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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 12:14:04 +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/2014/Nov/30/t1417349681jeai8o7sds3uzdg.htm/, Retrieved Sun, 19 May 2024 15:21:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261374, Retrieved Sun, 19 May 2024 15:21:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 12:14:04] [0993c513a8c2c772d500c06e3e1f7dc8] [Current]
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Dataseries X:
18293.9
18613.4
18728.5
20091.8
18947.2
20124.9
19819.2
15908.6
19927.4
19551.9
15588.6
14206.2
13566.7
13941.5
14964.1
14086
13505.1
15300.4
14725.2
12484.9
16082.6
15915.8
15916.1
15713
14746
15253.2
18384.3
16848.5
16485.5
19257.1
17093.4
15700.1
19124.3
18640.8
18439.2
17106.3
18347.7
19372.7
22263.8
19422.9
21268.6
20310
19256
17535.9
19857.4
19628.4
19727.5
18112.2
19080.2
20684.6
22537.7
19954.6
20230.2
20445.5
19615.3
18071.6
19287.2
21031.4
19860.9
17671.3
19359.2
19287
21498
20859.7
20833.1
20318.8
21375.9
17403.4
21050.1
22010.2
20372.1
19028.4




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' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261374&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261374&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.757223624137803
beta0.03613798954172
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.757223624137803 \tabularnewline
beta & 0.03613798954172 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261374&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]0.757223624137803[/C][/ROW]
[ROW][C]beta[/C][C]0.03613798954172[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261374&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
alpha0.757223624137803
beta0.03613798954172
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1313566.716062.4014423077-2495.7014423077
1413941.514484.7461717168-543.24617171685
1514964.114966.4204758146-2.32047581457118
161408613965.7829970008120.217002999198
1713505.113184.5776415701320.522358429926
1815300.414725.7316800218574.668319978198
1914725.215775.8190784267-1050.61907842672
2012484.911027.8465889031457.05341109703
2116082.616107.8978788706-25.2978788705932
2215915.815726.0646546669189.735345333085
2315916.111994.35585480633921.74414519375
241571313727.60817257341985.39182742663
251474614171.4365855146574.563414485372
2615253.215598.515757129-345.315757128998
2718384.316572.65524743471811.64475256534
2816848.517236.2462411932-387.746241193196
2916485.516366.0302883739119.469711626065
3019257.118058.14319842851198.9568015715
3117093.419444.9586157849-2351.55861578486
3215700.114543.67141934581156.4285806542
3319124.319250.9599572377-126.659957237738
3418640.819056.5615784478-415.761578447778
3518439.215967.8142491232471.38575087696
3617106.316288.4464141569817.853585843059
3718347.715629.44841821512718.25158178489
3819372.718638.8919594997733.808040500251
3922263.821165.79624197141098.00375802858
4019422.920947.4804876358-1524.58048763577
4121268.619500.89713863791767.70286136208
422031022909.5985333808-2599.59853338085
431925620660.5645730184-1404.56457301844
4417535.917456.42183657779.4781634230239
4519857.421135.6460200165-1278.24602001655
4619628.420066.4713318505-438.071331850522
4719727.517728.57010570921998.92989429084
4818112.217343.8888617833768.311138216744
4919080.217161.27205939921918.92794060085
5020684.619114.32388905821570.27611094179
5122537.722416.580279057121.119720943047
5219954.620848.6519808554-894.051980855398
5320230.220722.871080452-492.67108045199
5420445.521341.8949781293-896.394978129349
5519615.320701.5090372337-1086.20903723369
5618071.618136.2508399325-64.6508399324703
5719287.221410.2974460306-2123.09744603059
5821031.419915.82056054041115.57943945962
5919860.919399.006360966461.893639033991
6017671.317562.599135771108.700864229013
6119359.217152.7218411862206.47815881396
621928719239.60715353647.3928464639939
632149820995.9445153156502.055484684442
6420859.719439.49929464591420.20070535408
6520833.121196.3886842295-363.288684229497
6620318.821851.7275372519-1532.92753725192
6721375.920702.2014885039673.698511496128
6817403.419784.6958725525-2381.29587255247
6921050.120808.4868122612241.613187738789
7022010.221959.31302507650.8869749240184
7120372.120516.8683557457-144.768355745655
7219028.418158.0137347363870.386265263736

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13566.7 & 16062.4014423077 & -2495.7014423077 \tabularnewline
14 & 13941.5 & 14484.7461717168 & -543.24617171685 \tabularnewline
15 & 14964.1 & 14966.4204758146 & -2.32047581457118 \tabularnewline
16 & 14086 & 13965.7829970008 & 120.217002999198 \tabularnewline
17 & 13505.1 & 13184.5776415701 & 320.522358429926 \tabularnewline
18 & 15300.4 & 14725.7316800218 & 574.668319978198 \tabularnewline
19 & 14725.2 & 15775.8190784267 & -1050.61907842672 \tabularnewline
20 & 12484.9 & 11027.846588903 & 1457.05341109703 \tabularnewline
21 & 16082.6 & 16107.8978788706 & -25.2978788705932 \tabularnewline
22 & 15915.8 & 15726.0646546669 & 189.735345333085 \tabularnewline
23 & 15916.1 & 11994.3558548063 & 3921.74414519375 \tabularnewline
24 & 15713 & 13727.6081725734 & 1985.39182742663 \tabularnewline
25 & 14746 & 14171.4365855146 & 574.563414485372 \tabularnewline
26 & 15253.2 & 15598.515757129 & -345.315757128998 \tabularnewline
27 & 18384.3 & 16572.6552474347 & 1811.64475256534 \tabularnewline
28 & 16848.5 & 17236.2462411932 & -387.746241193196 \tabularnewline
29 & 16485.5 & 16366.0302883739 & 119.469711626065 \tabularnewline
30 & 19257.1 & 18058.1431984285 & 1198.9568015715 \tabularnewline
31 & 17093.4 & 19444.9586157849 & -2351.55861578486 \tabularnewline
32 & 15700.1 & 14543.6714193458 & 1156.4285806542 \tabularnewline
33 & 19124.3 & 19250.9599572377 & -126.659957237738 \tabularnewline
34 & 18640.8 & 19056.5615784478 & -415.761578447778 \tabularnewline
35 & 18439.2 & 15967.814249123 & 2471.38575087696 \tabularnewline
36 & 17106.3 & 16288.4464141569 & 817.853585843059 \tabularnewline
37 & 18347.7 & 15629.4484182151 & 2718.25158178489 \tabularnewline
38 & 19372.7 & 18638.8919594997 & 733.808040500251 \tabularnewline
39 & 22263.8 & 21165.7962419714 & 1098.00375802858 \tabularnewline
40 & 19422.9 & 20947.4804876358 & -1524.58048763577 \tabularnewline
41 & 21268.6 & 19500.8971386379 & 1767.70286136208 \tabularnewline
42 & 20310 & 22909.5985333808 & -2599.59853338085 \tabularnewline
43 & 19256 & 20660.5645730184 & -1404.56457301844 \tabularnewline
44 & 17535.9 & 17456.421836577 & 79.4781634230239 \tabularnewline
45 & 19857.4 & 21135.6460200165 & -1278.24602001655 \tabularnewline
46 & 19628.4 & 20066.4713318505 & -438.071331850522 \tabularnewline
47 & 19727.5 & 17728.5701057092 & 1998.92989429084 \tabularnewline
48 & 18112.2 & 17343.8888617833 & 768.311138216744 \tabularnewline
49 & 19080.2 & 17161.2720593992 & 1918.92794060085 \tabularnewline
50 & 20684.6 & 19114.3238890582 & 1570.27611094179 \tabularnewline
51 & 22537.7 & 22416.580279057 & 121.119720943047 \tabularnewline
52 & 19954.6 & 20848.6519808554 & -894.051980855398 \tabularnewline
53 & 20230.2 & 20722.871080452 & -492.67108045199 \tabularnewline
54 & 20445.5 & 21341.8949781293 & -896.394978129349 \tabularnewline
55 & 19615.3 & 20701.5090372337 & -1086.20903723369 \tabularnewline
56 & 18071.6 & 18136.2508399325 & -64.6508399324703 \tabularnewline
57 & 19287.2 & 21410.2974460306 & -2123.09744603059 \tabularnewline
58 & 21031.4 & 19915.8205605404 & 1115.57943945962 \tabularnewline
59 & 19860.9 & 19399.006360966 & 461.893639033991 \tabularnewline
60 & 17671.3 & 17562.599135771 & 108.700864229013 \tabularnewline
61 & 19359.2 & 17152.721841186 & 2206.47815881396 \tabularnewline
62 & 19287 & 19239.607153536 & 47.3928464639939 \tabularnewline
63 & 21498 & 20995.9445153156 & 502.055484684442 \tabularnewline
64 & 20859.7 & 19439.4992946459 & 1420.20070535408 \tabularnewline
65 & 20833.1 & 21196.3886842295 & -363.288684229497 \tabularnewline
66 & 20318.8 & 21851.7275372519 & -1532.92753725192 \tabularnewline
67 & 21375.9 & 20702.2014885039 & 673.698511496128 \tabularnewline
68 & 17403.4 & 19784.6958725525 & -2381.29587255247 \tabularnewline
69 & 21050.1 & 20808.4868122612 & 241.613187738789 \tabularnewline
70 & 22010.2 & 21959.313025076 & 50.8869749240184 \tabularnewline
71 & 20372.1 & 20516.8683557457 & -144.768355745655 \tabularnewline
72 & 19028.4 & 18158.0137347363 & 870.386265263736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261374&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]13566.7[/C][C]16062.4014423077[/C][C]-2495.7014423077[/C][/ROW]
[ROW][C]14[/C][C]13941.5[/C][C]14484.7461717168[/C][C]-543.24617171685[/C][/ROW]
[ROW][C]15[/C][C]14964.1[/C][C]14966.4204758146[/C][C]-2.32047581457118[/C][/ROW]
[ROW][C]16[/C][C]14086[/C][C]13965.7829970008[/C][C]120.217002999198[/C][/ROW]
[ROW][C]17[/C][C]13505.1[/C][C]13184.5776415701[/C][C]320.522358429926[/C][/ROW]
[ROW][C]18[/C][C]15300.4[/C][C]14725.7316800218[/C][C]574.668319978198[/C][/ROW]
[ROW][C]19[/C][C]14725.2[/C][C]15775.8190784267[/C][C]-1050.61907842672[/C][/ROW]
[ROW][C]20[/C][C]12484.9[/C][C]11027.846588903[/C][C]1457.05341109703[/C][/ROW]
[ROW][C]21[/C][C]16082.6[/C][C]16107.8978788706[/C][C]-25.2978788705932[/C][/ROW]
[ROW][C]22[/C][C]15915.8[/C][C]15726.0646546669[/C][C]189.735345333085[/C][/ROW]
[ROW][C]23[/C][C]15916.1[/C][C]11994.3558548063[/C][C]3921.74414519375[/C][/ROW]
[ROW][C]24[/C][C]15713[/C][C]13727.6081725734[/C][C]1985.39182742663[/C][/ROW]
[ROW][C]25[/C][C]14746[/C][C]14171.4365855146[/C][C]574.563414485372[/C][/ROW]
[ROW][C]26[/C][C]15253.2[/C][C]15598.515757129[/C][C]-345.315757128998[/C][/ROW]
[ROW][C]27[/C][C]18384.3[/C][C]16572.6552474347[/C][C]1811.64475256534[/C][/ROW]
[ROW][C]28[/C][C]16848.5[/C][C]17236.2462411932[/C][C]-387.746241193196[/C][/ROW]
[ROW][C]29[/C][C]16485.5[/C][C]16366.0302883739[/C][C]119.469711626065[/C][/ROW]
[ROW][C]30[/C][C]19257.1[/C][C]18058.1431984285[/C][C]1198.9568015715[/C][/ROW]
[ROW][C]31[/C][C]17093.4[/C][C]19444.9586157849[/C][C]-2351.55861578486[/C][/ROW]
[ROW][C]32[/C][C]15700.1[/C][C]14543.6714193458[/C][C]1156.4285806542[/C][/ROW]
[ROW][C]33[/C][C]19124.3[/C][C]19250.9599572377[/C][C]-126.659957237738[/C][/ROW]
[ROW][C]34[/C][C]18640.8[/C][C]19056.5615784478[/C][C]-415.761578447778[/C][/ROW]
[ROW][C]35[/C][C]18439.2[/C][C]15967.814249123[/C][C]2471.38575087696[/C][/ROW]
[ROW][C]36[/C][C]17106.3[/C][C]16288.4464141569[/C][C]817.853585843059[/C][/ROW]
[ROW][C]37[/C][C]18347.7[/C][C]15629.4484182151[/C][C]2718.25158178489[/C][/ROW]
[ROW][C]38[/C][C]19372.7[/C][C]18638.8919594997[/C][C]733.808040500251[/C][/ROW]
[ROW][C]39[/C][C]22263.8[/C][C]21165.7962419714[/C][C]1098.00375802858[/C][/ROW]
[ROW][C]40[/C][C]19422.9[/C][C]20947.4804876358[/C][C]-1524.58048763577[/C][/ROW]
[ROW][C]41[/C][C]21268.6[/C][C]19500.8971386379[/C][C]1767.70286136208[/C][/ROW]
[ROW][C]42[/C][C]20310[/C][C]22909.5985333808[/C][C]-2599.59853338085[/C][/ROW]
[ROW][C]43[/C][C]19256[/C][C]20660.5645730184[/C][C]-1404.56457301844[/C][/ROW]
[ROW][C]44[/C][C]17535.9[/C][C]17456.421836577[/C][C]79.4781634230239[/C][/ROW]
[ROW][C]45[/C][C]19857.4[/C][C]21135.6460200165[/C][C]-1278.24602001655[/C][/ROW]
[ROW][C]46[/C][C]19628.4[/C][C]20066.4713318505[/C][C]-438.071331850522[/C][/ROW]
[ROW][C]47[/C][C]19727.5[/C][C]17728.5701057092[/C][C]1998.92989429084[/C][/ROW]
[ROW][C]48[/C][C]18112.2[/C][C]17343.8888617833[/C][C]768.311138216744[/C][/ROW]
[ROW][C]49[/C][C]19080.2[/C][C]17161.2720593992[/C][C]1918.92794060085[/C][/ROW]
[ROW][C]50[/C][C]20684.6[/C][C]19114.3238890582[/C][C]1570.27611094179[/C][/ROW]
[ROW][C]51[/C][C]22537.7[/C][C]22416.580279057[/C][C]121.119720943047[/C][/ROW]
[ROW][C]52[/C][C]19954.6[/C][C]20848.6519808554[/C][C]-894.051980855398[/C][/ROW]
[ROW][C]53[/C][C]20230.2[/C][C]20722.871080452[/C][C]-492.67108045199[/C][/ROW]
[ROW][C]54[/C][C]20445.5[/C][C]21341.8949781293[/C][C]-896.394978129349[/C][/ROW]
[ROW][C]55[/C][C]19615.3[/C][C]20701.5090372337[/C][C]-1086.20903723369[/C][/ROW]
[ROW][C]56[/C][C]18071.6[/C][C]18136.2508399325[/C][C]-64.6508399324703[/C][/ROW]
[ROW][C]57[/C][C]19287.2[/C][C]21410.2974460306[/C][C]-2123.09744603059[/C][/ROW]
[ROW][C]58[/C][C]21031.4[/C][C]19915.8205605404[/C][C]1115.57943945962[/C][/ROW]
[ROW][C]59[/C][C]19860.9[/C][C]19399.006360966[/C][C]461.893639033991[/C][/ROW]
[ROW][C]60[/C][C]17671.3[/C][C]17562.599135771[/C][C]108.700864229013[/C][/ROW]
[ROW][C]61[/C][C]19359.2[/C][C]17152.721841186[/C][C]2206.47815881396[/C][/ROW]
[ROW][C]62[/C][C]19287[/C][C]19239.607153536[/C][C]47.3928464639939[/C][/ROW]
[ROW][C]63[/C][C]21498[/C][C]20995.9445153156[/C][C]502.055484684442[/C][/ROW]
[ROW][C]64[/C][C]20859.7[/C][C]19439.4992946459[/C][C]1420.20070535408[/C][/ROW]
[ROW][C]65[/C][C]20833.1[/C][C]21196.3886842295[/C][C]-363.288684229497[/C][/ROW]
[ROW][C]66[/C][C]20318.8[/C][C]21851.7275372519[/C][C]-1532.92753725192[/C][/ROW]
[ROW][C]67[/C][C]21375.9[/C][C]20702.2014885039[/C][C]673.698511496128[/C][/ROW]
[ROW][C]68[/C][C]17403.4[/C][C]19784.6958725525[/C][C]-2381.29587255247[/C][/ROW]
[ROW][C]69[/C][C]21050.1[/C][C]20808.4868122612[/C][C]241.613187738789[/C][/ROW]
[ROW][C]70[/C][C]22010.2[/C][C]21959.313025076[/C][C]50.8869749240184[/C][/ROW]
[ROW][C]71[/C][C]20372.1[/C][C]20516.8683557457[/C][C]-144.768355745655[/C][/ROW]
[ROW][C]72[/C][C]19028.4[/C][C]18158.0137347363[/C][C]870.386265263736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261374&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261374&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
1313566.716062.4014423077-2495.7014423077
1413941.514484.7461717168-543.24617171685
1514964.114966.4204758146-2.32047581457118
161408613965.7829970008120.217002999198
1713505.113184.5776415701320.522358429926
1815300.414725.7316800218574.668319978198
1914725.215775.8190784267-1050.61907842672
2012484.911027.8465889031457.05341109703
2116082.616107.8978788706-25.2978788705932
2215915.815726.0646546669189.735345333085
2315916.111994.35585480633921.74414519375
241571313727.60817257341985.39182742663
251474614171.4365855146574.563414485372
2615253.215598.515757129-345.315757128998
2718384.316572.65524743471811.64475256534
2816848.517236.2462411932-387.746241193196
2916485.516366.0302883739119.469711626065
3019257.118058.14319842851198.9568015715
3117093.419444.9586157849-2351.55861578486
3215700.114543.67141934581156.4285806542
3319124.319250.9599572377-126.659957237738
3418640.819056.5615784478-415.761578447778
3518439.215967.8142491232471.38575087696
3617106.316288.4464141569817.853585843059
3718347.715629.44841821512718.25158178489
3819372.718638.8919594997733.808040500251
3922263.821165.79624197141098.00375802858
4019422.920947.4804876358-1524.58048763577
4121268.619500.89713863791767.70286136208
422031022909.5985333808-2599.59853338085
431925620660.5645730184-1404.56457301844
4417535.917456.42183657779.4781634230239
4519857.421135.6460200165-1278.24602001655
4619628.420066.4713318505-438.071331850522
4719727.517728.57010570921998.92989429084
4818112.217343.8888617833768.311138216744
4919080.217161.27205939921918.92794060085
5020684.619114.32388905821570.27611094179
5122537.722416.580279057121.119720943047
5219954.620848.6519808554-894.051980855398
5320230.220722.871080452-492.67108045199
5420445.521341.8949781293-896.394978129349
5519615.320701.5090372337-1086.20903723369
5618071.618136.2508399325-64.6508399324703
5719287.221410.2974460306-2123.09744603059
5821031.419915.82056054041115.57943945962
5919860.919399.006360966461.893639033991
6017671.317562.599135771108.700864229013
6119359.217152.7218411862206.47815881396
621928719239.60715353647.3928464639939
632149820995.9445153156502.055484684442
6420859.719439.49929464591420.20070535408
6520833.121196.3886842295-363.288684229497
6620318.821851.7275372519-1532.92753725192
6721375.920702.2014885039673.698511496128
6817403.419784.6958725525-2381.29587255247
6921050.120808.4868122612241.613187738789
7022010.221959.31302507650.8869749240184
7120372.120516.8683557457-144.768355745655
7219028.418158.0137347363870.386265263736







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318877.714819442816229.420435029421526.0092038561
7418752.77000847315386.644509346622118.8955075994
7520565.447023415116571.132685566324559.7613612639
7618819.844269780414248.716922760123390.9716168006
7718997.578677165913882.573391694924112.5839626369
7819583.232483286213946.808777793725219.6561887787
7920111.324771662113969.363505899126253.2860374252
8017904.695529779811268.655242649524540.7358169102
8121396.300648230814274.516931364728518.084365097
8222339.116527169714737.635772903729940.5972814357
8320830.494746049412753.635619475628907.3538726232
8418851.535423124210302.281771250327400.7890749982

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18877.7148194428 & 16229.4204350294 & 21526.0092038561 \tabularnewline
74 & 18752.770008473 & 15386.6445093466 & 22118.8955075994 \tabularnewline
75 & 20565.4470234151 & 16571.1326855663 & 24559.7613612639 \tabularnewline
76 & 18819.8442697804 & 14248.7169227601 & 23390.9716168006 \tabularnewline
77 & 18997.5786771659 & 13882.5733916949 & 24112.5839626369 \tabularnewline
78 & 19583.2324832862 & 13946.8087777937 & 25219.6561887787 \tabularnewline
79 & 20111.3247716621 & 13969.3635058991 & 26253.2860374252 \tabularnewline
80 & 17904.6955297798 & 11268.6552426495 & 24540.7358169102 \tabularnewline
81 & 21396.3006482308 & 14274.5169313647 & 28518.084365097 \tabularnewline
82 & 22339.1165271697 & 14737.6357729037 & 29940.5972814357 \tabularnewline
83 & 20830.4947460494 & 12753.6356194756 & 28907.3538726232 \tabularnewline
84 & 18851.5354231242 & 10302.2817712503 & 27400.7890749982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261374&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]18877.7148194428[/C][C]16229.4204350294[/C][C]21526.0092038561[/C][/ROW]
[ROW][C]74[/C][C]18752.770008473[/C][C]15386.6445093466[/C][C]22118.8955075994[/C][/ROW]
[ROW][C]75[/C][C]20565.4470234151[/C][C]16571.1326855663[/C][C]24559.7613612639[/C][/ROW]
[ROW][C]76[/C][C]18819.8442697804[/C][C]14248.7169227601[/C][C]23390.9716168006[/C][/ROW]
[ROW][C]77[/C][C]18997.5786771659[/C][C]13882.5733916949[/C][C]24112.5839626369[/C][/ROW]
[ROW][C]78[/C][C]19583.2324832862[/C][C]13946.8087777937[/C][C]25219.6561887787[/C][/ROW]
[ROW][C]79[/C][C]20111.3247716621[/C][C]13969.3635058991[/C][C]26253.2860374252[/C][/ROW]
[ROW][C]80[/C][C]17904.6955297798[/C][C]11268.6552426495[/C][C]24540.7358169102[/C][/ROW]
[ROW][C]81[/C][C]21396.3006482308[/C][C]14274.5169313647[/C][C]28518.084365097[/C][/ROW]
[ROW][C]82[/C][C]22339.1165271697[/C][C]14737.6357729037[/C][C]29940.5972814357[/C][/ROW]
[ROW][C]83[/C][C]20830.4947460494[/C][C]12753.6356194756[/C][C]28907.3538726232[/C][/ROW]
[ROW][C]84[/C][C]18851.5354231242[/C][C]10302.2817712503[/C][C]27400.7890749982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261374&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261374&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
7318877.714819442816229.420435029421526.0092038561
7418752.77000847315386.644509346622118.8955075994
7520565.447023415116571.132685566324559.7613612639
7618819.844269780414248.716922760123390.9716168006
7718997.578677165913882.573391694924112.5839626369
7819583.232483286213946.808777793725219.6561887787
7920111.324771662113969.363505899126253.2860374252
8017904.695529779811268.655242649524540.7358169102
8121396.300648230814274.516931364728518.084365097
8222339.116527169714737.635772903729940.5972814357
8320830.494746049412753.635619475628907.3538726232
8418851.535423124210302.281771250327400.7890749982



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')