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Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 09:22:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481876616m86aqlujlcc5qqe.htm/, Retrieved Fri, 01 Nov 2024 03:44:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300104, Retrieved Fri, 01 Nov 2024 03:44:44 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-16 08:22:32] [3b055ff671ad33431c4331443bac114d] [Current]
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Dataseries X:
9137.8
9009.4
8926.6
9145
9186.2
9152.2
9093.6
9199.2
9310.6
9282
9248.4
9341.6
9478.8
9438
9374.6
9488.8
9631.8
9588.4
9514.6
9623.2
9744.6
9685.8
9598
9703.4
9817.8
9762.6
9669.6
9789.2
9917.4
9864.4
9779.2
9898.8
10048.8
9983.4
9913.4
10031.6
10184.6
10125
10065.4
10188.6
10350.4
10320.6
10232.6
10357.2
10520.2
10473.8
10407
10536
10700.2
10664.2
10606
10716.6
10882.8
10849.4
10794
10907.8




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300104&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300104&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.358844021865748
beta0.307694228735539
gamma0.897450580773701

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.358844021865748 \tabularnewline
beta & 0.307694228735539 \tabularnewline
gamma & 0.897450580773701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300104&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]0.358844021865748[/C][/ROW]
[ROW][C]beta[/C][C]0.307694228735539[/C][/ROW]
[ROW][C]gamma[/C][C]0.897450580773701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300104&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
alpha0.358844021865748
beta0.307694228735539
gamma0.897450580773701







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
59186.29123.792562.4075000000012
69152.29122.3827346369129.81726536309
79093.69038.8954089344454.7045910655634
89199.29300.20391682909-101.003916829086
99310.69338.36972512143-27.7697251214304
1092829280.961764394921.03823560507954
119248.49193.4039260201354.9960739798735
129341.69357.18999379003-15.5899937900285
139478.89469.544912005329.25508799468298
1494389447.48687358357-9.48687358356801
159374.69391.52521587216-16.9252158721592
169488.89485.27139117663.52860882339701
179631.89617.278141388214.5218586118008
189588.49585.402576533852.9974234661513
199514.69530.09597086154-15.4959708615406
209623.29636.73728265839-13.5372826583844
219744.69767.67431313404-23.0743131340387
229685.89710.25390105371-24.4539010537155
2395989626.00186938336-28.0018693833645
249703.49719.44824975465-16.0482497546491
259817.89833.88502042608-16.0850204260842
269762.69768.83901718301-6.23901718300658
279669.69681.75311441525-12.1531144152468
289789.29782.186184322837.01381567717544
299917.49901.8451379877515.5548620122536
309864.49854.2795149714510.1204850285467
319779.29771.928587948497.2714120515102
329898.89894.773012169484.02698783051892
3310048.810022.357156123526.4428438765008
349983.49980.856264394692.54373560530803
359913.49898.5951281664214.8048718335776
3610031.610027.55586521914.04413478088463
3710184.610173.326105568211.2738944318062
381012510116.2371030628.76289693801118
3910065.410047.55635027917.8436497209968
4010188.610176.044813998312.5551860017422
4110350.410334.598051028415.8019489715934
4210320.610283.757844125536.8421558744685
4310232.610239.5474061321-6.9474061321107
4410357.210362.5285722011-5.32857220109327
4510520.210520.9897515607-0.789751560692821
4610473.810478.9276251732-5.12762517318515
471040710392.451008603814.5489913962265
481053610524.442217763611.5577822363775
4910700.210693.80382501286.39617498721964
5010664.210654.84691313469.35308686541794
511060610589.510155027416.4898449725715
5210716.610725.3124687572-8.71246875724864
5310882.810887.0278745753-4.22787457530103
5410849.410847.38463971652.0153602835253
551079410784.13575430439.86424569571682
5610907.810902.94183322134.85816677872754

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 9186.2 & 9123.7925 & 62.4075000000012 \tabularnewline
6 & 9152.2 & 9122.38273463691 & 29.81726536309 \tabularnewline
7 & 9093.6 & 9038.89540893444 & 54.7045910655634 \tabularnewline
8 & 9199.2 & 9300.20391682909 & -101.003916829086 \tabularnewline
9 & 9310.6 & 9338.36972512143 & -27.7697251214304 \tabularnewline
10 & 9282 & 9280.96176439492 & 1.03823560507954 \tabularnewline
11 & 9248.4 & 9193.40392602013 & 54.9960739798735 \tabularnewline
12 & 9341.6 & 9357.18999379003 & -15.5899937900285 \tabularnewline
13 & 9478.8 & 9469.54491200532 & 9.25508799468298 \tabularnewline
14 & 9438 & 9447.48687358357 & -9.48687358356801 \tabularnewline
15 & 9374.6 & 9391.52521587216 & -16.9252158721592 \tabularnewline
16 & 9488.8 & 9485.2713911766 & 3.52860882339701 \tabularnewline
17 & 9631.8 & 9617.2781413882 & 14.5218586118008 \tabularnewline
18 & 9588.4 & 9585.40257653385 & 2.9974234661513 \tabularnewline
19 & 9514.6 & 9530.09597086154 & -15.4959708615406 \tabularnewline
20 & 9623.2 & 9636.73728265839 & -13.5372826583844 \tabularnewline
21 & 9744.6 & 9767.67431313404 & -23.0743131340387 \tabularnewline
22 & 9685.8 & 9710.25390105371 & -24.4539010537155 \tabularnewline
23 & 9598 & 9626.00186938336 & -28.0018693833645 \tabularnewline
24 & 9703.4 & 9719.44824975465 & -16.0482497546491 \tabularnewline
25 & 9817.8 & 9833.88502042608 & -16.0850204260842 \tabularnewline
26 & 9762.6 & 9768.83901718301 & -6.23901718300658 \tabularnewline
27 & 9669.6 & 9681.75311441525 & -12.1531144152468 \tabularnewline
28 & 9789.2 & 9782.18618432283 & 7.01381567717544 \tabularnewline
29 & 9917.4 & 9901.84513798775 & 15.5548620122536 \tabularnewline
30 & 9864.4 & 9854.27951497145 & 10.1204850285467 \tabularnewline
31 & 9779.2 & 9771.92858794849 & 7.2714120515102 \tabularnewline
32 & 9898.8 & 9894.77301216948 & 4.02698783051892 \tabularnewline
33 & 10048.8 & 10022.3571561235 & 26.4428438765008 \tabularnewline
34 & 9983.4 & 9980.85626439469 & 2.54373560530803 \tabularnewline
35 & 9913.4 & 9898.59512816642 & 14.8048718335776 \tabularnewline
36 & 10031.6 & 10027.5558652191 & 4.04413478088463 \tabularnewline
37 & 10184.6 & 10173.3261055682 & 11.2738944318062 \tabularnewline
38 & 10125 & 10116.237103062 & 8.76289693801118 \tabularnewline
39 & 10065.4 & 10047.556350279 & 17.8436497209968 \tabularnewline
40 & 10188.6 & 10176.0448139983 & 12.5551860017422 \tabularnewline
41 & 10350.4 & 10334.5980510284 & 15.8019489715934 \tabularnewline
42 & 10320.6 & 10283.7578441255 & 36.8421558744685 \tabularnewline
43 & 10232.6 & 10239.5474061321 & -6.9474061321107 \tabularnewline
44 & 10357.2 & 10362.5285722011 & -5.32857220109327 \tabularnewline
45 & 10520.2 & 10520.9897515607 & -0.789751560692821 \tabularnewline
46 & 10473.8 & 10478.9276251732 & -5.12762517318515 \tabularnewline
47 & 10407 & 10392.4510086038 & 14.5489913962265 \tabularnewline
48 & 10536 & 10524.4422177636 & 11.5577822363775 \tabularnewline
49 & 10700.2 & 10693.8038250128 & 6.39617498721964 \tabularnewline
50 & 10664.2 & 10654.8469131346 & 9.35308686541794 \tabularnewline
51 & 10606 & 10589.5101550274 & 16.4898449725715 \tabularnewline
52 & 10716.6 & 10725.3124687572 & -8.71246875724864 \tabularnewline
53 & 10882.8 & 10887.0278745753 & -4.22787457530103 \tabularnewline
54 & 10849.4 & 10847.3846397165 & 2.0153602835253 \tabularnewline
55 & 10794 & 10784.1357543043 & 9.86424569571682 \tabularnewline
56 & 10907.8 & 10902.9418332213 & 4.85816677872754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300104&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]5[/C][C]9186.2[/C][C]9123.7925[/C][C]62.4075000000012[/C][/ROW]
[ROW][C]6[/C][C]9152.2[/C][C]9122.38273463691[/C][C]29.81726536309[/C][/ROW]
[ROW][C]7[/C][C]9093.6[/C][C]9038.89540893444[/C][C]54.7045910655634[/C][/ROW]
[ROW][C]8[/C][C]9199.2[/C][C]9300.20391682909[/C][C]-101.003916829086[/C][/ROW]
[ROW][C]9[/C][C]9310.6[/C][C]9338.36972512143[/C][C]-27.7697251214304[/C][/ROW]
[ROW][C]10[/C][C]9282[/C][C]9280.96176439492[/C][C]1.03823560507954[/C][/ROW]
[ROW][C]11[/C][C]9248.4[/C][C]9193.40392602013[/C][C]54.9960739798735[/C][/ROW]
[ROW][C]12[/C][C]9341.6[/C][C]9357.18999379003[/C][C]-15.5899937900285[/C][/ROW]
[ROW][C]13[/C][C]9478.8[/C][C]9469.54491200532[/C][C]9.25508799468298[/C][/ROW]
[ROW][C]14[/C][C]9438[/C][C]9447.48687358357[/C][C]-9.48687358356801[/C][/ROW]
[ROW][C]15[/C][C]9374.6[/C][C]9391.52521587216[/C][C]-16.9252158721592[/C][/ROW]
[ROW][C]16[/C][C]9488.8[/C][C]9485.2713911766[/C][C]3.52860882339701[/C][/ROW]
[ROW][C]17[/C][C]9631.8[/C][C]9617.2781413882[/C][C]14.5218586118008[/C][/ROW]
[ROW][C]18[/C][C]9588.4[/C][C]9585.40257653385[/C][C]2.9974234661513[/C][/ROW]
[ROW][C]19[/C][C]9514.6[/C][C]9530.09597086154[/C][C]-15.4959708615406[/C][/ROW]
[ROW][C]20[/C][C]9623.2[/C][C]9636.73728265839[/C][C]-13.5372826583844[/C][/ROW]
[ROW][C]21[/C][C]9744.6[/C][C]9767.67431313404[/C][C]-23.0743131340387[/C][/ROW]
[ROW][C]22[/C][C]9685.8[/C][C]9710.25390105371[/C][C]-24.4539010537155[/C][/ROW]
[ROW][C]23[/C][C]9598[/C][C]9626.00186938336[/C][C]-28.0018693833645[/C][/ROW]
[ROW][C]24[/C][C]9703.4[/C][C]9719.44824975465[/C][C]-16.0482497546491[/C][/ROW]
[ROW][C]25[/C][C]9817.8[/C][C]9833.88502042608[/C][C]-16.0850204260842[/C][/ROW]
[ROW][C]26[/C][C]9762.6[/C][C]9768.83901718301[/C][C]-6.23901718300658[/C][/ROW]
[ROW][C]27[/C][C]9669.6[/C][C]9681.75311441525[/C][C]-12.1531144152468[/C][/ROW]
[ROW][C]28[/C][C]9789.2[/C][C]9782.18618432283[/C][C]7.01381567717544[/C][/ROW]
[ROW][C]29[/C][C]9917.4[/C][C]9901.84513798775[/C][C]15.5548620122536[/C][/ROW]
[ROW][C]30[/C][C]9864.4[/C][C]9854.27951497145[/C][C]10.1204850285467[/C][/ROW]
[ROW][C]31[/C][C]9779.2[/C][C]9771.92858794849[/C][C]7.2714120515102[/C][/ROW]
[ROW][C]32[/C][C]9898.8[/C][C]9894.77301216948[/C][C]4.02698783051892[/C][/ROW]
[ROW][C]33[/C][C]10048.8[/C][C]10022.3571561235[/C][C]26.4428438765008[/C][/ROW]
[ROW][C]34[/C][C]9983.4[/C][C]9980.85626439469[/C][C]2.54373560530803[/C][/ROW]
[ROW][C]35[/C][C]9913.4[/C][C]9898.59512816642[/C][C]14.8048718335776[/C][/ROW]
[ROW][C]36[/C][C]10031.6[/C][C]10027.5558652191[/C][C]4.04413478088463[/C][/ROW]
[ROW][C]37[/C][C]10184.6[/C][C]10173.3261055682[/C][C]11.2738944318062[/C][/ROW]
[ROW][C]38[/C][C]10125[/C][C]10116.237103062[/C][C]8.76289693801118[/C][/ROW]
[ROW][C]39[/C][C]10065.4[/C][C]10047.556350279[/C][C]17.8436497209968[/C][/ROW]
[ROW][C]40[/C][C]10188.6[/C][C]10176.0448139983[/C][C]12.5551860017422[/C][/ROW]
[ROW][C]41[/C][C]10350.4[/C][C]10334.5980510284[/C][C]15.8019489715934[/C][/ROW]
[ROW][C]42[/C][C]10320.6[/C][C]10283.7578441255[/C][C]36.8421558744685[/C][/ROW]
[ROW][C]43[/C][C]10232.6[/C][C]10239.5474061321[/C][C]-6.9474061321107[/C][/ROW]
[ROW][C]44[/C][C]10357.2[/C][C]10362.5285722011[/C][C]-5.32857220109327[/C][/ROW]
[ROW][C]45[/C][C]10520.2[/C][C]10520.9897515607[/C][C]-0.789751560692821[/C][/ROW]
[ROW][C]46[/C][C]10473.8[/C][C]10478.9276251732[/C][C]-5.12762517318515[/C][/ROW]
[ROW][C]47[/C][C]10407[/C][C]10392.4510086038[/C][C]14.5489913962265[/C][/ROW]
[ROW][C]48[/C][C]10536[/C][C]10524.4422177636[/C][C]11.5577822363775[/C][/ROW]
[ROW][C]49[/C][C]10700.2[/C][C]10693.8038250128[/C][C]6.39617498721964[/C][/ROW]
[ROW][C]50[/C][C]10664.2[/C][C]10654.8469131346[/C][C]9.35308686541794[/C][/ROW]
[ROW][C]51[/C][C]10606[/C][C]10589.5101550274[/C][C]16.4898449725715[/C][/ROW]
[ROW][C]52[/C][C]10716.6[/C][C]10725.3124687572[/C][C]-8.71246875724864[/C][/ROW]
[ROW][C]53[/C][C]10882.8[/C][C]10887.0278745753[/C][C]-4.22787457530103[/C][/ROW]
[ROW][C]54[/C][C]10849.4[/C][C]10847.3846397165[/C][C]2.0153602835253[/C][/ROW]
[ROW][C]55[/C][C]10794[/C][C]10784.1357543043[/C][C]9.86424569571682[/C][/ROW]
[ROW][C]56[/C][C]10907.8[/C][C]10902.9418332213[/C][C]4.85816677872754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300104&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
59186.29123.792562.4075000000012
69152.29122.3827346369129.81726536309
79093.69038.8954089344454.7045910655634
89199.29300.20391682909-101.003916829086
99310.69338.36972512143-27.7697251214304
1092829280.961764394921.03823560507954
119248.49193.4039260201354.9960739798735
129341.69357.18999379003-15.5899937900285
139478.89469.544912005329.25508799468298
1494389447.48687358357-9.48687358356801
159374.69391.52521587216-16.9252158721592
169488.89485.27139117663.52860882339701
179631.89617.278141388214.5218586118008
189588.49585.402576533852.9974234661513
199514.69530.09597086154-15.4959708615406
209623.29636.73728265839-13.5372826583844
219744.69767.67431313404-23.0743131340387
229685.89710.25390105371-24.4539010537155
2395989626.00186938336-28.0018693833645
249703.49719.44824975465-16.0482497546491
259817.89833.88502042608-16.0850204260842
269762.69768.83901718301-6.23901718300658
279669.69681.75311441525-12.1531144152468
289789.29782.186184322837.01381567717544
299917.49901.8451379877515.5548620122536
309864.49854.2795149714510.1204850285467
319779.29771.928587948497.2714120515102
329898.89894.773012169484.02698783051892
3310048.810022.357156123526.4428438765008
349983.49980.856264394692.54373560530803
359913.49898.5951281664214.8048718335776
3610031.610027.55586521914.04413478088463
3710184.610173.326105568211.2738944318062
381012510116.2371030628.76289693801118
3910065.410047.55635027917.8436497209968
4010188.610176.044813998312.5551860017422
4110350.410334.598051028415.8019489715934
4210320.610283.757844125536.8421558744685
4310232.610239.5474061321-6.9474061321107
4410357.210362.5285722011-5.32857220109327
4510520.210520.9897515607-0.789751560692821
4610473.810478.9276251732-5.12762517318515
471040710392.451008603814.5489913962265
481053610524.442217763611.5577822363775
4910700.210693.80382501286.39617498721964
5010664.210654.84691313469.35308686541794
511060610589.510155027416.4898449725715
5210716.610725.3124687572-8.71246875724864
5310882.810887.0278745753-4.22787457530103
5410849.410847.38463971652.0153602835253
551079410784.13575430439.86424569571682
5610907.810902.94183322134.85816677872754







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
5711073.488712831511025.872941953611121.1044837094
5811040.803107435710988.205387371111093.4008275002
5910982.972880166310923.572830863811042.3729294689
6011095.895117382511028.012273542611163.7779612225
6111261.903255521111167.561973278711356.2445377636
6211229.217650125311125.383285539511333.0520147111
6311171.38742285611056.728855028111286.0459906838
6411284.309660072211157.618717201711411.0006029426
6511450.317798210711296.888402208811603.7471942127
6611417.632192814911251.233801975311584.0305836545
6711359.801965545611179.410417638611540.1935134526
6811472.724202761811277.393919517311668.0544860062

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
57 & 11073.4887128315 & 11025.8729419536 & 11121.1044837094 \tabularnewline
58 & 11040.8031074357 & 10988.2053873711 & 11093.4008275002 \tabularnewline
59 & 10982.9728801663 & 10923.5728308638 & 11042.3729294689 \tabularnewline
60 & 11095.8951173825 & 11028.0122735426 & 11163.7779612225 \tabularnewline
61 & 11261.9032555211 & 11167.5619732787 & 11356.2445377636 \tabularnewline
62 & 11229.2176501253 & 11125.3832855395 & 11333.0520147111 \tabularnewline
63 & 11171.387422856 & 11056.7288550281 & 11286.0459906838 \tabularnewline
64 & 11284.3096600722 & 11157.6187172017 & 11411.0006029426 \tabularnewline
65 & 11450.3177982107 & 11296.8884022088 & 11603.7471942127 \tabularnewline
66 & 11417.6321928149 & 11251.2338019753 & 11584.0305836545 \tabularnewline
67 & 11359.8019655456 & 11179.4104176386 & 11540.1935134526 \tabularnewline
68 & 11472.7242027618 & 11277.3939195173 & 11668.0544860062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300104&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]57[/C][C]11073.4887128315[/C][C]11025.8729419536[/C][C]11121.1044837094[/C][/ROW]
[ROW][C]58[/C][C]11040.8031074357[/C][C]10988.2053873711[/C][C]11093.4008275002[/C][/ROW]
[ROW][C]59[/C][C]10982.9728801663[/C][C]10923.5728308638[/C][C]11042.3729294689[/C][/ROW]
[ROW][C]60[/C][C]11095.8951173825[/C][C]11028.0122735426[/C][C]11163.7779612225[/C][/ROW]
[ROW][C]61[/C][C]11261.9032555211[/C][C]11167.5619732787[/C][C]11356.2445377636[/C][/ROW]
[ROW][C]62[/C][C]11229.2176501253[/C][C]11125.3832855395[/C][C]11333.0520147111[/C][/ROW]
[ROW][C]63[/C][C]11171.387422856[/C][C]11056.7288550281[/C][C]11286.0459906838[/C][/ROW]
[ROW][C]64[/C][C]11284.3096600722[/C][C]11157.6187172017[/C][C]11411.0006029426[/C][/ROW]
[ROW][C]65[/C][C]11450.3177982107[/C][C]11296.8884022088[/C][C]11603.7471942127[/C][/ROW]
[ROW][C]66[/C][C]11417.6321928149[/C][C]11251.2338019753[/C][C]11584.0305836545[/C][/ROW]
[ROW][C]67[/C][C]11359.8019655456[/C][C]11179.4104176386[/C][C]11540.1935134526[/C][/ROW]
[ROW][C]68[/C][C]11472.7242027618[/C][C]11277.3939195173[/C][C]11668.0544860062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300104&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
5711073.488712831511025.872941953611121.1044837094
5811040.803107435710988.205387371111093.4008275002
5910982.972880166310923.572830863811042.3729294689
6011095.895117382511028.012273542611163.7779612225
6111261.903255521111167.561973278711356.2445377636
6211229.217650125311125.383285539511333.0520147111
6311171.38742285611056.728855028111286.0459906838
6411284.309660072211157.618717201711411.0006029426
6511450.317798210711296.888402208811603.7471942127
6611417.632192814911251.233801975311584.0305836545
6711359.801965545611179.410417638611540.1935134526
6811472.724202761811277.393919517311668.0544860062



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')