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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 14:53:15 -0400
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/May/26/t1369594440n0y24bqm6vtu7na.htm/, Retrieved Mon, 29 Apr 2024 10:16:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210653, Retrieved Mon, 29 Apr 2024 10:16:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [oefening 10 deel 2] [2013-05-26 18:53:15] [2be90c1d19c01cf448207b2567a21744] [Current]
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Dataseries X:
105,28
107
106,29
108,07
105,41
104,4
102,77
102,44
103,43
102,95
103,52
105,2
105,88
104,88
106,59
107,8
106,31
106,53
106,25
105,87
107,83
108,01
107,9
108,55
108,83
109,39
108,65
108,33
109,76
110,07
109,23
108,4
108,9
109,14
109,27
109,38
109,66
109,87
109,98
111,24
110,03
111,43
110,28
109,53
111,97
111,89
112,93
113,11
112,95
114,08
115,27
114,73
114,97
113,78
113,7
113,91
114,22
115,32
113,5
115,35
113,23
113,65
114,82
113,54
113,97
113,79
113,27
114,35
113,68
115,3
113,69
115,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210653&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210653&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.388308845367119
beta0
gamma0.904032606187551

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.388308845367119 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.904032606187551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210653&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]0.388308845367119[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.904032606187551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210653&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
alpha0.388308845367119
beta0
gamma0.904032606187551







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13105.88105.5033760683760.376623931623897
14104.88104.5507384397690.329261560231444
15106.59106.2513762500780.338623749921567
16107.8107.387732814790.412267185209672
17106.31105.8535191101610.456480889838843
18106.53106.1177239781260.412276021874078
19106.25104.6789303715181.57106962848165
20105.87105.2113565723110.658643427688631
21107.83106.7219796085921.10802039140822
22108.01106.8600163614551.14998363854467
23107.9108.039347814362-0.13934781436231
24108.55109.728020459495-1.1780204594955
25108.83110.114136125764-1.28413612576351
26109.39108.4904198183480.89958018165197
27108.65110.417694579595-1.76769457959496
28108.33110.776873096927-2.44687309692698
29109.76108.1568796117971.60312038820281
30110.07108.8418899448021.22811005519847
31109.23108.360691736210.869308263789804
32108.4108.1160563686950.283943631305405
33108.9109.729680564546-0.829680564546138
34109.14109.1384961000620.00150389993812894
35109.27109.1588769249340.111123075065549
36109.38110.370435345594-0.990435345593511
37109.66110.770711201341-1.11071120134136
38109.87110.42190787445-0.551907874449711
39109.98110.310584051894-0.330584051894235
40111.24110.8522272204560.387772779543866
41110.03111.572552632247-1.54255263224725
42111.43110.8286938119790.601306188021269
43110.28109.9056887637880.374311236211881
44109.53109.145141616380.384858383619914
45111.97110.1821302525921.78786974740777
46111.89111.0669993843910.82300061560899
47112.93111.4669928208861.46300717911365
48113.11112.5943503843930.515649615606804
49112.95113.51294115748-0.56294115748014
50114.08113.6858537363570.39414626364325
51115.27114.0642806875121.20571931248757
52114.73115.599727286971-0.869727286971425
53114.97114.7643060658260.205693934174207
54113.78115.884836657601-2.10483665760113
55113.7113.785486751265-0.0854867512650372
56113.91112.8522284320851.0577715679147
57114.22114.926364708403-0.706364708402688
58115.32114.3091387647341.01086123526632
59113.5115.135996570253-1.63599657025331
60115.35114.5361054924360.813894507564427
61113.23114.974058833182-1.74405883318151
62113.65115.217591546572-1.56759154657178
63114.82115.283049118493-0.463049118492677
64113.54115.022799557295-1.48279955729451
65113.97114.544012786145-0.574012786144849
66113.79114.084078940838-0.294078940838475
67113.27113.80454005064-0.53454005063972
68114.35113.3291193506411.02088064935913
69113.68114.413383044984-0.733383044984194
70115.3114.7352722680660.564727731933843
71113.69113.925209902154-0.23520990215377
72115.31115.2240188796160.0859811203835079

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105.88 & 105.503376068376 & 0.376623931623897 \tabularnewline
14 & 104.88 & 104.550738439769 & 0.329261560231444 \tabularnewline
15 & 106.59 & 106.251376250078 & 0.338623749921567 \tabularnewline
16 & 107.8 & 107.38773281479 & 0.412267185209672 \tabularnewline
17 & 106.31 & 105.853519110161 & 0.456480889838843 \tabularnewline
18 & 106.53 & 106.117723978126 & 0.412276021874078 \tabularnewline
19 & 106.25 & 104.678930371518 & 1.57106962848165 \tabularnewline
20 & 105.87 & 105.211356572311 & 0.658643427688631 \tabularnewline
21 & 107.83 & 106.721979608592 & 1.10802039140822 \tabularnewline
22 & 108.01 & 106.860016361455 & 1.14998363854467 \tabularnewline
23 & 107.9 & 108.039347814362 & -0.13934781436231 \tabularnewline
24 & 108.55 & 109.728020459495 & -1.1780204594955 \tabularnewline
25 & 108.83 & 110.114136125764 & -1.28413612576351 \tabularnewline
26 & 109.39 & 108.490419818348 & 0.89958018165197 \tabularnewline
27 & 108.65 & 110.417694579595 & -1.76769457959496 \tabularnewline
28 & 108.33 & 110.776873096927 & -2.44687309692698 \tabularnewline
29 & 109.76 & 108.156879611797 & 1.60312038820281 \tabularnewline
30 & 110.07 & 108.841889944802 & 1.22811005519847 \tabularnewline
31 & 109.23 & 108.36069173621 & 0.869308263789804 \tabularnewline
32 & 108.4 & 108.116056368695 & 0.283943631305405 \tabularnewline
33 & 108.9 & 109.729680564546 & -0.829680564546138 \tabularnewline
34 & 109.14 & 109.138496100062 & 0.00150389993812894 \tabularnewline
35 & 109.27 & 109.158876924934 & 0.111123075065549 \tabularnewline
36 & 109.38 & 110.370435345594 & -0.990435345593511 \tabularnewline
37 & 109.66 & 110.770711201341 & -1.11071120134136 \tabularnewline
38 & 109.87 & 110.42190787445 & -0.551907874449711 \tabularnewline
39 & 109.98 & 110.310584051894 & -0.330584051894235 \tabularnewline
40 & 111.24 & 110.852227220456 & 0.387772779543866 \tabularnewline
41 & 110.03 & 111.572552632247 & -1.54255263224725 \tabularnewline
42 & 111.43 & 110.828693811979 & 0.601306188021269 \tabularnewline
43 & 110.28 & 109.905688763788 & 0.374311236211881 \tabularnewline
44 & 109.53 & 109.14514161638 & 0.384858383619914 \tabularnewline
45 & 111.97 & 110.182130252592 & 1.78786974740777 \tabularnewline
46 & 111.89 & 111.066999384391 & 0.82300061560899 \tabularnewline
47 & 112.93 & 111.466992820886 & 1.46300717911365 \tabularnewline
48 & 113.11 & 112.594350384393 & 0.515649615606804 \tabularnewline
49 & 112.95 & 113.51294115748 & -0.56294115748014 \tabularnewline
50 & 114.08 & 113.685853736357 & 0.39414626364325 \tabularnewline
51 & 115.27 & 114.064280687512 & 1.20571931248757 \tabularnewline
52 & 114.73 & 115.599727286971 & -0.869727286971425 \tabularnewline
53 & 114.97 & 114.764306065826 & 0.205693934174207 \tabularnewline
54 & 113.78 & 115.884836657601 & -2.10483665760113 \tabularnewline
55 & 113.7 & 113.785486751265 & -0.0854867512650372 \tabularnewline
56 & 113.91 & 112.852228432085 & 1.0577715679147 \tabularnewline
57 & 114.22 & 114.926364708403 & -0.706364708402688 \tabularnewline
58 & 115.32 & 114.309138764734 & 1.01086123526632 \tabularnewline
59 & 113.5 & 115.135996570253 & -1.63599657025331 \tabularnewline
60 & 115.35 & 114.536105492436 & 0.813894507564427 \tabularnewline
61 & 113.23 & 114.974058833182 & -1.74405883318151 \tabularnewline
62 & 113.65 & 115.217591546572 & -1.56759154657178 \tabularnewline
63 & 114.82 & 115.283049118493 & -0.463049118492677 \tabularnewline
64 & 113.54 & 115.022799557295 & -1.48279955729451 \tabularnewline
65 & 113.97 & 114.544012786145 & -0.574012786144849 \tabularnewline
66 & 113.79 & 114.084078940838 & -0.294078940838475 \tabularnewline
67 & 113.27 & 113.80454005064 & -0.53454005063972 \tabularnewline
68 & 114.35 & 113.329119350641 & 1.02088064935913 \tabularnewline
69 & 113.68 & 114.413383044984 & -0.733383044984194 \tabularnewline
70 & 115.3 & 114.735272268066 & 0.564727731933843 \tabularnewline
71 & 113.69 & 113.925209902154 & -0.23520990215377 \tabularnewline
72 & 115.31 & 115.224018879616 & 0.0859811203835079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210653&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]105.88[/C][C]105.503376068376[/C][C]0.376623931623897[/C][/ROW]
[ROW][C]14[/C][C]104.88[/C][C]104.550738439769[/C][C]0.329261560231444[/C][/ROW]
[ROW][C]15[/C][C]106.59[/C][C]106.251376250078[/C][C]0.338623749921567[/C][/ROW]
[ROW][C]16[/C][C]107.8[/C][C]107.38773281479[/C][C]0.412267185209672[/C][/ROW]
[ROW][C]17[/C][C]106.31[/C][C]105.853519110161[/C][C]0.456480889838843[/C][/ROW]
[ROW][C]18[/C][C]106.53[/C][C]106.117723978126[/C][C]0.412276021874078[/C][/ROW]
[ROW][C]19[/C][C]106.25[/C][C]104.678930371518[/C][C]1.57106962848165[/C][/ROW]
[ROW][C]20[/C][C]105.87[/C][C]105.211356572311[/C][C]0.658643427688631[/C][/ROW]
[ROW][C]21[/C][C]107.83[/C][C]106.721979608592[/C][C]1.10802039140822[/C][/ROW]
[ROW][C]22[/C][C]108.01[/C][C]106.860016361455[/C][C]1.14998363854467[/C][/ROW]
[ROW][C]23[/C][C]107.9[/C][C]108.039347814362[/C][C]-0.13934781436231[/C][/ROW]
[ROW][C]24[/C][C]108.55[/C][C]109.728020459495[/C][C]-1.1780204594955[/C][/ROW]
[ROW][C]25[/C][C]108.83[/C][C]110.114136125764[/C][C]-1.28413612576351[/C][/ROW]
[ROW][C]26[/C][C]109.39[/C][C]108.490419818348[/C][C]0.89958018165197[/C][/ROW]
[ROW][C]27[/C][C]108.65[/C][C]110.417694579595[/C][C]-1.76769457959496[/C][/ROW]
[ROW][C]28[/C][C]108.33[/C][C]110.776873096927[/C][C]-2.44687309692698[/C][/ROW]
[ROW][C]29[/C][C]109.76[/C][C]108.156879611797[/C][C]1.60312038820281[/C][/ROW]
[ROW][C]30[/C][C]110.07[/C][C]108.841889944802[/C][C]1.22811005519847[/C][/ROW]
[ROW][C]31[/C][C]109.23[/C][C]108.36069173621[/C][C]0.869308263789804[/C][/ROW]
[ROW][C]32[/C][C]108.4[/C][C]108.116056368695[/C][C]0.283943631305405[/C][/ROW]
[ROW][C]33[/C][C]108.9[/C][C]109.729680564546[/C][C]-0.829680564546138[/C][/ROW]
[ROW][C]34[/C][C]109.14[/C][C]109.138496100062[/C][C]0.00150389993812894[/C][/ROW]
[ROW][C]35[/C][C]109.27[/C][C]109.158876924934[/C][C]0.111123075065549[/C][/ROW]
[ROW][C]36[/C][C]109.38[/C][C]110.370435345594[/C][C]-0.990435345593511[/C][/ROW]
[ROW][C]37[/C][C]109.66[/C][C]110.770711201341[/C][C]-1.11071120134136[/C][/ROW]
[ROW][C]38[/C][C]109.87[/C][C]110.42190787445[/C][C]-0.551907874449711[/C][/ROW]
[ROW][C]39[/C][C]109.98[/C][C]110.310584051894[/C][C]-0.330584051894235[/C][/ROW]
[ROW][C]40[/C][C]111.24[/C][C]110.852227220456[/C][C]0.387772779543866[/C][/ROW]
[ROW][C]41[/C][C]110.03[/C][C]111.572552632247[/C][C]-1.54255263224725[/C][/ROW]
[ROW][C]42[/C][C]111.43[/C][C]110.828693811979[/C][C]0.601306188021269[/C][/ROW]
[ROW][C]43[/C][C]110.28[/C][C]109.905688763788[/C][C]0.374311236211881[/C][/ROW]
[ROW][C]44[/C][C]109.53[/C][C]109.14514161638[/C][C]0.384858383619914[/C][/ROW]
[ROW][C]45[/C][C]111.97[/C][C]110.182130252592[/C][C]1.78786974740777[/C][/ROW]
[ROW][C]46[/C][C]111.89[/C][C]111.066999384391[/C][C]0.82300061560899[/C][/ROW]
[ROW][C]47[/C][C]112.93[/C][C]111.466992820886[/C][C]1.46300717911365[/C][/ROW]
[ROW][C]48[/C][C]113.11[/C][C]112.594350384393[/C][C]0.515649615606804[/C][/ROW]
[ROW][C]49[/C][C]112.95[/C][C]113.51294115748[/C][C]-0.56294115748014[/C][/ROW]
[ROW][C]50[/C][C]114.08[/C][C]113.685853736357[/C][C]0.39414626364325[/C][/ROW]
[ROW][C]51[/C][C]115.27[/C][C]114.064280687512[/C][C]1.20571931248757[/C][/ROW]
[ROW][C]52[/C][C]114.73[/C][C]115.599727286971[/C][C]-0.869727286971425[/C][/ROW]
[ROW][C]53[/C][C]114.97[/C][C]114.764306065826[/C][C]0.205693934174207[/C][/ROW]
[ROW][C]54[/C][C]113.78[/C][C]115.884836657601[/C][C]-2.10483665760113[/C][/ROW]
[ROW][C]55[/C][C]113.7[/C][C]113.785486751265[/C][C]-0.0854867512650372[/C][/ROW]
[ROW][C]56[/C][C]113.91[/C][C]112.852228432085[/C][C]1.0577715679147[/C][/ROW]
[ROW][C]57[/C][C]114.22[/C][C]114.926364708403[/C][C]-0.706364708402688[/C][/ROW]
[ROW][C]58[/C][C]115.32[/C][C]114.309138764734[/C][C]1.01086123526632[/C][/ROW]
[ROW][C]59[/C][C]113.5[/C][C]115.135996570253[/C][C]-1.63599657025331[/C][/ROW]
[ROW][C]60[/C][C]115.35[/C][C]114.536105492436[/C][C]0.813894507564427[/C][/ROW]
[ROW][C]61[/C][C]113.23[/C][C]114.974058833182[/C][C]-1.74405883318151[/C][/ROW]
[ROW][C]62[/C][C]113.65[/C][C]115.217591546572[/C][C]-1.56759154657178[/C][/ROW]
[ROW][C]63[/C][C]114.82[/C][C]115.283049118493[/C][C]-0.463049118492677[/C][/ROW]
[ROW][C]64[/C][C]113.54[/C][C]115.022799557295[/C][C]-1.48279955729451[/C][/ROW]
[ROW][C]65[/C][C]113.97[/C][C]114.544012786145[/C][C]-0.574012786144849[/C][/ROW]
[ROW][C]66[/C][C]113.79[/C][C]114.084078940838[/C][C]-0.294078940838475[/C][/ROW]
[ROW][C]67[/C][C]113.27[/C][C]113.80454005064[/C][C]-0.53454005063972[/C][/ROW]
[ROW][C]68[/C][C]114.35[/C][C]113.329119350641[/C][C]1.02088064935913[/C][/ROW]
[ROW][C]69[/C][C]113.68[/C][C]114.413383044984[/C][C]-0.733383044984194[/C][/ROW]
[ROW][C]70[/C][C]115.3[/C][C]114.735272268066[/C][C]0.564727731933843[/C][/ROW]
[ROW][C]71[/C][C]113.69[/C][C]113.925209902154[/C][C]-0.23520990215377[/C][/ROW]
[ROW][C]72[/C][C]115.31[/C][C]115.224018879616[/C][C]0.0859811203835079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210653&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210653&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
13105.88105.5033760683760.376623931623897
14104.88104.5507384397690.329261560231444
15106.59106.2513762500780.338623749921567
16107.8107.387732814790.412267185209672
17106.31105.8535191101610.456480889838843
18106.53106.1177239781260.412276021874078
19106.25104.6789303715181.57106962848165
20105.87105.2113565723110.658643427688631
21107.83106.7219796085921.10802039140822
22108.01106.8600163614551.14998363854467
23107.9108.039347814362-0.13934781436231
24108.55109.728020459495-1.1780204594955
25108.83110.114136125764-1.28413612576351
26109.39108.4904198183480.89958018165197
27108.65110.417694579595-1.76769457959496
28108.33110.776873096927-2.44687309692698
29109.76108.1568796117971.60312038820281
30110.07108.8418899448021.22811005519847
31109.23108.360691736210.869308263789804
32108.4108.1160563686950.283943631305405
33108.9109.729680564546-0.829680564546138
34109.14109.1384961000620.00150389993812894
35109.27109.1588769249340.111123075065549
36109.38110.370435345594-0.990435345593511
37109.66110.770711201341-1.11071120134136
38109.87110.42190787445-0.551907874449711
39109.98110.310584051894-0.330584051894235
40111.24110.8522272204560.387772779543866
41110.03111.572552632247-1.54255263224725
42111.43110.8286938119790.601306188021269
43110.28109.9056887637880.374311236211881
44109.53109.145141616380.384858383619914
45111.97110.1821302525921.78786974740777
46111.89111.0669993843910.82300061560899
47112.93111.4669928208861.46300717911365
48113.11112.5943503843930.515649615606804
49112.95113.51294115748-0.56294115748014
50114.08113.6858537363570.39414626364325
51115.27114.0642806875121.20571931248757
52114.73115.599727286971-0.869727286971425
53114.97114.7643060658260.205693934174207
54113.78115.884836657601-2.10483665760113
55113.7113.785486751265-0.0854867512650372
56113.91112.8522284320851.0577715679147
57114.22114.926364708403-0.706364708402688
58115.32114.3091387647341.01086123526632
59113.5115.135996570253-1.63599657025331
60115.35114.5361054924360.813894507564427
61113.23114.974058833182-1.74405883318151
62113.65115.217591546572-1.56759154657178
63114.82115.283049118493-0.463049118492677
64113.54115.022799557295-1.48279955729451
65113.97114.544012786145-0.574012786144849
66113.79114.084078940838-0.294078940838475
67113.27113.80454005064-0.53454005063972
68114.35113.3291193506411.02088064935913
69113.68114.413383044984-0.733383044984194
70115.3114.7352722680660.564727731933843
71113.69113.925209902154-0.23520990215377
72115.31115.2240188796160.0859811203835079







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73113.964797596315111.976199617429115.953395575201
74114.98314820548112.849887882977117.116408527983
75116.268114976052113.999397874803118.536832077301
76115.62376096426113.227231188222118.020290740298
77116.223307236532113.705444521972118.741169951092
78116.141067900275113.507456248701118.774679551849
79115.842750175819113.098266979798118.58723337184
80116.435026252288113.583979831204119.286072673372
81116.152784875188113.199017217245119.106552533132
82117.477293875888114.424259146468120.530328605308
83116.005586225126112.856411930016119.154760520236
84117.573344309761114.330879749751120.81580886977

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 113.964797596315 & 111.976199617429 & 115.953395575201 \tabularnewline
74 & 114.98314820548 & 112.849887882977 & 117.116408527983 \tabularnewline
75 & 116.268114976052 & 113.999397874803 & 118.536832077301 \tabularnewline
76 & 115.62376096426 & 113.227231188222 & 118.020290740298 \tabularnewline
77 & 116.223307236532 & 113.705444521972 & 118.741169951092 \tabularnewline
78 & 116.141067900275 & 113.507456248701 & 118.774679551849 \tabularnewline
79 & 115.842750175819 & 113.098266979798 & 118.58723337184 \tabularnewline
80 & 116.435026252288 & 113.583979831204 & 119.286072673372 \tabularnewline
81 & 116.152784875188 & 113.199017217245 & 119.106552533132 \tabularnewline
82 & 117.477293875888 & 114.424259146468 & 120.530328605308 \tabularnewline
83 & 116.005586225126 & 112.856411930016 & 119.154760520236 \tabularnewline
84 & 117.573344309761 & 114.330879749751 & 120.81580886977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210653&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]113.964797596315[/C][C]111.976199617429[/C][C]115.953395575201[/C][/ROW]
[ROW][C]74[/C][C]114.98314820548[/C][C]112.849887882977[/C][C]117.116408527983[/C][/ROW]
[ROW][C]75[/C][C]116.268114976052[/C][C]113.999397874803[/C][C]118.536832077301[/C][/ROW]
[ROW][C]76[/C][C]115.62376096426[/C][C]113.227231188222[/C][C]118.020290740298[/C][/ROW]
[ROW][C]77[/C][C]116.223307236532[/C][C]113.705444521972[/C][C]118.741169951092[/C][/ROW]
[ROW][C]78[/C][C]116.141067900275[/C][C]113.507456248701[/C][C]118.774679551849[/C][/ROW]
[ROW][C]79[/C][C]115.842750175819[/C][C]113.098266979798[/C][C]118.58723337184[/C][/ROW]
[ROW][C]80[/C][C]116.435026252288[/C][C]113.583979831204[/C][C]119.286072673372[/C][/ROW]
[ROW][C]81[/C][C]116.152784875188[/C][C]113.199017217245[/C][C]119.106552533132[/C][/ROW]
[ROW][C]82[/C][C]117.477293875888[/C][C]114.424259146468[/C][C]120.530328605308[/C][/ROW]
[ROW][C]83[/C][C]116.005586225126[/C][C]112.856411930016[/C][C]119.154760520236[/C][/ROW]
[ROW][C]84[/C][C]117.573344309761[/C][C]114.330879749751[/C][C]120.81580886977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210653&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210653&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
73113.964797596315111.976199617429115.953395575201
74114.98314820548112.849887882977117.116408527983
75116.268114976052113.999397874803118.536832077301
76115.62376096426113.227231188222118.020290740298
77116.223307236532113.705444521972118.741169951092
78116.141067900275113.507456248701118.774679551849
79115.842750175819113.098266979798118.58723337184
80116.435026252288113.583979831204119.286072673372
81116.152784875188113.199017217245119.106552533132
82117.477293875888114.424259146468120.530328605308
83116.005586225126112.856411930016119.154760520236
84117.573344309761114.330879749751120.81580886977



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')