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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 20:04:16 +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/29/t1293653077vvwnm79uqzdg3b0.htm/, Retrieved Fri, 03 May 2024 13:24:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117094, Retrieved Fri, 03 May 2024 13:24:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-29 20:04:16] [95fdfecfb4f2f50e2168e1a971ea5f83] [Current]
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Dataseries X:
60178
53200
59909
55970
47682
50173
43090
36031
42143
48478
36046
31060
54874
60051
71622
66526
50140
55973
40393
38483
42879
47875
40578
31027
62027
56493
65566
62653
53470
59600
42542
42018
44038
44988
43309
26843
69770
64886
79354
63025
54003
55926
45629
40361
43039
44570
43269
25563
68707
60223
74283
61232
61531
65305
51699
44599
35221
55066
45335
28702
69517
69240
71525
77740
62107
65450
51493
43067
49172
54483
38158
27898
58648
56000
62381
59849
48345
55376
45400
38389
44098
48290
41267
31238




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=117094&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=117094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117094&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
alpha0.36119285707601
beta0
gamma0.448850016394393

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.36119285707601 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.448850016394393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117094&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]0.36119285707601[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.448850016394393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117094&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
alpha0.36119285707601
beta0
gamma0.448850016394393







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135487451792.13274572653081.86725427349
146005158388.50452358741662.49547641262
157162270723.167687083898.832312917031
166652666242.2928373786283.707162621446
175014050091.072510512948.927489487105
185597356050.3014427245-77.301442724478
194039346696.1873862649-6303.1873862649
203848337592.0777980286890.922201971422
214287943548.3875394186-669.387539418589
224787549009.7495473924-1134.7495473924
234057835921.65112213154656.34887786847
243102732569.4227493657-1542.42274936569
256202756876.69348151025150.30651848981
265649363813.1962690184-7320.19626901836
276556672684.411269624-7118.41126962406
286265365131.3913334055-2478.39133340553
295347047915.20271305265554.79728694745
305960055826.91904351723773.08095648275
314254246078.3960676396-3536.39606763959
324201840036.38868654731981.61131345273
334403845939.262121925-1901.26212192497
344498850822.2472344387-5834.24723443866
354330937697.19733687015611.80266312993
362684332912.7069574455-6069.70695744554
376977057503.751841902412266.2481580976
386488663434.83215816871451.16784183127
397935475532.05875211233821.94124788773
406302573261.0424035012-10236.0424035012
415400355546.1905280719-1543.19052807194
425592660383.2953372114-4457.29533721144
434562945566.183144185162.8168558148973
444036142406.3562744074-2045.35627440737
454303945741.386930572-2702.38693057196
464457049207.3121829173-4637.31218291735
474326939796.49649979133472.50350020872
482556330889.8836841943-5326.88368419428
496870761006.67370614827700.32629385182
506022362187.5828581605-1964.58285816047
517428373730.8332292288552.166770771175
526123266247.9717722068-5015.97177220677
536153152911.06134070338619.93865929668
546530560583.45863566614721.54136433386
555169950377.72212096991321.27787903014
564459947067.9688607218-2468.96886072178
573522150061.6041985938-14840.6041985938
585506648588.49367401186477.50632598816
594533545517.5871132976-182.587113297566
602870232767.7457380389-4065.74573803887
616951767075.32341221532441.67658778466
626924063585.64001535685654.35998464317
637152578602.4222087487-7077.42220874867
647774066767.26315993910972.7368400611
656210763115.165534094-1008.165534094
666545066192.1783819468-742.17838194684
675149353038.0325447049-1545.03254470488
684306747606.2163048819-4539.21630488187
694917246304.79141578642867.20858421356
705448357340.1282951227-2857.12829512273
713815848987.9791409488-10829.9791409488
722789831278.963196067-3380.96319606697
735864867699.7435038536-9051.7435038536
745600060979.8870681402-4979.88706814021
756238168505.0891454843-6124.08914548432
765984962189.763961548-2340.76396154797
774834550293.6576200511-1948.65762005108
785537653107.23756716162268.76243283836
794540040810.42079795734589.57920204272
803838936735.8643945531653.13560544699
814409839794.70659805264303.29340194743
824829049707.4159759791-1417.41597597911
834126739589.23629400431677.76370599568
843123828533.77361131792704.22638868213

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 54874 & 51792.1327457265 & 3081.86725427349 \tabularnewline
14 & 60051 & 58388.5045235874 & 1662.49547641262 \tabularnewline
15 & 71622 & 70723.167687083 & 898.832312917031 \tabularnewline
16 & 66526 & 66242.2928373786 & 283.707162621446 \tabularnewline
17 & 50140 & 50091.0725105129 & 48.927489487105 \tabularnewline
18 & 55973 & 56050.3014427245 & -77.301442724478 \tabularnewline
19 & 40393 & 46696.1873862649 & -6303.1873862649 \tabularnewline
20 & 38483 & 37592.0777980286 & 890.922201971422 \tabularnewline
21 & 42879 & 43548.3875394186 & -669.387539418589 \tabularnewline
22 & 47875 & 49009.7495473924 & -1134.7495473924 \tabularnewline
23 & 40578 & 35921.6511221315 & 4656.34887786847 \tabularnewline
24 & 31027 & 32569.4227493657 & -1542.42274936569 \tabularnewline
25 & 62027 & 56876.6934815102 & 5150.30651848981 \tabularnewline
26 & 56493 & 63813.1962690184 & -7320.19626901836 \tabularnewline
27 & 65566 & 72684.411269624 & -7118.41126962406 \tabularnewline
28 & 62653 & 65131.3913334055 & -2478.39133340553 \tabularnewline
29 & 53470 & 47915.2027130526 & 5554.79728694745 \tabularnewline
30 & 59600 & 55826.9190435172 & 3773.08095648275 \tabularnewline
31 & 42542 & 46078.3960676396 & -3536.39606763959 \tabularnewline
32 & 42018 & 40036.3886865473 & 1981.61131345273 \tabularnewline
33 & 44038 & 45939.262121925 & -1901.26212192497 \tabularnewline
34 & 44988 & 50822.2472344387 & -5834.24723443866 \tabularnewline
35 & 43309 & 37697.1973368701 & 5611.80266312993 \tabularnewline
36 & 26843 & 32912.7069574455 & -6069.70695744554 \tabularnewline
37 & 69770 & 57503.7518419024 & 12266.2481580976 \tabularnewline
38 & 64886 & 63434.8321581687 & 1451.16784183127 \tabularnewline
39 & 79354 & 75532.0587521123 & 3821.94124788773 \tabularnewline
40 & 63025 & 73261.0424035012 & -10236.0424035012 \tabularnewline
41 & 54003 & 55546.1905280719 & -1543.19052807194 \tabularnewline
42 & 55926 & 60383.2953372114 & -4457.29533721144 \tabularnewline
43 & 45629 & 45566.1831441851 & 62.8168558148973 \tabularnewline
44 & 40361 & 42406.3562744074 & -2045.35627440737 \tabularnewline
45 & 43039 & 45741.386930572 & -2702.38693057196 \tabularnewline
46 & 44570 & 49207.3121829173 & -4637.31218291735 \tabularnewline
47 & 43269 & 39796.4964997913 & 3472.50350020872 \tabularnewline
48 & 25563 & 30889.8836841943 & -5326.88368419428 \tabularnewline
49 & 68707 & 61006.6737061482 & 7700.32629385182 \tabularnewline
50 & 60223 & 62187.5828581605 & -1964.58285816047 \tabularnewline
51 & 74283 & 73730.8332292288 & 552.166770771175 \tabularnewline
52 & 61232 & 66247.9717722068 & -5015.97177220677 \tabularnewline
53 & 61531 & 52911.0613407033 & 8619.93865929668 \tabularnewline
54 & 65305 & 60583.4586356661 & 4721.54136433386 \tabularnewline
55 & 51699 & 50377.7221209699 & 1321.27787903014 \tabularnewline
56 & 44599 & 47067.9688607218 & -2468.96886072178 \tabularnewline
57 & 35221 & 50061.6041985938 & -14840.6041985938 \tabularnewline
58 & 55066 & 48588.4936740118 & 6477.50632598816 \tabularnewline
59 & 45335 & 45517.5871132976 & -182.587113297566 \tabularnewline
60 & 28702 & 32767.7457380389 & -4065.74573803887 \tabularnewline
61 & 69517 & 67075.3234122153 & 2441.67658778466 \tabularnewline
62 & 69240 & 63585.6400153568 & 5654.35998464317 \tabularnewline
63 & 71525 & 78602.4222087487 & -7077.42220874867 \tabularnewline
64 & 77740 & 66767.263159939 & 10972.7368400611 \tabularnewline
65 & 62107 & 63115.165534094 & -1008.165534094 \tabularnewline
66 & 65450 & 66192.1783819468 & -742.17838194684 \tabularnewline
67 & 51493 & 53038.0325447049 & -1545.03254470488 \tabularnewline
68 & 43067 & 47606.2163048819 & -4539.21630488187 \tabularnewline
69 & 49172 & 46304.7914157864 & 2867.20858421356 \tabularnewline
70 & 54483 & 57340.1282951227 & -2857.12829512273 \tabularnewline
71 & 38158 & 48987.9791409488 & -10829.9791409488 \tabularnewline
72 & 27898 & 31278.963196067 & -3380.96319606697 \tabularnewline
73 & 58648 & 67699.7435038536 & -9051.7435038536 \tabularnewline
74 & 56000 & 60979.8870681402 & -4979.88706814021 \tabularnewline
75 & 62381 & 68505.0891454843 & -6124.08914548432 \tabularnewline
76 & 59849 & 62189.763961548 & -2340.76396154797 \tabularnewline
77 & 48345 & 50293.6576200511 & -1948.65762005108 \tabularnewline
78 & 55376 & 53107.2375671616 & 2268.76243283836 \tabularnewline
79 & 45400 & 40810.4207979573 & 4589.57920204272 \tabularnewline
80 & 38389 & 36735.864394553 & 1653.13560544699 \tabularnewline
81 & 44098 & 39794.7065980526 & 4303.29340194743 \tabularnewline
82 & 48290 & 49707.4159759791 & -1417.41597597911 \tabularnewline
83 & 41267 & 39589.2362940043 & 1677.76370599568 \tabularnewline
84 & 31238 & 28533.7736113179 & 2704.22638868213 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117094&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]54874[/C][C]51792.1327457265[/C][C]3081.86725427349[/C][/ROW]
[ROW][C]14[/C][C]60051[/C][C]58388.5045235874[/C][C]1662.49547641262[/C][/ROW]
[ROW][C]15[/C][C]71622[/C][C]70723.167687083[/C][C]898.832312917031[/C][/ROW]
[ROW][C]16[/C][C]66526[/C][C]66242.2928373786[/C][C]283.707162621446[/C][/ROW]
[ROW][C]17[/C][C]50140[/C][C]50091.0725105129[/C][C]48.927489487105[/C][/ROW]
[ROW][C]18[/C][C]55973[/C][C]56050.3014427245[/C][C]-77.301442724478[/C][/ROW]
[ROW][C]19[/C][C]40393[/C][C]46696.1873862649[/C][C]-6303.1873862649[/C][/ROW]
[ROW][C]20[/C][C]38483[/C][C]37592.0777980286[/C][C]890.922201971422[/C][/ROW]
[ROW][C]21[/C][C]42879[/C][C]43548.3875394186[/C][C]-669.387539418589[/C][/ROW]
[ROW][C]22[/C][C]47875[/C][C]49009.7495473924[/C][C]-1134.7495473924[/C][/ROW]
[ROW][C]23[/C][C]40578[/C][C]35921.6511221315[/C][C]4656.34887786847[/C][/ROW]
[ROW][C]24[/C][C]31027[/C][C]32569.4227493657[/C][C]-1542.42274936569[/C][/ROW]
[ROW][C]25[/C][C]62027[/C][C]56876.6934815102[/C][C]5150.30651848981[/C][/ROW]
[ROW][C]26[/C][C]56493[/C][C]63813.1962690184[/C][C]-7320.19626901836[/C][/ROW]
[ROW][C]27[/C][C]65566[/C][C]72684.411269624[/C][C]-7118.41126962406[/C][/ROW]
[ROW][C]28[/C][C]62653[/C][C]65131.3913334055[/C][C]-2478.39133340553[/C][/ROW]
[ROW][C]29[/C][C]53470[/C][C]47915.2027130526[/C][C]5554.79728694745[/C][/ROW]
[ROW][C]30[/C][C]59600[/C][C]55826.9190435172[/C][C]3773.08095648275[/C][/ROW]
[ROW][C]31[/C][C]42542[/C][C]46078.3960676396[/C][C]-3536.39606763959[/C][/ROW]
[ROW][C]32[/C][C]42018[/C][C]40036.3886865473[/C][C]1981.61131345273[/C][/ROW]
[ROW][C]33[/C][C]44038[/C][C]45939.262121925[/C][C]-1901.26212192497[/C][/ROW]
[ROW][C]34[/C][C]44988[/C][C]50822.2472344387[/C][C]-5834.24723443866[/C][/ROW]
[ROW][C]35[/C][C]43309[/C][C]37697.1973368701[/C][C]5611.80266312993[/C][/ROW]
[ROW][C]36[/C][C]26843[/C][C]32912.7069574455[/C][C]-6069.70695744554[/C][/ROW]
[ROW][C]37[/C][C]69770[/C][C]57503.7518419024[/C][C]12266.2481580976[/C][/ROW]
[ROW][C]38[/C][C]64886[/C][C]63434.8321581687[/C][C]1451.16784183127[/C][/ROW]
[ROW][C]39[/C][C]79354[/C][C]75532.0587521123[/C][C]3821.94124788773[/C][/ROW]
[ROW][C]40[/C][C]63025[/C][C]73261.0424035012[/C][C]-10236.0424035012[/C][/ROW]
[ROW][C]41[/C][C]54003[/C][C]55546.1905280719[/C][C]-1543.19052807194[/C][/ROW]
[ROW][C]42[/C][C]55926[/C][C]60383.2953372114[/C][C]-4457.29533721144[/C][/ROW]
[ROW][C]43[/C][C]45629[/C][C]45566.1831441851[/C][C]62.8168558148973[/C][/ROW]
[ROW][C]44[/C][C]40361[/C][C]42406.3562744074[/C][C]-2045.35627440737[/C][/ROW]
[ROW][C]45[/C][C]43039[/C][C]45741.386930572[/C][C]-2702.38693057196[/C][/ROW]
[ROW][C]46[/C][C]44570[/C][C]49207.3121829173[/C][C]-4637.31218291735[/C][/ROW]
[ROW][C]47[/C][C]43269[/C][C]39796.4964997913[/C][C]3472.50350020872[/C][/ROW]
[ROW][C]48[/C][C]25563[/C][C]30889.8836841943[/C][C]-5326.88368419428[/C][/ROW]
[ROW][C]49[/C][C]68707[/C][C]61006.6737061482[/C][C]7700.32629385182[/C][/ROW]
[ROW][C]50[/C][C]60223[/C][C]62187.5828581605[/C][C]-1964.58285816047[/C][/ROW]
[ROW][C]51[/C][C]74283[/C][C]73730.8332292288[/C][C]552.166770771175[/C][/ROW]
[ROW][C]52[/C][C]61232[/C][C]66247.9717722068[/C][C]-5015.97177220677[/C][/ROW]
[ROW][C]53[/C][C]61531[/C][C]52911.0613407033[/C][C]8619.93865929668[/C][/ROW]
[ROW][C]54[/C][C]65305[/C][C]60583.4586356661[/C][C]4721.54136433386[/C][/ROW]
[ROW][C]55[/C][C]51699[/C][C]50377.7221209699[/C][C]1321.27787903014[/C][/ROW]
[ROW][C]56[/C][C]44599[/C][C]47067.9688607218[/C][C]-2468.96886072178[/C][/ROW]
[ROW][C]57[/C][C]35221[/C][C]50061.6041985938[/C][C]-14840.6041985938[/C][/ROW]
[ROW][C]58[/C][C]55066[/C][C]48588.4936740118[/C][C]6477.50632598816[/C][/ROW]
[ROW][C]59[/C][C]45335[/C][C]45517.5871132976[/C][C]-182.587113297566[/C][/ROW]
[ROW][C]60[/C][C]28702[/C][C]32767.7457380389[/C][C]-4065.74573803887[/C][/ROW]
[ROW][C]61[/C][C]69517[/C][C]67075.3234122153[/C][C]2441.67658778466[/C][/ROW]
[ROW][C]62[/C][C]69240[/C][C]63585.6400153568[/C][C]5654.35998464317[/C][/ROW]
[ROW][C]63[/C][C]71525[/C][C]78602.4222087487[/C][C]-7077.42220874867[/C][/ROW]
[ROW][C]64[/C][C]77740[/C][C]66767.263159939[/C][C]10972.7368400611[/C][/ROW]
[ROW][C]65[/C][C]62107[/C][C]63115.165534094[/C][C]-1008.165534094[/C][/ROW]
[ROW][C]66[/C][C]65450[/C][C]66192.1783819468[/C][C]-742.17838194684[/C][/ROW]
[ROW][C]67[/C][C]51493[/C][C]53038.0325447049[/C][C]-1545.03254470488[/C][/ROW]
[ROW][C]68[/C][C]43067[/C][C]47606.2163048819[/C][C]-4539.21630488187[/C][/ROW]
[ROW][C]69[/C][C]49172[/C][C]46304.7914157864[/C][C]2867.20858421356[/C][/ROW]
[ROW][C]70[/C][C]54483[/C][C]57340.1282951227[/C][C]-2857.12829512273[/C][/ROW]
[ROW][C]71[/C][C]38158[/C][C]48987.9791409488[/C][C]-10829.9791409488[/C][/ROW]
[ROW][C]72[/C][C]27898[/C][C]31278.963196067[/C][C]-3380.96319606697[/C][/ROW]
[ROW][C]73[/C][C]58648[/C][C]67699.7435038536[/C][C]-9051.7435038536[/C][/ROW]
[ROW][C]74[/C][C]56000[/C][C]60979.8870681402[/C][C]-4979.88706814021[/C][/ROW]
[ROW][C]75[/C][C]62381[/C][C]68505.0891454843[/C][C]-6124.08914548432[/C][/ROW]
[ROW][C]76[/C][C]59849[/C][C]62189.763961548[/C][C]-2340.76396154797[/C][/ROW]
[ROW][C]77[/C][C]48345[/C][C]50293.6576200511[/C][C]-1948.65762005108[/C][/ROW]
[ROW][C]78[/C][C]55376[/C][C]53107.2375671616[/C][C]2268.76243283836[/C][/ROW]
[ROW][C]79[/C][C]45400[/C][C]40810.4207979573[/C][C]4589.57920204272[/C][/ROW]
[ROW][C]80[/C][C]38389[/C][C]36735.864394553[/C][C]1653.13560544699[/C][/ROW]
[ROW][C]81[/C][C]44098[/C][C]39794.7065980526[/C][C]4303.29340194743[/C][/ROW]
[ROW][C]82[/C][C]48290[/C][C]49707.4159759791[/C][C]-1417.41597597911[/C][/ROW]
[ROW][C]83[/C][C]41267[/C][C]39589.2362940043[/C][C]1677.76370599568[/C][/ROW]
[ROW][C]84[/C][C]31238[/C][C]28533.7736113179[/C][C]2704.22638868213[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117094&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117094&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
135487451792.13274572653081.86725427349
146005158388.50452358741662.49547641262
157162270723.167687083898.832312917031
166652666242.2928373786283.707162621446
175014050091.072510512948.927489487105
185597356050.3014427245-77.301442724478
194039346696.1873862649-6303.1873862649
203848337592.0777980286890.922201971422
214287943548.3875394186-669.387539418589
224787549009.7495473924-1134.7495473924
234057835921.65112213154656.34887786847
243102732569.4227493657-1542.42274936569
256202756876.69348151025150.30651848981
265649363813.1962690184-7320.19626901836
276556672684.411269624-7118.41126962406
286265365131.3913334055-2478.39133340553
295347047915.20271305265554.79728694745
305960055826.91904351723773.08095648275
314254246078.3960676396-3536.39606763959
324201840036.38868654731981.61131345273
334403845939.262121925-1901.26212192497
344498850822.2472344387-5834.24723443866
354330937697.19733687015611.80266312993
362684332912.7069574455-6069.70695744554
376977057503.751841902412266.2481580976
386488663434.83215816871451.16784183127
397935475532.05875211233821.94124788773
406302573261.0424035012-10236.0424035012
415400355546.1905280719-1543.19052807194
425592660383.2953372114-4457.29533721144
434562945566.183144185162.8168558148973
444036142406.3562744074-2045.35627440737
454303945741.386930572-2702.38693057196
464457049207.3121829173-4637.31218291735
474326939796.49649979133472.50350020872
482556330889.8836841943-5326.88368419428
496870761006.67370614827700.32629385182
506022362187.5828581605-1964.58285816047
517428373730.8332292288552.166770771175
526123266247.9717722068-5015.97177220677
536153152911.06134070338619.93865929668
546530560583.45863566614721.54136433386
555169950377.72212096991321.27787903014
564459947067.9688607218-2468.96886072178
573522150061.6041985938-14840.6041985938
585506648588.49367401186477.50632598816
594533545517.5871132976-182.587113297566
602870232767.7457380389-4065.74573803887
616951767075.32341221532441.67658778466
626924063585.64001535685654.35998464317
637152578602.4222087487-7077.42220874867
647774066767.26315993910972.7368400611
656210763115.165534094-1008.165534094
666545066192.1783819468-742.17838194684
675149353038.0325447049-1545.03254470488
684306747606.2163048819-4539.21630488187
694917246304.79141578642867.20858421356
705448357340.1282951227-2857.12829512273
713815848987.9791409488-10829.9791409488
722789831278.963196067-3380.96319606697
735864867699.7435038536-9051.7435038536
745600060979.8870681402-4979.88706814021
756238168505.0891454843-6124.08914548432
765984962189.763961548-2340.76396154797
774834550293.6576200511-1948.65762005108
785537653107.23756716162268.76243283836
794540040810.42079795734589.57920204272
803838936735.8643945531653.13560544699
814409839794.70659805264303.29340194743
824829049707.4159759791-1417.41597597911
834126739589.23629400431677.76370599568
843123828533.77361131792704.22638868213







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8565526.506051936455673.32067425575379.6914296179
8663243.592395163252767.379693859573719.805096467
8772239.418654730561175.20593809583303.6313713661
8869220.85824661457598.355352875480843.3611403527
8958282.647229134546127.469567291670437.8248909775
9063009.323322423550343.853948295775674.7926965513
9150558.490303215637402.507445862463714.4731605688
9243984.248323677530355.394541389957613.102105965
9347205.865780402533120.006704897961291.7248559072
9453923.965348301139395.469336291468452.4613603107
9545205.222718713230247.182511286960163.2629261396
9633838.079974002318462.490966650949213.6689813537

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 65526.5060519364 & 55673.320674255 & 75379.6914296179 \tabularnewline
86 & 63243.5923951632 & 52767.3796938595 & 73719.805096467 \tabularnewline
87 & 72239.4186547305 & 61175.205938095 & 83303.6313713661 \tabularnewline
88 & 69220.858246614 & 57598.3553528754 & 80843.3611403527 \tabularnewline
89 & 58282.6472291345 & 46127.4695672916 & 70437.8248909775 \tabularnewline
90 & 63009.3233224235 & 50343.8539482957 & 75674.7926965513 \tabularnewline
91 & 50558.4903032156 & 37402.5074458624 & 63714.4731605688 \tabularnewline
92 & 43984.2483236775 & 30355.3945413899 & 57613.102105965 \tabularnewline
93 & 47205.8657804025 & 33120.0067048979 & 61291.7248559072 \tabularnewline
94 & 53923.9653483011 & 39395.4693362914 & 68452.4613603107 \tabularnewline
95 & 45205.2227187132 & 30247.1825112869 & 60163.2629261396 \tabularnewline
96 & 33838.0799740023 & 18462.4909666509 & 49213.6689813537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117094&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]65526.5060519364[/C][C]55673.320674255[/C][C]75379.6914296179[/C][/ROW]
[ROW][C]86[/C][C]63243.5923951632[/C][C]52767.3796938595[/C][C]73719.805096467[/C][/ROW]
[ROW][C]87[/C][C]72239.4186547305[/C][C]61175.205938095[/C][C]83303.6313713661[/C][/ROW]
[ROW][C]88[/C][C]69220.858246614[/C][C]57598.3553528754[/C][C]80843.3611403527[/C][/ROW]
[ROW][C]89[/C][C]58282.6472291345[/C][C]46127.4695672916[/C][C]70437.8248909775[/C][/ROW]
[ROW][C]90[/C][C]63009.3233224235[/C][C]50343.8539482957[/C][C]75674.7926965513[/C][/ROW]
[ROW][C]91[/C][C]50558.4903032156[/C][C]37402.5074458624[/C][C]63714.4731605688[/C][/ROW]
[ROW][C]92[/C][C]43984.2483236775[/C][C]30355.3945413899[/C][C]57613.102105965[/C][/ROW]
[ROW][C]93[/C][C]47205.8657804025[/C][C]33120.0067048979[/C][C]61291.7248559072[/C][/ROW]
[ROW][C]94[/C][C]53923.9653483011[/C][C]39395.4693362914[/C][C]68452.4613603107[/C][/ROW]
[ROW][C]95[/C][C]45205.2227187132[/C][C]30247.1825112869[/C][C]60163.2629261396[/C][/ROW]
[ROW][C]96[/C][C]33838.0799740023[/C][C]18462.4909666509[/C][C]49213.6689813537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117094&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117094&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
8565526.506051936455673.32067425575379.6914296179
8663243.592395163252767.379693859573719.805096467
8772239.418654730561175.20593809583303.6313713661
8869220.85824661457598.355352875480843.3611403527
8958282.647229134546127.469567291670437.8248909775
9063009.323322423550343.853948295775674.7926965513
9150558.490303215637402.507445862463714.4731605688
9243984.248323677530355.394541389957613.102105965
9347205.865780402533120.006704897961291.7248559072
9453923.965348301139395.469336291468452.4613603107
9545205.222718713230247.182511286960163.2629261396
9633838.079974002318462.490966650949213.6689813537



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')