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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 computationTue, 07 Dec 2010 18:46:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291747532g25nltqxgmqognl.htm/, Retrieved Fri, 03 May 2024 22:53:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106608, Retrieved Fri, 03 May 2024 22:53:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [] [2010-12-07 18:46:49] [8eb7c21ac2cd23d1a3046c9313164b8d] [Current]
- R         [Exponential Smoothing] [] [2010-12-09 20:27:06] [1253bc7c4737195066123d9caa6dfc18]
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Dataseries X:
13328
12873
14000
13477
14237
13674
13529
14058
12975
14326
14008
16193
14483
14011
15057
14884
15414
14440
14900
15074
14442
15307
14938
17193
15528
14765
15838
15723
16150
15486
15986
15983
15692
16490
15686
18897
16316
15636
17163
16534
16518
16375
16290
16352
15943
16362
16393
19051
16747
16320
17910
16961
17480
17049
16879
17473
16998
17307
17418
20169
17871
17226
19062
17804
19100
18522
18060
18869
18127
18871
18890
21263
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19509
21971




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106608&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106608&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.441210707478134
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.441210707478134 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106608&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]0.441210707478134[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106608&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
alpha0.441210707478134
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131448313934.6017628205548.398237179485
141401113700.065161968310.934838032037
151505714874.7571667774182.242833222597
161488414775.1272144314108.872785568577
171541415368.500611452345.4993885476906
181444014429.121320471610.878679528354
191490014650.1753353045249.824664695496
201507415288.8215439687-214.821543968683
211444214114.5442035144327.455796485561
221530715602.317098758-295.317098758043
231493815141.315924293-203.315924293007
241719317250.6149864358-57.6149864358413
251552815827.5545920913-299.554592091294
261476515086.2001187187-321.200118718656
271583815910.0756977178-72.0756977177753
281572315657.239289389965.7607106100913
291615016196.1788016315-46.178801631504
301548615197.004430002288.995569997956
311598615674.2870528431311.712947156899
321598316080.5997081843-97.599708184258
331569215261.0606682514430.939331748588
341649016446.492781765843.5072182342119
351568616186.3937951022-500.393795102198
361889718246.0350436742650.96495632581
371631617000.4144461031-684.414446103096
381563616077.1603957516-441.160395751614
391716316987.3162750128175.683724987248
401653416920.8154859542-386.815485954226
411651817197.5229334712-679.522933471191
421637516106.2021993499268.797800650093
431629016587.2675771981-297.267577198112
441635216496.1719754499-144.171975449859
451594315951.4267087222-8.42670872215604
461636216726.5129040676-364.512904067622
471639315982.4650081337410.534991866254
481905119087.3847334156-36.3847334156053
491674716792.3023814173-45.302381417303
501632016286.959175982633.0408240173674
511791017751.023600729158.976399271021
521696117362.832824545-401.832824545036
531748017469.35267396410.6473260359744
541704917212.4539204237-163.453920423715
551687917186.4939385994-307.493938599382
561747317176.4345396915296.565460308535
571699816902.000350364895.9996496352142
581730717524.1834199866-217.183419986577
591741817278.2273353959139.772664604061
602016920013.9498656037155.050134396297
611787117798.347540850872.6524591491543
621722617388.8246184117-162.824618411705
631906218836.8425637327225.157436267276
641780418164.4773802876-360.477380287623
651910018519.733186048580.266813952025
661852218416.8707374281105.129262571947
671806018428.9245119387-368.924511938749
681886918729.3032104639139.696789536079
691812718273.5828564744-146.582856474353
701887118613.7325810499257.267418950065
711889018776.5725247399113.427475260094
722126321509.2081618553-246.208161855302
731954719070.523441675476.47655832499
741845018707.5899661546-257.58996615461
752025420330.5966431988-76.59664319882
761924019197.847864049242.1521359508151
772021620256.4259062639-40.425906263903
781942019614.2054072447-194.205407244735
791941519229.2933470367185.706652963272
802001820058.5933914304-40.5933914304114
811865219363.3570782877-711.357078287678
821997819679.9895785808298.01042141924
831950919780.429550844-271.429550844034
842197122142.3016039647-171.301603964734

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14483 & 13934.6017628205 & 548.398237179485 \tabularnewline
14 & 14011 & 13700.065161968 & 310.934838032037 \tabularnewline
15 & 15057 & 14874.7571667774 & 182.242833222597 \tabularnewline
16 & 14884 & 14775.1272144314 & 108.872785568577 \tabularnewline
17 & 15414 & 15368.5006114523 & 45.4993885476906 \tabularnewline
18 & 14440 & 14429.1213204716 & 10.878679528354 \tabularnewline
19 & 14900 & 14650.1753353045 & 249.824664695496 \tabularnewline
20 & 15074 & 15288.8215439687 & -214.821543968683 \tabularnewline
21 & 14442 & 14114.5442035144 & 327.455796485561 \tabularnewline
22 & 15307 & 15602.317098758 & -295.317098758043 \tabularnewline
23 & 14938 & 15141.315924293 & -203.315924293007 \tabularnewline
24 & 17193 & 17250.6149864358 & -57.6149864358413 \tabularnewline
25 & 15528 & 15827.5545920913 & -299.554592091294 \tabularnewline
26 & 14765 & 15086.2001187187 & -321.200118718656 \tabularnewline
27 & 15838 & 15910.0756977178 & -72.0756977177753 \tabularnewline
28 & 15723 & 15657.2392893899 & 65.7607106100913 \tabularnewline
29 & 16150 & 16196.1788016315 & -46.178801631504 \tabularnewline
30 & 15486 & 15197.004430002 & 288.995569997956 \tabularnewline
31 & 15986 & 15674.2870528431 & 311.712947156899 \tabularnewline
32 & 15983 & 16080.5997081843 & -97.599708184258 \tabularnewline
33 & 15692 & 15261.0606682514 & 430.939331748588 \tabularnewline
34 & 16490 & 16446.4927817658 & 43.5072182342119 \tabularnewline
35 & 15686 & 16186.3937951022 & -500.393795102198 \tabularnewline
36 & 18897 & 18246.0350436742 & 650.96495632581 \tabularnewline
37 & 16316 & 17000.4144461031 & -684.414446103096 \tabularnewline
38 & 15636 & 16077.1603957516 & -441.160395751614 \tabularnewline
39 & 17163 & 16987.3162750128 & 175.683724987248 \tabularnewline
40 & 16534 & 16920.8154859542 & -386.815485954226 \tabularnewline
41 & 16518 & 17197.5229334712 & -679.522933471191 \tabularnewline
42 & 16375 & 16106.2021993499 & 268.797800650093 \tabularnewline
43 & 16290 & 16587.2675771981 & -297.267577198112 \tabularnewline
44 & 16352 & 16496.1719754499 & -144.171975449859 \tabularnewline
45 & 15943 & 15951.4267087222 & -8.42670872215604 \tabularnewline
46 & 16362 & 16726.5129040676 & -364.512904067622 \tabularnewline
47 & 16393 & 15982.4650081337 & 410.534991866254 \tabularnewline
48 & 19051 & 19087.3847334156 & -36.3847334156053 \tabularnewline
49 & 16747 & 16792.3023814173 & -45.302381417303 \tabularnewline
50 & 16320 & 16286.9591759826 & 33.0408240173674 \tabularnewline
51 & 17910 & 17751.023600729 & 158.976399271021 \tabularnewline
52 & 16961 & 17362.832824545 & -401.832824545036 \tabularnewline
53 & 17480 & 17469.352673964 & 10.6473260359744 \tabularnewline
54 & 17049 & 17212.4539204237 & -163.453920423715 \tabularnewline
55 & 16879 & 17186.4939385994 & -307.493938599382 \tabularnewline
56 & 17473 & 17176.4345396915 & 296.565460308535 \tabularnewline
57 & 16998 & 16902.0003503648 & 95.9996496352142 \tabularnewline
58 & 17307 & 17524.1834199866 & -217.183419986577 \tabularnewline
59 & 17418 & 17278.2273353959 & 139.772664604061 \tabularnewline
60 & 20169 & 20013.9498656037 & 155.050134396297 \tabularnewline
61 & 17871 & 17798.3475408508 & 72.6524591491543 \tabularnewline
62 & 17226 & 17388.8246184117 & -162.824618411705 \tabularnewline
63 & 19062 & 18836.8425637327 & 225.157436267276 \tabularnewline
64 & 17804 & 18164.4773802876 & -360.477380287623 \tabularnewline
65 & 19100 & 18519.733186048 & 580.266813952025 \tabularnewline
66 & 18522 & 18416.8707374281 & 105.129262571947 \tabularnewline
67 & 18060 & 18428.9245119387 & -368.924511938749 \tabularnewline
68 & 18869 & 18729.3032104639 & 139.696789536079 \tabularnewline
69 & 18127 & 18273.5828564744 & -146.582856474353 \tabularnewline
70 & 18871 & 18613.7325810499 & 257.267418950065 \tabularnewline
71 & 18890 & 18776.5725247399 & 113.427475260094 \tabularnewline
72 & 21263 & 21509.2081618553 & -246.208161855302 \tabularnewline
73 & 19547 & 19070.523441675 & 476.47655832499 \tabularnewline
74 & 18450 & 18707.5899661546 & -257.58996615461 \tabularnewline
75 & 20254 & 20330.5966431988 & -76.59664319882 \tabularnewline
76 & 19240 & 19197.8478640492 & 42.1521359508151 \tabularnewline
77 & 20216 & 20256.4259062639 & -40.425906263903 \tabularnewline
78 & 19420 & 19614.2054072447 & -194.205407244735 \tabularnewline
79 & 19415 & 19229.2933470367 & 185.706652963272 \tabularnewline
80 & 20018 & 20058.5933914304 & -40.5933914304114 \tabularnewline
81 & 18652 & 19363.3570782877 & -711.357078287678 \tabularnewline
82 & 19978 & 19679.9895785808 & 298.01042141924 \tabularnewline
83 & 19509 & 19780.429550844 & -271.429550844034 \tabularnewline
84 & 21971 & 22142.3016039647 & -171.301603964734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106608&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]14483[/C][C]13934.6017628205[/C][C]548.398237179485[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]13700.065161968[/C][C]310.934838032037[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14874.7571667774[/C][C]182.242833222597[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14775.1272144314[/C][C]108.872785568577[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15368.5006114523[/C][C]45.4993885476906[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14429.1213204716[/C][C]10.878679528354[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14650.1753353045[/C][C]249.824664695496[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15288.8215439687[/C][C]-214.821543968683[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14114.5442035144[/C][C]327.455796485561[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15602.317098758[/C][C]-295.317098758043[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]15141.315924293[/C][C]-203.315924293007[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]17250.6149864358[/C][C]-57.6149864358413[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15827.5545920913[/C][C]-299.554592091294[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15086.2001187187[/C][C]-321.200118718656[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15910.0756977178[/C][C]-72.0756977177753[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15657.2392893899[/C][C]65.7607106100913[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]16196.1788016315[/C][C]-46.178801631504[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15197.004430002[/C][C]288.995569997956[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15674.2870528431[/C][C]311.712947156899[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]16080.5997081843[/C][C]-97.599708184258[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15261.0606682514[/C][C]430.939331748588[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]16446.4927817658[/C][C]43.5072182342119[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16186.3937951022[/C][C]-500.393795102198[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]18246.0350436742[/C][C]650.96495632581[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]17000.4144461031[/C][C]-684.414446103096[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16077.1603957516[/C][C]-441.160395751614[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16987.3162750128[/C][C]175.683724987248[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16920.8154859542[/C][C]-386.815485954226[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]17197.5229334712[/C][C]-679.522933471191[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16106.2021993499[/C][C]268.797800650093[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16587.2675771981[/C][C]-297.267577198112[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16496.1719754499[/C][C]-144.171975449859[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]15951.4267087222[/C][C]-8.42670872215604[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16726.5129040676[/C][C]-364.512904067622[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]15982.4650081337[/C][C]410.534991866254[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]19087.3847334156[/C][C]-36.3847334156053[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]16792.3023814173[/C][C]-45.302381417303[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]16286.9591759826[/C][C]33.0408240173674[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]17751.023600729[/C][C]158.976399271021[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17362.832824545[/C][C]-401.832824545036[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17469.352673964[/C][C]10.6473260359744[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17212.4539204237[/C][C]-163.453920423715[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17186.4939385994[/C][C]-307.493938599382[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17176.4345396915[/C][C]296.565460308535[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]16902.0003503648[/C][C]95.9996496352142[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17524.1834199866[/C][C]-217.183419986577[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17278.2273353959[/C][C]139.772664604061[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]20013.9498656037[/C][C]155.050134396297[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]17798.3475408508[/C][C]72.6524591491543[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]17388.8246184117[/C][C]-162.824618411705[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18836.8425637327[/C][C]225.157436267276[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18164.4773802876[/C][C]-360.477380287623[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18519.733186048[/C][C]580.266813952025[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18416.8707374281[/C][C]105.129262571947[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18428.9245119387[/C][C]-368.924511938749[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18729.3032104639[/C][C]139.696789536079[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18273.5828564744[/C][C]-146.582856474353[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18613.7325810499[/C][C]257.267418950065[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18776.5725247399[/C][C]113.427475260094[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]21509.2081618553[/C][C]-246.208161855302[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19070.523441675[/C][C]476.47655832499[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]18707.5899661546[/C][C]-257.58996615461[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]20330.5966431988[/C][C]-76.59664319882[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19197.8478640492[/C][C]42.1521359508151[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]20256.4259062639[/C][C]-40.425906263903[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19614.2054072447[/C][C]-194.205407244735[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19229.2933470367[/C][C]185.706652963272[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]20058.5933914304[/C][C]-40.5933914304114[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19363.3570782877[/C][C]-711.357078287678[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19679.9895785808[/C][C]298.01042141924[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19780.429550844[/C][C]-271.429550844034[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]22142.3016039647[/C][C]-171.301603964734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106608&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106608&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
131448313934.6017628205548.398237179485
141401113700.065161968310.934838032037
151505714874.7571667774182.242833222597
161488414775.1272144314108.872785568577
171541415368.500611452345.4993885476906
181444014429.121320471610.878679528354
191490014650.1753353045249.824664695496
201507415288.8215439687-214.821543968683
211444214114.5442035144327.455796485561
221530715602.317098758-295.317098758043
231493815141.315924293-203.315924293007
241719317250.6149864358-57.6149864358413
251552815827.5545920913-299.554592091294
261476515086.2001187187-321.200118718656
271583815910.0756977178-72.0756977177753
281572315657.239289389965.7607106100913
291615016196.1788016315-46.178801631504
301548615197.004430002288.995569997956
311598615674.2870528431311.712947156899
321598316080.5997081843-97.599708184258
331569215261.0606682514430.939331748588
341649016446.492781765843.5072182342119
351568616186.3937951022-500.393795102198
361889718246.0350436742650.96495632581
371631617000.4144461031-684.414446103096
381563616077.1603957516-441.160395751614
391716316987.3162750128175.683724987248
401653416920.8154859542-386.815485954226
411651817197.5229334712-679.522933471191
421637516106.2021993499268.797800650093
431629016587.2675771981-297.267577198112
441635216496.1719754499-144.171975449859
451594315951.4267087222-8.42670872215604
461636216726.5129040676-364.512904067622
471639315982.4650081337410.534991866254
481905119087.3847334156-36.3847334156053
491674716792.3023814173-45.302381417303
501632016286.959175982633.0408240173674
511791017751.023600729158.976399271021
521696117362.832824545-401.832824545036
531748017469.35267396410.6473260359744
541704917212.4539204237-163.453920423715
551687917186.4939385994-307.493938599382
561747317176.4345396915296.565460308535
571699816902.000350364895.9996496352142
581730717524.1834199866-217.183419986577
591741817278.2273353959139.772664604061
602016920013.9498656037155.050134396297
611787117798.347540850872.6524591491543
621722617388.8246184117-162.824618411705
631906218836.8425637327225.157436267276
641780418164.4773802876-360.477380287623
651910018519.733186048580.266813952025
661852218416.8707374281105.129262571947
671806018428.9245119387-368.924511938749
681886918729.3032104639139.696789536079
691812718273.5828564744-146.582856474353
701887118613.7325810499257.267418950065
711889018776.5725247399113.427475260094
722126321509.2081618553-246.208161855302
731954719070.523441675476.47655832499
741845018707.5899661546-257.58996615461
752025420330.5966431988-76.59664319882
761924019197.847864049242.1521359508151
772021620256.4259062639-40.425906263903
781942019614.2054072447-194.205407244735
791941519229.2933470367185.706652963272
802001820058.5933914304-40.5933914304114
811865219363.3570782877-711.357078287678
821997819679.9895785808298.01042141924
831950919780.429550844-271.429550844034
842197122142.3016039647-171.301603964734







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520140.49494269219558.662634311420722.3272510726
8619157.146393898318521.198919627819793.0938681689
8720994.941653034520309.135889726421680.7474163427
8819962.3436793119230.066477737920694.6208808821
8920956.180022013120180.209497509921732.1505465163
9020245.865527139619428.534131772121063.1969225071
9120158.929763402319302.232054283821015.6274725209
9220779.840002354319885.507111443621674.1728932649
9319727.698362135118797.251332627220658.1453916431
9420922.212973264919957.002100121887.4238464298
9520572.970597423319574.205167188921571.7360276577
9623110.550699300722079.321946992624141.7794516088

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20140.494942692 & 19558.6626343114 & 20722.3272510726 \tabularnewline
86 & 19157.1463938983 & 18521.1989196278 & 19793.0938681689 \tabularnewline
87 & 20994.9416530345 & 20309.1358897264 & 21680.7474163427 \tabularnewline
88 & 19962.34367931 & 19230.0664777379 & 20694.6208808821 \tabularnewline
89 & 20956.1800220131 & 20180.2094975099 & 21732.1505465163 \tabularnewline
90 & 20245.8655271396 & 19428.5341317721 & 21063.1969225071 \tabularnewline
91 & 20158.9297634023 & 19302.2320542838 & 21015.6274725209 \tabularnewline
92 & 20779.8400023543 & 19885.5071114436 & 21674.1728932649 \tabularnewline
93 & 19727.6983621351 & 18797.2513326272 & 20658.1453916431 \tabularnewline
94 & 20922.2129732649 & 19957.0021001 & 21887.4238464298 \tabularnewline
95 & 20572.9705974233 & 19574.2051671889 & 21571.7360276577 \tabularnewline
96 & 23110.5506993007 & 22079.3219469926 & 24141.7794516088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106608&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]85[/C][C]20140.494942692[/C][C]19558.6626343114[/C][C]20722.3272510726[/C][/ROW]
[ROW][C]86[/C][C]19157.1463938983[/C][C]18521.1989196278[/C][C]19793.0938681689[/C][/ROW]
[ROW][C]87[/C][C]20994.9416530345[/C][C]20309.1358897264[/C][C]21680.7474163427[/C][/ROW]
[ROW][C]88[/C][C]19962.34367931[/C][C]19230.0664777379[/C][C]20694.6208808821[/C][/ROW]
[ROW][C]89[/C][C]20956.1800220131[/C][C]20180.2094975099[/C][C]21732.1505465163[/C][/ROW]
[ROW][C]90[/C][C]20245.8655271396[/C][C]19428.5341317721[/C][C]21063.1969225071[/C][/ROW]
[ROW][C]91[/C][C]20158.9297634023[/C][C]19302.2320542838[/C][C]21015.6274725209[/C][/ROW]
[ROW][C]92[/C][C]20779.8400023543[/C][C]19885.5071114436[/C][C]21674.1728932649[/C][/ROW]
[ROW][C]93[/C][C]19727.6983621351[/C][C]18797.2513326272[/C][C]20658.1453916431[/C][/ROW]
[ROW][C]94[/C][C]20922.2129732649[/C][C]19957.0021001[/C][C]21887.4238464298[/C][/ROW]
[ROW][C]95[/C][C]20572.9705974233[/C][C]19574.2051671889[/C][C]21571.7360276577[/C][/ROW]
[ROW][C]96[/C][C]23110.5506993007[/C][C]22079.3219469926[/C][C]24141.7794516088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106608&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106608&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
8520140.49494269219558.662634311420722.3272510726
8619157.146393898318521.198919627819793.0938681689
8720994.941653034520309.135889726421680.7474163427
8819962.3436793119230.066477737920694.6208808821
8920956.180022013120180.209497509921732.1505465163
9020245.865527139619428.534131772121063.1969225071
9120158.929763402319302.232054283821015.6274725209
9220779.840002354319885.507111443621674.1728932649
9319727.698362135118797.251332627220658.1453916431
9420922.212973264919957.002100121887.4238464298
9520572.970597423319574.205167188921571.7360276577
9623110.550699300722079.321946992624141.7794516088



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