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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:09:26 -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/2012/Dec/21/t135608102902cqbi15mb2xx9d.htm/, Retrieved Thu, 18 Apr 2024 16:22:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203327, Retrieved Thu, 18 Apr 2024 16:22:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:09:26] [bb2828c705ec5f2a7fd95594c4342988] [Current]
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Dataseries X:
8.41
8.39
8.43
8.44
8.49
8.47
8.53
8.52
8.51
8.53
8.54
8.53
8.47
8.63
8.67
8.73
8.57
8.55
8.63
8.65
8.44
8.62
8.37
8.59
8.84
8.72
8.8
8.69
8.68
8.57
8.85
8.85
8.85
8.93
8.75
8.78
8.77
9.03
9.01
9.07
8.99
9.02
8.99
8.98
8.94
8.94
8.75
8.86
8.87
8.84
8.84
9.91
10.18
10.34
10.36
10.26
10.16
10.31
10.46
10.54
10.47
10.48
10.46
11.3
11.58
11.69
11.63
11.51
11.37
11.42
11.7
11.75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203327&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203327&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203327&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917775295045143
beta0.0352630086751072
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917775295045143 \tabularnewline
beta & 0.0352630086751072 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203327&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]0.917775295045143[/C][/ROW]
[ROW][C]beta[/C][C]0.0352630086751072[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203327&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203327&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
alpha0.917775295045143
beta0.0352630086751072
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.478.393107442943250.0768925570567536
148.638.625066037221560.00493396277843594
158.678.67841676805531-0.00841676805531399
168.738.74100235368648-0.0110023536864752
178.578.58482178239901-0.0148217823990056
188.558.56589244444184-0.0158924444418371
198.638.63062624644042-0.000626246440415201
208.658.616877630735730.0331223692642748
218.448.62750409313047-0.187504093130475
228.628.457960571993830.162039428006166
238.378.611064676613-0.241064676613
248.598.375492875207150.214507124792851
258.848.519866035275640.320133964724365
268.728.98345065410431-0.263450654104311
278.88.789615760817920.0103842391820805
288.698.87049064078614-0.180490640786143
298.688.55387092484510.126129075154898
308.578.66357108004615-0.0935710800461464
318.858.655498538969490.194501461030505
328.858.826432684646320.0235673153536844
338.858.811697217452120.038302782547877
348.938.889490132164660.0405098678353379
358.758.90233919126471-0.15233919126471
368.788.79543823452029-0.0154382345202908
378.778.737135758408530.0328642415914704
389.038.87998462554960.150015374450398
399.019.09589237670187-0.0858923767018727
409.079.07614143584576-0.00614143584576432
418.998.946988349151810.0430116508481859
429.028.966490057695050.0535099423049523
438.999.13197184176964-0.141971841769635
448.988.978839011862570.00116098813742838
458.948.94269669175771-0.00269669175770559
468.948.98065178220993-0.040651782209931
478.758.89761622527351-0.147616225273508
488.868.801221525209930.0587784747900706
498.878.81184934879840.0581506512015988
508.848.98663001650521-0.14663001650521
518.848.89842089229508-0.058420892295084
529.918.898743816688091.01125618331191
5310.189.718091967289360.461908032710644
5410.3410.15377450494720.186225495052808
5510.3610.4767783928352-0.11677839283521
5610.2610.3955798556225-0.135579855622462
5710.1610.2624664662807-0.102466466280706
5810.3110.24203272607510.0679672739248751
5910.4610.27581483287230.18418516712768
6010.5410.5576652514789-0.0176652514789311
6110.4710.5326888853605-0.062688885360453
6210.4810.6375356438337-0.157535643833654
6310.4610.5963448398414-0.136344839841373
6411.310.66816362211550.631836377884516
6511.5811.09245673065650.487543269343453
6611.6911.54687680054460.143123199455353
6711.6311.8395234759126-0.20952347591259
6811.5111.6900268387986-0.180026838798623
6911.3711.532576148495-0.162576148495029
7011.4211.4947001396173-0.0747001396173133
7111.711.41360179249020.286398207509823
7211.7511.7949559787446-0.0449559787445999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.47 & 8.39310744294325 & 0.0768925570567536 \tabularnewline
14 & 8.63 & 8.62506603722156 & 0.00493396277843594 \tabularnewline
15 & 8.67 & 8.67841676805531 & -0.00841676805531399 \tabularnewline
16 & 8.73 & 8.74100235368648 & -0.0110023536864752 \tabularnewline
17 & 8.57 & 8.58482178239901 & -0.0148217823990056 \tabularnewline
18 & 8.55 & 8.56589244444184 & -0.0158924444418371 \tabularnewline
19 & 8.63 & 8.63062624644042 & -0.000626246440415201 \tabularnewline
20 & 8.65 & 8.61687763073573 & 0.0331223692642748 \tabularnewline
21 & 8.44 & 8.62750409313047 & -0.187504093130475 \tabularnewline
22 & 8.62 & 8.45796057199383 & 0.162039428006166 \tabularnewline
23 & 8.37 & 8.611064676613 & -0.241064676613 \tabularnewline
24 & 8.59 & 8.37549287520715 & 0.214507124792851 \tabularnewline
25 & 8.84 & 8.51986603527564 & 0.320133964724365 \tabularnewline
26 & 8.72 & 8.98345065410431 & -0.263450654104311 \tabularnewline
27 & 8.8 & 8.78961576081792 & 0.0103842391820805 \tabularnewline
28 & 8.69 & 8.87049064078614 & -0.180490640786143 \tabularnewline
29 & 8.68 & 8.5538709248451 & 0.126129075154898 \tabularnewline
30 & 8.57 & 8.66357108004615 & -0.0935710800461464 \tabularnewline
31 & 8.85 & 8.65549853896949 & 0.194501461030505 \tabularnewline
32 & 8.85 & 8.82643268464632 & 0.0235673153536844 \tabularnewline
33 & 8.85 & 8.81169721745212 & 0.038302782547877 \tabularnewline
34 & 8.93 & 8.88949013216466 & 0.0405098678353379 \tabularnewline
35 & 8.75 & 8.90233919126471 & -0.15233919126471 \tabularnewline
36 & 8.78 & 8.79543823452029 & -0.0154382345202908 \tabularnewline
37 & 8.77 & 8.73713575840853 & 0.0328642415914704 \tabularnewline
38 & 9.03 & 8.8799846255496 & 0.150015374450398 \tabularnewline
39 & 9.01 & 9.09589237670187 & -0.0858923767018727 \tabularnewline
40 & 9.07 & 9.07614143584576 & -0.00614143584576432 \tabularnewline
41 & 8.99 & 8.94698834915181 & 0.0430116508481859 \tabularnewline
42 & 9.02 & 8.96649005769505 & 0.0535099423049523 \tabularnewline
43 & 8.99 & 9.13197184176964 & -0.141971841769635 \tabularnewline
44 & 8.98 & 8.97883901186257 & 0.00116098813742838 \tabularnewline
45 & 8.94 & 8.94269669175771 & -0.00269669175770559 \tabularnewline
46 & 8.94 & 8.98065178220993 & -0.040651782209931 \tabularnewline
47 & 8.75 & 8.89761622527351 & -0.147616225273508 \tabularnewline
48 & 8.86 & 8.80122152520993 & 0.0587784747900706 \tabularnewline
49 & 8.87 & 8.8118493487984 & 0.0581506512015988 \tabularnewline
50 & 8.84 & 8.98663001650521 & -0.14663001650521 \tabularnewline
51 & 8.84 & 8.89842089229508 & -0.058420892295084 \tabularnewline
52 & 9.91 & 8.89874381668809 & 1.01125618331191 \tabularnewline
53 & 10.18 & 9.71809196728936 & 0.461908032710644 \tabularnewline
54 & 10.34 & 10.1537745049472 & 0.186225495052808 \tabularnewline
55 & 10.36 & 10.4767783928352 & -0.11677839283521 \tabularnewline
56 & 10.26 & 10.3955798556225 & -0.135579855622462 \tabularnewline
57 & 10.16 & 10.2624664662807 & -0.102466466280706 \tabularnewline
58 & 10.31 & 10.2420327260751 & 0.0679672739248751 \tabularnewline
59 & 10.46 & 10.2758148328723 & 0.18418516712768 \tabularnewline
60 & 10.54 & 10.5576652514789 & -0.0176652514789311 \tabularnewline
61 & 10.47 & 10.5326888853605 & -0.062688885360453 \tabularnewline
62 & 10.48 & 10.6375356438337 & -0.157535643833654 \tabularnewline
63 & 10.46 & 10.5963448398414 & -0.136344839841373 \tabularnewline
64 & 11.3 & 10.6681636221155 & 0.631836377884516 \tabularnewline
65 & 11.58 & 11.0924567306565 & 0.487543269343453 \tabularnewline
66 & 11.69 & 11.5468768005446 & 0.143123199455353 \tabularnewline
67 & 11.63 & 11.8395234759126 & -0.20952347591259 \tabularnewline
68 & 11.51 & 11.6900268387986 & -0.180026838798623 \tabularnewline
69 & 11.37 & 11.532576148495 & -0.162576148495029 \tabularnewline
70 & 11.42 & 11.4947001396173 & -0.0747001396173133 \tabularnewline
71 & 11.7 & 11.4136017924902 & 0.286398207509823 \tabularnewline
72 & 11.75 & 11.7949559787446 & -0.0449559787445999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203327&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]8.47[/C][C]8.39310744294325[/C][C]0.0768925570567536[/C][/ROW]
[ROW][C]14[/C][C]8.63[/C][C]8.62506603722156[/C][C]0.00493396277843594[/C][/ROW]
[ROW][C]15[/C][C]8.67[/C][C]8.67841676805531[/C][C]-0.00841676805531399[/C][/ROW]
[ROW][C]16[/C][C]8.73[/C][C]8.74100235368648[/C][C]-0.0110023536864752[/C][/ROW]
[ROW][C]17[/C][C]8.57[/C][C]8.58482178239901[/C][C]-0.0148217823990056[/C][/ROW]
[ROW][C]18[/C][C]8.55[/C][C]8.56589244444184[/C][C]-0.0158924444418371[/C][/ROW]
[ROW][C]19[/C][C]8.63[/C][C]8.63062624644042[/C][C]-0.000626246440415201[/C][/ROW]
[ROW][C]20[/C][C]8.65[/C][C]8.61687763073573[/C][C]0.0331223692642748[/C][/ROW]
[ROW][C]21[/C][C]8.44[/C][C]8.62750409313047[/C][C]-0.187504093130475[/C][/ROW]
[ROW][C]22[/C][C]8.62[/C][C]8.45796057199383[/C][C]0.162039428006166[/C][/ROW]
[ROW][C]23[/C][C]8.37[/C][C]8.611064676613[/C][C]-0.241064676613[/C][/ROW]
[ROW][C]24[/C][C]8.59[/C][C]8.37549287520715[/C][C]0.214507124792851[/C][/ROW]
[ROW][C]25[/C][C]8.84[/C][C]8.51986603527564[/C][C]0.320133964724365[/C][/ROW]
[ROW][C]26[/C][C]8.72[/C][C]8.98345065410431[/C][C]-0.263450654104311[/C][/ROW]
[ROW][C]27[/C][C]8.8[/C][C]8.78961576081792[/C][C]0.0103842391820805[/C][/ROW]
[ROW][C]28[/C][C]8.69[/C][C]8.87049064078614[/C][C]-0.180490640786143[/C][/ROW]
[ROW][C]29[/C][C]8.68[/C][C]8.5538709248451[/C][C]0.126129075154898[/C][/ROW]
[ROW][C]30[/C][C]8.57[/C][C]8.66357108004615[/C][C]-0.0935710800461464[/C][/ROW]
[ROW][C]31[/C][C]8.85[/C][C]8.65549853896949[/C][C]0.194501461030505[/C][/ROW]
[ROW][C]32[/C][C]8.85[/C][C]8.82643268464632[/C][C]0.0235673153536844[/C][/ROW]
[ROW][C]33[/C][C]8.85[/C][C]8.81169721745212[/C][C]0.038302782547877[/C][/ROW]
[ROW][C]34[/C][C]8.93[/C][C]8.88949013216466[/C][C]0.0405098678353379[/C][/ROW]
[ROW][C]35[/C][C]8.75[/C][C]8.90233919126471[/C][C]-0.15233919126471[/C][/ROW]
[ROW][C]36[/C][C]8.78[/C][C]8.79543823452029[/C][C]-0.0154382345202908[/C][/ROW]
[ROW][C]37[/C][C]8.77[/C][C]8.73713575840853[/C][C]0.0328642415914704[/C][/ROW]
[ROW][C]38[/C][C]9.03[/C][C]8.8799846255496[/C][C]0.150015374450398[/C][/ROW]
[ROW][C]39[/C][C]9.01[/C][C]9.09589237670187[/C][C]-0.0858923767018727[/C][/ROW]
[ROW][C]40[/C][C]9.07[/C][C]9.07614143584576[/C][C]-0.00614143584576432[/C][/ROW]
[ROW][C]41[/C][C]8.99[/C][C]8.94698834915181[/C][C]0.0430116508481859[/C][/ROW]
[ROW][C]42[/C][C]9.02[/C][C]8.96649005769505[/C][C]0.0535099423049523[/C][/ROW]
[ROW][C]43[/C][C]8.99[/C][C]9.13197184176964[/C][C]-0.141971841769635[/C][/ROW]
[ROW][C]44[/C][C]8.98[/C][C]8.97883901186257[/C][C]0.00116098813742838[/C][/ROW]
[ROW][C]45[/C][C]8.94[/C][C]8.94269669175771[/C][C]-0.00269669175770559[/C][/ROW]
[ROW][C]46[/C][C]8.94[/C][C]8.98065178220993[/C][C]-0.040651782209931[/C][/ROW]
[ROW][C]47[/C][C]8.75[/C][C]8.89761622527351[/C][C]-0.147616225273508[/C][/ROW]
[ROW][C]48[/C][C]8.86[/C][C]8.80122152520993[/C][C]0.0587784747900706[/C][/ROW]
[ROW][C]49[/C][C]8.87[/C][C]8.8118493487984[/C][C]0.0581506512015988[/C][/ROW]
[ROW][C]50[/C][C]8.84[/C][C]8.98663001650521[/C][C]-0.14663001650521[/C][/ROW]
[ROW][C]51[/C][C]8.84[/C][C]8.89842089229508[/C][C]-0.058420892295084[/C][/ROW]
[ROW][C]52[/C][C]9.91[/C][C]8.89874381668809[/C][C]1.01125618331191[/C][/ROW]
[ROW][C]53[/C][C]10.18[/C][C]9.71809196728936[/C][C]0.461908032710644[/C][/ROW]
[ROW][C]54[/C][C]10.34[/C][C]10.1537745049472[/C][C]0.186225495052808[/C][/ROW]
[ROW][C]55[/C][C]10.36[/C][C]10.4767783928352[/C][C]-0.11677839283521[/C][/ROW]
[ROW][C]56[/C][C]10.26[/C][C]10.3955798556225[/C][C]-0.135579855622462[/C][/ROW]
[ROW][C]57[/C][C]10.16[/C][C]10.2624664662807[/C][C]-0.102466466280706[/C][/ROW]
[ROW][C]58[/C][C]10.31[/C][C]10.2420327260751[/C][C]0.0679672739248751[/C][/ROW]
[ROW][C]59[/C][C]10.46[/C][C]10.2758148328723[/C][C]0.18418516712768[/C][/ROW]
[ROW][C]60[/C][C]10.54[/C][C]10.5576652514789[/C][C]-0.0176652514789311[/C][/ROW]
[ROW][C]61[/C][C]10.47[/C][C]10.5326888853605[/C][C]-0.062688885360453[/C][/ROW]
[ROW][C]62[/C][C]10.48[/C][C]10.6375356438337[/C][C]-0.157535643833654[/C][/ROW]
[ROW][C]63[/C][C]10.46[/C][C]10.5963448398414[/C][C]-0.136344839841373[/C][/ROW]
[ROW][C]64[/C][C]11.3[/C][C]10.6681636221155[/C][C]0.631836377884516[/C][/ROW]
[ROW][C]65[/C][C]11.58[/C][C]11.0924567306565[/C][C]0.487543269343453[/C][/ROW]
[ROW][C]66[/C][C]11.69[/C][C]11.5468768005446[/C][C]0.143123199455353[/C][/ROW]
[ROW][C]67[/C][C]11.63[/C][C]11.8395234759126[/C][C]-0.20952347591259[/C][/ROW]
[ROW][C]68[/C][C]11.51[/C][C]11.6900268387986[/C][C]-0.180026838798623[/C][/ROW]
[ROW][C]69[/C][C]11.37[/C][C]11.532576148495[/C][C]-0.162576148495029[/C][/ROW]
[ROW][C]70[/C][C]11.42[/C][C]11.4947001396173[/C][C]-0.0747001396173133[/C][/ROW]
[ROW][C]71[/C][C]11.7[/C][C]11.4136017924902[/C][C]0.286398207509823[/C][/ROW]
[ROW][C]72[/C][C]11.75[/C][C]11.7949559787446[/C][C]-0.0449559787445999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203327&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203327&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
138.478.393107442943250.0768925570567536
148.638.625066037221560.00493396277843594
158.678.67841676805531-0.00841676805531399
168.738.74100235368648-0.0110023536864752
178.578.58482178239901-0.0148217823990056
188.558.56589244444184-0.0158924444418371
198.638.63062624644042-0.000626246440415201
208.658.616877630735730.0331223692642748
218.448.62750409313047-0.187504093130475
228.628.457960571993830.162039428006166
238.378.611064676613-0.241064676613
248.598.375492875207150.214507124792851
258.848.519866035275640.320133964724365
268.728.98345065410431-0.263450654104311
278.88.789615760817920.0103842391820805
288.698.87049064078614-0.180490640786143
298.688.55387092484510.126129075154898
308.578.66357108004615-0.0935710800461464
318.858.655498538969490.194501461030505
328.858.826432684646320.0235673153536844
338.858.811697217452120.038302782547877
348.938.889490132164660.0405098678353379
358.758.90233919126471-0.15233919126471
368.788.79543823452029-0.0154382345202908
378.778.737135758408530.0328642415914704
389.038.87998462554960.150015374450398
399.019.09589237670187-0.0858923767018727
409.079.07614143584576-0.00614143584576432
418.998.946988349151810.0430116508481859
429.028.966490057695050.0535099423049523
438.999.13197184176964-0.141971841769635
448.988.978839011862570.00116098813742838
458.948.94269669175771-0.00269669175770559
468.948.98065178220993-0.040651782209931
478.758.89761622527351-0.147616225273508
488.868.801221525209930.0587784747900706
498.878.81184934879840.0581506512015988
508.848.98663001650521-0.14663001650521
518.848.89842089229508-0.058420892295084
529.918.898743816688091.01125618331191
5310.189.718091967289360.461908032710644
5410.3410.15377450494720.186225495052808
5510.3610.4767783928352-0.11677839283521
5610.2610.3955798556225-0.135579855622462
5710.1610.2624664662807-0.102466466280706
5810.3110.24203272607510.0679672739248751
5910.4610.27581483287230.18418516712768
6010.5410.5576652514789-0.0176652514789311
6110.4710.5326888853605-0.062688885360453
6210.4810.6375356438337-0.157535643833654
6310.4610.5963448398414-0.136344839841373
6411.310.66816362211550.631836377884516
6511.5811.09245673065650.487543269343453
6611.6911.54687680054460.143123199455353
6711.6311.8395234759126-0.20952347591259
6811.5111.6900268387986-0.180026838798623
6911.3711.532576148495-0.162576148495029
7011.4211.4947001396173-0.0747001396173133
7111.711.41360179249020.286398207509823
7211.7511.7949559787446-0.0449559787445999







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7311.750049192767711.325501742146312.1745966433892
7411.935640120518411.347259814761712.5240204262751
7512.072585574975311.348536540584912.7966346093656
7612.391905720361711.536102030861213.2477094098623
7712.208628150115811.259065674002513.158190626229
7812.17405787644511.127138755605313.2209769972847
7912.295711992107311.143445456978613.4479785272359
8012.333365691955611.085860885715713.5808704981956
8112.338299902937811.00106589760613.6755339082695
8212.466936377578611.028939154380913.9049336007763
8312.487316488482110.96156220467714.0130707722872
8412.57850482995856.2721887803752418.8848208795418

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 11.7500491927677 & 11.3255017421463 & 12.1745966433892 \tabularnewline
74 & 11.9356401205184 & 11.3472598147617 & 12.5240204262751 \tabularnewline
75 & 12.0725855749753 & 11.3485365405849 & 12.7966346093656 \tabularnewline
76 & 12.3919057203617 & 11.5361020308612 & 13.2477094098623 \tabularnewline
77 & 12.2086281501158 & 11.2590656740025 & 13.158190626229 \tabularnewline
78 & 12.174057876445 & 11.1271387556053 & 13.2209769972847 \tabularnewline
79 & 12.2957119921073 & 11.1434454569786 & 13.4479785272359 \tabularnewline
80 & 12.3333656919556 & 11.0858608857157 & 13.5808704981956 \tabularnewline
81 & 12.3382999029378 & 11.001065897606 & 13.6755339082695 \tabularnewline
82 & 12.4669363775786 & 11.0289391543809 & 13.9049336007763 \tabularnewline
83 & 12.4873164884821 & 10.961562204677 & 14.0130707722872 \tabularnewline
84 & 12.5785048299585 & 6.27218878037524 & 18.8848208795418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203327&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]11.7500491927677[/C][C]11.3255017421463[/C][C]12.1745966433892[/C][/ROW]
[ROW][C]74[/C][C]11.9356401205184[/C][C]11.3472598147617[/C][C]12.5240204262751[/C][/ROW]
[ROW][C]75[/C][C]12.0725855749753[/C][C]11.3485365405849[/C][C]12.7966346093656[/C][/ROW]
[ROW][C]76[/C][C]12.3919057203617[/C][C]11.5361020308612[/C][C]13.2477094098623[/C][/ROW]
[ROW][C]77[/C][C]12.2086281501158[/C][C]11.2590656740025[/C][C]13.158190626229[/C][/ROW]
[ROW][C]78[/C][C]12.174057876445[/C][C]11.1271387556053[/C][C]13.2209769972847[/C][/ROW]
[ROW][C]79[/C][C]12.2957119921073[/C][C]11.1434454569786[/C][C]13.4479785272359[/C][/ROW]
[ROW][C]80[/C][C]12.3333656919556[/C][C]11.0858608857157[/C][C]13.5808704981956[/C][/ROW]
[ROW][C]81[/C][C]12.3382999029378[/C][C]11.001065897606[/C][C]13.6755339082695[/C][/ROW]
[ROW][C]82[/C][C]12.4669363775786[/C][C]11.0289391543809[/C][C]13.9049336007763[/C][/ROW]
[ROW][C]83[/C][C]12.4873164884821[/C][C]10.961562204677[/C][C]14.0130707722872[/C][/ROW]
[ROW][C]84[/C][C]12.5785048299585[/C][C]6.27218878037524[/C][C]18.8848208795418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203327&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203327&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
7311.750049192767711.325501742146312.1745966433892
7411.935640120518411.347259814761712.5240204262751
7512.072585574975311.348536540584912.7966346093656
7612.391905720361711.536102030861213.2477094098623
7712.208628150115811.259065674002513.158190626229
7812.17405787644511.127138755605313.2209769972847
7912.295711992107311.143445456978613.4479785272359
8012.333365691955611.085860885715713.5808704981956
8112.338299902937811.00106589760613.6755339082695
8212.466936377578611.028939154380913.9049336007763
8312.487316488482110.96156220467714.0130707722872
8412.57850482995856.2721887803752418.8848208795418



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=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')