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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Dec 2009 10:24:44 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t1259861166kf3snmj64ndsz6w.htm/, Retrieved Fri, 29 Mar 2024 08:00:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62944, Retrieved Fri, 29 Mar 2024 08:00:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [w] [2009-12-03 17:24:44] [950726a732ba3ca782ecb1a5307d0f6f] [Current]
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Dataseries X:
13132.1
17665.9
16913
17318.8
16224.2
15469.6
16557.5
19414.8
17335
16525.2
18160.4
15553.8
15262.2
18581
17564.1
18948.6
17187.8
17564.8
17668.4
20811.7
17257.8
18984.2
20532.6
17082.3
16894.9
20274.9
20078.6
19900.9
17012.2
19642.9
19024
21691
18835.9
19873.4
21468.2
19406.8
18385.3
20739.3
22268.3
21569
17514.8
21124.7
21251
21393
22145.2
20310.5
23466.9
21264.6
18388.1
22635.4
22014.3
18422.7
16120.2
16037.7
16410.7
17749.8
16349.8
15662.3
17782.3
16398.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62944&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62944&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62944&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.311491073238867
beta0.198311700434253
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.311491073238867 \tabularnewline
beta & 0.198311700434253 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62944&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]0.311491073238867[/C][/ROW]
[ROW][C]beta[/C][C]0.198311700434253[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62944&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62944&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
alpha0.311491073238867
beta0.198311700434253
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315262.214642.7843279036619.415672096362
141858118118.4834432848462.516556715174
1517564.117390.8746132434173.225386756629
1618948.618920.821842666827.7781573331667
1717187.817163.994995872223.8050041278475
1817564.817580.668405127-15.8684051270102
1917668.418022.9436502772-354.543650277174
2020811.721044.3377955138-232.637795513809
2117257.818816.9020020803-1559.10200208033
2218984.217441.42146635551542.77853364446
2320532.619745.2406121274787.359387872613
2417082.317184.1730324847-101.873032484731
2516894.917365.1292307161-470.229230716148
2620274.920793.3156484679-518.415648467897
2720078.619381.2679325466697.33206745343
2819900.921100.5621325104-1199.66213251041
2917012.218698.9432523858-1686.74325238578
3019642.918382.53586303041260.36413696965
311902418884.0072523413139.992747658656
322169122270.1591755163-579.159175516299
3318835.918701.2075968680134.692403132041
3419873.420066.6909084720-193.290908472030
3521468.221251.2814731504216.918526849619
3619406.817639.65465400461767.14534599536
3718385.318125.0818283013260.218171698732
3820739.322050.6191387497-1311.31913874966
3922268.321181.06121145901087.23878854096
402156921719.030309965-150.030309964983
4117514.819123.4283381395-1608.62833813954
4221124.721129.4605710907-4.76057109073736
432125120404.8071634457846.192836554284
442139323794.4895257723-2401.48952577232
4522145.219905.66473403662239.53526596338
4620310.521871.8211575444-1561.32115754439
4723466.923013.3021334836453.597866516368
4821264.620296.2891951033968.310804896715
4918388.119366.8994649676-978.799464967553
5022635.421757.2621186045878.13788139549
5122014.323261.6939461822-1247.39394618223
5218422.722044.6205255027-3621.92052550270
5316120.217143.7070166730-1023.50701667302
5416037.719969.4835900108-3931.78359001076
5516410.718061.4499175978-1650.74991759779
5617749.817518.9750607891230.824939210892
5716349.817001.9720051595-652.172005159511
5815662.315064.6069679350597.693032065039
5917782.316842.0211896562940.278810343767
6016398.914736.55834753521662.34165246485

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15262.2 & 14642.7843279036 & 619.415672096362 \tabularnewline
14 & 18581 & 18118.4834432848 & 462.516556715174 \tabularnewline
15 & 17564.1 & 17390.8746132434 & 173.225386756629 \tabularnewline
16 & 18948.6 & 18920.8218426668 & 27.7781573331667 \tabularnewline
17 & 17187.8 & 17163.9949958722 & 23.8050041278475 \tabularnewline
18 & 17564.8 & 17580.668405127 & -15.8684051270102 \tabularnewline
19 & 17668.4 & 18022.9436502772 & -354.543650277174 \tabularnewline
20 & 20811.7 & 21044.3377955138 & -232.637795513809 \tabularnewline
21 & 17257.8 & 18816.9020020803 & -1559.10200208033 \tabularnewline
22 & 18984.2 & 17441.4214663555 & 1542.77853364446 \tabularnewline
23 & 20532.6 & 19745.2406121274 & 787.359387872613 \tabularnewline
24 & 17082.3 & 17184.1730324847 & -101.873032484731 \tabularnewline
25 & 16894.9 & 17365.1292307161 & -470.229230716148 \tabularnewline
26 & 20274.9 & 20793.3156484679 & -518.415648467897 \tabularnewline
27 & 20078.6 & 19381.2679325466 & 697.33206745343 \tabularnewline
28 & 19900.9 & 21100.5621325104 & -1199.66213251041 \tabularnewline
29 & 17012.2 & 18698.9432523858 & -1686.74325238578 \tabularnewline
30 & 19642.9 & 18382.5358630304 & 1260.36413696965 \tabularnewline
31 & 19024 & 18884.0072523413 & 139.992747658656 \tabularnewline
32 & 21691 & 22270.1591755163 & -579.159175516299 \tabularnewline
33 & 18835.9 & 18701.2075968680 & 134.692403132041 \tabularnewline
34 & 19873.4 & 20066.6909084720 & -193.290908472030 \tabularnewline
35 & 21468.2 & 21251.2814731504 & 216.918526849619 \tabularnewline
36 & 19406.8 & 17639.6546540046 & 1767.14534599536 \tabularnewline
37 & 18385.3 & 18125.0818283013 & 260.218171698732 \tabularnewline
38 & 20739.3 & 22050.6191387497 & -1311.31913874966 \tabularnewline
39 & 22268.3 & 21181.0612114590 & 1087.23878854096 \tabularnewline
40 & 21569 & 21719.030309965 & -150.030309964983 \tabularnewline
41 & 17514.8 & 19123.4283381395 & -1608.62833813954 \tabularnewline
42 & 21124.7 & 21129.4605710907 & -4.76057109073736 \tabularnewline
43 & 21251 & 20404.8071634457 & 846.192836554284 \tabularnewline
44 & 21393 & 23794.4895257723 & -2401.48952577232 \tabularnewline
45 & 22145.2 & 19905.6647340366 & 2239.53526596338 \tabularnewline
46 & 20310.5 & 21871.8211575444 & -1561.32115754439 \tabularnewline
47 & 23466.9 & 23013.3021334836 & 453.597866516368 \tabularnewline
48 & 21264.6 & 20296.2891951033 & 968.310804896715 \tabularnewline
49 & 18388.1 & 19366.8994649676 & -978.799464967553 \tabularnewline
50 & 22635.4 & 21757.2621186045 & 878.13788139549 \tabularnewline
51 & 22014.3 & 23261.6939461822 & -1247.39394618223 \tabularnewline
52 & 18422.7 & 22044.6205255027 & -3621.92052550270 \tabularnewline
53 & 16120.2 & 17143.7070166730 & -1023.50701667302 \tabularnewline
54 & 16037.7 & 19969.4835900108 & -3931.78359001076 \tabularnewline
55 & 16410.7 & 18061.4499175978 & -1650.74991759779 \tabularnewline
56 & 17749.8 & 17518.9750607891 & 230.824939210892 \tabularnewline
57 & 16349.8 & 17001.9720051595 & -652.172005159511 \tabularnewline
58 & 15662.3 & 15064.6069679350 & 597.693032065039 \tabularnewline
59 & 17782.3 & 16842.0211896562 & 940.278810343767 \tabularnewline
60 & 16398.9 & 14736.5583475352 & 1662.34165246485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62944&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]15262.2[/C][C]14642.7843279036[/C][C]619.415672096362[/C][/ROW]
[ROW][C]14[/C][C]18581[/C][C]18118.4834432848[/C][C]462.516556715174[/C][/ROW]
[ROW][C]15[/C][C]17564.1[/C][C]17390.8746132434[/C][C]173.225386756629[/C][/ROW]
[ROW][C]16[/C][C]18948.6[/C][C]18920.8218426668[/C][C]27.7781573331667[/C][/ROW]
[ROW][C]17[/C][C]17187.8[/C][C]17163.9949958722[/C][C]23.8050041278475[/C][/ROW]
[ROW][C]18[/C][C]17564.8[/C][C]17580.668405127[/C][C]-15.8684051270102[/C][/ROW]
[ROW][C]19[/C][C]17668.4[/C][C]18022.9436502772[/C][C]-354.543650277174[/C][/ROW]
[ROW][C]20[/C][C]20811.7[/C][C]21044.3377955138[/C][C]-232.637795513809[/C][/ROW]
[ROW][C]21[/C][C]17257.8[/C][C]18816.9020020803[/C][C]-1559.10200208033[/C][/ROW]
[ROW][C]22[/C][C]18984.2[/C][C]17441.4214663555[/C][C]1542.77853364446[/C][/ROW]
[ROW][C]23[/C][C]20532.6[/C][C]19745.2406121274[/C][C]787.359387872613[/C][/ROW]
[ROW][C]24[/C][C]17082.3[/C][C]17184.1730324847[/C][C]-101.873032484731[/C][/ROW]
[ROW][C]25[/C][C]16894.9[/C][C]17365.1292307161[/C][C]-470.229230716148[/C][/ROW]
[ROW][C]26[/C][C]20274.9[/C][C]20793.3156484679[/C][C]-518.415648467897[/C][/ROW]
[ROW][C]27[/C][C]20078.6[/C][C]19381.2679325466[/C][C]697.33206745343[/C][/ROW]
[ROW][C]28[/C][C]19900.9[/C][C]21100.5621325104[/C][C]-1199.66213251041[/C][/ROW]
[ROW][C]29[/C][C]17012.2[/C][C]18698.9432523858[/C][C]-1686.74325238578[/C][/ROW]
[ROW][C]30[/C][C]19642.9[/C][C]18382.5358630304[/C][C]1260.36413696965[/C][/ROW]
[ROW][C]31[/C][C]19024[/C][C]18884.0072523413[/C][C]139.992747658656[/C][/ROW]
[ROW][C]32[/C][C]21691[/C][C]22270.1591755163[/C][C]-579.159175516299[/C][/ROW]
[ROW][C]33[/C][C]18835.9[/C][C]18701.2075968680[/C][C]134.692403132041[/C][/ROW]
[ROW][C]34[/C][C]19873.4[/C][C]20066.6909084720[/C][C]-193.290908472030[/C][/ROW]
[ROW][C]35[/C][C]21468.2[/C][C]21251.2814731504[/C][C]216.918526849619[/C][/ROW]
[ROW][C]36[/C][C]19406.8[/C][C]17639.6546540046[/C][C]1767.14534599536[/C][/ROW]
[ROW][C]37[/C][C]18385.3[/C][C]18125.0818283013[/C][C]260.218171698732[/C][/ROW]
[ROW][C]38[/C][C]20739.3[/C][C]22050.6191387497[/C][C]-1311.31913874966[/C][/ROW]
[ROW][C]39[/C][C]22268.3[/C][C]21181.0612114590[/C][C]1087.23878854096[/C][/ROW]
[ROW][C]40[/C][C]21569[/C][C]21719.030309965[/C][C]-150.030309964983[/C][/ROW]
[ROW][C]41[/C][C]17514.8[/C][C]19123.4283381395[/C][C]-1608.62833813954[/C][/ROW]
[ROW][C]42[/C][C]21124.7[/C][C]21129.4605710907[/C][C]-4.76057109073736[/C][/ROW]
[ROW][C]43[/C][C]21251[/C][C]20404.8071634457[/C][C]846.192836554284[/C][/ROW]
[ROW][C]44[/C][C]21393[/C][C]23794.4895257723[/C][C]-2401.48952577232[/C][/ROW]
[ROW][C]45[/C][C]22145.2[/C][C]19905.6647340366[/C][C]2239.53526596338[/C][/ROW]
[ROW][C]46[/C][C]20310.5[/C][C]21871.8211575444[/C][C]-1561.32115754439[/C][/ROW]
[ROW][C]47[/C][C]23466.9[/C][C]23013.3021334836[/C][C]453.597866516368[/C][/ROW]
[ROW][C]48[/C][C]21264.6[/C][C]20296.2891951033[/C][C]968.310804896715[/C][/ROW]
[ROW][C]49[/C][C]18388.1[/C][C]19366.8994649676[/C][C]-978.799464967553[/C][/ROW]
[ROW][C]50[/C][C]22635.4[/C][C]21757.2621186045[/C][C]878.13788139549[/C][/ROW]
[ROW][C]51[/C][C]22014.3[/C][C]23261.6939461822[/C][C]-1247.39394618223[/C][/ROW]
[ROW][C]52[/C][C]18422.7[/C][C]22044.6205255027[/C][C]-3621.92052550270[/C][/ROW]
[ROW][C]53[/C][C]16120.2[/C][C]17143.7070166730[/C][C]-1023.50701667302[/C][/ROW]
[ROW][C]54[/C][C]16037.7[/C][C]19969.4835900108[/C][C]-3931.78359001076[/C][/ROW]
[ROW][C]55[/C][C]16410.7[/C][C]18061.4499175978[/C][C]-1650.74991759779[/C][/ROW]
[ROW][C]56[/C][C]17749.8[/C][C]17518.9750607891[/C][C]230.824939210892[/C][/ROW]
[ROW][C]57[/C][C]16349.8[/C][C]17001.9720051595[/C][C]-652.172005159511[/C][/ROW]
[ROW][C]58[/C][C]15662.3[/C][C]15064.6069679350[/C][C]597.693032065039[/C][/ROW]
[ROW][C]59[/C][C]17782.3[/C][C]16842.0211896562[/C][C]940.278810343767[/C][/ROW]
[ROW][C]60[/C][C]16398.9[/C][C]14736.5583475352[/C][C]1662.34165246485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62944&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62944&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
1315262.214642.7843279036619.415672096362
141858118118.4834432848462.516556715174
1517564.117390.8746132434173.225386756629
1618948.618920.821842666827.7781573331667
1717187.817163.994995872223.8050041278475
1817564.817580.668405127-15.8684051270102
1917668.418022.9436502772-354.543650277174
2020811.721044.3377955138-232.637795513809
2117257.818816.9020020803-1559.10200208033
2218984.217441.42146635551542.77853364446
2320532.619745.2406121274787.359387872613
2417082.317184.1730324847-101.873032484731
2516894.917365.1292307161-470.229230716148
2620274.920793.3156484679-518.415648467897
2720078.619381.2679325466697.33206745343
2819900.921100.5621325104-1199.66213251041
2917012.218698.9432523858-1686.74325238578
3019642.918382.53586303041260.36413696965
311902418884.0072523413139.992747658656
322169122270.1591755163-579.159175516299
3318835.918701.2075968680134.692403132041
3419873.420066.6909084720-193.290908472030
3521468.221251.2814731504216.918526849619
3619406.817639.65465400461767.14534599536
3718385.318125.0818283013260.218171698732
3820739.322050.6191387497-1311.31913874966
3922268.321181.06121145901087.23878854096
402156921719.030309965-150.030309964983
4117514.819123.4283381395-1608.62833813954
4221124.721129.4605710907-4.76057109073736
432125120404.8071634457846.192836554284
442139323794.4895257723-2401.48952577232
4522145.219905.66473403662239.53526596338
4620310.521871.8211575444-1561.32115754439
4723466.923013.3021334836453.597866516368
4821264.620296.2891951033968.310804896715
4918388.119366.8994649676-978.799464967553
5022635.421757.2621186045878.13788139549
5122014.323261.6939461822-1247.39394618223
5218422.722044.6205255027-3621.92052550270
5316120.217143.7070166730-1023.50701667302
5416037.719969.4835900108-3931.78359001076
5516410.718061.4499175978-1650.74991759779
5617749.817518.9750607891230.824939210892
5716349.817001.9720051595-652.172005159511
5815662.315064.6069679350597.693032065039
5917782.316842.0211896562940.278810343767
6016398.914736.55834753521662.34165246485







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6112962.31898115710473.996643210315450.6413191037
6215277.350912668112546.402949187918008.2988761483
6314602.888214109211655.114314191217550.6621140273
6412477.56403257299409.0637601682415546.0643049776
6510882.97357332127679.7534031176514086.1937435248
6611318.62475517007691.9076395693314945.3418707707
6711853.10135344777676.4197522083716029.7829546871
6812776.99504095887816.7076810784217737.2824008391
6911908.89391368026620.37023829217197.4175890683
7011299.13772268505602.1767293712916996.0987159986
7112607.81206173085579.2020334272219636.4220900345
7211184.10877431444539.1721556887717829.0453929401

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 12962.318981157 & 10473.9966432103 & 15450.6413191037 \tabularnewline
62 & 15277.3509126681 & 12546.4029491879 & 18008.2988761483 \tabularnewline
63 & 14602.8882141092 & 11655.1143141912 & 17550.6621140273 \tabularnewline
64 & 12477.5640325729 & 9409.06376016824 & 15546.0643049776 \tabularnewline
65 & 10882.9735733212 & 7679.75340311765 & 14086.1937435248 \tabularnewline
66 & 11318.6247551700 & 7691.90763956933 & 14945.3418707707 \tabularnewline
67 & 11853.1013534477 & 7676.41975220837 & 16029.7829546871 \tabularnewline
68 & 12776.9950409588 & 7816.70768107842 & 17737.2824008391 \tabularnewline
69 & 11908.8939136802 & 6620.370238292 & 17197.4175890683 \tabularnewline
70 & 11299.1377226850 & 5602.17672937129 & 16996.0987159986 \tabularnewline
71 & 12607.8120617308 & 5579.20203342722 & 19636.4220900345 \tabularnewline
72 & 11184.1087743144 & 4539.17215568877 & 17829.0453929401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62944&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]61[/C][C]12962.318981157[/C][C]10473.9966432103[/C][C]15450.6413191037[/C][/ROW]
[ROW][C]62[/C][C]15277.3509126681[/C][C]12546.4029491879[/C][C]18008.2988761483[/C][/ROW]
[ROW][C]63[/C][C]14602.8882141092[/C][C]11655.1143141912[/C][C]17550.6621140273[/C][/ROW]
[ROW][C]64[/C][C]12477.5640325729[/C][C]9409.06376016824[/C][C]15546.0643049776[/C][/ROW]
[ROW][C]65[/C][C]10882.9735733212[/C][C]7679.75340311765[/C][C]14086.1937435248[/C][/ROW]
[ROW][C]66[/C][C]11318.6247551700[/C][C]7691.90763956933[/C][C]14945.3418707707[/C][/ROW]
[ROW][C]67[/C][C]11853.1013534477[/C][C]7676.41975220837[/C][C]16029.7829546871[/C][/ROW]
[ROW][C]68[/C][C]12776.9950409588[/C][C]7816.70768107842[/C][C]17737.2824008391[/C][/ROW]
[ROW][C]69[/C][C]11908.8939136802[/C][C]6620.370238292[/C][C]17197.4175890683[/C][/ROW]
[ROW][C]70[/C][C]11299.1377226850[/C][C]5602.17672937129[/C][C]16996.0987159986[/C][/ROW]
[ROW][C]71[/C][C]12607.8120617308[/C][C]5579.20203342722[/C][C]19636.4220900345[/C][/ROW]
[ROW][C]72[/C][C]11184.1087743144[/C][C]4539.17215568877[/C][C]17829.0453929401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62944&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62944&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
6112962.31898115710473.996643210315450.6413191037
6215277.350912668112546.402949187918008.2988761483
6314602.888214109211655.114314191217550.6621140273
6412477.56403257299409.0637601682415546.0643049776
6510882.97357332127679.7534031176514086.1937435248
6611318.62475517007691.9076395693314945.3418707707
6711853.10135344777676.4197522083716029.7829546871
6812776.99504095887816.7076810784217737.2824008391
6911908.89391368026620.37023829217197.4175890683
7011299.13772268505602.1767293712916996.0987159986
7112607.81206173085579.2020334272219636.4220900345
7211184.10877431444539.1721556887717829.0453929401



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