Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 Dec 2011 12:08:56 -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/2011/Dec/28/t1325092200j21yc23ohie1hiy.htm/, Retrieved Fri, 03 May 2024 06:56:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160874, Retrieved Fri, 03 May 2024 06:56:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2011-12-28 17:08:56] [459538fe31c621d37110fb87514358a8] [Current]
Feedback Forum

Post a new message
Dataseries X:
105,71
105,82
105,82
105,72
105,76
105,8
105,09
105,06
105,16
105,2
105,21
105,23
105,19
105,16
104,88
104,52
104,09
104,35
104,48
104,47
104,55
104,59
104,59
104,72
104,65
104,72
104,92
105,05
103,74
103,81
103,79
104,28
103,8
103,8
104,02
104,02
104,91
104,97
103,86
104,17
103,21
103,21
101,91
101,84
101,91
101,79
101,79
101,79
102,09
102,18
102,2
101,97
102,05
102,04
101,78
101,79
101,8
101,83
101,83
101,88
101,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160874&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160874&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160874&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.915723510928378
beta0.0529666681350412
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.915723510928378 \tabularnewline
beta & 0.0529666681350412 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160874&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]0.915723510928378[/C][/ROW]
[ROW][C]beta[/C][C]0.0529666681350412[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160874&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160874&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
alpha0.915723510928378
beta0.0529666681350412
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3105.82105.93-0.109999999999999
4105.72105.933935103234-0.213935103234121
5105.76105.832317932315-0.0723179323147036
6105.8105.856875310464-0.056875310464406
7105.09105.892815247379-0.802815247378817
8105.06105.206741640229-0.146741640228655
9105.16105.1143326761980.0456673238022773
10105.2105.200332118381-0.000332118380555357
11105.21105.244192681188-0.0341926811878608
12105.23105.255387888965-0.0253878889651986
13105.19105.273414467697-0.0834144676970681
14105.16105.234258906837-0.0742589068374855
15104.88105.199885541675-0.319885541675461
16104.52104.925070740176-0.405070740175802
17104.09104.552602775089-0.462602775088769
18104.35104.1050138323390.244986167660969
19104.48104.3172632413410.162736758659179
20104.47104.462088125010.00791187498950308
21104.55104.4655199709020.084480029098259
22104.59104.5431645956230.0468354043769494
23104.59104.588608801770.0013911982300101
24104.72104.5925061569550.127493843045357
25104.65104.718062480129-0.0680624801288872
26104.72104.6612420580140.0587579419857462
27104.92104.7234040041740.196595995826144
28105.05104.9213229577840.128677042215884
29103.74105.063288128578-1.32328812857804
30103.81103.811471445142-0.00147144514241404
31103.79103.7700020066220.0199979933775865
32104.28103.7491625968610.530837403139088
33103.8104.221857957696-0.421857957695877
34103.8103.801686475879-0.00168647587918258
35104.02103.7661940997420.25380590025793
36104.02103.9769724020310.0430275979689014
37104.91103.9968230173020.913176982697905
38104.97104.8577815440290.11221845597106
39103.86104.990726428495-1.13072642849518
40104.17103.9306340352980.239365964702102
41103.21104.136777383787-0.926777383787112
42103.21103.230104531261-0.0201045312614241
43101.91103.152718199987-1.24271819998657
44101.84101.895480446204-0.0554804462036032
45101.91101.7227332583420.18726674165768
46101.79101.7813583432990.00864165670078876
47101.79101.6768313830680.113168616932455
48101.79101.6735112152770.11648878472316
49102.09101.6788814381350.411118561865038
50102.18101.9739914859060.206008514094236
51102.2102.0912694351640.108730564835966
52101.97102.124741418566-0.154741418565877
53102.05101.9094405166130.140559483387221
54102.04101.9713711251630.0686288748367048
55101.78101.970761878499-0.190761878498691
56101.79101.7233699308010.0666300691990642
57101.8101.7149095876070.0850904123930292
58101.83101.7274809399330.102519060067081
59101.83101.7609845785540.0690154214463092
60101.88101.767155590380.112844409620379
61101.9101.8189351095980.0810648904022742

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 105.82 & 105.93 & -0.109999999999999 \tabularnewline
4 & 105.72 & 105.933935103234 & -0.213935103234121 \tabularnewline
5 & 105.76 & 105.832317932315 & -0.0723179323147036 \tabularnewline
6 & 105.8 & 105.856875310464 & -0.056875310464406 \tabularnewline
7 & 105.09 & 105.892815247379 & -0.802815247378817 \tabularnewline
8 & 105.06 & 105.206741640229 & -0.146741640228655 \tabularnewline
9 & 105.16 & 105.114332676198 & 0.0456673238022773 \tabularnewline
10 & 105.2 & 105.200332118381 & -0.000332118380555357 \tabularnewline
11 & 105.21 & 105.244192681188 & -0.0341926811878608 \tabularnewline
12 & 105.23 & 105.255387888965 & -0.0253878889651986 \tabularnewline
13 & 105.19 & 105.273414467697 & -0.0834144676970681 \tabularnewline
14 & 105.16 & 105.234258906837 & -0.0742589068374855 \tabularnewline
15 & 104.88 & 105.199885541675 & -0.319885541675461 \tabularnewline
16 & 104.52 & 104.925070740176 & -0.405070740175802 \tabularnewline
17 & 104.09 & 104.552602775089 & -0.462602775088769 \tabularnewline
18 & 104.35 & 104.105013832339 & 0.244986167660969 \tabularnewline
19 & 104.48 & 104.317263241341 & 0.162736758659179 \tabularnewline
20 & 104.47 & 104.46208812501 & 0.00791187498950308 \tabularnewline
21 & 104.55 & 104.465519970902 & 0.084480029098259 \tabularnewline
22 & 104.59 & 104.543164595623 & 0.0468354043769494 \tabularnewline
23 & 104.59 & 104.58860880177 & 0.0013911982300101 \tabularnewline
24 & 104.72 & 104.592506156955 & 0.127493843045357 \tabularnewline
25 & 104.65 & 104.718062480129 & -0.0680624801288872 \tabularnewline
26 & 104.72 & 104.661242058014 & 0.0587579419857462 \tabularnewline
27 & 104.92 & 104.723404004174 & 0.196595995826144 \tabularnewline
28 & 105.05 & 104.921322957784 & 0.128677042215884 \tabularnewline
29 & 103.74 & 105.063288128578 & -1.32328812857804 \tabularnewline
30 & 103.81 & 103.811471445142 & -0.00147144514241404 \tabularnewline
31 & 103.79 & 103.770002006622 & 0.0199979933775865 \tabularnewline
32 & 104.28 & 103.749162596861 & 0.530837403139088 \tabularnewline
33 & 103.8 & 104.221857957696 & -0.421857957695877 \tabularnewline
34 & 103.8 & 103.801686475879 & -0.00168647587918258 \tabularnewline
35 & 104.02 & 103.766194099742 & 0.25380590025793 \tabularnewline
36 & 104.02 & 103.976972402031 & 0.0430275979689014 \tabularnewline
37 & 104.91 & 103.996823017302 & 0.913176982697905 \tabularnewline
38 & 104.97 & 104.857781544029 & 0.11221845597106 \tabularnewline
39 & 103.86 & 104.990726428495 & -1.13072642849518 \tabularnewline
40 & 104.17 & 103.930634035298 & 0.239365964702102 \tabularnewline
41 & 103.21 & 104.136777383787 & -0.926777383787112 \tabularnewline
42 & 103.21 & 103.230104531261 & -0.0201045312614241 \tabularnewline
43 & 101.91 & 103.152718199987 & -1.24271819998657 \tabularnewline
44 & 101.84 & 101.895480446204 & -0.0554804462036032 \tabularnewline
45 & 101.91 & 101.722733258342 & 0.18726674165768 \tabularnewline
46 & 101.79 & 101.781358343299 & 0.00864165670078876 \tabularnewline
47 & 101.79 & 101.676831383068 & 0.113168616932455 \tabularnewline
48 & 101.79 & 101.673511215277 & 0.11648878472316 \tabularnewline
49 & 102.09 & 101.678881438135 & 0.411118561865038 \tabularnewline
50 & 102.18 & 101.973991485906 & 0.206008514094236 \tabularnewline
51 & 102.2 & 102.091269435164 & 0.108730564835966 \tabularnewline
52 & 101.97 & 102.124741418566 & -0.154741418565877 \tabularnewline
53 & 102.05 & 101.909440516613 & 0.140559483387221 \tabularnewline
54 & 102.04 & 101.971371125163 & 0.0686288748367048 \tabularnewline
55 & 101.78 & 101.970761878499 & -0.190761878498691 \tabularnewline
56 & 101.79 & 101.723369930801 & 0.0666300691990642 \tabularnewline
57 & 101.8 & 101.714909587607 & 0.0850904123930292 \tabularnewline
58 & 101.83 & 101.727480939933 & 0.102519060067081 \tabularnewline
59 & 101.83 & 101.760984578554 & 0.0690154214463092 \tabularnewline
60 & 101.88 & 101.76715559038 & 0.112844409620379 \tabularnewline
61 & 101.9 & 101.818935109598 & 0.0810648904022742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160874&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]105.82[/C][C]105.93[/C][C]-0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]105.72[/C][C]105.933935103234[/C][C]-0.213935103234121[/C][/ROW]
[ROW][C]5[/C][C]105.76[/C][C]105.832317932315[/C][C]-0.0723179323147036[/C][/ROW]
[ROW][C]6[/C][C]105.8[/C][C]105.856875310464[/C][C]-0.056875310464406[/C][/ROW]
[ROW][C]7[/C][C]105.09[/C][C]105.892815247379[/C][C]-0.802815247378817[/C][/ROW]
[ROW][C]8[/C][C]105.06[/C][C]105.206741640229[/C][C]-0.146741640228655[/C][/ROW]
[ROW][C]9[/C][C]105.16[/C][C]105.114332676198[/C][C]0.0456673238022773[/C][/ROW]
[ROW][C]10[/C][C]105.2[/C][C]105.200332118381[/C][C]-0.000332118380555357[/C][/ROW]
[ROW][C]11[/C][C]105.21[/C][C]105.244192681188[/C][C]-0.0341926811878608[/C][/ROW]
[ROW][C]12[/C][C]105.23[/C][C]105.255387888965[/C][C]-0.0253878889651986[/C][/ROW]
[ROW][C]13[/C][C]105.19[/C][C]105.273414467697[/C][C]-0.0834144676970681[/C][/ROW]
[ROW][C]14[/C][C]105.16[/C][C]105.234258906837[/C][C]-0.0742589068374855[/C][/ROW]
[ROW][C]15[/C][C]104.88[/C][C]105.199885541675[/C][C]-0.319885541675461[/C][/ROW]
[ROW][C]16[/C][C]104.52[/C][C]104.925070740176[/C][C]-0.405070740175802[/C][/ROW]
[ROW][C]17[/C][C]104.09[/C][C]104.552602775089[/C][C]-0.462602775088769[/C][/ROW]
[ROW][C]18[/C][C]104.35[/C][C]104.105013832339[/C][C]0.244986167660969[/C][/ROW]
[ROW][C]19[/C][C]104.48[/C][C]104.317263241341[/C][C]0.162736758659179[/C][/ROW]
[ROW][C]20[/C][C]104.47[/C][C]104.46208812501[/C][C]0.00791187498950308[/C][/ROW]
[ROW][C]21[/C][C]104.55[/C][C]104.465519970902[/C][C]0.084480029098259[/C][/ROW]
[ROW][C]22[/C][C]104.59[/C][C]104.543164595623[/C][C]0.0468354043769494[/C][/ROW]
[ROW][C]23[/C][C]104.59[/C][C]104.58860880177[/C][C]0.0013911982300101[/C][/ROW]
[ROW][C]24[/C][C]104.72[/C][C]104.592506156955[/C][C]0.127493843045357[/C][/ROW]
[ROW][C]25[/C][C]104.65[/C][C]104.718062480129[/C][C]-0.0680624801288872[/C][/ROW]
[ROW][C]26[/C][C]104.72[/C][C]104.661242058014[/C][C]0.0587579419857462[/C][/ROW]
[ROW][C]27[/C][C]104.92[/C][C]104.723404004174[/C][C]0.196595995826144[/C][/ROW]
[ROW][C]28[/C][C]105.05[/C][C]104.921322957784[/C][C]0.128677042215884[/C][/ROW]
[ROW][C]29[/C][C]103.74[/C][C]105.063288128578[/C][C]-1.32328812857804[/C][/ROW]
[ROW][C]30[/C][C]103.81[/C][C]103.811471445142[/C][C]-0.00147144514241404[/C][/ROW]
[ROW][C]31[/C][C]103.79[/C][C]103.770002006622[/C][C]0.0199979933775865[/C][/ROW]
[ROW][C]32[/C][C]104.28[/C][C]103.749162596861[/C][C]0.530837403139088[/C][/ROW]
[ROW][C]33[/C][C]103.8[/C][C]104.221857957696[/C][C]-0.421857957695877[/C][/ROW]
[ROW][C]34[/C][C]103.8[/C][C]103.801686475879[/C][C]-0.00168647587918258[/C][/ROW]
[ROW][C]35[/C][C]104.02[/C][C]103.766194099742[/C][C]0.25380590025793[/C][/ROW]
[ROW][C]36[/C][C]104.02[/C][C]103.976972402031[/C][C]0.0430275979689014[/C][/ROW]
[ROW][C]37[/C][C]104.91[/C][C]103.996823017302[/C][C]0.913176982697905[/C][/ROW]
[ROW][C]38[/C][C]104.97[/C][C]104.857781544029[/C][C]0.11221845597106[/C][/ROW]
[ROW][C]39[/C][C]103.86[/C][C]104.990726428495[/C][C]-1.13072642849518[/C][/ROW]
[ROW][C]40[/C][C]104.17[/C][C]103.930634035298[/C][C]0.239365964702102[/C][/ROW]
[ROW][C]41[/C][C]103.21[/C][C]104.136777383787[/C][C]-0.926777383787112[/C][/ROW]
[ROW][C]42[/C][C]103.21[/C][C]103.230104531261[/C][C]-0.0201045312614241[/C][/ROW]
[ROW][C]43[/C][C]101.91[/C][C]103.152718199987[/C][C]-1.24271819998657[/C][/ROW]
[ROW][C]44[/C][C]101.84[/C][C]101.895480446204[/C][C]-0.0554804462036032[/C][/ROW]
[ROW][C]45[/C][C]101.91[/C][C]101.722733258342[/C][C]0.18726674165768[/C][/ROW]
[ROW][C]46[/C][C]101.79[/C][C]101.781358343299[/C][C]0.00864165670078876[/C][/ROW]
[ROW][C]47[/C][C]101.79[/C][C]101.676831383068[/C][C]0.113168616932455[/C][/ROW]
[ROW][C]48[/C][C]101.79[/C][C]101.673511215277[/C][C]0.11648878472316[/C][/ROW]
[ROW][C]49[/C][C]102.09[/C][C]101.678881438135[/C][C]0.411118561865038[/C][/ROW]
[ROW][C]50[/C][C]102.18[/C][C]101.973991485906[/C][C]0.206008514094236[/C][/ROW]
[ROW][C]51[/C][C]102.2[/C][C]102.091269435164[/C][C]0.108730564835966[/C][/ROW]
[ROW][C]52[/C][C]101.97[/C][C]102.124741418566[/C][C]-0.154741418565877[/C][/ROW]
[ROW][C]53[/C][C]102.05[/C][C]101.909440516613[/C][C]0.140559483387221[/C][/ROW]
[ROW][C]54[/C][C]102.04[/C][C]101.971371125163[/C][C]0.0686288748367048[/C][/ROW]
[ROW][C]55[/C][C]101.78[/C][C]101.970761878499[/C][C]-0.190761878498691[/C][/ROW]
[ROW][C]56[/C][C]101.79[/C][C]101.723369930801[/C][C]0.0666300691990642[/C][/ROW]
[ROW][C]57[/C][C]101.8[/C][C]101.714909587607[/C][C]0.0850904123930292[/C][/ROW]
[ROW][C]58[/C][C]101.83[/C][C]101.727480939933[/C][C]0.102519060067081[/C][/ROW]
[ROW][C]59[/C][C]101.83[/C][C]101.760984578554[/C][C]0.0690154214463092[/C][/ROW]
[ROW][C]60[/C][C]101.88[/C][C]101.76715559038[/C][C]0.112844409620379[/C][/ROW]
[ROW][C]61[/C][C]101.9[/C][C]101.818935109598[/C][C]0.0810648904022742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160874&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160874&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
3105.82105.93-0.109999999999999
4105.72105.933935103234-0.213935103234121
5105.76105.832317932315-0.0723179323147036
6105.8105.856875310464-0.056875310464406
7105.09105.892815247379-0.802815247378817
8105.06105.206741640229-0.146741640228655
9105.16105.1143326761980.0456673238022773
10105.2105.200332118381-0.000332118380555357
11105.21105.244192681188-0.0341926811878608
12105.23105.255387888965-0.0253878889651986
13105.19105.273414467697-0.0834144676970681
14105.16105.234258906837-0.0742589068374855
15104.88105.199885541675-0.319885541675461
16104.52104.925070740176-0.405070740175802
17104.09104.552602775089-0.462602775088769
18104.35104.1050138323390.244986167660969
19104.48104.3172632413410.162736758659179
20104.47104.462088125010.00791187498950308
21104.55104.4655199709020.084480029098259
22104.59104.5431645956230.0468354043769494
23104.59104.588608801770.0013911982300101
24104.72104.5925061569550.127493843045357
25104.65104.718062480129-0.0680624801288872
26104.72104.6612420580140.0587579419857462
27104.92104.7234040041740.196595995826144
28105.05104.9213229577840.128677042215884
29103.74105.063288128578-1.32328812857804
30103.81103.811471445142-0.00147144514241404
31103.79103.7700020066220.0199979933775865
32104.28103.7491625968610.530837403139088
33103.8104.221857957696-0.421857957695877
34103.8103.801686475879-0.00168647587918258
35104.02103.7661940997420.25380590025793
36104.02103.9769724020310.0430275979689014
37104.91103.9968230173020.913176982697905
38104.97104.8577815440290.11221845597106
39103.86104.990726428495-1.13072642849518
40104.17103.9306340352980.239365964702102
41103.21104.136777383787-0.926777383787112
42103.21103.230104531261-0.0201045312614241
43101.91103.152718199987-1.24271819998657
44101.84101.895480446204-0.0554804462036032
45101.91101.7227332583420.18726674165768
46101.79101.7813583432990.00864165670078876
47101.79101.6768313830680.113168616932455
48101.79101.6735112152770.11648878472316
49102.09101.6788814381350.411118561865038
50102.18101.9739914859060.206008514094236
51102.2102.0912694351640.108730564835966
52101.97102.124741418566-0.154741418565877
53102.05101.9094405166130.140559483387221
54102.04101.9713711251630.0686288748367048
55101.78101.970761878499-0.190761878498691
56101.79101.7233699308010.0666300691990642
57101.8101.7149095876070.0850904123930292
58101.83101.7274809399330.102519060067081
59101.83101.7609845785540.0690154214463092
60101.88101.767155590380.112844409620379
61101.9101.8189351095980.0810648904022742







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
62101.845545251957101.094874991109102.596215512806
63101.797922368265100.755130207112102.840714529418
64101.750299484572100.459811767934103.04078720121
65101.70267660088100.186106019371103.219247182388
66101.65505371718799.9247502296595103.385357204715
67101.60743083349599.6709646294425103.543897037547
68101.55980794980299.4219372212422103.697678678362
69101.5121850661199.1758693428774103.848500789342
70101.46456218241798.9315417717054103.997582593129
71101.41693929872598.6880922342496104.145786363199
72101.36931641503298.4448909704128104.293741859651
73101.32169353133998.2014663981823104.441920664497

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 101.845545251957 & 101.094874991109 & 102.596215512806 \tabularnewline
63 & 101.797922368265 & 100.755130207112 & 102.840714529418 \tabularnewline
64 & 101.750299484572 & 100.459811767934 & 103.04078720121 \tabularnewline
65 & 101.70267660088 & 100.186106019371 & 103.219247182388 \tabularnewline
66 & 101.655053717187 & 99.9247502296595 & 103.385357204715 \tabularnewline
67 & 101.607430833495 & 99.6709646294425 & 103.543897037547 \tabularnewline
68 & 101.559807949802 & 99.4219372212422 & 103.697678678362 \tabularnewline
69 & 101.51218506611 & 99.1758693428774 & 103.848500789342 \tabularnewline
70 & 101.464562182417 & 98.9315417717054 & 103.997582593129 \tabularnewline
71 & 101.416939298725 & 98.6880922342496 & 104.145786363199 \tabularnewline
72 & 101.369316415032 & 98.4448909704128 & 104.293741859651 \tabularnewline
73 & 101.321693531339 & 98.2014663981823 & 104.441920664497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160874&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]62[/C][C]101.845545251957[/C][C]101.094874991109[/C][C]102.596215512806[/C][/ROW]
[ROW][C]63[/C][C]101.797922368265[/C][C]100.755130207112[/C][C]102.840714529418[/C][/ROW]
[ROW][C]64[/C][C]101.750299484572[/C][C]100.459811767934[/C][C]103.04078720121[/C][/ROW]
[ROW][C]65[/C][C]101.70267660088[/C][C]100.186106019371[/C][C]103.219247182388[/C][/ROW]
[ROW][C]66[/C][C]101.655053717187[/C][C]99.9247502296595[/C][C]103.385357204715[/C][/ROW]
[ROW][C]67[/C][C]101.607430833495[/C][C]99.6709646294425[/C][C]103.543897037547[/C][/ROW]
[ROW][C]68[/C][C]101.559807949802[/C][C]99.4219372212422[/C][C]103.697678678362[/C][/ROW]
[ROW][C]69[/C][C]101.51218506611[/C][C]99.1758693428774[/C][C]103.848500789342[/C][/ROW]
[ROW][C]70[/C][C]101.464562182417[/C][C]98.9315417717054[/C][C]103.997582593129[/C][/ROW]
[ROW][C]71[/C][C]101.416939298725[/C][C]98.6880922342496[/C][C]104.145786363199[/C][/ROW]
[ROW][C]72[/C][C]101.369316415032[/C][C]98.4448909704128[/C][C]104.293741859651[/C][/ROW]
[ROW][C]73[/C][C]101.321693531339[/C][C]98.2014663981823[/C][C]104.441920664497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160874&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160874&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
62101.845545251957101.094874991109102.596215512806
63101.797922368265100.755130207112102.840714529418
64101.750299484572100.459811767934103.04078720121
65101.70267660088100.186106019371103.219247182388
66101.65505371718799.9247502296595103.385357204715
67101.60743083349599.6709646294425103.543897037547
68101.55980794980299.4219372212422103.697678678362
69101.5121850661199.1758693428774103.848500789342
70101.46456218241798.9315417717054103.997582593129
71101.41693929872598.6880922342496104.145786363199
72101.36931641503298.4448909704128104.293741859651
73101.32169353133998.2014663981823104.441920664497



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