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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Jan 2013 16:34:08 -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/2013/Jan/14/t1358199269i6129xm8nzcsmje.htm/, Retrieved Sat, 27 Apr 2024 15:22:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205376, Retrieved Sat, 27 Apr 2024 15:22:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-14 21:34:08] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
106,68
109,73
108,06
111,33
105,66
103,65
100,34
100,56
102,67
101,5
102,35
104,98
106,31
103,73
106,62
108,54
105,12
105,29
104,62
104,34
108,23
107,6
106,87
107,96
108,34
109,04
106,95
105,59
108,08
108,48
106,84
105,6
106,9
106,84
106,81
106,98
107,53
107,37
106,98
108,94
106,38
109,02
106,53
105,02
109,7
108,39
110,18
109,54
109,1
110,85
112,23
110,58
110,77
108,08
108,05
108,87
109,61
111,27
107,61
110,98
106,63
106,83
108,77
106,12
106,8
106,34
105,16
107,97
106,76
108,78
105,58
109,22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205376&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205376&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205376&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.758720703032662
beta0.233067049683503
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.758720703032662 \tabularnewline
beta & 0.233067049683503 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205376&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]0.758720703032662[/C][/ROW]
[ROW][C]beta[/C][C]0.233067049683503[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205376&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205376&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
alpha0.758720703032662
beta0.233067049683503
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3108.06112.78-4.72
4111.33111.414187485559-0.0841874855588571
5105.66113.55077479276-7.89077479276023
6103.65108.368994922406-4.7189949224059
7100.34104.759237039706-4.41923703970562
8100.56100.595445627519-0.0354456275191097
9102.6799.75145956812262.91854043187742
10101.5101.664817552654-0.164817552653986
11102.35101.2096228508291.14037714917065
12104.98101.946362470313.03363752968997
13106.31104.656004542511.65399545749041
14103.73106.611364252728-2.88136425272782
15106.62104.6161329586052.00386704139484
16108.54106.6817771977571.85822280224309
17105.12108.965512870707-3.84551287070745
18105.29106.241693411792-0.951693411792334
19104.62105.545184080453-0.925184080453093
20104.34104.705185040058-0.365185040057924
21108.23104.2254921736754.00450782632498
22107.6107.769304065601-0.169304065601409
23106.87108.1164199533-1.24641995330045
24107.96107.4258977923670.534102207633239
25108.34108.1807414437550.159258556244907
26109.04108.6793455921890.360654407811055
27106.95109.394528469958-2.44452846995802
28105.59107.549088218841-1.95908821884095
29108.08105.7255304893962.35446951060436
30108.48107.5911057391690.888894260831378
31106.84108.501904362391-1.66190436239073
32105.6107.183480066171-1.58348006617052
33106.9105.6445466999351.25545330006473
34106.84106.4815761702270.358423829773329
35106.81106.7013918980740.108608101925995
36106.98106.7508727355690.22912726443063
37107.53106.932311171530.597688828469941
38107.37107.49907588302-0.129075883020022
39106.98107.491604312406-0.511604312405552
40108.94107.1034320820171.83656791798298
41106.38108.821632176705-2.44163217670508
42109.02106.862112643742.15788735625964
43106.53108.773929058646-2.24392905864555
44105.02106.949195979619-1.92919597961932
45109.7105.0221122848774.67788771512268
46108.39108.935163739061-0.545163739060655
47110.18108.7889750938091.39102490619096
48109.54110.357791681861-0.817791681861323
49109.1110.106121005879-1.00612100587935
50110.85109.5336457824041.31635421759556
51112.23110.9560551898071.27394481019279
52110.58112.571562924278-1.99156292427823
53110.77111.357288694802-0.587288694801728
54108.08111.104614494127-3.02461449412688
55108.05108.467839712286-0.417839712286153
56108.87107.7349911610561.13500883894406
57109.61108.3810277405551.22897225944523
58111.27109.3156789131011.9543210868988
59107.61111.146255319624-3.53625531962402
60110.98108.185691820142.79430817985971
61106.63110.52238323732-3.89238323732015
62106.83107.097442431355-0.26744243135488
63108.77106.3755266692942.39447333070589
64106.12108.09668291915-1.97668291915021
65106.8106.1518100590670.648189940933037
66106.34106.3131038202150.0268961797846714
67105.16106.007765268783-0.84776526878278
68107.97104.8888902655253.08110973447462
69106.76107.295775315349-0.535775315348616
70108.78106.8637121504541.91628784954649
71105.58108.630942611881-3.05094261188107
72109.22106.0899257736363.13007422636353

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 108.06 & 112.78 & -4.72 \tabularnewline
4 & 111.33 & 111.414187485559 & -0.0841874855588571 \tabularnewline
5 & 105.66 & 113.55077479276 & -7.89077479276023 \tabularnewline
6 & 103.65 & 108.368994922406 & -4.7189949224059 \tabularnewline
7 & 100.34 & 104.759237039706 & -4.41923703970562 \tabularnewline
8 & 100.56 & 100.595445627519 & -0.0354456275191097 \tabularnewline
9 & 102.67 & 99.7514595681226 & 2.91854043187742 \tabularnewline
10 & 101.5 & 101.664817552654 & -0.164817552653986 \tabularnewline
11 & 102.35 & 101.209622850829 & 1.14037714917065 \tabularnewline
12 & 104.98 & 101.94636247031 & 3.03363752968997 \tabularnewline
13 & 106.31 & 104.65600454251 & 1.65399545749041 \tabularnewline
14 & 103.73 & 106.611364252728 & -2.88136425272782 \tabularnewline
15 & 106.62 & 104.616132958605 & 2.00386704139484 \tabularnewline
16 & 108.54 & 106.681777197757 & 1.85822280224309 \tabularnewline
17 & 105.12 & 108.965512870707 & -3.84551287070745 \tabularnewline
18 & 105.29 & 106.241693411792 & -0.951693411792334 \tabularnewline
19 & 104.62 & 105.545184080453 & -0.925184080453093 \tabularnewline
20 & 104.34 & 104.705185040058 & -0.365185040057924 \tabularnewline
21 & 108.23 & 104.225492173675 & 4.00450782632498 \tabularnewline
22 & 107.6 & 107.769304065601 & -0.169304065601409 \tabularnewline
23 & 106.87 & 108.1164199533 & -1.24641995330045 \tabularnewline
24 & 107.96 & 107.425897792367 & 0.534102207633239 \tabularnewline
25 & 108.34 & 108.180741443755 & 0.159258556244907 \tabularnewline
26 & 109.04 & 108.679345592189 & 0.360654407811055 \tabularnewline
27 & 106.95 & 109.394528469958 & -2.44452846995802 \tabularnewline
28 & 105.59 & 107.549088218841 & -1.95908821884095 \tabularnewline
29 & 108.08 & 105.725530489396 & 2.35446951060436 \tabularnewline
30 & 108.48 & 107.591105739169 & 0.888894260831378 \tabularnewline
31 & 106.84 & 108.501904362391 & -1.66190436239073 \tabularnewline
32 & 105.6 & 107.183480066171 & -1.58348006617052 \tabularnewline
33 & 106.9 & 105.644546699935 & 1.25545330006473 \tabularnewline
34 & 106.84 & 106.481576170227 & 0.358423829773329 \tabularnewline
35 & 106.81 & 106.701391898074 & 0.108608101925995 \tabularnewline
36 & 106.98 & 106.750872735569 & 0.22912726443063 \tabularnewline
37 & 107.53 & 106.93231117153 & 0.597688828469941 \tabularnewline
38 & 107.37 & 107.49907588302 & -0.129075883020022 \tabularnewline
39 & 106.98 & 107.491604312406 & -0.511604312405552 \tabularnewline
40 & 108.94 & 107.103432082017 & 1.83656791798298 \tabularnewline
41 & 106.38 & 108.821632176705 & -2.44163217670508 \tabularnewline
42 & 109.02 & 106.86211264374 & 2.15788735625964 \tabularnewline
43 & 106.53 & 108.773929058646 & -2.24392905864555 \tabularnewline
44 & 105.02 & 106.949195979619 & -1.92919597961932 \tabularnewline
45 & 109.7 & 105.022112284877 & 4.67788771512268 \tabularnewline
46 & 108.39 & 108.935163739061 & -0.545163739060655 \tabularnewline
47 & 110.18 & 108.788975093809 & 1.39102490619096 \tabularnewline
48 & 109.54 & 110.357791681861 & -0.817791681861323 \tabularnewline
49 & 109.1 & 110.106121005879 & -1.00612100587935 \tabularnewline
50 & 110.85 & 109.533645782404 & 1.31635421759556 \tabularnewline
51 & 112.23 & 110.956055189807 & 1.27394481019279 \tabularnewline
52 & 110.58 & 112.571562924278 & -1.99156292427823 \tabularnewline
53 & 110.77 & 111.357288694802 & -0.587288694801728 \tabularnewline
54 & 108.08 & 111.104614494127 & -3.02461449412688 \tabularnewline
55 & 108.05 & 108.467839712286 & -0.417839712286153 \tabularnewline
56 & 108.87 & 107.734991161056 & 1.13500883894406 \tabularnewline
57 & 109.61 & 108.381027740555 & 1.22897225944523 \tabularnewline
58 & 111.27 & 109.315678913101 & 1.9543210868988 \tabularnewline
59 & 107.61 & 111.146255319624 & -3.53625531962402 \tabularnewline
60 & 110.98 & 108.18569182014 & 2.79430817985971 \tabularnewline
61 & 106.63 & 110.52238323732 & -3.89238323732015 \tabularnewline
62 & 106.83 & 107.097442431355 & -0.26744243135488 \tabularnewline
63 & 108.77 & 106.375526669294 & 2.39447333070589 \tabularnewline
64 & 106.12 & 108.09668291915 & -1.97668291915021 \tabularnewline
65 & 106.8 & 106.151810059067 & 0.648189940933037 \tabularnewline
66 & 106.34 & 106.313103820215 & 0.0268961797846714 \tabularnewline
67 & 105.16 & 106.007765268783 & -0.84776526878278 \tabularnewline
68 & 107.97 & 104.888890265525 & 3.08110973447462 \tabularnewline
69 & 106.76 & 107.295775315349 & -0.535775315348616 \tabularnewline
70 & 108.78 & 106.863712150454 & 1.91628784954649 \tabularnewline
71 & 105.58 & 108.630942611881 & -3.05094261188107 \tabularnewline
72 & 109.22 & 106.089925773636 & 3.13007422636353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205376&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]3[/C][C]108.06[/C][C]112.78[/C][C]-4.72[/C][/ROW]
[ROW][C]4[/C][C]111.33[/C][C]111.414187485559[/C][C]-0.0841874855588571[/C][/ROW]
[ROW][C]5[/C][C]105.66[/C][C]113.55077479276[/C][C]-7.89077479276023[/C][/ROW]
[ROW][C]6[/C][C]103.65[/C][C]108.368994922406[/C][C]-4.7189949224059[/C][/ROW]
[ROW][C]7[/C][C]100.34[/C][C]104.759237039706[/C][C]-4.41923703970562[/C][/ROW]
[ROW][C]8[/C][C]100.56[/C][C]100.595445627519[/C][C]-0.0354456275191097[/C][/ROW]
[ROW][C]9[/C][C]102.67[/C][C]99.7514595681226[/C][C]2.91854043187742[/C][/ROW]
[ROW][C]10[/C][C]101.5[/C][C]101.664817552654[/C][C]-0.164817552653986[/C][/ROW]
[ROW][C]11[/C][C]102.35[/C][C]101.209622850829[/C][C]1.14037714917065[/C][/ROW]
[ROW][C]12[/C][C]104.98[/C][C]101.94636247031[/C][C]3.03363752968997[/C][/ROW]
[ROW][C]13[/C][C]106.31[/C][C]104.65600454251[/C][C]1.65399545749041[/C][/ROW]
[ROW][C]14[/C][C]103.73[/C][C]106.611364252728[/C][C]-2.88136425272782[/C][/ROW]
[ROW][C]15[/C][C]106.62[/C][C]104.616132958605[/C][C]2.00386704139484[/C][/ROW]
[ROW][C]16[/C][C]108.54[/C][C]106.681777197757[/C][C]1.85822280224309[/C][/ROW]
[ROW][C]17[/C][C]105.12[/C][C]108.965512870707[/C][C]-3.84551287070745[/C][/ROW]
[ROW][C]18[/C][C]105.29[/C][C]106.241693411792[/C][C]-0.951693411792334[/C][/ROW]
[ROW][C]19[/C][C]104.62[/C][C]105.545184080453[/C][C]-0.925184080453093[/C][/ROW]
[ROW][C]20[/C][C]104.34[/C][C]104.705185040058[/C][C]-0.365185040057924[/C][/ROW]
[ROW][C]21[/C][C]108.23[/C][C]104.225492173675[/C][C]4.00450782632498[/C][/ROW]
[ROW][C]22[/C][C]107.6[/C][C]107.769304065601[/C][C]-0.169304065601409[/C][/ROW]
[ROW][C]23[/C][C]106.87[/C][C]108.1164199533[/C][C]-1.24641995330045[/C][/ROW]
[ROW][C]24[/C][C]107.96[/C][C]107.425897792367[/C][C]0.534102207633239[/C][/ROW]
[ROW][C]25[/C][C]108.34[/C][C]108.180741443755[/C][C]0.159258556244907[/C][/ROW]
[ROW][C]26[/C][C]109.04[/C][C]108.679345592189[/C][C]0.360654407811055[/C][/ROW]
[ROW][C]27[/C][C]106.95[/C][C]109.394528469958[/C][C]-2.44452846995802[/C][/ROW]
[ROW][C]28[/C][C]105.59[/C][C]107.549088218841[/C][C]-1.95908821884095[/C][/ROW]
[ROW][C]29[/C][C]108.08[/C][C]105.725530489396[/C][C]2.35446951060436[/C][/ROW]
[ROW][C]30[/C][C]108.48[/C][C]107.591105739169[/C][C]0.888894260831378[/C][/ROW]
[ROW][C]31[/C][C]106.84[/C][C]108.501904362391[/C][C]-1.66190436239073[/C][/ROW]
[ROW][C]32[/C][C]105.6[/C][C]107.183480066171[/C][C]-1.58348006617052[/C][/ROW]
[ROW][C]33[/C][C]106.9[/C][C]105.644546699935[/C][C]1.25545330006473[/C][/ROW]
[ROW][C]34[/C][C]106.84[/C][C]106.481576170227[/C][C]0.358423829773329[/C][/ROW]
[ROW][C]35[/C][C]106.81[/C][C]106.701391898074[/C][C]0.108608101925995[/C][/ROW]
[ROW][C]36[/C][C]106.98[/C][C]106.750872735569[/C][C]0.22912726443063[/C][/ROW]
[ROW][C]37[/C][C]107.53[/C][C]106.93231117153[/C][C]0.597688828469941[/C][/ROW]
[ROW][C]38[/C][C]107.37[/C][C]107.49907588302[/C][C]-0.129075883020022[/C][/ROW]
[ROW][C]39[/C][C]106.98[/C][C]107.491604312406[/C][C]-0.511604312405552[/C][/ROW]
[ROW][C]40[/C][C]108.94[/C][C]107.103432082017[/C][C]1.83656791798298[/C][/ROW]
[ROW][C]41[/C][C]106.38[/C][C]108.821632176705[/C][C]-2.44163217670508[/C][/ROW]
[ROW][C]42[/C][C]109.02[/C][C]106.86211264374[/C][C]2.15788735625964[/C][/ROW]
[ROW][C]43[/C][C]106.53[/C][C]108.773929058646[/C][C]-2.24392905864555[/C][/ROW]
[ROW][C]44[/C][C]105.02[/C][C]106.949195979619[/C][C]-1.92919597961932[/C][/ROW]
[ROW][C]45[/C][C]109.7[/C][C]105.022112284877[/C][C]4.67788771512268[/C][/ROW]
[ROW][C]46[/C][C]108.39[/C][C]108.935163739061[/C][C]-0.545163739060655[/C][/ROW]
[ROW][C]47[/C][C]110.18[/C][C]108.788975093809[/C][C]1.39102490619096[/C][/ROW]
[ROW][C]48[/C][C]109.54[/C][C]110.357791681861[/C][C]-0.817791681861323[/C][/ROW]
[ROW][C]49[/C][C]109.1[/C][C]110.106121005879[/C][C]-1.00612100587935[/C][/ROW]
[ROW][C]50[/C][C]110.85[/C][C]109.533645782404[/C][C]1.31635421759556[/C][/ROW]
[ROW][C]51[/C][C]112.23[/C][C]110.956055189807[/C][C]1.27394481019279[/C][/ROW]
[ROW][C]52[/C][C]110.58[/C][C]112.571562924278[/C][C]-1.99156292427823[/C][/ROW]
[ROW][C]53[/C][C]110.77[/C][C]111.357288694802[/C][C]-0.587288694801728[/C][/ROW]
[ROW][C]54[/C][C]108.08[/C][C]111.104614494127[/C][C]-3.02461449412688[/C][/ROW]
[ROW][C]55[/C][C]108.05[/C][C]108.467839712286[/C][C]-0.417839712286153[/C][/ROW]
[ROW][C]56[/C][C]108.87[/C][C]107.734991161056[/C][C]1.13500883894406[/C][/ROW]
[ROW][C]57[/C][C]109.61[/C][C]108.381027740555[/C][C]1.22897225944523[/C][/ROW]
[ROW][C]58[/C][C]111.27[/C][C]109.315678913101[/C][C]1.9543210868988[/C][/ROW]
[ROW][C]59[/C][C]107.61[/C][C]111.146255319624[/C][C]-3.53625531962402[/C][/ROW]
[ROW][C]60[/C][C]110.98[/C][C]108.18569182014[/C][C]2.79430817985971[/C][/ROW]
[ROW][C]61[/C][C]106.63[/C][C]110.52238323732[/C][C]-3.89238323732015[/C][/ROW]
[ROW][C]62[/C][C]106.83[/C][C]107.097442431355[/C][C]-0.26744243135488[/C][/ROW]
[ROW][C]63[/C][C]108.77[/C][C]106.375526669294[/C][C]2.39447333070589[/C][/ROW]
[ROW][C]64[/C][C]106.12[/C][C]108.09668291915[/C][C]-1.97668291915021[/C][/ROW]
[ROW][C]65[/C][C]106.8[/C][C]106.151810059067[/C][C]0.648189940933037[/C][/ROW]
[ROW][C]66[/C][C]106.34[/C][C]106.313103820215[/C][C]0.0268961797846714[/C][/ROW]
[ROW][C]67[/C][C]105.16[/C][C]106.007765268783[/C][C]-0.84776526878278[/C][/ROW]
[ROW][C]68[/C][C]107.97[/C][C]104.888890265525[/C][C]3.08110973447462[/C][/ROW]
[ROW][C]69[/C][C]106.76[/C][C]107.295775315349[/C][C]-0.535775315348616[/C][/ROW]
[ROW][C]70[/C][C]108.78[/C][C]106.863712150454[/C][C]1.91628784954649[/C][/ROW]
[ROW][C]71[/C][C]105.58[/C][C]108.630942611881[/C][C]-3.05094261188107[/C][/ROW]
[ROW][C]72[/C][C]109.22[/C][C]106.089925773636[/C][C]3.13007422636353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205376&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205376&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
3108.06112.78-4.72
4111.33111.414187485559-0.0841874855588571
5105.66113.55077479276-7.89077479276023
6103.65108.368994922406-4.7189949224059
7100.34104.759237039706-4.41923703970562
8100.56100.595445627519-0.0354456275191097
9102.6799.75145956812262.91854043187742
10101.5101.664817552654-0.164817552653986
11102.35101.2096228508291.14037714917065
12104.98101.946362470313.03363752968997
13106.31104.656004542511.65399545749041
14103.73106.611364252728-2.88136425272782
15106.62104.6161329586052.00386704139484
16108.54106.6817771977571.85822280224309
17105.12108.965512870707-3.84551287070745
18105.29106.241693411792-0.951693411792334
19104.62105.545184080453-0.925184080453093
20104.34104.705185040058-0.365185040057924
21108.23104.2254921736754.00450782632498
22107.6107.769304065601-0.169304065601409
23106.87108.1164199533-1.24641995330045
24107.96107.4258977923670.534102207633239
25108.34108.1807414437550.159258556244907
26109.04108.6793455921890.360654407811055
27106.95109.394528469958-2.44452846995802
28105.59107.549088218841-1.95908821884095
29108.08105.7255304893962.35446951060436
30108.48107.5911057391690.888894260831378
31106.84108.501904362391-1.66190436239073
32105.6107.183480066171-1.58348006617052
33106.9105.6445466999351.25545330006473
34106.84106.4815761702270.358423829773329
35106.81106.7013918980740.108608101925995
36106.98106.7508727355690.22912726443063
37107.53106.932311171530.597688828469941
38107.37107.49907588302-0.129075883020022
39106.98107.491604312406-0.511604312405552
40108.94107.1034320820171.83656791798298
41106.38108.821632176705-2.44163217670508
42109.02106.862112643742.15788735625964
43106.53108.773929058646-2.24392905864555
44105.02106.949195979619-1.92919597961932
45109.7105.0221122848774.67788771512268
46108.39108.935163739061-0.545163739060655
47110.18108.7889750938091.39102490619096
48109.54110.357791681861-0.817791681861323
49109.1110.106121005879-1.00612100587935
50110.85109.5336457824041.31635421759556
51112.23110.9560551898071.27394481019279
52110.58112.571562924278-1.99156292427823
53110.77111.357288694802-0.587288694801728
54108.08111.104614494127-3.02461449412688
55108.05108.467839712286-0.417839712286153
56108.87107.7349911610561.13500883894406
57109.61108.3810277405551.22897225944523
58111.27109.3156789131011.9543210868988
59107.61111.146255319624-3.53625531962402
60110.98108.185691820142.79430817985971
61106.63110.52238323732-3.89238323732015
62106.83107.097442431355-0.26744243135488
63108.77106.3755266692942.39447333070589
64106.12108.09668291915-1.97668291915021
65106.8106.1518100590670.648189940933037
66106.34106.3131038202150.0268961797846714
67105.16106.007765268783-0.84776526878278
68107.97104.8888902655253.08110973447462
69106.76107.295775315349-0.535775315348616
70108.78106.8637121504541.91628784954649
71105.58108.630942611881-3.05094261188107
72109.22106.0899257736363.13007422636353







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73108.792074152838104.252793474002113.331354831674
74109.119370414469102.903272841253115.335467987686
75109.4466666761101.438130675848117.455202676353
76109.77396293773199.8550898719757119.692836003487
77110.10125919936298.1567757257234122.045742673001
78110.42855546099396.3471773015132124.509933620473
79110.75585172262494.430526198155127.081177247094
80111.08314798425592.4109106354152129.755385333095
81111.41044424588690.2921482067776132.528740284995
82111.73774050751788.0777568269965135.397724188038
83112.06503676914885.7709636262667138.35910991203
84112.39233303077983.3747275822228141.409938479336

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 108.792074152838 & 104.252793474002 & 113.331354831674 \tabularnewline
74 & 109.119370414469 & 102.903272841253 & 115.335467987686 \tabularnewline
75 & 109.4466666761 & 101.438130675848 & 117.455202676353 \tabularnewline
76 & 109.773962937731 & 99.8550898719757 & 119.692836003487 \tabularnewline
77 & 110.101259199362 & 98.1567757257234 & 122.045742673001 \tabularnewline
78 & 110.428555460993 & 96.3471773015132 & 124.509933620473 \tabularnewline
79 & 110.755851722624 & 94.430526198155 & 127.081177247094 \tabularnewline
80 & 111.083147984255 & 92.4109106354152 & 129.755385333095 \tabularnewline
81 & 111.410444245886 & 90.2921482067776 & 132.528740284995 \tabularnewline
82 & 111.737740507517 & 88.0777568269965 & 135.397724188038 \tabularnewline
83 & 112.065036769148 & 85.7709636262667 & 138.35910991203 \tabularnewline
84 & 112.392333030779 & 83.3747275822228 & 141.409938479336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205376&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]108.792074152838[/C][C]104.252793474002[/C][C]113.331354831674[/C][/ROW]
[ROW][C]74[/C][C]109.119370414469[/C][C]102.903272841253[/C][C]115.335467987686[/C][/ROW]
[ROW][C]75[/C][C]109.4466666761[/C][C]101.438130675848[/C][C]117.455202676353[/C][/ROW]
[ROW][C]76[/C][C]109.773962937731[/C][C]99.8550898719757[/C][C]119.692836003487[/C][/ROW]
[ROW][C]77[/C][C]110.101259199362[/C][C]98.1567757257234[/C][C]122.045742673001[/C][/ROW]
[ROW][C]78[/C][C]110.428555460993[/C][C]96.3471773015132[/C][C]124.509933620473[/C][/ROW]
[ROW][C]79[/C][C]110.755851722624[/C][C]94.430526198155[/C][C]127.081177247094[/C][/ROW]
[ROW][C]80[/C][C]111.083147984255[/C][C]92.4109106354152[/C][C]129.755385333095[/C][/ROW]
[ROW][C]81[/C][C]111.410444245886[/C][C]90.2921482067776[/C][C]132.528740284995[/C][/ROW]
[ROW][C]82[/C][C]111.737740507517[/C][C]88.0777568269965[/C][C]135.397724188038[/C][/ROW]
[ROW][C]83[/C][C]112.065036769148[/C][C]85.7709636262667[/C][C]138.35910991203[/C][/ROW]
[ROW][C]84[/C][C]112.392333030779[/C][C]83.3747275822228[/C][C]141.409938479336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205376&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205376&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
73108.792074152838104.252793474002113.331354831674
74109.119370414469102.903272841253115.335467987686
75109.4466666761101.438130675848117.455202676353
76109.77396293773199.8550898719757119.692836003487
77110.10125919936298.1567757257234122.045742673001
78110.42855546099396.3471773015132124.509933620473
79110.75585172262494.430526198155127.081177247094
80111.08314798425592.4109106354152129.755385333095
81111.41044424588690.2921482067776132.528740284995
82111.73774050751788.0777568269965135.397724188038
83112.06503676914885.7709636262667138.35910991203
84112.39233303077983.3747275822228141.409938479336



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')