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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 07:20:29 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t12599364788plxyn3eusumub8.htm/, Retrieved Sun, 28 Apr 2024 16:36:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63589, Retrieved Sun, 28 Apr 2024 16:36:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [WS9 Exponential s...] [2009-12-04 14:20:29] [c6e373ff11c42d4585d53e9e88ed5606] [Current]
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Dataseries X:
7.1
6.9
6.8
7.5
7.6
7.8
8.0
8.1
8.2
8.3
8.2
8.0
7.9
7.6
7.6
8.3
8.4
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.0
8.2
8.1
8.1
8.0
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.2




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63589&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63589&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63589&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]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63589&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
beta1
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.97.544856902550720.355143097449276
147.67.9583753600631-0.358375360063103
157.67.6-8.88178419700125e-16
168.38.287347560975610.0126524390243912
178.48.391515151515160.00848484848484432
188.48.41266968325791-0.0126696832579114
198.48.60279870828849-0.202798708288487
208.48.272119594233850.127880405766152
218.68.399096437539240.200903562460763
228.98.796189830945930.103810169054075
238.88.98232931726907-0.182329317269073
248.38.60118740657386-0.301187406573861
257.57.93479492873633-0.434794928736326
267.26.56231072672890.637689273271094
277.47.184918736504570.215081263495430
288.88.285793752674370.51420624732563
299.39.61602621010358-0.316026210103576
309.39.70384342801068-0.403843428010676
318.79.5245271413194-0.824527141319397
328.27.953148501258480.246851498741519
338.37.694761489066750.60523851093325
348.58.395577829144310.104422170855692
358.68.493554216867460.106445783132536
368.58.59333011416109-0.0933301141610894
378.28.51806716099568-0.318067160995684
388.17.71596941523010.384030584769903
397.98.30988091697806-0.409880916978059
408.68.39794541613180.202054583868204
418.78.667169155089260.0328308449107393
428.78.70954587581093-0.00954587581093058
438.58.91004151929879-0.410041519298787
448.48.16579589657540.234204103424608
458.58.298225145166360.201774854833642
468.78.595451974827870.104548025172129
478.78.68877510040160.0112248995983961
488.68.597258760367480.00274123963252393
498.58.61939915186189-0.119399151861886
508.38.196941393248510.103058606751489
5188.42190687992139-0.421906879921387
528.28.39872232028242-0.198722320282416
538.17.753139255586940.346860744413058
548.17.915520907158040.184479092841961
5588.29555589727818-0.295555897278181
567.97.775808481427810.124191518572191
577.97.798278928646160.101721071353839
5887.89502875450090.104971245499104
5987.90716867469880.0928313253012085
607.97.90552529688963-0.00552529688963332
6187.910075215798450.0899247842015463
627.77.89757326654945-0.197573266549445
637.27.70377031587386-0.503770315873858
647.57.309835660034240.190164339965764
657.37.219244826194730.080755173805267
6677.02371476857656-0.0237147685765633
6776.864524065815780.135475934184220
6876.893432995194870.106567004805127
697.26.99924703128270.200752968717303
707.37.39707081116096-0.0970708111609593
717.17.22389558232931-0.123895582329315
726.86.82637286098008-0.0263728609800795
736.46.60511919100673-0.205119191006725
746.15.86603196024110.233968039758905
756.56.043445261892140.45655473810786
767.77.520931616388530.179068383611465
777.98.38669837243712-0.486698372437122
787.58.01801232077631-0.518012320776311
796.97.27510379824697-0.375103798246966
806.66.180551445351230.419448554648769
816.96.29667618094790.603323819052103
827.77.198060375911880.501939624088116
8388.30267068273092-0.302670682730922
8488.19019655690384-0.190196556903835
857.78.1065592692964-0.406559269296396
867.37.228256849781670.0717431502183272
877.47.193174383574040.206825616425958
888.18.17752660997005-0.0775266099700502
898.38.207745815799080.0922541842009164
908.28.41384724418034-0.213847244180336

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.9 & 7.54485690255072 & 0.355143097449276 \tabularnewline
14 & 7.6 & 7.9583753600631 & -0.358375360063103 \tabularnewline
15 & 7.6 & 7.6 & -8.88178419700125e-16 \tabularnewline
16 & 8.3 & 8.28734756097561 & 0.0126524390243912 \tabularnewline
17 & 8.4 & 8.39151515151516 & 0.00848484848484432 \tabularnewline
18 & 8.4 & 8.41266968325791 & -0.0126696832579114 \tabularnewline
19 & 8.4 & 8.60279870828849 & -0.202798708288487 \tabularnewline
20 & 8.4 & 8.27211959423385 & 0.127880405766152 \tabularnewline
21 & 8.6 & 8.39909643753924 & 0.200903562460763 \tabularnewline
22 & 8.9 & 8.79618983094593 & 0.103810169054075 \tabularnewline
23 & 8.8 & 8.98232931726907 & -0.182329317269073 \tabularnewline
24 & 8.3 & 8.60118740657386 & -0.301187406573861 \tabularnewline
25 & 7.5 & 7.93479492873633 & -0.434794928736326 \tabularnewline
26 & 7.2 & 6.5623107267289 & 0.637689273271094 \tabularnewline
27 & 7.4 & 7.18491873650457 & 0.215081263495430 \tabularnewline
28 & 8.8 & 8.28579375267437 & 0.51420624732563 \tabularnewline
29 & 9.3 & 9.61602621010358 & -0.316026210103576 \tabularnewline
30 & 9.3 & 9.70384342801068 & -0.403843428010676 \tabularnewline
31 & 8.7 & 9.5245271413194 & -0.824527141319397 \tabularnewline
32 & 8.2 & 7.95314850125848 & 0.246851498741519 \tabularnewline
33 & 8.3 & 7.69476148906675 & 0.60523851093325 \tabularnewline
34 & 8.5 & 8.39557782914431 & 0.104422170855692 \tabularnewline
35 & 8.6 & 8.49355421686746 & 0.106445783132536 \tabularnewline
36 & 8.5 & 8.59333011416109 & -0.0933301141610894 \tabularnewline
37 & 8.2 & 8.51806716099568 & -0.318067160995684 \tabularnewline
38 & 8.1 & 7.7159694152301 & 0.384030584769903 \tabularnewline
39 & 7.9 & 8.30988091697806 & -0.409880916978059 \tabularnewline
40 & 8.6 & 8.3979454161318 & 0.202054583868204 \tabularnewline
41 & 8.7 & 8.66716915508926 & 0.0328308449107393 \tabularnewline
42 & 8.7 & 8.70954587581093 & -0.00954587581093058 \tabularnewline
43 & 8.5 & 8.91004151929879 & -0.410041519298787 \tabularnewline
44 & 8.4 & 8.1657958965754 & 0.234204103424608 \tabularnewline
45 & 8.5 & 8.29822514516636 & 0.201774854833642 \tabularnewline
46 & 8.7 & 8.59545197482787 & 0.104548025172129 \tabularnewline
47 & 8.7 & 8.6887751004016 & 0.0112248995983961 \tabularnewline
48 & 8.6 & 8.59725876036748 & 0.00274123963252393 \tabularnewline
49 & 8.5 & 8.61939915186189 & -0.119399151861886 \tabularnewline
50 & 8.3 & 8.19694139324851 & 0.103058606751489 \tabularnewline
51 & 8 & 8.42190687992139 & -0.421906879921387 \tabularnewline
52 & 8.2 & 8.39872232028242 & -0.198722320282416 \tabularnewline
53 & 8.1 & 7.75313925558694 & 0.346860744413058 \tabularnewline
54 & 8.1 & 7.91552090715804 & 0.184479092841961 \tabularnewline
55 & 8 & 8.29555589727818 & -0.295555897278181 \tabularnewline
56 & 7.9 & 7.77580848142781 & 0.124191518572191 \tabularnewline
57 & 7.9 & 7.79827892864616 & 0.101721071353839 \tabularnewline
58 & 8 & 7.8950287545009 & 0.104971245499104 \tabularnewline
59 & 8 & 7.9071686746988 & 0.0928313253012085 \tabularnewline
60 & 7.9 & 7.90552529688963 & -0.00552529688963332 \tabularnewline
61 & 8 & 7.91007521579845 & 0.0899247842015463 \tabularnewline
62 & 7.7 & 7.89757326654945 & -0.197573266549445 \tabularnewline
63 & 7.2 & 7.70377031587386 & -0.503770315873858 \tabularnewline
64 & 7.5 & 7.30983566003424 & 0.190164339965764 \tabularnewline
65 & 7.3 & 7.21924482619473 & 0.080755173805267 \tabularnewline
66 & 7 & 7.02371476857656 & -0.0237147685765633 \tabularnewline
67 & 7 & 6.86452406581578 & 0.135475934184220 \tabularnewline
68 & 7 & 6.89343299519487 & 0.106567004805127 \tabularnewline
69 & 7.2 & 6.9992470312827 & 0.200752968717303 \tabularnewline
70 & 7.3 & 7.39707081116096 & -0.0970708111609593 \tabularnewline
71 & 7.1 & 7.22389558232931 & -0.123895582329315 \tabularnewline
72 & 6.8 & 6.82637286098008 & -0.0263728609800795 \tabularnewline
73 & 6.4 & 6.60511919100673 & -0.205119191006725 \tabularnewline
74 & 6.1 & 5.8660319602411 & 0.233968039758905 \tabularnewline
75 & 6.5 & 6.04344526189214 & 0.45655473810786 \tabularnewline
76 & 7.7 & 7.52093161638853 & 0.179068383611465 \tabularnewline
77 & 7.9 & 8.38669837243712 & -0.486698372437122 \tabularnewline
78 & 7.5 & 8.01801232077631 & -0.518012320776311 \tabularnewline
79 & 6.9 & 7.27510379824697 & -0.375103798246966 \tabularnewline
80 & 6.6 & 6.18055144535123 & 0.419448554648769 \tabularnewline
81 & 6.9 & 6.2966761809479 & 0.603323819052103 \tabularnewline
82 & 7.7 & 7.19806037591188 & 0.501939624088116 \tabularnewline
83 & 8 & 8.30267068273092 & -0.302670682730922 \tabularnewline
84 & 8 & 8.19019655690384 & -0.190196556903835 \tabularnewline
85 & 7.7 & 8.1065592692964 & -0.406559269296396 \tabularnewline
86 & 7.3 & 7.22825684978167 & 0.0717431502183272 \tabularnewline
87 & 7.4 & 7.19317438357404 & 0.206825616425958 \tabularnewline
88 & 8.1 & 8.17752660997005 & -0.0775266099700502 \tabularnewline
89 & 8.3 & 8.20774581579908 & 0.0922541842009164 \tabularnewline
90 & 8.2 & 8.41384724418034 & -0.213847244180336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63589&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]7.9[/C][C]7.54485690255072[/C][C]0.355143097449276[/C][/ROW]
[ROW][C]14[/C][C]7.6[/C][C]7.9583753600631[/C][C]-0.358375360063103[/C][/ROW]
[ROW][C]15[/C][C]7.6[/C][C]7.6[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.28734756097561[/C][C]0.0126524390243912[/C][/ROW]
[ROW][C]17[/C][C]8.4[/C][C]8.39151515151516[/C][C]0.00848484848484432[/C][/ROW]
[ROW][C]18[/C][C]8.4[/C][C]8.41266968325791[/C][C]-0.0126696832579114[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.60279870828849[/C][C]-0.202798708288487[/C][/ROW]
[ROW][C]20[/C][C]8.4[/C][C]8.27211959423385[/C][C]0.127880405766152[/C][/ROW]
[ROW][C]21[/C][C]8.6[/C][C]8.39909643753924[/C][C]0.200903562460763[/C][/ROW]
[ROW][C]22[/C][C]8.9[/C][C]8.79618983094593[/C][C]0.103810169054075[/C][/ROW]
[ROW][C]23[/C][C]8.8[/C][C]8.98232931726907[/C][C]-0.182329317269073[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]8.60118740657386[/C][C]-0.301187406573861[/C][/ROW]
[ROW][C]25[/C][C]7.5[/C][C]7.93479492873633[/C][C]-0.434794928736326[/C][/ROW]
[ROW][C]26[/C][C]7.2[/C][C]6.5623107267289[/C][C]0.637689273271094[/C][/ROW]
[ROW][C]27[/C][C]7.4[/C][C]7.18491873650457[/C][C]0.215081263495430[/C][/ROW]
[ROW][C]28[/C][C]8.8[/C][C]8.28579375267437[/C][C]0.51420624732563[/C][/ROW]
[ROW][C]29[/C][C]9.3[/C][C]9.61602621010358[/C][C]-0.316026210103576[/C][/ROW]
[ROW][C]30[/C][C]9.3[/C][C]9.70384342801068[/C][C]-0.403843428010676[/C][/ROW]
[ROW][C]31[/C][C]8.7[/C][C]9.5245271413194[/C][C]-0.824527141319397[/C][/ROW]
[ROW][C]32[/C][C]8.2[/C][C]7.95314850125848[/C][C]0.246851498741519[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]7.69476148906675[/C][C]0.60523851093325[/C][/ROW]
[ROW][C]34[/C][C]8.5[/C][C]8.39557782914431[/C][C]0.104422170855692[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.49355421686746[/C][C]0.106445783132536[/C][/ROW]
[ROW][C]36[/C][C]8.5[/C][C]8.59333011416109[/C][C]-0.0933301141610894[/C][/ROW]
[ROW][C]37[/C][C]8.2[/C][C]8.51806716099568[/C][C]-0.318067160995684[/C][/ROW]
[ROW][C]38[/C][C]8.1[/C][C]7.7159694152301[/C][C]0.384030584769903[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]8.30988091697806[/C][C]-0.409880916978059[/C][/ROW]
[ROW][C]40[/C][C]8.6[/C][C]8.3979454161318[/C][C]0.202054583868204[/C][/ROW]
[ROW][C]41[/C][C]8.7[/C][C]8.66716915508926[/C][C]0.0328308449107393[/C][/ROW]
[ROW][C]42[/C][C]8.7[/C][C]8.70954587581093[/C][C]-0.00954587581093058[/C][/ROW]
[ROW][C]43[/C][C]8.5[/C][C]8.91004151929879[/C][C]-0.410041519298787[/C][/ROW]
[ROW][C]44[/C][C]8.4[/C][C]8.1657958965754[/C][C]0.234204103424608[/C][/ROW]
[ROW][C]45[/C][C]8.5[/C][C]8.29822514516636[/C][C]0.201774854833642[/C][/ROW]
[ROW][C]46[/C][C]8.7[/C][C]8.59545197482787[/C][C]0.104548025172129[/C][/ROW]
[ROW][C]47[/C][C]8.7[/C][C]8.6887751004016[/C][C]0.0112248995983961[/C][/ROW]
[ROW][C]48[/C][C]8.6[/C][C]8.59725876036748[/C][C]0.00274123963252393[/C][/ROW]
[ROW][C]49[/C][C]8.5[/C][C]8.61939915186189[/C][C]-0.119399151861886[/C][/ROW]
[ROW][C]50[/C][C]8.3[/C][C]8.19694139324851[/C][C]0.103058606751489[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.42190687992139[/C][C]-0.421906879921387[/C][/ROW]
[ROW][C]52[/C][C]8.2[/C][C]8.39872232028242[/C][C]-0.198722320282416[/C][/ROW]
[ROW][C]53[/C][C]8.1[/C][C]7.75313925558694[/C][C]0.346860744413058[/C][/ROW]
[ROW][C]54[/C][C]8.1[/C][C]7.91552090715804[/C][C]0.184479092841961[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]8.29555589727818[/C][C]-0.295555897278181[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]7.77580848142781[/C][C]0.124191518572191[/C][/ROW]
[ROW][C]57[/C][C]7.9[/C][C]7.79827892864616[/C][C]0.101721071353839[/C][/ROW]
[ROW][C]58[/C][C]8[/C][C]7.8950287545009[/C][C]0.104971245499104[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]7.9071686746988[/C][C]0.0928313253012085[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.90552529688963[/C][C]-0.00552529688963332[/C][/ROW]
[ROW][C]61[/C][C]8[/C][C]7.91007521579845[/C][C]0.0899247842015463[/C][/ROW]
[ROW][C]62[/C][C]7.7[/C][C]7.89757326654945[/C][C]-0.197573266549445[/C][/ROW]
[ROW][C]63[/C][C]7.2[/C][C]7.70377031587386[/C][C]-0.503770315873858[/C][/ROW]
[ROW][C]64[/C][C]7.5[/C][C]7.30983566003424[/C][C]0.190164339965764[/C][/ROW]
[ROW][C]65[/C][C]7.3[/C][C]7.21924482619473[/C][C]0.080755173805267[/C][/ROW]
[ROW][C]66[/C][C]7[/C][C]7.02371476857656[/C][C]-0.0237147685765633[/C][/ROW]
[ROW][C]67[/C][C]7[/C][C]6.86452406581578[/C][C]0.135475934184220[/C][/ROW]
[ROW][C]68[/C][C]7[/C][C]6.89343299519487[/C][C]0.106567004805127[/C][/ROW]
[ROW][C]69[/C][C]7.2[/C][C]6.9992470312827[/C][C]0.200752968717303[/C][/ROW]
[ROW][C]70[/C][C]7.3[/C][C]7.39707081116096[/C][C]-0.0970708111609593[/C][/ROW]
[ROW][C]71[/C][C]7.1[/C][C]7.22389558232931[/C][C]-0.123895582329315[/C][/ROW]
[ROW][C]72[/C][C]6.8[/C][C]6.82637286098008[/C][C]-0.0263728609800795[/C][/ROW]
[ROW][C]73[/C][C]6.4[/C][C]6.60511919100673[/C][C]-0.205119191006725[/C][/ROW]
[ROW][C]74[/C][C]6.1[/C][C]5.8660319602411[/C][C]0.233968039758905[/C][/ROW]
[ROW][C]75[/C][C]6.5[/C][C]6.04344526189214[/C][C]0.45655473810786[/C][/ROW]
[ROW][C]76[/C][C]7.7[/C][C]7.52093161638853[/C][C]0.179068383611465[/C][/ROW]
[ROW][C]77[/C][C]7.9[/C][C]8.38669837243712[/C][C]-0.486698372437122[/C][/ROW]
[ROW][C]78[/C][C]7.5[/C][C]8.01801232077631[/C][C]-0.518012320776311[/C][/ROW]
[ROW][C]79[/C][C]6.9[/C][C]7.27510379824697[/C][C]-0.375103798246966[/C][/ROW]
[ROW][C]80[/C][C]6.6[/C][C]6.18055144535123[/C][C]0.419448554648769[/C][/ROW]
[ROW][C]81[/C][C]6.9[/C][C]6.2966761809479[/C][C]0.603323819052103[/C][/ROW]
[ROW][C]82[/C][C]7.7[/C][C]7.19806037591188[/C][C]0.501939624088116[/C][/ROW]
[ROW][C]83[/C][C]8[/C][C]8.30267068273092[/C][C]-0.302670682730922[/C][/ROW]
[ROW][C]84[/C][C]8[/C][C]8.19019655690384[/C][C]-0.190196556903835[/C][/ROW]
[ROW][C]85[/C][C]7.7[/C][C]8.1065592692964[/C][C]-0.406559269296396[/C][/ROW]
[ROW][C]86[/C][C]7.3[/C][C]7.22825684978167[/C][C]0.0717431502183272[/C][/ROW]
[ROW][C]87[/C][C]7.4[/C][C]7.19317438357404[/C][C]0.206825616425958[/C][/ROW]
[ROW][C]88[/C][C]8.1[/C][C]8.17752660997005[/C][C]-0.0775266099700502[/C][/ROW]
[ROW][C]89[/C][C]8.3[/C][C]8.20774581579908[/C][C]0.0922541842009164[/C][/ROW]
[ROW][C]90[/C][C]8.2[/C][C]8.41384724418034[/C][C]-0.213847244180336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63589&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
137.97.544856902550720.355143097449276
147.67.9583753600631-0.358375360063103
157.67.6-8.88178419700125e-16
168.38.287347560975610.0126524390243912
178.48.391515151515160.00848484848484432
188.48.41266968325791-0.0126696832579114
198.48.60279870828849-0.202798708288487
208.48.272119594233850.127880405766152
218.68.399096437539240.200903562460763
228.98.796189830945930.103810169054075
238.88.98232931726907-0.182329317269073
248.38.60118740657386-0.301187406573861
257.57.93479492873633-0.434794928736326
267.26.56231072672890.637689273271094
277.47.184918736504570.215081263495430
288.88.285793752674370.51420624732563
299.39.61602621010358-0.316026210103576
309.39.70384342801068-0.403843428010676
318.79.5245271413194-0.824527141319397
328.27.953148501258480.246851498741519
338.37.694761489066750.60523851093325
348.58.395577829144310.104422170855692
358.68.493554216867460.106445783132536
368.58.59333011416109-0.0933301141610894
378.28.51806716099568-0.318067160995684
388.17.71596941523010.384030584769903
397.98.30988091697806-0.409880916978059
408.68.39794541613180.202054583868204
418.78.667169155089260.0328308449107393
428.78.70954587581093-0.00954587581093058
438.58.91004151929879-0.410041519298787
448.48.16579589657540.234204103424608
458.58.298225145166360.201774854833642
468.78.595451974827870.104548025172129
478.78.68877510040160.0112248995983961
488.68.597258760367480.00274123963252393
498.58.61939915186189-0.119399151861886
508.38.196941393248510.103058606751489
5188.42190687992139-0.421906879921387
528.28.39872232028242-0.198722320282416
538.17.753139255586940.346860744413058
548.17.915520907158040.184479092841961
5588.29555589727818-0.295555897278181
567.97.775808481427810.124191518572191
577.97.798278928646160.101721071353839
5887.89502875450090.104971245499104
5987.90716867469880.0928313253012085
607.97.90552529688963-0.00552529688963332
6187.910075215798450.0899247842015463
627.77.89757326654945-0.197573266549445
637.27.70377031587386-0.503770315873858
647.57.309835660034240.190164339965764
657.37.219244826194730.080755173805267
6677.02371476857656-0.0237147685765633
6776.864524065815780.135475934184220
6876.893432995194870.106567004805127
697.26.99924703128270.200752968717303
707.37.39707081116096-0.0970708111609593
717.17.22389558232931-0.123895582329315
726.86.82637286098008-0.0263728609800795
736.46.60511919100673-0.205119191006725
746.15.86603196024110.233968039758905
756.56.043445261892140.45655473810786
767.77.520931616388530.179068383611465
777.98.38669837243712-0.486698372437122
787.58.01801232077631-0.518012320776311
796.97.27510379824697-0.375103798246966
806.66.180551445351230.419448554648769
816.96.29667618094790.603323819052103
827.77.198060375911880.501939624088116
8388.30267068273092-0.302670682730922
8488.19019655690384-0.190196556903835
857.78.1065592692964-0.406559269296396
867.37.228256849781670.0717431502183272
877.47.193174383574040.206825616425958
888.18.17752660997005-0.0775266099700502
898.38.207745815799080.0922541842009164
908.28.41384724418034-0.213847244180336







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
918.29647854836237.71946060086188.87349649586279
928.268968804820386.974182709420299.56375490022047
938.24032990314776.066571387303910.4140884189915
948.206276260504215.0156925900294611.3968599309790
957.976696428571433.7465952041657212.2067976529771
967.664647658442912.392964839362312.9363304775235
977.46981922398591.0382742847655813.9013641632062
987.10277513363111-0.35466256536112714.5602128326234
997.01999124471036-1.7874449791850015.8274274686057
1007.56525479094078-3.5906500405984318.72115962248
1017.54727272727274-5.3532338377277620.4477792922733
1027.45067873303169-9.8924290141020524.7937864801654

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 8.2964785483623 & 7.7194606008618 & 8.87349649586279 \tabularnewline
92 & 8.26896880482038 & 6.97418270942029 & 9.56375490022047 \tabularnewline
93 & 8.2403299031477 & 6.0665713873039 & 10.4140884189915 \tabularnewline
94 & 8.20627626050421 & 5.01569259002946 & 11.3968599309790 \tabularnewline
95 & 7.97669642857143 & 3.74659520416572 & 12.2067976529771 \tabularnewline
96 & 7.66464765844291 & 2.3929648393623 & 12.9363304775235 \tabularnewline
97 & 7.4698192239859 & 1.03827428476558 & 13.9013641632062 \tabularnewline
98 & 7.10277513363111 & -0.354662565361127 & 14.5602128326234 \tabularnewline
99 & 7.01999124471036 & -1.78744497918500 & 15.8274274686057 \tabularnewline
100 & 7.56525479094078 & -3.59065004059843 & 18.72115962248 \tabularnewline
101 & 7.54727272727274 & -5.35323383772776 & 20.4477792922733 \tabularnewline
102 & 7.45067873303169 & -9.89242901410205 & 24.7937864801654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63589&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]91[/C][C]8.2964785483623[/C][C]7.7194606008618[/C][C]8.87349649586279[/C][/ROW]
[ROW][C]92[/C][C]8.26896880482038[/C][C]6.97418270942029[/C][C]9.56375490022047[/C][/ROW]
[ROW][C]93[/C][C]8.2403299031477[/C][C]6.0665713873039[/C][C]10.4140884189915[/C][/ROW]
[ROW][C]94[/C][C]8.20627626050421[/C][C]5.01569259002946[/C][C]11.3968599309790[/C][/ROW]
[ROW][C]95[/C][C]7.97669642857143[/C][C]3.74659520416572[/C][C]12.2067976529771[/C][/ROW]
[ROW][C]96[/C][C]7.66464765844291[/C][C]2.3929648393623[/C][C]12.9363304775235[/C][/ROW]
[ROW][C]97[/C][C]7.4698192239859[/C][C]1.03827428476558[/C][C]13.9013641632062[/C][/ROW]
[ROW][C]98[/C][C]7.10277513363111[/C][C]-0.354662565361127[/C][C]14.5602128326234[/C][/ROW]
[ROW][C]99[/C][C]7.01999124471036[/C][C]-1.78744497918500[/C][C]15.8274274686057[/C][/ROW]
[ROW][C]100[/C][C]7.56525479094078[/C][C]-3.59065004059843[/C][C]18.72115962248[/C][/ROW]
[ROW][C]101[/C][C]7.54727272727274[/C][C]-5.35323383772776[/C][C]20.4477792922733[/C][/ROW]
[ROW][C]102[/C][C]7.45067873303169[/C][C]-9.89242901410205[/C][C]24.7937864801654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63589&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63589&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
918.29647854836237.71946060086188.87349649586279
928.268968804820386.974182709420299.56375490022047
938.24032990314776.066571387303910.4140884189915
948.206276260504215.0156925900294611.3968599309790
957.976696428571433.7465952041657212.2067976529771
967.664647658442912.392964839362312.9363304775235
977.46981922398591.0382742847655813.9013641632062
987.10277513363111-0.35466256536112714.5602128326234
997.01999124471036-1.7874449791850015.8274274686057
1007.56525479094078-3.5906500405984318.72115962248
1017.54727272727274-5.3532338377277620.4477792922733
1027.45067873303169-9.8924290141020524.7937864801654



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')