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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 13:17:55 +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/2015/Nov/29/t1448803099zoe9cd4f7zwu2d9.htm/, Retrieved Wed, 15 May 2024 11:56:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284429, Retrieved Wed, 15 May 2024 11:56:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-29 13:17:55] [822b7cc50e4a16589bd43fa8379da378] [Current]
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Dataseries X:
98.71
100.46
100.46
100.67
100.01
100.01
99.99
99.98
99.87
99.91
96.59
96.99
96.68
96.57
96.55
96.78
95.99
97.54
97.45
97.58
97.66
97.67
97.71
98.52
98.87
97.91
97.92
97.97
97.97
97.97
97.58
97.57
96.7
96.72
96.72
96.74
101.2
100.59
100.58
99.62
99.63
99.17
99.17
98.99
98.92
99.52
99.45
99.04
99.23
98.71
98.73
97.1
100.94
100.93
101.02
101.01
100.86
100.56
100.75
100.15
99.49
99.15
99.15
99.14
98.77
98.8
99.29
98.38
98.31
98.24
96.99
96.81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284429&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284429&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284429&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.78395876363994
beta0.0103815588666306
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.78395876363994 \tabularnewline
beta & 0.0103815588666306 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284429&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]0.78395876363994[/C][/ROW]
[ROW][C]beta[/C][C]0.0103815588666306[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284429&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284429&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
alpha0.78395876363994
beta0.0103815588666306
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1396.6898.3733787393162-1.69337873931619
1496.5796.9055469302379-0.335546930237939
1596.5596.5757183469189-0.0257183469188931
1696.7896.73190661578070.0480933842192712
1795.9995.78760165642980.202398343570167
1897.5497.14882935114510.391170648854896
1997.4597.44664704164470.00335295835526495
2097.5897.45212561041860.127874389581422
2197.6697.53459791288810.125402087111922
2297.6797.766152643899-0.0961526438989608
2397.7194.46781837636713.24218162363287
2498.5297.47382103630471.04617896369525
2598.8797.62925641430791.24074358569214
2697.9198.8035911226809-0.893591122680945
2797.9298.1472608366533-0.227260836653315
2897.9798.2038003676569-0.233800367656926
2997.9797.11195019822390.858049801776133
3097.9799.0734119943764-1.10341199437642
3197.5898.1490377222891-0.569037722289082
3297.5797.7613126525208-0.191312652520779
3396.797.6190488725659-0.919048872565853
3496.7297.0014591905863-0.281459190586304
3596.7294.29508896541412.42491103458588
3696.7496.19532539452580.544674605474185
37101.296.00492175624335.1950782437567
38100.5999.85565640288020.734343597119803
39100.58100.670232858986-0.0902328589863544
4099.62100.884617330205-1.26461733020486
4199.6399.26397776992020.366022230079764
4299.17100.455393076185-1.28539307618483
4399.1799.5417583950396-0.371758395039578
4498.9999.4298603502854-0.439860350285372
4598.9298.9730655095769-0.0530655095769106
4699.5299.2167058461450.303294153855035
4799.4597.60279394845271.84720605154727
4899.0498.68857136389710.351428636102924
4999.2399.3944235056678-0.164423505667756
5098.7198.07928140644910.630718593550881
5198.7398.63308848903470.0969115109653274
5297.198.7406049437424-1.64060494374245
53100.9497.1745659175163.76543408248398
54100.93100.6989469052520.231053094747793
55101.02101.208608950324-0.188608950324138
56101.01101.26415298299-0.254152982990419
57100.86101.0765934109-0.216593410899677
58100.56101.307776806524-0.747776806524072
59100.7599.23361669556821.51638330443177
60100.1599.76440008743130.38559991256875
6199.49100.413380846996-0.923380846996324
6299.1598.69663911486270.453360885137315
6399.1599.01624540571610.133754594283886
6499.1498.79773465089720.34226534910276
6598.7799.9907140727612-1.2207140727612
6698.898.8386101947791-0.0386101947790678
6799.2999.04003003707070.249969962929271
6898.3899.4226381101885-1.04263811018848
6998.3198.6160323457488-0.306032345748804
7098.2498.6525930858731-0.412593085873098
7196.9997.323334403107-0.333334403107003
7296.8196.13764448561770.672355514382346

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.68 & 98.3733787393162 & -1.69337873931619 \tabularnewline
14 & 96.57 & 96.9055469302379 & -0.335546930237939 \tabularnewline
15 & 96.55 & 96.5757183469189 & -0.0257183469188931 \tabularnewline
16 & 96.78 & 96.7319066157807 & 0.0480933842192712 \tabularnewline
17 & 95.99 & 95.7876016564298 & 0.202398343570167 \tabularnewline
18 & 97.54 & 97.1488293511451 & 0.391170648854896 \tabularnewline
19 & 97.45 & 97.4466470416447 & 0.00335295835526495 \tabularnewline
20 & 97.58 & 97.4521256104186 & 0.127874389581422 \tabularnewline
21 & 97.66 & 97.5345979128881 & 0.125402087111922 \tabularnewline
22 & 97.67 & 97.766152643899 & -0.0961526438989608 \tabularnewline
23 & 97.71 & 94.4678183763671 & 3.24218162363287 \tabularnewline
24 & 98.52 & 97.4738210363047 & 1.04617896369525 \tabularnewline
25 & 98.87 & 97.6292564143079 & 1.24074358569214 \tabularnewline
26 & 97.91 & 98.8035911226809 & -0.893591122680945 \tabularnewline
27 & 97.92 & 98.1472608366533 & -0.227260836653315 \tabularnewline
28 & 97.97 & 98.2038003676569 & -0.233800367656926 \tabularnewline
29 & 97.97 & 97.1119501982239 & 0.858049801776133 \tabularnewline
30 & 97.97 & 99.0734119943764 & -1.10341199437642 \tabularnewline
31 & 97.58 & 98.1490377222891 & -0.569037722289082 \tabularnewline
32 & 97.57 & 97.7613126525208 & -0.191312652520779 \tabularnewline
33 & 96.7 & 97.6190488725659 & -0.919048872565853 \tabularnewline
34 & 96.72 & 97.0014591905863 & -0.281459190586304 \tabularnewline
35 & 96.72 & 94.2950889654141 & 2.42491103458588 \tabularnewline
36 & 96.74 & 96.1953253945258 & 0.544674605474185 \tabularnewline
37 & 101.2 & 96.0049217562433 & 5.1950782437567 \tabularnewline
38 & 100.59 & 99.8556564028802 & 0.734343597119803 \tabularnewline
39 & 100.58 & 100.670232858986 & -0.0902328589863544 \tabularnewline
40 & 99.62 & 100.884617330205 & -1.26461733020486 \tabularnewline
41 & 99.63 & 99.2639777699202 & 0.366022230079764 \tabularnewline
42 & 99.17 & 100.455393076185 & -1.28539307618483 \tabularnewline
43 & 99.17 & 99.5417583950396 & -0.371758395039578 \tabularnewline
44 & 98.99 & 99.4298603502854 & -0.439860350285372 \tabularnewline
45 & 98.92 & 98.9730655095769 & -0.0530655095769106 \tabularnewline
46 & 99.52 & 99.216705846145 & 0.303294153855035 \tabularnewline
47 & 99.45 & 97.6027939484527 & 1.84720605154727 \tabularnewline
48 & 99.04 & 98.6885713638971 & 0.351428636102924 \tabularnewline
49 & 99.23 & 99.3944235056678 & -0.164423505667756 \tabularnewline
50 & 98.71 & 98.0792814064491 & 0.630718593550881 \tabularnewline
51 & 98.73 & 98.6330884890347 & 0.0969115109653274 \tabularnewline
52 & 97.1 & 98.7406049437424 & -1.64060494374245 \tabularnewline
53 & 100.94 & 97.174565917516 & 3.76543408248398 \tabularnewline
54 & 100.93 & 100.698946905252 & 0.231053094747793 \tabularnewline
55 & 101.02 & 101.208608950324 & -0.188608950324138 \tabularnewline
56 & 101.01 & 101.26415298299 & -0.254152982990419 \tabularnewline
57 & 100.86 & 101.0765934109 & -0.216593410899677 \tabularnewline
58 & 100.56 & 101.307776806524 & -0.747776806524072 \tabularnewline
59 & 100.75 & 99.2336166955682 & 1.51638330443177 \tabularnewline
60 & 100.15 & 99.7644000874313 & 0.38559991256875 \tabularnewline
61 & 99.49 & 100.413380846996 & -0.923380846996324 \tabularnewline
62 & 99.15 & 98.6966391148627 & 0.453360885137315 \tabularnewline
63 & 99.15 & 99.0162454057161 & 0.133754594283886 \tabularnewline
64 & 99.14 & 98.7977346508972 & 0.34226534910276 \tabularnewline
65 & 98.77 & 99.9907140727612 & -1.2207140727612 \tabularnewline
66 & 98.8 & 98.8386101947791 & -0.0386101947790678 \tabularnewline
67 & 99.29 & 99.0400300370707 & 0.249969962929271 \tabularnewline
68 & 98.38 & 99.4226381101885 & -1.04263811018848 \tabularnewline
69 & 98.31 & 98.6160323457488 & -0.306032345748804 \tabularnewline
70 & 98.24 & 98.6525930858731 & -0.412593085873098 \tabularnewline
71 & 96.99 & 97.323334403107 & -0.333334403107003 \tabularnewline
72 & 96.81 & 96.1376444856177 & 0.672355514382346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284429&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]96.68[/C][C]98.3733787393162[/C][C]-1.69337873931619[/C][/ROW]
[ROW][C]14[/C][C]96.57[/C][C]96.9055469302379[/C][C]-0.335546930237939[/C][/ROW]
[ROW][C]15[/C][C]96.55[/C][C]96.5757183469189[/C][C]-0.0257183469188931[/C][/ROW]
[ROW][C]16[/C][C]96.78[/C][C]96.7319066157807[/C][C]0.0480933842192712[/C][/ROW]
[ROW][C]17[/C][C]95.99[/C][C]95.7876016564298[/C][C]0.202398343570167[/C][/ROW]
[ROW][C]18[/C][C]97.54[/C][C]97.1488293511451[/C][C]0.391170648854896[/C][/ROW]
[ROW][C]19[/C][C]97.45[/C][C]97.4466470416447[/C][C]0.00335295835526495[/C][/ROW]
[ROW][C]20[/C][C]97.58[/C][C]97.4521256104186[/C][C]0.127874389581422[/C][/ROW]
[ROW][C]21[/C][C]97.66[/C][C]97.5345979128881[/C][C]0.125402087111922[/C][/ROW]
[ROW][C]22[/C][C]97.67[/C][C]97.766152643899[/C][C]-0.0961526438989608[/C][/ROW]
[ROW][C]23[/C][C]97.71[/C][C]94.4678183763671[/C][C]3.24218162363287[/C][/ROW]
[ROW][C]24[/C][C]98.52[/C][C]97.4738210363047[/C][C]1.04617896369525[/C][/ROW]
[ROW][C]25[/C][C]98.87[/C][C]97.6292564143079[/C][C]1.24074358569214[/C][/ROW]
[ROW][C]26[/C][C]97.91[/C][C]98.8035911226809[/C][C]-0.893591122680945[/C][/ROW]
[ROW][C]27[/C][C]97.92[/C][C]98.1472608366533[/C][C]-0.227260836653315[/C][/ROW]
[ROW][C]28[/C][C]97.97[/C][C]98.2038003676569[/C][C]-0.233800367656926[/C][/ROW]
[ROW][C]29[/C][C]97.97[/C][C]97.1119501982239[/C][C]0.858049801776133[/C][/ROW]
[ROW][C]30[/C][C]97.97[/C][C]99.0734119943764[/C][C]-1.10341199437642[/C][/ROW]
[ROW][C]31[/C][C]97.58[/C][C]98.1490377222891[/C][C]-0.569037722289082[/C][/ROW]
[ROW][C]32[/C][C]97.57[/C][C]97.7613126525208[/C][C]-0.191312652520779[/C][/ROW]
[ROW][C]33[/C][C]96.7[/C][C]97.6190488725659[/C][C]-0.919048872565853[/C][/ROW]
[ROW][C]34[/C][C]96.72[/C][C]97.0014591905863[/C][C]-0.281459190586304[/C][/ROW]
[ROW][C]35[/C][C]96.72[/C][C]94.2950889654141[/C][C]2.42491103458588[/C][/ROW]
[ROW][C]36[/C][C]96.74[/C][C]96.1953253945258[/C][C]0.544674605474185[/C][/ROW]
[ROW][C]37[/C][C]101.2[/C][C]96.0049217562433[/C][C]5.1950782437567[/C][/ROW]
[ROW][C]38[/C][C]100.59[/C][C]99.8556564028802[/C][C]0.734343597119803[/C][/ROW]
[ROW][C]39[/C][C]100.58[/C][C]100.670232858986[/C][C]-0.0902328589863544[/C][/ROW]
[ROW][C]40[/C][C]99.62[/C][C]100.884617330205[/C][C]-1.26461733020486[/C][/ROW]
[ROW][C]41[/C][C]99.63[/C][C]99.2639777699202[/C][C]0.366022230079764[/C][/ROW]
[ROW][C]42[/C][C]99.17[/C][C]100.455393076185[/C][C]-1.28539307618483[/C][/ROW]
[ROW][C]43[/C][C]99.17[/C][C]99.5417583950396[/C][C]-0.371758395039578[/C][/ROW]
[ROW][C]44[/C][C]98.99[/C][C]99.4298603502854[/C][C]-0.439860350285372[/C][/ROW]
[ROW][C]45[/C][C]98.92[/C][C]98.9730655095769[/C][C]-0.0530655095769106[/C][/ROW]
[ROW][C]46[/C][C]99.52[/C][C]99.216705846145[/C][C]0.303294153855035[/C][/ROW]
[ROW][C]47[/C][C]99.45[/C][C]97.6027939484527[/C][C]1.84720605154727[/C][/ROW]
[ROW][C]48[/C][C]99.04[/C][C]98.6885713638971[/C][C]0.351428636102924[/C][/ROW]
[ROW][C]49[/C][C]99.23[/C][C]99.3944235056678[/C][C]-0.164423505667756[/C][/ROW]
[ROW][C]50[/C][C]98.71[/C][C]98.0792814064491[/C][C]0.630718593550881[/C][/ROW]
[ROW][C]51[/C][C]98.73[/C][C]98.6330884890347[/C][C]0.0969115109653274[/C][/ROW]
[ROW][C]52[/C][C]97.1[/C][C]98.7406049437424[/C][C]-1.64060494374245[/C][/ROW]
[ROW][C]53[/C][C]100.94[/C][C]97.174565917516[/C][C]3.76543408248398[/C][/ROW]
[ROW][C]54[/C][C]100.93[/C][C]100.698946905252[/C][C]0.231053094747793[/C][/ROW]
[ROW][C]55[/C][C]101.02[/C][C]101.208608950324[/C][C]-0.188608950324138[/C][/ROW]
[ROW][C]56[/C][C]101.01[/C][C]101.26415298299[/C][C]-0.254152982990419[/C][/ROW]
[ROW][C]57[/C][C]100.86[/C][C]101.0765934109[/C][C]-0.216593410899677[/C][/ROW]
[ROW][C]58[/C][C]100.56[/C][C]101.307776806524[/C][C]-0.747776806524072[/C][/ROW]
[ROW][C]59[/C][C]100.75[/C][C]99.2336166955682[/C][C]1.51638330443177[/C][/ROW]
[ROW][C]60[/C][C]100.15[/C][C]99.7644000874313[/C][C]0.38559991256875[/C][/ROW]
[ROW][C]61[/C][C]99.49[/C][C]100.413380846996[/C][C]-0.923380846996324[/C][/ROW]
[ROW][C]62[/C][C]99.15[/C][C]98.6966391148627[/C][C]0.453360885137315[/C][/ROW]
[ROW][C]63[/C][C]99.15[/C][C]99.0162454057161[/C][C]0.133754594283886[/C][/ROW]
[ROW][C]64[/C][C]99.14[/C][C]98.7977346508972[/C][C]0.34226534910276[/C][/ROW]
[ROW][C]65[/C][C]98.77[/C][C]99.9907140727612[/C][C]-1.2207140727612[/C][/ROW]
[ROW][C]66[/C][C]98.8[/C][C]98.8386101947791[/C][C]-0.0386101947790678[/C][/ROW]
[ROW][C]67[/C][C]99.29[/C][C]99.0400300370707[/C][C]0.249969962929271[/C][/ROW]
[ROW][C]68[/C][C]98.38[/C][C]99.4226381101885[/C][C]-1.04263811018848[/C][/ROW]
[ROW][C]69[/C][C]98.31[/C][C]98.6160323457488[/C][C]-0.306032345748804[/C][/ROW]
[ROW][C]70[/C][C]98.24[/C][C]98.6525930858731[/C][C]-0.412593085873098[/C][/ROW]
[ROW][C]71[/C][C]96.99[/C][C]97.323334403107[/C][C]-0.333334403107003[/C][/ROW]
[ROW][C]72[/C][C]96.81[/C][C]96.1376444856177[/C][C]0.672355514382346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284429&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284429&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
1396.6898.3733787393162-1.69337873931619
1496.5796.9055469302379-0.335546930237939
1596.5596.5757183469189-0.0257183469188931
1696.7896.73190661578070.0480933842192712
1795.9995.78760165642980.202398343570167
1897.5497.14882935114510.391170648854896
1997.4597.44664704164470.00335295835526495
2097.5897.45212561041860.127874389581422
2197.6697.53459791288810.125402087111922
2297.6797.766152643899-0.0961526438989608
2397.7194.46781837636713.24218162363287
2498.5297.47382103630471.04617896369525
2598.8797.62925641430791.24074358569214
2697.9198.8035911226809-0.893591122680945
2797.9298.1472608366533-0.227260836653315
2897.9798.2038003676569-0.233800367656926
2997.9797.11195019822390.858049801776133
3097.9799.0734119943764-1.10341199437642
3197.5898.1490377222891-0.569037722289082
3297.5797.7613126525208-0.191312652520779
3396.797.6190488725659-0.919048872565853
3496.7297.0014591905863-0.281459190586304
3596.7294.29508896541412.42491103458588
3696.7496.19532539452580.544674605474185
37101.296.00492175624335.1950782437567
38100.5999.85565640288020.734343597119803
39100.58100.670232858986-0.0902328589863544
4099.62100.884617330205-1.26461733020486
4199.6399.26397776992020.366022230079764
4299.17100.455393076185-1.28539307618483
4399.1799.5417583950396-0.371758395039578
4498.9999.4298603502854-0.439860350285372
4598.9298.9730655095769-0.0530655095769106
4699.5299.2167058461450.303294153855035
4799.4597.60279394845271.84720605154727
4899.0498.68857136389710.351428636102924
4999.2399.3944235056678-0.164423505667756
5098.7198.07928140644910.630718593550881
5198.7398.63308848903470.0969115109653274
5297.198.7406049437424-1.64060494374245
53100.9497.1745659175163.76543408248398
54100.93100.6989469052520.231053094747793
55101.02101.208608950324-0.188608950324138
56101.01101.26415298299-0.254152982990419
57100.86101.0765934109-0.216593410899677
58100.56101.307776806524-0.747776806524072
59100.7599.23361669556821.51638330443177
60100.1599.76440008743130.38559991256875
6199.49100.413380846996-0.923380846996324
6299.1598.69663911486270.453360885137315
6399.1599.01624540571610.133754594283886
6499.1498.79773465089720.34226534910276
6598.7799.9907140727612-1.2207140727612
6698.898.8386101947791-0.0386101947790678
6799.2999.04003003707070.249969962929271
6898.3899.4226381101885-1.04263811018848
6998.3198.6160323457488-0.306032345748804
7098.2498.6525930858731-0.412593085873098
7196.9997.323334403107-0.333334403107003
7296.8196.13764448561770.672355514382346







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7396.70889475219294.355197107455399.0625923969287
7496.00125240748692.99863301196299.0038718030101
7595.880478440801892.335997043995299.4249598376085
7695.585152050167991.56227970235199.6080243979848
7796.152351474886391.6939977643629100.61070518541
7896.202765247707491.340221682203101.065308813212
7996.487258314215491.2445040579205101.73001257051
8096.383068373545490.7791341738296101.987002573261
8196.549895621935690.6002836341532102.499507609718
8296.802752806159490.5203472976498103.085158314669
8395.816832428580789.2125140739353102.421150783226
8495.115205540073188.1982826271137102.032128453032

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 96.708894752192 & 94.3551971074553 & 99.0625923969287 \tabularnewline
74 & 96.001252407486 & 92.998633011962 & 99.0038718030101 \tabularnewline
75 & 95.8804784408018 & 92.3359970439952 & 99.4249598376085 \tabularnewline
76 & 95.5851520501679 & 91.562279702351 & 99.6080243979848 \tabularnewline
77 & 96.1523514748863 & 91.6939977643629 & 100.61070518541 \tabularnewline
78 & 96.2027652477074 & 91.340221682203 & 101.065308813212 \tabularnewline
79 & 96.4872583142154 & 91.2445040579205 & 101.73001257051 \tabularnewline
80 & 96.3830683735454 & 90.7791341738296 & 101.987002573261 \tabularnewline
81 & 96.5498956219356 & 90.6002836341532 & 102.499507609718 \tabularnewline
82 & 96.8027528061594 & 90.5203472976498 & 103.085158314669 \tabularnewline
83 & 95.8168324285807 & 89.2125140739353 & 102.421150783226 \tabularnewline
84 & 95.1152055400731 & 88.1982826271137 & 102.032128453032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284429&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]96.708894752192[/C][C]94.3551971074553[/C][C]99.0625923969287[/C][/ROW]
[ROW][C]74[/C][C]96.001252407486[/C][C]92.998633011962[/C][C]99.0038718030101[/C][/ROW]
[ROW][C]75[/C][C]95.8804784408018[/C][C]92.3359970439952[/C][C]99.4249598376085[/C][/ROW]
[ROW][C]76[/C][C]95.5851520501679[/C][C]91.562279702351[/C][C]99.6080243979848[/C][/ROW]
[ROW][C]77[/C][C]96.1523514748863[/C][C]91.6939977643629[/C][C]100.61070518541[/C][/ROW]
[ROW][C]78[/C][C]96.2027652477074[/C][C]91.340221682203[/C][C]101.065308813212[/C][/ROW]
[ROW][C]79[/C][C]96.4872583142154[/C][C]91.2445040579205[/C][C]101.73001257051[/C][/ROW]
[ROW][C]80[/C][C]96.3830683735454[/C][C]90.7791341738296[/C][C]101.987002573261[/C][/ROW]
[ROW][C]81[/C][C]96.5498956219356[/C][C]90.6002836341532[/C][C]102.499507609718[/C][/ROW]
[ROW][C]82[/C][C]96.8027528061594[/C][C]90.5203472976498[/C][C]103.085158314669[/C][/ROW]
[ROW][C]83[/C][C]95.8168324285807[/C][C]89.2125140739353[/C][C]102.421150783226[/C][/ROW]
[ROW][C]84[/C][C]95.1152055400731[/C][C]88.1982826271137[/C][C]102.032128453032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284429&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284429&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
7396.70889475219294.355197107455399.0625923969287
7496.00125240748692.99863301196299.0038718030101
7595.880478440801892.335997043995299.4249598376085
7695.585152050167991.56227970235199.6080243979848
7796.152351474886391.6939977643629100.61070518541
7896.202765247707491.340221682203101.065308813212
7996.487258314215491.2445040579205101.73001257051
8096.383068373545490.7791341738296101.987002573261
8196.549895621935690.6002836341532102.499507609718
8296.802752806159490.5203472976498103.085158314669
8395.816832428580789.2125140739353102.421150783226
8495.115205540073188.1982826271137102.032128453032



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')