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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 10:40:46 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/13/t1386949301lz5c8jyk2ipt9qn.htm/, Retrieved Tue, 19 Nov 2019 08:22:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232300, Retrieved Tue, 19 Nov 2019 08:22:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 15:40:46] [4a7f7842fc88d649abcd00dd10ef7b6c] [Current]
- R  D    [Exponential Smoothing] [] [2013-12-23 13:27:44] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 7 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232300&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232300&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 time7 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225679028753517
beta0.000941496286984221
gamma0.443442884267436

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.225679028753517 \tabularnewline
beta & 0.000941496286984221 \tabularnewline
gamma & 0.443442884267436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232300&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]0.225679028753517[/C][/ROW]
[ROW][C]beta[/C][C]0.000941496286984221[/C][/ROW]
[ROW][C]gamma[/C][C]0.443442884267436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232300&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
alpha0.225679028753517
beta0.000941496286984221
gamma0.443442884267436







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.2423306438-2020.24233064382
153260934048.8239474293-1439.82394742926
163021230953.0817784325-741.081778432501
172996530167.1615625248-202.161562524776
182835228194.287671247157.712328752958
192581422076.5443444743737.45565552597
202241420801.92075326871612.07924673129
212050621128.7820231167-622.782023116659
222880626754.52591915842051.47408084161
232222822076.0673310002151.932668999838
241397113470.8643970095500.13560299046
253684537059.4733194596-214.473319459634
263533829795.48397040985542.51602959024
273502233348.72441949491673.27558050511
283477731163.74413083493613.25586916514
292688731542.0186569781-4655.01865697814
302397028668.3449958555-4698.34499585547
312278022752.225994223527.7740057765332
321735120061.3545527705-2710.35455277052
332138218709.04253007222672.95746992783
342456125498.9960342699-937.996034269949
351740920022.1189854634-2613.11898546338
361151411945.671121086-431.671121085963
373151431811.1427395241-297.142739524053
382707127135.2239715722-64.2239715721844
392946227863.02418044131598.97581955868
402610526585.9480635962-480.948063596243
412239723768.4474504729-1371.44745047293
422384321869.56385517691973.43614482306
432170519509.10820626772195.89179373231
441808916761.28097596481327.7190240352
452076418040.74222789222723.25777210781
462531623196.82850721212119.17149278791
471770418102.3007276656-398.300727665624
481554811461.22353787114086.77646212886
492802933585.8002125544-5556.80021255436
502938327714.0486189851668.95138101496
513643829460.21037802796977.78962197209
523203428524.13301245723509.86698754283
532267925984.1070779233-3305.10707792329
542431924768.360331227-449.360331226999
551800421738.5190502819-3734.51905028195
561753717326.1475284397210.852471560258
572036618790.72385674391575.27614325608
582278223364.3485694365-582.348569436483
591916917096.14672940712072.85327059293
601380712536.44630626191270.55369373809
612974329375.0615334878367.938466512169
622559127375.1673514994-1784.16735149938
632909629845.1799392567-749.17993925673
642648226329.5061513027152.493848697286
652240521403.18892294861001.81107705142
662704422062.65158253654981.34841746355
671797019291.1739870888-1321.1739870888
681873016843.79259252331886.20740747672
691968419125.967097602558.032902398038
701978522648.0790967242-2863.07909672418
711847916985.5773885741493.42261142599
721069812280.7803828344-1582.78038283436

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 41487.9961256583 & -3785.99612565827 \tabularnewline
14 & 30364 & 32384.2423306438 & -2020.24233064382 \tabularnewline
15 & 32609 & 34048.8239474293 & -1439.82394742926 \tabularnewline
16 & 30212 & 30953.0817784325 & -741.081778432501 \tabularnewline
17 & 29965 & 30167.1615625248 & -202.161562524776 \tabularnewline
18 & 28352 & 28194.287671247 & 157.712328752958 \tabularnewline
19 & 25814 & 22076.544344474 & 3737.45565552597 \tabularnewline
20 & 22414 & 20801.9207532687 & 1612.07924673129 \tabularnewline
21 & 20506 & 21128.7820231167 & -622.782023116659 \tabularnewline
22 & 28806 & 26754.5259191584 & 2051.47408084161 \tabularnewline
23 & 22228 & 22076.0673310002 & 151.932668999838 \tabularnewline
24 & 13971 & 13470.8643970095 & 500.13560299046 \tabularnewline
25 & 36845 & 37059.4733194596 & -214.473319459634 \tabularnewline
26 & 35338 & 29795.4839704098 & 5542.51602959024 \tabularnewline
27 & 35022 & 33348.7244194949 & 1673.27558050511 \tabularnewline
28 & 34777 & 31163.7441308349 & 3613.25586916514 \tabularnewline
29 & 26887 & 31542.0186569781 & -4655.01865697814 \tabularnewline
30 & 23970 & 28668.3449958555 & -4698.34499585547 \tabularnewline
31 & 22780 & 22752.2259942235 & 27.7740057765332 \tabularnewline
32 & 17351 & 20061.3545527705 & -2710.35455277052 \tabularnewline
33 & 21382 & 18709.0425300722 & 2672.95746992783 \tabularnewline
34 & 24561 & 25498.9960342699 & -937.996034269949 \tabularnewline
35 & 17409 & 20022.1189854634 & -2613.11898546338 \tabularnewline
36 & 11514 & 11945.671121086 & -431.671121085963 \tabularnewline
37 & 31514 & 31811.1427395241 & -297.142739524053 \tabularnewline
38 & 27071 & 27135.2239715722 & -64.2239715721844 \tabularnewline
39 & 29462 & 27863.0241804413 & 1598.97581955868 \tabularnewline
40 & 26105 & 26585.9480635962 & -480.948063596243 \tabularnewline
41 & 22397 & 23768.4474504729 & -1371.44745047293 \tabularnewline
42 & 23843 & 21869.5638551769 & 1973.43614482306 \tabularnewline
43 & 21705 & 19509.1082062677 & 2195.89179373231 \tabularnewline
44 & 18089 & 16761.2809759648 & 1327.7190240352 \tabularnewline
45 & 20764 & 18040.7422278922 & 2723.25777210781 \tabularnewline
46 & 25316 & 23196.8285072121 & 2119.17149278791 \tabularnewline
47 & 17704 & 18102.3007276656 & -398.300727665624 \tabularnewline
48 & 15548 & 11461.2235378711 & 4086.77646212886 \tabularnewline
49 & 28029 & 33585.8002125544 & -5556.80021255436 \tabularnewline
50 & 29383 & 27714.048618985 & 1668.95138101496 \tabularnewline
51 & 36438 & 29460.2103780279 & 6977.78962197209 \tabularnewline
52 & 32034 & 28524.1330124572 & 3509.86698754283 \tabularnewline
53 & 22679 & 25984.1070779233 & -3305.10707792329 \tabularnewline
54 & 24319 & 24768.360331227 & -449.360331226999 \tabularnewline
55 & 18004 & 21738.5190502819 & -3734.51905028195 \tabularnewline
56 & 17537 & 17326.1475284397 & 210.852471560258 \tabularnewline
57 & 20366 & 18790.7238567439 & 1575.27614325608 \tabularnewline
58 & 22782 & 23364.3485694365 & -582.348569436483 \tabularnewline
59 & 19169 & 17096.1467294071 & 2072.85327059293 \tabularnewline
60 & 13807 & 12536.4463062619 & 1270.55369373809 \tabularnewline
61 & 29743 & 29375.0615334878 & 367.938466512169 \tabularnewline
62 & 25591 & 27375.1673514994 & -1784.16735149938 \tabularnewline
63 & 29096 & 29845.1799392567 & -749.17993925673 \tabularnewline
64 & 26482 & 26329.5061513027 & 152.493848697286 \tabularnewline
65 & 22405 & 21403.1889229486 & 1001.81107705142 \tabularnewline
66 & 27044 & 22062.6515825365 & 4981.34841746355 \tabularnewline
67 & 17970 & 19291.1739870888 & -1321.1739870888 \tabularnewline
68 & 18730 & 16843.7925925233 & 1886.20740747672 \tabularnewline
69 & 19684 & 19125.967097602 & 558.032902398038 \tabularnewline
70 & 19785 & 22648.0790967242 & -2863.07909672418 \tabularnewline
71 & 18479 & 16985.577388574 & 1493.42261142599 \tabularnewline
72 & 10698 & 12280.7803828344 & -1582.78038283436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232300&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]37702[/C][C]41487.9961256583[/C][C]-3785.99612565827[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]32384.2423306438[/C][C]-2020.24233064382[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]34048.8239474293[/C][C]-1439.82394742926[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30953.0817784325[/C][C]-741.081778432501[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30167.1615625248[/C][C]-202.161562524776[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28194.287671247[/C][C]157.712328752958[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]22076.544344474[/C][C]3737.45565552597[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20801.9207532687[/C][C]1612.07924673129[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21128.7820231167[/C][C]-622.782023116659[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]26754.5259191584[/C][C]2051.47408084161[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22076.0673310002[/C][C]151.932668999838[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13470.8643970095[/C][C]500.13560299046[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37059.4733194596[/C][C]-214.473319459634[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29795.4839704098[/C][C]5542.51602959024[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33348.7244194949[/C][C]1673.27558050511[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31163.7441308349[/C][C]3613.25586916514[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]31542.0186569781[/C][C]-4655.01865697814[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28668.3449958555[/C][C]-4698.34499585547[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22752.2259942235[/C][C]27.7740057765332[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]20061.3545527705[/C][C]-2710.35455277052[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18709.0425300722[/C][C]2672.95746992783[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25498.9960342699[/C][C]-937.996034269949[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]20022.1189854634[/C][C]-2613.11898546338[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]11945.671121086[/C][C]-431.671121085963[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]31811.1427395241[/C][C]-297.142739524053[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]27135.2239715722[/C][C]-64.2239715721844[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]27863.0241804413[/C][C]1598.97581955868[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]26585.9480635962[/C][C]-480.948063596243[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]23768.4474504729[/C][C]-1371.44745047293[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21869.5638551769[/C][C]1973.43614482306[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19509.1082062677[/C][C]2195.89179373231[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]16761.2809759648[/C][C]1327.7190240352[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18040.7422278922[/C][C]2723.25777210781[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23196.8285072121[/C][C]2119.17149278791[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]18102.3007276656[/C][C]-398.300727665624[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]11461.2235378711[/C][C]4086.77646212886[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33585.8002125544[/C][C]-5556.80021255436[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27714.048618985[/C][C]1668.95138101496[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29460.2103780279[/C][C]6977.78962197209[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]28524.1330124572[/C][C]3509.86698754283[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]25984.1070779233[/C][C]-3305.10707792329[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]24768.360331227[/C][C]-449.360331226999[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]21738.5190502819[/C][C]-3734.51905028195[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]17326.1475284397[/C][C]210.852471560258[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18790.7238567439[/C][C]1575.27614325608[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23364.3485694365[/C][C]-582.348569436483[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]17096.1467294071[/C][C]2072.85327059293[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12536.4463062619[/C][C]1270.55369373809[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29375.0615334878[/C][C]367.938466512169[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]27375.1673514994[/C][C]-1784.16735149938[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]29845.1799392567[/C][C]-749.17993925673[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26329.5061513027[/C][C]152.493848697286[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]21403.1889229486[/C][C]1001.81107705142[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]22062.6515825365[/C][C]4981.34841746355[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19291.1739870888[/C][C]-1321.1739870888[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16843.7925925233[/C][C]1886.20740747672[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19125.967097602[/C][C]558.032902398038[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22648.0790967242[/C][C]-2863.07909672418[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16985.577388574[/C][C]1493.42261142599[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12280.7803828344[/C][C]-1582.78038283436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232300&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
133770241487.9961256583-3785.99612565827
143036432384.2423306438-2020.24233064382
153260934048.8239474293-1439.82394742926
163021230953.0817784325-741.081778432501
172996530167.1615625248-202.161562524776
182835228194.287671247157.712328752958
192581422076.5443444743737.45565552597
202241420801.92075326871612.07924673129
212050621128.7820231167-622.782023116659
222880626754.52591915842051.47408084161
232222822076.0673310002151.932668999838
241397113470.8643970095500.13560299046
253684537059.4733194596-214.473319459634
263533829795.48397040985542.51602959024
273502233348.72441949491673.27558050511
283477731163.74413083493613.25586916514
292688731542.0186569781-4655.01865697814
302397028668.3449958555-4698.34499585547
312278022752.225994223527.7740057765332
321735120061.3545527705-2710.35455277052
332138218709.04253007222672.95746992783
342456125498.9960342699-937.996034269949
351740920022.1189854634-2613.11898546338
361151411945.671121086-431.671121085963
373151431811.1427395241-297.142739524053
382707127135.2239715722-64.2239715721844
392946227863.02418044131598.97581955868
402610526585.9480635962-480.948063596243
412239723768.4474504729-1371.44745047293
422384321869.56385517691973.43614482306
432170519509.10820626772195.89179373231
441808916761.28097596481327.7190240352
452076418040.74222789222723.25777210781
462531623196.82850721212119.17149278791
471770418102.3007276656-398.300727665624
481554811461.22353787114086.77646212886
492802933585.8002125544-5556.80021255436
502938327714.0486189851668.95138101496
513643829460.21037802796977.78962197209
523203428524.13301245723509.86698754283
532267925984.1070779233-3305.10707792329
542431924768.360331227-449.360331226999
551800421738.5190502819-3734.51905028195
561753717326.1475284397210.852471560258
572036618790.72385674391575.27614325608
582278223364.3485694365-582.348569436483
591916917096.14672940712072.85327059293
601380712536.44630626191270.55369373809
612974329375.0615334878367.938466512169
622559127375.1673514994-1784.16735149938
632909629845.1799392567-749.17993925673
642648226329.5061513027152.493848697286
652240521403.18892294861001.81107705142
662704422062.65158253654981.34841746355
671797019291.1739870888-1321.1739870888
681873016843.79259252331886.20740747672
691968419125.967097602558.032902398038
701978522648.0790967242-2863.07909672418
711847916985.5773885741493.42261142599
721069812280.7803828344-1582.78038283436







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326498.98186514623698.880672305529299.0830579865
7423934.863394320120956.288363423126913.4384252172
7526836.693618631523556.492578443230116.8946588198
7624042.233314809420686.84160915727397.6250204618
7719769.007584474416442.310680403923095.704488545
7821288.456756202317662.497386314924914.4161260897
7916072.17661504812656.443904698419487.9093253977
8015124.888989786111597.600805592718652.1771739794
8116273.780768292112429.524494838720118.0370417456
8218070.926523695713805.659849378122336.1931980133
8315008.434190428111001.710892852519015.1574880036
849842.625886159537798.8339209969111886.4178513221

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 26498.981865146 & 23698.8806723055 & 29299.0830579865 \tabularnewline
74 & 23934.8633943201 & 20956.2883634231 & 26913.4384252172 \tabularnewline
75 & 26836.6936186315 & 23556.4925784432 & 30116.8946588198 \tabularnewline
76 & 24042.2333148094 & 20686.841609157 & 27397.6250204618 \tabularnewline
77 & 19769.0075844744 & 16442.3106804039 & 23095.704488545 \tabularnewline
78 & 21288.4567562023 & 17662.4973863149 & 24914.4161260897 \tabularnewline
79 & 16072.176615048 & 12656.4439046984 & 19487.9093253977 \tabularnewline
80 & 15124.8889897861 & 11597.6008055927 & 18652.1771739794 \tabularnewline
81 & 16273.7807682921 & 12429.5244948387 & 20118.0370417456 \tabularnewline
82 & 18070.9265236957 & 13805.6598493781 & 22336.1931980133 \tabularnewline
83 & 15008.4341904281 & 11001.7108928525 & 19015.1574880036 \tabularnewline
84 & 9842.62588615953 & 7798.83392099691 & 11886.4178513221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232300&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]73[/C][C]26498.981865146[/C][C]23698.8806723055[/C][C]29299.0830579865[/C][/ROW]
[ROW][C]74[/C][C]23934.8633943201[/C][C]20956.2883634231[/C][C]26913.4384252172[/C][/ROW]
[ROW][C]75[/C][C]26836.6936186315[/C][C]23556.4925784432[/C][C]30116.8946588198[/C][/ROW]
[ROW][C]76[/C][C]24042.2333148094[/C][C]20686.841609157[/C][C]27397.6250204618[/C][/ROW]
[ROW][C]77[/C][C]19769.0075844744[/C][C]16442.3106804039[/C][C]23095.704488545[/C][/ROW]
[ROW][C]78[/C][C]21288.4567562023[/C][C]17662.4973863149[/C][C]24914.4161260897[/C][/ROW]
[ROW][C]79[/C][C]16072.176615048[/C][C]12656.4439046984[/C][C]19487.9093253977[/C][/ROW]
[ROW][C]80[/C][C]15124.8889897861[/C][C]11597.6008055927[/C][C]18652.1771739794[/C][/ROW]
[ROW][C]81[/C][C]16273.7807682921[/C][C]12429.5244948387[/C][C]20118.0370417456[/C][/ROW]
[ROW][C]82[/C][C]18070.9265236957[/C][C]13805.6598493781[/C][C]22336.1931980133[/C][/ROW]
[ROW][C]83[/C][C]15008.4341904281[/C][C]11001.7108928525[/C][C]19015.1574880036[/C][/ROW]
[ROW][C]84[/C][C]9842.62588615953[/C][C]7798.83392099691[/C][C]11886.4178513221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232300&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232300&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
7326498.98186514623698.880672305529299.0830579865
7423934.863394320120956.288363423126913.4384252172
7526836.693618631523556.492578443230116.8946588198
7624042.233314809420686.84160915727397.6250204618
7719769.007584474416442.310680403923095.704488545
7821288.456756202317662.497386314924914.4161260897
7916072.17661504812656.443904698419487.9093253977
8015124.888989786111597.600805592718652.1771739794
8116273.780768292112429.524494838720118.0370417456
8218070.926523695713805.659849378122336.1931980133
8315008.434190428111001.710892852519015.1574880036
849842.625886159537798.8339209969111886.4178513221



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=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')