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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 computationFri, 11 Dec 2009 06:06:10 -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/11/t1260536808owd5g696ds068d3.htm/, Retrieved Mon, 29 Apr 2024 03:04:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66162, Retrieved Mon, 29 Apr 2024 03:04:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
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]
- R PD    [Exponential Smoothing] [] [2009-12-03 20:15:03] [325e037ef8beb77178124dff9c2e015a]
-   PD        [Exponential Smoothing] [] [2009-12-11 13:06:10] [2f6049721194fa571920c3539d7b729e] [Current]
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Dataseries X:
15859.4
15258.9
15498.6
15106.5
15023.6
12083.0
15761.3
16942.6
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861.0
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872.0
17422.0
16704.5
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
17170.0
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6




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=66162&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=66162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66162&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
alpha0.174213016968126
beta0.071262125638547
gamma0.820829629452682

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.174213016968126 \tabularnewline
beta & 0.071262125638547 \tabularnewline
gamma & 0.820829629452682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66162&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]0.174213016968126[/C][/ROW]
[ROW][C]beta[/C][C]0.071262125638547[/C][/ROW]
[ROW][C]gamma[/C][C]0.820829629452682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66162&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
alpha0.174213016968126
beta0.071262125638547
gamma0.820829629452682







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315998.116019.0046906877-20.9046906877138
1415370.615381.7795139018-11.1795139018432
1514956.914986.4485311220-29.5485311219745
1615469.715454.880192030114.8198079698795
1715101.815054.661604282047.1383957180406
1811703.711666.812732805336.8872671946519
1916283.615835.0451371595448.554862840509
2016726.517109.3856576046-382.885657604569
2114968.915186.9490245128-218.049024512839
221486113743.87448892771117.12551107228
2314583.315073.5723660567-490.272366056741
2415305.814971.7315619558334.068438044204
2517903.916329.66952142831574.23047857171
2616379.415984.5847732169394.815226783079
2715420.315664.8373794033-244.537379403268
2817870.516181.86290131581688.63709868421
2915912.816123.2749764559-210.474976455887
3013866.512498.49739330481368.00260669516
3117823.217645.9248718308177.275128169211
321787218439.6057917032-567.605791703198
331742216499.272029197922.727970803007
3416704.516169.2672153693535.232784630674
3515991.216377.7493962974-386.549396297412
3616583.616984.088031371-400.488031370984
3719123.519337.7247223212-214.224722321214
3817838.717790.818726245147.8812737548942
3917209.416936.8887144717272.511285528333
4018586.519062.4184921581-475.918492158104
4116258.117227.6074888604-969.50748886043
4215141.614351.0528873066790.547112693432
4319202.118833.0722295353369.027770464727
4417746.519166.0280206825-1419.52802068245
4519090.118024.59123230281065.50876769723
4618040.317403.617036241636.682963759016
4717515.516966.9836008095548.516399190496
4817751.817768.9934852483-17.1934852483391
4921072.420494.3883128606578.011687139438
501717019178.077194932-2008.07719493199
5119439.518069.52930656121369.97069343875
5219795.419986.0304630315-190.630463031473
5317574.917721.4772259718-146.577225971789
5416165.416071.597318074593.8026819255138
5519464.620440.5032438393-975.903243839315
5619932.119250.3052946916681.794705308432
5719961.220231.1940490922-269.994049092227
5817343.419011.8849180024-1668.48491800241
5918924.218059.6935282454864.50647175462
6018574.118524.925457974849.174542025241
6121350.621775.1998836831-424.599883683055

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15998.1 & 16019.0046906877 & -20.9046906877138 \tabularnewline
14 & 15370.6 & 15381.7795139018 & -11.1795139018432 \tabularnewline
15 & 14956.9 & 14986.4485311220 & -29.5485311219745 \tabularnewline
16 & 15469.7 & 15454.8801920301 & 14.8198079698795 \tabularnewline
17 & 15101.8 & 15054.6616042820 & 47.1383957180406 \tabularnewline
18 & 11703.7 & 11666.8127328053 & 36.8872671946519 \tabularnewline
19 & 16283.6 & 15835.0451371595 & 448.554862840509 \tabularnewline
20 & 16726.5 & 17109.3856576046 & -382.885657604569 \tabularnewline
21 & 14968.9 & 15186.9490245128 & -218.049024512839 \tabularnewline
22 & 14861 & 13743.8744889277 & 1117.12551107228 \tabularnewline
23 & 14583.3 & 15073.5723660567 & -490.272366056741 \tabularnewline
24 & 15305.8 & 14971.7315619558 & 334.068438044204 \tabularnewline
25 & 17903.9 & 16329.6695214283 & 1574.23047857171 \tabularnewline
26 & 16379.4 & 15984.5847732169 & 394.815226783079 \tabularnewline
27 & 15420.3 & 15664.8373794033 & -244.537379403268 \tabularnewline
28 & 17870.5 & 16181.8629013158 & 1688.63709868421 \tabularnewline
29 & 15912.8 & 16123.2749764559 & -210.474976455887 \tabularnewline
30 & 13866.5 & 12498.4973933048 & 1368.00260669516 \tabularnewline
31 & 17823.2 & 17645.9248718308 & 177.275128169211 \tabularnewline
32 & 17872 & 18439.6057917032 & -567.605791703198 \tabularnewline
33 & 17422 & 16499.272029197 & 922.727970803007 \tabularnewline
34 & 16704.5 & 16169.2672153693 & 535.232784630674 \tabularnewline
35 & 15991.2 & 16377.7493962974 & -386.549396297412 \tabularnewline
36 & 16583.6 & 16984.088031371 & -400.488031370984 \tabularnewline
37 & 19123.5 & 19337.7247223212 & -214.224722321214 \tabularnewline
38 & 17838.7 & 17790.8187262451 & 47.8812737548942 \tabularnewline
39 & 17209.4 & 16936.8887144717 & 272.511285528333 \tabularnewline
40 & 18586.5 & 19062.4184921581 & -475.918492158104 \tabularnewline
41 & 16258.1 & 17227.6074888604 & -969.50748886043 \tabularnewline
42 & 15141.6 & 14351.0528873066 & 790.547112693432 \tabularnewline
43 & 19202.1 & 18833.0722295353 & 369.027770464727 \tabularnewline
44 & 17746.5 & 19166.0280206825 & -1419.52802068245 \tabularnewline
45 & 19090.1 & 18024.5912323028 & 1065.50876769723 \tabularnewline
46 & 18040.3 & 17403.617036241 & 636.682963759016 \tabularnewline
47 & 17515.5 & 16966.9836008095 & 548.516399190496 \tabularnewline
48 & 17751.8 & 17768.9934852483 & -17.1934852483391 \tabularnewline
49 & 21072.4 & 20494.3883128606 & 578.011687139438 \tabularnewline
50 & 17170 & 19178.077194932 & -2008.07719493199 \tabularnewline
51 & 19439.5 & 18069.5293065612 & 1369.97069343875 \tabularnewline
52 & 19795.4 & 19986.0304630315 & -190.630463031473 \tabularnewline
53 & 17574.9 & 17721.4772259718 & -146.577225971789 \tabularnewline
54 & 16165.4 & 16071.5973180745 & 93.8026819255138 \tabularnewline
55 & 19464.6 & 20440.5032438393 & -975.903243839315 \tabularnewline
56 & 19932.1 & 19250.3052946916 & 681.794705308432 \tabularnewline
57 & 19961.2 & 20231.1940490922 & -269.994049092227 \tabularnewline
58 & 17343.4 & 19011.8849180024 & -1668.48491800241 \tabularnewline
59 & 18924.2 & 18059.6935282454 & 864.50647175462 \tabularnewline
60 & 18574.1 & 18524.9254579748 & 49.174542025241 \tabularnewline
61 & 21350.6 & 21775.1998836831 & -424.599883683055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66162&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]15998.1[/C][C]16019.0046906877[/C][C]-20.9046906877138[/C][/ROW]
[ROW][C]14[/C][C]15370.6[/C][C]15381.7795139018[/C][C]-11.1795139018432[/C][/ROW]
[ROW][C]15[/C][C]14956.9[/C][C]14986.4485311220[/C][C]-29.5485311219745[/C][/ROW]
[ROW][C]16[/C][C]15469.7[/C][C]15454.8801920301[/C][C]14.8198079698795[/C][/ROW]
[ROW][C]17[/C][C]15101.8[/C][C]15054.6616042820[/C][C]47.1383957180406[/C][/ROW]
[ROW][C]18[/C][C]11703.7[/C][C]11666.8127328053[/C][C]36.8872671946519[/C][/ROW]
[ROW][C]19[/C][C]16283.6[/C][C]15835.0451371595[/C][C]448.554862840509[/C][/ROW]
[ROW][C]20[/C][C]16726.5[/C][C]17109.3856576046[/C][C]-382.885657604569[/C][/ROW]
[ROW][C]21[/C][C]14968.9[/C][C]15186.9490245128[/C][C]-218.049024512839[/C][/ROW]
[ROW][C]22[/C][C]14861[/C][C]13743.8744889277[/C][C]1117.12551107228[/C][/ROW]
[ROW][C]23[/C][C]14583.3[/C][C]15073.5723660567[/C][C]-490.272366056741[/C][/ROW]
[ROW][C]24[/C][C]15305.8[/C][C]14971.7315619558[/C][C]334.068438044204[/C][/ROW]
[ROW][C]25[/C][C]17903.9[/C][C]16329.6695214283[/C][C]1574.23047857171[/C][/ROW]
[ROW][C]26[/C][C]16379.4[/C][C]15984.5847732169[/C][C]394.815226783079[/C][/ROW]
[ROW][C]27[/C][C]15420.3[/C][C]15664.8373794033[/C][C]-244.537379403268[/C][/ROW]
[ROW][C]28[/C][C]17870.5[/C][C]16181.8629013158[/C][C]1688.63709868421[/C][/ROW]
[ROW][C]29[/C][C]15912.8[/C][C]16123.2749764559[/C][C]-210.474976455887[/C][/ROW]
[ROW][C]30[/C][C]13866.5[/C][C]12498.4973933048[/C][C]1368.00260669516[/C][/ROW]
[ROW][C]31[/C][C]17823.2[/C][C]17645.9248718308[/C][C]177.275128169211[/C][/ROW]
[ROW][C]32[/C][C]17872[/C][C]18439.6057917032[/C][C]-567.605791703198[/C][/ROW]
[ROW][C]33[/C][C]17422[/C][C]16499.272029197[/C][C]922.727970803007[/C][/ROW]
[ROW][C]34[/C][C]16704.5[/C][C]16169.2672153693[/C][C]535.232784630674[/C][/ROW]
[ROW][C]35[/C][C]15991.2[/C][C]16377.7493962974[/C][C]-386.549396297412[/C][/ROW]
[ROW][C]36[/C][C]16583.6[/C][C]16984.088031371[/C][C]-400.488031370984[/C][/ROW]
[ROW][C]37[/C][C]19123.5[/C][C]19337.7247223212[/C][C]-214.224722321214[/C][/ROW]
[ROW][C]38[/C][C]17838.7[/C][C]17790.8187262451[/C][C]47.8812737548942[/C][/ROW]
[ROW][C]39[/C][C]17209.4[/C][C]16936.8887144717[/C][C]272.511285528333[/C][/ROW]
[ROW][C]40[/C][C]18586.5[/C][C]19062.4184921581[/C][C]-475.918492158104[/C][/ROW]
[ROW][C]41[/C][C]16258.1[/C][C]17227.6074888604[/C][C]-969.50748886043[/C][/ROW]
[ROW][C]42[/C][C]15141.6[/C][C]14351.0528873066[/C][C]790.547112693432[/C][/ROW]
[ROW][C]43[/C][C]19202.1[/C][C]18833.0722295353[/C][C]369.027770464727[/C][/ROW]
[ROW][C]44[/C][C]17746.5[/C][C]19166.0280206825[/C][C]-1419.52802068245[/C][/ROW]
[ROW][C]45[/C][C]19090.1[/C][C]18024.5912323028[/C][C]1065.50876769723[/C][/ROW]
[ROW][C]46[/C][C]18040.3[/C][C]17403.617036241[/C][C]636.682963759016[/C][/ROW]
[ROW][C]47[/C][C]17515.5[/C][C]16966.9836008095[/C][C]548.516399190496[/C][/ROW]
[ROW][C]48[/C][C]17751.8[/C][C]17768.9934852483[/C][C]-17.1934852483391[/C][/ROW]
[ROW][C]49[/C][C]21072.4[/C][C]20494.3883128606[/C][C]578.011687139438[/C][/ROW]
[ROW][C]50[/C][C]17170[/C][C]19178.077194932[/C][C]-2008.07719493199[/C][/ROW]
[ROW][C]51[/C][C]19439.5[/C][C]18069.5293065612[/C][C]1369.97069343875[/C][/ROW]
[ROW][C]52[/C][C]19795.4[/C][C]19986.0304630315[/C][C]-190.630463031473[/C][/ROW]
[ROW][C]53[/C][C]17574.9[/C][C]17721.4772259718[/C][C]-146.577225971789[/C][/ROW]
[ROW][C]54[/C][C]16165.4[/C][C]16071.5973180745[/C][C]93.8026819255138[/C][/ROW]
[ROW][C]55[/C][C]19464.6[/C][C]20440.5032438393[/C][C]-975.903243839315[/C][/ROW]
[ROW][C]56[/C][C]19932.1[/C][C]19250.3052946916[/C][C]681.794705308432[/C][/ROW]
[ROW][C]57[/C][C]19961.2[/C][C]20231.1940490922[/C][C]-269.994049092227[/C][/ROW]
[ROW][C]58[/C][C]17343.4[/C][C]19011.8849180024[/C][C]-1668.48491800241[/C][/ROW]
[ROW][C]59[/C][C]18924.2[/C][C]18059.6935282454[/C][C]864.50647175462[/C][/ROW]
[ROW][C]60[/C][C]18574.1[/C][C]18524.9254579748[/C][C]49.174542025241[/C][/ROW]
[ROW][C]61[/C][C]21350.6[/C][C]21775.1998836831[/C][C]-424.599883683055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66162&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
1315998.116019.0046906877-20.9046906877138
1415370.615381.7795139018-11.1795139018432
1514956.914986.4485311220-29.5485311219745
1615469.715454.880192030114.8198079698795
1715101.815054.661604282047.1383957180406
1811703.711666.812732805336.8872671946519
1916283.615835.0451371595448.554862840509
2016726.517109.3856576046-382.885657604569
2114968.915186.9490245128-218.049024512839
221486113743.87448892771117.12551107228
2314583.315073.5723660567-490.272366056741
2415305.814971.7315619558334.068438044204
2517903.916329.66952142831574.23047857171
2616379.415984.5847732169394.815226783079
2715420.315664.8373794033-244.537379403268
2817870.516181.86290131581688.63709868421
2915912.816123.2749764559-210.474976455887
3013866.512498.49739330481368.00260669516
3117823.217645.9248718308177.275128169211
321787218439.6057917032-567.605791703198
331742216499.272029197922.727970803007
3416704.516169.2672153693535.232784630674
3515991.216377.7493962974-386.549396297412
3616583.616984.088031371-400.488031370984
3719123.519337.7247223212-214.224722321214
3817838.717790.818726245147.8812737548942
3917209.416936.8887144717272.511285528333
4018586.519062.4184921581-475.918492158104
4116258.117227.6074888604-969.50748886043
4215141.614351.0528873066790.547112693432
4319202.118833.0722295353369.027770464727
4417746.519166.0280206825-1419.52802068245
4519090.118024.59123230281065.50876769723
4618040.317403.617036241636.682963759016
4717515.516966.9836008095548.516399190496
4817751.817768.9934852483-17.1934852483391
4921072.420494.3883128606578.011687139438
501717019178.077194932-2008.07719493199
5119439.518069.52930656121369.97069343875
5219795.419986.0304630315-190.630463031473
5317574.917721.4772259718-146.577225971789
5416165.416071.597318074593.8026819255138
5519464.620440.5032438393-975.903243839315
5619932.119250.3052946916681.794705308432
5719961.220231.1940490922-269.994049092227
5817343.419011.8849180024-1668.48491800241
5918924.218059.6935282454864.50647175462
6018574.118524.925457974849.174542025241
6121350.621775.1998836831-424.599883683055







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6218365.777060672617083.289034888319648.2650864569
6319953.251848956118635.221157815221271.2825400971
6420568.436664582719212.392697840221924.4806313251
6518261.721772164516891.159643790419632.2839005387
6616726.293353707815337.098714178318115.4879932373
6720453.062221995318957.254601274021948.8698427166
6820545.441738477918999.761482229722091.1219947261
6920748.699595057619146.836530576822350.5626595384
7018515.240212442516928.676280380420101.8041445047
7119624.704322499517947.959641101321301.4490038978
7219368.928771244617645.969386265221091.888156224
7322405.647381767520975.850474222923835.4442893122

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 18365.7770606726 & 17083.2890348883 & 19648.2650864569 \tabularnewline
63 & 19953.2518489561 & 18635.2211578152 & 21271.2825400971 \tabularnewline
64 & 20568.4366645827 & 19212.3926978402 & 21924.4806313251 \tabularnewline
65 & 18261.7217721645 & 16891.1596437904 & 19632.2839005387 \tabularnewline
66 & 16726.2933537078 & 15337.0987141783 & 18115.4879932373 \tabularnewline
67 & 20453.0622219953 & 18957.2546012740 & 21948.8698427166 \tabularnewline
68 & 20545.4417384779 & 18999.7614822297 & 22091.1219947261 \tabularnewline
69 & 20748.6995950576 & 19146.8365305768 & 22350.5626595384 \tabularnewline
70 & 18515.2402124425 & 16928.6762803804 & 20101.8041445047 \tabularnewline
71 & 19624.7043224995 & 17947.9596411013 & 21301.4490038978 \tabularnewline
72 & 19368.9287712446 & 17645.9693862652 & 21091.888156224 \tabularnewline
73 & 22405.6473817675 & 20975.8504742229 & 23835.4442893122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66162&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]62[/C][C]18365.7770606726[/C][C]17083.2890348883[/C][C]19648.2650864569[/C][/ROW]
[ROW][C]63[/C][C]19953.2518489561[/C][C]18635.2211578152[/C][C]21271.2825400971[/C][/ROW]
[ROW][C]64[/C][C]20568.4366645827[/C][C]19212.3926978402[/C][C]21924.4806313251[/C][/ROW]
[ROW][C]65[/C][C]18261.7217721645[/C][C]16891.1596437904[/C][C]19632.2839005387[/C][/ROW]
[ROW][C]66[/C][C]16726.2933537078[/C][C]15337.0987141783[/C][C]18115.4879932373[/C][/ROW]
[ROW][C]67[/C][C]20453.0622219953[/C][C]18957.2546012740[/C][C]21948.8698427166[/C][/ROW]
[ROW][C]68[/C][C]20545.4417384779[/C][C]18999.7614822297[/C][C]22091.1219947261[/C][/ROW]
[ROW][C]69[/C][C]20748.6995950576[/C][C]19146.8365305768[/C][C]22350.5626595384[/C][/ROW]
[ROW][C]70[/C][C]18515.2402124425[/C][C]16928.6762803804[/C][C]20101.8041445047[/C][/ROW]
[ROW][C]71[/C][C]19624.7043224995[/C][C]17947.9596411013[/C][C]21301.4490038978[/C][/ROW]
[ROW][C]72[/C][C]19368.9287712446[/C][C]17645.9693862652[/C][C]21091.888156224[/C][/ROW]
[ROW][C]73[/C][C]22405.6473817675[/C][C]20975.8504742229[/C][C]23835.4442893122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66162&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66162&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
6218365.777060672617083.289034888319648.2650864569
6319953.251848956118635.221157815221271.2825400971
6420568.436664582719212.392697840221924.4806313251
6518261.721772164516891.159643790419632.2839005387
6616726.293353707815337.098714178318115.4879932373
6720453.062221995318957.254601274021948.8698427166
6820545.441738477918999.761482229722091.1219947261
6920748.699595057619146.836530576822350.5626595384
7018515.240212442516928.676280380420101.8041445047
7119624.704322499517947.959641101321301.4490038978
7219368.928771244617645.969386265221091.888156224
7322405.647381767520975.850474222923835.4442893122



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')