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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 22:48:37 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1428011385lrd1go7y8wikoim.htm/, Retrieved Thu, 09 May 2024 14:00:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278680, Retrieved Thu, 09 May 2024 14:00:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-02 21:48:37] [567f06ca3de45fa0ce67a0a89b883c29] [Current]
- R PD    [Exponential Smoothing] [] [2015-05-27 06:56:14] [693750cd301bd4fecbcaa8326eb70b61]
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Dataseries X:
94,67
94,6
93,9
93,41
93,37
93,35
93,08
93,05
92,61
92,37
92,24
91,95
92,63
92,7
92,47
92,58
92,55
92,56
89,92
89,96
90,03
90,31
90,8
90,36
90,31
93,8
93,95
93,99
94,44
94,15
91,91
91,86
93,12
93,47
93,57
94,57
95,85
96,62
95,69
95,39
95,14
95,07
94,21
95,4
95,1
94,89
95,43
94,88
96,03
96,37
96,04
95,72
95,74
95,78
93,66
95,29
94,33
95,66
95,2
94,61
96,21
96,27
95,12
95,55
93,51
92,86
92,45
93,34
92,01
91,77
92,19
91,97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278680&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278680&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.911162626834157
beta0.0127439084794517
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.911162626834157 \tabularnewline
beta & 0.0127439084794517 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278680&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]0.911162626834157[/C][/ROW]
[ROW][C]beta[/C][C]0.0127439084794517[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278680&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
alpha0.911162626834157
beta0.0127439084794517
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.6393.1837376454169-0.55373764541693
1492.792.851162958723-0.15116295872302
1592.4792.5591704342222-0.0891704342222113
1692.5892.6195916102733-0.039591610273277
1792.5592.53675177320170.0132482267982965
1892.5692.52236426865290.0376357313471516
1989.9291.2562781549184-1.33627815491838
2089.9689.991106048618-0.0311060486180423
2190.0389.49387833349730.536121666502652
2290.3189.6694985926870.640501407313025
2390.890.02967234392450.77032765607548
2490.3690.3578789949310.00212100506897173
2590.3190.9864681054127-0.676468105412695
2693.890.56515902306313.23484097693691
2793.9593.39962676360570.550373236394279
2893.9994.0951847025459-0.105184702545913
2994.4494.00165347950750.438346520492544
3094.1594.427080773229-0.277080773229031
3191.9192.7718182179469-0.861818217946862
3291.8692.1094407889745-0.249440788974468
3393.1291.50447747479071.61552252520931
3493.4792.72682895479860.74317104520135
3593.5793.24970158956530.320298410434702
3694.5793.14533820197531.42466179802466
3795.8595.11349194159980.736508058400219
3896.6296.44892918339030.171070816609671
3995.6996.2990876593732-0.609087659373188
4095.3995.9242379313443-0.534237931344293
4195.1495.5250293742436-0.385029374243643
4295.0795.1621658260215-0.0921658260214713
4394.2193.63631568544540.57368431455464
4495.494.3872581551931.01274184480705
4595.195.1507572236542-0.0507572236542018
4694.8994.81094138578480.0790586142151568
4795.4394.7206105214230.709389478577009
4894.8895.0986403568399-0.218640356839941
4996.0395.52665558601790.503344413982092
5096.3796.6141029186162-0.244102918616193
5196.0496.02595692044490.0140430795551367
5295.7296.242432833223-0.522432833222965
5395.7495.8841877672734-0.144187767273422
5495.7895.7866137434055-0.00661374340552356
5593.6694.4078044994179-0.747804499417953
5695.2993.99552607463071.29447392536927
5794.3394.929460485005-0.599460485004954
5895.6694.10419621452851.55580378547153
5995.295.4333163944259-0.233316394425856
6094.6194.8781098512689-0.268109851268889
6196.2195.33006696046530.879933039534649
6296.2796.7063621473819-0.436362147381928
6395.1295.975390144136-0.855390144136024
6495.5595.34899083364010.201009166359867
6593.5195.6906289940365-2.18062899403651
6692.8693.7311196892674-0.871119689267374
6792.4591.51309152141810.936908478581856
6893.3492.80230075429080.537699245709234
6992.0192.8704395545034-0.860439554503401
7091.7791.979176964635-0.20917696463502
7192.1991.51047351127880.679526488721194
7291.9791.76539496674040.204605033259597

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.63 & 93.1837376454169 & -0.55373764541693 \tabularnewline
14 & 92.7 & 92.851162958723 & -0.15116295872302 \tabularnewline
15 & 92.47 & 92.5591704342222 & -0.0891704342222113 \tabularnewline
16 & 92.58 & 92.6195916102733 & -0.039591610273277 \tabularnewline
17 & 92.55 & 92.5367517732017 & 0.0132482267982965 \tabularnewline
18 & 92.56 & 92.5223642686529 & 0.0376357313471516 \tabularnewline
19 & 89.92 & 91.2562781549184 & -1.33627815491838 \tabularnewline
20 & 89.96 & 89.991106048618 & -0.0311060486180423 \tabularnewline
21 & 90.03 & 89.4938783334973 & 0.536121666502652 \tabularnewline
22 & 90.31 & 89.669498592687 & 0.640501407313025 \tabularnewline
23 & 90.8 & 90.0296723439245 & 0.77032765607548 \tabularnewline
24 & 90.36 & 90.357878994931 & 0.00212100506897173 \tabularnewline
25 & 90.31 & 90.9864681054127 & -0.676468105412695 \tabularnewline
26 & 93.8 & 90.5651590230631 & 3.23484097693691 \tabularnewline
27 & 93.95 & 93.3996267636057 & 0.550373236394279 \tabularnewline
28 & 93.99 & 94.0951847025459 & -0.105184702545913 \tabularnewline
29 & 94.44 & 94.0016534795075 & 0.438346520492544 \tabularnewline
30 & 94.15 & 94.427080773229 & -0.277080773229031 \tabularnewline
31 & 91.91 & 92.7718182179469 & -0.861818217946862 \tabularnewline
32 & 91.86 & 92.1094407889745 & -0.249440788974468 \tabularnewline
33 & 93.12 & 91.5044774747907 & 1.61552252520931 \tabularnewline
34 & 93.47 & 92.7268289547986 & 0.74317104520135 \tabularnewline
35 & 93.57 & 93.2497015895653 & 0.320298410434702 \tabularnewline
36 & 94.57 & 93.1453382019753 & 1.42466179802466 \tabularnewline
37 & 95.85 & 95.1134919415998 & 0.736508058400219 \tabularnewline
38 & 96.62 & 96.4489291833903 & 0.171070816609671 \tabularnewline
39 & 95.69 & 96.2990876593732 & -0.609087659373188 \tabularnewline
40 & 95.39 & 95.9242379313443 & -0.534237931344293 \tabularnewline
41 & 95.14 & 95.5250293742436 & -0.385029374243643 \tabularnewline
42 & 95.07 & 95.1621658260215 & -0.0921658260214713 \tabularnewline
43 & 94.21 & 93.6363156854454 & 0.57368431455464 \tabularnewline
44 & 95.4 & 94.387258155193 & 1.01274184480705 \tabularnewline
45 & 95.1 & 95.1507572236542 & -0.0507572236542018 \tabularnewline
46 & 94.89 & 94.8109413857848 & 0.0790586142151568 \tabularnewline
47 & 95.43 & 94.720610521423 & 0.709389478577009 \tabularnewline
48 & 94.88 & 95.0986403568399 & -0.218640356839941 \tabularnewline
49 & 96.03 & 95.5266555860179 & 0.503344413982092 \tabularnewline
50 & 96.37 & 96.6141029186162 & -0.244102918616193 \tabularnewline
51 & 96.04 & 96.0259569204449 & 0.0140430795551367 \tabularnewline
52 & 95.72 & 96.242432833223 & -0.522432833222965 \tabularnewline
53 & 95.74 & 95.8841877672734 & -0.144187767273422 \tabularnewline
54 & 95.78 & 95.7866137434055 & -0.00661374340552356 \tabularnewline
55 & 93.66 & 94.4078044994179 & -0.747804499417953 \tabularnewline
56 & 95.29 & 93.9955260746307 & 1.29447392536927 \tabularnewline
57 & 94.33 & 94.929460485005 & -0.599460485004954 \tabularnewline
58 & 95.66 & 94.1041962145285 & 1.55580378547153 \tabularnewline
59 & 95.2 & 95.4333163944259 & -0.233316394425856 \tabularnewline
60 & 94.61 & 94.8781098512689 & -0.268109851268889 \tabularnewline
61 & 96.21 & 95.3300669604653 & 0.879933039534649 \tabularnewline
62 & 96.27 & 96.7063621473819 & -0.436362147381928 \tabularnewline
63 & 95.12 & 95.975390144136 & -0.855390144136024 \tabularnewline
64 & 95.55 & 95.3489908336401 & 0.201009166359867 \tabularnewline
65 & 93.51 & 95.6906289940365 & -2.18062899403651 \tabularnewline
66 & 92.86 & 93.7311196892674 & -0.871119689267374 \tabularnewline
67 & 92.45 & 91.5130915214181 & 0.936908478581856 \tabularnewline
68 & 93.34 & 92.8023007542908 & 0.537699245709234 \tabularnewline
69 & 92.01 & 92.8704395545034 & -0.860439554503401 \tabularnewline
70 & 91.77 & 91.979176964635 & -0.20917696463502 \tabularnewline
71 & 92.19 & 91.5104735112788 & 0.679526488721194 \tabularnewline
72 & 91.97 & 91.7653949667404 & 0.204605033259597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278680&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]92.63[/C][C]93.1837376454169[/C][C]-0.55373764541693[/C][/ROW]
[ROW][C]14[/C][C]92.7[/C][C]92.851162958723[/C][C]-0.15116295872302[/C][/ROW]
[ROW][C]15[/C][C]92.47[/C][C]92.5591704342222[/C][C]-0.0891704342222113[/C][/ROW]
[ROW][C]16[/C][C]92.58[/C][C]92.6195916102733[/C][C]-0.039591610273277[/C][/ROW]
[ROW][C]17[/C][C]92.55[/C][C]92.5367517732017[/C][C]0.0132482267982965[/C][/ROW]
[ROW][C]18[/C][C]92.56[/C][C]92.5223642686529[/C][C]0.0376357313471516[/C][/ROW]
[ROW][C]19[/C][C]89.92[/C][C]91.2562781549184[/C][C]-1.33627815491838[/C][/ROW]
[ROW][C]20[/C][C]89.96[/C][C]89.991106048618[/C][C]-0.0311060486180423[/C][/ROW]
[ROW][C]21[/C][C]90.03[/C][C]89.4938783334973[/C][C]0.536121666502652[/C][/ROW]
[ROW][C]22[/C][C]90.31[/C][C]89.669498592687[/C][C]0.640501407313025[/C][/ROW]
[ROW][C]23[/C][C]90.8[/C][C]90.0296723439245[/C][C]0.77032765607548[/C][/ROW]
[ROW][C]24[/C][C]90.36[/C][C]90.357878994931[/C][C]0.00212100506897173[/C][/ROW]
[ROW][C]25[/C][C]90.31[/C][C]90.9864681054127[/C][C]-0.676468105412695[/C][/ROW]
[ROW][C]26[/C][C]93.8[/C][C]90.5651590230631[/C][C]3.23484097693691[/C][/ROW]
[ROW][C]27[/C][C]93.95[/C][C]93.3996267636057[/C][C]0.550373236394279[/C][/ROW]
[ROW][C]28[/C][C]93.99[/C][C]94.0951847025459[/C][C]-0.105184702545913[/C][/ROW]
[ROW][C]29[/C][C]94.44[/C][C]94.0016534795075[/C][C]0.438346520492544[/C][/ROW]
[ROW][C]30[/C][C]94.15[/C][C]94.427080773229[/C][C]-0.277080773229031[/C][/ROW]
[ROW][C]31[/C][C]91.91[/C][C]92.7718182179469[/C][C]-0.861818217946862[/C][/ROW]
[ROW][C]32[/C][C]91.86[/C][C]92.1094407889745[/C][C]-0.249440788974468[/C][/ROW]
[ROW][C]33[/C][C]93.12[/C][C]91.5044774747907[/C][C]1.61552252520931[/C][/ROW]
[ROW][C]34[/C][C]93.47[/C][C]92.7268289547986[/C][C]0.74317104520135[/C][/ROW]
[ROW][C]35[/C][C]93.57[/C][C]93.2497015895653[/C][C]0.320298410434702[/C][/ROW]
[ROW][C]36[/C][C]94.57[/C][C]93.1453382019753[/C][C]1.42466179802466[/C][/ROW]
[ROW][C]37[/C][C]95.85[/C][C]95.1134919415998[/C][C]0.736508058400219[/C][/ROW]
[ROW][C]38[/C][C]96.62[/C][C]96.4489291833903[/C][C]0.171070816609671[/C][/ROW]
[ROW][C]39[/C][C]95.69[/C][C]96.2990876593732[/C][C]-0.609087659373188[/C][/ROW]
[ROW][C]40[/C][C]95.39[/C][C]95.9242379313443[/C][C]-0.534237931344293[/C][/ROW]
[ROW][C]41[/C][C]95.14[/C][C]95.5250293742436[/C][C]-0.385029374243643[/C][/ROW]
[ROW][C]42[/C][C]95.07[/C][C]95.1621658260215[/C][C]-0.0921658260214713[/C][/ROW]
[ROW][C]43[/C][C]94.21[/C][C]93.6363156854454[/C][C]0.57368431455464[/C][/ROW]
[ROW][C]44[/C][C]95.4[/C][C]94.387258155193[/C][C]1.01274184480705[/C][/ROW]
[ROW][C]45[/C][C]95.1[/C][C]95.1507572236542[/C][C]-0.0507572236542018[/C][/ROW]
[ROW][C]46[/C][C]94.89[/C][C]94.8109413857848[/C][C]0.0790586142151568[/C][/ROW]
[ROW][C]47[/C][C]95.43[/C][C]94.720610521423[/C][C]0.709389478577009[/C][/ROW]
[ROW][C]48[/C][C]94.88[/C][C]95.0986403568399[/C][C]-0.218640356839941[/C][/ROW]
[ROW][C]49[/C][C]96.03[/C][C]95.5266555860179[/C][C]0.503344413982092[/C][/ROW]
[ROW][C]50[/C][C]96.37[/C][C]96.6141029186162[/C][C]-0.244102918616193[/C][/ROW]
[ROW][C]51[/C][C]96.04[/C][C]96.0259569204449[/C][C]0.0140430795551367[/C][/ROW]
[ROW][C]52[/C][C]95.72[/C][C]96.242432833223[/C][C]-0.522432833222965[/C][/ROW]
[ROW][C]53[/C][C]95.74[/C][C]95.8841877672734[/C][C]-0.144187767273422[/C][/ROW]
[ROW][C]54[/C][C]95.78[/C][C]95.7866137434055[/C][C]-0.00661374340552356[/C][/ROW]
[ROW][C]55[/C][C]93.66[/C][C]94.4078044994179[/C][C]-0.747804499417953[/C][/ROW]
[ROW][C]56[/C][C]95.29[/C][C]93.9955260746307[/C][C]1.29447392536927[/C][/ROW]
[ROW][C]57[/C][C]94.33[/C][C]94.929460485005[/C][C]-0.599460485004954[/C][/ROW]
[ROW][C]58[/C][C]95.66[/C][C]94.1041962145285[/C][C]1.55580378547153[/C][/ROW]
[ROW][C]59[/C][C]95.2[/C][C]95.4333163944259[/C][C]-0.233316394425856[/C][/ROW]
[ROW][C]60[/C][C]94.61[/C][C]94.8781098512689[/C][C]-0.268109851268889[/C][/ROW]
[ROW][C]61[/C][C]96.21[/C][C]95.3300669604653[/C][C]0.879933039534649[/C][/ROW]
[ROW][C]62[/C][C]96.27[/C][C]96.7063621473819[/C][C]-0.436362147381928[/C][/ROW]
[ROW][C]63[/C][C]95.12[/C][C]95.975390144136[/C][C]-0.855390144136024[/C][/ROW]
[ROW][C]64[/C][C]95.55[/C][C]95.3489908336401[/C][C]0.201009166359867[/C][/ROW]
[ROW][C]65[/C][C]93.51[/C][C]95.6906289940365[/C][C]-2.18062899403651[/C][/ROW]
[ROW][C]66[/C][C]92.86[/C][C]93.7311196892674[/C][C]-0.871119689267374[/C][/ROW]
[ROW][C]67[/C][C]92.45[/C][C]91.5130915214181[/C][C]0.936908478581856[/C][/ROW]
[ROW][C]68[/C][C]93.34[/C][C]92.8023007542908[/C][C]0.537699245709234[/C][/ROW]
[ROW][C]69[/C][C]92.01[/C][C]92.8704395545034[/C][C]-0.860439554503401[/C][/ROW]
[ROW][C]70[/C][C]91.77[/C][C]91.979176964635[/C][C]-0.20917696463502[/C][/ROW]
[ROW][C]71[/C][C]92.19[/C][C]91.5104735112788[/C][C]0.679526488721194[/C][/ROW]
[ROW][C]72[/C][C]91.97[/C][C]91.7653949667404[/C][C]0.204605033259597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278680&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
1392.6393.1837376454169-0.55373764541693
1492.792.851162958723-0.15116295872302
1592.4792.5591704342222-0.0891704342222113
1692.5892.6195916102733-0.039591610273277
1792.5592.53675177320170.0132482267982965
1892.5692.52236426865290.0376357313471516
1989.9291.2562781549184-1.33627815491838
2089.9689.991106048618-0.0311060486180423
2190.0389.49387833349730.536121666502652
2290.3189.6694985926870.640501407313025
2390.890.02967234392450.77032765607548
2490.3690.3578789949310.00212100506897173
2590.3190.9864681054127-0.676468105412695
2693.890.56515902306313.23484097693691
2793.9593.39962676360570.550373236394279
2893.9994.0951847025459-0.105184702545913
2994.4494.00165347950750.438346520492544
3094.1594.427080773229-0.277080773229031
3191.9192.7718182179469-0.861818217946862
3291.8692.1094407889745-0.249440788974468
3393.1291.50447747479071.61552252520931
3493.4792.72682895479860.74317104520135
3593.5793.24970158956530.320298410434702
3694.5793.14533820197531.42466179802466
3795.8595.11349194159980.736508058400219
3896.6296.44892918339030.171070816609671
3995.6996.2990876593732-0.609087659373188
4095.3995.9242379313443-0.534237931344293
4195.1495.5250293742436-0.385029374243643
4295.0795.1621658260215-0.0921658260214713
4394.2193.63631568544540.57368431455464
4495.494.3872581551931.01274184480705
4595.195.1507572236542-0.0507572236542018
4694.8994.81094138578480.0790586142151568
4795.4394.7206105214230.709389478577009
4894.8895.0986403568399-0.218640356839941
4996.0395.52665558601790.503344413982092
5096.3796.6141029186162-0.244102918616193
5196.0496.02595692044490.0140430795551367
5295.7296.242432833223-0.522432833222965
5395.7495.8841877672734-0.144187767273422
5495.7895.7866137434055-0.00661374340552356
5593.6694.4078044994179-0.747804499417953
5695.2993.99552607463071.29447392536927
5794.3394.929460485005-0.599460485004954
5895.6694.10419621452851.55580378547153
5995.295.4333163944259-0.233316394425856
6094.6194.8781098512689-0.268109851268889
6196.2195.33006696046530.879933039534649
6296.2796.7063621473819-0.436362147381928
6395.1295.975390144136-0.855390144136024
6495.5595.34899083364010.201009166359867
6593.5195.6906289940365-2.18062899403651
6692.8693.7311196892674-0.871119689267374
6792.4591.51309152141810.936908478581856
6893.3492.80230075429080.537699245709234
6992.0192.8704395545034-0.860439554503401
7091.7791.979176964635-0.20917696463502
7192.1991.51047351127880.679526488721194
7291.9791.76539496674040.204605033259597







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7392.702799748445591.105620262625194.2999792342658
7493.108820748428490.930250472041395.2873910248154
7592.720225440509990.084893564504995.3555573165148
7692.941280995514489.896343153885895.986218837143
7792.863703512415589.455916101302596.2714909235285
7893.010238027819289.259607626171896.7608684294667
7991.758885747601187.737097411346495.7806740838557
8092.159177635391787.817337724251196.5010175465323
8191.616303400282787.008354564806396.2242522357591
8291.574547678600386.68812890825696.4609664489446
8391.385490704678386.236993412709896.5339879966469
8490.984211144964171.1782085125972110.790213777331

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 92.7027997484455 & 91.1056202626251 & 94.2999792342658 \tabularnewline
74 & 93.1088207484284 & 90.9302504720413 & 95.2873910248154 \tabularnewline
75 & 92.7202254405099 & 90.0848935645049 & 95.3555573165148 \tabularnewline
76 & 92.9412809955144 & 89.8963431538858 & 95.986218837143 \tabularnewline
77 & 92.8637035124155 & 89.4559161013025 & 96.2714909235285 \tabularnewline
78 & 93.0102380278192 & 89.2596076261718 & 96.7608684294667 \tabularnewline
79 & 91.7588857476011 & 87.7370974113464 & 95.7806740838557 \tabularnewline
80 & 92.1591776353917 & 87.8173377242511 & 96.5010175465323 \tabularnewline
81 & 91.6163034002827 & 87.0083545648063 & 96.2242522357591 \tabularnewline
82 & 91.5745476786003 & 86.688128908256 & 96.4609664489446 \tabularnewline
83 & 91.3854907046783 & 86.2369934127098 & 96.5339879966469 \tabularnewline
84 & 90.9842111449641 & 71.1782085125972 & 110.790213777331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278680&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]92.7027997484455[/C][C]91.1056202626251[/C][C]94.2999792342658[/C][/ROW]
[ROW][C]74[/C][C]93.1088207484284[/C][C]90.9302504720413[/C][C]95.2873910248154[/C][/ROW]
[ROW][C]75[/C][C]92.7202254405099[/C][C]90.0848935645049[/C][C]95.3555573165148[/C][/ROW]
[ROW][C]76[/C][C]92.9412809955144[/C][C]89.8963431538858[/C][C]95.986218837143[/C][/ROW]
[ROW][C]77[/C][C]92.8637035124155[/C][C]89.4559161013025[/C][C]96.2714909235285[/C][/ROW]
[ROW][C]78[/C][C]93.0102380278192[/C][C]89.2596076261718[/C][C]96.7608684294667[/C][/ROW]
[ROW][C]79[/C][C]91.7588857476011[/C][C]87.7370974113464[/C][C]95.7806740838557[/C][/ROW]
[ROW][C]80[/C][C]92.1591776353917[/C][C]87.8173377242511[/C][C]96.5010175465323[/C][/ROW]
[ROW][C]81[/C][C]91.6163034002827[/C][C]87.0083545648063[/C][C]96.2242522357591[/C][/ROW]
[ROW][C]82[/C][C]91.5745476786003[/C][C]86.688128908256[/C][C]96.4609664489446[/C][/ROW]
[ROW][C]83[/C][C]91.3854907046783[/C][C]86.2369934127098[/C][C]96.5339879966469[/C][/ROW]
[ROW][C]84[/C][C]90.9842111449641[/C][C]71.1782085125972[/C][C]110.790213777331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278680&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278680&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
7392.702799748445591.105620262625194.2999792342658
7493.108820748428490.930250472041395.2873910248154
7592.720225440509990.084893564504995.3555573165148
7692.941280995514489.896343153885895.986218837143
7792.863703512415589.455916101302596.2714909235285
7893.010238027819289.259607626171896.7608684294667
7991.758885747601187.737097411346495.7806740838557
8092.159177635391787.817337724251196.5010175465323
8191.616303400282787.008354564806396.2242522357591
8291.574547678600386.68812890825696.4609664489446
8391.385490704678386.236993412709896.5339879966469
8490.984211144964171.1782085125972110.790213777331



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