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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Jan 2012 15:07:34 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/15/t1326658079yggaoyj02k0xywr.htm/, Retrieved Fri, 03 May 2024 11:47:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161128, Retrieved Fri, 03 May 2024 11:47:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Quartiles] [] [2011-10-12 15:00:07] [79a597247be783b3a6aed86ad77bf9f6]
- RMPD    [Exponential Smoothing] [] [2012-01-15 20:07:34] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
1594
2467
2222
3607
4685
4962
5770
5480
5000
3228
1993
2288
1580
2111
2192
3601
4665
4876
5813
5589
5331
3075
2002
2306
1507
1992
2487
3490
4647
5594
5611
5788
6204
3013
1931
2549
1504
2090
2702
2939
4500
6208
6415
5657
5964
3163
1997
2422
1376
2202
2683
3303
5202
5231
4880
7998
4977
3531
2025
2205
1442
2238
2179
3218
5139
4990
4914
6084
5672
3548
1793
2086




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161128&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161128&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161128&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00409143795748759
beta0
gamma0.312432034412726

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00409143795748759 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.312432034412726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161128&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]0.00409143795748759[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.312432034412726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161128&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161128&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
alpha0.00409143795748759
beta0
gamma0.312432034412726







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315801596.64202958955-16.6420295895489
1421112129.60340771504-18.6034077150352
1521922200.19945235032-8.19945235031901
1636013607.37333716792-6.37333716792227
1746654681.55356708701-16.5535670870149
1848764892.2510712559-16.2510712559024
1958135768.8057481229144.1942518770938
2055895503.1730153792685.8269846207377
2153315044.61664446486286.383355535139
2230753259.29488140586-184.29488140586
2320022012.69275419659-10.6927541965881
2423062313.67725935304-7.6772593530377
2515071593.50731045476-86.5073104547555
2619922126.16012263667-134.160122636669
2724872199.5855103319287.414489668096
2834903610.55232651715-120.552326517148
2946474682.49173411111-35.4917341111068
3055944893.47615793152700.523842068485
3156115793.45786647775-182.457866477747
3257885539.41308951627248.586910483727
3362045143.173349875341060.82665012466
3430133209.80359445223-196.803594452227
3519312014.26202670377-83.2620267037669
3625492316.57849190663232.421508093367
3715041570.83524330887-66.8352433088735
3820902090.16079628078-0.160796280777959
3927022295.87979867975406.120201320255
4029393584.50249058499-645.50249058499
4145004683.62383939229-183.623839392291
4262085123.976958874511084.02304112549
4364155752.49132712536662.508672874643
4456575635.6082713457121.391728654291
4559645490.42830242939473.571697570614
4631633157.042164043875.95783595613466
4719971994.22696935932.77303064070179
4824222396.3460652610625.6539347389416
4913761554.31761099591-178.317610995905
5022022095.2651508234106.734849176597
5126832428.63357339648254.366426603521
5233033391.55315921191-88.5531592119146
5352024640.40775910439561.59224089561
5452315481.01285110977-250.012851109766
5548805974.10206659195-1094.10206659195
5679985650.10175920692347.8982407931
5749775655.06989136647-678.069891366475
5835313165.93924434904365.06075565096
5920252000.4654847660924.534515233913
6022052410.91290747272-205.912907472718
6114421502.32085543747-60.3208554374728
6222382134.1093259122103.890674087801
6321792514.36793184533-335.367931845331
6432183369.59330263644-151.59330263644
6551394822.70026477856316.299735221443
6649905410.54856095396-420.548560953957
6749145640.3262536018-726.326253601804
6860846388.66882451101-304.668824511006
6956725441.56056818169230.439431818307
7035483280.19389655637267.806103443633
7117932008.26233271593-215.262332715928
7220862345.86379833904-259.863798339044

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1580 & 1596.64202958955 & -16.6420295895489 \tabularnewline
14 & 2111 & 2129.60340771504 & -18.6034077150352 \tabularnewline
15 & 2192 & 2200.19945235032 & -8.19945235031901 \tabularnewline
16 & 3601 & 3607.37333716792 & -6.37333716792227 \tabularnewline
17 & 4665 & 4681.55356708701 & -16.5535670870149 \tabularnewline
18 & 4876 & 4892.2510712559 & -16.2510712559024 \tabularnewline
19 & 5813 & 5768.80574812291 & 44.1942518770938 \tabularnewline
20 & 5589 & 5503.17301537926 & 85.8269846207377 \tabularnewline
21 & 5331 & 5044.61664446486 & 286.383355535139 \tabularnewline
22 & 3075 & 3259.29488140586 & -184.29488140586 \tabularnewline
23 & 2002 & 2012.69275419659 & -10.6927541965881 \tabularnewline
24 & 2306 & 2313.67725935304 & -7.6772593530377 \tabularnewline
25 & 1507 & 1593.50731045476 & -86.5073104547555 \tabularnewline
26 & 1992 & 2126.16012263667 & -134.160122636669 \tabularnewline
27 & 2487 & 2199.5855103319 & 287.414489668096 \tabularnewline
28 & 3490 & 3610.55232651715 & -120.552326517148 \tabularnewline
29 & 4647 & 4682.49173411111 & -35.4917341111068 \tabularnewline
30 & 5594 & 4893.47615793152 & 700.523842068485 \tabularnewline
31 & 5611 & 5793.45786647775 & -182.457866477747 \tabularnewline
32 & 5788 & 5539.41308951627 & 248.586910483727 \tabularnewline
33 & 6204 & 5143.17334987534 & 1060.82665012466 \tabularnewline
34 & 3013 & 3209.80359445223 & -196.803594452227 \tabularnewline
35 & 1931 & 2014.26202670377 & -83.2620267037669 \tabularnewline
36 & 2549 & 2316.57849190663 & 232.421508093367 \tabularnewline
37 & 1504 & 1570.83524330887 & -66.8352433088735 \tabularnewline
38 & 2090 & 2090.16079628078 & -0.160796280777959 \tabularnewline
39 & 2702 & 2295.87979867975 & 406.120201320255 \tabularnewline
40 & 2939 & 3584.50249058499 & -645.50249058499 \tabularnewline
41 & 4500 & 4683.62383939229 & -183.623839392291 \tabularnewline
42 & 6208 & 5123.97695887451 & 1084.02304112549 \tabularnewline
43 & 6415 & 5752.49132712536 & 662.508672874643 \tabularnewline
44 & 5657 & 5635.60827134571 & 21.391728654291 \tabularnewline
45 & 5964 & 5490.42830242939 & 473.571697570614 \tabularnewline
46 & 3163 & 3157.04216404387 & 5.95783595613466 \tabularnewline
47 & 1997 & 1994.2269693593 & 2.77303064070179 \tabularnewline
48 & 2422 & 2396.34606526106 & 25.6539347389416 \tabularnewline
49 & 1376 & 1554.31761099591 & -178.317610995905 \tabularnewline
50 & 2202 & 2095.2651508234 & 106.734849176597 \tabularnewline
51 & 2683 & 2428.63357339648 & 254.366426603521 \tabularnewline
52 & 3303 & 3391.55315921191 & -88.5531592119146 \tabularnewline
53 & 5202 & 4640.40775910439 & 561.59224089561 \tabularnewline
54 & 5231 & 5481.01285110977 & -250.012851109766 \tabularnewline
55 & 4880 & 5974.10206659195 & -1094.10206659195 \tabularnewline
56 & 7998 & 5650.1017592069 & 2347.8982407931 \tabularnewline
57 & 4977 & 5655.06989136647 & -678.069891366475 \tabularnewline
58 & 3531 & 3165.93924434904 & 365.06075565096 \tabularnewline
59 & 2025 & 2000.46548476609 & 24.534515233913 \tabularnewline
60 & 2205 & 2410.91290747272 & -205.912907472718 \tabularnewline
61 & 1442 & 1502.32085543747 & -60.3208554374728 \tabularnewline
62 & 2238 & 2134.1093259122 & 103.890674087801 \tabularnewline
63 & 2179 & 2514.36793184533 & -335.367931845331 \tabularnewline
64 & 3218 & 3369.59330263644 & -151.59330263644 \tabularnewline
65 & 5139 & 4822.70026477856 & 316.299735221443 \tabularnewline
66 & 4990 & 5410.54856095396 & -420.548560953957 \tabularnewline
67 & 4914 & 5640.3262536018 & -726.326253601804 \tabularnewline
68 & 6084 & 6388.66882451101 & -304.668824511006 \tabularnewline
69 & 5672 & 5441.56056818169 & 230.439431818307 \tabularnewline
70 & 3548 & 3280.19389655637 & 267.806103443633 \tabularnewline
71 & 1793 & 2008.26233271593 & -215.262332715928 \tabularnewline
72 & 2086 & 2345.86379833904 & -259.863798339044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161128&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]1580[/C][C]1596.64202958955[/C][C]-16.6420295895489[/C][/ROW]
[ROW][C]14[/C][C]2111[/C][C]2129.60340771504[/C][C]-18.6034077150352[/C][/ROW]
[ROW][C]15[/C][C]2192[/C][C]2200.19945235032[/C][C]-8.19945235031901[/C][/ROW]
[ROW][C]16[/C][C]3601[/C][C]3607.37333716792[/C][C]-6.37333716792227[/C][/ROW]
[ROW][C]17[/C][C]4665[/C][C]4681.55356708701[/C][C]-16.5535670870149[/C][/ROW]
[ROW][C]18[/C][C]4876[/C][C]4892.2510712559[/C][C]-16.2510712559024[/C][/ROW]
[ROW][C]19[/C][C]5813[/C][C]5768.80574812291[/C][C]44.1942518770938[/C][/ROW]
[ROW][C]20[/C][C]5589[/C][C]5503.17301537926[/C][C]85.8269846207377[/C][/ROW]
[ROW][C]21[/C][C]5331[/C][C]5044.61664446486[/C][C]286.383355535139[/C][/ROW]
[ROW][C]22[/C][C]3075[/C][C]3259.29488140586[/C][C]-184.29488140586[/C][/ROW]
[ROW][C]23[/C][C]2002[/C][C]2012.69275419659[/C][C]-10.6927541965881[/C][/ROW]
[ROW][C]24[/C][C]2306[/C][C]2313.67725935304[/C][C]-7.6772593530377[/C][/ROW]
[ROW][C]25[/C][C]1507[/C][C]1593.50731045476[/C][C]-86.5073104547555[/C][/ROW]
[ROW][C]26[/C][C]1992[/C][C]2126.16012263667[/C][C]-134.160122636669[/C][/ROW]
[ROW][C]27[/C][C]2487[/C][C]2199.5855103319[/C][C]287.414489668096[/C][/ROW]
[ROW][C]28[/C][C]3490[/C][C]3610.55232651715[/C][C]-120.552326517148[/C][/ROW]
[ROW][C]29[/C][C]4647[/C][C]4682.49173411111[/C][C]-35.4917341111068[/C][/ROW]
[ROW][C]30[/C][C]5594[/C][C]4893.47615793152[/C][C]700.523842068485[/C][/ROW]
[ROW][C]31[/C][C]5611[/C][C]5793.45786647775[/C][C]-182.457866477747[/C][/ROW]
[ROW][C]32[/C][C]5788[/C][C]5539.41308951627[/C][C]248.586910483727[/C][/ROW]
[ROW][C]33[/C][C]6204[/C][C]5143.17334987534[/C][C]1060.82665012466[/C][/ROW]
[ROW][C]34[/C][C]3013[/C][C]3209.80359445223[/C][C]-196.803594452227[/C][/ROW]
[ROW][C]35[/C][C]1931[/C][C]2014.26202670377[/C][C]-83.2620267037669[/C][/ROW]
[ROW][C]36[/C][C]2549[/C][C]2316.57849190663[/C][C]232.421508093367[/C][/ROW]
[ROW][C]37[/C][C]1504[/C][C]1570.83524330887[/C][C]-66.8352433088735[/C][/ROW]
[ROW][C]38[/C][C]2090[/C][C]2090.16079628078[/C][C]-0.160796280777959[/C][/ROW]
[ROW][C]39[/C][C]2702[/C][C]2295.87979867975[/C][C]406.120201320255[/C][/ROW]
[ROW][C]40[/C][C]2939[/C][C]3584.50249058499[/C][C]-645.50249058499[/C][/ROW]
[ROW][C]41[/C][C]4500[/C][C]4683.62383939229[/C][C]-183.623839392291[/C][/ROW]
[ROW][C]42[/C][C]6208[/C][C]5123.97695887451[/C][C]1084.02304112549[/C][/ROW]
[ROW][C]43[/C][C]6415[/C][C]5752.49132712536[/C][C]662.508672874643[/C][/ROW]
[ROW][C]44[/C][C]5657[/C][C]5635.60827134571[/C][C]21.391728654291[/C][/ROW]
[ROW][C]45[/C][C]5964[/C][C]5490.42830242939[/C][C]473.571697570614[/C][/ROW]
[ROW][C]46[/C][C]3163[/C][C]3157.04216404387[/C][C]5.95783595613466[/C][/ROW]
[ROW][C]47[/C][C]1997[/C][C]1994.2269693593[/C][C]2.77303064070179[/C][/ROW]
[ROW][C]48[/C][C]2422[/C][C]2396.34606526106[/C][C]25.6539347389416[/C][/ROW]
[ROW][C]49[/C][C]1376[/C][C]1554.31761099591[/C][C]-178.317610995905[/C][/ROW]
[ROW][C]50[/C][C]2202[/C][C]2095.2651508234[/C][C]106.734849176597[/C][/ROW]
[ROW][C]51[/C][C]2683[/C][C]2428.63357339648[/C][C]254.366426603521[/C][/ROW]
[ROW][C]52[/C][C]3303[/C][C]3391.55315921191[/C][C]-88.5531592119146[/C][/ROW]
[ROW][C]53[/C][C]5202[/C][C]4640.40775910439[/C][C]561.59224089561[/C][/ROW]
[ROW][C]54[/C][C]5231[/C][C]5481.01285110977[/C][C]-250.012851109766[/C][/ROW]
[ROW][C]55[/C][C]4880[/C][C]5974.10206659195[/C][C]-1094.10206659195[/C][/ROW]
[ROW][C]56[/C][C]7998[/C][C]5650.1017592069[/C][C]2347.8982407931[/C][/ROW]
[ROW][C]57[/C][C]4977[/C][C]5655.06989136647[/C][C]-678.069891366475[/C][/ROW]
[ROW][C]58[/C][C]3531[/C][C]3165.93924434904[/C][C]365.06075565096[/C][/ROW]
[ROW][C]59[/C][C]2025[/C][C]2000.46548476609[/C][C]24.534515233913[/C][/ROW]
[ROW][C]60[/C][C]2205[/C][C]2410.91290747272[/C][C]-205.912907472718[/C][/ROW]
[ROW][C]61[/C][C]1442[/C][C]1502.32085543747[/C][C]-60.3208554374728[/C][/ROW]
[ROW][C]62[/C][C]2238[/C][C]2134.1093259122[/C][C]103.890674087801[/C][/ROW]
[ROW][C]63[/C][C]2179[/C][C]2514.36793184533[/C][C]-335.367931845331[/C][/ROW]
[ROW][C]64[/C][C]3218[/C][C]3369.59330263644[/C][C]-151.59330263644[/C][/ROW]
[ROW][C]65[/C][C]5139[/C][C]4822.70026477856[/C][C]316.299735221443[/C][/ROW]
[ROW][C]66[/C][C]4990[/C][C]5410.54856095396[/C][C]-420.548560953957[/C][/ROW]
[ROW][C]67[/C][C]4914[/C][C]5640.3262536018[/C][C]-726.326253601804[/C][/ROW]
[ROW][C]68[/C][C]6084[/C][C]6388.66882451101[/C][C]-304.668824511006[/C][/ROW]
[ROW][C]69[/C][C]5672[/C][C]5441.56056818169[/C][C]230.439431818307[/C][/ROW]
[ROW][C]70[/C][C]3548[/C][C]3280.19389655637[/C][C]267.806103443633[/C][/ROW]
[ROW][C]71[/C][C]1793[/C][C]2008.26233271593[/C][C]-215.262332715928[/C][/ROW]
[ROW][C]72[/C][C]2086[/C][C]2345.86379833904[/C][C]-259.863798339044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161128&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161128&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
1315801596.64202958955-16.6420295895489
1421112129.60340771504-18.6034077150352
1521922200.19945235032-8.19945235031901
1636013607.37333716792-6.37333716792227
1746654681.55356708701-16.5535670870149
1848764892.2510712559-16.2510712559024
1958135768.8057481229144.1942518770938
2055895503.1730153792685.8269846207377
2153315044.61664446486286.383355535139
2230753259.29488140586-184.29488140586
2320022012.69275419659-10.6927541965881
2423062313.67725935304-7.6772593530377
2515071593.50731045476-86.5073104547555
2619922126.16012263667-134.160122636669
2724872199.5855103319287.414489668096
2834903610.55232651715-120.552326517148
2946474682.49173411111-35.4917341111068
3055944893.47615793152700.523842068485
3156115793.45786647775-182.457866477747
3257885539.41308951627248.586910483727
3362045143.173349875341060.82665012466
3430133209.80359445223-196.803594452227
3519312014.26202670377-83.2620267037669
3625492316.57849190663232.421508093367
3715041570.83524330887-66.8352433088735
3820902090.16079628078-0.160796280777959
3927022295.87979867975406.120201320255
4029393584.50249058499-645.50249058499
4145004683.62383939229-183.623839392291
4262085123.976958874511084.02304112549
4364155752.49132712536662.508672874643
4456575635.6082713457121.391728654291
4559645490.42830242939473.571697570614
4631633157.042164043875.95783595613466
4719971994.22696935932.77303064070179
4824222396.3460652610625.6539347389416
4913761554.31761099591-178.317610995905
5022022095.2651508234106.734849176597
5126832428.63357339648254.366426603521
5233033391.55315921191-88.5531592119146
5352024640.40775910439561.59224089561
5452315481.01285110977-250.012851109766
5548805974.10206659195-1094.10206659195
5679985650.10175920692347.8982407931
5749775655.06989136647-678.069891366475
5835313165.93924434904365.06075565096
5920252000.4654847660924.534515233913
6022052410.91290747272-205.912907472718
6114421502.32085543747-60.3208554374728
6222382134.1093259122103.890674087801
6321792514.36793184533-335.367931845331
6432183369.59330263644-151.59330263644
6551394822.70026477856316.299735221443
6649905410.54856095396-420.548560953957
6749145640.3262536018-726.326253601804
6860846388.66882451101-304.668824511006
6956725441.56056818169230.439431818307
7035483280.19389655637267.806103443633
7117932008.26233271593-215.262332715928
7220862345.86379833904-259.863798339044







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731482.790406618191187.527005605951778.05380763043
742165.677363837511870.360932218782460.99379545625
752408.644399764212113.284672592112704.00412693631
763322.415231385643026.92135067943617.90911209188
774921.996752633014626.173400004065217.82010526196
785279.206095642124983.270215075195575.14197620905
795415.473125899595119.476182571885711.4700692273
806298.640192430376002.351621126336594.92876373441
815518.521189330085222.451662437575814.5907162226
823366.127091658483070.55433108393661.69985223305
831942.123579511271646.748911527952237.4982474946
842266.978955492371808.499425419942725.45848556479

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1482.79040661819 & 1187.52700560595 & 1778.05380763043 \tabularnewline
74 & 2165.67736383751 & 1870.36093221878 & 2460.99379545625 \tabularnewline
75 & 2408.64439976421 & 2113.28467259211 & 2704.00412693631 \tabularnewline
76 & 3322.41523138564 & 3026.9213506794 & 3617.90911209188 \tabularnewline
77 & 4921.99675263301 & 4626.17340000406 & 5217.82010526196 \tabularnewline
78 & 5279.20609564212 & 4983.27021507519 & 5575.14197620905 \tabularnewline
79 & 5415.47312589959 & 5119.47618257188 & 5711.4700692273 \tabularnewline
80 & 6298.64019243037 & 6002.35162112633 & 6594.92876373441 \tabularnewline
81 & 5518.52118933008 & 5222.45166243757 & 5814.5907162226 \tabularnewline
82 & 3366.12709165848 & 3070.5543310839 & 3661.69985223305 \tabularnewline
83 & 1942.12357951127 & 1646.74891152795 & 2237.4982474946 \tabularnewline
84 & 2266.97895549237 & 1808.49942541994 & 2725.45848556479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161128&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]1482.79040661819[/C][C]1187.52700560595[/C][C]1778.05380763043[/C][/ROW]
[ROW][C]74[/C][C]2165.67736383751[/C][C]1870.36093221878[/C][C]2460.99379545625[/C][/ROW]
[ROW][C]75[/C][C]2408.64439976421[/C][C]2113.28467259211[/C][C]2704.00412693631[/C][/ROW]
[ROW][C]76[/C][C]3322.41523138564[/C][C]3026.9213506794[/C][C]3617.90911209188[/C][/ROW]
[ROW][C]77[/C][C]4921.99675263301[/C][C]4626.17340000406[/C][C]5217.82010526196[/C][/ROW]
[ROW][C]78[/C][C]5279.20609564212[/C][C]4983.27021507519[/C][C]5575.14197620905[/C][/ROW]
[ROW][C]79[/C][C]5415.47312589959[/C][C]5119.47618257188[/C][C]5711.4700692273[/C][/ROW]
[ROW][C]80[/C][C]6298.64019243037[/C][C]6002.35162112633[/C][C]6594.92876373441[/C][/ROW]
[ROW][C]81[/C][C]5518.52118933008[/C][C]5222.45166243757[/C][C]5814.5907162226[/C][/ROW]
[ROW][C]82[/C][C]3366.12709165848[/C][C]3070.5543310839[/C][C]3661.69985223305[/C][/ROW]
[ROW][C]83[/C][C]1942.12357951127[/C][C]1646.74891152795[/C][C]2237.4982474946[/C][/ROW]
[ROW][C]84[/C][C]2266.97895549237[/C][C]1808.49942541994[/C][C]2725.45848556479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161128&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161128&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
731482.790406618191187.527005605951778.05380763043
742165.677363837511870.360932218782460.99379545625
752408.644399764212113.284672592112704.00412693631
763322.415231385643026.92135067943617.90911209188
774921.996752633014626.173400004065217.82010526196
785279.206095642124983.270215075195575.14197620905
795415.473125899595119.476182571885711.4700692273
806298.640192430376002.351621126336594.92876373441
815518.521189330085222.451662437575814.5907162226
823366.127091658483070.55433108393661.69985223305
831942.123579511271646.748911527952237.4982474946
842266.978955492371808.499425419942725.45848556479



Parameters (Session):
par1 = 12 ;
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')