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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 18:39:37 +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/28/t1417199991gqj4c3bjn2q1t4w.htm/, Retrieved Sun, 19 May 2024 13:33:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261006, Retrieved Sun, 19 May 2024 13:33:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 18:39:37] [a3f3211dd8483244715f7a4805f88a28] [Current]
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Dataseries X:
12849
11380
12079
11366
11328
10444
10854
10434
10137
10992
10906
12367
14371
11695
11546
10922
10670
10254
10573
10239
10253
11176
10719
11817
12487
11519
12025
10976
11276
10657
11141
10423
10640
11426
10948
12540
12200
10644
12044
11338
11292
10612
10995
10686
10635
11285
11475
12535
12490
12511
12799
11876
11602
11062
11055
10855
10704
11510
11663
12686
13516
12539
13811
12354
11441
10814
11261
10788
10326
11490
11029
11876




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261006&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261006&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261006&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.746213269556632
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.746213269556632 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261006&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]0.746213269556632[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261006&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261006&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
alpha0.746213269556632
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21138012849-1469
31207911752.8127070213326.187292978691
41136611996.2179934028-630.217993402764
51132811525.9409640123-197.940964012269
61044411378.2347900775-934.234790077482
71085410681.0963928402172.903607159789
81043410810.1193588571-376.119358857053
91013710529.4541023408-392.454102340787
101099210236.5996434822755.400356517845
111090610800.2894133436105.71058665642
121236710879.17205583921487.82794416078
131437111989.40901058922381.59098941084
141169513766.583809544-2071.58380954403
151154612220.7404818636-674.740481863599
161092211717.2401807899-795.240180789944
171067011123.8214053999-453.821405399873
181025410785.1738506816-531.173850681647
191057310388.8048748615184.195125138491
201023910526.2537214275-287.253721427496
211025310311.9011827688-58.9011827687755
221117610267.9483385941908.051661405865
231071910945.5485377781-226.548537778137
241181710776.49501268941040.50498731056
251248711552.9336412604934.066358739565
261151912249.9463527983-730.946352798343
271202511704.5044850062320.495514993803
281097611943.662491128-967.662491127958
291127611221.579899796154.4201002039499
301065711262.1889006988-605.188900698839
311114110810.588912409330.411087591025
321042311057.146050378-634.146050378036
331064010583.93785274956.0621472509829
341142610625.7721709475800.227829052463
351094811222.912795655-274.912795654982
361254011017.76921956631522.23078043368
371220012153.678027253546.3219727465203
381064412188.244097989-1544.24409798897
391204411035.90866063511008.09133936491
401133811788.1597949943-450.159794994304
411129211452.2445825487-160.244582548661
421061211332.6679486763-720.667948676288
431099510794.8959624299200.104037570116
441068610944.2162505566-258.216250556563
451063510751.5318579761-116.531857976095
461128510664.5742392282620.425760771755
471147511127.5441746909347.455825309104
481253511386.82032212131148.1796778787
491249012243.6072335896246.392766410354
501251112427.468785407883.5312145921798
511279912489.8008861587309.199113841314
521187612720.5293678422-844.529367842226
531160212090.3303470281-488.330347028084
541106211725.9317621485-663.931762148533
551105511230.4970711532-175.497071153181
561085511099.5388278904-244.538827890354
571070410917.0607095967-213.060709596746
581151010758.0719808745751.928019125498
591166311319.1706464974343.829353502619
601268611575.74067254411110.25932745589
611351612404.23091534071111.76908465928
621253913233.8477589963-694.847758996304
631381112715.34314091161095.65685908843
641235413532.9368280441-1178.9368280441
651144112653.1985229886-1212.19852298859
661081411748.6398997976-934.639899797554
671126111051.1992043115209.800795688461
681078811207.7553420178-419.755342017808
691032610894.5283358368-568.528335836836
701149010470.28494751641019.71505248356
711102911231.2098508463-202.20985084631
721187611080.3181769097795.681823090275

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 11380 & 12849 & -1469 \tabularnewline
3 & 12079 & 11752.8127070213 & 326.187292978691 \tabularnewline
4 & 11366 & 11996.2179934028 & -630.217993402764 \tabularnewline
5 & 11328 & 11525.9409640123 & -197.940964012269 \tabularnewline
6 & 10444 & 11378.2347900775 & -934.234790077482 \tabularnewline
7 & 10854 & 10681.0963928402 & 172.903607159789 \tabularnewline
8 & 10434 & 10810.1193588571 & -376.119358857053 \tabularnewline
9 & 10137 & 10529.4541023408 & -392.454102340787 \tabularnewline
10 & 10992 & 10236.5996434822 & 755.400356517845 \tabularnewline
11 & 10906 & 10800.2894133436 & 105.71058665642 \tabularnewline
12 & 12367 & 10879.1720558392 & 1487.82794416078 \tabularnewline
13 & 14371 & 11989.4090105892 & 2381.59098941084 \tabularnewline
14 & 11695 & 13766.583809544 & -2071.58380954403 \tabularnewline
15 & 11546 & 12220.7404818636 & -674.740481863599 \tabularnewline
16 & 10922 & 11717.2401807899 & -795.240180789944 \tabularnewline
17 & 10670 & 11123.8214053999 & -453.821405399873 \tabularnewline
18 & 10254 & 10785.1738506816 & -531.173850681647 \tabularnewline
19 & 10573 & 10388.8048748615 & 184.195125138491 \tabularnewline
20 & 10239 & 10526.2537214275 & -287.253721427496 \tabularnewline
21 & 10253 & 10311.9011827688 & -58.9011827687755 \tabularnewline
22 & 11176 & 10267.9483385941 & 908.051661405865 \tabularnewline
23 & 10719 & 10945.5485377781 & -226.548537778137 \tabularnewline
24 & 11817 & 10776.4950126894 & 1040.50498731056 \tabularnewline
25 & 12487 & 11552.9336412604 & 934.066358739565 \tabularnewline
26 & 11519 & 12249.9463527983 & -730.946352798343 \tabularnewline
27 & 12025 & 11704.5044850062 & 320.495514993803 \tabularnewline
28 & 10976 & 11943.662491128 & -967.662491127958 \tabularnewline
29 & 11276 & 11221.5798997961 & 54.4201002039499 \tabularnewline
30 & 10657 & 11262.1889006988 & -605.188900698839 \tabularnewline
31 & 11141 & 10810.588912409 & 330.411087591025 \tabularnewline
32 & 10423 & 11057.146050378 & -634.146050378036 \tabularnewline
33 & 10640 & 10583.937852749 & 56.0621472509829 \tabularnewline
34 & 11426 & 10625.7721709475 & 800.227829052463 \tabularnewline
35 & 10948 & 11222.912795655 & -274.912795654982 \tabularnewline
36 & 12540 & 11017.7692195663 & 1522.23078043368 \tabularnewline
37 & 12200 & 12153.6780272535 & 46.3219727465203 \tabularnewline
38 & 10644 & 12188.244097989 & -1544.24409798897 \tabularnewline
39 & 12044 & 11035.9086606351 & 1008.09133936491 \tabularnewline
40 & 11338 & 11788.1597949943 & -450.159794994304 \tabularnewline
41 & 11292 & 11452.2445825487 & -160.244582548661 \tabularnewline
42 & 10612 & 11332.6679486763 & -720.667948676288 \tabularnewline
43 & 10995 & 10794.8959624299 & 200.104037570116 \tabularnewline
44 & 10686 & 10944.2162505566 & -258.216250556563 \tabularnewline
45 & 10635 & 10751.5318579761 & -116.531857976095 \tabularnewline
46 & 11285 & 10664.5742392282 & 620.425760771755 \tabularnewline
47 & 11475 & 11127.5441746909 & 347.455825309104 \tabularnewline
48 & 12535 & 11386.8203221213 & 1148.1796778787 \tabularnewline
49 & 12490 & 12243.6072335896 & 246.392766410354 \tabularnewline
50 & 12511 & 12427.4687854078 & 83.5312145921798 \tabularnewline
51 & 12799 & 12489.8008861587 & 309.199113841314 \tabularnewline
52 & 11876 & 12720.5293678422 & -844.529367842226 \tabularnewline
53 & 11602 & 12090.3303470281 & -488.330347028084 \tabularnewline
54 & 11062 & 11725.9317621485 & -663.931762148533 \tabularnewline
55 & 11055 & 11230.4970711532 & -175.497071153181 \tabularnewline
56 & 10855 & 11099.5388278904 & -244.538827890354 \tabularnewline
57 & 10704 & 10917.0607095967 & -213.060709596746 \tabularnewline
58 & 11510 & 10758.0719808745 & 751.928019125498 \tabularnewline
59 & 11663 & 11319.1706464974 & 343.829353502619 \tabularnewline
60 & 12686 & 11575.7406725441 & 1110.25932745589 \tabularnewline
61 & 13516 & 12404.2309153407 & 1111.76908465928 \tabularnewline
62 & 12539 & 13233.8477589963 & -694.847758996304 \tabularnewline
63 & 13811 & 12715.3431409116 & 1095.65685908843 \tabularnewline
64 & 12354 & 13532.9368280441 & -1178.9368280441 \tabularnewline
65 & 11441 & 12653.1985229886 & -1212.19852298859 \tabularnewline
66 & 10814 & 11748.6398997976 & -934.639899797554 \tabularnewline
67 & 11261 & 11051.1992043115 & 209.800795688461 \tabularnewline
68 & 10788 & 11207.7553420178 & -419.755342017808 \tabularnewline
69 & 10326 & 10894.5283358368 & -568.528335836836 \tabularnewline
70 & 11490 & 10470.2849475164 & 1019.71505248356 \tabularnewline
71 & 11029 & 11231.2098508463 & -202.20985084631 \tabularnewline
72 & 11876 & 11080.3181769097 & 795.681823090275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261006&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]2[/C][C]11380[/C][C]12849[/C][C]-1469[/C][/ROW]
[ROW][C]3[/C][C]12079[/C][C]11752.8127070213[/C][C]326.187292978691[/C][/ROW]
[ROW][C]4[/C][C]11366[/C][C]11996.2179934028[/C][C]-630.217993402764[/C][/ROW]
[ROW][C]5[/C][C]11328[/C][C]11525.9409640123[/C][C]-197.940964012269[/C][/ROW]
[ROW][C]6[/C][C]10444[/C][C]11378.2347900775[/C][C]-934.234790077482[/C][/ROW]
[ROW][C]7[/C][C]10854[/C][C]10681.0963928402[/C][C]172.903607159789[/C][/ROW]
[ROW][C]8[/C][C]10434[/C][C]10810.1193588571[/C][C]-376.119358857053[/C][/ROW]
[ROW][C]9[/C][C]10137[/C][C]10529.4541023408[/C][C]-392.454102340787[/C][/ROW]
[ROW][C]10[/C][C]10992[/C][C]10236.5996434822[/C][C]755.400356517845[/C][/ROW]
[ROW][C]11[/C][C]10906[/C][C]10800.2894133436[/C][C]105.71058665642[/C][/ROW]
[ROW][C]12[/C][C]12367[/C][C]10879.1720558392[/C][C]1487.82794416078[/C][/ROW]
[ROW][C]13[/C][C]14371[/C][C]11989.4090105892[/C][C]2381.59098941084[/C][/ROW]
[ROW][C]14[/C][C]11695[/C][C]13766.583809544[/C][C]-2071.58380954403[/C][/ROW]
[ROW][C]15[/C][C]11546[/C][C]12220.7404818636[/C][C]-674.740481863599[/C][/ROW]
[ROW][C]16[/C][C]10922[/C][C]11717.2401807899[/C][C]-795.240180789944[/C][/ROW]
[ROW][C]17[/C][C]10670[/C][C]11123.8214053999[/C][C]-453.821405399873[/C][/ROW]
[ROW][C]18[/C][C]10254[/C][C]10785.1738506816[/C][C]-531.173850681647[/C][/ROW]
[ROW][C]19[/C][C]10573[/C][C]10388.8048748615[/C][C]184.195125138491[/C][/ROW]
[ROW][C]20[/C][C]10239[/C][C]10526.2537214275[/C][C]-287.253721427496[/C][/ROW]
[ROW][C]21[/C][C]10253[/C][C]10311.9011827688[/C][C]-58.9011827687755[/C][/ROW]
[ROW][C]22[/C][C]11176[/C][C]10267.9483385941[/C][C]908.051661405865[/C][/ROW]
[ROW][C]23[/C][C]10719[/C][C]10945.5485377781[/C][C]-226.548537778137[/C][/ROW]
[ROW][C]24[/C][C]11817[/C][C]10776.4950126894[/C][C]1040.50498731056[/C][/ROW]
[ROW][C]25[/C][C]12487[/C][C]11552.9336412604[/C][C]934.066358739565[/C][/ROW]
[ROW][C]26[/C][C]11519[/C][C]12249.9463527983[/C][C]-730.946352798343[/C][/ROW]
[ROW][C]27[/C][C]12025[/C][C]11704.5044850062[/C][C]320.495514993803[/C][/ROW]
[ROW][C]28[/C][C]10976[/C][C]11943.662491128[/C][C]-967.662491127958[/C][/ROW]
[ROW][C]29[/C][C]11276[/C][C]11221.5798997961[/C][C]54.4201002039499[/C][/ROW]
[ROW][C]30[/C][C]10657[/C][C]11262.1889006988[/C][C]-605.188900698839[/C][/ROW]
[ROW][C]31[/C][C]11141[/C][C]10810.588912409[/C][C]330.411087591025[/C][/ROW]
[ROW][C]32[/C][C]10423[/C][C]11057.146050378[/C][C]-634.146050378036[/C][/ROW]
[ROW][C]33[/C][C]10640[/C][C]10583.937852749[/C][C]56.0621472509829[/C][/ROW]
[ROW][C]34[/C][C]11426[/C][C]10625.7721709475[/C][C]800.227829052463[/C][/ROW]
[ROW][C]35[/C][C]10948[/C][C]11222.912795655[/C][C]-274.912795654982[/C][/ROW]
[ROW][C]36[/C][C]12540[/C][C]11017.7692195663[/C][C]1522.23078043368[/C][/ROW]
[ROW][C]37[/C][C]12200[/C][C]12153.6780272535[/C][C]46.3219727465203[/C][/ROW]
[ROW][C]38[/C][C]10644[/C][C]12188.244097989[/C][C]-1544.24409798897[/C][/ROW]
[ROW][C]39[/C][C]12044[/C][C]11035.9086606351[/C][C]1008.09133936491[/C][/ROW]
[ROW][C]40[/C][C]11338[/C][C]11788.1597949943[/C][C]-450.159794994304[/C][/ROW]
[ROW][C]41[/C][C]11292[/C][C]11452.2445825487[/C][C]-160.244582548661[/C][/ROW]
[ROW][C]42[/C][C]10612[/C][C]11332.6679486763[/C][C]-720.667948676288[/C][/ROW]
[ROW][C]43[/C][C]10995[/C][C]10794.8959624299[/C][C]200.104037570116[/C][/ROW]
[ROW][C]44[/C][C]10686[/C][C]10944.2162505566[/C][C]-258.216250556563[/C][/ROW]
[ROW][C]45[/C][C]10635[/C][C]10751.5318579761[/C][C]-116.531857976095[/C][/ROW]
[ROW][C]46[/C][C]11285[/C][C]10664.5742392282[/C][C]620.425760771755[/C][/ROW]
[ROW][C]47[/C][C]11475[/C][C]11127.5441746909[/C][C]347.455825309104[/C][/ROW]
[ROW][C]48[/C][C]12535[/C][C]11386.8203221213[/C][C]1148.1796778787[/C][/ROW]
[ROW][C]49[/C][C]12490[/C][C]12243.6072335896[/C][C]246.392766410354[/C][/ROW]
[ROW][C]50[/C][C]12511[/C][C]12427.4687854078[/C][C]83.5312145921798[/C][/ROW]
[ROW][C]51[/C][C]12799[/C][C]12489.8008861587[/C][C]309.199113841314[/C][/ROW]
[ROW][C]52[/C][C]11876[/C][C]12720.5293678422[/C][C]-844.529367842226[/C][/ROW]
[ROW][C]53[/C][C]11602[/C][C]12090.3303470281[/C][C]-488.330347028084[/C][/ROW]
[ROW][C]54[/C][C]11062[/C][C]11725.9317621485[/C][C]-663.931762148533[/C][/ROW]
[ROW][C]55[/C][C]11055[/C][C]11230.4970711532[/C][C]-175.497071153181[/C][/ROW]
[ROW][C]56[/C][C]10855[/C][C]11099.5388278904[/C][C]-244.538827890354[/C][/ROW]
[ROW][C]57[/C][C]10704[/C][C]10917.0607095967[/C][C]-213.060709596746[/C][/ROW]
[ROW][C]58[/C][C]11510[/C][C]10758.0719808745[/C][C]751.928019125498[/C][/ROW]
[ROW][C]59[/C][C]11663[/C][C]11319.1706464974[/C][C]343.829353502619[/C][/ROW]
[ROW][C]60[/C][C]12686[/C][C]11575.7406725441[/C][C]1110.25932745589[/C][/ROW]
[ROW][C]61[/C][C]13516[/C][C]12404.2309153407[/C][C]1111.76908465928[/C][/ROW]
[ROW][C]62[/C][C]12539[/C][C]13233.8477589963[/C][C]-694.847758996304[/C][/ROW]
[ROW][C]63[/C][C]13811[/C][C]12715.3431409116[/C][C]1095.65685908843[/C][/ROW]
[ROW][C]64[/C][C]12354[/C][C]13532.9368280441[/C][C]-1178.9368280441[/C][/ROW]
[ROW][C]65[/C][C]11441[/C][C]12653.1985229886[/C][C]-1212.19852298859[/C][/ROW]
[ROW][C]66[/C][C]10814[/C][C]11748.6398997976[/C][C]-934.639899797554[/C][/ROW]
[ROW][C]67[/C][C]11261[/C][C]11051.1992043115[/C][C]209.800795688461[/C][/ROW]
[ROW][C]68[/C][C]10788[/C][C]11207.7553420178[/C][C]-419.755342017808[/C][/ROW]
[ROW][C]69[/C][C]10326[/C][C]10894.5283358368[/C][C]-568.528335836836[/C][/ROW]
[ROW][C]70[/C][C]11490[/C][C]10470.2849475164[/C][C]1019.71505248356[/C][/ROW]
[ROW][C]71[/C][C]11029[/C][C]11231.2098508463[/C][C]-202.20985084631[/C][/ROW]
[ROW][C]72[/C][C]11876[/C][C]11080.3181769097[/C][C]795.681823090275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261006&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261006&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
21138012849-1469
31207911752.8127070213326.187292978691
41136611996.2179934028-630.217993402764
51132811525.9409640123-197.940964012269
61044411378.2347900775-934.234790077482
71085410681.0963928402172.903607159789
81043410810.1193588571-376.119358857053
91013710529.4541023408-392.454102340787
101099210236.5996434822755.400356517845
111090610800.2894133436105.71058665642
121236710879.17205583921487.82794416078
131437111989.40901058922381.59098941084
141169513766.583809544-2071.58380954403
151154612220.7404818636-674.740481863599
161092211717.2401807899-795.240180789944
171067011123.8214053999-453.821405399873
181025410785.1738506816-531.173850681647
191057310388.8048748615184.195125138491
201023910526.2537214275-287.253721427496
211025310311.9011827688-58.9011827687755
221117610267.9483385941908.051661405865
231071910945.5485377781-226.548537778137
241181710776.49501268941040.50498731056
251248711552.9336412604934.066358739565
261151912249.9463527983-730.946352798343
271202511704.5044850062320.495514993803
281097611943.662491128-967.662491127958
291127611221.579899796154.4201002039499
301065711262.1889006988-605.188900698839
311114110810.588912409330.411087591025
321042311057.146050378-634.146050378036
331064010583.93785274956.0621472509829
341142610625.7721709475800.227829052463
351094811222.912795655-274.912795654982
361254011017.76921956631522.23078043368
371220012153.678027253546.3219727465203
381064412188.244097989-1544.24409798897
391204411035.90866063511008.09133936491
401133811788.1597949943-450.159794994304
411129211452.2445825487-160.244582548661
421061211332.6679486763-720.667948676288
431099510794.8959624299200.104037570116
441068610944.2162505566-258.216250556563
451063510751.5318579761-116.531857976095
461128510664.5742392282620.425760771755
471147511127.5441746909347.455825309104
481253511386.82032212131148.1796778787
491249012243.6072335896246.392766410354
501251112427.468785407883.5312145921798
511279912489.8008861587309.199113841314
521187612720.5293678422-844.529367842226
531160212090.3303470281-488.330347028084
541106211725.9317621485-663.931762148533
551105511230.4970711532-175.497071153181
561085511099.5388278904-244.538827890354
571070410917.0607095967-213.060709596746
581151010758.0719808745751.928019125498
591166311319.1706464974343.829353502619
601268611575.74067254411110.25932745589
611351612404.23091534071111.76908465928
621253913233.8477589963-694.847758996304
631381112715.34314091161095.65685908843
641235413532.9368280441-1178.9368280441
651144112653.1985229886-1212.19852298859
661081411748.6398997976-934.639899797554
671126111051.1992043115209.800795688461
681078811207.7553420178-419.755342017808
691032610894.5283358368-568.528335836836
701149010470.28494751641019.71505248356
711102911231.2098508463-202.20985084631
721187611080.3181769097795.681823090275







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7311674.066511644710098.200771296613249.9322519928
7411674.06651164479707.8089681536913640.3240551357
7511674.06651164479383.0002482931213965.1327749963
7611674.06651164479098.8382656827614249.2947576066
7711674.06651164478843.0567245664814505.0762987229
7811674.06651164478608.5433409175414739.5896823719
7911674.06651164478390.7376816312414957.3953416582
8011674.06651164478186.5080387685815161.6249845208
8111674.06651164477993.5937162741815354.5393070152
8211674.06651164477810.2994517412615537.8335715481
8311674.06651164477635.3152456062315712.8177776832
8411674.06651164477467.6039021995815880.5291210898

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 11674.0665116447 & 10098.2007712966 & 13249.9322519928 \tabularnewline
74 & 11674.0665116447 & 9707.80896815369 & 13640.3240551357 \tabularnewline
75 & 11674.0665116447 & 9383.00024829312 & 13965.1327749963 \tabularnewline
76 & 11674.0665116447 & 9098.83826568276 & 14249.2947576066 \tabularnewline
77 & 11674.0665116447 & 8843.05672456648 & 14505.0762987229 \tabularnewline
78 & 11674.0665116447 & 8608.54334091754 & 14739.5896823719 \tabularnewline
79 & 11674.0665116447 & 8390.73768163124 & 14957.3953416582 \tabularnewline
80 & 11674.0665116447 & 8186.50803876858 & 15161.6249845208 \tabularnewline
81 & 11674.0665116447 & 7993.59371627418 & 15354.5393070152 \tabularnewline
82 & 11674.0665116447 & 7810.29945174126 & 15537.8335715481 \tabularnewline
83 & 11674.0665116447 & 7635.31524560623 & 15712.8177776832 \tabularnewline
84 & 11674.0665116447 & 7467.60390219958 & 15880.5291210898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261006&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]11674.0665116447[/C][C]10098.2007712966[/C][C]13249.9322519928[/C][/ROW]
[ROW][C]74[/C][C]11674.0665116447[/C][C]9707.80896815369[/C][C]13640.3240551357[/C][/ROW]
[ROW][C]75[/C][C]11674.0665116447[/C][C]9383.00024829312[/C][C]13965.1327749963[/C][/ROW]
[ROW][C]76[/C][C]11674.0665116447[/C][C]9098.83826568276[/C][C]14249.2947576066[/C][/ROW]
[ROW][C]77[/C][C]11674.0665116447[/C][C]8843.05672456648[/C][C]14505.0762987229[/C][/ROW]
[ROW][C]78[/C][C]11674.0665116447[/C][C]8608.54334091754[/C][C]14739.5896823719[/C][/ROW]
[ROW][C]79[/C][C]11674.0665116447[/C][C]8390.73768163124[/C][C]14957.3953416582[/C][/ROW]
[ROW][C]80[/C][C]11674.0665116447[/C][C]8186.50803876858[/C][C]15161.6249845208[/C][/ROW]
[ROW][C]81[/C][C]11674.0665116447[/C][C]7993.59371627418[/C][C]15354.5393070152[/C][/ROW]
[ROW][C]82[/C][C]11674.0665116447[/C][C]7810.29945174126[/C][C]15537.8335715481[/C][/ROW]
[ROW][C]83[/C][C]11674.0665116447[/C][C]7635.31524560623[/C][C]15712.8177776832[/C][/ROW]
[ROW][C]84[/C][C]11674.0665116447[/C][C]7467.60390219958[/C][C]15880.5291210898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261006&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261006&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
7311674.066511644710098.200771296613249.9322519928
7411674.06651164479707.8089681536913640.3240551357
7511674.06651164479383.0002482931213965.1327749963
7611674.06651164479098.8382656827614249.2947576066
7711674.06651164478843.0567245664814505.0762987229
7811674.06651164478608.5433409175414739.5896823719
7911674.06651164478390.7376816312414957.3953416582
8011674.06651164478186.5080387685815161.6249845208
8111674.06651164477993.5937162741815354.5393070152
8211674.06651164477810.2994517412615537.8335715481
8311674.06651164477635.3152456062315712.8177776832
8411674.06651164477467.6039021995815880.5291210898



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')