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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 10:18:49 -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/2013/Jan/15/t1358263348vf1tlciu6uvgzre.htm/, Retrieved Sat, 27 Apr 2024 20:30:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205478, Retrieved Sat, 27 Apr 2024 20:30:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [] [2012-11-20 10:23:22] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [] [2013-01-15 15:18:49] [fd38808b420d32739e394c14d51f62a5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20,7
20,4
20,3
20,4
19,8
19,5
23,1
23,5
23,5
22,9
21,9
21,5
20,5
20,2
19,4
19,2
18,8
18,8
22,6
23,3
23
21,4
19,9
18,8
18,6
18,4
18,6
19,9
19,2
18,4
21,1
20,5
19,1
18,1
17
17,1
17,4
16,8
15,3
14,3
13,4
15,3
22,1
23,7
22,2
19,5
16,6
17,3
19,8
21,2
21,5
20,6
19,1
19,6
23,4
24,3
24,1
22,8
22,5
23,8
24,9
25,2
24,3
22,8
20,7
19,8
22,5
22,6
22,5
21,8
21,2
20,6
19,9
18,7
17,6
16,4
15,9
16,8
22,8
24
22,2
17,9
16
16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205478&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205478&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205478&T=0

As an alternative you can also use a QR Code:  
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'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205478&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]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205478&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205478&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.520.9280982905983-0.428098290598289
1420.220.15941142191140.0405885780885811
1519.419.35941142191140.0405885780885811
1619.219.2135780885781-0.0135780885780861
1718.818.8760780885781-0.0760780885780861
1818.818.9260780885781-0.12607808857809
1922.622.18441142191140.415588578088585
2023.322.94691142191140.353088578088578
212323.2760780885781-0.276078088578089
2221.422.4177447552448-1.01774475524475
2319.920.4219114219114-0.521911421911422
2418.819.5010780885781-0.701078088578086
2518.617.78024475524480.819755244755243
2618.418.25941142191140.140588578088579
2718.617.55941142191141.04058857808858
2819.918.41357808857811.48642191142191
2919.219.5760780885781-0.376078088578087
3018.419.3260780885781-0.926078088578091
3121.121.7844114219114-0.684411421911413
3220.521.4469114219114-0.946911421911423
3319.120.4760780885781-1.37607808857809
3418.118.5177447552448-0.417744755244751
351717.1219114219114-0.121911421911424
3617.116.60107808857810.498921911421913
3717.416.08024475524481.31975524475524
3816.817.0594114219114-0.259411421911416
3915.315.9594114219114-0.659411421911418
4014.315.1135780885781-0.813578088578087
4113.413.9760780885781-0.57607808857809
4215.313.52607808857811.77392191142191
4322.118.68441142191143.41558857808858
4423.722.44691142191141.25308857808858
4522.223.6760780885781-1.47607808857809
4619.521.6177447552448-2.11774475524475
4716.618.5219114219114-1.92191142191142
4817.316.20107808857811.09892191142191
4919.816.28024475524483.51975524475524
5021.219.45941142191141.74058857808858
5121.520.35941142191141.14058857808858
5220.621.3135780885781-0.713578088578085
5319.120.2760780885781-1.17607808857809
5419.619.22607808857810.37392191142191
5523.422.98441142191140.415588578088581
5624.323.74691142191140.55308857808858
5724.124.2760780885781-0.176078088578087
5822.823.5177447552448-0.717744755244752
5922.521.82191142191140.678088578088577
6023.822.10107808857811.69892191142191
6124.922.78024475524482.11975524475524
6225.224.55941142191140.640588578088582
6324.324.3594114219114-0.0594114219114168
6422.824.1135780885781-1.31357808857809
6520.722.4760780885781-1.77607808857809
6619.820.8260780885781-1.02607808857809
6722.523.1844114219114-0.684411421911417
6822.622.8469114219114-0.24691142191142
6922.522.5760780885781-0.0760780885780896
7021.821.9177447552448-0.11774475524475
7121.220.82191142191140.378088578088576
7220.620.8010780885781-0.201078088578086
7319.919.58024475524480.319755244755239
7418.719.5594114219114-0.859411421911418
7517.617.8594114219114-0.259411421911416
7616.417.4135780885781-1.01357808857809
7715.916.0760780885781-0.176078088578086
7816.816.02607808857810.773921911421912
7922.820.18441142191142.61558857808858
802423.14691142191140.853088578088578
8122.223.9760780885781-1.77607808857809
8217.921.6177447552448-3.71774475524475
831616.9219114219114-0.921911421911421
841615.60107808857810.39892191142191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 20.5 & 20.9280982905983 & -0.428098290598289 \tabularnewline
14 & 20.2 & 20.1594114219114 & 0.0405885780885811 \tabularnewline
15 & 19.4 & 19.3594114219114 & 0.0405885780885811 \tabularnewline
16 & 19.2 & 19.2135780885781 & -0.0135780885780861 \tabularnewline
17 & 18.8 & 18.8760780885781 & -0.0760780885780861 \tabularnewline
18 & 18.8 & 18.9260780885781 & -0.12607808857809 \tabularnewline
19 & 22.6 & 22.1844114219114 & 0.415588578088585 \tabularnewline
20 & 23.3 & 22.9469114219114 & 0.353088578088578 \tabularnewline
21 & 23 & 23.2760780885781 & -0.276078088578089 \tabularnewline
22 & 21.4 & 22.4177447552448 & -1.01774475524475 \tabularnewline
23 & 19.9 & 20.4219114219114 & -0.521911421911422 \tabularnewline
24 & 18.8 & 19.5010780885781 & -0.701078088578086 \tabularnewline
25 & 18.6 & 17.7802447552448 & 0.819755244755243 \tabularnewline
26 & 18.4 & 18.2594114219114 & 0.140588578088579 \tabularnewline
27 & 18.6 & 17.5594114219114 & 1.04058857808858 \tabularnewline
28 & 19.9 & 18.4135780885781 & 1.48642191142191 \tabularnewline
29 & 19.2 & 19.5760780885781 & -0.376078088578087 \tabularnewline
30 & 18.4 & 19.3260780885781 & -0.926078088578091 \tabularnewline
31 & 21.1 & 21.7844114219114 & -0.684411421911413 \tabularnewline
32 & 20.5 & 21.4469114219114 & -0.946911421911423 \tabularnewline
33 & 19.1 & 20.4760780885781 & -1.37607808857809 \tabularnewline
34 & 18.1 & 18.5177447552448 & -0.417744755244751 \tabularnewline
35 & 17 & 17.1219114219114 & -0.121911421911424 \tabularnewline
36 & 17.1 & 16.6010780885781 & 0.498921911421913 \tabularnewline
37 & 17.4 & 16.0802447552448 & 1.31975524475524 \tabularnewline
38 & 16.8 & 17.0594114219114 & -0.259411421911416 \tabularnewline
39 & 15.3 & 15.9594114219114 & -0.659411421911418 \tabularnewline
40 & 14.3 & 15.1135780885781 & -0.813578088578087 \tabularnewline
41 & 13.4 & 13.9760780885781 & -0.57607808857809 \tabularnewline
42 & 15.3 & 13.5260780885781 & 1.77392191142191 \tabularnewline
43 & 22.1 & 18.6844114219114 & 3.41558857808858 \tabularnewline
44 & 23.7 & 22.4469114219114 & 1.25308857808858 \tabularnewline
45 & 22.2 & 23.6760780885781 & -1.47607808857809 \tabularnewline
46 & 19.5 & 21.6177447552448 & -2.11774475524475 \tabularnewline
47 & 16.6 & 18.5219114219114 & -1.92191142191142 \tabularnewline
48 & 17.3 & 16.2010780885781 & 1.09892191142191 \tabularnewline
49 & 19.8 & 16.2802447552448 & 3.51975524475524 \tabularnewline
50 & 21.2 & 19.4594114219114 & 1.74058857808858 \tabularnewline
51 & 21.5 & 20.3594114219114 & 1.14058857808858 \tabularnewline
52 & 20.6 & 21.3135780885781 & -0.713578088578085 \tabularnewline
53 & 19.1 & 20.2760780885781 & -1.17607808857809 \tabularnewline
54 & 19.6 & 19.2260780885781 & 0.37392191142191 \tabularnewline
55 & 23.4 & 22.9844114219114 & 0.415588578088581 \tabularnewline
56 & 24.3 & 23.7469114219114 & 0.55308857808858 \tabularnewline
57 & 24.1 & 24.2760780885781 & -0.176078088578087 \tabularnewline
58 & 22.8 & 23.5177447552448 & -0.717744755244752 \tabularnewline
59 & 22.5 & 21.8219114219114 & 0.678088578088577 \tabularnewline
60 & 23.8 & 22.1010780885781 & 1.69892191142191 \tabularnewline
61 & 24.9 & 22.7802447552448 & 2.11975524475524 \tabularnewline
62 & 25.2 & 24.5594114219114 & 0.640588578088582 \tabularnewline
63 & 24.3 & 24.3594114219114 & -0.0594114219114168 \tabularnewline
64 & 22.8 & 24.1135780885781 & -1.31357808857809 \tabularnewline
65 & 20.7 & 22.4760780885781 & -1.77607808857809 \tabularnewline
66 & 19.8 & 20.8260780885781 & -1.02607808857809 \tabularnewline
67 & 22.5 & 23.1844114219114 & -0.684411421911417 \tabularnewline
68 & 22.6 & 22.8469114219114 & -0.24691142191142 \tabularnewline
69 & 22.5 & 22.5760780885781 & -0.0760780885780896 \tabularnewline
70 & 21.8 & 21.9177447552448 & -0.11774475524475 \tabularnewline
71 & 21.2 & 20.8219114219114 & 0.378088578088576 \tabularnewline
72 & 20.6 & 20.8010780885781 & -0.201078088578086 \tabularnewline
73 & 19.9 & 19.5802447552448 & 0.319755244755239 \tabularnewline
74 & 18.7 & 19.5594114219114 & -0.859411421911418 \tabularnewline
75 & 17.6 & 17.8594114219114 & -0.259411421911416 \tabularnewline
76 & 16.4 & 17.4135780885781 & -1.01357808857809 \tabularnewline
77 & 15.9 & 16.0760780885781 & -0.176078088578086 \tabularnewline
78 & 16.8 & 16.0260780885781 & 0.773921911421912 \tabularnewline
79 & 22.8 & 20.1844114219114 & 2.61558857808858 \tabularnewline
80 & 24 & 23.1469114219114 & 0.853088578088578 \tabularnewline
81 & 22.2 & 23.9760780885781 & -1.77607808857809 \tabularnewline
82 & 17.9 & 21.6177447552448 & -3.71774475524475 \tabularnewline
83 & 16 & 16.9219114219114 & -0.921911421911421 \tabularnewline
84 & 16 & 15.6010780885781 & 0.39892191142191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205478&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]20.5[/C][C]20.9280982905983[/C][C]-0.428098290598289[/C][/ROW]
[ROW][C]14[/C][C]20.2[/C][C]20.1594114219114[/C][C]0.0405885780885811[/C][/ROW]
[ROW][C]15[/C][C]19.4[/C][C]19.3594114219114[/C][C]0.0405885780885811[/C][/ROW]
[ROW][C]16[/C][C]19.2[/C][C]19.2135780885781[/C][C]-0.0135780885780861[/C][/ROW]
[ROW][C]17[/C][C]18.8[/C][C]18.8760780885781[/C][C]-0.0760780885780861[/C][/ROW]
[ROW][C]18[/C][C]18.8[/C][C]18.9260780885781[/C][C]-0.12607808857809[/C][/ROW]
[ROW][C]19[/C][C]22.6[/C][C]22.1844114219114[/C][C]0.415588578088585[/C][/ROW]
[ROW][C]20[/C][C]23.3[/C][C]22.9469114219114[/C][C]0.353088578088578[/C][/ROW]
[ROW][C]21[/C][C]23[/C][C]23.2760780885781[/C][C]-0.276078088578089[/C][/ROW]
[ROW][C]22[/C][C]21.4[/C][C]22.4177447552448[/C][C]-1.01774475524475[/C][/ROW]
[ROW][C]23[/C][C]19.9[/C][C]20.4219114219114[/C][C]-0.521911421911422[/C][/ROW]
[ROW][C]24[/C][C]18.8[/C][C]19.5010780885781[/C][C]-0.701078088578086[/C][/ROW]
[ROW][C]25[/C][C]18.6[/C][C]17.7802447552448[/C][C]0.819755244755243[/C][/ROW]
[ROW][C]26[/C][C]18.4[/C][C]18.2594114219114[/C][C]0.140588578088579[/C][/ROW]
[ROW][C]27[/C][C]18.6[/C][C]17.5594114219114[/C][C]1.04058857808858[/C][/ROW]
[ROW][C]28[/C][C]19.9[/C][C]18.4135780885781[/C][C]1.48642191142191[/C][/ROW]
[ROW][C]29[/C][C]19.2[/C][C]19.5760780885781[/C][C]-0.376078088578087[/C][/ROW]
[ROW][C]30[/C][C]18.4[/C][C]19.3260780885781[/C][C]-0.926078088578091[/C][/ROW]
[ROW][C]31[/C][C]21.1[/C][C]21.7844114219114[/C][C]-0.684411421911413[/C][/ROW]
[ROW][C]32[/C][C]20.5[/C][C]21.4469114219114[/C][C]-0.946911421911423[/C][/ROW]
[ROW][C]33[/C][C]19.1[/C][C]20.4760780885781[/C][C]-1.37607808857809[/C][/ROW]
[ROW][C]34[/C][C]18.1[/C][C]18.5177447552448[/C][C]-0.417744755244751[/C][/ROW]
[ROW][C]35[/C][C]17[/C][C]17.1219114219114[/C][C]-0.121911421911424[/C][/ROW]
[ROW][C]36[/C][C]17.1[/C][C]16.6010780885781[/C][C]0.498921911421913[/C][/ROW]
[ROW][C]37[/C][C]17.4[/C][C]16.0802447552448[/C][C]1.31975524475524[/C][/ROW]
[ROW][C]38[/C][C]16.8[/C][C]17.0594114219114[/C][C]-0.259411421911416[/C][/ROW]
[ROW][C]39[/C][C]15.3[/C][C]15.9594114219114[/C][C]-0.659411421911418[/C][/ROW]
[ROW][C]40[/C][C]14.3[/C][C]15.1135780885781[/C][C]-0.813578088578087[/C][/ROW]
[ROW][C]41[/C][C]13.4[/C][C]13.9760780885781[/C][C]-0.57607808857809[/C][/ROW]
[ROW][C]42[/C][C]15.3[/C][C]13.5260780885781[/C][C]1.77392191142191[/C][/ROW]
[ROW][C]43[/C][C]22.1[/C][C]18.6844114219114[/C][C]3.41558857808858[/C][/ROW]
[ROW][C]44[/C][C]23.7[/C][C]22.4469114219114[/C][C]1.25308857808858[/C][/ROW]
[ROW][C]45[/C][C]22.2[/C][C]23.6760780885781[/C][C]-1.47607808857809[/C][/ROW]
[ROW][C]46[/C][C]19.5[/C][C]21.6177447552448[/C][C]-2.11774475524475[/C][/ROW]
[ROW][C]47[/C][C]16.6[/C][C]18.5219114219114[/C][C]-1.92191142191142[/C][/ROW]
[ROW][C]48[/C][C]17.3[/C][C]16.2010780885781[/C][C]1.09892191142191[/C][/ROW]
[ROW][C]49[/C][C]19.8[/C][C]16.2802447552448[/C][C]3.51975524475524[/C][/ROW]
[ROW][C]50[/C][C]21.2[/C][C]19.4594114219114[/C][C]1.74058857808858[/C][/ROW]
[ROW][C]51[/C][C]21.5[/C][C]20.3594114219114[/C][C]1.14058857808858[/C][/ROW]
[ROW][C]52[/C][C]20.6[/C][C]21.3135780885781[/C][C]-0.713578088578085[/C][/ROW]
[ROW][C]53[/C][C]19.1[/C][C]20.2760780885781[/C][C]-1.17607808857809[/C][/ROW]
[ROW][C]54[/C][C]19.6[/C][C]19.2260780885781[/C][C]0.37392191142191[/C][/ROW]
[ROW][C]55[/C][C]23.4[/C][C]22.9844114219114[/C][C]0.415588578088581[/C][/ROW]
[ROW][C]56[/C][C]24.3[/C][C]23.7469114219114[/C][C]0.55308857808858[/C][/ROW]
[ROW][C]57[/C][C]24.1[/C][C]24.2760780885781[/C][C]-0.176078088578087[/C][/ROW]
[ROW][C]58[/C][C]22.8[/C][C]23.5177447552448[/C][C]-0.717744755244752[/C][/ROW]
[ROW][C]59[/C][C]22.5[/C][C]21.8219114219114[/C][C]0.678088578088577[/C][/ROW]
[ROW][C]60[/C][C]23.8[/C][C]22.1010780885781[/C][C]1.69892191142191[/C][/ROW]
[ROW][C]61[/C][C]24.9[/C][C]22.7802447552448[/C][C]2.11975524475524[/C][/ROW]
[ROW][C]62[/C][C]25.2[/C][C]24.5594114219114[/C][C]0.640588578088582[/C][/ROW]
[ROW][C]63[/C][C]24.3[/C][C]24.3594114219114[/C][C]-0.0594114219114168[/C][/ROW]
[ROW][C]64[/C][C]22.8[/C][C]24.1135780885781[/C][C]-1.31357808857809[/C][/ROW]
[ROW][C]65[/C][C]20.7[/C][C]22.4760780885781[/C][C]-1.77607808857809[/C][/ROW]
[ROW][C]66[/C][C]19.8[/C][C]20.8260780885781[/C][C]-1.02607808857809[/C][/ROW]
[ROW][C]67[/C][C]22.5[/C][C]23.1844114219114[/C][C]-0.684411421911417[/C][/ROW]
[ROW][C]68[/C][C]22.6[/C][C]22.8469114219114[/C][C]-0.24691142191142[/C][/ROW]
[ROW][C]69[/C][C]22.5[/C][C]22.5760780885781[/C][C]-0.0760780885780896[/C][/ROW]
[ROW][C]70[/C][C]21.8[/C][C]21.9177447552448[/C][C]-0.11774475524475[/C][/ROW]
[ROW][C]71[/C][C]21.2[/C][C]20.8219114219114[/C][C]0.378088578088576[/C][/ROW]
[ROW][C]72[/C][C]20.6[/C][C]20.8010780885781[/C][C]-0.201078088578086[/C][/ROW]
[ROW][C]73[/C][C]19.9[/C][C]19.5802447552448[/C][C]0.319755244755239[/C][/ROW]
[ROW][C]74[/C][C]18.7[/C][C]19.5594114219114[/C][C]-0.859411421911418[/C][/ROW]
[ROW][C]75[/C][C]17.6[/C][C]17.8594114219114[/C][C]-0.259411421911416[/C][/ROW]
[ROW][C]76[/C][C]16.4[/C][C]17.4135780885781[/C][C]-1.01357808857809[/C][/ROW]
[ROW][C]77[/C][C]15.9[/C][C]16.0760780885781[/C][C]-0.176078088578086[/C][/ROW]
[ROW][C]78[/C][C]16.8[/C][C]16.0260780885781[/C][C]0.773921911421912[/C][/ROW]
[ROW][C]79[/C][C]22.8[/C][C]20.1844114219114[/C][C]2.61558857808858[/C][/ROW]
[ROW][C]80[/C][C]24[/C][C]23.1469114219114[/C][C]0.853088578088578[/C][/ROW]
[ROW][C]81[/C][C]22.2[/C][C]23.9760780885781[/C][C]-1.77607808857809[/C][/ROW]
[ROW][C]82[/C][C]17.9[/C][C]21.6177447552448[/C][C]-3.71774475524475[/C][/ROW]
[ROW][C]83[/C][C]16[/C][C]16.9219114219114[/C][C]-0.921911421911421[/C][/ROW]
[ROW][C]84[/C][C]16[/C][C]15.6010780885781[/C][C]0.39892191142191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205478&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205478&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.520.9280982905983-0.428098290598289
1420.220.15941142191140.0405885780885811
1519.419.35941142191140.0405885780885811
1619.219.2135780885781-0.0135780885780861
1718.818.8760780885781-0.0760780885780861
1818.818.9260780885781-0.12607808857809
1922.622.18441142191140.415588578088585
2023.322.94691142191140.353088578088578
212323.2760780885781-0.276078088578089
2221.422.4177447552448-1.01774475524475
2319.920.4219114219114-0.521911421911422
2418.819.5010780885781-0.701078088578086
2518.617.78024475524480.819755244755243
2618.418.25941142191140.140588578088579
2718.617.55941142191141.04058857808858
2819.918.41357808857811.48642191142191
2919.219.5760780885781-0.376078088578087
3018.419.3260780885781-0.926078088578091
3121.121.7844114219114-0.684411421911413
3220.521.4469114219114-0.946911421911423
3319.120.4760780885781-1.37607808857809
3418.118.5177447552448-0.417744755244751
351717.1219114219114-0.121911421911424
3617.116.60107808857810.498921911421913
3717.416.08024475524481.31975524475524
3816.817.0594114219114-0.259411421911416
3915.315.9594114219114-0.659411421911418
4014.315.1135780885781-0.813578088578087
4113.413.9760780885781-0.57607808857809
4215.313.52607808857811.77392191142191
4322.118.68441142191143.41558857808858
4423.722.44691142191141.25308857808858
4522.223.6760780885781-1.47607808857809
4619.521.6177447552448-2.11774475524475
4716.618.5219114219114-1.92191142191142
4817.316.20107808857811.09892191142191
4919.816.28024475524483.51975524475524
5021.219.45941142191141.74058857808858
5121.520.35941142191141.14058857808858
5220.621.3135780885781-0.713578088578085
5319.120.2760780885781-1.17607808857809
5419.619.22607808857810.37392191142191
5523.422.98441142191140.415588578088581
5624.323.74691142191140.55308857808858
5724.124.2760780885781-0.176078088578087
5822.823.5177447552448-0.717744755244752
5922.521.82191142191140.678088578088577
6023.822.10107808857811.69892191142191
6124.922.78024475524482.11975524475524
6225.224.55941142191140.640588578088582
6324.324.3594114219114-0.0594114219114168
6422.824.1135780885781-1.31357808857809
6520.722.4760780885781-1.77607808857809
6619.820.8260780885781-1.02607808857809
6722.523.1844114219114-0.684411421911417
6822.622.8469114219114-0.24691142191142
6922.522.5760780885781-0.0760780885780896
7021.821.9177447552448-0.11774475524475
7121.220.82191142191140.378088578088576
7220.620.8010780885781-0.201078088578086
7319.919.58024475524480.319755244755239
7418.719.5594114219114-0.859411421911418
7517.617.8594114219114-0.259411421911416
7616.417.4135780885781-1.01357808857809
7715.916.0760780885781-0.176078088578086
7816.816.02607808857810.773921911421912
7922.820.18441142191142.61558857808858
802423.14691142191140.853088578088578
8122.223.9760780885781-1.77607808857809
8217.921.6177447552448-3.71774475524475
831616.9219114219114-0.921911421911421
841615.60107808857810.39892191142191






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8514.980244755244812.596183084707517.364306425782
8614.639656177156211.268083829148518.0112285251638
8713.79906759906769.6697516573195517.9283835408157
8813.61264568764578.8445223465711918.3807690287202
8913.28872377622387.9577998183507818.6196477340968
9013.41480186480197.5750672566583419.2545364729454
9116.799213286713310.491578996230523.1068475771961
9217.146124708624710.402980012609423.88926940464
9317.12220279720289.9700177855910424.2743878088145
9416.53994755244769.000882591243924.0790125136512
9515.5618589743597.6548209361190223.4688970125989
9615.16293706293716.9043051794409623.4215689464332

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 14.9802447552448 & 12.5961830847075 & 17.364306425782 \tabularnewline
86 & 14.6396561771562 & 11.2680838291485 & 18.0112285251638 \tabularnewline
87 & 13.7990675990676 & 9.66975165731955 & 17.9283835408157 \tabularnewline
88 & 13.6126456876457 & 8.84452234657119 & 18.3807690287202 \tabularnewline
89 & 13.2887237762238 & 7.95779981835078 & 18.6196477340968 \tabularnewline
90 & 13.4148018648019 & 7.57506725665834 & 19.2545364729454 \tabularnewline
91 & 16.7992132867133 & 10.4915789962305 & 23.1068475771961 \tabularnewline
92 & 17.1461247086247 & 10.4029800126094 & 23.88926940464 \tabularnewline
93 & 17.1222027972028 & 9.97001778559104 & 24.2743878088145 \tabularnewline
94 & 16.5399475524476 & 9.0008825912439 & 24.0790125136512 \tabularnewline
95 & 15.561858974359 & 7.65482093611902 & 23.4688970125989 \tabularnewline
96 & 15.1629370629371 & 6.90430517944096 & 23.4215689464332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205478&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]14.9802447552448[/C][C]12.5961830847075[/C][C]17.364306425782[/C][/ROW]
[ROW][C]86[/C][C]14.6396561771562[/C][C]11.2680838291485[/C][C]18.0112285251638[/C][/ROW]
[ROW][C]87[/C][C]13.7990675990676[/C][C]9.66975165731955[/C][C]17.9283835408157[/C][/ROW]
[ROW][C]88[/C][C]13.6126456876457[/C][C]8.84452234657119[/C][C]18.3807690287202[/C][/ROW]
[ROW][C]89[/C][C]13.2887237762238[/C][C]7.95779981835078[/C][C]18.6196477340968[/C][/ROW]
[ROW][C]90[/C][C]13.4148018648019[/C][C]7.57506725665834[/C][C]19.2545364729454[/C][/ROW]
[ROW][C]91[/C][C]16.7992132867133[/C][C]10.4915789962305[/C][C]23.1068475771961[/C][/ROW]
[ROW][C]92[/C][C]17.1461247086247[/C][C]10.4029800126094[/C][C]23.88926940464[/C][/ROW]
[ROW][C]93[/C][C]17.1222027972028[/C][C]9.97001778559104[/C][C]24.2743878088145[/C][/ROW]
[ROW][C]94[/C][C]16.5399475524476[/C][C]9.0008825912439[/C][C]24.0790125136512[/C][/ROW]
[ROW][C]95[/C][C]15.561858974359[/C][C]7.65482093611902[/C][C]23.4688970125989[/C][/ROW]
[ROW][C]96[/C][C]15.1629370629371[/C][C]6.90430517944096[/C][C]23.4215689464332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205478&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205478&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8514.980244755244812.596183084707517.364306425782
8614.639656177156211.268083829148518.0112285251638
8713.79906759906769.6697516573195517.9283835408157
8813.61264568764578.8445223465711918.3807690287202
8913.28872377622387.9577998183507818.6196477340968
9013.41480186480197.5750672566583419.2545364729454
9116.799213286713310.491578996230523.1068475771961
9217.146124708624710.402980012609423.88926940464
9317.12220279720289.9700177855910424.2743878088145
9416.53994755244769.000882591243924.0790125136512
9515.5618589743597.6548209361190223.4688970125989
9615.16293706293716.9043051794409623.4215689464332


Figures (Output of Computation)

Input Parameters & R Code

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')