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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 20 Dec 2012 08:44:34 -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/2012/Dec/20/t1356011100jmef858a5o9lr6s.htm/, Retrieved Thu, 28 Mar 2024 17:58:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202681, Retrieved Thu, 28 Mar 2024 17:58:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-20 13:44:34] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
79,49
79,69
79,86
79,87
79,83
79,83
79,83
79,37
79,53
79,78
79,94
79,97
79,97
79,98
80,25
80,38
80,13
80,15
80,15
80,18
80,47
80,83
80,62
80,66
80,66
80,67
80,8
81,04
81,24
81,26
81,26
81,47
81,94
82,83
82,29
82,32
82,32
82,3
82,54
82,54
82,62
82,63
82,63
82,63
82,71
83,25
83,14
83,34
83,34
83,37
83,33
83,26
83,66
83,64
83,64
83,71
83,87
84,17
84,35
84,44
84,44
84,45
84,67
84,95
84,89
84,93
84,93
84,93
85,45
85,77
85,79
85,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202681&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202681&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202681&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.050569900667479
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.050569900667479 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202681&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.050569900667479[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202681&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202681&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
alpha1
beta0.050569900667479
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
379.8679.89-0.0300000000000011
479.8780.05848290298-0.18848290297997
579.8380.0589513412988-0.228951341298767
679.8380.0073732947116-0.1773732947116
779.8379.998403544817-0.168403544816968
879.3779.9898873942835-0.619887394283523
979.5379.49853975032960.0314602496704168
1079.7879.66013069203040.119869307969608
1179.9479.91619247102750.0238075289724975
1279.9780.0773964154028-0.107396415402775
1379.9780.1019653893438-0.131965389343804
1479.9880.0952919127132-0.115291912713147
1580.2580.09946161213950.150538387860522
1680.3880.37707432346020.0029256765397605
1780.1380.5072222746322-0.377222274632231
1880.1580.2381461816745-0.0881461816745031
1980.1580.253688638023-0.103688638023016
2080.1880.2484451138979-0.0684451138978517
2180.4780.27498385128690.195016148713137
2280.8380.57484579855580.255154201444157
2380.6280.9477489211778-0.327748921177758
2480.6680.7211746907899-0.0611746907899402
2580.6680.7580810927533-0.0980810927533184
2680.6780.7531211416354-0.0831211416354165
2780.880.75891771375960.0410822862404387
2881.0480.89099524089390.149004759106077
2981.2481.13853039676090.101469603239082
3081.2681.3436617045175-0.0836617045174677
3181.2681.3594309404304-0.0994309404303522
3281.4781.35440272764950.115597272350485
3381.9481.57024847022970.369751529770284
3482.8382.05894676836180.771053231638163
3582.2982.9879388536951-0.697938853695121
3682.3282.4126441551918-0.0926441551917918
3782.3282.4379591494663-0.117959149466316
3882.382.431993966995-0.131993966994983
3982.5482.40531904519530.134680954804665
4082.5482.6521298477016-0.11212984770161
4182.6282.6464594524415-0.0264594524414861
4282.6382.7251214005598-0.0951214005598047
4382.6382.7303111207821-0.100311120782138
4482.6382.7252383973683-0.0952383973683482
4582.7182.7204222010737-0.0104222010736947
4683.2582.79989515140070.450104848599338
4783.1483.3626569088843-0.222656908884275
4883.3483.24139717111910.098602828880928
4983.3483.4463835063811-0.106383506381121
5083.3783.4410037030308-0.0710037030307689
5183.3383.4674130528215-0.137413052821486
5283.2683.4204640883899-0.160464088389872
5383.6683.34234943537930.317650564620692
5483.6483.7584129928791-0.118412992879144
5583.6483.7324248595915-0.0924248595915032
5683.7183.7277509436228-0.0177509436227581
5783.8783.7968532801670.0731467198330051
5884.1783.96055230252310.20944769747689
5984.3584.27114405177950.0788559482204505
6084.4484.4551317892481-0.0151317892480876
6184.4484.5443665761689-0.1043665761689
6284.4584.539088768779-0.0890887687790212
6384.6784.54458355859130.125416441408717
6484.9584.77092585557540.179074144424604
6584.8985.0599816172711-0.169981617271063
6684.9384.9913856637704-0.0613856637703662
6784.9385.0282813968511-0.0982813968510925
6884.9385.0233113163749-0.0933113163748658
6985.4585.01859257237460.431407427625359
7085.7785.56040880313690.20959119686313
7185.7985.891007809143-0.101007809142999
7285.985.905899854268-0.00589985426800865

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 79.86 & 79.89 & -0.0300000000000011 \tabularnewline
4 & 79.87 & 80.05848290298 & -0.18848290297997 \tabularnewline
5 & 79.83 & 80.0589513412988 & -0.228951341298767 \tabularnewline
6 & 79.83 & 80.0073732947116 & -0.1773732947116 \tabularnewline
7 & 79.83 & 79.998403544817 & -0.168403544816968 \tabularnewline
8 & 79.37 & 79.9898873942835 & -0.619887394283523 \tabularnewline
9 & 79.53 & 79.4985397503296 & 0.0314602496704168 \tabularnewline
10 & 79.78 & 79.6601306920304 & 0.119869307969608 \tabularnewline
11 & 79.94 & 79.9161924710275 & 0.0238075289724975 \tabularnewline
12 & 79.97 & 80.0773964154028 & -0.107396415402775 \tabularnewline
13 & 79.97 & 80.1019653893438 & -0.131965389343804 \tabularnewline
14 & 79.98 & 80.0952919127132 & -0.115291912713147 \tabularnewline
15 & 80.25 & 80.0994616121395 & 0.150538387860522 \tabularnewline
16 & 80.38 & 80.3770743234602 & 0.0029256765397605 \tabularnewline
17 & 80.13 & 80.5072222746322 & -0.377222274632231 \tabularnewline
18 & 80.15 & 80.2381461816745 & -0.0881461816745031 \tabularnewline
19 & 80.15 & 80.253688638023 & -0.103688638023016 \tabularnewline
20 & 80.18 & 80.2484451138979 & -0.0684451138978517 \tabularnewline
21 & 80.47 & 80.2749838512869 & 0.195016148713137 \tabularnewline
22 & 80.83 & 80.5748457985558 & 0.255154201444157 \tabularnewline
23 & 80.62 & 80.9477489211778 & -0.327748921177758 \tabularnewline
24 & 80.66 & 80.7211746907899 & -0.0611746907899402 \tabularnewline
25 & 80.66 & 80.7580810927533 & -0.0980810927533184 \tabularnewline
26 & 80.67 & 80.7531211416354 & -0.0831211416354165 \tabularnewline
27 & 80.8 & 80.7589177137596 & 0.0410822862404387 \tabularnewline
28 & 81.04 & 80.8909952408939 & 0.149004759106077 \tabularnewline
29 & 81.24 & 81.1385303967609 & 0.101469603239082 \tabularnewline
30 & 81.26 & 81.3436617045175 & -0.0836617045174677 \tabularnewline
31 & 81.26 & 81.3594309404304 & -0.0994309404303522 \tabularnewline
32 & 81.47 & 81.3544027276495 & 0.115597272350485 \tabularnewline
33 & 81.94 & 81.5702484702297 & 0.369751529770284 \tabularnewline
34 & 82.83 & 82.0589467683618 & 0.771053231638163 \tabularnewline
35 & 82.29 & 82.9879388536951 & -0.697938853695121 \tabularnewline
36 & 82.32 & 82.4126441551918 & -0.0926441551917918 \tabularnewline
37 & 82.32 & 82.4379591494663 & -0.117959149466316 \tabularnewline
38 & 82.3 & 82.431993966995 & -0.131993966994983 \tabularnewline
39 & 82.54 & 82.4053190451953 & 0.134680954804665 \tabularnewline
40 & 82.54 & 82.6521298477016 & -0.11212984770161 \tabularnewline
41 & 82.62 & 82.6464594524415 & -0.0264594524414861 \tabularnewline
42 & 82.63 & 82.7251214005598 & -0.0951214005598047 \tabularnewline
43 & 82.63 & 82.7303111207821 & -0.100311120782138 \tabularnewline
44 & 82.63 & 82.7252383973683 & -0.0952383973683482 \tabularnewline
45 & 82.71 & 82.7204222010737 & -0.0104222010736947 \tabularnewline
46 & 83.25 & 82.7998951514007 & 0.450104848599338 \tabularnewline
47 & 83.14 & 83.3626569088843 & -0.222656908884275 \tabularnewline
48 & 83.34 & 83.2413971711191 & 0.098602828880928 \tabularnewline
49 & 83.34 & 83.4463835063811 & -0.106383506381121 \tabularnewline
50 & 83.37 & 83.4410037030308 & -0.0710037030307689 \tabularnewline
51 & 83.33 & 83.4674130528215 & -0.137413052821486 \tabularnewline
52 & 83.26 & 83.4204640883899 & -0.160464088389872 \tabularnewline
53 & 83.66 & 83.3423494353793 & 0.317650564620692 \tabularnewline
54 & 83.64 & 83.7584129928791 & -0.118412992879144 \tabularnewline
55 & 83.64 & 83.7324248595915 & -0.0924248595915032 \tabularnewline
56 & 83.71 & 83.7277509436228 & -0.0177509436227581 \tabularnewline
57 & 83.87 & 83.796853280167 & 0.0731467198330051 \tabularnewline
58 & 84.17 & 83.9605523025231 & 0.20944769747689 \tabularnewline
59 & 84.35 & 84.2711440517795 & 0.0788559482204505 \tabularnewline
60 & 84.44 & 84.4551317892481 & -0.0151317892480876 \tabularnewline
61 & 84.44 & 84.5443665761689 & -0.1043665761689 \tabularnewline
62 & 84.45 & 84.539088768779 & -0.0890887687790212 \tabularnewline
63 & 84.67 & 84.5445835585913 & 0.125416441408717 \tabularnewline
64 & 84.95 & 84.7709258555754 & 0.179074144424604 \tabularnewline
65 & 84.89 & 85.0599816172711 & -0.169981617271063 \tabularnewline
66 & 84.93 & 84.9913856637704 & -0.0613856637703662 \tabularnewline
67 & 84.93 & 85.0282813968511 & -0.0982813968510925 \tabularnewline
68 & 84.93 & 85.0233113163749 & -0.0933113163748658 \tabularnewline
69 & 85.45 & 85.0185925723746 & 0.431407427625359 \tabularnewline
70 & 85.77 & 85.5604088031369 & 0.20959119686313 \tabularnewline
71 & 85.79 & 85.891007809143 & -0.101007809142999 \tabularnewline
72 & 85.9 & 85.905899854268 & -0.00589985426800865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202681&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]79.86[/C][C]79.89[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]4[/C][C]79.87[/C][C]80.05848290298[/C][C]-0.18848290297997[/C][/ROW]
[ROW][C]5[/C][C]79.83[/C][C]80.0589513412988[/C][C]-0.228951341298767[/C][/ROW]
[ROW][C]6[/C][C]79.83[/C][C]80.0073732947116[/C][C]-0.1773732947116[/C][/ROW]
[ROW][C]7[/C][C]79.83[/C][C]79.998403544817[/C][C]-0.168403544816968[/C][/ROW]
[ROW][C]8[/C][C]79.37[/C][C]79.9898873942835[/C][C]-0.619887394283523[/C][/ROW]
[ROW][C]9[/C][C]79.53[/C][C]79.4985397503296[/C][C]0.0314602496704168[/C][/ROW]
[ROW][C]10[/C][C]79.78[/C][C]79.6601306920304[/C][C]0.119869307969608[/C][/ROW]
[ROW][C]11[/C][C]79.94[/C][C]79.9161924710275[/C][C]0.0238075289724975[/C][/ROW]
[ROW][C]12[/C][C]79.97[/C][C]80.0773964154028[/C][C]-0.107396415402775[/C][/ROW]
[ROW][C]13[/C][C]79.97[/C][C]80.1019653893438[/C][C]-0.131965389343804[/C][/ROW]
[ROW][C]14[/C][C]79.98[/C][C]80.0952919127132[/C][C]-0.115291912713147[/C][/ROW]
[ROW][C]15[/C][C]80.25[/C][C]80.0994616121395[/C][C]0.150538387860522[/C][/ROW]
[ROW][C]16[/C][C]80.38[/C][C]80.3770743234602[/C][C]0.0029256765397605[/C][/ROW]
[ROW][C]17[/C][C]80.13[/C][C]80.5072222746322[/C][C]-0.377222274632231[/C][/ROW]
[ROW][C]18[/C][C]80.15[/C][C]80.2381461816745[/C][C]-0.0881461816745031[/C][/ROW]
[ROW][C]19[/C][C]80.15[/C][C]80.253688638023[/C][C]-0.103688638023016[/C][/ROW]
[ROW][C]20[/C][C]80.18[/C][C]80.2484451138979[/C][C]-0.0684451138978517[/C][/ROW]
[ROW][C]21[/C][C]80.47[/C][C]80.2749838512869[/C][C]0.195016148713137[/C][/ROW]
[ROW][C]22[/C][C]80.83[/C][C]80.5748457985558[/C][C]0.255154201444157[/C][/ROW]
[ROW][C]23[/C][C]80.62[/C][C]80.9477489211778[/C][C]-0.327748921177758[/C][/ROW]
[ROW][C]24[/C][C]80.66[/C][C]80.7211746907899[/C][C]-0.0611746907899402[/C][/ROW]
[ROW][C]25[/C][C]80.66[/C][C]80.7580810927533[/C][C]-0.0980810927533184[/C][/ROW]
[ROW][C]26[/C][C]80.67[/C][C]80.7531211416354[/C][C]-0.0831211416354165[/C][/ROW]
[ROW][C]27[/C][C]80.8[/C][C]80.7589177137596[/C][C]0.0410822862404387[/C][/ROW]
[ROW][C]28[/C][C]81.04[/C][C]80.8909952408939[/C][C]0.149004759106077[/C][/ROW]
[ROW][C]29[/C][C]81.24[/C][C]81.1385303967609[/C][C]0.101469603239082[/C][/ROW]
[ROW][C]30[/C][C]81.26[/C][C]81.3436617045175[/C][C]-0.0836617045174677[/C][/ROW]
[ROW][C]31[/C][C]81.26[/C][C]81.3594309404304[/C][C]-0.0994309404303522[/C][/ROW]
[ROW][C]32[/C][C]81.47[/C][C]81.3544027276495[/C][C]0.115597272350485[/C][/ROW]
[ROW][C]33[/C][C]81.94[/C][C]81.5702484702297[/C][C]0.369751529770284[/C][/ROW]
[ROW][C]34[/C][C]82.83[/C][C]82.0589467683618[/C][C]0.771053231638163[/C][/ROW]
[ROW][C]35[/C][C]82.29[/C][C]82.9879388536951[/C][C]-0.697938853695121[/C][/ROW]
[ROW][C]36[/C][C]82.32[/C][C]82.4126441551918[/C][C]-0.0926441551917918[/C][/ROW]
[ROW][C]37[/C][C]82.32[/C][C]82.4379591494663[/C][C]-0.117959149466316[/C][/ROW]
[ROW][C]38[/C][C]82.3[/C][C]82.431993966995[/C][C]-0.131993966994983[/C][/ROW]
[ROW][C]39[/C][C]82.54[/C][C]82.4053190451953[/C][C]0.134680954804665[/C][/ROW]
[ROW][C]40[/C][C]82.54[/C][C]82.6521298477016[/C][C]-0.11212984770161[/C][/ROW]
[ROW][C]41[/C][C]82.62[/C][C]82.6464594524415[/C][C]-0.0264594524414861[/C][/ROW]
[ROW][C]42[/C][C]82.63[/C][C]82.7251214005598[/C][C]-0.0951214005598047[/C][/ROW]
[ROW][C]43[/C][C]82.63[/C][C]82.7303111207821[/C][C]-0.100311120782138[/C][/ROW]
[ROW][C]44[/C][C]82.63[/C][C]82.7252383973683[/C][C]-0.0952383973683482[/C][/ROW]
[ROW][C]45[/C][C]82.71[/C][C]82.7204222010737[/C][C]-0.0104222010736947[/C][/ROW]
[ROW][C]46[/C][C]83.25[/C][C]82.7998951514007[/C][C]0.450104848599338[/C][/ROW]
[ROW][C]47[/C][C]83.14[/C][C]83.3626569088843[/C][C]-0.222656908884275[/C][/ROW]
[ROW][C]48[/C][C]83.34[/C][C]83.2413971711191[/C][C]0.098602828880928[/C][/ROW]
[ROW][C]49[/C][C]83.34[/C][C]83.4463835063811[/C][C]-0.106383506381121[/C][/ROW]
[ROW][C]50[/C][C]83.37[/C][C]83.4410037030308[/C][C]-0.0710037030307689[/C][/ROW]
[ROW][C]51[/C][C]83.33[/C][C]83.4674130528215[/C][C]-0.137413052821486[/C][/ROW]
[ROW][C]52[/C][C]83.26[/C][C]83.4204640883899[/C][C]-0.160464088389872[/C][/ROW]
[ROW][C]53[/C][C]83.66[/C][C]83.3423494353793[/C][C]0.317650564620692[/C][/ROW]
[ROW][C]54[/C][C]83.64[/C][C]83.7584129928791[/C][C]-0.118412992879144[/C][/ROW]
[ROW][C]55[/C][C]83.64[/C][C]83.7324248595915[/C][C]-0.0924248595915032[/C][/ROW]
[ROW][C]56[/C][C]83.71[/C][C]83.7277509436228[/C][C]-0.0177509436227581[/C][/ROW]
[ROW][C]57[/C][C]83.87[/C][C]83.796853280167[/C][C]0.0731467198330051[/C][/ROW]
[ROW][C]58[/C][C]84.17[/C][C]83.9605523025231[/C][C]0.20944769747689[/C][/ROW]
[ROW][C]59[/C][C]84.35[/C][C]84.2711440517795[/C][C]0.0788559482204505[/C][/ROW]
[ROW][C]60[/C][C]84.44[/C][C]84.4551317892481[/C][C]-0.0151317892480876[/C][/ROW]
[ROW][C]61[/C][C]84.44[/C][C]84.5443665761689[/C][C]-0.1043665761689[/C][/ROW]
[ROW][C]62[/C][C]84.45[/C][C]84.539088768779[/C][C]-0.0890887687790212[/C][/ROW]
[ROW][C]63[/C][C]84.67[/C][C]84.5445835585913[/C][C]0.125416441408717[/C][/ROW]
[ROW][C]64[/C][C]84.95[/C][C]84.7709258555754[/C][C]0.179074144424604[/C][/ROW]
[ROW][C]65[/C][C]84.89[/C][C]85.0599816172711[/C][C]-0.169981617271063[/C][/ROW]
[ROW][C]66[/C][C]84.93[/C][C]84.9913856637704[/C][C]-0.0613856637703662[/C][/ROW]
[ROW][C]67[/C][C]84.93[/C][C]85.0282813968511[/C][C]-0.0982813968510925[/C][/ROW]
[ROW][C]68[/C][C]84.93[/C][C]85.0233113163749[/C][C]-0.0933113163748658[/C][/ROW]
[ROW][C]69[/C][C]85.45[/C][C]85.0185925723746[/C][C]0.431407427625359[/C][/ROW]
[ROW][C]70[/C][C]85.77[/C][C]85.5604088031369[/C][C]0.20959119686313[/C][/ROW]
[ROW][C]71[/C][C]85.79[/C][C]85.891007809143[/C][C]-0.101007809142999[/C][/ROW]
[ROW][C]72[/C][C]85.9[/C][C]85.905899854268[/C][C]-0.00589985426800865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202681&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202681&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
379.8679.89-0.0300000000000011
479.8780.05848290298-0.18848290297997
579.8380.0589513412988-0.228951341298767
679.8380.0073732947116-0.1773732947116
779.8379.998403544817-0.168403544816968
879.3779.9898873942835-0.619887394283523
979.5379.49853975032960.0314602496704168
1079.7879.66013069203040.119869307969608
1179.9479.91619247102750.0238075289724975
1279.9780.0773964154028-0.107396415402775
1379.9780.1019653893438-0.131965389343804
1479.9880.0952919127132-0.115291912713147
1580.2580.09946161213950.150538387860522
1680.3880.37707432346020.0029256765397605
1780.1380.5072222746322-0.377222274632231
1880.1580.2381461816745-0.0881461816745031
1980.1580.253688638023-0.103688638023016
2080.1880.2484451138979-0.0684451138978517
2180.4780.27498385128690.195016148713137
2280.8380.57484579855580.255154201444157
2380.6280.9477489211778-0.327748921177758
2480.6680.7211746907899-0.0611746907899402
2580.6680.7580810927533-0.0980810927533184
2680.6780.7531211416354-0.0831211416354165
2780.880.75891771375960.0410822862404387
2881.0480.89099524089390.149004759106077
2981.2481.13853039676090.101469603239082
3081.2681.3436617045175-0.0836617045174677
3181.2681.3594309404304-0.0994309404303522
3281.4781.35440272764950.115597272350485
3381.9481.57024847022970.369751529770284
3482.8382.05894676836180.771053231638163
3582.2982.9879388536951-0.697938853695121
3682.3282.4126441551918-0.0926441551917918
3782.3282.4379591494663-0.117959149466316
3882.382.431993966995-0.131993966994983
3982.5482.40531904519530.134680954804665
4082.5482.6521298477016-0.11212984770161
4182.6282.6464594524415-0.0264594524414861
4282.6382.7251214005598-0.0951214005598047
4382.6382.7303111207821-0.100311120782138
4482.6382.7252383973683-0.0952383973683482
4582.7182.7204222010737-0.0104222010736947
4683.2582.79989515140070.450104848599338
4783.1483.3626569088843-0.222656908884275
4883.3483.24139717111910.098602828880928
4983.3483.4463835063811-0.106383506381121
5083.3783.4410037030308-0.0710037030307689
5183.3383.4674130528215-0.137413052821486
5283.2683.4204640883899-0.160464088389872
5383.6683.34234943537930.317650564620692
5483.6483.7584129928791-0.118412992879144
5583.6483.7324248595915-0.0924248595915032
5683.7183.7277509436228-0.0177509436227581
5783.8783.7968532801670.0731467198330051
5884.1783.96055230252310.20944769747689
5984.3584.27114405177950.0788559482204505
6084.4484.4551317892481-0.0151317892480876
6184.4484.5443665761689-0.1043665761689
6284.4584.539088768779-0.0890887687790212
6384.6784.54458355859130.125416441408717
6484.9584.77092585557540.179074144424604
6584.8985.0599816172711-0.169981617271063
6684.9384.9913856637704-0.0613856637703662
6784.9385.0282813968511-0.0982813968510925
6884.9385.0233113163749-0.0933113163748658
6985.4585.01859257237460.431407427625359
7085.7785.56040880313690.20959119686313
7185.7985.891007809143-0.101007809142999
7285.985.905899854268-0.00589985426800865







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7386.015601499223785.592662940747986.4385400576996
7486.131202998447585.51776752502186.7446384718739
7586.246804497671285.476614224310887.0169947710316
7686.362405996894985.451109203665187.2737027901247
7786.478007496118685.43444420895587.5215707832823
7886.593608995342485.423226402419987.7639915882648
7986.709210494566185.415498790362688.0029221987696
8086.824811993789885.410024764772888.2395992228068
8186.940413493013685.405972522188188.474854463839
8287.056014992237385.402756563554988.7092734209196
8387.17161649146185.399950380051688.9432826028704
8487.287217990684785.397234890863189.1772010905064

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 86.0156014992237 & 85.5926629407479 & 86.4385400576996 \tabularnewline
74 & 86.1312029984475 & 85.517767525021 & 86.7446384718739 \tabularnewline
75 & 86.2468044976712 & 85.4766142243108 & 87.0169947710316 \tabularnewline
76 & 86.3624059968949 & 85.4511092036651 & 87.2737027901247 \tabularnewline
77 & 86.4780074961186 & 85.434444208955 & 87.5215707832823 \tabularnewline
78 & 86.5936089953424 & 85.4232264024199 & 87.7639915882648 \tabularnewline
79 & 86.7092104945661 & 85.4154987903626 & 88.0029221987696 \tabularnewline
80 & 86.8248119937898 & 85.4100247647728 & 88.2395992228068 \tabularnewline
81 & 86.9404134930136 & 85.4059725221881 & 88.474854463839 \tabularnewline
82 & 87.0560149922373 & 85.4027565635549 & 88.7092734209196 \tabularnewline
83 & 87.171616491461 & 85.3999503800516 & 88.9432826028704 \tabularnewline
84 & 87.2872179906847 & 85.3972348908631 & 89.1772010905064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202681&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]86.0156014992237[/C][C]85.5926629407479[/C][C]86.4385400576996[/C][/ROW]
[ROW][C]74[/C][C]86.1312029984475[/C][C]85.517767525021[/C][C]86.7446384718739[/C][/ROW]
[ROW][C]75[/C][C]86.2468044976712[/C][C]85.4766142243108[/C][C]87.0169947710316[/C][/ROW]
[ROW][C]76[/C][C]86.3624059968949[/C][C]85.4511092036651[/C][C]87.2737027901247[/C][/ROW]
[ROW][C]77[/C][C]86.4780074961186[/C][C]85.434444208955[/C][C]87.5215707832823[/C][/ROW]
[ROW][C]78[/C][C]86.5936089953424[/C][C]85.4232264024199[/C][C]87.7639915882648[/C][/ROW]
[ROW][C]79[/C][C]86.7092104945661[/C][C]85.4154987903626[/C][C]88.0029221987696[/C][/ROW]
[ROW][C]80[/C][C]86.8248119937898[/C][C]85.4100247647728[/C][C]88.2395992228068[/C][/ROW]
[ROW][C]81[/C][C]86.9404134930136[/C][C]85.4059725221881[/C][C]88.474854463839[/C][/ROW]
[ROW][C]82[/C][C]87.0560149922373[/C][C]85.4027565635549[/C][C]88.7092734209196[/C][/ROW]
[ROW][C]83[/C][C]87.171616491461[/C][C]85.3999503800516[/C][C]88.9432826028704[/C][/ROW]
[ROW][C]84[/C][C]87.2872179906847[/C][C]85.3972348908631[/C][C]89.1772010905064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202681&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202681&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
7386.015601499223785.592662940747986.4385400576996
7486.131202998447585.51776752502186.7446384718739
7586.246804497671285.476614224310887.0169947710316
7686.362405996894985.451109203665187.2737027901247
7786.478007496118685.43444420895587.5215707832823
7886.593608995342485.423226402419987.7639915882648
7986.709210494566185.415498790362688.0029221987696
8086.824811993789885.410024764772888.2395992228068
8186.940413493013685.405972522188188.474854463839
8287.056014992237385.402756563554988.7092734209196
8387.17161649146185.399950380051688.9432826028704
8487.287217990684785.397234890863189.1772010905064



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')