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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 23 Jan 2010 08:31:48 -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/2010/Jan/23/t1264260782an71zfrgjvifte3.htm/, Retrieved Sat, 04 May 2024 22:56:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72363, Retrieved Sat, 04 May 2024 22:56:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact206
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [KDGP2W62] [2010-01-20 22:23:55] [8c77cc01643940e7a8195154a75bb218]
-   P     [Exponential Smoothing] [Exponental smooth...] [2010-01-23 15:31:48] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   P       [Exponential Smoothing] [] [2010-01-27 01:30:26] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6
9
6
11
12
13
11
16
16
19
14
15
12
14
16
13
13
15
12
13
12
15
10
8
11
8
13
9
8
8
6
8
6
12
16




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=72363&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=72363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72363&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
alpha0.6087902561648
beta0.147224753220598
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.6087902561648 \tabularnewline
beta & 0.147224753220598 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72363&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]0.6087902561648[/C][/ROW]
[ROW][C]beta[/C][C]0.147224753220598[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72363&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
alpha0.6087902561648
beta0.147224753220598
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-37-10
4-33.01580748608233-6.01580748608233
500.91796177286605-0.91796177286605
661.841358865928594.15864113407141
7-16.2280771695089-7.2280771695089
803.03482702605008-3.03482702605008
9-12.12237821455813-3.12237821455813
1010.8767734704974090.123226529502591
11-41.61810594000773-5.61810594000773
12-1-1.639374045803970.63937404580397
13-1-1.030054734807650.0300547348076465
140-0.7889893075563120.788989307556312
153-0.01517558846790163.0151755884679
1602.38416580527450-2.38416580527450
1781.282750383218016.71724961678199
1886.324248321258451.67575167874155
1988.44672737736045-0.446727377360446
2089.2370221392205-1.23702213922049
21119.435320099150211.56467990084979
221311.47950764911681.52049235088324
23513.6330744508798-8.63307445087983
24128.83147492965923.16852507034080
251311.49856592252291.50143407747705
26913.2853201905549-4.28532019055495
271111.1650659024837-0.16506590248372
28711.5383875869256-4.53838758692564
29128.84250252343843.15749747656159
301111.1148006254223-0.114800625422323
311011.3846660629438-1.38466606294383
321310.75734356751532.24265643248474
331412.53930670595391.46069329404611
341013.9761387773112-3.97613877731116
351311.74670313572851.25329686427155
361212.8132286966480-0.813228696647988
371312.54878476099390.451215239006084
381713.09456394133593.90543605866408
391516.0932794091885-1.09327940918854
40615.9508360719243-9.9508360719243
4199.5241151061641-0.524115106164102
4268.78931410159438-2.78931410159438
43116.42547860003414.57452139996591
44128.954684156547353.04531584345265
451310.82587286977972.17412713022031
461112.3615552132928-1.36155521329276
471611.62271377146774.37728622853231
481614.76995484758471.23004515241534
491916.11143393385482.88856606614521
501418.7215036662045-4.72150366620451
511516.2754534672027-1.27545346720271
521215.8130074388838-3.81300743888383
531413.46396725257310.536032747426901
541613.81062443191812.18937556808189
551315.3600521429195-2.36005214291955
561313.9283034900841-0.928303490084055
571513.28498655729001.71501344271003
581214.4046101488072-2.40461014880719
591312.80072424719190.19927575280807
601212.7999195961422-0.799919596142221
611512.11911856298182.8808814370182
621013.9373638422587-3.93736384225873
63811.2518258663456-3.25182586634558
64118.692178845345682.30782115465432
6589.72403844970138-1.72403844970138
66138.146817378721484.85318262127852
67911.0087302903941-2.00873029039412
6889.51313700517903-1.51313700517903
6988.18363513360865-0.183635133608647
7067.64706201448947-1.64706201448947
7186.07194435624521.92805564375480
7266.84613318307419-0.846133183074189
73125.85558481634136.1444151836587
74169.67153193969286.3284680603072

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -3 & 7 & -10 \tabularnewline
4 & -3 & 3.01580748608233 & -6.01580748608233 \tabularnewline
5 & 0 & 0.91796177286605 & -0.91796177286605 \tabularnewline
6 & 6 & 1.84135886592859 & 4.15864113407141 \tabularnewline
7 & -1 & 6.2280771695089 & -7.2280771695089 \tabularnewline
8 & 0 & 3.03482702605008 & -3.03482702605008 \tabularnewline
9 & -1 & 2.12237821455813 & -3.12237821455813 \tabularnewline
10 & 1 & 0.876773470497409 & 0.123226529502591 \tabularnewline
11 & -4 & 1.61810594000773 & -5.61810594000773 \tabularnewline
12 & -1 & -1.63937404580397 & 0.63937404580397 \tabularnewline
13 & -1 & -1.03005473480765 & 0.0300547348076465 \tabularnewline
14 & 0 & -0.788989307556312 & 0.788989307556312 \tabularnewline
15 & 3 & -0.0151755884679016 & 3.0151755884679 \tabularnewline
16 & 0 & 2.38416580527450 & -2.38416580527450 \tabularnewline
17 & 8 & 1.28275038321801 & 6.71724961678199 \tabularnewline
18 & 8 & 6.32424832125845 & 1.67575167874155 \tabularnewline
19 & 8 & 8.44672737736045 & -0.446727377360446 \tabularnewline
20 & 8 & 9.2370221392205 & -1.23702213922049 \tabularnewline
21 & 11 & 9.43532009915021 & 1.56467990084979 \tabularnewline
22 & 13 & 11.4795076491168 & 1.52049235088324 \tabularnewline
23 & 5 & 13.6330744508798 & -8.63307445087983 \tabularnewline
24 & 12 & 8.8314749296592 & 3.16852507034080 \tabularnewline
25 & 13 & 11.4985659225229 & 1.50143407747705 \tabularnewline
26 & 9 & 13.2853201905549 & -4.28532019055495 \tabularnewline
27 & 11 & 11.1650659024837 & -0.16506590248372 \tabularnewline
28 & 7 & 11.5383875869256 & -4.53838758692564 \tabularnewline
29 & 12 & 8.8425025234384 & 3.15749747656159 \tabularnewline
30 & 11 & 11.1148006254223 & -0.114800625422323 \tabularnewline
31 & 10 & 11.3846660629438 & -1.38466606294383 \tabularnewline
32 & 13 & 10.7573435675153 & 2.24265643248474 \tabularnewline
33 & 14 & 12.5393067059539 & 1.46069329404611 \tabularnewline
34 & 10 & 13.9761387773112 & -3.97613877731116 \tabularnewline
35 & 13 & 11.7467031357285 & 1.25329686427155 \tabularnewline
36 & 12 & 12.8132286966480 & -0.813228696647988 \tabularnewline
37 & 13 & 12.5487847609939 & 0.451215239006084 \tabularnewline
38 & 17 & 13.0945639413359 & 3.90543605866408 \tabularnewline
39 & 15 & 16.0932794091885 & -1.09327940918854 \tabularnewline
40 & 6 & 15.9508360719243 & -9.9508360719243 \tabularnewline
41 & 9 & 9.5241151061641 & -0.524115106164102 \tabularnewline
42 & 6 & 8.78931410159438 & -2.78931410159438 \tabularnewline
43 & 11 & 6.4254786000341 & 4.57452139996591 \tabularnewline
44 & 12 & 8.95468415654735 & 3.04531584345265 \tabularnewline
45 & 13 & 10.8258728697797 & 2.17412713022031 \tabularnewline
46 & 11 & 12.3615552132928 & -1.36155521329276 \tabularnewline
47 & 16 & 11.6227137714677 & 4.37728622853231 \tabularnewline
48 & 16 & 14.7699548475847 & 1.23004515241534 \tabularnewline
49 & 19 & 16.1114339338548 & 2.88856606614521 \tabularnewline
50 & 14 & 18.7215036662045 & -4.72150366620451 \tabularnewline
51 & 15 & 16.2754534672027 & -1.27545346720271 \tabularnewline
52 & 12 & 15.8130074388838 & -3.81300743888383 \tabularnewline
53 & 14 & 13.4639672525731 & 0.536032747426901 \tabularnewline
54 & 16 & 13.8106244319181 & 2.18937556808189 \tabularnewline
55 & 13 & 15.3600521429195 & -2.36005214291955 \tabularnewline
56 & 13 & 13.9283034900841 & -0.928303490084055 \tabularnewline
57 & 15 & 13.2849865572900 & 1.71501344271003 \tabularnewline
58 & 12 & 14.4046101488072 & -2.40461014880719 \tabularnewline
59 & 13 & 12.8007242471919 & 0.19927575280807 \tabularnewline
60 & 12 & 12.7999195961422 & -0.799919596142221 \tabularnewline
61 & 15 & 12.1191185629818 & 2.8808814370182 \tabularnewline
62 & 10 & 13.9373638422587 & -3.93736384225873 \tabularnewline
63 & 8 & 11.2518258663456 & -3.25182586634558 \tabularnewline
64 & 11 & 8.69217884534568 & 2.30782115465432 \tabularnewline
65 & 8 & 9.72403844970138 & -1.72403844970138 \tabularnewline
66 & 13 & 8.14681737872148 & 4.85318262127852 \tabularnewline
67 & 9 & 11.0087302903941 & -2.00873029039412 \tabularnewline
68 & 8 & 9.51313700517903 & -1.51313700517903 \tabularnewline
69 & 8 & 8.18363513360865 & -0.183635133608647 \tabularnewline
70 & 6 & 7.64706201448947 & -1.64706201448947 \tabularnewline
71 & 8 & 6.0719443562452 & 1.92805564375480 \tabularnewline
72 & 6 & 6.84613318307419 & -0.846133183074189 \tabularnewline
73 & 12 & 5.8555848163413 & 6.1444151836587 \tabularnewline
74 & 16 & 9.6715319396928 & 6.3284680603072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72363&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]-3[/C][C]7[/C][C]-10[/C][/ROW]
[ROW][C]4[/C][C]-3[/C][C]3.01580748608233[/C][C]-6.01580748608233[/C][/ROW]
[ROW][C]5[/C][C]0[/C][C]0.91796177286605[/C][C]-0.91796177286605[/C][/ROW]
[ROW][C]6[/C][C]6[/C][C]1.84135886592859[/C][C]4.15864113407141[/C][/ROW]
[ROW][C]7[/C][C]-1[/C][C]6.2280771695089[/C][C]-7.2280771695089[/C][/ROW]
[ROW][C]8[/C][C]0[/C][C]3.03482702605008[/C][C]-3.03482702605008[/C][/ROW]
[ROW][C]9[/C][C]-1[/C][C]2.12237821455813[/C][C]-3.12237821455813[/C][/ROW]
[ROW][C]10[/C][C]1[/C][C]0.876773470497409[/C][C]0.123226529502591[/C][/ROW]
[ROW][C]11[/C][C]-4[/C][C]1.61810594000773[/C][C]-5.61810594000773[/C][/ROW]
[ROW][C]12[/C][C]-1[/C][C]-1.63937404580397[/C][C]0.63937404580397[/C][/ROW]
[ROW][C]13[/C][C]-1[/C][C]-1.03005473480765[/C][C]0.0300547348076465[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]-0.788989307556312[/C][C]0.788989307556312[/C][/ROW]
[ROW][C]15[/C][C]3[/C][C]-0.0151755884679016[/C][C]3.0151755884679[/C][/ROW]
[ROW][C]16[/C][C]0[/C][C]2.38416580527450[/C][C]-2.38416580527450[/C][/ROW]
[ROW][C]17[/C][C]8[/C][C]1.28275038321801[/C][C]6.71724961678199[/C][/ROW]
[ROW][C]18[/C][C]8[/C][C]6.32424832125845[/C][C]1.67575167874155[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]8.44672737736045[/C][C]-0.446727377360446[/C][/ROW]
[ROW][C]20[/C][C]8[/C][C]9.2370221392205[/C][C]-1.23702213922049[/C][/ROW]
[ROW][C]21[/C][C]11[/C][C]9.43532009915021[/C][C]1.56467990084979[/C][/ROW]
[ROW][C]22[/C][C]13[/C][C]11.4795076491168[/C][C]1.52049235088324[/C][/ROW]
[ROW][C]23[/C][C]5[/C][C]13.6330744508798[/C][C]-8.63307445087983[/C][/ROW]
[ROW][C]24[/C][C]12[/C][C]8.8314749296592[/C][C]3.16852507034080[/C][/ROW]
[ROW][C]25[/C][C]13[/C][C]11.4985659225229[/C][C]1.50143407747705[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]13.2853201905549[/C][C]-4.28532019055495[/C][/ROW]
[ROW][C]27[/C][C]11[/C][C]11.1650659024837[/C][C]-0.16506590248372[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]11.5383875869256[/C][C]-4.53838758692564[/C][/ROW]
[ROW][C]29[/C][C]12[/C][C]8.8425025234384[/C][C]3.15749747656159[/C][/ROW]
[ROW][C]30[/C][C]11[/C][C]11.1148006254223[/C][C]-0.114800625422323[/C][/ROW]
[ROW][C]31[/C][C]10[/C][C]11.3846660629438[/C][C]-1.38466606294383[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]10.7573435675153[/C][C]2.24265643248474[/C][/ROW]
[ROW][C]33[/C][C]14[/C][C]12.5393067059539[/C][C]1.46069329404611[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]13.9761387773112[/C][C]-3.97613877731116[/C][/ROW]
[ROW][C]35[/C][C]13[/C][C]11.7467031357285[/C][C]1.25329686427155[/C][/ROW]
[ROW][C]36[/C][C]12[/C][C]12.8132286966480[/C][C]-0.813228696647988[/C][/ROW]
[ROW][C]37[/C][C]13[/C][C]12.5487847609939[/C][C]0.451215239006084[/C][/ROW]
[ROW][C]38[/C][C]17[/C][C]13.0945639413359[/C][C]3.90543605866408[/C][/ROW]
[ROW][C]39[/C][C]15[/C][C]16.0932794091885[/C][C]-1.09327940918854[/C][/ROW]
[ROW][C]40[/C][C]6[/C][C]15.9508360719243[/C][C]-9.9508360719243[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]9.5241151061641[/C][C]-0.524115106164102[/C][/ROW]
[ROW][C]42[/C][C]6[/C][C]8.78931410159438[/C][C]-2.78931410159438[/C][/ROW]
[ROW][C]43[/C][C]11[/C][C]6.4254786000341[/C][C]4.57452139996591[/C][/ROW]
[ROW][C]44[/C][C]12[/C][C]8.95468415654735[/C][C]3.04531584345265[/C][/ROW]
[ROW][C]45[/C][C]13[/C][C]10.8258728697797[/C][C]2.17412713022031[/C][/ROW]
[ROW][C]46[/C][C]11[/C][C]12.3615552132928[/C][C]-1.36155521329276[/C][/ROW]
[ROW][C]47[/C][C]16[/C][C]11.6227137714677[/C][C]4.37728622853231[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]14.7699548475847[/C][C]1.23004515241534[/C][/ROW]
[ROW][C]49[/C][C]19[/C][C]16.1114339338548[/C][C]2.88856606614521[/C][/ROW]
[ROW][C]50[/C][C]14[/C][C]18.7215036662045[/C][C]-4.72150366620451[/C][/ROW]
[ROW][C]51[/C][C]15[/C][C]16.2754534672027[/C][C]-1.27545346720271[/C][/ROW]
[ROW][C]52[/C][C]12[/C][C]15.8130074388838[/C][C]-3.81300743888383[/C][/ROW]
[ROW][C]53[/C][C]14[/C][C]13.4639672525731[/C][C]0.536032747426901[/C][/ROW]
[ROW][C]54[/C][C]16[/C][C]13.8106244319181[/C][C]2.18937556808189[/C][/ROW]
[ROW][C]55[/C][C]13[/C][C]15.3600521429195[/C][C]-2.36005214291955[/C][/ROW]
[ROW][C]56[/C][C]13[/C][C]13.9283034900841[/C][C]-0.928303490084055[/C][/ROW]
[ROW][C]57[/C][C]15[/C][C]13.2849865572900[/C][C]1.71501344271003[/C][/ROW]
[ROW][C]58[/C][C]12[/C][C]14.4046101488072[/C][C]-2.40461014880719[/C][/ROW]
[ROW][C]59[/C][C]13[/C][C]12.8007242471919[/C][C]0.19927575280807[/C][/ROW]
[ROW][C]60[/C][C]12[/C][C]12.7999195961422[/C][C]-0.799919596142221[/C][/ROW]
[ROW][C]61[/C][C]15[/C][C]12.1191185629818[/C][C]2.8808814370182[/C][/ROW]
[ROW][C]62[/C][C]10[/C][C]13.9373638422587[/C][C]-3.93736384225873[/C][/ROW]
[ROW][C]63[/C][C]8[/C][C]11.2518258663456[/C][C]-3.25182586634558[/C][/ROW]
[ROW][C]64[/C][C]11[/C][C]8.69217884534568[/C][C]2.30782115465432[/C][/ROW]
[ROW][C]65[/C][C]8[/C][C]9.72403844970138[/C][C]-1.72403844970138[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]8.14681737872148[/C][C]4.85318262127852[/C][/ROW]
[ROW][C]67[/C][C]9[/C][C]11.0087302903941[/C][C]-2.00873029039412[/C][/ROW]
[ROW][C]68[/C][C]8[/C][C]9.51313700517903[/C][C]-1.51313700517903[/C][/ROW]
[ROW][C]69[/C][C]8[/C][C]8.18363513360865[/C][C]-0.183635133608647[/C][/ROW]
[ROW][C]70[/C][C]6[/C][C]7.64706201448947[/C][C]-1.64706201448947[/C][/ROW]
[ROW][C]71[/C][C]8[/C][C]6.0719443562452[/C][C]1.92805564375480[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]6.84613318307419[/C][C]-0.846133183074189[/C][/ROW]
[ROW][C]73[/C][C]12[/C][C]5.8555848163413[/C][C]6.1444151836587[/C][/ROW]
[ROW][C]74[/C][C]16[/C][C]9.6715319396928[/C][C]6.3284680603072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72363&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72363&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
3-37-10
4-33.01580748608233-6.01580748608233
500.91796177286605-0.91796177286605
661.841358865928594.15864113407141
7-16.2280771695089-7.2280771695089
803.03482702605008-3.03482702605008
9-12.12237821455813-3.12237821455813
1010.8767734704974090.123226529502591
11-41.61810594000773-5.61810594000773
12-1-1.639374045803970.63937404580397
13-1-1.030054734807650.0300547348076465
140-0.7889893075563120.788989307556312
153-0.01517558846790163.0151755884679
1602.38416580527450-2.38416580527450
1781.282750383218016.71724961678199
1886.324248321258451.67575167874155
1988.44672737736045-0.446727377360446
2089.2370221392205-1.23702213922049
21119.435320099150211.56467990084979
221311.47950764911681.52049235088324
23513.6330744508798-8.63307445087983
24128.83147492965923.16852507034080
251311.49856592252291.50143407747705
26913.2853201905549-4.28532019055495
271111.1650659024837-0.16506590248372
28711.5383875869256-4.53838758692564
29128.84250252343843.15749747656159
301111.1148006254223-0.114800625422323
311011.3846660629438-1.38466606294383
321310.75734356751532.24265643248474
331412.53930670595391.46069329404611
341013.9761387773112-3.97613877731116
351311.74670313572851.25329686427155
361212.8132286966480-0.813228696647988
371312.54878476099390.451215239006084
381713.09456394133593.90543605866408
391516.0932794091885-1.09327940918854
40615.9508360719243-9.9508360719243
4199.5241151061641-0.524115106164102
4268.78931410159438-2.78931410159438
43116.42547860003414.57452139996591
44128.954684156547353.04531584345265
451310.82587286977972.17412713022031
461112.3615552132928-1.36155521329276
471611.62271377146774.37728622853231
481614.76995484758471.23004515241534
491916.11143393385482.88856606614521
501418.7215036662045-4.72150366620451
511516.2754534672027-1.27545346720271
521215.8130074388838-3.81300743888383
531413.46396725257310.536032747426901
541613.81062443191812.18937556808189
551315.3600521429195-2.36005214291955
561313.9283034900841-0.928303490084055
571513.28498655729001.71501344271003
581214.4046101488072-2.40461014880719
591312.80072424719190.19927575280807
601212.7999195961422-0.799919596142221
611512.11911856298182.8808814370182
621013.9373638422587-3.93736384225873
63811.2518258663456-3.25182586634558
64118.692178845345682.30782115465432
6589.72403844970138-1.72403844970138
66138.146817378721484.85318262127852
67911.0087302903941-2.00873029039412
6889.51313700517903-1.51313700517903
6988.18363513360865-0.183635133608647
7067.64706201448947-1.64706201448947
7186.07194435624521.92805564375480
7266.84613318307419-0.846133183074189
73125.85558481634136.1444151836587
74169.67153193969286.3284680603072







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7514.16674289453837.2388681077667621.0946176813098
7614.80924415781866.358970624048123.2595176915891
7715.45174542109895.391265390638825.5122254515591
7816.09424668437934.3390357063837227.8494576623748
7916.73674794765963.2055457834020130.2679501119171
8017.37924921093991.9938753710060532.7646230508737
8118.02175047422020.70687239715914935.3366285512813
8218.6642517375005-0.65284910682090937.981352581822
8319.3067530007808-2.0828941198677540.6964001214294
8419.9492542640612-3.5810663607160943.4795748888384
8520.5917555273415-5.1453474261630646.328858480846
8621.2342567906218-6.7738772472262549.2423908284699

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
75 & 14.1667428945383 & 7.23886810776676 & 21.0946176813098 \tabularnewline
76 & 14.8092441578186 & 6.3589706240481 & 23.2595176915891 \tabularnewline
77 & 15.4517454210989 & 5.3912653906388 & 25.5122254515591 \tabularnewline
78 & 16.0942466843793 & 4.33903570638372 & 27.8494576623748 \tabularnewline
79 & 16.7367479476596 & 3.20554578340201 & 30.2679501119171 \tabularnewline
80 & 17.3792492109399 & 1.99387537100605 & 32.7646230508737 \tabularnewline
81 & 18.0217504742202 & 0.706872397159149 & 35.3366285512813 \tabularnewline
82 & 18.6642517375005 & -0.652849106820909 & 37.981352581822 \tabularnewline
83 & 19.3067530007808 & -2.08289411986775 & 40.6964001214294 \tabularnewline
84 & 19.9492542640612 & -3.58106636071609 & 43.4795748888384 \tabularnewline
85 & 20.5917555273415 & -5.14534742616306 & 46.328858480846 \tabularnewline
86 & 21.2342567906218 & -6.77387724722625 & 49.2423908284699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72363&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]75[/C][C]14.1667428945383[/C][C]7.23886810776676[/C][C]21.0946176813098[/C][/ROW]
[ROW][C]76[/C][C]14.8092441578186[/C][C]6.3589706240481[/C][C]23.2595176915891[/C][/ROW]
[ROW][C]77[/C][C]15.4517454210989[/C][C]5.3912653906388[/C][C]25.5122254515591[/C][/ROW]
[ROW][C]78[/C][C]16.0942466843793[/C][C]4.33903570638372[/C][C]27.8494576623748[/C][/ROW]
[ROW][C]79[/C][C]16.7367479476596[/C][C]3.20554578340201[/C][C]30.2679501119171[/C][/ROW]
[ROW][C]80[/C][C]17.3792492109399[/C][C]1.99387537100605[/C][C]32.7646230508737[/C][/ROW]
[ROW][C]81[/C][C]18.0217504742202[/C][C]0.706872397159149[/C][C]35.3366285512813[/C][/ROW]
[ROW][C]82[/C][C]18.6642517375005[/C][C]-0.652849106820909[/C][C]37.981352581822[/C][/ROW]
[ROW][C]83[/C][C]19.3067530007808[/C][C]-2.08289411986775[/C][C]40.6964001214294[/C][/ROW]
[ROW][C]84[/C][C]19.9492542640612[/C][C]-3.58106636071609[/C][C]43.4795748888384[/C][/ROW]
[ROW][C]85[/C][C]20.5917555273415[/C][C]-5.14534742616306[/C][C]46.328858480846[/C][/ROW]
[ROW][C]86[/C][C]21.2342567906218[/C][C]-6.77387724722625[/C][C]49.2423908284699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72363&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72363&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
7514.16674289453837.2388681077667621.0946176813098
7614.80924415781866.358970624048123.2595176915891
7715.45174542109895.391265390638825.5122254515591
7816.09424668437934.3390357063837227.8494576623748
7916.73674794765963.2055457834020130.2679501119171
8017.37924921093991.9938753710060532.7646230508737
8118.02175047422020.70687239715914935.3366285512813
8218.6642517375005-0.65284910682090937.981352581822
8319.3067530007808-2.0828941198677540.6964001214294
8419.9492542640612-3.5810663607160943.4795748888384
8520.5917555273415-5.1453474261630646.328858480846
8621.2342567906218-6.7738772472262549.2423908284699



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')