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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 13:04:57 -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/2011/Dec/19/t1324318190dvjc7cso07ttob9.htm/, Retrieved Wed, 15 May 2024 20:13:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157580, Retrieved Wed, 15 May 2024 20:13:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde consum...] [2011-12-19 18:04:57] [e00fba6fedfb8a49e13346f7099a23fc] [Current]
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Dataseries X:
20,61
20,61
20,61
20,61
20,61
20,61
20,61
19,47
19,47
19,47
19,47
19,47
98,19
98,19
98,19
98,19
98,19
98,19
98,19
100,48
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
104,47
104,47
104,47
104,47
104,47
104,47
104,47
104,47
105,5
105,5
105,5
105,5
106,61
106,61
106,61
106,61
106,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157580&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157580&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.9992915151629
beta0.00156046725333177
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.9992915151629 \tabularnewline
beta & 0.00156046725333177 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157580&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]0.9992915151629[/C][/ROW]
[ROW][C]beta[/C][C]0.00156046725333177[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157580&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
alpha0.9992915151629
beta0.00156046725333177
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
320.6120.610
420.6120.610
520.6120.610
620.6120.610
720.6120.610
819.4720.61-1.14
919.4719.46903000039230.000969999607679739
1019.4719.46822315302820.00177684697176517
1119.4719.46822535213620.00177464786380099
1219.4719.46822812101210.00177187898788134
1398.1919.46823088597478.721769114026
1498.1998.2552146721626-0.065214672162611
1598.1998.3109323622748-0.120932362274829
1698.1998.3107832601211-0.120783260121101
1798.1998.3105948096963-0.120594809696343
1898.1998.3104066252563-0.120406625256322
1998.1998.3102187344523-0.120218734452337
20100.4898.31003113684612.1699688631539
21102.78100.6017923399642.17820766003601
22102.78102.90518311647-0.12518311647041
23102.78102.906619828154-0.126619828153935
24102.78102.906423399934-0.126423399933671
25102.78102.906226120961-0.126226120961192
26102.78102.906029149015-0.126029149015238
27102.78102.905832484437-0.125832484437311
28102.78102.905636126748-0.125636126748361
29102.78102.905440075469-0.125440075469498
30102.78102.905244330123-0.12524433012257
31102.78102.90504889023-0.125048890230175
32101.67102.904853755316-1.2348537553157
33101.67101.793714451601-0.123714451600947
34101.67101.792734310677-0.122734310676549
35101.67101.79254222908-0.12254222907994
36101.67101.792351005336-0.122351005336114
37101.67101.792160080387-0.122160080387019
38101.67101.791969453371-0.121969453370696
39101.67101.791779123822-0.121779123821895
40101.67101.791589091276-0.121589091276462
41101.67101.791399355271-0.12139935527091
42101.67101.791209915343-0.121209915342533
43101.67101.791020771029-0.121020771029279
44105.79101.790831921873.99916807813015
45105.79105.914148980021-0.124148980020919
46105.79105.916876694472-0.126876694472386
47105.79105.916680780361-0.126680780360502
48105.79105.916483100403-0.126483100403078
49105.79105.916285727449-0.126285727449158
50105.79105.916088662489-0.126088662488542
51105.79105.915891905042-0.125891905041684
52105.79105.915695454629-0.125695454628726
53105.79105.915499310771-0.125499310770536
54105.79105.915303472989-0.125303472988762
55105.79105.915107940806-0.125107940805776
56104.47105.914912713745-1.44491271374469
57104.47104.593594633889-0.123594633888899
58104.47104.592465771328-0.122465771327654
59104.47104.592274003114-0.122274003114001
60104.47104.592083197853-0.122083197853485
61104.47104.59189269081-0.121892690809631
62104.47104.591702481046-0.121702481046427
63104.47104.5915125681-0.121512568099661
64105.5104.5913229515060.908677048493843
65105.5105.622010033958-0.122010033957793
66105.5105.622550002355-0.12255000235524
67105.5105.622359285136-0.122359285136383
68106.61105.6221683476350.987831652365045
69106.61106.73292218102-0.122922181020314
70106.61106.73351745313-0.123517453129594
71106.61106.733325266487-0.123325266486901
72106.61106.73313282163-0.123132821630094

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 20.61 & 20.61 & 0 \tabularnewline
4 & 20.61 & 20.61 & 0 \tabularnewline
5 & 20.61 & 20.61 & 0 \tabularnewline
6 & 20.61 & 20.61 & 0 \tabularnewline
7 & 20.61 & 20.61 & 0 \tabularnewline
8 & 19.47 & 20.61 & -1.14 \tabularnewline
9 & 19.47 & 19.4690300003923 & 0.000969999607679739 \tabularnewline
10 & 19.47 & 19.4682231530282 & 0.00177684697176517 \tabularnewline
11 & 19.47 & 19.4682253521362 & 0.00177464786380099 \tabularnewline
12 & 19.47 & 19.4682281210121 & 0.00177187898788134 \tabularnewline
13 & 98.19 & 19.468230885974 & 78.721769114026 \tabularnewline
14 & 98.19 & 98.2552146721626 & -0.065214672162611 \tabularnewline
15 & 98.19 & 98.3109323622748 & -0.120932362274829 \tabularnewline
16 & 98.19 & 98.3107832601211 & -0.120783260121101 \tabularnewline
17 & 98.19 & 98.3105948096963 & -0.120594809696343 \tabularnewline
18 & 98.19 & 98.3104066252563 & -0.120406625256322 \tabularnewline
19 & 98.19 & 98.3102187344523 & -0.120218734452337 \tabularnewline
20 & 100.48 & 98.3100311368461 & 2.1699688631539 \tabularnewline
21 & 102.78 & 100.601792339964 & 2.17820766003601 \tabularnewline
22 & 102.78 & 102.90518311647 & -0.12518311647041 \tabularnewline
23 & 102.78 & 102.906619828154 & -0.126619828153935 \tabularnewline
24 & 102.78 & 102.906423399934 & -0.126423399933671 \tabularnewline
25 & 102.78 & 102.906226120961 & -0.126226120961192 \tabularnewline
26 & 102.78 & 102.906029149015 & -0.126029149015238 \tabularnewline
27 & 102.78 & 102.905832484437 & -0.125832484437311 \tabularnewline
28 & 102.78 & 102.905636126748 & -0.125636126748361 \tabularnewline
29 & 102.78 & 102.905440075469 & -0.125440075469498 \tabularnewline
30 & 102.78 & 102.905244330123 & -0.12524433012257 \tabularnewline
31 & 102.78 & 102.90504889023 & -0.125048890230175 \tabularnewline
32 & 101.67 & 102.904853755316 & -1.2348537553157 \tabularnewline
33 & 101.67 & 101.793714451601 & -0.123714451600947 \tabularnewline
34 & 101.67 & 101.792734310677 & -0.122734310676549 \tabularnewline
35 & 101.67 & 101.79254222908 & -0.12254222907994 \tabularnewline
36 & 101.67 & 101.792351005336 & -0.122351005336114 \tabularnewline
37 & 101.67 & 101.792160080387 & -0.122160080387019 \tabularnewline
38 & 101.67 & 101.791969453371 & -0.121969453370696 \tabularnewline
39 & 101.67 & 101.791779123822 & -0.121779123821895 \tabularnewline
40 & 101.67 & 101.791589091276 & -0.121589091276462 \tabularnewline
41 & 101.67 & 101.791399355271 & -0.12139935527091 \tabularnewline
42 & 101.67 & 101.791209915343 & -0.121209915342533 \tabularnewline
43 & 101.67 & 101.791020771029 & -0.121020771029279 \tabularnewline
44 & 105.79 & 101.79083192187 & 3.99916807813015 \tabularnewline
45 & 105.79 & 105.914148980021 & -0.124148980020919 \tabularnewline
46 & 105.79 & 105.916876694472 & -0.126876694472386 \tabularnewline
47 & 105.79 & 105.916680780361 & -0.126680780360502 \tabularnewline
48 & 105.79 & 105.916483100403 & -0.126483100403078 \tabularnewline
49 & 105.79 & 105.916285727449 & -0.126285727449158 \tabularnewline
50 & 105.79 & 105.916088662489 & -0.126088662488542 \tabularnewline
51 & 105.79 & 105.915891905042 & -0.125891905041684 \tabularnewline
52 & 105.79 & 105.915695454629 & -0.125695454628726 \tabularnewline
53 & 105.79 & 105.915499310771 & -0.125499310770536 \tabularnewline
54 & 105.79 & 105.915303472989 & -0.125303472988762 \tabularnewline
55 & 105.79 & 105.915107940806 & -0.125107940805776 \tabularnewline
56 & 104.47 & 105.914912713745 & -1.44491271374469 \tabularnewline
57 & 104.47 & 104.593594633889 & -0.123594633888899 \tabularnewline
58 & 104.47 & 104.592465771328 & -0.122465771327654 \tabularnewline
59 & 104.47 & 104.592274003114 & -0.122274003114001 \tabularnewline
60 & 104.47 & 104.592083197853 & -0.122083197853485 \tabularnewline
61 & 104.47 & 104.59189269081 & -0.121892690809631 \tabularnewline
62 & 104.47 & 104.591702481046 & -0.121702481046427 \tabularnewline
63 & 104.47 & 104.5915125681 & -0.121512568099661 \tabularnewline
64 & 105.5 & 104.591322951506 & 0.908677048493843 \tabularnewline
65 & 105.5 & 105.622010033958 & -0.122010033957793 \tabularnewline
66 & 105.5 & 105.622550002355 & -0.12255000235524 \tabularnewline
67 & 105.5 & 105.622359285136 & -0.122359285136383 \tabularnewline
68 & 106.61 & 105.622168347635 & 0.987831652365045 \tabularnewline
69 & 106.61 & 106.73292218102 & -0.122922181020314 \tabularnewline
70 & 106.61 & 106.73351745313 & -0.123517453129594 \tabularnewline
71 & 106.61 & 106.733325266487 & -0.123325266486901 \tabularnewline
72 & 106.61 & 106.73313282163 & -0.123132821630094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157580&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]19.47[/C][C]20.61[/C][C]-1.14[/C][/ROW]
[ROW][C]9[/C][C]19.47[/C][C]19.4690300003923[/C][C]0.000969999607679739[/C][/ROW]
[ROW][C]10[/C][C]19.47[/C][C]19.4682231530282[/C][C]0.00177684697176517[/C][/ROW]
[ROW][C]11[/C][C]19.47[/C][C]19.4682253521362[/C][C]0.00177464786380099[/C][/ROW]
[ROW][C]12[/C][C]19.47[/C][C]19.4682281210121[/C][C]0.00177187898788134[/C][/ROW]
[ROW][C]13[/C][C]98.19[/C][C]19.468230885974[/C][C]78.721769114026[/C][/ROW]
[ROW][C]14[/C][C]98.19[/C][C]98.2552146721626[/C][C]-0.065214672162611[/C][/ROW]
[ROW][C]15[/C][C]98.19[/C][C]98.3109323622748[/C][C]-0.120932362274829[/C][/ROW]
[ROW][C]16[/C][C]98.19[/C][C]98.3107832601211[/C][C]-0.120783260121101[/C][/ROW]
[ROW][C]17[/C][C]98.19[/C][C]98.3105948096963[/C][C]-0.120594809696343[/C][/ROW]
[ROW][C]18[/C][C]98.19[/C][C]98.3104066252563[/C][C]-0.120406625256322[/C][/ROW]
[ROW][C]19[/C][C]98.19[/C][C]98.3102187344523[/C][C]-0.120218734452337[/C][/ROW]
[ROW][C]20[/C][C]100.48[/C][C]98.3100311368461[/C][C]2.1699688631539[/C][/ROW]
[ROW][C]21[/C][C]102.78[/C][C]100.601792339964[/C][C]2.17820766003601[/C][/ROW]
[ROW][C]22[/C][C]102.78[/C][C]102.90518311647[/C][C]-0.12518311647041[/C][/ROW]
[ROW][C]23[/C][C]102.78[/C][C]102.906619828154[/C][C]-0.126619828153935[/C][/ROW]
[ROW][C]24[/C][C]102.78[/C][C]102.906423399934[/C][C]-0.126423399933671[/C][/ROW]
[ROW][C]25[/C][C]102.78[/C][C]102.906226120961[/C][C]-0.126226120961192[/C][/ROW]
[ROW][C]26[/C][C]102.78[/C][C]102.906029149015[/C][C]-0.126029149015238[/C][/ROW]
[ROW][C]27[/C][C]102.78[/C][C]102.905832484437[/C][C]-0.125832484437311[/C][/ROW]
[ROW][C]28[/C][C]102.78[/C][C]102.905636126748[/C][C]-0.125636126748361[/C][/ROW]
[ROW][C]29[/C][C]102.78[/C][C]102.905440075469[/C][C]-0.125440075469498[/C][/ROW]
[ROW][C]30[/C][C]102.78[/C][C]102.905244330123[/C][C]-0.12524433012257[/C][/ROW]
[ROW][C]31[/C][C]102.78[/C][C]102.90504889023[/C][C]-0.125048890230175[/C][/ROW]
[ROW][C]32[/C][C]101.67[/C][C]102.904853755316[/C][C]-1.2348537553157[/C][/ROW]
[ROW][C]33[/C][C]101.67[/C][C]101.793714451601[/C][C]-0.123714451600947[/C][/ROW]
[ROW][C]34[/C][C]101.67[/C][C]101.792734310677[/C][C]-0.122734310676549[/C][/ROW]
[ROW][C]35[/C][C]101.67[/C][C]101.79254222908[/C][C]-0.12254222907994[/C][/ROW]
[ROW][C]36[/C][C]101.67[/C][C]101.792351005336[/C][C]-0.122351005336114[/C][/ROW]
[ROW][C]37[/C][C]101.67[/C][C]101.792160080387[/C][C]-0.122160080387019[/C][/ROW]
[ROW][C]38[/C][C]101.67[/C][C]101.791969453371[/C][C]-0.121969453370696[/C][/ROW]
[ROW][C]39[/C][C]101.67[/C][C]101.791779123822[/C][C]-0.121779123821895[/C][/ROW]
[ROW][C]40[/C][C]101.67[/C][C]101.791589091276[/C][C]-0.121589091276462[/C][/ROW]
[ROW][C]41[/C][C]101.67[/C][C]101.791399355271[/C][C]-0.12139935527091[/C][/ROW]
[ROW][C]42[/C][C]101.67[/C][C]101.791209915343[/C][C]-0.121209915342533[/C][/ROW]
[ROW][C]43[/C][C]101.67[/C][C]101.791020771029[/C][C]-0.121020771029279[/C][/ROW]
[ROW][C]44[/C][C]105.79[/C][C]101.79083192187[/C][C]3.99916807813015[/C][/ROW]
[ROW][C]45[/C][C]105.79[/C][C]105.914148980021[/C][C]-0.124148980020919[/C][/ROW]
[ROW][C]46[/C][C]105.79[/C][C]105.916876694472[/C][C]-0.126876694472386[/C][/ROW]
[ROW][C]47[/C][C]105.79[/C][C]105.916680780361[/C][C]-0.126680780360502[/C][/ROW]
[ROW][C]48[/C][C]105.79[/C][C]105.916483100403[/C][C]-0.126483100403078[/C][/ROW]
[ROW][C]49[/C][C]105.79[/C][C]105.916285727449[/C][C]-0.126285727449158[/C][/ROW]
[ROW][C]50[/C][C]105.79[/C][C]105.916088662489[/C][C]-0.126088662488542[/C][/ROW]
[ROW][C]51[/C][C]105.79[/C][C]105.915891905042[/C][C]-0.125891905041684[/C][/ROW]
[ROW][C]52[/C][C]105.79[/C][C]105.915695454629[/C][C]-0.125695454628726[/C][/ROW]
[ROW][C]53[/C][C]105.79[/C][C]105.915499310771[/C][C]-0.125499310770536[/C][/ROW]
[ROW][C]54[/C][C]105.79[/C][C]105.915303472989[/C][C]-0.125303472988762[/C][/ROW]
[ROW][C]55[/C][C]105.79[/C][C]105.915107940806[/C][C]-0.125107940805776[/C][/ROW]
[ROW][C]56[/C][C]104.47[/C][C]105.914912713745[/C][C]-1.44491271374469[/C][/ROW]
[ROW][C]57[/C][C]104.47[/C][C]104.593594633889[/C][C]-0.123594633888899[/C][/ROW]
[ROW][C]58[/C][C]104.47[/C][C]104.592465771328[/C][C]-0.122465771327654[/C][/ROW]
[ROW][C]59[/C][C]104.47[/C][C]104.592274003114[/C][C]-0.122274003114001[/C][/ROW]
[ROW][C]60[/C][C]104.47[/C][C]104.592083197853[/C][C]-0.122083197853485[/C][/ROW]
[ROW][C]61[/C][C]104.47[/C][C]104.59189269081[/C][C]-0.121892690809631[/C][/ROW]
[ROW][C]62[/C][C]104.47[/C][C]104.591702481046[/C][C]-0.121702481046427[/C][/ROW]
[ROW][C]63[/C][C]104.47[/C][C]104.5915125681[/C][C]-0.121512568099661[/C][/ROW]
[ROW][C]64[/C][C]105.5[/C][C]104.591322951506[/C][C]0.908677048493843[/C][/ROW]
[ROW][C]65[/C][C]105.5[/C][C]105.622010033958[/C][C]-0.122010033957793[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]105.622550002355[/C][C]-0.12255000235524[/C][/ROW]
[ROW][C]67[/C][C]105.5[/C][C]105.622359285136[/C][C]-0.122359285136383[/C][/ROW]
[ROW][C]68[/C][C]106.61[/C][C]105.622168347635[/C][C]0.987831652365045[/C][/ROW]
[ROW][C]69[/C][C]106.61[/C][C]106.73292218102[/C][C]-0.122922181020314[/C][/ROW]
[ROW][C]70[/C][C]106.61[/C][C]106.73351745313[/C][C]-0.123517453129594[/C][/ROW]
[ROW][C]71[/C][C]106.61[/C][C]106.733325266487[/C][C]-0.123325266486901[/C][/ROW]
[ROW][C]72[/C][C]106.61[/C][C]106.73313282163[/C][C]-0.123132821630094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157580&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157580&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
320.6120.610
420.6120.610
520.6120.610
620.6120.610
720.6120.610
819.4720.61-1.14
919.4719.46903000039230.000969999607679739
1019.4719.46822315302820.00177684697176517
1119.4719.46822535213620.00177464786380099
1219.4719.46822812101210.00177187898788134
1398.1919.46823088597478.721769114026
1498.1998.2552146721626-0.065214672162611
1598.1998.3109323622748-0.120932362274829
1698.1998.3107832601211-0.120783260121101
1798.1998.3105948096963-0.120594809696343
1898.1998.3104066252563-0.120406625256322
1998.1998.3102187344523-0.120218734452337
20100.4898.31003113684612.1699688631539
21102.78100.6017923399642.17820766003601
22102.78102.90518311647-0.12518311647041
23102.78102.906619828154-0.126619828153935
24102.78102.906423399934-0.126423399933671
25102.78102.906226120961-0.126226120961192
26102.78102.906029149015-0.126029149015238
27102.78102.905832484437-0.125832484437311
28102.78102.905636126748-0.125636126748361
29102.78102.905440075469-0.125440075469498
30102.78102.905244330123-0.12524433012257
31102.78102.90504889023-0.125048890230175
32101.67102.904853755316-1.2348537553157
33101.67101.793714451601-0.123714451600947
34101.67101.792734310677-0.122734310676549
35101.67101.79254222908-0.12254222907994
36101.67101.792351005336-0.122351005336114
37101.67101.792160080387-0.122160080387019
38101.67101.791969453371-0.121969453370696
39101.67101.791779123822-0.121779123821895
40101.67101.791589091276-0.121589091276462
41101.67101.791399355271-0.12139935527091
42101.67101.791209915343-0.121209915342533
43101.67101.791020771029-0.121020771029279
44105.79101.790831921873.99916807813015
45105.79105.914148980021-0.124148980020919
46105.79105.916876694472-0.126876694472386
47105.79105.916680780361-0.126680780360502
48105.79105.916483100403-0.126483100403078
49105.79105.916285727449-0.126285727449158
50105.79105.916088662489-0.126088662488542
51105.79105.915891905042-0.125891905041684
52105.79105.915695454629-0.125695454628726
53105.79105.915499310771-0.125499310770536
54105.79105.915303472989-0.125303472988762
55105.79105.915107940806-0.125107940805776
56104.47105.914912713745-1.44491271374469
57104.47104.593594633889-0.123594633888899
58104.47104.592465771328-0.122465771327654
59104.47104.592274003114-0.122274003114001
60104.47104.592083197853-0.122083197853485
61104.47104.59189269081-0.121892690809631
62104.47104.591702481046-0.121702481046427
63104.47104.5915125681-0.121512568099661
64105.5104.5913229515060.908677048493843
65105.5105.622010033958-0.122010033957793
66105.5105.622550002355-0.12255000235524
67105.5105.622359285136-0.122359285136383
68106.61105.6221683476350.987831652365045
69106.61106.73292218102-0.122922181020314
70106.61106.73351745313-0.123517453129594
71106.61106.733325266487-0.123325266486901
72106.61106.73313282163-0.123132821630094







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73106.73294067668288.2420911443946125.223790208968
74106.85579411562680.6946563425911133.016931888661
75106.9786475545774.916726076288139.040569032853
76107.10150099351570.052908346623144.150093640407
77107.22435443245965.7719598444838148.676749020435
78107.34720787140461.9040909937582152.790324749049
79107.47006131034858.3485034834643156.591619137232
80107.59291474929355.0395666616495160.146262836936
81107.71576818823751.9317257568322163.499810619642
82107.83862162718148.9918367495569166.685406504806
83107.96147506612646.1948970538621169.72805307839
84108.0843285050743.5214966316629172.647160378478

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.732940676682 & 88.2420911443946 & 125.223790208968 \tabularnewline
74 & 106.855794115626 & 80.6946563425911 & 133.016931888661 \tabularnewline
75 & 106.97864755457 & 74.916726076288 & 139.040569032853 \tabularnewline
76 & 107.101500993515 & 70.052908346623 & 144.150093640407 \tabularnewline
77 & 107.224354432459 & 65.7719598444838 & 148.676749020435 \tabularnewline
78 & 107.347207871404 & 61.9040909937582 & 152.790324749049 \tabularnewline
79 & 107.470061310348 & 58.3485034834643 & 156.591619137232 \tabularnewline
80 & 107.592914749293 & 55.0395666616495 & 160.146262836936 \tabularnewline
81 & 107.715768188237 & 51.9317257568322 & 163.499810619642 \tabularnewline
82 & 107.838621627181 & 48.9918367495569 & 166.685406504806 \tabularnewline
83 & 107.961475066126 & 46.1948970538621 & 169.72805307839 \tabularnewline
84 & 108.08432850507 & 43.5214966316629 & 172.647160378478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157580&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]106.732940676682[/C][C]88.2420911443946[/C][C]125.223790208968[/C][/ROW]
[ROW][C]74[/C][C]106.855794115626[/C][C]80.6946563425911[/C][C]133.016931888661[/C][/ROW]
[ROW][C]75[/C][C]106.97864755457[/C][C]74.916726076288[/C][C]139.040569032853[/C][/ROW]
[ROW][C]76[/C][C]107.101500993515[/C][C]70.052908346623[/C][C]144.150093640407[/C][/ROW]
[ROW][C]77[/C][C]107.224354432459[/C][C]65.7719598444838[/C][C]148.676749020435[/C][/ROW]
[ROW][C]78[/C][C]107.347207871404[/C][C]61.9040909937582[/C][C]152.790324749049[/C][/ROW]
[ROW][C]79[/C][C]107.470061310348[/C][C]58.3485034834643[/C][C]156.591619137232[/C][/ROW]
[ROW][C]80[/C][C]107.592914749293[/C][C]55.0395666616495[/C][C]160.146262836936[/C][/ROW]
[ROW][C]81[/C][C]107.715768188237[/C][C]51.9317257568322[/C][C]163.499810619642[/C][/ROW]
[ROW][C]82[/C][C]107.838621627181[/C][C]48.9918367495569[/C][C]166.685406504806[/C][/ROW]
[ROW][C]83[/C][C]107.961475066126[/C][C]46.1948970538621[/C][C]169.72805307839[/C][/ROW]
[ROW][C]84[/C][C]108.08432850507[/C][C]43.5214966316629[/C][C]172.647160378478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157580&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157580&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
73106.73294067668288.2420911443946125.223790208968
74106.85579411562680.6946563425911133.016931888661
75106.9786475545774.916726076288139.040569032853
76107.10150099351570.052908346623144.150093640407
77107.22435443245965.7719598444838148.676749020435
78107.34720787140461.9040909937582152.790324749049
79107.47006131034858.3485034834643156.591619137232
80107.59291474929355.0395666616495160.146262836936
81107.71576818823751.9317257568322163.499810619642
82107.83862162718148.9918367495569166.685406504806
83107.96147506612646.1948970538621169.72805307839
84108.0843285050743.5214966316629172.647160378478



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