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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Jan 2014 13:00:20 -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/2014/Jan/12/t1389549648th2cyi8yldknd3j.htm/, Retrieved Fri, 10 May 2024 06:45:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233025, Retrieved Fri, 10 May 2024 06:45:28 +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)
-     [Harrell-Davis Quantiles] [] [2013-10-02 19:59:29] [2469e5bd993431c0aa919cce58f0e013]
- RMP     [Exponential Smoothing] [] [2014-01-12 18:00:20] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
78,7
75,7
77,1
86,1
86,8
86,3
91,5
90,7
78,2
73
73,7
77,3
67,5
72,7
76,6
82,4
82,3
86,3
93
88,8
96,9
103,9
115,7
112,8
114,7
118
129,3
137
156
166,2
167,8
144,3
126
90,4
67,5
52,4
54,6
52,9
59,1
63,3
73,8
87,6
81,8
90,7
86,3
93,6
98
94,3
97,6
94,2
100,2
106,7
95,7
94,6
94,7
96,2
96,3
103,3
106,8
113,7
117,4
123,6
137,6
147,4
137,2
133,8
136,7
127,3
128,7
127
133,7
132
135,1
142,6
149,3
143,5
131,4
114,7
122,3
133,4
134,6
130,9
127,9
128




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233025&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233025&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233025&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[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233025&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1367.568.3768696581196-0.876869658119631
1472.773.2218822843823-0.521882284382301
1576.676.40521561771560.194784382284382
1682.480.8385489510491.56145104895104
1782.379.76771561771562.53228438228439
1886.383.5760489510492.72395104895104
199399.6427156177156-6.64271561771562
2088.893.2968822843823-4.49688228438229
2196.976.951048951048919.9489510489511
22103.992.380215617715611.5197843822844
23115.7105.44688228438210.2531177156177
24112.8119.992715617716-7.19271561771561
25114.7103.44271561771611.2572843822844
26118120.421882284382-2.42188228438231
27129.3121.7052156177167.5947843822844
28137133.5385489510493.46145104895103
29156134.36771561771621.6322843822844
30166.2157.2760489510498.92395104895104
31167.8179.542715617716-11.7427156177156
32144.3168.096882284382-23.7968822843823
33126132.451048951049-6.45104895104896
3490.4121.480215617716-31.0802156177156
3567.591.9468822843823-24.4468822843823
3652.471.7927156177156-19.3927156177156
3754.643.042715617715611.5572843822844
3852.960.3218822843823-7.42188228438231
3959.156.60521561771562.49478438228439
4063.363.338548951049-0.0385489510489734
4173.860.667715617715613.1322843822844
4287.675.07604895104912.523951048951
4381.8100.942715617716-19.1427156177156
4490.782.09688228438238.60311771561771
4586.378.8510489510497.44895104895105
4693.681.780215617715611.8197843822844
479895.14688228438232.85311771561769
4894.3102.292715617716-7.9927156177156
4997.684.942715617715612.6572843822844
5094.2103.321882284382-9.12188228438229
51100.297.90521561771562.29478438228439
52106.7104.4385489510492.26145104895103
5395.7104.067715617716-8.3677156177156
5494.696.976048951049-2.37604895104897
5594.7107.942715617716-13.2427156177156
5696.294.99688228438231.20311771561771
5796.384.35104895104911.948951048951
58103.391.780215617715611.5197843822844
59106.8104.8468822843821.95311771561768
60113.7111.0927156177162.6072843822844
61117.4104.34271561771613.0572843822844
62123.6123.1218822843820.478117715617685
63137.6127.30521561771610.2947843822844
64147.4141.8385489510495.56145104895106
65137.2144.767715617716-7.56771561771561
66133.8138.476048951049-4.67604895104893
67136.7147.142715617716-10.4427156177156
68127.3136.996882284382-9.69688228438228
69128.7115.45104895104913.248951048951
70127124.1802156177162.81978438228444
71133.7128.5468822843825.15311771561767
72132137.992715617716-5.99271561771556
73135.1122.64271561771612.4572843822844
74142.6140.8218822843821.7781177156177
75149.3146.3052156177162.99478438228442
76143.5153.538548951049-10.038548951049
77131.4140.867715617716-9.46771561771558
78114.7132.676048951049-17.976048951049
79122.3128.042715617716-5.74271561771563
80133.4122.59688228438210.8031177156177
81134.6121.55104895104913.048951048951
82130.9130.0802156177160.819784382284439
83127.9132.446882284382-4.54688228438232
84128132.192715617716-4.19271561771558

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 67.5 & 68.3768696581196 & -0.876869658119631 \tabularnewline
14 & 72.7 & 73.2218822843823 & -0.521882284382301 \tabularnewline
15 & 76.6 & 76.4052156177156 & 0.194784382284382 \tabularnewline
16 & 82.4 & 80.838548951049 & 1.56145104895104 \tabularnewline
17 & 82.3 & 79.7677156177156 & 2.53228438228439 \tabularnewline
18 & 86.3 & 83.576048951049 & 2.72395104895104 \tabularnewline
19 & 93 & 99.6427156177156 & -6.64271561771562 \tabularnewline
20 & 88.8 & 93.2968822843823 & -4.49688228438229 \tabularnewline
21 & 96.9 & 76.9510489510489 & 19.9489510489511 \tabularnewline
22 & 103.9 & 92.3802156177156 & 11.5197843822844 \tabularnewline
23 & 115.7 & 105.446882284382 & 10.2531177156177 \tabularnewline
24 & 112.8 & 119.992715617716 & -7.19271561771561 \tabularnewline
25 & 114.7 & 103.442715617716 & 11.2572843822844 \tabularnewline
26 & 118 & 120.421882284382 & -2.42188228438231 \tabularnewline
27 & 129.3 & 121.705215617716 & 7.5947843822844 \tabularnewline
28 & 137 & 133.538548951049 & 3.46145104895103 \tabularnewline
29 & 156 & 134.367715617716 & 21.6322843822844 \tabularnewline
30 & 166.2 & 157.276048951049 & 8.92395104895104 \tabularnewline
31 & 167.8 & 179.542715617716 & -11.7427156177156 \tabularnewline
32 & 144.3 & 168.096882284382 & -23.7968822843823 \tabularnewline
33 & 126 & 132.451048951049 & -6.45104895104896 \tabularnewline
34 & 90.4 & 121.480215617716 & -31.0802156177156 \tabularnewline
35 & 67.5 & 91.9468822843823 & -24.4468822843823 \tabularnewline
36 & 52.4 & 71.7927156177156 & -19.3927156177156 \tabularnewline
37 & 54.6 & 43.0427156177156 & 11.5572843822844 \tabularnewline
38 & 52.9 & 60.3218822843823 & -7.42188228438231 \tabularnewline
39 & 59.1 & 56.6052156177156 & 2.49478438228439 \tabularnewline
40 & 63.3 & 63.338548951049 & -0.0385489510489734 \tabularnewline
41 & 73.8 & 60.6677156177156 & 13.1322843822844 \tabularnewline
42 & 87.6 & 75.076048951049 & 12.523951048951 \tabularnewline
43 & 81.8 & 100.942715617716 & -19.1427156177156 \tabularnewline
44 & 90.7 & 82.0968822843823 & 8.60311771561771 \tabularnewline
45 & 86.3 & 78.851048951049 & 7.44895104895105 \tabularnewline
46 & 93.6 & 81.7802156177156 & 11.8197843822844 \tabularnewline
47 & 98 & 95.1468822843823 & 2.85311771561769 \tabularnewline
48 & 94.3 & 102.292715617716 & -7.9927156177156 \tabularnewline
49 & 97.6 & 84.9427156177156 & 12.6572843822844 \tabularnewline
50 & 94.2 & 103.321882284382 & -9.12188228438229 \tabularnewline
51 & 100.2 & 97.9052156177156 & 2.29478438228439 \tabularnewline
52 & 106.7 & 104.438548951049 & 2.26145104895103 \tabularnewline
53 & 95.7 & 104.067715617716 & -8.3677156177156 \tabularnewline
54 & 94.6 & 96.976048951049 & -2.37604895104897 \tabularnewline
55 & 94.7 & 107.942715617716 & -13.2427156177156 \tabularnewline
56 & 96.2 & 94.9968822843823 & 1.20311771561771 \tabularnewline
57 & 96.3 & 84.351048951049 & 11.948951048951 \tabularnewline
58 & 103.3 & 91.7802156177156 & 11.5197843822844 \tabularnewline
59 & 106.8 & 104.846882284382 & 1.95311771561768 \tabularnewline
60 & 113.7 & 111.092715617716 & 2.6072843822844 \tabularnewline
61 & 117.4 & 104.342715617716 & 13.0572843822844 \tabularnewline
62 & 123.6 & 123.121882284382 & 0.478117715617685 \tabularnewline
63 & 137.6 & 127.305215617716 & 10.2947843822844 \tabularnewline
64 & 147.4 & 141.838548951049 & 5.56145104895106 \tabularnewline
65 & 137.2 & 144.767715617716 & -7.56771561771561 \tabularnewline
66 & 133.8 & 138.476048951049 & -4.67604895104893 \tabularnewline
67 & 136.7 & 147.142715617716 & -10.4427156177156 \tabularnewline
68 & 127.3 & 136.996882284382 & -9.69688228438228 \tabularnewline
69 & 128.7 & 115.451048951049 & 13.248951048951 \tabularnewline
70 & 127 & 124.180215617716 & 2.81978438228444 \tabularnewline
71 & 133.7 & 128.546882284382 & 5.15311771561767 \tabularnewline
72 & 132 & 137.992715617716 & -5.99271561771556 \tabularnewline
73 & 135.1 & 122.642715617716 & 12.4572843822844 \tabularnewline
74 & 142.6 & 140.821882284382 & 1.7781177156177 \tabularnewline
75 & 149.3 & 146.305215617716 & 2.99478438228442 \tabularnewline
76 & 143.5 & 153.538548951049 & -10.038548951049 \tabularnewline
77 & 131.4 & 140.867715617716 & -9.46771561771558 \tabularnewline
78 & 114.7 & 132.676048951049 & -17.976048951049 \tabularnewline
79 & 122.3 & 128.042715617716 & -5.74271561771563 \tabularnewline
80 & 133.4 & 122.596882284382 & 10.8031177156177 \tabularnewline
81 & 134.6 & 121.551048951049 & 13.048951048951 \tabularnewline
82 & 130.9 & 130.080215617716 & 0.819784382284439 \tabularnewline
83 & 127.9 & 132.446882284382 & -4.54688228438232 \tabularnewline
84 & 128 & 132.192715617716 & -4.19271561771558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233025&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]67.5[/C][C]68.3768696581196[/C][C]-0.876869658119631[/C][/ROW]
[ROW][C]14[/C][C]72.7[/C][C]73.2218822843823[/C][C]-0.521882284382301[/C][/ROW]
[ROW][C]15[/C][C]76.6[/C][C]76.4052156177156[/C][C]0.194784382284382[/C][/ROW]
[ROW][C]16[/C][C]82.4[/C][C]80.838548951049[/C][C]1.56145104895104[/C][/ROW]
[ROW][C]17[/C][C]82.3[/C][C]79.7677156177156[/C][C]2.53228438228439[/C][/ROW]
[ROW][C]18[/C][C]86.3[/C][C]83.576048951049[/C][C]2.72395104895104[/C][/ROW]
[ROW][C]19[/C][C]93[/C][C]99.6427156177156[/C][C]-6.64271561771562[/C][/ROW]
[ROW][C]20[/C][C]88.8[/C][C]93.2968822843823[/C][C]-4.49688228438229[/C][/ROW]
[ROW][C]21[/C][C]96.9[/C][C]76.9510489510489[/C][C]19.9489510489511[/C][/ROW]
[ROW][C]22[/C][C]103.9[/C][C]92.3802156177156[/C][C]11.5197843822844[/C][/ROW]
[ROW][C]23[/C][C]115.7[/C][C]105.446882284382[/C][C]10.2531177156177[/C][/ROW]
[ROW][C]24[/C][C]112.8[/C][C]119.992715617716[/C][C]-7.19271561771561[/C][/ROW]
[ROW][C]25[/C][C]114.7[/C][C]103.442715617716[/C][C]11.2572843822844[/C][/ROW]
[ROW][C]26[/C][C]118[/C][C]120.421882284382[/C][C]-2.42188228438231[/C][/ROW]
[ROW][C]27[/C][C]129.3[/C][C]121.705215617716[/C][C]7.5947843822844[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]133.538548951049[/C][C]3.46145104895103[/C][/ROW]
[ROW][C]29[/C][C]156[/C][C]134.367715617716[/C][C]21.6322843822844[/C][/ROW]
[ROW][C]30[/C][C]166.2[/C][C]157.276048951049[/C][C]8.92395104895104[/C][/ROW]
[ROW][C]31[/C][C]167.8[/C][C]179.542715617716[/C][C]-11.7427156177156[/C][/ROW]
[ROW][C]32[/C][C]144.3[/C][C]168.096882284382[/C][C]-23.7968822843823[/C][/ROW]
[ROW][C]33[/C][C]126[/C][C]132.451048951049[/C][C]-6.45104895104896[/C][/ROW]
[ROW][C]34[/C][C]90.4[/C][C]121.480215617716[/C][C]-31.0802156177156[/C][/ROW]
[ROW][C]35[/C][C]67.5[/C][C]91.9468822843823[/C][C]-24.4468822843823[/C][/ROW]
[ROW][C]36[/C][C]52.4[/C][C]71.7927156177156[/C][C]-19.3927156177156[/C][/ROW]
[ROW][C]37[/C][C]54.6[/C][C]43.0427156177156[/C][C]11.5572843822844[/C][/ROW]
[ROW][C]38[/C][C]52.9[/C][C]60.3218822843823[/C][C]-7.42188228438231[/C][/ROW]
[ROW][C]39[/C][C]59.1[/C][C]56.6052156177156[/C][C]2.49478438228439[/C][/ROW]
[ROW][C]40[/C][C]63.3[/C][C]63.338548951049[/C][C]-0.0385489510489734[/C][/ROW]
[ROW][C]41[/C][C]73.8[/C][C]60.6677156177156[/C][C]13.1322843822844[/C][/ROW]
[ROW][C]42[/C][C]87.6[/C][C]75.076048951049[/C][C]12.523951048951[/C][/ROW]
[ROW][C]43[/C][C]81.8[/C][C]100.942715617716[/C][C]-19.1427156177156[/C][/ROW]
[ROW][C]44[/C][C]90.7[/C][C]82.0968822843823[/C][C]8.60311771561771[/C][/ROW]
[ROW][C]45[/C][C]86.3[/C][C]78.851048951049[/C][C]7.44895104895105[/C][/ROW]
[ROW][C]46[/C][C]93.6[/C][C]81.7802156177156[/C][C]11.8197843822844[/C][/ROW]
[ROW][C]47[/C][C]98[/C][C]95.1468822843823[/C][C]2.85311771561769[/C][/ROW]
[ROW][C]48[/C][C]94.3[/C][C]102.292715617716[/C][C]-7.9927156177156[/C][/ROW]
[ROW][C]49[/C][C]97.6[/C][C]84.9427156177156[/C][C]12.6572843822844[/C][/ROW]
[ROW][C]50[/C][C]94.2[/C][C]103.321882284382[/C][C]-9.12188228438229[/C][/ROW]
[ROW][C]51[/C][C]100.2[/C][C]97.9052156177156[/C][C]2.29478438228439[/C][/ROW]
[ROW][C]52[/C][C]106.7[/C][C]104.438548951049[/C][C]2.26145104895103[/C][/ROW]
[ROW][C]53[/C][C]95.7[/C][C]104.067715617716[/C][C]-8.3677156177156[/C][/ROW]
[ROW][C]54[/C][C]94.6[/C][C]96.976048951049[/C][C]-2.37604895104897[/C][/ROW]
[ROW][C]55[/C][C]94.7[/C][C]107.942715617716[/C][C]-13.2427156177156[/C][/ROW]
[ROW][C]56[/C][C]96.2[/C][C]94.9968822843823[/C][C]1.20311771561771[/C][/ROW]
[ROW][C]57[/C][C]96.3[/C][C]84.351048951049[/C][C]11.948951048951[/C][/ROW]
[ROW][C]58[/C][C]103.3[/C][C]91.7802156177156[/C][C]11.5197843822844[/C][/ROW]
[ROW][C]59[/C][C]106.8[/C][C]104.846882284382[/C][C]1.95311771561768[/C][/ROW]
[ROW][C]60[/C][C]113.7[/C][C]111.092715617716[/C][C]2.6072843822844[/C][/ROW]
[ROW][C]61[/C][C]117.4[/C][C]104.342715617716[/C][C]13.0572843822844[/C][/ROW]
[ROW][C]62[/C][C]123.6[/C][C]123.121882284382[/C][C]0.478117715617685[/C][/ROW]
[ROW][C]63[/C][C]137.6[/C][C]127.305215617716[/C][C]10.2947843822844[/C][/ROW]
[ROW][C]64[/C][C]147.4[/C][C]141.838548951049[/C][C]5.56145104895106[/C][/ROW]
[ROW][C]65[/C][C]137.2[/C][C]144.767715617716[/C][C]-7.56771561771561[/C][/ROW]
[ROW][C]66[/C][C]133.8[/C][C]138.476048951049[/C][C]-4.67604895104893[/C][/ROW]
[ROW][C]67[/C][C]136.7[/C][C]147.142715617716[/C][C]-10.4427156177156[/C][/ROW]
[ROW][C]68[/C][C]127.3[/C][C]136.996882284382[/C][C]-9.69688228438228[/C][/ROW]
[ROW][C]69[/C][C]128.7[/C][C]115.451048951049[/C][C]13.248951048951[/C][/ROW]
[ROW][C]70[/C][C]127[/C][C]124.180215617716[/C][C]2.81978438228444[/C][/ROW]
[ROW][C]71[/C][C]133.7[/C][C]128.546882284382[/C][C]5.15311771561767[/C][/ROW]
[ROW][C]72[/C][C]132[/C][C]137.992715617716[/C][C]-5.99271561771556[/C][/ROW]
[ROW][C]73[/C][C]135.1[/C][C]122.642715617716[/C][C]12.4572843822844[/C][/ROW]
[ROW][C]74[/C][C]142.6[/C][C]140.821882284382[/C][C]1.7781177156177[/C][/ROW]
[ROW][C]75[/C][C]149.3[/C][C]146.305215617716[/C][C]2.99478438228442[/C][/ROW]
[ROW][C]76[/C][C]143.5[/C][C]153.538548951049[/C][C]-10.038548951049[/C][/ROW]
[ROW][C]77[/C][C]131.4[/C][C]140.867715617716[/C][C]-9.46771561771558[/C][/ROW]
[ROW][C]78[/C][C]114.7[/C][C]132.676048951049[/C][C]-17.976048951049[/C][/ROW]
[ROW][C]79[/C][C]122.3[/C][C]128.042715617716[/C][C]-5.74271561771563[/C][/ROW]
[ROW][C]80[/C][C]133.4[/C][C]122.596882284382[/C][C]10.8031177156177[/C][/ROW]
[ROW][C]81[/C][C]134.6[/C][C]121.551048951049[/C][C]13.048951048951[/C][/ROW]
[ROW][C]82[/C][C]130.9[/C][C]130.080215617716[/C][C]0.819784382284439[/C][/ROW]
[ROW][C]83[/C][C]127.9[/C][C]132.446882284382[/C][C]-4.54688228438232[/C][/ROW]
[ROW][C]84[/C][C]128[/C][C]132.192715617716[/C][C]-4.19271561771558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233025&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233025&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
1367.568.3768696581196-0.876869658119631
1472.773.2218822843823-0.521882284382301
1576.676.40521561771560.194784382284382
1682.480.8385489510491.56145104895104
1782.379.76771561771562.53228438228439
1886.383.5760489510492.72395104895104
199399.6427156177156-6.64271561771562
2088.893.2968822843823-4.49688228438229
2196.976.951048951048919.9489510489511
22103.992.380215617715611.5197843822844
23115.7105.44688228438210.2531177156177
24112.8119.992715617716-7.19271561771561
25114.7103.44271561771611.2572843822844
26118120.421882284382-2.42188228438231
27129.3121.7052156177167.5947843822844
28137133.5385489510493.46145104895103
29156134.36771561771621.6322843822844
30166.2157.2760489510498.92395104895104
31167.8179.542715617716-11.7427156177156
32144.3168.096882284382-23.7968822843823
33126132.451048951049-6.45104895104896
3490.4121.480215617716-31.0802156177156
3567.591.9468822843823-24.4468822843823
3652.471.7927156177156-19.3927156177156
3754.643.042715617715611.5572843822844
3852.960.3218822843823-7.42188228438231
3959.156.60521561771562.49478438228439
4063.363.338548951049-0.0385489510489734
4173.860.667715617715613.1322843822844
4287.675.07604895104912.523951048951
4381.8100.942715617716-19.1427156177156
4490.782.09688228438238.60311771561771
4586.378.8510489510497.44895104895105
4693.681.780215617715611.8197843822844
479895.14688228438232.85311771561769
4894.3102.292715617716-7.9927156177156
4997.684.942715617715612.6572843822844
5094.2103.321882284382-9.12188228438229
51100.297.90521561771562.29478438228439
52106.7104.4385489510492.26145104895103
5395.7104.067715617716-8.3677156177156
5494.696.976048951049-2.37604895104897
5594.7107.942715617716-13.2427156177156
5696.294.99688228438231.20311771561771
5796.384.35104895104911.948951048951
58103.391.780215617715611.5197843822844
59106.8104.8468822843821.95311771561768
60113.7111.0927156177162.6072843822844
61117.4104.34271561771613.0572843822844
62123.6123.1218822843820.478117715617685
63137.6127.30521561771610.2947843822844
64147.4141.8385489510495.56145104895106
65137.2144.767715617716-7.56771561771561
66133.8138.476048951049-4.67604895104893
67136.7147.142715617716-10.4427156177156
68127.3136.996882284382-9.69688228438228
69128.7115.45104895104913.248951048951
70127124.1802156177162.81978438228444
71133.7128.5468822843825.15311771561767
72132137.992715617716-5.99271561771556
73135.1122.64271561771612.4572843822844
74142.6140.8218822843821.7781177156177
75149.3146.3052156177162.99478438228442
76143.5153.538548951049-10.038548951049
77131.4140.867715617716-9.46771561771558
78114.7132.676048951049-17.976048951049
79122.3128.042715617716-5.74271561771563
80133.4122.59688228438210.8031177156177
81134.6121.55104895104913.048951048951
82130.9130.0802156177160.819784382284439
83127.9132.446882284382-4.54688228438232
84128132.192715617716-4.19271561771558







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85118.64271561771697.7060951753486139.579336060083
86124.36459790209894.7557453222447153.973450481951
87128.06981351981491.8065231748487164.333103864778
88132.30836247086390.4351215861285174.181603355597
89129.67607808857882.8603715603337176.491784616822
90130.95212703962779.6680900175045182.23616406175
91144.29484265734388.9017516726884199.687933641997
92144.59172494172585.3740197820185203.809430101431
93132.74277389277469.9329125656729195.552635219875
94128.22298951048962.0155824061677194.430396614811
95129.76987179487260.3309574094557199.208786180288
96134.06258741258761.5360067226577206.589168102517

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 118.642715617716 & 97.7060951753486 & 139.579336060083 \tabularnewline
86 & 124.364597902098 & 94.7557453222447 & 153.973450481951 \tabularnewline
87 & 128.069813519814 & 91.8065231748487 & 164.333103864778 \tabularnewline
88 & 132.308362470863 & 90.4351215861285 & 174.181603355597 \tabularnewline
89 & 129.676078088578 & 82.8603715603337 & 176.491784616822 \tabularnewline
90 & 130.952127039627 & 79.6680900175045 & 182.23616406175 \tabularnewline
91 & 144.294842657343 & 88.9017516726884 & 199.687933641997 \tabularnewline
92 & 144.591724941725 & 85.3740197820185 & 203.809430101431 \tabularnewline
93 & 132.742773892774 & 69.9329125656729 & 195.552635219875 \tabularnewline
94 & 128.222989510489 & 62.0155824061677 & 194.430396614811 \tabularnewline
95 & 129.769871794872 & 60.3309574094557 & 199.208786180288 \tabularnewline
96 & 134.062587412587 & 61.5360067226577 & 206.589168102517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233025&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]85[/C][C]118.642715617716[/C][C]97.7060951753486[/C][C]139.579336060083[/C][/ROW]
[ROW][C]86[/C][C]124.364597902098[/C][C]94.7557453222447[/C][C]153.973450481951[/C][/ROW]
[ROW][C]87[/C][C]128.069813519814[/C][C]91.8065231748487[/C][C]164.333103864778[/C][/ROW]
[ROW][C]88[/C][C]132.308362470863[/C][C]90.4351215861285[/C][C]174.181603355597[/C][/ROW]
[ROW][C]89[/C][C]129.676078088578[/C][C]82.8603715603337[/C][C]176.491784616822[/C][/ROW]
[ROW][C]90[/C][C]130.952127039627[/C][C]79.6680900175045[/C][C]182.23616406175[/C][/ROW]
[ROW][C]91[/C][C]144.294842657343[/C][C]88.9017516726884[/C][C]199.687933641997[/C][/ROW]
[ROW][C]92[/C][C]144.591724941725[/C][C]85.3740197820185[/C][C]203.809430101431[/C][/ROW]
[ROW][C]93[/C][C]132.742773892774[/C][C]69.9329125656729[/C][C]195.552635219875[/C][/ROW]
[ROW][C]94[/C][C]128.222989510489[/C][C]62.0155824061677[/C][C]194.430396614811[/C][/ROW]
[ROW][C]95[/C][C]129.769871794872[/C][C]60.3309574094557[/C][C]199.208786180288[/C][/ROW]
[ROW][C]96[/C][C]134.062587412587[/C][C]61.5360067226577[/C][C]206.589168102517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233025&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233025&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
85118.64271561771697.7060951753486139.579336060083
86124.36459790209894.7557453222447153.973450481951
87128.06981351981491.8065231748487164.333103864778
88132.30836247086390.4351215861285174.181603355597
89129.67607808857882.8603715603337176.491784616822
90130.95212703962779.6680900175045182.23616406175
91144.29484265734388.9017516726884199.687933641997
92144.59172494172585.3740197820185203.809430101431
93132.74277389277469.9329125656729195.552635219875
94128.22298951048962.0155824061677194.430396614811
95129.76987179487260.3309574094557199.208786180288
96134.06258741258761.5360067226577206.589168102517



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')