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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 15:49:42 +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/2014/Nov/30/t1417362609rctfm3ik6xccl04.htm/, Retrieved Sun, 19 May 2024 16:33:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261518, Retrieved Sun, 19 May 2024 16:33:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 15:49:42] [23f6b347f5ddfa38e8c261c083a091fc] [Current]
- R P     [Exponential Smoothing] [] [2014-12-17 19:26:37] [379af119b8c9c9402cda7215f859bbd6]
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Dataseries X:
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118
21925
20801
18785
20659
29367
23992
20645
22356
17902
15879
16963
21035
17988
10437
24470
22237
27053
26419
22311
20624
17336
15586
17733
19231
16102
11770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261518&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]1 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=261518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261518&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.709576037716635
beta0.0335487849072062
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.709576037716635 \tabularnewline
beta & 0.0335487849072062 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261518&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]0.709576037716635[/C][/ROW]
[ROW][C]beta[/C][C]0.0335487849072062[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261518&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
alpha0.709576037716635
beta0.0335487849072062
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
330019286561363
43193428200.59891850533733.40108149469
52582629516.0528020846-3690.05280208461
62683525476.15845864551358.84154135454
72020525051.1863435422-4846.18634354223
81778920107.9096563794-2318.90965637942
92052016902.72534302233617.27465697765
102251817995.82589416434522.17410583566
111557219838.6736369164-4266.67363691644
121150915343.5956905195-3834.59569051948
132544711063.825763895114383.1742361049
142409020053.34625321624036.6537467838
152778621797.31794264145988.68205735862
162619525068.96520107421126.03479892576
172051624917.0002094691-4401.0002094691
182275920738.41598488112020.58401511888
191902821164.5348889682-2136.53488896816
201697118590.000735508-1619.00073550802
212003616344.15543348723691.84456651281
222248517954.64458563024530.35541436984
231873020267.967928371-1537.96792837102
241453818238.742474941-3700.74247494101
252756114586.76632205912974.233677941
262598523075.81067903862909.18932096142
273467024492.195197546610177.8048024534
283206631308.5019446536757.498055346401
292718631458.4173107823-4272.41731078234
302958627937.51859907771648.48140092229
312135928657.1905169431-7298.19051694313
322155322854.7819788599-1301.78197885993
331957321276.2917929917-1703.29179299169
342425619372.3522980434883.64770195696
352238022258.6044853136121.395514686439
361616721768.5665054017-5601.56650540171
372729717084.304202321410212.6957976786
382828723864.580933814422.41906619
393347426641.49356103976832.50643896027
402822931291.1970803031-3062.1970803031
412878528846.959213155-61.9592131549507
422559728530.1432792733-2933.14327927331
431813026106.1792425128-7976.17924251282
442019819913.9214809676284.078519032417
452284919589.70729909333259.29270090667
462311821454.22261940291663.7773805971
472192522226.2054097348-301.205409734797
482080121596.7131780846-795.713178084603
491878520597.3878020268-1812.38780202679
502065918833.50983295451825.49016704549
512936719694.43944780569672.56055219443
522399226353.7214813102-2361.72148131016
532064524417.5435954204-3772.54359542043
542235621390.4731822659965.526817734146
551790221748.4087647935-3846.40876479351
561587918600.3448103849-2721.34481038494
571696316185.8165394437777.183460556262
582103516272.26127076394762.73872923606
591798819300.1394843133-1312.13948431333
601043717986.193662009-7549.193662009
612447012066.871969802812403.1280301972
622223720600.50124317511636.49875682485
632705321533.34590737925519.65409262076
642641925352.98219866021066.01780133977
652231126037.801891891-3726.80189189103
662062423233.0335162808-2609.03351628079
671733621159.2976730792-3823.29767307918
681558618132.9338973198-2546.93389731978
691773315951.61645673711781.38354326285
701923116883.9759281222347.02407187798
711610218273.5722439549-2171.57224395494
721177016405.1857139538-4635.18571395379

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 30019 & 28656 & 1363 \tabularnewline
4 & 31934 & 28200.5989185053 & 3733.40108149469 \tabularnewline
5 & 25826 & 29516.0528020846 & -3690.05280208461 \tabularnewline
6 & 26835 & 25476.1584586455 & 1358.84154135454 \tabularnewline
7 & 20205 & 25051.1863435422 & -4846.18634354223 \tabularnewline
8 & 17789 & 20107.9096563794 & -2318.90965637942 \tabularnewline
9 & 20520 & 16902.7253430223 & 3617.27465697765 \tabularnewline
10 & 22518 & 17995.8258941643 & 4522.17410583566 \tabularnewline
11 & 15572 & 19838.6736369164 & -4266.67363691644 \tabularnewline
12 & 11509 & 15343.5956905195 & -3834.59569051948 \tabularnewline
13 & 25447 & 11063.8257638951 & 14383.1742361049 \tabularnewline
14 & 24090 & 20053.3462532162 & 4036.6537467838 \tabularnewline
15 & 27786 & 21797.3179426414 & 5988.68205735862 \tabularnewline
16 & 26195 & 25068.9652010742 & 1126.03479892576 \tabularnewline
17 & 20516 & 24917.0002094691 & -4401.0002094691 \tabularnewline
18 & 22759 & 20738.4159848811 & 2020.58401511888 \tabularnewline
19 & 19028 & 21164.5348889682 & -2136.53488896816 \tabularnewline
20 & 16971 & 18590.000735508 & -1619.00073550802 \tabularnewline
21 & 20036 & 16344.1554334872 & 3691.84456651281 \tabularnewline
22 & 22485 & 17954.6445856302 & 4530.35541436984 \tabularnewline
23 & 18730 & 20267.967928371 & -1537.96792837102 \tabularnewline
24 & 14538 & 18238.742474941 & -3700.74247494101 \tabularnewline
25 & 27561 & 14586.766322059 & 12974.233677941 \tabularnewline
26 & 25985 & 23075.8106790386 & 2909.18932096142 \tabularnewline
27 & 34670 & 24492.1951975466 & 10177.8048024534 \tabularnewline
28 & 32066 & 31308.5019446536 & 757.498055346401 \tabularnewline
29 & 27186 & 31458.4173107823 & -4272.41731078234 \tabularnewline
30 & 29586 & 27937.5185990777 & 1648.48140092229 \tabularnewline
31 & 21359 & 28657.1905169431 & -7298.19051694313 \tabularnewline
32 & 21553 & 22854.7819788599 & -1301.78197885993 \tabularnewline
33 & 19573 & 21276.2917929917 & -1703.29179299169 \tabularnewline
34 & 24256 & 19372.352298043 & 4883.64770195696 \tabularnewline
35 & 22380 & 22258.6044853136 & 121.395514686439 \tabularnewline
36 & 16167 & 21768.5665054017 & -5601.56650540171 \tabularnewline
37 & 27297 & 17084.3042023214 & 10212.6957976786 \tabularnewline
38 & 28287 & 23864.58093381 & 4422.41906619 \tabularnewline
39 & 33474 & 26641.4935610397 & 6832.50643896027 \tabularnewline
40 & 28229 & 31291.1970803031 & -3062.1970803031 \tabularnewline
41 & 28785 & 28846.959213155 & -61.9592131549507 \tabularnewline
42 & 25597 & 28530.1432792733 & -2933.14327927331 \tabularnewline
43 & 18130 & 26106.1792425128 & -7976.17924251282 \tabularnewline
44 & 20198 & 19913.9214809676 & 284.078519032417 \tabularnewline
45 & 22849 & 19589.7072990933 & 3259.29270090667 \tabularnewline
46 & 23118 & 21454.2226194029 & 1663.7773805971 \tabularnewline
47 & 21925 & 22226.2054097348 & -301.205409734797 \tabularnewline
48 & 20801 & 21596.7131780846 & -795.713178084603 \tabularnewline
49 & 18785 & 20597.3878020268 & -1812.38780202679 \tabularnewline
50 & 20659 & 18833.5098329545 & 1825.49016704549 \tabularnewline
51 & 29367 & 19694.4394478056 & 9672.56055219443 \tabularnewline
52 & 23992 & 26353.7214813102 & -2361.72148131016 \tabularnewline
53 & 20645 & 24417.5435954204 & -3772.54359542043 \tabularnewline
54 & 22356 & 21390.4731822659 & 965.526817734146 \tabularnewline
55 & 17902 & 21748.4087647935 & -3846.40876479351 \tabularnewline
56 & 15879 & 18600.3448103849 & -2721.34481038494 \tabularnewline
57 & 16963 & 16185.8165394437 & 777.183460556262 \tabularnewline
58 & 21035 & 16272.2612707639 & 4762.73872923606 \tabularnewline
59 & 17988 & 19300.1394843133 & -1312.13948431333 \tabularnewline
60 & 10437 & 17986.193662009 & -7549.193662009 \tabularnewline
61 & 24470 & 12066.8719698028 & 12403.1280301972 \tabularnewline
62 & 22237 & 20600.5012431751 & 1636.49875682485 \tabularnewline
63 & 27053 & 21533.3459073792 & 5519.65409262076 \tabularnewline
64 & 26419 & 25352.9821986602 & 1066.01780133977 \tabularnewline
65 & 22311 & 26037.801891891 & -3726.80189189103 \tabularnewline
66 & 20624 & 23233.0335162808 & -2609.03351628079 \tabularnewline
67 & 17336 & 21159.2976730792 & -3823.29767307918 \tabularnewline
68 & 15586 & 18132.9338973198 & -2546.93389731978 \tabularnewline
69 & 17733 & 15951.6164567371 & 1781.38354326285 \tabularnewline
70 & 19231 & 16883.975928122 & 2347.02407187798 \tabularnewline
71 & 16102 & 18273.5722439549 & -2171.57224395494 \tabularnewline
72 & 11770 & 16405.1857139538 & -4635.18571395379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261518&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]3[/C][C]30019[/C][C]28656[/C][C]1363[/C][/ROW]
[ROW][C]4[/C][C]31934[/C][C]28200.5989185053[/C][C]3733.40108149469[/C][/ROW]
[ROW][C]5[/C][C]25826[/C][C]29516.0528020846[/C][C]-3690.05280208461[/C][/ROW]
[ROW][C]6[/C][C]26835[/C][C]25476.1584586455[/C][C]1358.84154135454[/C][/ROW]
[ROW][C]7[/C][C]20205[/C][C]25051.1863435422[/C][C]-4846.18634354223[/C][/ROW]
[ROW][C]8[/C][C]17789[/C][C]20107.9096563794[/C][C]-2318.90965637942[/C][/ROW]
[ROW][C]9[/C][C]20520[/C][C]16902.7253430223[/C][C]3617.27465697765[/C][/ROW]
[ROW][C]10[/C][C]22518[/C][C]17995.8258941643[/C][C]4522.17410583566[/C][/ROW]
[ROW][C]11[/C][C]15572[/C][C]19838.6736369164[/C][C]-4266.67363691644[/C][/ROW]
[ROW][C]12[/C][C]11509[/C][C]15343.5956905195[/C][C]-3834.59569051948[/C][/ROW]
[ROW][C]13[/C][C]25447[/C][C]11063.8257638951[/C][C]14383.1742361049[/C][/ROW]
[ROW][C]14[/C][C]24090[/C][C]20053.3462532162[/C][C]4036.6537467838[/C][/ROW]
[ROW][C]15[/C][C]27786[/C][C]21797.3179426414[/C][C]5988.68205735862[/C][/ROW]
[ROW][C]16[/C][C]26195[/C][C]25068.9652010742[/C][C]1126.03479892576[/C][/ROW]
[ROW][C]17[/C][C]20516[/C][C]24917.0002094691[/C][C]-4401.0002094691[/C][/ROW]
[ROW][C]18[/C][C]22759[/C][C]20738.4159848811[/C][C]2020.58401511888[/C][/ROW]
[ROW][C]19[/C][C]19028[/C][C]21164.5348889682[/C][C]-2136.53488896816[/C][/ROW]
[ROW][C]20[/C][C]16971[/C][C]18590.000735508[/C][C]-1619.00073550802[/C][/ROW]
[ROW][C]21[/C][C]20036[/C][C]16344.1554334872[/C][C]3691.84456651281[/C][/ROW]
[ROW][C]22[/C][C]22485[/C][C]17954.6445856302[/C][C]4530.35541436984[/C][/ROW]
[ROW][C]23[/C][C]18730[/C][C]20267.967928371[/C][C]-1537.96792837102[/C][/ROW]
[ROW][C]24[/C][C]14538[/C][C]18238.742474941[/C][C]-3700.74247494101[/C][/ROW]
[ROW][C]25[/C][C]27561[/C][C]14586.766322059[/C][C]12974.233677941[/C][/ROW]
[ROW][C]26[/C][C]25985[/C][C]23075.8106790386[/C][C]2909.18932096142[/C][/ROW]
[ROW][C]27[/C][C]34670[/C][C]24492.1951975466[/C][C]10177.8048024534[/C][/ROW]
[ROW][C]28[/C][C]32066[/C][C]31308.5019446536[/C][C]757.498055346401[/C][/ROW]
[ROW][C]29[/C][C]27186[/C][C]31458.4173107823[/C][C]-4272.41731078234[/C][/ROW]
[ROW][C]30[/C][C]29586[/C][C]27937.5185990777[/C][C]1648.48140092229[/C][/ROW]
[ROW][C]31[/C][C]21359[/C][C]28657.1905169431[/C][C]-7298.19051694313[/C][/ROW]
[ROW][C]32[/C][C]21553[/C][C]22854.7819788599[/C][C]-1301.78197885993[/C][/ROW]
[ROW][C]33[/C][C]19573[/C][C]21276.2917929917[/C][C]-1703.29179299169[/C][/ROW]
[ROW][C]34[/C][C]24256[/C][C]19372.352298043[/C][C]4883.64770195696[/C][/ROW]
[ROW][C]35[/C][C]22380[/C][C]22258.6044853136[/C][C]121.395514686439[/C][/ROW]
[ROW][C]36[/C][C]16167[/C][C]21768.5665054017[/C][C]-5601.56650540171[/C][/ROW]
[ROW][C]37[/C][C]27297[/C][C]17084.3042023214[/C][C]10212.6957976786[/C][/ROW]
[ROW][C]38[/C][C]28287[/C][C]23864.58093381[/C][C]4422.41906619[/C][/ROW]
[ROW][C]39[/C][C]33474[/C][C]26641.4935610397[/C][C]6832.50643896027[/C][/ROW]
[ROW][C]40[/C][C]28229[/C][C]31291.1970803031[/C][C]-3062.1970803031[/C][/ROW]
[ROW][C]41[/C][C]28785[/C][C]28846.959213155[/C][C]-61.9592131549507[/C][/ROW]
[ROW][C]42[/C][C]25597[/C][C]28530.1432792733[/C][C]-2933.14327927331[/C][/ROW]
[ROW][C]43[/C][C]18130[/C][C]26106.1792425128[/C][C]-7976.17924251282[/C][/ROW]
[ROW][C]44[/C][C]20198[/C][C]19913.9214809676[/C][C]284.078519032417[/C][/ROW]
[ROW][C]45[/C][C]22849[/C][C]19589.7072990933[/C][C]3259.29270090667[/C][/ROW]
[ROW][C]46[/C][C]23118[/C][C]21454.2226194029[/C][C]1663.7773805971[/C][/ROW]
[ROW][C]47[/C][C]21925[/C][C]22226.2054097348[/C][C]-301.205409734797[/C][/ROW]
[ROW][C]48[/C][C]20801[/C][C]21596.7131780846[/C][C]-795.713178084603[/C][/ROW]
[ROW][C]49[/C][C]18785[/C][C]20597.3878020268[/C][C]-1812.38780202679[/C][/ROW]
[ROW][C]50[/C][C]20659[/C][C]18833.5098329545[/C][C]1825.49016704549[/C][/ROW]
[ROW][C]51[/C][C]29367[/C][C]19694.4394478056[/C][C]9672.56055219443[/C][/ROW]
[ROW][C]52[/C][C]23992[/C][C]26353.7214813102[/C][C]-2361.72148131016[/C][/ROW]
[ROW][C]53[/C][C]20645[/C][C]24417.5435954204[/C][C]-3772.54359542043[/C][/ROW]
[ROW][C]54[/C][C]22356[/C][C]21390.4731822659[/C][C]965.526817734146[/C][/ROW]
[ROW][C]55[/C][C]17902[/C][C]21748.4087647935[/C][C]-3846.40876479351[/C][/ROW]
[ROW][C]56[/C][C]15879[/C][C]18600.3448103849[/C][C]-2721.34481038494[/C][/ROW]
[ROW][C]57[/C][C]16963[/C][C]16185.8165394437[/C][C]777.183460556262[/C][/ROW]
[ROW][C]58[/C][C]21035[/C][C]16272.2612707639[/C][C]4762.73872923606[/C][/ROW]
[ROW][C]59[/C][C]17988[/C][C]19300.1394843133[/C][C]-1312.13948431333[/C][/ROW]
[ROW][C]60[/C][C]10437[/C][C]17986.193662009[/C][C]-7549.193662009[/C][/ROW]
[ROW][C]61[/C][C]24470[/C][C]12066.8719698028[/C][C]12403.1280301972[/C][/ROW]
[ROW][C]62[/C][C]22237[/C][C]20600.5012431751[/C][C]1636.49875682485[/C][/ROW]
[ROW][C]63[/C][C]27053[/C][C]21533.3459073792[/C][C]5519.65409262076[/C][/ROW]
[ROW][C]64[/C][C]26419[/C][C]25352.9821986602[/C][C]1066.01780133977[/C][/ROW]
[ROW][C]65[/C][C]22311[/C][C]26037.801891891[/C][C]-3726.80189189103[/C][/ROW]
[ROW][C]66[/C][C]20624[/C][C]23233.0335162808[/C][C]-2609.03351628079[/C][/ROW]
[ROW][C]67[/C][C]17336[/C][C]21159.2976730792[/C][C]-3823.29767307918[/C][/ROW]
[ROW][C]68[/C][C]15586[/C][C]18132.9338973198[/C][C]-2546.93389731978[/C][/ROW]
[ROW][C]69[/C][C]17733[/C][C]15951.6164567371[/C][C]1781.38354326285[/C][/ROW]
[ROW][C]70[/C][C]19231[/C][C]16883.975928122[/C][C]2347.02407187798[/C][/ROW]
[ROW][C]71[/C][C]16102[/C][C]18273.5722439549[/C][C]-2171.57224395494[/C][/ROW]
[ROW][C]72[/C][C]11770[/C][C]16405.1857139538[/C][C]-4635.18571395379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261518&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261518&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
330019286561363
43193428200.59891850533733.40108149469
52582629516.0528020846-3690.05280208461
62683525476.15845864551358.84154135454
72020525051.1863435422-4846.18634354223
81778920107.9096563794-2318.90965637942
92052016902.72534302233617.27465697765
102251817995.82589416434522.17410583566
111557219838.6736369164-4266.67363691644
121150915343.5956905195-3834.59569051948
132544711063.825763895114383.1742361049
142409020053.34625321624036.6537467838
152778621797.31794264145988.68205735862
162619525068.96520107421126.03479892576
172051624917.0002094691-4401.0002094691
182275920738.41598488112020.58401511888
191902821164.5348889682-2136.53488896816
201697118590.000735508-1619.00073550802
212003616344.15543348723691.84456651281
222248517954.64458563024530.35541436984
231873020267.967928371-1537.96792837102
241453818238.742474941-3700.74247494101
252756114586.76632205912974.233677941
262598523075.81067903862909.18932096142
273467024492.195197546610177.8048024534
283206631308.5019446536757.498055346401
292718631458.4173107823-4272.41731078234
302958627937.51859907771648.48140092229
312135928657.1905169431-7298.19051694313
322155322854.7819788599-1301.78197885993
331957321276.2917929917-1703.29179299169
342425619372.3522980434883.64770195696
352238022258.6044853136121.395514686439
361616721768.5665054017-5601.56650540171
372729717084.304202321410212.6957976786
382828723864.580933814422.41906619
393347426641.49356103976832.50643896027
402822931291.1970803031-3062.1970803031
412878528846.959213155-61.9592131549507
422559728530.1432792733-2933.14327927331
431813026106.1792425128-7976.17924251282
442019819913.9214809676284.078519032417
452284919589.70729909333259.29270090667
462311821454.22261940291663.7773805971
472192522226.2054097348-301.205409734797
482080121596.7131780846-795.713178084603
491878520597.3878020268-1812.38780202679
502065918833.50983295451825.49016704549
512936719694.43944780569672.56055219443
522399226353.7214813102-2361.72148131016
532064524417.5435954204-3772.54359542043
542235621390.4731822659965.526817734146
551790221748.4087647935-3846.40876479351
561587918600.3448103849-2721.34481038494
571696316185.8165394437777.183460556262
582103516272.26127076394762.73872923606
591798819300.1394843133-1312.13948431333
601043717986.193662009-7549.193662009
612447012066.871969802812403.1280301972
622223720600.50124317511636.49875682485
632705321533.34590737925519.65409262076
642641925352.98219866021066.01780133977
652231126037.801891891-3726.80189189103
662062423233.0335162808-2609.03351628079
671733621159.2976730792-3823.29767307918
681558618132.9338973198-2546.93389731978
691773315951.61645673711781.38354326285
701923116883.9759281222347.02407187798
711610218273.5722439549-2171.57224395494
721177016405.1857139538-4635.18571395379







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7312678.33558518533202.2110553350922154.4601150355
7412240.5021694049489.15882743411923991.8455113756
7511802.6687536244-1966.0466094959425571.3841167448
7611364.835337844-4266.8334398022826996.5041154903
7710927.0019220636-6465.8265957680228319.8304398952
7810489.1685062831-8593.9010429314729572.2380554977
7910051.3350905027-10670.875769393830773.5459503992
809613.50167472228-12710.290516476331937.2938659209
819175.66825894185-14721.828335495733073.1648533794
828737.83484316142-16712.660936245134188.3306225679
838300.001427381-18688.248776081535288.2516308435
847862.16801160057-20652.843119416836377.1791426179

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 12678.3355851853 & 3202.21105533509 & 22154.4601150355 \tabularnewline
74 & 12240.5021694049 & 489.158827434119 & 23991.8455113756 \tabularnewline
75 & 11802.6687536244 & -1966.04660949594 & 25571.3841167448 \tabularnewline
76 & 11364.835337844 & -4266.83343980228 & 26996.5041154903 \tabularnewline
77 & 10927.0019220636 & -6465.82659576802 & 28319.8304398952 \tabularnewline
78 & 10489.1685062831 & -8593.90104293147 & 29572.2380554977 \tabularnewline
79 & 10051.3350905027 & -10670.8757693938 & 30773.5459503992 \tabularnewline
80 & 9613.50167472228 & -12710.2905164763 & 31937.2938659209 \tabularnewline
81 & 9175.66825894185 & -14721.8283354957 & 33073.1648533794 \tabularnewline
82 & 8737.83484316142 & -16712.6609362451 & 34188.3306225679 \tabularnewline
83 & 8300.001427381 & -18688.2487760815 & 35288.2516308435 \tabularnewline
84 & 7862.16801160057 & -20652.8431194168 & 36377.1791426179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261518&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]12678.3355851853[/C][C]3202.21105533509[/C][C]22154.4601150355[/C][/ROW]
[ROW][C]74[/C][C]12240.5021694049[/C][C]489.158827434119[/C][C]23991.8455113756[/C][/ROW]
[ROW][C]75[/C][C]11802.6687536244[/C][C]-1966.04660949594[/C][C]25571.3841167448[/C][/ROW]
[ROW][C]76[/C][C]11364.835337844[/C][C]-4266.83343980228[/C][C]26996.5041154903[/C][/ROW]
[ROW][C]77[/C][C]10927.0019220636[/C][C]-6465.82659576802[/C][C]28319.8304398952[/C][/ROW]
[ROW][C]78[/C][C]10489.1685062831[/C][C]-8593.90104293147[/C][C]29572.2380554977[/C][/ROW]
[ROW][C]79[/C][C]10051.3350905027[/C][C]-10670.8757693938[/C][C]30773.5459503992[/C][/ROW]
[ROW][C]80[/C][C]9613.50167472228[/C][C]-12710.2905164763[/C][C]31937.2938659209[/C][/ROW]
[ROW][C]81[/C][C]9175.66825894185[/C][C]-14721.8283354957[/C][C]33073.1648533794[/C][/ROW]
[ROW][C]82[/C][C]8737.83484316142[/C][C]-16712.6609362451[/C][C]34188.3306225679[/C][/ROW]
[ROW][C]83[/C][C]8300.001427381[/C][C]-18688.2487760815[/C][C]35288.2516308435[/C][/ROW]
[ROW][C]84[/C][C]7862.16801160057[/C][C]-20652.8431194168[/C][C]36377.1791426179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261518&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261518&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
7312678.33558518533202.2110553350922154.4601150355
7412240.5021694049489.15882743411923991.8455113756
7511802.6687536244-1966.0466094959425571.3841167448
7611364.835337844-4266.8334398022826996.5041154903
7710927.0019220636-6465.8265957680228319.8304398952
7810489.1685062831-8593.9010429314729572.2380554977
7910051.3350905027-10670.875769393830773.5459503992
809613.50167472228-12710.290516476331937.2938659209
819175.66825894185-14721.828335495733073.1648533794
828737.83484316142-16712.660936245134188.3306225679
838300.001427381-18688.248776081535288.2516308435
847862.16801160057-20652.843119416836377.1791426179



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')