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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 16:04:13 +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/02/t12754948569nzoc2cvz21mhho.htm/, Retrieved Tue, 16 Apr 2024 17:23:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77312, Retrieved Tue, 16 Apr 2024 17:23:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords KDGP2W62
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [hoofdstuk 10 oef 2] [2010-06-02 16:04:13] [de7054811a4039cd82332eb5d7e753fd] [Current]
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Dataseries X:
14861
14583,3
15305,8
17903,9
16379,4
15420,3
17870,5
15912,8
13866,5
17823,2
17872
17420,4
16704,4
15991,2
16583,6
19123,5
17838,7
17209,4
18586,5
16258,1
15141,6
19202,1
17746,5
19090,1
18040,3
17515,5
17751,8
21072,4
17170
19439,5
19795,4
17574,9
16165,4
19464,6
19932,1
19961,2
17343,4
18924,2
18574,1
21350,6
18594,6
19823,1
20844,4
19640,2
17735,4
19813,6
22160
20664,3
17877,4
20906,5
21164,1
21374,4
22952,3
21343,5
23899,3
22392,9
18274,1
22786,7
22321,5
17842,2
16373,5
16087,1
16555,9
17880,2
16764,5
16049
18288,3
17570,4
15133,4
19334,2
19291,8
20176,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77312&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77312&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77312&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.548494920609622
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548494920609622 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77312&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]0.548494920609622[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77312&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77312&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
alpha0.548494920609622
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1316704.415975.8158653846728.584134615385
1415991.215712.6032081456278.596791854447
1516583.616484.878945730298.721054269834
1619123.519062.927088242060.5729117579613
1717838.717853.7095016888-15.0095016887972
1817209.417246.4186786059-37.0186786059203
1918586.519023.4684337772-436.968433777198
2016258.116785.2061130713-527.106113071311
2115141.614432.4703997837709.129600216274
2219202.118768.6495292439433.45047075607
2317746.519038.1575564771-1291.65755647713
2419090.117837.32342660341252.77657339663
2518040.317798.6693261245241.630673875545
2617515.517268.3651690963247.134830903684
2717751.818023.384180907-271.584180907012
2821072.420398.3217828492674.078217150771
291717019525.608740071-2355.608740071
3019439.517634.51112355271804.98887644726
3119795.420421.8926663952-626.492666395232
3217574.918079.6772667659-504.777266765916
3316165.415739.1888122599426.211187740086
3419464.619920.18862953-455.588629529993
3519932.119702.0632260329230.036773967062
3619961.219335.8707071283625.329292871727
3717343.418953.0649603311-1609.66496033113
3818924.217407.33455139391516.86544860614
3918574.118858.7943575569-284.694357556877
4021350.621226.5410941984124.058905801645
4118594.620052.1452529079-1457.54525290793
4219823.118653.63089748361169.46910251642
4320844.421092.4330723780-248.033072378032
4419640.218957.8008377231682.39916227687
4517735.417268.4726244146466.927375585434
4619813.621471.8050639044-1658.20506390440
472216020594.05065471131565.94934528867
4820664.320960.5993955551-296.299395555103
4917877.420072.2849944677-2194.88499446773
5020906.518205.56436936752700.93563063245
5121164.120306.4806560173857.619343982693
5221374.423300.780655696-1926.38065569601
5322952.321001.72912990711950.5708700929
5421343.521472.5491567965-129.049156796456
5523899.323199.1206621390700.179337861049
5622392.921584.5781181592808.32188184081
5718274.119964.3178769208-1690.2178769208
5822786.722984.4671023938-197.767102393806
5922321.522907.7554969548-586.255496954767
6017842.222093.8308137166-4251.63081371658
6116373.519036.03722044-2662.53722043999
6216087.116912.8117247822-825.711724782237
6316555.917079.3798502057-523.47985020568
6417880.219316.1539570140-1435.95395701402
6516764.517286.0989843835-521.59898438353
661604916400.9464032083-351.946403208338
6718288.318005.2599010760283.040098923953
6817570.416161.91860335231408.48139664768
6915133.414870.8428075410262.557192458968
7019334.218962.0792396619372.120760338057
7119291.819197.948232248493.8517677515956
7220176.718757.05892917141419.64107082863

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 16704.4 & 15975.8158653846 & 728.584134615385 \tabularnewline
14 & 15991.2 & 15712.6032081456 & 278.596791854447 \tabularnewline
15 & 16583.6 & 16484.8789457302 & 98.721054269834 \tabularnewline
16 & 19123.5 & 19062.9270882420 & 60.5729117579613 \tabularnewline
17 & 17838.7 & 17853.7095016888 & -15.0095016887972 \tabularnewline
18 & 17209.4 & 17246.4186786059 & -37.0186786059203 \tabularnewline
19 & 18586.5 & 19023.4684337772 & -436.968433777198 \tabularnewline
20 & 16258.1 & 16785.2061130713 & -527.106113071311 \tabularnewline
21 & 15141.6 & 14432.4703997837 & 709.129600216274 \tabularnewline
22 & 19202.1 & 18768.6495292439 & 433.45047075607 \tabularnewline
23 & 17746.5 & 19038.1575564771 & -1291.65755647713 \tabularnewline
24 & 19090.1 & 17837.3234266034 & 1252.77657339663 \tabularnewline
25 & 18040.3 & 17798.6693261245 & 241.630673875545 \tabularnewline
26 & 17515.5 & 17268.3651690963 & 247.134830903684 \tabularnewline
27 & 17751.8 & 18023.384180907 & -271.584180907012 \tabularnewline
28 & 21072.4 & 20398.3217828492 & 674.078217150771 \tabularnewline
29 & 17170 & 19525.608740071 & -2355.608740071 \tabularnewline
30 & 19439.5 & 17634.5111235527 & 1804.98887644726 \tabularnewline
31 & 19795.4 & 20421.8926663952 & -626.492666395232 \tabularnewline
32 & 17574.9 & 18079.6772667659 & -504.777266765916 \tabularnewline
33 & 16165.4 & 15739.1888122599 & 426.211187740086 \tabularnewline
34 & 19464.6 & 19920.18862953 & -455.588629529993 \tabularnewline
35 & 19932.1 & 19702.0632260329 & 230.036773967062 \tabularnewline
36 & 19961.2 & 19335.8707071283 & 625.329292871727 \tabularnewline
37 & 17343.4 & 18953.0649603311 & -1609.66496033113 \tabularnewline
38 & 18924.2 & 17407.3345513939 & 1516.86544860614 \tabularnewline
39 & 18574.1 & 18858.7943575569 & -284.694357556877 \tabularnewline
40 & 21350.6 & 21226.5410941984 & 124.058905801645 \tabularnewline
41 & 18594.6 & 20052.1452529079 & -1457.54525290793 \tabularnewline
42 & 19823.1 & 18653.6308974836 & 1169.46910251642 \tabularnewline
43 & 20844.4 & 21092.4330723780 & -248.033072378032 \tabularnewline
44 & 19640.2 & 18957.8008377231 & 682.39916227687 \tabularnewline
45 & 17735.4 & 17268.4726244146 & 466.927375585434 \tabularnewline
46 & 19813.6 & 21471.8050639044 & -1658.20506390440 \tabularnewline
47 & 22160 & 20594.0506547113 & 1565.94934528867 \tabularnewline
48 & 20664.3 & 20960.5993955551 & -296.299395555103 \tabularnewline
49 & 17877.4 & 20072.2849944677 & -2194.88499446773 \tabularnewline
50 & 20906.5 & 18205.5643693675 & 2700.93563063245 \tabularnewline
51 & 21164.1 & 20306.4806560173 & 857.619343982693 \tabularnewline
52 & 21374.4 & 23300.780655696 & -1926.38065569601 \tabularnewline
53 & 22952.3 & 21001.7291299071 & 1950.5708700929 \tabularnewline
54 & 21343.5 & 21472.5491567965 & -129.049156796456 \tabularnewline
55 & 23899.3 & 23199.1206621390 & 700.179337861049 \tabularnewline
56 & 22392.9 & 21584.5781181592 & 808.32188184081 \tabularnewline
57 & 18274.1 & 19964.3178769208 & -1690.2178769208 \tabularnewline
58 & 22786.7 & 22984.4671023938 & -197.767102393806 \tabularnewline
59 & 22321.5 & 22907.7554969548 & -586.255496954767 \tabularnewline
60 & 17842.2 & 22093.8308137166 & -4251.63081371658 \tabularnewline
61 & 16373.5 & 19036.03722044 & -2662.53722043999 \tabularnewline
62 & 16087.1 & 16912.8117247822 & -825.711724782237 \tabularnewline
63 & 16555.9 & 17079.3798502057 & -523.47985020568 \tabularnewline
64 & 17880.2 & 19316.1539570140 & -1435.95395701402 \tabularnewline
65 & 16764.5 & 17286.0989843835 & -521.59898438353 \tabularnewline
66 & 16049 & 16400.9464032083 & -351.946403208338 \tabularnewline
67 & 18288.3 & 18005.2599010760 & 283.040098923953 \tabularnewline
68 & 17570.4 & 16161.9186033523 & 1408.48139664768 \tabularnewline
69 & 15133.4 & 14870.8428075410 & 262.557192458968 \tabularnewline
70 & 19334.2 & 18962.0792396619 & 372.120760338057 \tabularnewline
71 & 19291.8 & 19197.9482322484 & 93.8517677515956 \tabularnewline
72 & 20176.7 & 18757.0589291714 & 1419.64107082863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77312&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]16704.4[/C][C]15975.8158653846[/C][C]728.584134615385[/C][/ROW]
[ROW][C]14[/C][C]15991.2[/C][C]15712.6032081456[/C][C]278.596791854447[/C][/ROW]
[ROW][C]15[/C][C]16583.6[/C][C]16484.8789457302[/C][C]98.721054269834[/C][/ROW]
[ROW][C]16[/C][C]19123.5[/C][C]19062.9270882420[/C][C]60.5729117579613[/C][/ROW]
[ROW][C]17[/C][C]17838.7[/C][C]17853.7095016888[/C][C]-15.0095016887972[/C][/ROW]
[ROW][C]18[/C][C]17209.4[/C][C]17246.4186786059[/C][C]-37.0186786059203[/C][/ROW]
[ROW][C]19[/C][C]18586.5[/C][C]19023.4684337772[/C][C]-436.968433777198[/C][/ROW]
[ROW][C]20[/C][C]16258.1[/C][C]16785.2061130713[/C][C]-527.106113071311[/C][/ROW]
[ROW][C]21[/C][C]15141.6[/C][C]14432.4703997837[/C][C]709.129600216274[/C][/ROW]
[ROW][C]22[/C][C]19202.1[/C][C]18768.6495292439[/C][C]433.45047075607[/C][/ROW]
[ROW][C]23[/C][C]17746.5[/C][C]19038.1575564771[/C][C]-1291.65755647713[/C][/ROW]
[ROW][C]24[/C][C]19090.1[/C][C]17837.3234266034[/C][C]1252.77657339663[/C][/ROW]
[ROW][C]25[/C][C]18040.3[/C][C]17798.6693261245[/C][C]241.630673875545[/C][/ROW]
[ROW][C]26[/C][C]17515.5[/C][C]17268.3651690963[/C][C]247.134830903684[/C][/ROW]
[ROW][C]27[/C][C]17751.8[/C][C]18023.384180907[/C][C]-271.584180907012[/C][/ROW]
[ROW][C]28[/C][C]21072.4[/C][C]20398.3217828492[/C][C]674.078217150771[/C][/ROW]
[ROW][C]29[/C][C]17170[/C][C]19525.608740071[/C][C]-2355.608740071[/C][/ROW]
[ROW][C]30[/C][C]19439.5[/C][C]17634.5111235527[/C][C]1804.98887644726[/C][/ROW]
[ROW][C]31[/C][C]19795.4[/C][C]20421.8926663952[/C][C]-626.492666395232[/C][/ROW]
[ROW][C]32[/C][C]17574.9[/C][C]18079.6772667659[/C][C]-504.777266765916[/C][/ROW]
[ROW][C]33[/C][C]16165.4[/C][C]15739.1888122599[/C][C]426.211187740086[/C][/ROW]
[ROW][C]34[/C][C]19464.6[/C][C]19920.18862953[/C][C]-455.588629529993[/C][/ROW]
[ROW][C]35[/C][C]19932.1[/C][C]19702.0632260329[/C][C]230.036773967062[/C][/ROW]
[ROW][C]36[/C][C]19961.2[/C][C]19335.8707071283[/C][C]625.329292871727[/C][/ROW]
[ROW][C]37[/C][C]17343.4[/C][C]18953.0649603311[/C][C]-1609.66496033113[/C][/ROW]
[ROW][C]38[/C][C]18924.2[/C][C]17407.3345513939[/C][C]1516.86544860614[/C][/ROW]
[ROW][C]39[/C][C]18574.1[/C][C]18858.7943575569[/C][C]-284.694357556877[/C][/ROW]
[ROW][C]40[/C][C]21350.6[/C][C]21226.5410941984[/C][C]124.058905801645[/C][/ROW]
[ROW][C]41[/C][C]18594.6[/C][C]20052.1452529079[/C][C]-1457.54525290793[/C][/ROW]
[ROW][C]42[/C][C]19823.1[/C][C]18653.6308974836[/C][C]1169.46910251642[/C][/ROW]
[ROW][C]43[/C][C]20844.4[/C][C]21092.4330723780[/C][C]-248.033072378032[/C][/ROW]
[ROW][C]44[/C][C]19640.2[/C][C]18957.8008377231[/C][C]682.39916227687[/C][/ROW]
[ROW][C]45[/C][C]17735.4[/C][C]17268.4726244146[/C][C]466.927375585434[/C][/ROW]
[ROW][C]46[/C][C]19813.6[/C][C]21471.8050639044[/C][C]-1658.20506390440[/C][/ROW]
[ROW][C]47[/C][C]22160[/C][C]20594.0506547113[/C][C]1565.94934528867[/C][/ROW]
[ROW][C]48[/C][C]20664.3[/C][C]20960.5993955551[/C][C]-296.299395555103[/C][/ROW]
[ROW][C]49[/C][C]17877.4[/C][C]20072.2849944677[/C][C]-2194.88499446773[/C][/ROW]
[ROW][C]50[/C][C]20906.5[/C][C]18205.5643693675[/C][C]2700.93563063245[/C][/ROW]
[ROW][C]51[/C][C]21164.1[/C][C]20306.4806560173[/C][C]857.619343982693[/C][/ROW]
[ROW][C]52[/C][C]21374.4[/C][C]23300.780655696[/C][C]-1926.38065569601[/C][/ROW]
[ROW][C]53[/C][C]22952.3[/C][C]21001.7291299071[/C][C]1950.5708700929[/C][/ROW]
[ROW][C]54[/C][C]21343.5[/C][C]21472.5491567965[/C][C]-129.049156796456[/C][/ROW]
[ROW][C]55[/C][C]23899.3[/C][C]23199.1206621390[/C][C]700.179337861049[/C][/ROW]
[ROW][C]56[/C][C]22392.9[/C][C]21584.5781181592[/C][C]808.32188184081[/C][/ROW]
[ROW][C]57[/C][C]18274.1[/C][C]19964.3178769208[/C][C]-1690.2178769208[/C][/ROW]
[ROW][C]58[/C][C]22786.7[/C][C]22984.4671023938[/C][C]-197.767102393806[/C][/ROW]
[ROW][C]59[/C][C]22321.5[/C][C]22907.7554969548[/C][C]-586.255496954767[/C][/ROW]
[ROW][C]60[/C][C]17842.2[/C][C]22093.8308137166[/C][C]-4251.63081371658[/C][/ROW]
[ROW][C]61[/C][C]16373.5[/C][C]19036.03722044[/C][C]-2662.53722043999[/C][/ROW]
[ROW][C]62[/C][C]16087.1[/C][C]16912.8117247822[/C][C]-825.711724782237[/C][/ROW]
[ROW][C]63[/C][C]16555.9[/C][C]17079.3798502057[/C][C]-523.47985020568[/C][/ROW]
[ROW][C]64[/C][C]17880.2[/C][C]19316.1539570140[/C][C]-1435.95395701402[/C][/ROW]
[ROW][C]65[/C][C]16764.5[/C][C]17286.0989843835[/C][C]-521.59898438353[/C][/ROW]
[ROW][C]66[/C][C]16049[/C][C]16400.9464032083[/C][C]-351.946403208338[/C][/ROW]
[ROW][C]67[/C][C]18288.3[/C][C]18005.2599010760[/C][C]283.040098923953[/C][/ROW]
[ROW][C]68[/C][C]17570.4[/C][C]16161.9186033523[/C][C]1408.48139664768[/C][/ROW]
[ROW][C]69[/C][C]15133.4[/C][C]14870.8428075410[/C][C]262.557192458968[/C][/ROW]
[ROW][C]70[/C][C]19334.2[/C][C]18962.0792396619[/C][C]372.120760338057[/C][/ROW]
[ROW][C]71[/C][C]19291.8[/C][C]19197.9482322484[/C][C]93.8517677515956[/C][/ROW]
[ROW][C]72[/C][C]20176.7[/C][C]18757.0589291714[/C][C]1419.64107082863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77312&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77312&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
1316704.415975.8158653846728.584134615385
1415991.215712.6032081456278.596791854447
1516583.616484.878945730298.721054269834
1619123.519062.927088242060.5729117579613
1717838.717853.7095016888-15.0095016887972
1817209.417246.4186786059-37.0186786059203
1918586.519023.4684337772-436.968433777198
2016258.116785.2061130713-527.106113071311
2115141.614432.4703997837709.129600216274
2219202.118768.6495292439433.45047075607
2317746.519038.1575564771-1291.65755647713
2419090.117837.32342660341252.77657339663
2518040.317798.6693261245241.630673875545
2617515.517268.3651690963247.134830903684
2717751.818023.384180907-271.584180907012
2821072.420398.3217828492674.078217150771
291717019525.608740071-2355.608740071
3019439.517634.51112355271804.98887644726
3119795.420421.8926663952-626.492666395232
3217574.918079.6772667659-504.777266765916
3316165.415739.1888122599426.211187740086
3419464.619920.18862953-455.588629529993
3519932.119702.0632260329230.036773967062
3619961.219335.8707071283625.329292871727
3717343.418953.0649603311-1609.66496033113
3818924.217407.33455139391516.86544860614
3918574.118858.7943575569-284.694357556877
4021350.621226.5410941984124.058905801645
4118594.620052.1452529079-1457.54525290793
4219823.118653.63089748361169.46910251642
4320844.421092.4330723780-248.033072378032
4419640.218957.8008377231682.39916227687
4517735.417268.4726244146466.927375585434
4619813.621471.8050639044-1658.20506390440
472216020594.05065471131565.94934528867
4820664.320960.5993955551-296.299395555103
4917877.420072.2849944677-2194.88499446773
5020906.518205.56436936752700.93563063245
5121164.120306.4806560173857.619343982693
5221374.423300.780655696-1926.38065569601
5322952.321001.72912990711950.5708700929
5421343.521472.5491567965-129.049156796456
5523899.323199.1206621390700.179337861049
5622392.921584.5781181592808.32188184081
5718274.119964.3178769208-1690.2178769208
5822786.722984.4671023938-197.767102393806
5922321.522907.7554969548-586.255496954767
6017842.222093.8308137166-4251.63081371658
6116373.519036.03722044-2662.53722043999
6216087.116912.8117247822-825.711724782237
6316555.917079.3798502057-523.47985020568
6417880.219316.1539570140-1435.95395701402
6516764.517286.0989843835-521.59898438353
661604916400.9464032083-351.946403208338
6718288.318005.2599010760283.040098923953
6817570.416161.91860335231408.48139664768
6915133.414870.8428075410262.557192458968
7019334.218962.0792396619372.120760338057
7119291.819197.948232248493.8517677515956
7220176.718757.05892917141419.64107082863







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318809.92915796416420.860513848721198.9978020793
7418147.091803651615422.247547067720871.9360602356
7518766.558616005915743.000536692521790.1166953194
7621290.458761693617995.154421374624585.7631020126
7720048.017240714616501.729331975523594.3051494536
7819448.959053068915668.312922046823229.6051840909
7921246.313365423217245.012026564125247.6147042823
8019247.726011110815037.317522531823458.1344996899
8117184.105323465212774.494583610421593.7160633199
8221131.330469152816531.135460961825731.5254773438
8321163.093114840416379.901570512625946.2846591682
8420670.726593861415711.286243774325630.1669439486

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18809.929157964 & 16420.8605138487 & 21198.9978020793 \tabularnewline
74 & 18147.0918036516 & 15422.2475470677 & 20871.9360602356 \tabularnewline
75 & 18766.5586160059 & 15743.0005366925 & 21790.1166953194 \tabularnewline
76 & 21290.4587616936 & 17995.1544213746 & 24585.7631020126 \tabularnewline
77 & 20048.0172407146 & 16501.7293319755 & 23594.3051494536 \tabularnewline
78 & 19448.9590530689 & 15668.3129220468 & 23229.6051840909 \tabularnewline
79 & 21246.3133654232 & 17245.0120265641 & 25247.6147042823 \tabularnewline
80 & 19247.7260111108 & 15037.3175225318 & 23458.1344996899 \tabularnewline
81 & 17184.1053234652 & 12774.4945836104 & 21593.7160633199 \tabularnewline
82 & 21131.3304691528 & 16531.1354609618 & 25731.5254773438 \tabularnewline
83 & 21163.0931148404 & 16379.9015705126 & 25946.2846591682 \tabularnewline
84 & 20670.7265938614 & 15711.2862437743 & 25630.1669439486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77312&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]18809.929157964[/C][C]16420.8605138487[/C][C]21198.9978020793[/C][/ROW]
[ROW][C]74[/C][C]18147.0918036516[/C][C]15422.2475470677[/C][C]20871.9360602356[/C][/ROW]
[ROW][C]75[/C][C]18766.5586160059[/C][C]15743.0005366925[/C][C]21790.1166953194[/C][/ROW]
[ROW][C]76[/C][C]21290.4587616936[/C][C]17995.1544213746[/C][C]24585.7631020126[/C][/ROW]
[ROW][C]77[/C][C]20048.0172407146[/C][C]16501.7293319755[/C][C]23594.3051494536[/C][/ROW]
[ROW][C]78[/C][C]19448.9590530689[/C][C]15668.3129220468[/C][C]23229.6051840909[/C][/ROW]
[ROW][C]79[/C][C]21246.3133654232[/C][C]17245.0120265641[/C][C]25247.6147042823[/C][/ROW]
[ROW][C]80[/C][C]19247.7260111108[/C][C]15037.3175225318[/C][C]23458.1344996899[/C][/ROW]
[ROW][C]81[/C][C]17184.1053234652[/C][C]12774.4945836104[/C][C]21593.7160633199[/C][/ROW]
[ROW][C]82[/C][C]21131.3304691528[/C][C]16531.1354609618[/C][C]25731.5254773438[/C][/ROW]
[ROW][C]83[/C][C]21163.0931148404[/C][C]16379.9015705126[/C][C]25946.2846591682[/C][/ROW]
[ROW][C]84[/C][C]20670.7265938614[/C][C]15711.2862437743[/C][C]25630.1669439486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77312&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77312&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
7318809.92915796416420.860513848721198.9978020793
7418147.091803651615422.247547067720871.9360602356
7518766.558616005915743.000536692521790.1166953194
7621290.458761693617995.154421374624585.7631020126
7720048.017240714616501.729331975523594.3051494536
7819448.959053068915668.312922046823229.6051840909
7921246.313365423217245.012026564125247.6147042823
8019247.726011110815037.317522531823458.1344996899
8117184.105323465212774.494583610421593.7160633199
8221131.330469152816531.135460961825731.5254773438
8321163.093114840416379.901570512625946.2846591682
8420670.726593861415711.286243774325630.1669439486



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')