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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 computationThu, 15 May 2014 07:19:57 -0400
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/May/15/t14001528463c2qpvw1dfj43n2.htm/, Retrieved Tue, 14 May 2024 14:47:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234872, Retrieved Tue, 14 May 2024 14:47:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-15 11:19:57] [941d89646656d1688f5e273fb31a8e6b] [Current]
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Dataseries X:
8584
5522
6423
5173
5583
5716
4752
4977
4999
5285
5747
1713
9923
6737
7433
6388
6855
7658
6585
6847
6353
7361
6929
1714
11798
8378
8131
7676
7505
8168
6455
6141
6554
6888
5339
1624
9187
5047
5289
4169
3862
4253
3768
3066
4108
3890
3420
1221
5984
4064
5151
4027
3530
4819
3855
3584
4322
4154
4656
1464
7780
5060
6084
4778
4989
4903
4142
4101
4595
5034
5407
1782
8395
5291
6116
4210
4621
5299
4293
4542
3831
4360
4088
1508




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234872&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234872&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234872&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.400482193774217
beta0.215384038260281
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.400482193774217 \tabularnewline
beta & 0.215384038260281 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234872&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]0.400482193774217[/C][/ROW]
[ROW][C]beta[/C][C]0.215384038260281[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234872&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234872&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
alpha0.400482193774217
beta0.215384038260281
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399238830.92864292381092.0713570762
1467376336.92994712866400.070052871342
1574337270.54525111328162.454748886717
1663886390.75560913612-2.75560913611935
1768556952.8108864297-97.8108864296992
1876587918.56763916338-260.567639163384
1965856189.33913763714395.660862362857
2068476736.706470196110.293529804005
2163536921.60464293301-568.604642933008
2273617143.040157565217.959842434998
2369297935.76071175983-1006.76071175983
2417142231.59411272658-517.594112726579
251179811380.6385358019417.361464198124
2683787641.8227210856736.177278914404
2781318635.71573045174-504.715730451742
2876767105.90134173302570.09865826698
2975057779.24848748288-274.248487482878
3081688555.07778873046-387.077788730456
3164556476.60420859593-21.6042085959289
3261416655.17077558706-514.170775587056
3365546338.31386203377215.686137966234
3468886667.48036833296220.519631667041
3553397220.27328990628-1881.27328990628
3616241838.30464373477-214.304643734765
3791879527.00063040882-340.000630408824
3850475958.60365104849-911.603651048493
3952895675.94663667278-386.946636672784
4041694305.48660325634-136.48660325634
4138624103.59439142285-241.594391422846
4242534015.18484897021237.815151029792
4337682849.21463649789918.785363502112
4430663063.841012872062.15898712794342
4541082789.771089075511318.22891092449
4638903321.62695957457568.373040425428
4734203705.38815029664-285.388150296643
4812211014.26143450395206.738565496054
4959846111.16578917183-127.165789171829
5040643952.72618643565111.273813564354
5151514262.77345610849888.226543891506
5240273900.73743024194126.262569758065
5335304184.61797456517-654.617974565171
5448194321.15000142546497.849998574537
5538553489.49762836788365.502371632123
5635843778.4589532095-194.458953209503
5743223682.25339418149639.746605818505
5841544181.308440793-27.308440793
5946564542.51970693237113.480293067631
6014641365.3631011838698.6368988161369
6177808138.00360400281-358.003604002814
6250605412.33549770014-352.335497700145
6360845788.58346039922295.41653960078
6447785066.72446793563-288.724467935626
6549895285.22047162634-296.220471626341
6649035790.0386867124-887.038686712396
6741424169.7341059564-27.7341059564023
6841014256.67152938967-155.671529389667
6945954115.26531436476479.734685635235
7050344493.72759856164540.272401438358
7154075095.12439939001311.875600609995
7217821547.55968942415234.440310575849
7383959528.24292624548-1133.24292624548
7452916119.53143583387-828.531435833868
7561166293.62995338613-177.629953386127
7642105253.30642729427-1043.30642729427
7746215012.47997551551-391.479975515514
7852995268.493168609530.5068313904976
7942933976.03607753574316.963922464264
8045424152.87183095541389.128169044587
8138314228.61720804212-397.617208042118
8243604167.83579648909192.164203510908
8340884482.40424290058-394.404242900583
8415081235.14257560968272.857424390315

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9923 & 8830.9286429238 & 1092.0713570762 \tabularnewline
14 & 6737 & 6336.92994712866 & 400.070052871342 \tabularnewline
15 & 7433 & 7270.54525111328 & 162.454748886717 \tabularnewline
16 & 6388 & 6390.75560913612 & -2.75560913611935 \tabularnewline
17 & 6855 & 6952.8108864297 & -97.8108864296992 \tabularnewline
18 & 7658 & 7918.56763916338 & -260.567639163384 \tabularnewline
19 & 6585 & 6189.33913763714 & 395.660862362857 \tabularnewline
20 & 6847 & 6736.706470196 & 110.293529804005 \tabularnewline
21 & 6353 & 6921.60464293301 & -568.604642933008 \tabularnewline
22 & 7361 & 7143.040157565 & 217.959842434998 \tabularnewline
23 & 6929 & 7935.76071175983 & -1006.76071175983 \tabularnewline
24 & 1714 & 2231.59411272658 & -517.594112726579 \tabularnewline
25 & 11798 & 11380.6385358019 & 417.361464198124 \tabularnewline
26 & 8378 & 7641.8227210856 & 736.177278914404 \tabularnewline
27 & 8131 & 8635.71573045174 & -504.715730451742 \tabularnewline
28 & 7676 & 7105.90134173302 & 570.09865826698 \tabularnewline
29 & 7505 & 7779.24848748288 & -274.248487482878 \tabularnewline
30 & 8168 & 8555.07778873046 & -387.077788730456 \tabularnewline
31 & 6455 & 6476.60420859593 & -21.6042085959289 \tabularnewline
32 & 6141 & 6655.17077558706 & -514.170775587056 \tabularnewline
33 & 6554 & 6338.31386203377 & 215.686137966234 \tabularnewline
34 & 6888 & 6667.48036833296 & 220.519631667041 \tabularnewline
35 & 5339 & 7220.27328990628 & -1881.27328990628 \tabularnewline
36 & 1624 & 1838.30464373477 & -214.304643734765 \tabularnewline
37 & 9187 & 9527.00063040882 & -340.000630408824 \tabularnewline
38 & 5047 & 5958.60365104849 & -911.603651048493 \tabularnewline
39 & 5289 & 5675.94663667278 & -386.946636672784 \tabularnewline
40 & 4169 & 4305.48660325634 & -136.48660325634 \tabularnewline
41 & 3862 & 4103.59439142285 & -241.594391422846 \tabularnewline
42 & 4253 & 4015.18484897021 & 237.815151029792 \tabularnewline
43 & 3768 & 2849.21463649789 & 918.785363502112 \tabularnewline
44 & 3066 & 3063.84101287206 & 2.15898712794342 \tabularnewline
45 & 4108 & 2789.77108907551 & 1318.22891092449 \tabularnewline
46 & 3890 & 3321.62695957457 & 568.373040425428 \tabularnewline
47 & 3420 & 3705.38815029664 & -285.388150296643 \tabularnewline
48 & 1221 & 1014.26143450395 & 206.738565496054 \tabularnewline
49 & 5984 & 6111.16578917183 & -127.165789171829 \tabularnewline
50 & 4064 & 3952.72618643565 & 111.273813564354 \tabularnewline
51 & 5151 & 4262.77345610849 & 888.226543891506 \tabularnewline
52 & 4027 & 3900.73743024194 & 126.262569758065 \tabularnewline
53 & 3530 & 4184.61797456517 & -654.617974565171 \tabularnewline
54 & 4819 & 4321.15000142546 & 497.849998574537 \tabularnewline
55 & 3855 & 3489.49762836788 & 365.502371632123 \tabularnewline
56 & 3584 & 3778.4589532095 & -194.458953209503 \tabularnewline
57 & 4322 & 3682.25339418149 & 639.746605818505 \tabularnewline
58 & 4154 & 4181.308440793 & -27.308440793 \tabularnewline
59 & 4656 & 4542.51970693237 & 113.480293067631 \tabularnewline
60 & 1464 & 1365.36310118386 & 98.6368988161369 \tabularnewline
61 & 7780 & 8138.00360400281 & -358.003604002814 \tabularnewline
62 & 5060 & 5412.33549770014 & -352.335497700145 \tabularnewline
63 & 6084 & 5788.58346039922 & 295.41653960078 \tabularnewline
64 & 4778 & 5066.72446793563 & -288.724467935626 \tabularnewline
65 & 4989 & 5285.22047162634 & -296.220471626341 \tabularnewline
66 & 4903 & 5790.0386867124 & -887.038686712396 \tabularnewline
67 & 4142 & 4169.7341059564 & -27.7341059564023 \tabularnewline
68 & 4101 & 4256.67152938967 & -155.671529389667 \tabularnewline
69 & 4595 & 4115.26531436476 & 479.734685635235 \tabularnewline
70 & 5034 & 4493.72759856164 & 540.272401438358 \tabularnewline
71 & 5407 & 5095.12439939001 & 311.875600609995 \tabularnewline
72 & 1782 & 1547.55968942415 & 234.440310575849 \tabularnewline
73 & 8395 & 9528.24292624548 & -1133.24292624548 \tabularnewline
74 & 5291 & 6119.53143583387 & -828.531435833868 \tabularnewline
75 & 6116 & 6293.62995338613 & -177.629953386127 \tabularnewline
76 & 4210 & 5253.30642729427 & -1043.30642729427 \tabularnewline
77 & 4621 & 5012.47997551551 & -391.479975515514 \tabularnewline
78 & 5299 & 5268.4931686095 & 30.5068313904976 \tabularnewline
79 & 4293 & 3976.03607753574 & 316.963922464264 \tabularnewline
80 & 4542 & 4152.87183095541 & 389.128169044587 \tabularnewline
81 & 3831 & 4228.61720804212 & -397.617208042118 \tabularnewline
82 & 4360 & 4167.83579648909 & 192.164203510908 \tabularnewline
83 & 4088 & 4482.40424290058 & -394.404242900583 \tabularnewline
84 & 1508 & 1235.14257560968 & 272.857424390315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234872&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]9923[/C][C]8830.9286429238[/C][C]1092.0713570762[/C][/ROW]
[ROW][C]14[/C][C]6737[/C][C]6336.92994712866[/C][C]400.070052871342[/C][/ROW]
[ROW][C]15[/C][C]7433[/C][C]7270.54525111328[/C][C]162.454748886717[/C][/ROW]
[ROW][C]16[/C][C]6388[/C][C]6390.75560913612[/C][C]-2.75560913611935[/C][/ROW]
[ROW][C]17[/C][C]6855[/C][C]6952.8108864297[/C][C]-97.8108864296992[/C][/ROW]
[ROW][C]18[/C][C]7658[/C][C]7918.56763916338[/C][C]-260.567639163384[/C][/ROW]
[ROW][C]19[/C][C]6585[/C][C]6189.33913763714[/C][C]395.660862362857[/C][/ROW]
[ROW][C]20[/C][C]6847[/C][C]6736.706470196[/C][C]110.293529804005[/C][/ROW]
[ROW][C]21[/C][C]6353[/C][C]6921.60464293301[/C][C]-568.604642933008[/C][/ROW]
[ROW][C]22[/C][C]7361[/C][C]7143.040157565[/C][C]217.959842434998[/C][/ROW]
[ROW][C]23[/C][C]6929[/C][C]7935.76071175983[/C][C]-1006.76071175983[/C][/ROW]
[ROW][C]24[/C][C]1714[/C][C]2231.59411272658[/C][C]-517.594112726579[/C][/ROW]
[ROW][C]25[/C][C]11798[/C][C]11380.6385358019[/C][C]417.361464198124[/C][/ROW]
[ROW][C]26[/C][C]8378[/C][C]7641.8227210856[/C][C]736.177278914404[/C][/ROW]
[ROW][C]27[/C][C]8131[/C][C]8635.71573045174[/C][C]-504.715730451742[/C][/ROW]
[ROW][C]28[/C][C]7676[/C][C]7105.90134173302[/C][C]570.09865826698[/C][/ROW]
[ROW][C]29[/C][C]7505[/C][C]7779.24848748288[/C][C]-274.248487482878[/C][/ROW]
[ROW][C]30[/C][C]8168[/C][C]8555.07778873046[/C][C]-387.077788730456[/C][/ROW]
[ROW][C]31[/C][C]6455[/C][C]6476.60420859593[/C][C]-21.6042085959289[/C][/ROW]
[ROW][C]32[/C][C]6141[/C][C]6655.17077558706[/C][C]-514.170775587056[/C][/ROW]
[ROW][C]33[/C][C]6554[/C][C]6338.31386203377[/C][C]215.686137966234[/C][/ROW]
[ROW][C]34[/C][C]6888[/C][C]6667.48036833296[/C][C]220.519631667041[/C][/ROW]
[ROW][C]35[/C][C]5339[/C][C]7220.27328990628[/C][C]-1881.27328990628[/C][/ROW]
[ROW][C]36[/C][C]1624[/C][C]1838.30464373477[/C][C]-214.304643734765[/C][/ROW]
[ROW][C]37[/C][C]9187[/C][C]9527.00063040882[/C][C]-340.000630408824[/C][/ROW]
[ROW][C]38[/C][C]5047[/C][C]5958.60365104849[/C][C]-911.603651048493[/C][/ROW]
[ROW][C]39[/C][C]5289[/C][C]5675.94663667278[/C][C]-386.946636672784[/C][/ROW]
[ROW][C]40[/C][C]4169[/C][C]4305.48660325634[/C][C]-136.48660325634[/C][/ROW]
[ROW][C]41[/C][C]3862[/C][C]4103.59439142285[/C][C]-241.594391422846[/C][/ROW]
[ROW][C]42[/C][C]4253[/C][C]4015.18484897021[/C][C]237.815151029792[/C][/ROW]
[ROW][C]43[/C][C]3768[/C][C]2849.21463649789[/C][C]918.785363502112[/C][/ROW]
[ROW][C]44[/C][C]3066[/C][C]3063.84101287206[/C][C]2.15898712794342[/C][/ROW]
[ROW][C]45[/C][C]4108[/C][C]2789.77108907551[/C][C]1318.22891092449[/C][/ROW]
[ROW][C]46[/C][C]3890[/C][C]3321.62695957457[/C][C]568.373040425428[/C][/ROW]
[ROW][C]47[/C][C]3420[/C][C]3705.38815029664[/C][C]-285.388150296643[/C][/ROW]
[ROW][C]48[/C][C]1221[/C][C]1014.26143450395[/C][C]206.738565496054[/C][/ROW]
[ROW][C]49[/C][C]5984[/C][C]6111.16578917183[/C][C]-127.165789171829[/C][/ROW]
[ROW][C]50[/C][C]4064[/C][C]3952.72618643565[/C][C]111.273813564354[/C][/ROW]
[ROW][C]51[/C][C]5151[/C][C]4262.77345610849[/C][C]888.226543891506[/C][/ROW]
[ROW][C]52[/C][C]4027[/C][C]3900.73743024194[/C][C]126.262569758065[/C][/ROW]
[ROW][C]53[/C][C]3530[/C][C]4184.61797456517[/C][C]-654.617974565171[/C][/ROW]
[ROW][C]54[/C][C]4819[/C][C]4321.15000142546[/C][C]497.849998574537[/C][/ROW]
[ROW][C]55[/C][C]3855[/C][C]3489.49762836788[/C][C]365.502371632123[/C][/ROW]
[ROW][C]56[/C][C]3584[/C][C]3778.4589532095[/C][C]-194.458953209503[/C][/ROW]
[ROW][C]57[/C][C]4322[/C][C]3682.25339418149[/C][C]639.746605818505[/C][/ROW]
[ROW][C]58[/C][C]4154[/C][C]4181.308440793[/C][C]-27.308440793[/C][/ROW]
[ROW][C]59[/C][C]4656[/C][C]4542.51970693237[/C][C]113.480293067631[/C][/ROW]
[ROW][C]60[/C][C]1464[/C][C]1365.36310118386[/C][C]98.6368988161369[/C][/ROW]
[ROW][C]61[/C][C]7780[/C][C]8138.00360400281[/C][C]-358.003604002814[/C][/ROW]
[ROW][C]62[/C][C]5060[/C][C]5412.33549770014[/C][C]-352.335497700145[/C][/ROW]
[ROW][C]63[/C][C]6084[/C][C]5788.58346039922[/C][C]295.41653960078[/C][/ROW]
[ROW][C]64[/C][C]4778[/C][C]5066.72446793563[/C][C]-288.724467935626[/C][/ROW]
[ROW][C]65[/C][C]4989[/C][C]5285.22047162634[/C][C]-296.220471626341[/C][/ROW]
[ROW][C]66[/C][C]4903[/C][C]5790.0386867124[/C][C]-887.038686712396[/C][/ROW]
[ROW][C]67[/C][C]4142[/C][C]4169.7341059564[/C][C]-27.7341059564023[/C][/ROW]
[ROW][C]68[/C][C]4101[/C][C]4256.67152938967[/C][C]-155.671529389667[/C][/ROW]
[ROW][C]69[/C][C]4595[/C][C]4115.26531436476[/C][C]479.734685635235[/C][/ROW]
[ROW][C]70[/C][C]5034[/C][C]4493.72759856164[/C][C]540.272401438358[/C][/ROW]
[ROW][C]71[/C][C]5407[/C][C]5095.12439939001[/C][C]311.875600609995[/C][/ROW]
[ROW][C]72[/C][C]1782[/C][C]1547.55968942415[/C][C]234.440310575849[/C][/ROW]
[ROW][C]73[/C][C]8395[/C][C]9528.24292624548[/C][C]-1133.24292624548[/C][/ROW]
[ROW][C]74[/C][C]5291[/C][C]6119.53143583387[/C][C]-828.531435833868[/C][/ROW]
[ROW][C]75[/C][C]6116[/C][C]6293.62995338613[/C][C]-177.629953386127[/C][/ROW]
[ROW][C]76[/C][C]4210[/C][C]5253.30642729427[/C][C]-1043.30642729427[/C][/ROW]
[ROW][C]77[/C][C]4621[/C][C]5012.47997551551[/C][C]-391.479975515514[/C][/ROW]
[ROW][C]78[/C][C]5299[/C][C]5268.4931686095[/C][C]30.5068313904976[/C][/ROW]
[ROW][C]79[/C][C]4293[/C][C]3976.03607753574[/C][C]316.963922464264[/C][/ROW]
[ROW][C]80[/C][C]4542[/C][C]4152.87183095541[/C][C]389.128169044587[/C][/ROW]
[ROW][C]81[/C][C]3831[/C][C]4228.61720804212[/C][C]-397.617208042118[/C][/ROW]
[ROW][C]82[/C][C]4360[/C][C]4167.83579648909[/C][C]192.164203510908[/C][/ROW]
[ROW][C]83[/C][C]4088[/C][C]4482.40424290058[/C][C]-394.404242900583[/C][/ROW]
[ROW][C]84[/C][C]1508[/C][C]1235.14257560968[/C][C]272.857424390315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234872&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234872&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
1399238830.92864292381092.0713570762
1467376336.92994712866400.070052871342
1574337270.54525111328162.454748886717
1663886390.75560913612-2.75560913611935
1768556952.8108864297-97.8108864296992
1876587918.56763916338-260.567639163384
1965856189.33913763714395.660862362857
2068476736.706470196110.293529804005
2163536921.60464293301-568.604642933008
2273617143.040157565217.959842434998
2369297935.76071175983-1006.76071175983
2417142231.59411272658-517.594112726579
251179811380.6385358019417.361464198124
2683787641.8227210856736.177278914404
2781318635.71573045174-504.715730451742
2876767105.90134173302570.09865826698
2975057779.24848748288-274.248487482878
3081688555.07778873046-387.077788730456
3164556476.60420859593-21.6042085959289
3261416655.17077558706-514.170775587056
3365546338.31386203377215.686137966234
3468886667.48036833296220.519631667041
3553397220.27328990628-1881.27328990628
3616241838.30464373477-214.304643734765
3791879527.00063040882-340.000630408824
3850475958.60365104849-911.603651048493
3952895675.94663667278-386.946636672784
4041694305.48660325634-136.48660325634
4138624103.59439142285-241.594391422846
4242534015.18484897021237.815151029792
4337682849.21463649789918.785363502112
4430663063.841012872062.15898712794342
4541082789.771089075511318.22891092449
4638903321.62695957457568.373040425428
4734203705.38815029664-285.388150296643
4812211014.26143450395206.738565496054
4959846111.16578917183-127.165789171829
5040643952.72618643565111.273813564354
5151514262.77345610849888.226543891506
5240273900.73743024194126.262569758065
5335304184.61797456517-654.617974565171
5448194321.15000142546497.849998574537
5538553489.49762836788365.502371632123
5635843778.4589532095-194.458953209503
5743223682.25339418149639.746605818505
5841544181.308440793-27.308440793
5946564542.51970693237113.480293067631
6014641365.3631011838698.6368988161369
6177808138.00360400281-358.003604002814
6250605412.33549770014-352.335497700145
6360845788.58346039922295.41653960078
6447785066.72446793563-288.724467935626
6549895285.22047162634-296.220471626341
6649035790.0386867124-887.038686712396
6741424169.7341059564-27.7341059564023
6841014256.67152938967-155.671529389667
6945954115.26531436476479.734685635235
7050344493.72759856164540.272401438358
7154075095.12439939001311.875600609995
7217821547.55968942415234.440310575849
7383959528.24292624548-1133.24292624548
7452916119.53143583387-828.531435833868
7561166293.62995338613-177.629953386127
7642105253.30642729427-1043.30642729427
7746215012.47997551551-391.479975515514
7852995268.493168609530.5068313904976
7942933976.03607753574316.963922464264
8045424152.87183095541389.128169044587
8138314228.61720804212-397.617208042118
8243604167.83579648909192.164203510908
8340884482.40424290058-394.404242900583
8415081235.14257560968272.857424390315







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
857580.054380218377153.762019761068006.34674067567
865014.680668454064467.465816406755561.89552050136
875411.309278648564583.498803671826239.11975362531
884544.494368709313619.169875167555469.81886225108
894772.903399956353560.706666721745985.10013319096
905287.691123795343680.97343998696894.40880760378
914064.808668321322593.695535661045535.9218009816
924171.253567050512410.40815086895932.09898323212
934116.556474233362118.339834970796114.77311349592
944277.257152438161921.52346345556632.99084142082
954563.833965752991744.604286139767383.06364536623
961328.42692906605423.8220096060652233.03184852604

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 7580.05438021837 & 7153.76201976106 & 8006.34674067567 \tabularnewline
86 & 5014.68066845406 & 4467.46581640675 & 5561.89552050136 \tabularnewline
87 & 5411.30927864856 & 4583.49880367182 & 6239.11975362531 \tabularnewline
88 & 4544.49436870931 & 3619.16987516755 & 5469.81886225108 \tabularnewline
89 & 4772.90339995635 & 3560.70666672174 & 5985.10013319096 \tabularnewline
90 & 5287.69112379534 & 3680.9734399869 & 6894.40880760378 \tabularnewline
91 & 4064.80866832132 & 2593.69553566104 & 5535.9218009816 \tabularnewline
92 & 4171.25356705051 & 2410.4081508689 & 5932.09898323212 \tabularnewline
93 & 4116.55647423336 & 2118.33983497079 & 6114.77311349592 \tabularnewline
94 & 4277.25715243816 & 1921.5234634555 & 6632.99084142082 \tabularnewline
95 & 4563.83396575299 & 1744.60428613976 & 7383.06364536623 \tabularnewline
96 & 1328.42692906605 & 423.822009606065 & 2233.03184852604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234872&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]7580.05438021837[/C][C]7153.76201976106[/C][C]8006.34674067567[/C][/ROW]
[ROW][C]86[/C][C]5014.68066845406[/C][C]4467.46581640675[/C][C]5561.89552050136[/C][/ROW]
[ROW][C]87[/C][C]5411.30927864856[/C][C]4583.49880367182[/C][C]6239.11975362531[/C][/ROW]
[ROW][C]88[/C][C]4544.49436870931[/C][C]3619.16987516755[/C][C]5469.81886225108[/C][/ROW]
[ROW][C]89[/C][C]4772.90339995635[/C][C]3560.70666672174[/C][C]5985.10013319096[/C][/ROW]
[ROW][C]90[/C][C]5287.69112379534[/C][C]3680.9734399869[/C][C]6894.40880760378[/C][/ROW]
[ROW][C]91[/C][C]4064.80866832132[/C][C]2593.69553566104[/C][C]5535.9218009816[/C][/ROW]
[ROW][C]92[/C][C]4171.25356705051[/C][C]2410.4081508689[/C][C]5932.09898323212[/C][/ROW]
[ROW][C]93[/C][C]4116.55647423336[/C][C]2118.33983497079[/C][C]6114.77311349592[/C][/ROW]
[ROW][C]94[/C][C]4277.25715243816[/C][C]1921.5234634555[/C][C]6632.99084142082[/C][/ROW]
[ROW][C]95[/C][C]4563.83396575299[/C][C]1744.60428613976[/C][C]7383.06364536623[/C][/ROW]
[ROW][C]96[/C][C]1328.42692906605[/C][C]423.822009606065[/C][C]2233.03184852604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234872&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234872&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
857580.054380218377153.762019761068006.34674067567
865014.680668454064467.465816406755561.89552050136
875411.309278648564583.498803671826239.11975362531
884544.494368709313619.169875167555469.81886225108
894772.903399956353560.706666721745985.10013319096
905287.691123795343680.97343998696894.40880760378
914064.808668321322593.695535661045535.9218009816
924171.253567050512410.40815086895932.09898323212
934116.556474233362118.339834970796114.77311349592
944277.257152438161921.52346345556632.99084142082
954563.833965752991744.604286139767383.06364536623
961328.42692906605423.8220096060652233.03184852604



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')