Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 22 Dec 2013 15:33:39 -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/Dec/22/t13877445255or6umnvynsn9si.htm/, Retrieved Sun, 05 Dec 2021 18:28:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232573, Retrieved Sun, 05 Dec 2021 18:28:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-22 20:33:39] [20efb5145ec2a2ddd8dcd418764211fa] [Current]
Feedback Forum

Post a new message
Dataseries X:
19,4
19,4
19,4
19,5
19,5
19,5
28,7
28,7
28,7
21,8
21,8
21,8
20
20
20
22,6
22,6
22,6
22,4
22,4
22,4
18,6
18,6
18,6
16,2
16,2
16,2
13,8
13,8
13,8
24,1
24,1
24,1
19,9
19,9
19,9
22,3
22,3
22,3
20,9
20,9
20,9
23,5
23,5
23,5
23,1
23,1
23,1
25,7
25,7
25,7
19,7
19,7
19,7
23,1
23,1
23,1
20,7
20,7
20,7
18
18
18
16,9
16,9
16,9
24,4
24,4
24,4
15,5
15,5
15,5
18,4
18,4
18,4
16,2
16,2
16,2
20,6
20,6
20,6
19,8
19,8
19,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232573&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]4 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=232573&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232573&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232573&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232573&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232573&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
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
319.419.40
419.519.40.100000000000001
519.519.50
619.519.50
728.719.59.2
828.728.70
928.728.70
1021.828.7-6.9
1121.821.80
1221.821.80
132021.8-1.8
1420200
1520200
1622.6202.6
1722.622.60
1822.622.60
1922.422.6-0.200000000000003
2022.422.40
2122.422.40
2218.622.4-3.8
2318.618.60
2418.618.60
2516.218.6-2.4
2616.216.20
2716.216.20
2813.816.2-2.4
2913.813.80
3013.813.80
3124.113.810.3
3224.124.10
3324.124.10
3419.924.1-4.2
3519.919.90
3619.919.90
3722.319.92.4
3822.322.30
3922.322.30
4020.922.3-1.4
4120.920.90
4220.920.90
4323.520.92.6
4423.523.50
4523.523.50
4623.123.5-0.399999999999999
4723.123.10
4823.123.10
4925.723.12.6
5025.725.70
5125.725.70
5219.725.7-6
5319.719.70
5419.719.70
5523.119.73.4
5623.123.10
5723.123.10
5820.723.1-2.4
5920.720.70
6020.720.70
611820.7-2.7
6218180
6318180
6416.918-1.1
6516.916.90
6616.916.90
6724.416.97.5
6824.424.40
6924.424.40
7015.524.4-8.9
7115.515.50
7215.515.50
7318.415.52.9
7418.418.40
7518.418.40
7616.218.4-2.2
7716.216.20
7816.216.20
7920.616.24.4
8020.620.60
8120.620.60
8219.820.6-0.800000000000001
8319.819.80
8419.819.80

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 19.4 & 19.4 & 0 \tabularnewline
4 & 19.5 & 19.4 & 0.100000000000001 \tabularnewline
5 & 19.5 & 19.5 & 0 \tabularnewline
6 & 19.5 & 19.5 & 0 \tabularnewline
7 & 28.7 & 19.5 & 9.2 \tabularnewline
8 & 28.7 & 28.7 & 0 \tabularnewline
9 & 28.7 & 28.7 & 0 \tabularnewline
10 & 21.8 & 28.7 & -6.9 \tabularnewline
11 & 21.8 & 21.8 & 0 \tabularnewline
12 & 21.8 & 21.8 & 0 \tabularnewline
13 & 20 & 21.8 & -1.8 \tabularnewline
14 & 20 & 20 & 0 \tabularnewline
15 & 20 & 20 & 0 \tabularnewline
16 & 22.6 & 20 & 2.6 \tabularnewline
17 & 22.6 & 22.6 & 0 \tabularnewline
18 & 22.6 & 22.6 & 0 \tabularnewline
19 & 22.4 & 22.6 & -0.200000000000003 \tabularnewline
20 & 22.4 & 22.4 & 0 \tabularnewline
21 & 22.4 & 22.4 & 0 \tabularnewline
22 & 18.6 & 22.4 & -3.8 \tabularnewline
23 & 18.6 & 18.6 & 0 \tabularnewline
24 & 18.6 & 18.6 & 0 \tabularnewline
25 & 16.2 & 18.6 & -2.4 \tabularnewline
26 & 16.2 & 16.2 & 0 \tabularnewline
27 & 16.2 & 16.2 & 0 \tabularnewline
28 & 13.8 & 16.2 & -2.4 \tabularnewline
29 & 13.8 & 13.8 & 0 \tabularnewline
30 & 13.8 & 13.8 & 0 \tabularnewline
31 & 24.1 & 13.8 & 10.3 \tabularnewline
32 & 24.1 & 24.1 & 0 \tabularnewline
33 & 24.1 & 24.1 & 0 \tabularnewline
34 & 19.9 & 24.1 & -4.2 \tabularnewline
35 & 19.9 & 19.9 & 0 \tabularnewline
36 & 19.9 & 19.9 & 0 \tabularnewline
37 & 22.3 & 19.9 & 2.4 \tabularnewline
38 & 22.3 & 22.3 & 0 \tabularnewline
39 & 22.3 & 22.3 & 0 \tabularnewline
40 & 20.9 & 22.3 & -1.4 \tabularnewline
41 & 20.9 & 20.9 & 0 \tabularnewline
42 & 20.9 & 20.9 & 0 \tabularnewline
43 & 23.5 & 20.9 & 2.6 \tabularnewline
44 & 23.5 & 23.5 & 0 \tabularnewline
45 & 23.5 & 23.5 & 0 \tabularnewline
46 & 23.1 & 23.5 & -0.399999999999999 \tabularnewline
47 & 23.1 & 23.1 & 0 \tabularnewline
48 & 23.1 & 23.1 & 0 \tabularnewline
49 & 25.7 & 23.1 & 2.6 \tabularnewline
50 & 25.7 & 25.7 & 0 \tabularnewline
51 & 25.7 & 25.7 & 0 \tabularnewline
52 & 19.7 & 25.7 & -6 \tabularnewline
53 & 19.7 & 19.7 & 0 \tabularnewline
54 & 19.7 & 19.7 & 0 \tabularnewline
55 & 23.1 & 19.7 & 3.4 \tabularnewline
56 & 23.1 & 23.1 & 0 \tabularnewline
57 & 23.1 & 23.1 & 0 \tabularnewline
58 & 20.7 & 23.1 & -2.4 \tabularnewline
59 & 20.7 & 20.7 & 0 \tabularnewline
60 & 20.7 & 20.7 & 0 \tabularnewline
61 & 18 & 20.7 & -2.7 \tabularnewline
62 & 18 & 18 & 0 \tabularnewline
63 & 18 & 18 & 0 \tabularnewline
64 & 16.9 & 18 & -1.1 \tabularnewline
65 & 16.9 & 16.9 & 0 \tabularnewline
66 & 16.9 & 16.9 & 0 \tabularnewline
67 & 24.4 & 16.9 & 7.5 \tabularnewline
68 & 24.4 & 24.4 & 0 \tabularnewline
69 & 24.4 & 24.4 & 0 \tabularnewline
70 & 15.5 & 24.4 & -8.9 \tabularnewline
71 & 15.5 & 15.5 & 0 \tabularnewline
72 & 15.5 & 15.5 & 0 \tabularnewline
73 & 18.4 & 15.5 & 2.9 \tabularnewline
74 & 18.4 & 18.4 & 0 \tabularnewline
75 & 18.4 & 18.4 & 0 \tabularnewline
76 & 16.2 & 18.4 & -2.2 \tabularnewline
77 & 16.2 & 16.2 & 0 \tabularnewline
78 & 16.2 & 16.2 & 0 \tabularnewline
79 & 20.6 & 16.2 & 4.4 \tabularnewline
80 & 20.6 & 20.6 & 0 \tabularnewline
81 & 20.6 & 20.6 & 0 \tabularnewline
82 & 19.8 & 20.6 & -0.800000000000001 \tabularnewline
83 & 19.8 & 19.8 & 0 \tabularnewline
84 & 19.8 & 19.8 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232573&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]19.4[/C][C]19.4[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]19.5[/C][C]19.4[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]5[/C][C]19.5[/C][C]19.5[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]19.5[/C][C]19.5[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]28.7[/C][C]19.5[/C][C]9.2[/C][/ROW]
[ROW][C]8[/C][C]28.7[/C][C]28.7[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]28.7[/C][C]28.7[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]21.8[/C][C]28.7[/C][C]-6.9[/C][/ROW]
[ROW][C]11[/C][C]21.8[/C][C]21.8[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]21.8[/C][C]21.8[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]20[/C][C]21.8[/C][C]-1.8[/C][/ROW]
[ROW][C]14[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]22.6[/C][C]20[/C][C]2.6[/C][/ROW]
[ROW][C]17[/C][C]22.6[/C][C]22.6[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]22.6[/C][C]22.6[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]22.4[/C][C]22.6[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]20[/C][C]22.4[/C][C]22.4[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]22.4[/C][C]22.4[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]18.6[/C][C]22.4[/C][C]-3.8[/C][/ROW]
[ROW][C]23[/C][C]18.6[/C][C]18.6[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]18.6[/C][C]18.6[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]16.2[/C][C]18.6[/C][C]-2.4[/C][/ROW]
[ROW][C]26[/C][C]16.2[/C][C]16.2[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]16.2[/C][C]16.2[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]13.8[/C][C]16.2[/C][C]-2.4[/C][/ROW]
[ROW][C]29[/C][C]13.8[/C][C]13.8[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]13.8[/C][C]13.8[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]24.1[/C][C]13.8[/C][C]10.3[/C][/ROW]
[ROW][C]32[/C][C]24.1[/C][C]24.1[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]24.1[/C][C]24.1[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]19.9[/C][C]24.1[/C][C]-4.2[/C][/ROW]
[ROW][C]35[/C][C]19.9[/C][C]19.9[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]19.9[/C][C]19.9[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]22.3[/C][C]19.9[/C][C]2.4[/C][/ROW]
[ROW][C]38[/C][C]22.3[/C][C]22.3[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]22.3[/C][C]22.3[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]20.9[/C][C]22.3[/C][C]-1.4[/C][/ROW]
[ROW][C]41[/C][C]20.9[/C][C]20.9[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]20.9[/C][C]20.9[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]23.5[/C][C]20.9[/C][C]2.6[/C][/ROW]
[ROW][C]44[/C][C]23.5[/C][C]23.5[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]23.5[/C][C]23.5[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]23.1[/C][C]23.5[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]47[/C][C]23.1[/C][C]23.1[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]23.1[/C][C]23.1[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]25.7[/C][C]23.1[/C][C]2.6[/C][/ROW]
[ROW][C]50[/C][C]25.7[/C][C]25.7[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]25.7[/C][C]25.7[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]19.7[/C][C]25.7[/C][C]-6[/C][/ROW]
[ROW][C]53[/C][C]19.7[/C][C]19.7[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]19.7[/C][C]19.7[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]23.1[/C][C]19.7[/C][C]3.4[/C][/ROW]
[ROW][C]56[/C][C]23.1[/C][C]23.1[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]23.1[/C][C]23.1[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]20.7[/C][C]23.1[/C][C]-2.4[/C][/ROW]
[ROW][C]59[/C][C]20.7[/C][C]20.7[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]20.7[/C][C]20.7[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]18[/C][C]20.7[/C][C]-2.7[/C][/ROW]
[ROW][C]62[/C][C]18[/C][C]18[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]18[/C][C]18[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]16.9[/C][C]18[/C][C]-1.1[/C][/ROW]
[ROW][C]65[/C][C]16.9[/C][C]16.9[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]16.9[/C][C]16.9[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]24.4[/C][C]16.9[/C][C]7.5[/C][/ROW]
[ROW][C]68[/C][C]24.4[/C][C]24.4[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]24.4[/C][C]24.4[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]15.5[/C][C]24.4[/C][C]-8.9[/C][/ROW]
[ROW][C]71[/C][C]15.5[/C][C]15.5[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]15.5[/C][C]15.5[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]18.4[/C][C]15.5[/C][C]2.9[/C][/ROW]
[ROW][C]74[/C][C]18.4[/C][C]18.4[/C][C]0[/C][/ROW]
[ROW][C]75[/C][C]18.4[/C][C]18.4[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]16.2[/C][C]18.4[/C][C]-2.2[/C][/ROW]
[ROW][C]77[/C][C]16.2[/C][C]16.2[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]16.2[/C][C]16.2[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]20.6[/C][C]16.2[/C][C]4.4[/C][/ROW]
[ROW][C]80[/C][C]20.6[/C][C]20.6[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]20.6[/C][C]20.6[/C][C]0[/C][/ROW]
[ROW][C]82[/C][C]19.8[/C][C]20.6[/C][C]-0.800000000000001[/C][/ROW]
[ROW][C]83[/C][C]19.8[/C][C]19.8[/C][C]0[/C][/ROW]
[ROW][C]84[/C][C]19.8[/C][C]19.8[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232573&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232573&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
319.419.40
419.519.40.100000000000001
519.519.50
619.519.50
728.719.59.2
828.728.70
928.728.70
1021.828.7-6.9
1121.821.80
1221.821.80
132021.8-1.8
1420200
1520200
1622.6202.6
1722.622.60
1822.622.60
1922.422.6-0.200000000000003
2022.422.40
2122.422.40
2218.622.4-3.8
2318.618.60
2418.618.60
2516.218.6-2.4
2616.216.20
2716.216.20
2813.816.2-2.4
2913.813.80
3013.813.80
3124.113.810.3
3224.124.10
3324.124.10
3419.924.1-4.2
3519.919.90
3619.919.90
3722.319.92.4
3822.322.30
3922.322.30
4020.922.3-1.4
4120.920.90
4220.920.90
4323.520.92.6
4423.523.50
4523.523.50
4623.123.5-0.399999999999999
4723.123.10
4823.123.10
4925.723.12.6
5025.725.70
5125.725.70
5219.725.7-6
5319.719.70
5419.719.70
5523.119.73.4
5623.123.10
5723.123.10
5820.723.1-2.4
5920.720.70
6020.720.70
611820.7-2.7
6218180
6318180
6416.918-1.1
6516.916.90
6616.916.90
6724.416.97.5
6824.424.40
6924.424.40
7015.524.4-8.9
7115.515.50
7215.515.50
7318.415.52.9
7418.418.40
7518.418.40
7616.218.4-2.2
7716.216.20
7816.216.20
7920.616.24.4
8020.620.60
8120.620.60
8219.820.6-0.800000000000001
8319.819.80
8419.819.80







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8519.814.721068953938424.8789310460616
8619.812.617306832301926.9826931676981
8719.811.003033380082328.5969666199177
8819.89.6421379078767429.9578620921233
8919.88.4431649279720931.1568350720279
9019.87.3592104983690132.240789501631
9119.86.362411526075833.2375884739242
9219.85.4346136646037534.1653863353962
9319.84.5632068618151235.0367931381849
9419.83.739009815503735.8609901844963
9519.82.9550913841263236.6449086158737
9619.82.2060667601646337.3939332398354

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 19.8 & 14.7210689539384 & 24.8789310460616 \tabularnewline
86 & 19.8 & 12.6173068323019 & 26.9826931676981 \tabularnewline
87 & 19.8 & 11.0030333800823 & 28.5969666199177 \tabularnewline
88 & 19.8 & 9.64213790787674 & 29.9578620921233 \tabularnewline
89 & 19.8 & 8.44316492797209 & 31.1568350720279 \tabularnewline
90 & 19.8 & 7.35921049836901 & 32.240789501631 \tabularnewline
91 & 19.8 & 6.3624115260758 & 33.2375884739242 \tabularnewline
92 & 19.8 & 5.43461366460375 & 34.1653863353962 \tabularnewline
93 & 19.8 & 4.56320686181512 & 35.0367931381849 \tabularnewline
94 & 19.8 & 3.7390098155037 & 35.8609901844963 \tabularnewline
95 & 19.8 & 2.95509138412632 & 36.6449086158737 \tabularnewline
96 & 19.8 & 2.20606676016463 & 37.3939332398354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232573&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]19.8[/C][C]14.7210689539384[/C][C]24.8789310460616[/C][/ROW]
[ROW][C]86[/C][C]19.8[/C][C]12.6173068323019[/C][C]26.9826931676981[/C][/ROW]
[ROW][C]87[/C][C]19.8[/C][C]11.0030333800823[/C][C]28.5969666199177[/C][/ROW]
[ROW][C]88[/C][C]19.8[/C][C]9.64213790787674[/C][C]29.9578620921233[/C][/ROW]
[ROW][C]89[/C][C]19.8[/C][C]8.44316492797209[/C][C]31.1568350720279[/C][/ROW]
[ROW][C]90[/C][C]19.8[/C][C]7.35921049836901[/C][C]32.240789501631[/C][/ROW]
[ROW][C]91[/C][C]19.8[/C][C]6.3624115260758[/C][C]33.2375884739242[/C][/ROW]
[ROW][C]92[/C][C]19.8[/C][C]5.43461366460375[/C][C]34.1653863353962[/C][/ROW]
[ROW][C]93[/C][C]19.8[/C][C]4.56320686181512[/C][C]35.0367931381849[/C][/ROW]
[ROW][C]94[/C][C]19.8[/C][C]3.7390098155037[/C][C]35.8609901844963[/C][/ROW]
[ROW][C]95[/C][C]19.8[/C][C]2.95509138412632[/C][C]36.6449086158737[/C][/ROW]
[ROW][C]96[/C][C]19.8[/C][C]2.20606676016463[/C][C]37.3939332398354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232573&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232573&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
8519.814.721068953938424.8789310460616
8619.812.617306832301926.9826931676981
8719.811.003033380082328.5969666199177
8819.89.6421379078767429.9578620921233
8919.88.4431649279720931.1568350720279
9019.87.3592104983690132.240789501631
9119.86.362411526075833.2375884739242
9219.85.4346136646037534.1653863353962
9319.84.5632068618151235.0367931381849
9419.83.739009815503735.8609901844963
9519.82.9550913841263236.6449086158737
9619.82.2060667601646337.3939332398354



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
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')