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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 07 Jun 2010 07:44:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/07/t1275896681ju8macmgszgv0zz.htm/, Retrieved Fri, 10 May 2024 21:44:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77860, Retrieved Fri, 10 May 2024 21:44:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Mean plot inschri...] [2010-01-06 17:47:10] [d04f6142e548bfc3f2eab462d2be4e18]
- R     [Standard Deviation-Mean Plot] [] [2010-06-06 14:19:53] [74be16979710d4c4e7c6647856088456]
- RMPD    [Classical Decomposition] [] [2010-06-06 15:21:37] [74be16979710d4c4e7c6647856088456]
- RMPD        [Exponential Smoothing] [] [2010-06-07 07:44:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77860&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77860&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77860&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.933411388023692
beta0.000993563346089219
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.933411388023692 \tabularnewline
beta & 0.000993563346089219 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77860&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]0.933411388023692[/C][/ROW]
[ROW][C]beta[/C][C]0.000993563346089219[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77860&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77860&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
alpha0.933411388023692
beta0.000993563346089219
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311.35310.53914423076920.813855769230768
1411.34611.22575471973170.120245280268254
1511.45111.32367779531870.127322204681256
1611.96411.82828296511650.135717034883516
1712.57412.40072482945720.17327517054275
1813.03112.77071791464090.260282085359146
1913.81213.52904063142670.282959368573293
2014.54413.73675133341150.807248666588531
2114.93114.71246328189380.218536718106209
2214.88615.1593674650798-0.273367465079810
2316.00515.10670249329610.898297506703855
2417.06416.07918269990030.984817300099735
2515.16817.7234449824935-2.55544498249354
2616.0515.22001945330570.829980546694332
2715.83915.9826411953866-0.143641195386605
2815.13716.2363861933076-1.09938619330764
2914.95415.6588252957237-0.704825295723738
3015.64815.21452443478010.43347556521992
3115.30516.1357199462489-0.830719946248909
3215.57915.33749053931950.241509460680513
3316.34815.74407803994070.603921960059346
3415.92816.5164518686078-0.588451868607802
3516.17116.2459127488755-0.0749127488754695
3615.93716.3130557728083-0.376055772808327
3715.71316.4473675217059-0.734367521705879
3815.59415.8669211347928-0.27292113479278
3915.68315.53196084736730.151039152632706
4016.43815.99410647294030.443893527059702
4117.03216.88174931433260.150250685667402
4217.69617.31059259727850.385407402721523
4317.74518.1019037464118-0.356903746411842
4419.39417.81694149521261.57705850478743
4520.14819.49512027185520.652879728144846
4620.10820.2346807678668-0.126680767866812
4718.58420.430675604756-1.84667560475602
4818.44118.82365486272-0.382654862719999
4918.39118.9276139004689-0.536613900468915
5019.17818.56232990395600.615670096044028
5118.07919.0856956341500-1.00669563415003
5218.48318.4862994210085-0.00329942100850289
5319.64418.93615950384580.707840496154201
5419.19519.9008248368261-0.705824836826093
5519.6519.62282851678050.0271714832195045
5620.8319.82419311261911.0058068873809
5723.59520.90613635345402.68886364654597
5822.93723.4946027629047-0.557602762904672
5921.81423.1738435845337-1.35984358453371
6021.92822.1191815440399-0.191181544039939
6121.77722.3922466530137-0.615246653013706
6221.38322.0308566311477-0.647856631147729
6321.46721.26619093352130.200809066478708
6422.05221.86121785453310.190782145466908
6522.6822.54027942802110.13972057197887
6624.3222.88068399166681.43931600833318
6724.97724.6559480337080.321051966291993
6825.20425.19921479886530.00478520113473024
6925.73925.46036186721920.278638132780795
7026.43425.58217984683650.851820153163484
7127.52526.52414027405811.00085972594191
7230.69527.75356280256892.94143719743115

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11.353 & 10.5391442307692 & 0.813855769230768 \tabularnewline
14 & 11.346 & 11.2257547197317 & 0.120245280268254 \tabularnewline
15 & 11.451 & 11.3236777953187 & 0.127322204681256 \tabularnewline
16 & 11.964 & 11.8282829651165 & 0.135717034883516 \tabularnewline
17 & 12.574 & 12.4007248294572 & 0.17327517054275 \tabularnewline
18 & 13.031 & 12.7707179146409 & 0.260282085359146 \tabularnewline
19 & 13.812 & 13.5290406314267 & 0.282959368573293 \tabularnewline
20 & 14.544 & 13.7367513334115 & 0.807248666588531 \tabularnewline
21 & 14.931 & 14.7124632818938 & 0.218536718106209 \tabularnewline
22 & 14.886 & 15.1593674650798 & -0.273367465079810 \tabularnewline
23 & 16.005 & 15.1067024932961 & 0.898297506703855 \tabularnewline
24 & 17.064 & 16.0791826999003 & 0.984817300099735 \tabularnewline
25 & 15.168 & 17.7234449824935 & -2.55544498249354 \tabularnewline
26 & 16.05 & 15.2200194533057 & 0.829980546694332 \tabularnewline
27 & 15.839 & 15.9826411953866 & -0.143641195386605 \tabularnewline
28 & 15.137 & 16.2363861933076 & -1.09938619330764 \tabularnewline
29 & 14.954 & 15.6588252957237 & -0.704825295723738 \tabularnewline
30 & 15.648 & 15.2145244347801 & 0.43347556521992 \tabularnewline
31 & 15.305 & 16.1357199462489 & -0.830719946248909 \tabularnewline
32 & 15.579 & 15.3374905393195 & 0.241509460680513 \tabularnewline
33 & 16.348 & 15.7440780399407 & 0.603921960059346 \tabularnewline
34 & 15.928 & 16.5164518686078 & -0.588451868607802 \tabularnewline
35 & 16.171 & 16.2459127488755 & -0.0749127488754695 \tabularnewline
36 & 15.937 & 16.3130557728083 & -0.376055772808327 \tabularnewline
37 & 15.713 & 16.4473675217059 & -0.734367521705879 \tabularnewline
38 & 15.594 & 15.8669211347928 & -0.27292113479278 \tabularnewline
39 & 15.683 & 15.5319608473673 & 0.151039152632706 \tabularnewline
40 & 16.438 & 15.9941064729403 & 0.443893527059702 \tabularnewline
41 & 17.032 & 16.8817493143326 & 0.150250685667402 \tabularnewline
42 & 17.696 & 17.3105925972785 & 0.385407402721523 \tabularnewline
43 & 17.745 & 18.1019037464118 & -0.356903746411842 \tabularnewline
44 & 19.394 & 17.8169414952126 & 1.57705850478743 \tabularnewline
45 & 20.148 & 19.4951202718552 & 0.652879728144846 \tabularnewline
46 & 20.108 & 20.2346807678668 & -0.126680767866812 \tabularnewline
47 & 18.584 & 20.430675604756 & -1.84667560475602 \tabularnewline
48 & 18.441 & 18.82365486272 & -0.382654862719999 \tabularnewline
49 & 18.391 & 18.9276139004689 & -0.536613900468915 \tabularnewline
50 & 19.178 & 18.5623299039560 & 0.615670096044028 \tabularnewline
51 & 18.079 & 19.0856956341500 & -1.00669563415003 \tabularnewline
52 & 18.483 & 18.4862994210085 & -0.00329942100850289 \tabularnewline
53 & 19.644 & 18.9361595038458 & 0.707840496154201 \tabularnewline
54 & 19.195 & 19.9008248368261 & -0.705824836826093 \tabularnewline
55 & 19.65 & 19.6228285167805 & 0.0271714832195045 \tabularnewline
56 & 20.83 & 19.8241931126191 & 1.0058068873809 \tabularnewline
57 & 23.595 & 20.9061363534540 & 2.68886364654597 \tabularnewline
58 & 22.937 & 23.4946027629047 & -0.557602762904672 \tabularnewline
59 & 21.814 & 23.1738435845337 & -1.35984358453371 \tabularnewline
60 & 21.928 & 22.1191815440399 & -0.191181544039939 \tabularnewline
61 & 21.777 & 22.3922466530137 & -0.615246653013706 \tabularnewline
62 & 21.383 & 22.0308566311477 & -0.647856631147729 \tabularnewline
63 & 21.467 & 21.2661909335213 & 0.200809066478708 \tabularnewline
64 & 22.052 & 21.8612178545331 & 0.190782145466908 \tabularnewline
65 & 22.68 & 22.5402794280211 & 0.13972057197887 \tabularnewline
66 & 24.32 & 22.8806839916668 & 1.43931600833318 \tabularnewline
67 & 24.977 & 24.655948033708 & 0.321051966291993 \tabularnewline
68 & 25.204 & 25.1992147988653 & 0.00478520113473024 \tabularnewline
69 & 25.739 & 25.4603618672192 & 0.278638132780795 \tabularnewline
70 & 26.434 & 25.5821798468365 & 0.851820153163484 \tabularnewline
71 & 27.525 & 26.5241402740581 & 1.00085972594191 \tabularnewline
72 & 30.695 & 27.7535628025689 & 2.94143719743115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77860&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]11.353[/C][C]10.5391442307692[/C][C]0.813855769230768[/C][/ROW]
[ROW][C]14[/C][C]11.346[/C][C]11.2257547197317[/C][C]0.120245280268254[/C][/ROW]
[ROW][C]15[/C][C]11.451[/C][C]11.3236777953187[/C][C]0.127322204681256[/C][/ROW]
[ROW][C]16[/C][C]11.964[/C][C]11.8282829651165[/C][C]0.135717034883516[/C][/ROW]
[ROW][C]17[/C][C]12.574[/C][C]12.4007248294572[/C][C]0.17327517054275[/C][/ROW]
[ROW][C]18[/C][C]13.031[/C][C]12.7707179146409[/C][C]0.260282085359146[/C][/ROW]
[ROW][C]19[/C][C]13.812[/C][C]13.5290406314267[/C][C]0.282959368573293[/C][/ROW]
[ROW][C]20[/C][C]14.544[/C][C]13.7367513334115[/C][C]0.807248666588531[/C][/ROW]
[ROW][C]21[/C][C]14.931[/C][C]14.7124632818938[/C][C]0.218536718106209[/C][/ROW]
[ROW][C]22[/C][C]14.886[/C][C]15.1593674650798[/C][C]-0.273367465079810[/C][/ROW]
[ROW][C]23[/C][C]16.005[/C][C]15.1067024932961[/C][C]0.898297506703855[/C][/ROW]
[ROW][C]24[/C][C]17.064[/C][C]16.0791826999003[/C][C]0.984817300099735[/C][/ROW]
[ROW][C]25[/C][C]15.168[/C][C]17.7234449824935[/C][C]-2.55544498249354[/C][/ROW]
[ROW][C]26[/C][C]16.05[/C][C]15.2200194533057[/C][C]0.829980546694332[/C][/ROW]
[ROW][C]27[/C][C]15.839[/C][C]15.9826411953866[/C][C]-0.143641195386605[/C][/ROW]
[ROW][C]28[/C][C]15.137[/C][C]16.2363861933076[/C][C]-1.09938619330764[/C][/ROW]
[ROW][C]29[/C][C]14.954[/C][C]15.6588252957237[/C][C]-0.704825295723738[/C][/ROW]
[ROW][C]30[/C][C]15.648[/C][C]15.2145244347801[/C][C]0.43347556521992[/C][/ROW]
[ROW][C]31[/C][C]15.305[/C][C]16.1357199462489[/C][C]-0.830719946248909[/C][/ROW]
[ROW][C]32[/C][C]15.579[/C][C]15.3374905393195[/C][C]0.241509460680513[/C][/ROW]
[ROW][C]33[/C][C]16.348[/C][C]15.7440780399407[/C][C]0.603921960059346[/C][/ROW]
[ROW][C]34[/C][C]15.928[/C][C]16.5164518686078[/C][C]-0.588451868607802[/C][/ROW]
[ROW][C]35[/C][C]16.171[/C][C]16.2459127488755[/C][C]-0.0749127488754695[/C][/ROW]
[ROW][C]36[/C][C]15.937[/C][C]16.3130557728083[/C][C]-0.376055772808327[/C][/ROW]
[ROW][C]37[/C][C]15.713[/C][C]16.4473675217059[/C][C]-0.734367521705879[/C][/ROW]
[ROW][C]38[/C][C]15.594[/C][C]15.8669211347928[/C][C]-0.27292113479278[/C][/ROW]
[ROW][C]39[/C][C]15.683[/C][C]15.5319608473673[/C][C]0.151039152632706[/C][/ROW]
[ROW][C]40[/C][C]16.438[/C][C]15.9941064729403[/C][C]0.443893527059702[/C][/ROW]
[ROW][C]41[/C][C]17.032[/C][C]16.8817493143326[/C][C]0.150250685667402[/C][/ROW]
[ROW][C]42[/C][C]17.696[/C][C]17.3105925972785[/C][C]0.385407402721523[/C][/ROW]
[ROW][C]43[/C][C]17.745[/C][C]18.1019037464118[/C][C]-0.356903746411842[/C][/ROW]
[ROW][C]44[/C][C]19.394[/C][C]17.8169414952126[/C][C]1.57705850478743[/C][/ROW]
[ROW][C]45[/C][C]20.148[/C][C]19.4951202718552[/C][C]0.652879728144846[/C][/ROW]
[ROW][C]46[/C][C]20.108[/C][C]20.2346807678668[/C][C]-0.126680767866812[/C][/ROW]
[ROW][C]47[/C][C]18.584[/C][C]20.430675604756[/C][C]-1.84667560475602[/C][/ROW]
[ROW][C]48[/C][C]18.441[/C][C]18.82365486272[/C][C]-0.382654862719999[/C][/ROW]
[ROW][C]49[/C][C]18.391[/C][C]18.9276139004689[/C][C]-0.536613900468915[/C][/ROW]
[ROW][C]50[/C][C]19.178[/C][C]18.5623299039560[/C][C]0.615670096044028[/C][/ROW]
[ROW][C]51[/C][C]18.079[/C][C]19.0856956341500[/C][C]-1.00669563415003[/C][/ROW]
[ROW][C]52[/C][C]18.483[/C][C]18.4862994210085[/C][C]-0.00329942100850289[/C][/ROW]
[ROW][C]53[/C][C]19.644[/C][C]18.9361595038458[/C][C]0.707840496154201[/C][/ROW]
[ROW][C]54[/C][C]19.195[/C][C]19.9008248368261[/C][C]-0.705824836826093[/C][/ROW]
[ROW][C]55[/C][C]19.65[/C][C]19.6228285167805[/C][C]0.0271714832195045[/C][/ROW]
[ROW][C]56[/C][C]20.83[/C][C]19.8241931126191[/C][C]1.0058068873809[/C][/ROW]
[ROW][C]57[/C][C]23.595[/C][C]20.9061363534540[/C][C]2.68886364654597[/C][/ROW]
[ROW][C]58[/C][C]22.937[/C][C]23.4946027629047[/C][C]-0.557602762904672[/C][/ROW]
[ROW][C]59[/C][C]21.814[/C][C]23.1738435845337[/C][C]-1.35984358453371[/C][/ROW]
[ROW][C]60[/C][C]21.928[/C][C]22.1191815440399[/C][C]-0.191181544039939[/C][/ROW]
[ROW][C]61[/C][C]21.777[/C][C]22.3922466530137[/C][C]-0.615246653013706[/C][/ROW]
[ROW][C]62[/C][C]21.383[/C][C]22.0308566311477[/C][C]-0.647856631147729[/C][/ROW]
[ROW][C]63[/C][C]21.467[/C][C]21.2661909335213[/C][C]0.200809066478708[/C][/ROW]
[ROW][C]64[/C][C]22.052[/C][C]21.8612178545331[/C][C]0.190782145466908[/C][/ROW]
[ROW][C]65[/C][C]22.68[/C][C]22.5402794280211[/C][C]0.13972057197887[/C][/ROW]
[ROW][C]66[/C][C]24.32[/C][C]22.8806839916668[/C][C]1.43931600833318[/C][/ROW]
[ROW][C]67[/C][C]24.977[/C][C]24.655948033708[/C][C]0.321051966291993[/C][/ROW]
[ROW][C]68[/C][C]25.204[/C][C]25.1992147988653[/C][C]0.00478520113473024[/C][/ROW]
[ROW][C]69[/C][C]25.739[/C][C]25.4603618672192[/C][C]0.278638132780795[/C][/ROW]
[ROW][C]70[/C][C]26.434[/C][C]25.5821798468365[/C][C]0.851820153163484[/C][/ROW]
[ROW][C]71[/C][C]27.525[/C][C]26.5241402740581[/C][C]1.00085972594191[/C][/ROW]
[ROW][C]72[/C][C]30.695[/C][C]27.7535628025689[/C][C]2.94143719743115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77860&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77860&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
1311.35310.53914423076920.813855769230768
1411.34611.22575471973170.120245280268254
1511.45111.32367779531870.127322204681256
1611.96411.82828296511650.135717034883516
1712.57412.40072482945720.17327517054275
1813.03112.77071791464090.260282085359146
1913.81213.52904063142670.282959368573293
2014.54413.73675133341150.807248666588531
2114.93114.71246328189380.218536718106209
2214.88615.1593674650798-0.273367465079810
2316.00515.10670249329610.898297506703855
2417.06416.07918269990030.984817300099735
2515.16817.7234449824935-2.55544498249354
2616.0515.22001945330570.829980546694332
2715.83915.9826411953866-0.143641195386605
2815.13716.2363861933076-1.09938619330764
2914.95415.6588252957237-0.704825295723738
3015.64815.21452443478010.43347556521992
3115.30516.1357199462489-0.830719946248909
3215.57915.33749053931950.241509460680513
3316.34815.74407803994070.603921960059346
3415.92816.5164518686078-0.588451868607802
3516.17116.2459127488755-0.0749127488754695
3615.93716.3130557728083-0.376055772808327
3715.71316.4473675217059-0.734367521705879
3815.59415.8669211347928-0.27292113479278
3915.68315.53196084736730.151039152632706
4016.43815.99410647294030.443893527059702
4117.03216.88174931433260.150250685667402
4217.69617.31059259727850.385407402721523
4317.74518.1019037464118-0.356903746411842
4419.39417.81694149521261.57705850478743
4520.14819.49512027185520.652879728144846
4620.10820.2346807678668-0.126680767866812
4718.58420.430675604756-1.84667560475602
4818.44118.82365486272-0.382654862719999
4918.39118.9276139004689-0.536613900468915
5019.17818.56232990395600.615670096044028
5118.07919.0856956341500-1.00669563415003
5218.48318.4862994210085-0.00329942100850289
5319.64418.93615950384580.707840496154201
5419.19519.9008248368261-0.705824836826093
5519.6519.62282851678050.0271714832195045
5620.8319.82419311261911.0058068873809
5723.59520.90613635345402.68886364654597
5822.93723.4946027629047-0.557602762904672
5921.81423.1738435845337-1.35984358453371
6021.92822.1191815440399-0.191181544039939
6121.77722.3922466530137-0.615246653013706
6221.38322.0308566311477-0.647856631147729
6321.46721.26619093352130.200809066478708
6422.05221.86121785453310.190782145466908
6522.6822.54027942802110.13972057197887
6624.3222.88068399166681.43931600833318
6724.97724.6559480337080.321051966291993
6825.20425.19921479886530.00478520113473024
6925.73925.46036186721920.278638132780795
7026.43425.58217984683650.851820153163484
7127.52526.52414027405811.00085972594191
7230.69527.75356280256892.94143719743115







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7330.928074845379429.165929577689332.6902201130696
7431.145025017706928.733402564675733.5566474707382
7531.048421787649728.127450420314433.969393154985
7631.461991568852328.107350916819334.8166322208854
7731.966045872239828.226988675064135.7051030694155
7832.268913418185228.180774045735436.3570527906350
7932.631246529312928.220960409332937.041532649293
8032.858488896025428.147461995270237.5695157967806
8133.138109379884228.143878581395538.132340178373
8233.042456828571927.779726602896638.3051870542472
8333.202899061905227.684226732442638.7215713913677
8433.630055983353527.866325319526939.3937866471802

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 30.9280748453794 & 29.1659295776893 & 32.6902201130696 \tabularnewline
74 & 31.1450250177069 & 28.7334025646757 & 33.5566474707382 \tabularnewline
75 & 31.0484217876497 & 28.1274504203144 & 33.969393154985 \tabularnewline
76 & 31.4619915688523 & 28.1073509168193 & 34.8166322208854 \tabularnewline
77 & 31.9660458722398 & 28.2269886750641 & 35.7051030694155 \tabularnewline
78 & 32.2689134181852 & 28.1807740457354 & 36.3570527906350 \tabularnewline
79 & 32.6312465293129 & 28.2209604093329 & 37.041532649293 \tabularnewline
80 & 32.8584888960254 & 28.1474619952702 & 37.5695157967806 \tabularnewline
81 & 33.1381093798842 & 28.1438785813955 & 38.132340178373 \tabularnewline
82 & 33.0424568285719 & 27.7797266028966 & 38.3051870542472 \tabularnewline
83 & 33.2028990619052 & 27.6842267324426 & 38.7215713913677 \tabularnewline
84 & 33.6300559833535 & 27.8663253195269 & 39.3937866471802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77860&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]30.9280748453794[/C][C]29.1659295776893[/C][C]32.6902201130696[/C][/ROW]
[ROW][C]74[/C][C]31.1450250177069[/C][C]28.7334025646757[/C][C]33.5566474707382[/C][/ROW]
[ROW][C]75[/C][C]31.0484217876497[/C][C]28.1274504203144[/C][C]33.969393154985[/C][/ROW]
[ROW][C]76[/C][C]31.4619915688523[/C][C]28.1073509168193[/C][C]34.8166322208854[/C][/ROW]
[ROW][C]77[/C][C]31.9660458722398[/C][C]28.2269886750641[/C][C]35.7051030694155[/C][/ROW]
[ROW][C]78[/C][C]32.2689134181852[/C][C]28.1807740457354[/C][C]36.3570527906350[/C][/ROW]
[ROW][C]79[/C][C]32.6312465293129[/C][C]28.2209604093329[/C][C]37.041532649293[/C][/ROW]
[ROW][C]80[/C][C]32.8584888960254[/C][C]28.1474619952702[/C][C]37.5695157967806[/C][/ROW]
[ROW][C]81[/C][C]33.1381093798842[/C][C]28.1438785813955[/C][C]38.132340178373[/C][/ROW]
[ROW][C]82[/C][C]33.0424568285719[/C][C]27.7797266028966[/C][C]38.3051870542472[/C][/ROW]
[ROW][C]83[/C][C]33.2028990619052[/C][C]27.6842267324426[/C][C]38.7215713913677[/C][/ROW]
[ROW][C]84[/C][C]33.6300559833535[/C][C]27.8663253195269[/C][C]39.3937866471802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77860&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77860&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
7330.928074845379429.165929577689332.6902201130696
7431.145025017706928.733402564675733.5566474707382
7531.048421787649728.127450420314433.969393154985
7631.461991568852328.107350916819334.8166322208854
7731.966045872239828.226988675064135.7051030694155
7832.268913418185228.180774045735436.3570527906350
7932.631246529312928.220960409332937.041532649293
8032.858488896025428.147461995270237.5695157967806
8133.138109379884228.143878581395538.132340178373
8233.042456828571927.779726602896638.3051870542472
8333.202899061905227.684226732442638.7215713913677
8433.630055983353527.866325319526939.3937866471802



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):
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')