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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 25 Nov 2015 14:14:45 +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/25/t1448461122kky3s1veoshbpnz.htm/, Retrieved Wed, 15 May 2024 08:12:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284130, Retrieved Wed, 15 May 2024 08:12:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2015-11-25 14:14:45] [25948359fd1b125334369436fee15348] [Current]
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Dataseries X:
98.91
98.15
98.59
98.6
98.7
98.33
98.33
98.6
98.52
99.17
99.49
98.83
98.83
97.39
99.28
98.78
98.75
98.47
98.47
97.82
97.79
97.96
98.21
98.34
98.34
98.49
98.14
98.05
97.77
97.59
97.59
97.67
97.67
97.36
97.31
97.24
97.24
96.89
96.48
96.47
97.13
97.21
97.43
97.98
97.97
98.2
98.67
98.75
98.77
98.72
99.23
99.67
99.76
99.57
99.57
100.21
100.62
101.05
101.42
101.42
101.52
101.87
101.53
101.77
101.76
102.04
102.05
101.9
102.17
102.14
102.09
102.27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284130&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284130&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.533553580778042
beta0.0842910696839133
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.533553580778042 \tabularnewline
beta & 0.0842910696839133 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284130&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]0.533553580778042[/C][/ROW]
[ROW][C]beta[/C][C]0.0842910696839133[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284130&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
alpha0.533553580778042
beta0.0842910696839133
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1398.8398.77294604700860.05705395299141
1497.3997.36997575701060.0200242429894359
1599.2899.3143986989863-0.0343986989863367
1698.7898.8561537117819-0.0761537117819273
1798.7598.8651219326921-0.115121932692063
1898.4798.5681210487857-0.0981210487856572
1998.4798.02161150407140.448388495928555
2097.8298.5522764859963-0.732276485996323
2197.7998.0379768480501-0.247976848050044
2297.9698.4617578877538-0.50175788775384
2398.2198.4242338517321-0.214233851732146
2498.3497.55215105051440.787848949485578
2598.3497.93302829090320.406971709096851
2698.4996.68343852655631.80656147344367
2798.1499.6199898199354-1.47998981993543
2898.0598.3702547099843-0.32025470998434
2997.7798.2191139045296-0.449113904529625
3097.5997.7251280430942-0.135128043094213
3197.5997.3854139925930.20458600740703
3297.6797.19593889412260.474061105877368
3397.6797.56609698144730.103903018552657
3497.3698.0899870537621-0.729987053762102
3597.3198.0852782797031-0.775278279703144
3697.2497.3765070419907-0.136507041990711
3797.2497.04020109751270.199798902487274
3896.8996.27725891476420.612741085235783
3996.4896.9345040814372-0.454504081437179
4096.4796.7096559398113-0.239655939811271
4197.1396.4818189112750.648181088724954
4297.2196.70951175560440.500488244395598
4397.4396.8857329869990.54426701300099
4497.9897.0368098797340.943190120265996
4597.9797.53933131318390.430668686816063
4698.297.91801602913360.281983970866406
4798.6798.54704696280950.122953037190456
4898.7598.7708045686365-0.020804568636521
4998.7798.8136261283315-0.0436261283314678
5098.7298.26299663372060.457003366279409
5199.2398.48190816150360.748091838496364
5299.6799.19558330153140.474416698468573
5399.7699.9916440263933-0.231644026393269
5499.5799.8702164886331-0.300216488633069
5599.5799.7928328131809-0.222832813180887
56100.2199.83939122678260.370608773217398
57100.6299.89028900966850.729710990331526
58101.05100.4655673983280.584432601672034
59101.42101.301785771480.118214228519818
60101.42101.575740925322-0.155740925322448
61101.52101.649634249758-0.1296342497578
62101.87101.3964761127020.473523887298214
63101.53101.870566853415-0.340566853415069
64101.77101.937355794756-0.167355794756091
65101.76102.094420395596-0.334420395595529
66102.04101.9143119191220.125688080878021
67102.05102.147562178491-0.0975621784905059
68101.9102.590697475886-0.690697475886068
69102.17102.248032060494-0.0780320604942943
70102.14102.293442999701-0.153442999701468
71102.09102.454185573445-0.364185573445482
72102.27102.2569600924450.0130399075549974

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.83 & 98.7729460470086 & 0.05705395299141 \tabularnewline
14 & 97.39 & 97.3699757570106 & 0.0200242429894359 \tabularnewline
15 & 99.28 & 99.3143986989863 & -0.0343986989863367 \tabularnewline
16 & 98.78 & 98.8561537117819 & -0.0761537117819273 \tabularnewline
17 & 98.75 & 98.8651219326921 & -0.115121932692063 \tabularnewline
18 & 98.47 & 98.5681210487857 & -0.0981210487856572 \tabularnewline
19 & 98.47 & 98.0216115040714 & 0.448388495928555 \tabularnewline
20 & 97.82 & 98.5522764859963 & -0.732276485996323 \tabularnewline
21 & 97.79 & 98.0379768480501 & -0.247976848050044 \tabularnewline
22 & 97.96 & 98.4617578877538 & -0.50175788775384 \tabularnewline
23 & 98.21 & 98.4242338517321 & -0.214233851732146 \tabularnewline
24 & 98.34 & 97.5521510505144 & 0.787848949485578 \tabularnewline
25 & 98.34 & 97.9330282909032 & 0.406971709096851 \tabularnewline
26 & 98.49 & 96.6834385265563 & 1.80656147344367 \tabularnewline
27 & 98.14 & 99.6199898199354 & -1.47998981993543 \tabularnewline
28 & 98.05 & 98.3702547099843 & -0.32025470998434 \tabularnewline
29 & 97.77 & 98.2191139045296 & -0.449113904529625 \tabularnewline
30 & 97.59 & 97.7251280430942 & -0.135128043094213 \tabularnewline
31 & 97.59 & 97.385413992593 & 0.20458600740703 \tabularnewline
32 & 97.67 & 97.1959388941226 & 0.474061105877368 \tabularnewline
33 & 97.67 & 97.5660969814473 & 0.103903018552657 \tabularnewline
34 & 97.36 & 98.0899870537621 & -0.729987053762102 \tabularnewline
35 & 97.31 & 98.0852782797031 & -0.775278279703144 \tabularnewline
36 & 97.24 & 97.3765070419907 & -0.136507041990711 \tabularnewline
37 & 97.24 & 97.0402010975127 & 0.199798902487274 \tabularnewline
38 & 96.89 & 96.2772589147642 & 0.612741085235783 \tabularnewline
39 & 96.48 & 96.9345040814372 & -0.454504081437179 \tabularnewline
40 & 96.47 & 96.7096559398113 & -0.239655939811271 \tabularnewline
41 & 97.13 & 96.481818911275 & 0.648181088724954 \tabularnewline
42 & 97.21 & 96.7095117556044 & 0.500488244395598 \tabularnewline
43 & 97.43 & 96.885732986999 & 0.54426701300099 \tabularnewline
44 & 97.98 & 97.036809879734 & 0.943190120265996 \tabularnewline
45 & 97.97 & 97.5393313131839 & 0.430668686816063 \tabularnewline
46 & 98.2 & 97.9180160291336 & 0.281983970866406 \tabularnewline
47 & 98.67 & 98.5470469628095 & 0.122953037190456 \tabularnewline
48 & 98.75 & 98.7708045686365 & -0.020804568636521 \tabularnewline
49 & 98.77 & 98.8136261283315 & -0.0436261283314678 \tabularnewline
50 & 98.72 & 98.2629966337206 & 0.457003366279409 \tabularnewline
51 & 99.23 & 98.4819081615036 & 0.748091838496364 \tabularnewline
52 & 99.67 & 99.1955833015314 & 0.474416698468573 \tabularnewline
53 & 99.76 & 99.9916440263933 & -0.231644026393269 \tabularnewline
54 & 99.57 & 99.8702164886331 & -0.300216488633069 \tabularnewline
55 & 99.57 & 99.7928328131809 & -0.222832813180887 \tabularnewline
56 & 100.21 & 99.8393912267826 & 0.370608773217398 \tabularnewline
57 & 100.62 & 99.8902890096685 & 0.729710990331526 \tabularnewline
58 & 101.05 & 100.465567398328 & 0.584432601672034 \tabularnewline
59 & 101.42 & 101.30178577148 & 0.118214228519818 \tabularnewline
60 & 101.42 & 101.575740925322 & -0.155740925322448 \tabularnewline
61 & 101.52 & 101.649634249758 & -0.1296342497578 \tabularnewline
62 & 101.87 & 101.396476112702 & 0.473523887298214 \tabularnewline
63 & 101.53 & 101.870566853415 & -0.340566853415069 \tabularnewline
64 & 101.77 & 101.937355794756 & -0.167355794756091 \tabularnewline
65 & 101.76 & 102.094420395596 & -0.334420395595529 \tabularnewline
66 & 102.04 & 101.914311919122 & 0.125688080878021 \tabularnewline
67 & 102.05 & 102.147562178491 & -0.0975621784905059 \tabularnewline
68 & 101.9 & 102.590697475886 & -0.690697475886068 \tabularnewline
69 & 102.17 & 102.248032060494 & -0.0780320604942943 \tabularnewline
70 & 102.14 & 102.293442999701 & -0.153442999701468 \tabularnewline
71 & 102.09 & 102.454185573445 & -0.364185573445482 \tabularnewline
72 & 102.27 & 102.256960092445 & 0.0130399075549974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284130&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]98.83[/C][C]98.7729460470086[/C][C]0.05705395299141[/C][/ROW]
[ROW][C]14[/C][C]97.39[/C][C]97.3699757570106[/C][C]0.0200242429894359[/C][/ROW]
[ROW][C]15[/C][C]99.28[/C][C]99.3143986989863[/C][C]-0.0343986989863367[/C][/ROW]
[ROW][C]16[/C][C]98.78[/C][C]98.8561537117819[/C][C]-0.0761537117819273[/C][/ROW]
[ROW][C]17[/C][C]98.75[/C][C]98.8651219326921[/C][C]-0.115121932692063[/C][/ROW]
[ROW][C]18[/C][C]98.47[/C][C]98.5681210487857[/C][C]-0.0981210487856572[/C][/ROW]
[ROW][C]19[/C][C]98.47[/C][C]98.0216115040714[/C][C]0.448388495928555[/C][/ROW]
[ROW][C]20[/C][C]97.82[/C][C]98.5522764859963[/C][C]-0.732276485996323[/C][/ROW]
[ROW][C]21[/C][C]97.79[/C][C]98.0379768480501[/C][C]-0.247976848050044[/C][/ROW]
[ROW][C]22[/C][C]97.96[/C][C]98.4617578877538[/C][C]-0.50175788775384[/C][/ROW]
[ROW][C]23[/C][C]98.21[/C][C]98.4242338517321[/C][C]-0.214233851732146[/C][/ROW]
[ROW][C]24[/C][C]98.34[/C][C]97.5521510505144[/C][C]0.787848949485578[/C][/ROW]
[ROW][C]25[/C][C]98.34[/C][C]97.9330282909032[/C][C]0.406971709096851[/C][/ROW]
[ROW][C]26[/C][C]98.49[/C][C]96.6834385265563[/C][C]1.80656147344367[/C][/ROW]
[ROW][C]27[/C][C]98.14[/C][C]99.6199898199354[/C][C]-1.47998981993543[/C][/ROW]
[ROW][C]28[/C][C]98.05[/C][C]98.3702547099843[/C][C]-0.32025470998434[/C][/ROW]
[ROW][C]29[/C][C]97.77[/C][C]98.2191139045296[/C][C]-0.449113904529625[/C][/ROW]
[ROW][C]30[/C][C]97.59[/C][C]97.7251280430942[/C][C]-0.135128043094213[/C][/ROW]
[ROW][C]31[/C][C]97.59[/C][C]97.385413992593[/C][C]0.20458600740703[/C][/ROW]
[ROW][C]32[/C][C]97.67[/C][C]97.1959388941226[/C][C]0.474061105877368[/C][/ROW]
[ROW][C]33[/C][C]97.67[/C][C]97.5660969814473[/C][C]0.103903018552657[/C][/ROW]
[ROW][C]34[/C][C]97.36[/C][C]98.0899870537621[/C][C]-0.729987053762102[/C][/ROW]
[ROW][C]35[/C][C]97.31[/C][C]98.0852782797031[/C][C]-0.775278279703144[/C][/ROW]
[ROW][C]36[/C][C]97.24[/C][C]97.3765070419907[/C][C]-0.136507041990711[/C][/ROW]
[ROW][C]37[/C][C]97.24[/C][C]97.0402010975127[/C][C]0.199798902487274[/C][/ROW]
[ROW][C]38[/C][C]96.89[/C][C]96.2772589147642[/C][C]0.612741085235783[/C][/ROW]
[ROW][C]39[/C][C]96.48[/C][C]96.9345040814372[/C][C]-0.454504081437179[/C][/ROW]
[ROW][C]40[/C][C]96.47[/C][C]96.7096559398113[/C][C]-0.239655939811271[/C][/ROW]
[ROW][C]41[/C][C]97.13[/C][C]96.481818911275[/C][C]0.648181088724954[/C][/ROW]
[ROW][C]42[/C][C]97.21[/C][C]96.7095117556044[/C][C]0.500488244395598[/C][/ROW]
[ROW][C]43[/C][C]97.43[/C][C]96.885732986999[/C][C]0.54426701300099[/C][/ROW]
[ROW][C]44[/C][C]97.98[/C][C]97.036809879734[/C][C]0.943190120265996[/C][/ROW]
[ROW][C]45[/C][C]97.97[/C][C]97.5393313131839[/C][C]0.430668686816063[/C][/ROW]
[ROW][C]46[/C][C]98.2[/C][C]97.9180160291336[/C][C]0.281983970866406[/C][/ROW]
[ROW][C]47[/C][C]98.67[/C][C]98.5470469628095[/C][C]0.122953037190456[/C][/ROW]
[ROW][C]48[/C][C]98.75[/C][C]98.7708045686365[/C][C]-0.020804568636521[/C][/ROW]
[ROW][C]49[/C][C]98.77[/C][C]98.8136261283315[/C][C]-0.0436261283314678[/C][/ROW]
[ROW][C]50[/C][C]98.72[/C][C]98.2629966337206[/C][C]0.457003366279409[/C][/ROW]
[ROW][C]51[/C][C]99.23[/C][C]98.4819081615036[/C][C]0.748091838496364[/C][/ROW]
[ROW][C]52[/C][C]99.67[/C][C]99.1955833015314[/C][C]0.474416698468573[/C][/ROW]
[ROW][C]53[/C][C]99.76[/C][C]99.9916440263933[/C][C]-0.231644026393269[/C][/ROW]
[ROW][C]54[/C][C]99.57[/C][C]99.8702164886331[/C][C]-0.300216488633069[/C][/ROW]
[ROW][C]55[/C][C]99.57[/C][C]99.7928328131809[/C][C]-0.222832813180887[/C][/ROW]
[ROW][C]56[/C][C]100.21[/C][C]99.8393912267826[/C][C]0.370608773217398[/C][/ROW]
[ROW][C]57[/C][C]100.62[/C][C]99.8902890096685[/C][C]0.729710990331526[/C][/ROW]
[ROW][C]58[/C][C]101.05[/C][C]100.465567398328[/C][C]0.584432601672034[/C][/ROW]
[ROW][C]59[/C][C]101.42[/C][C]101.30178577148[/C][C]0.118214228519818[/C][/ROW]
[ROW][C]60[/C][C]101.42[/C][C]101.575740925322[/C][C]-0.155740925322448[/C][/ROW]
[ROW][C]61[/C][C]101.52[/C][C]101.649634249758[/C][C]-0.1296342497578[/C][/ROW]
[ROW][C]62[/C][C]101.87[/C][C]101.396476112702[/C][C]0.473523887298214[/C][/ROW]
[ROW][C]63[/C][C]101.53[/C][C]101.870566853415[/C][C]-0.340566853415069[/C][/ROW]
[ROW][C]64[/C][C]101.77[/C][C]101.937355794756[/C][C]-0.167355794756091[/C][/ROW]
[ROW][C]65[/C][C]101.76[/C][C]102.094420395596[/C][C]-0.334420395595529[/C][/ROW]
[ROW][C]66[/C][C]102.04[/C][C]101.914311919122[/C][C]0.125688080878021[/C][/ROW]
[ROW][C]67[/C][C]102.05[/C][C]102.147562178491[/C][C]-0.0975621784905059[/C][/ROW]
[ROW][C]68[/C][C]101.9[/C][C]102.590697475886[/C][C]-0.690697475886068[/C][/ROW]
[ROW][C]69[/C][C]102.17[/C][C]102.248032060494[/C][C]-0.0780320604942943[/C][/ROW]
[ROW][C]70[/C][C]102.14[/C][C]102.293442999701[/C][C]-0.153442999701468[/C][/ROW]
[ROW][C]71[/C][C]102.09[/C][C]102.454185573445[/C][C]-0.364185573445482[/C][/ROW]
[ROW][C]72[/C][C]102.27[/C][C]102.256960092445[/C][C]0.0130399075549974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284130&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284130&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
1398.8398.77294604700860.05705395299141
1497.3997.36997575701060.0200242429894359
1599.2899.3143986989863-0.0343986989863367
1698.7898.8561537117819-0.0761537117819273
1798.7598.8651219326921-0.115121932692063
1898.4798.5681210487857-0.0981210487856572
1998.4798.02161150407140.448388495928555
2097.8298.5522764859963-0.732276485996323
2197.7998.0379768480501-0.247976848050044
2297.9698.4617578877538-0.50175788775384
2398.2198.4242338517321-0.214233851732146
2498.3497.55215105051440.787848949485578
2598.3497.93302829090320.406971709096851
2698.4996.68343852655631.80656147344367
2798.1499.6199898199354-1.47998981993543
2898.0598.3702547099843-0.32025470998434
2997.7798.2191139045296-0.449113904529625
3097.5997.7251280430942-0.135128043094213
3197.5997.3854139925930.20458600740703
3297.6797.19593889412260.474061105877368
3397.6797.56609698144730.103903018552657
3497.3698.0899870537621-0.729987053762102
3597.3198.0852782797031-0.775278279703144
3697.2497.3765070419907-0.136507041990711
3797.2497.04020109751270.199798902487274
3896.8996.27725891476420.612741085235783
3996.4896.9345040814372-0.454504081437179
4096.4796.7096559398113-0.239655939811271
4197.1396.4818189112750.648181088724954
4297.2196.70951175560440.500488244395598
4397.4396.8857329869990.54426701300099
4497.9897.0368098797340.943190120265996
4597.9797.53933131318390.430668686816063
4698.297.91801602913360.281983970866406
4798.6798.54704696280950.122953037190456
4898.7598.7708045686365-0.020804568636521
4998.7798.8136261283315-0.0436261283314678
5098.7298.26299663372060.457003366279409
5199.2398.48190816150360.748091838496364
5299.6799.19558330153140.474416698468573
5399.7699.9916440263933-0.231644026393269
5499.5799.8702164886331-0.300216488633069
5599.5799.7928328131809-0.222832813180887
56100.2199.83939122678260.370608773217398
57100.6299.89028900966850.729710990331526
58101.05100.4655673983280.584432601672034
59101.42101.301785771480.118214228519818
60101.42101.575740925322-0.155740925322448
61101.52101.649634249758-0.1296342497578
62101.87101.3964761127020.473523887298214
63101.53101.870566853415-0.340566853415069
64101.77101.937355794756-0.167355794756091
65101.76102.094420395596-0.334420395595529
66102.04101.9143119191220.125688080878021
67102.05102.147562178491-0.0975621784905059
68101.9102.590697475886-0.690697475886068
69102.17102.248032060494-0.0780320604942943
70102.14102.293442999701-0.153442999701468
71102.09102.454185573445-0.364185573445482
72102.27102.2569600924450.0130399075549974







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.354666023132101.359022263178103.350309783086
74102.379427425737101.229170599359103.529684252115
75102.127253688551100.820171111821103.434336265282
76102.37797915704100.911200747715103.844757566366
77102.475369167915100.845638207394104.105100128436
78102.632306810297100.836136638715104.428476981878
79102.632707757103100.666477387868104.598938126338
80102.793965907825100.653980660076104.933951155574
81103.079397523908100.761928561793105.396866486022
82103.108574315077100.60988494417105.607263685984
83103.237094476185100.553457853173105.920731099198
84103.410723441038100.538434568957106.283012313118

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.354666023132 & 101.359022263178 & 103.350309783086 \tabularnewline
74 & 102.379427425737 & 101.229170599359 & 103.529684252115 \tabularnewline
75 & 102.127253688551 & 100.820171111821 & 103.434336265282 \tabularnewline
76 & 102.37797915704 & 100.911200747715 & 103.844757566366 \tabularnewline
77 & 102.475369167915 & 100.845638207394 & 104.105100128436 \tabularnewline
78 & 102.632306810297 & 100.836136638715 & 104.428476981878 \tabularnewline
79 & 102.632707757103 & 100.666477387868 & 104.598938126338 \tabularnewline
80 & 102.793965907825 & 100.653980660076 & 104.933951155574 \tabularnewline
81 & 103.079397523908 & 100.761928561793 & 105.396866486022 \tabularnewline
82 & 103.108574315077 & 100.60988494417 & 105.607263685984 \tabularnewline
83 & 103.237094476185 & 100.553457853173 & 105.920731099198 \tabularnewline
84 & 103.410723441038 & 100.538434568957 & 106.283012313118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284130&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]102.354666023132[/C][C]101.359022263178[/C][C]103.350309783086[/C][/ROW]
[ROW][C]74[/C][C]102.379427425737[/C][C]101.229170599359[/C][C]103.529684252115[/C][/ROW]
[ROW][C]75[/C][C]102.127253688551[/C][C]100.820171111821[/C][C]103.434336265282[/C][/ROW]
[ROW][C]76[/C][C]102.37797915704[/C][C]100.911200747715[/C][C]103.844757566366[/C][/ROW]
[ROW][C]77[/C][C]102.475369167915[/C][C]100.845638207394[/C][C]104.105100128436[/C][/ROW]
[ROW][C]78[/C][C]102.632306810297[/C][C]100.836136638715[/C][C]104.428476981878[/C][/ROW]
[ROW][C]79[/C][C]102.632707757103[/C][C]100.666477387868[/C][C]104.598938126338[/C][/ROW]
[ROW][C]80[/C][C]102.793965907825[/C][C]100.653980660076[/C][C]104.933951155574[/C][/ROW]
[ROW][C]81[/C][C]103.079397523908[/C][C]100.761928561793[/C][C]105.396866486022[/C][/ROW]
[ROW][C]82[/C][C]103.108574315077[/C][C]100.60988494417[/C][C]105.607263685984[/C][/ROW]
[ROW][C]83[/C][C]103.237094476185[/C][C]100.553457853173[/C][C]105.920731099198[/C][/ROW]
[ROW][C]84[/C][C]103.410723441038[/C][C]100.538434568957[/C][C]106.283012313118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284130&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284130&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
73102.354666023132101.359022263178103.350309783086
74102.379427425737101.229170599359103.529684252115
75102.127253688551100.820171111821103.434336265282
76102.37797915704100.911200747715103.844757566366
77102.475369167915100.845638207394104.105100128436
78102.632306810297100.836136638715104.428476981878
79102.632707757103100.666477387868104.598938126338
80102.793965907825100.653980660076104.933951155574
81103.079397523908100.761928561793105.396866486022
82103.108574315077100.60988494417105.607263685984
83103.237094476185100.553457853173105.920731099198
84103.410723441038100.538434568957106.283012313118



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):
par3 <- 'additive'
par2 <- 'Double'
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')