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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 computationFri, 10 May 2013 10:11:26 -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/2013/May/10/t1368195115tu6mx2v2xh9s8r8.htm/, Retrieved Fri, 01 Nov 2024 00:29:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208877, Retrieved Fri, 01 Nov 2024 00:29:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple exponentia...] [2013-05-10 14:11:26] [3d5865aeea343c832d5219814a9dc8a5] [Current]
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Dataseries X:
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
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




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=208877&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=208877&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208877&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
alpha0.331260492389542
beta0
gamma0.916831042153381

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.331260492389542 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.916831042153381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208877&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]0.331260492389542[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.916831042153381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208877&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208877&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
alpha0.331260492389542
beta0
gamma0.916831042153381







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133112431525.9345619658-401.934561965812
142655126720.243338077-169.243338076958
153065130666.3835235883-15.3835235882507
162585925670.616387006188.383612993966
172510024766.4742524209333.525747579144
182577825364.4953061382413.504693861836
192041818403.26022498192014.73977501813
201868818450.7843985742237.215601425843
212042419741.4433725213682.55662747872
222477623023.91790070661752.08209929339
231981420165.2256299751-351.225629975092
241273812066.4156051994671.584394800631
253156633669.6125561379-2103.61255613787
263011128442.89055039811668.10944960189
273001933092.0078298613-3073.00782986126
283193427208.30449905384725.6955009462
292582627896.1842455707-2070.18424557074
302683527746.9879260917-911.987926091737
312020521328.4205848637-1123.42058486369
321778919246.5585653018-1457.55856530185
332052020248.8538117347271.146188265338
342251824050.7929914602-1532.79299146021
351557218814.3689486362-3242.3689486362
361150910384.94381263061124.05618736942
372544730436.4948749396-4989.49487493964
382409026566.3165660545-2476.31656605451
392778626935.6700131031850.329986896864
402619527133.1633735871-938.163373587107
412051621778.1329051095-1262.1329051095
422275922606.7267179333152.273282066661
431902816411.07323583662616.92676416336
441697115363.37346144091607.62653855909
452003618440.94886334131595.05113665875
462248521575.4122023408909.587797659169
471873016099.87526307012630.1247369299
481453812292.92283266562245.07716733445
492756128967.4764618909-1406.4764618909
502598527825.093345745-1840.09334574504
513467030444.83973591984225.16026408016
523206630663.71794824381402.28205175617
532718625885.35201538391300.64798461608
542958628430.09622109311155.90377890689
552135924078.037023445-2719.03702344495
562155320643.9199527798909.080047220188
571957323482.384255257-3909.38425525702
582425624373.1735523799-117.173552379903
592238019612.40871181592767.59128818409
601616715614.9127141611552.087285838943
612729729489.8009588359-2192.80095883592
622828727821.0799246359465.920075364094
633347434923.452661919-1449.45266191904
642822931531.7894955057-3302.78949550571
652878525132.50525009543652.49474990463
662559728367.5776409306-2770.57764093062
671813020339.0221538131-2209.02215381312
682019819298.3281332891899.671866710902
692284919179.373552563669.62644743998
702311824905.8742149828-1787.87421498276
712192521360.3825570784564.617442921633
722080115274.75601981145526.24398018864
731878529114.436851378-10329.436851378
742065926380.4878756309-5721.48787563092
752936730258.8612928352-891.861292835154
762399225915.5861262556-1923.58612625556
772064524237.6092714736-3592.60927147361
782235621134.54347218291221.45652781714
791790214772.69272970223129.3072702978
801587917406.382363563-1527.382363563
811696318181.7583128879-1218.75831288795
822103518942.82120660242092.17879339756
831798818125.000185161-137.00018516104
841043714849.0335641996-4412.03356419959

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31124 & 31525.9345619658 & -401.934561965812 \tabularnewline
14 & 26551 & 26720.243338077 & -169.243338076958 \tabularnewline
15 & 30651 & 30666.3835235883 & -15.3835235882507 \tabularnewline
16 & 25859 & 25670.616387006 & 188.383612993966 \tabularnewline
17 & 25100 & 24766.4742524209 & 333.525747579144 \tabularnewline
18 & 25778 & 25364.4953061382 & 413.504693861836 \tabularnewline
19 & 20418 & 18403.2602249819 & 2014.73977501813 \tabularnewline
20 & 18688 & 18450.7843985742 & 237.215601425843 \tabularnewline
21 & 20424 & 19741.4433725213 & 682.55662747872 \tabularnewline
22 & 24776 & 23023.9179007066 & 1752.08209929339 \tabularnewline
23 & 19814 & 20165.2256299751 & -351.225629975092 \tabularnewline
24 & 12738 & 12066.4156051994 & 671.584394800631 \tabularnewline
25 & 31566 & 33669.6125561379 & -2103.61255613787 \tabularnewline
26 & 30111 & 28442.8905503981 & 1668.10944960189 \tabularnewline
27 & 30019 & 33092.0078298613 & -3073.00782986126 \tabularnewline
28 & 31934 & 27208.3044990538 & 4725.6955009462 \tabularnewline
29 & 25826 & 27896.1842455707 & -2070.18424557074 \tabularnewline
30 & 26835 & 27746.9879260917 & -911.987926091737 \tabularnewline
31 & 20205 & 21328.4205848637 & -1123.42058486369 \tabularnewline
32 & 17789 & 19246.5585653018 & -1457.55856530185 \tabularnewline
33 & 20520 & 20248.8538117347 & 271.146188265338 \tabularnewline
34 & 22518 & 24050.7929914602 & -1532.79299146021 \tabularnewline
35 & 15572 & 18814.3689486362 & -3242.3689486362 \tabularnewline
36 & 11509 & 10384.9438126306 & 1124.05618736942 \tabularnewline
37 & 25447 & 30436.4948749396 & -4989.49487493964 \tabularnewline
38 & 24090 & 26566.3165660545 & -2476.31656605451 \tabularnewline
39 & 27786 & 26935.6700131031 & 850.329986896864 \tabularnewline
40 & 26195 & 27133.1633735871 & -938.163373587107 \tabularnewline
41 & 20516 & 21778.1329051095 & -1262.1329051095 \tabularnewline
42 & 22759 & 22606.7267179333 & 152.273282066661 \tabularnewline
43 & 19028 & 16411.0732358366 & 2616.92676416336 \tabularnewline
44 & 16971 & 15363.3734614409 & 1607.62653855909 \tabularnewline
45 & 20036 & 18440.9488633413 & 1595.05113665875 \tabularnewline
46 & 22485 & 21575.4122023408 & 909.587797659169 \tabularnewline
47 & 18730 & 16099.8752630701 & 2630.1247369299 \tabularnewline
48 & 14538 & 12292.9228326656 & 2245.07716733445 \tabularnewline
49 & 27561 & 28967.4764618909 & -1406.4764618909 \tabularnewline
50 & 25985 & 27825.093345745 & -1840.09334574504 \tabularnewline
51 & 34670 & 30444.8397359198 & 4225.16026408016 \tabularnewline
52 & 32066 & 30663.7179482438 & 1402.28205175617 \tabularnewline
53 & 27186 & 25885.3520153839 & 1300.64798461608 \tabularnewline
54 & 29586 & 28430.0962210931 & 1155.90377890689 \tabularnewline
55 & 21359 & 24078.037023445 & -2719.03702344495 \tabularnewline
56 & 21553 & 20643.9199527798 & 909.080047220188 \tabularnewline
57 & 19573 & 23482.384255257 & -3909.38425525702 \tabularnewline
58 & 24256 & 24373.1735523799 & -117.173552379903 \tabularnewline
59 & 22380 & 19612.4087118159 & 2767.59128818409 \tabularnewline
60 & 16167 & 15614.9127141611 & 552.087285838943 \tabularnewline
61 & 27297 & 29489.8009588359 & -2192.80095883592 \tabularnewline
62 & 28287 & 27821.0799246359 & 465.920075364094 \tabularnewline
63 & 33474 & 34923.452661919 & -1449.45266191904 \tabularnewline
64 & 28229 & 31531.7894955057 & -3302.78949550571 \tabularnewline
65 & 28785 & 25132.5052500954 & 3652.49474990463 \tabularnewline
66 & 25597 & 28367.5776409306 & -2770.57764093062 \tabularnewline
67 & 18130 & 20339.0221538131 & -2209.02215381312 \tabularnewline
68 & 20198 & 19298.3281332891 & 899.671866710902 \tabularnewline
69 & 22849 & 19179.37355256 & 3669.62644743998 \tabularnewline
70 & 23118 & 24905.8742149828 & -1787.87421498276 \tabularnewline
71 & 21925 & 21360.3825570784 & 564.617442921633 \tabularnewline
72 & 20801 & 15274.7560198114 & 5526.24398018864 \tabularnewline
73 & 18785 & 29114.436851378 & -10329.436851378 \tabularnewline
74 & 20659 & 26380.4878756309 & -5721.48787563092 \tabularnewline
75 & 29367 & 30258.8612928352 & -891.861292835154 \tabularnewline
76 & 23992 & 25915.5861262556 & -1923.58612625556 \tabularnewline
77 & 20645 & 24237.6092714736 & -3592.60927147361 \tabularnewline
78 & 22356 & 21134.5434721829 & 1221.45652781714 \tabularnewline
79 & 17902 & 14772.6927297022 & 3129.3072702978 \tabularnewline
80 & 15879 & 17406.382363563 & -1527.382363563 \tabularnewline
81 & 16963 & 18181.7583128879 & -1218.75831288795 \tabularnewline
82 & 21035 & 18942.8212066024 & 2092.17879339756 \tabularnewline
83 & 17988 & 18125.000185161 & -137.00018516104 \tabularnewline
84 & 10437 & 14849.0335641996 & -4412.03356419959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208877&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]31124[/C][C]31525.9345619658[/C][C]-401.934561965812[/C][/ROW]
[ROW][C]14[/C][C]26551[/C][C]26720.243338077[/C][C]-169.243338076958[/C][/ROW]
[ROW][C]15[/C][C]30651[/C][C]30666.3835235883[/C][C]-15.3835235882507[/C][/ROW]
[ROW][C]16[/C][C]25859[/C][C]25670.616387006[/C][C]188.383612993966[/C][/ROW]
[ROW][C]17[/C][C]25100[/C][C]24766.4742524209[/C][C]333.525747579144[/C][/ROW]
[ROW][C]18[/C][C]25778[/C][C]25364.4953061382[/C][C]413.504693861836[/C][/ROW]
[ROW][C]19[/C][C]20418[/C][C]18403.2602249819[/C][C]2014.73977501813[/C][/ROW]
[ROW][C]20[/C][C]18688[/C][C]18450.7843985742[/C][C]237.215601425843[/C][/ROW]
[ROW][C]21[/C][C]20424[/C][C]19741.4433725213[/C][C]682.55662747872[/C][/ROW]
[ROW][C]22[/C][C]24776[/C][C]23023.9179007066[/C][C]1752.08209929339[/C][/ROW]
[ROW][C]23[/C][C]19814[/C][C]20165.2256299751[/C][C]-351.225629975092[/C][/ROW]
[ROW][C]24[/C][C]12738[/C][C]12066.4156051994[/C][C]671.584394800631[/C][/ROW]
[ROW][C]25[/C][C]31566[/C][C]33669.6125561379[/C][C]-2103.61255613787[/C][/ROW]
[ROW][C]26[/C][C]30111[/C][C]28442.8905503981[/C][C]1668.10944960189[/C][/ROW]
[ROW][C]27[/C][C]30019[/C][C]33092.0078298613[/C][C]-3073.00782986126[/C][/ROW]
[ROW][C]28[/C][C]31934[/C][C]27208.3044990538[/C][C]4725.6955009462[/C][/ROW]
[ROW][C]29[/C][C]25826[/C][C]27896.1842455707[/C][C]-2070.18424557074[/C][/ROW]
[ROW][C]30[/C][C]26835[/C][C]27746.9879260917[/C][C]-911.987926091737[/C][/ROW]
[ROW][C]31[/C][C]20205[/C][C]21328.4205848637[/C][C]-1123.42058486369[/C][/ROW]
[ROW][C]32[/C][C]17789[/C][C]19246.5585653018[/C][C]-1457.55856530185[/C][/ROW]
[ROW][C]33[/C][C]20520[/C][C]20248.8538117347[/C][C]271.146188265338[/C][/ROW]
[ROW][C]34[/C][C]22518[/C][C]24050.7929914602[/C][C]-1532.79299146021[/C][/ROW]
[ROW][C]35[/C][C]15572[/C][C]18814.3689486362[/C][C]-3242.3689486362[/C][/ROW]
[ROW][C]36[/C][C]11509[/C][C]10384.9438126306[/C][C]1124.05618736942[/C][/ROW]
[ROW][C]37[/C][C]25447[/C][C]30436.4948749396[/C][C]-4989.49487493964[/C][/ROW]
[ROW][C]38[/C][C]24090[/C][C]26566.3165660545[/C][C]-2476.31656605451[/C][/ROW]
[ROW][C]39[/C][C]27786[/C][C]26935.6700131031[/C][C]850.329986896864[/C][/ROW]
[ROW][C]40[/C][C]26195[/C][C]27133.1633735871[/C][C]-938.163373587107[/C][/ROW]
[ROW][C]41[/C][C]20516[/C][C]21778.1329051095[/C][C]-1262.1329051095[/C][/ROW]
[ROW][C]42[/C][C]22759[/C][C]22606.7267179333[/C][C]152.273282066661[/C][/ROW]
[ROW][C]43[/C][C]19028[/C][C]16411.0732358366[/C][C]2616.92676416336[/C][/ROW]
[ROW][C]44[/C][C]16971[/C][C]15363.3734614409[/C][C]1607.62653855909[/C][/ROW]
[ROW][C]45[/C][C]20036[/C][C]18440.9488633413[/C][C]1595.05113665875[/C][/ROW]
[ROW][C]46[/C][C]22485[/C][C]21575.4122023408[/C][C]909.587797659169[/C][/ROW]
[ROW][C]47[/C][C]18730[/C][C]16099.8752630701[/C][C]2630.1247369299[/C][/ROW]
[ROW][C]48[/C][C]14538[/C][C]12292.9228326656[/C][C]2245.07716733445[/C][/ROW]
[ROW][C]49[/C][C]27561[/C][C]28967.4764618909[/C][C]-1406.4764618909[/C][/ROW]
[ROW][C]50[/C][C]25985[/C][C]27825.093345745[/C][C]-1840.09334574504[/C][/ROW]
[ROW][C]51[/C][C]34670[/C][C]30444.8397359198[/C][C]4225.16026408016[/C][/ROW]
[ROW][C]52[/C][C]32066[/C][C]30663.7179482438[/C][C]1402.28205175617[/C][/ROW]
[ROW][C]53[/C][C]27186[/C][C]25885.3520153839[/C][C]1300.64798461608[/C][/ROW]
[ROW][C]54[/C][C]29586[/C][C]28430.0962210931[/C][C]1155.90377890689[/C][/ROW]
[ROW][C]55[/C][C]21359[/C][C]24078.037023445[/C][C]-2719.03702344495[/C][/ROW]
[ROW][C]56[/C][C]21553[/C][C]20643.9199527798[/C][C]909.080047220188[/C][/ROW]
[ROW][C]57[/C][C]19573[/C][C]23482.384255257[/C][C]-3909.38425525702[/C][/ROW]
[ROW][C]58[/C][C]24256[/C][C]24373.1735523799[/C][C]-117.173552379903[/C][/ROW]
[ROW][C]59[/C][C]22380[/C][C]19612.4087118159[/C][C]2767.59128818409[/C][/ROW]
[ROW][C]60[/C][C]16167[/C][C]15614.9127141611[/C][C]552.087285838943[/C][/ROW]
[ROW][C]61[/C][C]27297[/C][C]29489.8009588359[/C][C]-2192.80095883592[/C][/ROW]
[ROW][C]62[/C][C]28287[/C][C]27821.0799246359[/C][C]465.920075364094[/C][/ROW]
[ROW][C]63[/C][C]33474[/C][C]34923.452661919[/C][C]-1449.45266191904[/C][/ROW]
[ROW][C]64[/C][C]28229[/C][C]31531.7894955057[/C][C]-3302.78949550571[/C][/ROW]
[ROW][C]65[/C][C]28785[/C][C]25132.5052500954[/C][C]3652.49474990463[/C][/ROW]
[ROW][C]66[/C][C]25597[/C][C]28367.5776409306[/C][C]-2770.57764093062[/C][/ROW]
[ROW][C]67[/C][C]18130[/C][C]20339.0221538131[/C][C]-2209.02215381312[/C][/ROW]
[ROW][C]68[/C][C]20198[/C][C]19298.3281332891[/C][C]899.671866710902[/C][/ROW]
[ROW][C]69[/C][C]22849[/C][C]19179.37355256[/C][C]3669.62644743998[/C][/ROW]
[ROW][C]70[/C][C]23118[/C][C]24905.8742149828[/C][C]-1787.87421498276[/C][/ROW]
[ROW][C]71[/C][C]21925[/C][C]21360.3825570784[/C][C]564.617442921633[/C][/ROW]
[ROW][C]72[/C][C]20801[/C][C]15274.7560198114[/C][C]5526.24398018864[/C][/ROW]
[ROW][C]73[/C][C]18785[/C][C]29114.436851378[/C][C]-10329.436851378[/C][/ROW]
[ROW][C]74[/C][C]20659[/C][C]26380.4878756309[/C][C]-5721.48787563092[/C][/ROW]
[ROW][C]75[/C][C]29367[/C][C]30258.8612928352[/C][C]-891.861292835154[/C][/ROW]
[ROW][C]76[/C][C]23992[/C][C]25915.5861262556[/C][C]-1923.58612625556[/C][/ROW]
[ROW][C]77[/C][C]20645[/C][C]24237.6092714736[/C][C]-3592.60927147361[/C][/ROW]
[ROW][C]78[/C][C]22356[/C][C]21134.5434721829[/C][C]1221.45652781714[/C][/ROW]
[ROW][C]79[/C][C]17902[/C][C]14772.6927297022[/C][C]3129.3072702978[/C][/ROW]
[ROW][C]80[/C][C]15879[/C][C]17406.382363563[/C][C]-1527.382363563[/C][/ROW]
[ROW][C]81[/C][C]16963[/C][C]18181.7583128879[/C][C]-1218.75831288795[/C][/ROW]
[ROW][C]82[/C][C]21035[/C][C]18942.8212066024[/C][C]2092.17879339756[/C][/ROW]
[ROW][C]83[/C][C]17988[/C][C]18125.000185161[/C][C]-137.00018516104[/C][/ROW]
[ROW][C]84[/C][C]10437[/C][C]14849.0335641996[/C][C]-4412.03356419959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208877&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208877&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
133112431525.9345619658-401.934561965812
142655126720.243338077-169.243338076958
153065130666.3835235883-15.3835235882507
162585925670.616387006188.383612993966
172510024766.4742524209333.525747579144
182577825364.4953061382413.504693861836
192041818403.26022498192014.73977501813
201868818450.7843985742237.215601425843
212042419741.4433725213682.55662747872
222477623023.91790070661752.08209929339
231981420165.2256299751-351.225629975092
241273812066.4156051994671.584394800631
253156633669.6125561379-2103.61255613787
263011128442.89055039811668.10944960189
273001933092.0078298613-3073.00782986126
283193427208.30449905384725.6955009462
292582627896.1842455707-2070.18424557074
302683527746.9879260917-911.987926091737
312020521328.4205848637-1123.42058486369
321778919246.5585653018-1457.55856530185
332052020248.8538117347271.146188265338
342251824050.7929914602-1532.79299146021
351557218814.3689486362-3242.3689486362
361150910384.94381263061124.05618736942
372544730436.4948749396-4989.49487493964
382409026566.3165660545-2476.31656605451
392778626935.6700131031850.329986896864
402619527133.1633735871-938.163373587107
412051621778.1329051095-1262.1329051095
422275922606.7267179333152.273282066661
431902816411.07323583662616.92676416336
441697115363.37346144091607.62653855909
452003618440.94886334131595.05113665875
462248521575.4122023408909.587797659169
471873016099.87526307012630.1247369299
481453812292.92283266562245.07716733445
492756128967.4764618909-1406.4764618909
502598527825.093345745-1840.09334574504
513467030444.83973591984225.16026408016
523206630663.71794824381402.28205175617
532718625885.35201538391300.64798461608
542958628430.09622109311155.90377890689
552135924078.037023445-2719.03702344495
562155320643.9199527798909.080047220188
571957323482.384255257-3909.38425525702
582425624373.1735523799-117.173552379903
592238019612.40871181592767.59128818409
601616715614.9127141611552.087285838943
612729729489.8009588359-2192.80095883592
622828727821.0799246359465.920075364094
633347434923.452661919-1449.45266191904
642822931531.7894955057-3302.78949550571
652878525132.50525009543652.49474990463
662559728367.5776409306-2770.57764093062
671813020339.0221538131-2209.02215381312
682019819298.3281332891899.671866710902
692284919179.373552563669.62644743998
702311824905.8742149828-1787.87421498276
712192521360.3825570784564.617442921633
722080115274.75601981145526.24398018864
731878529114.436851378-10329.436851378
742065926380.4878756309-5721.48787563092
752936730258.8612928352-891.861292835154
762399225915.5861262556-1923.58612625556
772064524237.6092714736-3592.60927147361
782235621134.54347218291221.45652781714
791790214772.69272970223129.3072702978
801587917406.382363563-1527.382363563
811696318181.7583128879-1218.75831288795
822103518942.82120660242092.17879339756
831798818125.000185161-137.00018516104
841043714849.0335641996-4412.03356419959







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8515675.102580871310621.738936502820728.4662252398
8619188.118870269313864.709036758624511.5287037801
8727922.941333084622342.538087008933503.3445791603
8823242.532271797917416.460823376929068.6037202188
8921178.450131385215116.658592953827240.2416698167
9022217.079357737715928.397080130428505.7616353451
9116620.351946011210112.684704826723128.0191871958
9215362.31085717218642.7914506013822081.8302637427
9316832.87217000419907.9787276056523757.7656124026
9420027.667074602812903.317467665627152.0166815401
9517150.03311998319831.6613437503324468.4048962159
9611298.33591023973790.9546365561418805.7171839232

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 15675.1025808713 & 10621.7389365028 & 20728.4662252398 \tabularnewline
86 & 19188.1188702693 & 13864.7090367586 & 24511.5287037801 \tabularnewline
87 & 27922.9413330846 & 22342.5380870089 & 33503.3445791603 \tabularnewline
88 & 23242.5322717979 & 17416.4608233769 & 29068.6037202188 \tabularnewline
89 & 21178.4501313852 & 15116.6585929538 & 27240.2416698167 \tabularnewline
90 & 22217.0793577377 & 15928.3970801304 & 28505.7616353451 \tabularnewline
91 & 16620.3519460112 & 10112.6847048267 & 23128.0191871958 \tabularnewline
92 & 15362.3108571721 & 8642.79145060138 & 22081.8302637427 \tabularnewline
93 & 16832.8721700041 & 9907.97872760565 & 23757.7656124026 \tabularnewline
94 & 20027.6670746028 & 12903.3174676656 & 27152.0166815401 \tabularnewline
95 & 17150.0331199831 & 9831.66134375033 & 24468.4048962159 \tabularnewline
96 & 11298.3359102397 & 3790.95463655614 & 18805.7171839232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208877&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]15675.1025808713[/C][C]10621.7389365028[/C][C]20728.4662252398[/C][/ROW]
[ROW][C]86[/C][C]19188.1188702693[/C][C]13864.7090367586[/C][C]24511.5287037801[/C][/ROW]
[ROW][C]87[/C][C]27922.9413330846[/C][C]22342.5380870089[/C][C]33503.3445791603[/C][/ROW]
[ROW][C]88[/C][C]23242.5322717979[/C][C]17416.4608233769[/C][C]29068.6037202188[/C][/ROW]
[ROW][C]89[/C][C]21178.4501313852[/C][C]15116.6585929538[/C][C]27240.2416698167[/C][/ROW]
[ROW][C]90[/C][C]22217.0793577377[/C][C]15928.3970801304[/C][C]28505.7616353451[/C][/ROW]
[ROW][C]91[/C][C]16620.3519460112[/C][C]10112.6847048267[/C][C]23128.0191871958[/C][/ROW]
[ROW][C]92[/C][C]15362.3108571721[/C][C]8642.79145060138[/C][C]22081.8302637427[/C][/ROW]
[ROW][C]93[/C][C]16832.8721700041[/C][C]9907.97872760565[/C][C]23757.7656124026[/C][/ROW]
[ROW][C]94[/C][C]20027.6670746028[/C][C]12903.3174676656[/C][C]27152.0166815401[/C][/ROW]
[ROW][C]95[/C][C]17150.0331199831[/C][C]9831.66134375033[/C][C]24468.4048962159[/C][/ROW]
[ROW][C]96[/C][C]11298.3359102397[/C][C]3790.95463655614[/C][C]18805.7171839232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208877&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208877&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
8515675.102580871310621.738936502820728.4662252398
8619188.118870269313864.709036758624511.5287037801
8727922.941333084622342.538087008933503.3445791603
8823242.532271797917416.460823376929068.6037202188
8921178.450131385215116.658592953827240.2416698167
9022217.079357737715928.397080130428505.7616353451
9116620.351946011210112.684704826723128.0191871958
9215362.31085717218642.7914506013822081.8302637427
9316832.87217000419907.9787276056523757.7656124026
9420027.667074602812903.317467665627152.0166815401
9517150.03311998319831.6613437503324468.4048962159
9611298.33591023973790.9546365561418805.7171839232



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')