][C]-0.0615458183177537[/C][/ROW]
[ROW][C]43[/C][C]54.04[/C][C]54.0351108309351[/C][C]0.00488916906488157[/C][/ROW]
[ROW][C]44[/C][C]54.08[/C][C]54.051433135002[/C][C]0.0285668649980195[/C][/ROW]
[ROW][C]45[/C][C]54.05[/C][C]54.2354213985394[/C][C]-0.185421398539376[/C][/ROW]
[ROW][C]46[/C][C]54.39[/C][C]54.12731205974[/C][C]0.262687940259994[/C][/ROW]
[ROW][C]47[/C][C]54.38[/C][C]54.6262183082572[/C][C]-0.246218308257227[/C][/ROW]
[ROW][C]48[/C][C]54.46[/C][C]54.4589118169785[/C][C]0.00108818302152969[/C][/ROW]
[ROW][C]49[/C][C]54.46[/C][C]54.5014797437545[/C][C]-0.0414797437545147[/C][/ROW]
[ROW][C]50[/C][C]54.69[/C][C]54.4553812994574[/C][C]0.234618700542555[/C][/ROW]
[ROW][C]51[/C][C]54.91[/C][C]54.7338412716104[/C][C]0.176158728389638[/C][/ROW]
[ROW][C]52[/C][C]55.52[/C][C]54.91799929133[/C][C]0.602000708669955[/C][/ROW]
[ROW][C]53[/C][C]56.01[/C][C]55.7289984779802[/C][C]0.281001522019842[/C][/ROW]
[ROW][C]54[/C][C]56.07[/C][C]56.0351039764439[/C][C]0.0348960235561151[/C][/ROW]
[ROW][C]55[/C][C]56.07[/C][C]56.0644954762645[/C][C]0.00550452373551735[/C][/ROW]
[ROW][C]56[/C][C]56.09[/C][C]56.0851778191945[/C][C]0.00482218080548336[/C][/ROW]
[ROW][C]57[/C][C]56.29[/C][C]56.2316072509134[/C][C]0.0583927490865577[/C][/ROW]
[ROW][C]58[/C][C]56.45[/C][C]56.386296082309[/C][C]0.063703917691015[/C][/ROW]
[ROW][C]59[/C][C]56.87[/C][C]56.6626457934547[/C][C]0.207354206545283[/C][/ROW]
[ROW][C]60[/C][C]56.87[/C][C]56.9345811717864[/C][C]-0.0645811717864362[/C][/ROW]
[ROW][C]61[/C][C]56.87[/C][C]56.9158837648952[/C][C]-0.0458837648952226[/C][/ROW]
[ROW][C]62[/C][C]56.87[/C][C]56.8909209240433[/C][C]-0.0209209240433523[/C][/ROW]
[ROW][C]63[/C][C]56.8[/C][C]56.9321186747215[/C][C]-0.132118674721497[/C][/ROW]
[ROW][C]64[/C][C]56.89[/C][C]56.8698940521543[/C][C]0.0201059478457211[/C][/ROW]
[ROW][C]65[/C][C]57.01[/C][C]57.1210895855878[/C][C]-0.111089585587791[/C][/ROW]
[ROW][C]66[/C][C]57.03[/C][C]57.0471274739372[/C][C]-0.0171274739371867[/C][/ROW]
[ROW][C]67[/C][C]57.03[/C][C]57.0263033696245[/C][C]0.00369663037555057[/C][/ROW]
[ROW][C]68[/C][C]57.03[/C][C]57.0452162937375[/C][C]-0.0152162937374811[/C][/ROW]
[ROW][C]69[/C][C]57.06[/C][C]57.1775673013669[/C][C]-0.117567301366883[/C][/ROW]
[ROW][C]70[/C][C]57.25[/C][C]57.1708171116063[/C][C]0.0791828883937029[/C][/ROW]
[ROW][C]71[/C][C]57.24[/C][C]57.4728300813725[/C][C]-0.232830081372477[/C][/ROW]
[ROW][C]72[/C][C]57.31[/C][C]57.3173512211716[/C][C]-0.00735122117164622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232502&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232502&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
1351.8251.37343750.446562500000006
1451.8451.80272938112790.0372706188721281
1551.951.89224133998030.00775866001972503
1651.9451.92301120361070.0169887963892563
1752.2252.20728030380940.0127196961906151
1852.2752.2747347026172-0.00473470261723463
1952.2752.25157746075550.0184225392444617
2052.2852.2834549022781-0.00345490227807943
2152.5352.44691301794520.0830869820548372
2252.7352.54285451274120.187145487258825
2352.7253.0275241469797-0.307524146979674
2452.6752.796829141609-0.126829141608951
2552.6752.7167971024509-0.0467971024508742
2652.6552.6594325684718-0.0094325684717731
2752.6952.7033764334951-0.0133764334950754
2852.7352.7151944903680.0148055096319979
2952.8452.9967945911348-0.156794591134819
3052.8352.9066384206996-0.076638420699588
3152.8352.81868399009760.0113160099023872
3252.8452.841528548643-0.00152854864302299
3352.8253.013153259599-0.193153259599022
3453.0952.86293872090810.227061279091878
3553.453.34252470235110.0574752976488782
3653.4353.4611869896648-0.031186989664846
3753.4353.4751647723974-0.045164772397392
3853.4253.42202006463-0.00202006463003102
3953.653.47210801211090.12789198788915
4053.6953.61579668969820.0742033103017761
4154.0553.93780695170950.112193048290536
4254.0454.1015458183178-0.0615458183177537
4354.0454.03511083093510.00488916906488157
4454.0854.0514331350020.0285668649980195
4554.0554.2354213985394-0.185421398539376
4654.3954.127312059740.262687940259994
4754.3854.6262183082572-0.246218308257227
4854.4654.45891181697850.00108818302152969
4954.4654.5014797437545-0.0414797437545147
5054.6954.45538129945740.234618700542555
5154.9154.73384127161040.176158728389638
5255.5254.917999291330.602000708669955
5356.0155.72899847798020.281001522019842
5456.0756.03510397644390.0348960235561151
5556.0756.06449547626450.00550452373551735
5656.0956.08517781919450.00482218080548336
5756.2956.23160725091340.0583927490865577
5856.4556.3862960823090.063703917691015
5956.8756.66264579345470.207354206545283
6056.8756.9345811717864-0.0645811717864362
6156.8756.9158837648952-0.0458837648952226
6256.8756.8909209240433-0.0209209240433523
6356.856.9321186747215-0.132118674721497
6456.8956.86989405215430.0201059478457211
6557.0157.1210895855878-0.111089585587791
6657.0357.0471274739372-0.0171274739371867
6757.0357.02630336962450.00369663037555057
6857.0357.0452162937375-0.0152162937374811
6957.0657.1775673013669-0.117567301366883
7057.2557.17081711160630.0791828883937029
7157.2457.4728300813725-0.232830081372477
7257.3157.3173512211716-0.00735122117164622







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7357.351760800636657.054726177667857.6487954236053
7457.370078971334256.966569014729357.773588927939
7557.420494781291756.932979121067257.9080104415162
7657.491401503288856.932130796882558.050672209695
7757.712695231041457.089672477470858.3357179846119
7857.747923020020157.066899629541558.4289464104986
7957.744064653202457.009428213915458.4787010924894
8057.7575597910956.972797837207158.5423217449729
8157.895023336239957.062992572669558.7270540998104
8258.012086168369657.135180954636558.8889913821028
8358.215406500663357.295670415993659.1351425853329
8458.292142106428257.33134515577359.2529390570834

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 57.3517608006366 & 57.0547261776678 & 57.6487954236053 \tabularnewline
74 & 57.3700789713342 & 56.9665690147293 & 57.773588927939 \tabularnewline
75 & 57.4204947812917 & 56.9329791210672 & 57.9080104415162 \tabularnewline
76 & 57.4914015032888 & 56.9321307968825 & 58.050672209695 \tabularnewline
77 & 57.7126952310414 & 57.0896724774708 & 58.3357179846119 \tabularnewline
78 & 57.7479230200201 & 57.0668996295415 & 58.4289464104986 \tabularnewline
79 & 57.7440646532024 & 57.0094282139154 & 58.4787010924894 \tabularnewline
80 & 57.75755979109 & 56.9727978372071 & 58.5423217449729 \tabularnewline
81 & 57.8950233362399 & 57.0629925726695 & 58.7270540998104 \tabularnewline
82 & 58.0120861683696 & 57.1351809546365 & 58.8889913821028 \tabularnewline
83 & 58.2154065006633 & 57.2956704159936 & 59.1351425853329 \tabularnewline
84 & 58.2921421064282 & 57.331345155773 & 59.2529390570834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232502&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]57.3517608006366[/C][C]57.0547261776678[/C][C]57.6487954236053[/C][/ROW]
[ROW][C]74[/C][C]57.3700789713342[/C][C]56.9665690147293[/C][C]57.773588927939[/C][/ROW]
[ROW][C]75[/C][C]57.4204947812917[/C][C]56.9329791210672[/C][C]57.9080104415162[/C][/ROW]
[ROW][C]76[/C][C]57.4914015032888[/C][C]56.9321307968825[/C][C]58.050672209695[/C][/ROW]
[ROW][C]77[/C][C]57.7126952310414[/C][C]57.0896724774708[/C][C]58.3357179846119[/C][/ROW]
[ROW][C]78[/C][C]57.7479230200201[/C][C]57.0668996295415[/C][C]58.4289464104986[/C][/ROW]
[ROW][C]79[/C][C]57.7440646532024[/C][C]57.0094282139154[/C][C]58.4787010924894[/C][/ROW]
[ROW][C]80[/C][C]57.75755979109[/C][C]56.9727978372071[/C][C]58.5423217449729[/C][/ROW]
[ROW][C]81[/C][C]57.8950233362399[/C][C]57.0629925726695[/C][C]58.7270540998104[/C][/ROW]
[ROW][C]82[/C][C]58.0120861683696[/C][C]57.1351809546365[/C][C]58.8889913821028[/C][/ROW]
[ROW][C]83[/C][C]58.2154065006633[/C][C]57.2956704159936[/C][C]59.1351425853329[/C][/ROW]
[ROW][C]84[/C][C]58.2921421064282[/C][C]57.331345155773[/C][C]59.2529390570834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232502&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232502&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
7357.351760800636657.054726177667857.6487954236053
7457.370078971334256.966569014729357.773588927939
7557.420494781291756.932979121067257.9080104415162
7657.491401503288856.932130796882558.050672209695
7757.712695231041457.089672477470858.3357179846119
7857.747923020020157.066899629541558.4289464104986
7957.744064653202457.009428213915458.4787010924894
8057.7575597910956.972797837207158.5423217449729
8157.895023336239957.062992572669558.7270540998104
8258.012086168369657.135180954636558.8889913821028
8358.215406500663357.295670415993659.1351425853329
8458.292142106428257.33134515577359.2529390570834



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')