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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 computationSat, 17 Dec 2016 18:15:48 +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/17/t148199520879e64a2s1nma9tr.htm/, Retrieved Thu, 02 May 2024 09:24:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300892, Retrieved Thu, 02 May 2024 09:24:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Histogram] [2016-12-02 11:39:44] [937b9e6718912fc8986df66e31b6c342]
- RMP   [Histogram] [HISTO&FREQ STATPAP] [2016-12-11 13:44:30] [937b9e6718912fc8986df66e31b6c342]
- RMP       [Exponential Smoothing] [exp smo pap] [2016-12-17 17:15:48] [863feeaf19a0ddfce7bd9c25059c4d8a] [Current]
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Dataseries X:
4790.92
4795.33
4822.62
4797.52
4822.17
4843.08
4850.79
4827.02
4796.65
4854.96
4870.81
4891.06
4881.38
4921.43
4956.21
4962.81
4949.38
4977.99
4992.73
5009.02
4990.98
5014.96
5022.23
5028.83
4894.36
4918.13
4936.4
4899.87
4862.89
4882.69
4895.46
4883.8
4855.4
4874.33
4880.94
4861.79
4851.44
4840.22
4842.42
4827.02
4749.77
4866.63
4734.37
4726.44
4753.51
4867.29
4793.35
4822.4
4865.09
4987.67
4900.96
4904.71
4889.52
5015.63
4938.81
4924.73
4871.48
4998.24
4891.06
4876.54
4824.15




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300892&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300892&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.572523804831787
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.572523804831787 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300892&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]0.572523804831787[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300892&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
alpha0.572523804831787
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24795.334790.924.40999999999985
34822.624793.4448299793129.1751700206923
44797.524810.14830932617-12.6283093261682
54822.174802.9183016221619.2516983778423
64843.084813.9403572269129.1396427730861
74850.794830.623496378820.1665036211998
84827.024842.16929976216-15.1492997621626
94796.654833.49596502179-36.8459650217928
104854.964812.4007729348242.5592270651832
114870.814836.7669435448834.0430564551252
124891.064856.2574037546734.802596245333
134881.384876.182718575075.19728142493022
144921.434879.1582859112542.2717140887471
154956.214903.359848498152.8501515018952
164962.814933.6178183219129.1921816780941
174949.384950.33103724759-0.951037247589738
184977.994949.7865457840628.2034542159363
194992.734965.9336947011726.7963052988289
205009.024981.2752173662927.7447826337102
214990.984997.15976588397-6.17976588397323
225014.964993.6217028071121.3382971928886
235022.235005.8383859046216.3916140953843
245028.835015.2229751738413.6070248261603
254894.365023.01332079975-128.653320799754
264918.134949.35623207123-31.2262320712334
274936.44931.478470875254.92152912474921
284899.874934.29616345534-34.4261634553422
294862.894914.58636536813-51.6963653681287
304882.694884.98896557159-2.29896557159464
314895.464883.6727530553711.7872469446329
324883.84890.4212325246-6.6212325246006
334855.44886.63041928694-31.2304192869415
344874.334868.750260810295.57973918971038
354880.944871.944794321158.99520567884792
364861.794877.09476370165-15.3047637016507
374851.444868.33242215513-16.8924221551306
384840.224858.66110835005-18.4411083500499
394842.424848.10313483216-5.6831348321648
404827.024844.84940485468-17.8294048546813
414749.774834.64164614939-84.8716461493932
424866.634786.0506083736180.5793916263947
434734.374832.18422825858-97.8142282585795
444726.444776.18325412929-49.7432541292928
454753.514747.704057010485.80594298952474
464867.294751.02809758147116.261902418525
474793.354817.59080431111-24.24080431111
484822.44803.7123667947318.6876332052689
494865.094814.4114816607150.6785183392876
504987.674843.42613980356144.243860196441
514900.964926.00918346685-25.0491834668492
524904.714911.66792964048-6.95792964047905
534889.524907.68434928896-18.1643492889598
545015.634897.28482692175118.345173078249
554938.814965.04025569599-26.2302556959867
564924.734950.02280990321-25.2928099032106
574871.484935.54207414254-64.0620741425373
584998.244898.8650117090499.3749882909642
594891.064955.75955811049-64.699558110492
604876.544918.71752093014-42.1775209301386
614824.154894.56988616884-70.4198861688437

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4795.33 & 4790.92 & 4.40999999999985 \tabularnewline
3 & 4822.62 & 4793.44482997931 & 29.1751700206923 \tabularnewline
4 & 4797.52 & 4810.14830932617 & -12.6283093261682 \tabularnewline
5 & 4822.17 & 4802.91830162216 & 19.2516983778423 \tabularnewline
6 & 4843.08 & 4813.94035722691 & 29.1396427730861 \tabularnewline
7 & 4850.79 & 4830.6234963788 & 20.1665036211998 \tabularnewline
8 & 4827.02 & 4842.16929976216 & -15.1492997621626 \tabularnewline
9 & 4796.65 & 4833.49596502179 & -36.8459650217928 \tabularnewline
10 & 4854.96 & 4812.40077293482 & 42.5592270651832 \tabularnewline
11 & 4870.81 & 4836.76694354488 & 34.0430564551252 \tabularnewline
12 & 4891.06 & 4856.25740375467 & 34.802596245333 \tabularnewline
13 & 4881.38 & 4876.18271857507 & 5.19728142493022 \tabularnewline
14 & 4921.43 & 4879.15828591125 & 42.2717140887471 \tabularnewline
15 & 4956.21 & 4903.3598484981 & 52.8501515018952 \tabularnewline
16 & 4962.81 & 4933.61781832191 & 29.1921816780941 \tabularnewline
17 & 4949.38 & 4950.33103724759 & -0.951037247589738 \tabularnewline
18 & 4977.99 & 4949.78654578406 & 28.2034542159363 \tabularnewline
19 & 4992.73 & 4965.93369470117 & 26.7963052988289 \tabularnewline
20 & 5009.02 & 4981.27521736629 & 27.7447826337102 \tabularnewline
21 & 4990.98 & 4997.15976588397 & -6.17976588397323 \tabularnewline
22 & 5014.96 & 4993.62170280711 & 21.3382971928886 \tabularnewline
23 & 5022.23 & 5005.83838590462 & 16.3916140953843 \tabularnewline
24 & 5028.83 & 5015.22297517384 & 13.6070248261603 \tabularnewline
25 & 4894.36 & 5023.01332079975 & -128.653320799754 \tabularnewline
26 & 4918.13 & 4949.35623207123 & -31.2262320712334 \tabularnewline
27 & 4936.4 & 4931.47847087525 & 4.92152912474921 \tabularnewline
28 & 4899.87 & 4934.29616345534 & -34.4261634553422 \tabularnewline
29 & 4862.89 & 4914.58636536813 & -51.6963653681287 \tabularnewline
30 & 4882.69 & 4884.98896557159 & -2.29896557159464 \tabularnewline
31 & 4895.46 & 4883.67275305537 & 11.7872469446329 \tabularnewline
32 & 4883.8 & 4890.4212325246 & -6.6212325246006 \tabularnewline
33 & 4855.4 & 4886.63041928694 & -31.2304192869415 \tabularnewline
34 & 4874.33 & 4868.75026081029 & 5.57973918971038 \tabularnewline
35 & 4880.94 & 4871.94479432115 & 8.99520567884792 \tabularnewline
36 & 4861.79 & 4877.09476370165 & -15.3047637016507 \tabularnewline
37 & 4851.44 & 4868.33242215513 & -16.8924221551306 \tabularnewline
38 & 4840.22 & 4858.66110835005 & -18.4411083500499 \tabularnewline
39 & 4842.42 & 4848.10313483216 & -5.6831348321648 \tabularnewline
40 & 4827.02 & 4844.84940485468 & -17.8294048546813 \tabularnewline
41 & 4749.77 & 4834.64164614939 & -84.8716461493932 \tabularnewline
42 & 4866.63 & 4786.05060837361 & 80.5793916263947 \tabularnewline
43 & 4734.37 & 4832.18422825858 & -97.8142282585795 \tabularnewline
44 & 4726.44 & 4776.18325412929 & -49.7432541292928 \tabularnewline
45 & 4753.51 & 4747.70405701048 & 5.80594298952474 \tabularnewline
46 & 4867.29 & 4751.02809758147 & 116.261902418525 \tabularnewline
47 & 4793.35 & 4817.59080431111 & -24.24080431111 \tabularnewline
48 & 4822.4 & 4803.71236679473 & 18.6876332052689 \tabularnewline
49 & 4865.09 & 4814.41148166071 & 50.6785183392876 \tabularnewline
50 & 4987.67 & 4843.42613980356 & 144.243860196441 \tabularnewline
51 & 4900.96 & 4926.00918346685 & -25.0491834668492 \tabularnewline
52 & 4904.71 & 4911.66792964048 & -6.95792964047905 \tabularnewline
53 & 4889.52 & 4907.68434928896 & -18.1643492889598 \tabularnewline
54 & 5015.63 & 4897.28482692175 & 118.345173078249 \tabularnewline
55 & 4938.81 & 4965.04025569599 & -26.2302556959867 \tabularnewline
56 & 4924.73 & 4950.02280990321 & -25.2928099032106 \tabularnewline
57 & 4871.48 & 4935.54207414254 & -64.0620741425373 \tabularnewline
58 & 4998.24 & 4898.86501170904 & 99.3749882909642 \tabularnewline
59 & 4891.06 & 4955.75955811049 & -64.699558110492 \tabularnewline
60 & 4876.54 & 4918.71752093014 & -42.1775209301386 \tabularnewline
61 & 4824.15 & 4894.56988616884 & -70.4198861688437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300892&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]2[/C][C]4795.33[/C][C]4790.92[/C][C]4.40999999999985[/C][/ROW]
[ROW][C]3[/C][C]4822.62[/C][C]4793.44482997931[/C][C]29.1751700206923[/C][/ROW]
[ROW][C]4[/C][C]4797.52[/C][C]4810.14830932617[/C][C]-12.6283093261682[/C][/ROW]
[ROW][C]5[/C][C]4822.17[/C][C]4802.91830162216[/C][C]19.2516983778423[/C][/ROW]
[ROW][C]6[/C][C]4843.08[/C][C]4813.94035722691[/C][C]29.1396427730861[/C][/ROW]
[ROW][C]7[/C][C]4850.79[/C][C]4830.6234963788[/C][C]20.1665036211998[/C][/ROW]
[ROW][C]8[/C][C]4827.02[/C][C]4842.16929976216[/C][C]-15.1492997621626[/C][/ROW]
[ROW][C]9[/C][C]4796.65[/C][C]4833.49596502179[/C][C]-36.8459650217928[/C][/ROW]
[ROW][C]10[/C][C]4854.96[/C][C]4812.40077293482[/C][C]42.5592270651832[/C][/ROW]
[ROW][C]11[/C][C]4870.81[/C][C]4836.76694354488[/C][C]34.0430564551252[/C][/ROW]
[ROW][C]12[/C][C]4891.06[/C][C]4856.25740375467[/C][C]34.802596245333[/C][/ROW]
[ROW][C]13[/C][C]4881.38[/C][C]4876.18271857507[/C][C]5.19728142493022[/C][/ROW]
[ROW][C]14[/C][C]4921.43[/C][C]4879.15828591125[/C][C]42.2717140887471[/C][/ROW]
[ROW][C]15[/C][C]4956.21[/C][C]4903.3598484981[/C][C]52.8501515018952[/C][/ROW]
[ROW][C]16[/C][C]4962.81[/C][C]4933.61781832191[/C][C]29.1921816780941[/C][/ROW]
[ROW][C]17[/C][C]4949.38[/C][C]4950.33103724759[/C][C]-0.951037247589738[/C][/ROW]
[ROW][C]18[/C][C]4977.99[/C][C]4949.78654578406[/C][C]28.2034542159363[/C][/ROW]
[ROW][C]19[/C][C]4992.73[/C][C]4965.93369470117[/C][C]26.7963052988289[/C][/ROW]
[ROW][C]20[/C][C]5009.02[/C][C]4981.27521736629[/C][C]27.7447826337102[/C][/ROW]
[ROW][C]21[/C][C]4990.98[/C][C]4997.15976588397[/C][C]-6.17976588397323[/C][/ROW]
[ROW][C]22[/C][C]5014.96[/C][C]4993.62170280711[/C][C]21.3382971928886[/C][/ROW]
[ROW][C]23[/C][C]5022.23[/C][C]5005.83838590462[/C][C]16.3916140953843[/C][/ROW]
[ROW][C]24[/C][C]5028.83[/C][C]5015.22297517384[/C][C]13.6070248261603[/C][/ROW]
[ROW][C]25[/C][C]4894.36[/C][C]5023.01332079975[/C][C]-128.653320799754[/C][/ROW]
[ROW][C]26[/C][C]4918.13[/C][C]4949.35623207123[/C][C]-31.2262320712334[/C][/ROW]
[ROW][C]27[/C][C]4936.4[/C][C]4931.47847087525[/C][C]4.92152912474921[/C][/ROW]
[ROW][C]28[/C][C]4899.87[/C][C]4934.29616345534[/C][C]-34.4261634553422[/C][/ROW]
[ROW][C]29[/C][C]4862.89[/C][C]4914.58636536813[/C][C]-51.6963653681287[/C][/ROW]
[ROW][C]30[/C][C]4882.69[/C][C]4884.98896557159[/C][C]-2.29896557159464[/C][/ROW]
[ROW][C]31[/C][C]4895.46[/C][C]4883.67275305537[/C][C]11.7872469446329[/C][/ROW]
[ROW][C]32[/C][C]4883.8[/C][C]4890.4212325246[/C][C]-6.6212325246006[/C][/ROW]
[ROW][C]33[/C][C]4855.4[/C][C]4886.63041928694[/C][C]-31.2304192869415[/C][/ROW]
[ROW][C]34[/C][C]4874.33[/C][C]4868.75026081029[/C][C]5.57973918971038[/C][/ROW]
[ROW][C]35[/C][C]4880.94[/C][C]4871.94479432115[/C][C]8.99520567884792[/C][/ROW]
[ROW][C]36[/C][C]4861.79[/C][C]4877.09476370165[/C][C]-15.3047637016507[/C][/ROW]
[ROW][C]37[/C][C]4851.44[/C][C]4868.33242215513[/C][C]-16.8924221551306[/C][/ROW]
[ROW][C]38[/C][C]4840.22[/C][C]4858.66110835005[/C][C]-18.4411083500499[/C][/ROW]
[ROW][C]39[/C][C]4842.42[/C][C]4848.10313483216[/C][C]-5.6831348321648[/C][/ROW]
[ROW][C]40[/C][C]4827.02[/C][C]4844.84940485468[/C][C]-17.8294048546813[/C][/ROW]
[ROW][C]41[/C][C]4749.77[/C][C]4834.64164614939[/C][C]-84.8716461493932[/C][/ROW]
[ROW][C]42[/C][C]4866.63[/C][C]4786.05060837361[/C][C]80.5793916263947[/C][/ROW]
[ROW][C]43[/C][C]4734.37[/C][C]4832.18422825858[/C][C]-97.8142282585795[/C][/ROW]
[ROW][C]44[/C][C]4726.44[/C][C]4776.18325412929[/C][C]-49.7432541292928[/C][/ROW]
[ROW][C]45[/C][C]4753.51[/C][C]4747.70405701048[/C][C]5.80594298952474[/C][/ROW]
[ROW][C]46[/C][C]4867.29[/C][C]4751.02809758147[/C][C]116.261902418525[/C][/ROW]
[ROW][C]47[/C][C]4793.35[/C][C]4817.59080431111[/C][C]-24.24080431111[/C][/ROW]
[ROW][C]48[/C][C]4822.4[/C][C]4803.71236679473[/C][C]18.6876332052689[/C][/ROW]
[ROW][C]49[/C][C]4865.09[/C][C]4814.41148166071[/C][C]50.6785183392876[/C][/ROW]
[ROW][C]50[/C][C]4987.67[/C][C]4843.42613980356[/C][C]144.243860196441[/C][/ROW]
[ROW][C]51[/C][C]4900.96[/C][C]4926.00918346685[/C][C]-25.0491834668492[/C][/ROW]
[ROW][C]52[/C][C]4904.71[/C][C]4911.66792964048[/C][C]-6.95792964047905[/C][/ROW]
[ROW][C]53[/C][C]4889.52[/C][C]4907.68434928896[/C][C]-18.1643492889598[/C][/ROW]
[ROW][C]54[/C][C]5015.63[/C][C]4897.28482692175[/C][C]118.345173078249[/C][/ROW]
[ROW][C]55[/C][C]4938.81[/C][C]4965.04025569599[/C][C]-26.2302556959867[/C][/ROW]
[ROW][C]56[/C][C]4924.73[/C][C]4950.02280990321[/C][C]-25.2928099032106[/C][/ROW]
[ROW][C]57[/C][C]4871.48[/C][C]4935.54207414254[/C][C]-64.0620741425373[/C][/ROW]
[ROW][C]58[/C][C]4998.24[/C][C]4898.86501170904[/C][C]99.3749882909642[/C][/ROW]
[ROW][C]59[/C][C]4891.06[/C][C]4955.75955811049[/C][C]-64.699558110492[/C][/ROW]
[ROW][C]60[/C][C]4876.54[/C][C]4918.71752093014[/C][C]-42.1775209301386[/C][/ROW]
[ROW][C]61[/C][C]4824.15[/C][C]4894.56988616884[/C][C]-70.4198861688437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300892&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
24795.334790.924.40999999999985
34822.624793.4448299793129.1751700206923
44797.524810.14830932617-12.6283093261682
54822.174802.9183016221619.2516983778423
64843.084813.9403572269129.1396427730861
74850.794830.623496378820.1665036211998
84827.024842.16929976216-15.1492997621626
94796.654833.49596502179-36.8459650217928
104854.964812.4007729348242.5592270651832
114870.814836.7669435448834.0430564551252
124891.064856.2574037546734.802596245333
134881.384876.182718575075.19728142493022
144921.434879.1582859112542.2717140887471
154956.214903.359848498152.8501515018952
164962.814933.6178183219129.1921816780941
174949.384950.33103724759-0.951037247589738
184977.994949.7865457840628.2034542159363
194992.734965.9336947011726.7963052988289
205009.024981.2752173662927.7447826337102
214990.984997.15976588397-6.17976588397323
225014.964993.6217028071121.3382971928886
235022.235005.8383859046216.3916140953843
245028.835015.2229751738413.6070248261603
254894.365023.01332079975-128.653320799754
264918.134949.35623207123-31.2262320712334
274936.44931.478470875254.92152912474921
284899.874934.29616345534-34.4261634553422
294862.894914.58636536813-51.6963653681287
304882.694884.98896557159-2.29896557159464
314895.464883.6727530553711.7872469446329
324883.84890.4212325246-6.6212325246006
334855.44886.63041928694-31.2304192869415
344874.334868.750260810295.57973918971038
354880.944871.944794321158.99520567884792
364861.794877.09476370165-15.3047637016507
374851.444868.33242215513-16.8924221551306
384840.224858.66110835005-18.4411083500499
394842.424848.10313483216-5.6831348321648
404827.024844.84940485468-17.8294048546813
414749.774834.64164614939-84.8716461493932
424866.634786.0506083736180.5793916263947
434734.374832.18422825858-97.8142282585795
444726.444776.18325412929-49.7432541292928
454753.514747.704057010485.80594298952474
464867.294751.02809758147116.261902418525
474793.354817.59080431111-24.24080431111
484822.44803.7123667947318.6876332052689
494865.094814.4114816607150.6785183392876
504987.674843.42613980356144.243860196441
514900.964926.00918346685-25.0491834668492
524904.714911.66792964048-6.95792964047905
534889.524907.68434928896-18.1643492889598
545015.634897.28482692175118.345173078249
554938.814965.04025569599-26.2302556959867
564924.734950.02280990321-25.2928099032106
574871.484935.54207414254-64.0620741425373
584998.244898.8650117090499.3749882909642
594891.064955.75955811049-64.699558110492
604876.544918.71752093014-42.1775209301386
614824.154894.56988616884-70.4198861688437







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
624854.252825003644756.871627710414951.63402229686
634854.252825003644742.04096925194966.46468075538
644854.252825003644728.953568995324979.55208101195
654854.252825003644717.109445501664991.39620450562
664854.252825003644706.209893641785002.29575636549
674854.252825003644696.059549194585012.44610081269
684854.252825003644686.522340308145021.98330969913
694854.252825003644677.498989172065031.00666083521
704854.252825003644668.914427831975039.5912221753
714854.252825003644660.710260044015047.79538996326
724854.252825003644652.839996623375055.6656533839
734854.252825003644645.265910530215063.23973947707

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 4854.25282500364 & 4756.87162771041 & 4951.63402229686 \tabularnewline
63 & 4854.25282500364 & 4742.0409692519 & 4966.46468075538 \tabularnewline
64 & 4854.25282500364 & 4728.95356899532 & 4979.55208101195 \tabularnewline
65 & 4854.25282500364 & 4717.10944550166 & 4991.39620450562 \tabularnewline
66 & 4854.25282500364 & 4706.20989364178 & 5002.29575636549 \tabularnewline
67 & 4854.25282500364 & 4696.05954919458 & 5012.44610081269 \tabularnewline
68 & 4854.25282500364 & 4686.52234030814 & 5021.98330969913 \tabularnewline
69 & 4854.25282500364 & 4677.49898917206 & 5031.00666083521 \tabularnewline
70 & 4854.25282500364 & 4668.91442783197 & 5039.5912221753 \tabularnewline
71 & 4854.25282500364 & 4660.71026004401 & 5047.79538996326 \tabularnewline
72 & 4854.25282500364 & 4652.83999662337 & 5055.6656533839 \tabularnewline
73 & 4854.25282500364 & 4645.26591053021 & 5063.23973947707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300892&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]4854.25282500364[/C][C]4756.87162771041[/C][C]4951.63402229686[/C][/ROW]
[ROW][C]63[/C][C]4854.25282500364[/C][C]4742.0409692519[/C][C]4966.46468075538[/C][/ROW]
[ROW][C]64[/C][C]4854.25282500364[/C][C]4728.95356899532[/C][C]4979.55208101195[/C][/ROW]
[ROW][C]65[/C][C]4854.25282500364[/C][C]4717.10944550166[/C][C]4991.39620450562[/C][/ROW]
[ROW][C]66[/C][C]4854.25282500364[/C][C]4706.20989364178[/C][C]5002.29575636549[/C][/ROW]
[ROW][C]67[/C][C]4854.25282500364[/C][C]4696.05954919458[/C][C]5012.44610081269[/C][/ROW]
[ROW][C]68[/C][C]4854.25282500364[/C][C]4686.52234030814[/C][C]5021.98330969913[/C][/ROW]
[ROW][C]69[/C][C]4854.25282500364[/C][C]4677.49898917206[/C][C]5031.00666083521[/C][/ROW]
[ROW][C]70[/C][C]4854.25282500364[/C][C]4668.91442783197[/C][C]5039.5912221753[/C][/ROW]
[ROW][C]71[/C][C]4854.25282500364[/C][C]4660.71026004401[/C][C]5047.79538996326[/C][/ROW]
[ROW][C]72[/C][C]4854.25282500364[/C][C]4652.83999662337[/C][C]5055.6656533839[/C][/ROW]
[ROW][C]73[/C][C]4854.25282500364[/C][C]4645.26591053021[/C][C]5063.23973947707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300892&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
624854.252825003644756.871627710414951.63402229686
634854.252825003644742.04096925194966.46468075538
644854.252825003644728.953568995324979.55208101195
654854.252825003644717.109445501664991.39620450562
664854.252825003644706.209893641785002.29575636549
674854.252825003644696.059549194585012.44610081269
684854.252825003644686.522340308145021.98330969913
694854.252825003644677.498989172065031.00666083521
704854.252825003644668.914427831975039.5912221753
714854.252825003644660.710260044015047.79538996326
724854.252825003644652.839996623375055.6656533839
734854.252825003644645.265910530215063.23973947707



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')