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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 21 Dec 2012 04:37:14 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356082646bc0xb7w9gke5czh.htm/, Retrieved Thu, 25 Apr 2024 01:46:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203380, Retrieved Thu, 25 Apr 2024 01:46:39 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [] [2012-12-21 08:56:25] [2f0f353a58a70fd7baf0f5141860d820]
- R PD    [Exponential Smoothing] [] [2012-12-21 09:37:14] [492ce95363299443ae43b669aa70c778] [Current]

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Dataseries X:

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Histogram

Boxplots

1.26
1.26
1.28
1.34
1.39
1.47
1.57
1.63
1.72
1.43
1.35
1.41
1.44
1.43
1.43
1.42
1.45
1.51
1.48
1.48
1.45
1.38
1.46
1.45
1.41
1.45
1.47
1.47
1.53
1.56
1.66
1.79
1.78
1.46
1.41
1.43
1.43
1.45
1.35
1.35
1.29
1.29
1.26
1.3
1.3
1.16
1.24
1.15
1.21
1.22
1.17
1.13
1.15
1.2
1.23
1.25
1.38
1.28
1.26
1.25
1.26
1.28
1.31
1.22
1.23
1.36
1.54
1.58
1.44
1.29
1.28
1.23

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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=203380&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=203380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203380&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	FALSE

\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=203380&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=203380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203380&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
Parameter	Value
alpha	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.28	1.26	0.02
4	1.34	1.28	0.0600000000000001
5	1.39	1.34	0.0499999999999998
6	1.47	1.39	0.0800000000000001
7	1.57	1.47	0.1
8	1.63	1.57	0.0599999999999998
9	1.72	1.63	0.0900000000000001
10	1.43	1.72	-0.29
11	1.35	1.43	-0.0799999999999998
12	1.41	1.35	0.0599999999999998
13	1.44	1.41	0.03
14	1.43	1.44	-0.01
15	1.43	1.43	0
16	1.42	1.43	-0.01
17	1.45	1.42	0.03
18	1.51	1.45	0.0600000000000001
19	1.48	1.51	-0.03
20	1.48	1.48	0
21	1.45	1.48	-0.03
22	1.38	1.45	-0.0700000000000001
23	1.46	1.38	0.0800000000000001
24	1.45	1.46	-0.01
25	1.41	1.45	-0.04
26	1.45	1.41	0.04
27	1.47	1.45	0.02
28	1.47	1.47	0
29	1.53	1.47	0.0600000000000001
30	1.56	1.53	0.03
31	1.66	1.56	0.0999999999999999
32	1.79	1.66	0.13
33	1.78	1.79	-0.01
34	1.46	1.78	-0.32
35	1.41	1.46	-0.05
36	1.43	1.41	0.02
37	1.43	1.43	0
38	1.45	1.43	0.02
39	1.35	1.45	-0.0999999999999999
40	1.35	1.35	0
41	1.29	1.35	-0.0600000000000001
42	1.29	1.29	0
43	1.26	1.29	-0.03
44	1.3	1.26	0.04
45	1.3	1.3	0
46	1.16	1.3	-0.14
47	1.24	1.16	0.0800000000000001
48	1.15	1.24	-0.0900000000000001
49	1.21	1.15	0.0600000000000001
50	1.22	1.21	0.01
51	1.17	1.22	-0.05
52	1.13	1.17	-0.04
53	1.15	1.13	0.02
54	1.2	1.15	0.05
55	1.23	1.2	0.03
56	1.25	1.23	0.02
57	1.38	1.25	0.13
58	1.28	1.38	-0.0999999999999999
59	1.26	1.28	-0.02
60	1.25	1.26	-0.01
61	1.26	1.25	0.01
62	1.28	1.26	0.02
63	1.31	1.28	0.03
64	1.22	1.31	-0.0900000000000001
65	1.23	1.22	0.01
66	1.36	1.23	0.13
67	1.54	1.36	0.18
68	1.58	1.54	0.04
69	1.44	1.58	-0.14
70	1.29	1.44	-0.15
71	1.28	1.29	-0.01
72	1.23	1.28	-0.05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.28 & 1.26 & 0.02 \tabularnewline
4 & 1.34 & 1.28 & 0.0600000000000001 \tabularnewline
5 & 1.39 & 1.34 & 0.0499999999999998 \tabularnewline
6 & 1.47 & 1.39 & 0.0800000000000001 \tabularnewline
7 & 1.57 & 1.47 & 0.1 \tabularnewline
8 & 1.63 & 1.57 & 0.0599999999999998 \tabularnewline
9 & 1.72 & 1.63 & 0.0900000000000001 \tabularnewline
10 & 1.43 & 1.72 & -0.29 \tabularnewline
11 & 1.35 & 1.43 & -0.0799999999999998 \tabularnewline
12 & 1.41 & 1.35 & 0.0599999999999998 \tabularnewline
13 & 1.44 & 1.41 & 0.03 \tabularnewline
14 & 1.43 & 1.44 & -0.01 \tabularnewline
15 & 1.43 & 1.43 & 0 \tabularnewline
16 & 1.42 & 1.43 & -0.01 \tabularnewline
17 & 1.45 & 1.42 & 0.03 \tabularnewline
18 & 1.51 & 1.45 & 0.0600000000000001 \tabularnewline
19 & 1.48 & 1.51 & -0.03 \tabularnewline
20 & 1.48 & 1.48 & 0 \tabularnewline
21 & 1.45 & 1.48 & -0.03 \tabularnewline
22 & 1.38 & 1.45 & -0.0700000000000001 \tabularnewline
23 & 1.46 & 1.38 & 0.0800000000000001 \tabularnewline
24 & 1.45 & 1.46 & -0.01 \tabularnewline
25 & 1.41 & 1.45 & -0.04 \tabularnewline
26 & 1.45 & 1.41 & 0.04 \tabularnewline
27 & 1.47 & 1.45 & 0.02 \tabularnewline
28 & 1.47 & 1.47 & 0 \tabularnewline
29 & 1.53 & 1.47 & 0.0600000000000001 \tabularnewline
30 & 1.56 & 1.53 & 0.03 \tabularnewline
31 & 1.66 & 1.56 & 0.0999999999999999 \tabularnewline
32 & 1.79 & 1.66 & 0.13 \tabularnewline
33 & 1.78 & 1.79 & -0.01 \tabularnewline
34 & 1.46 & 1.78 & -0.32 \tabularnewline
35 & 1.41 & 1.46 & -0.05 \tabularnewline
36 & 1.43 & 1.41 & 0.02 \tabularnewline
37 & 1.43 & 1.43 & 0 \tabularnewline
38 & 1.45 & 1.43 & 0.02 \tabularnewline
39 & 1.35 & 1.45 & -0.0999999999999999 \tabularnewline
40 & 1.35 & 1.35 & 0 \tabularnewline
41 & 1.29 & 1.35 & -0.0600000000000001 \tabularnewline
42 & 1.29 & 1.29 & 0 \tabularnewline
43 & 1.26 & 1.29 & -0.03 \tabularnewline
44 & 1.3 & 1.26 & 0.04 \tabularnewline
45 & 1.3 & 1.3 & 0 \tabularnewline
46 & 1.16 & 1.3 & -0.14 \tabularnewline
47 & 1.24 & 1.16 & 0.0800000000000001 \tabularnewline
48 & 1.15 & 1.24 & -0.0900000000000001 \tabularnewline
49 & 1.21 & 1.15 & 0.0600000000000001 \tabularnewline
50 & 1.22 & 1.21 & 0.01 \tabularnewline
51 & 1.17 & 1.22 & -0.05 \tabularnewline
52 & 1.13 & 1.17 & -0.04 \tabularnewline
53 & 1.15 & 1.13 & 0.02 \tabularnewline
54 & 1.2 & 1.15 & 0.05 \tabularnewline
55 & 1.23 & 1.2 & 0.03 \tabularnewline
56 & 1.25 & 1.23 & 0.02 \tabularnewline
57 & 1.38 & 1.25 & 0.13 \tabularnewline
58 & 1.28 & 1.38 & -0.0999999999999999 \tabularnewline
59 & 1.26 & 1.28 & -0.02 \tabularnewline
60 & 1.25 & 1.26 & -0.01 \tabularnewline
61 & 1.26 & 1.25 & 0.01 \tabularnewline
62 & 1.28 & 1.26 & 0.02 \tabularnewline
63 & 1.31 & 1.28 & 0.03 \tabularnewline
64 & 1.22 & 1.31 & -0.0900000000000001 \tabularnewline
65 & 1.23 & 1.22 & 0.01 \tabularnewline
66 & 1.36 & 1.23 & 0.13 \tabularnewline
67 & 1.54 & 1.36 & 0.18 \tabularnewline
68 & 1.58 & 1.54 & 0.04 \tabularnewline
69 & 1.44 & 1.58 & -0.14 \tabularnewline
70 & 1.29 & 1.44 & -0.15 \tabularnewline
71 & 1.28 & 1.29 & -0.01 \tabularnewline
72 & 1.23 & 1.28 & -0.05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203380&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]1.28[/C][C]1.26[/C][C]0.02[/C][/ROW]
[ROW][C]4[/C][C]1.34[/C][C]1.28[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]5[/C][C]1.39[/C][C]1.34[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]6[/C][C]1.47[/C][C]1.39[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]7[/C][C]1.57[/C][C]1.47[/C][C]0.1[/C][/ROW]
[ROW][C]8[/C][C]1.63[/C][C]1.57[/C][C]0.0599999999999998[/C][/ROW]
[ROW][C]9[/C][C]1.72[/C][C]1.63[/C][C]0.0900000000000001[/C][/ROW]
[ROW][C]10[/C][C]1.43[/C][C]1.72[/C][C]-0.29[/C][/ROW]
[ROW][C]11[/C][C]1.35[/C][C]1.43[/C][C]-0.0799999999999998[/C][/ROW]
[ROW][C]12[/C][C]1.41[/C][C]1.35[/C][C]0.0599999999999998[/C][/ROW]
[ROW][C]13[/C][C]1.44[/C][C]1.41[/C][C]0.03[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.44[/C][C]-0.01[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]1.42[/C][C]1.43[/C][C]-0.01[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.42[/C][C]0.03[/C][/ROW]
[ROW][C]18[/C][C]1.51[/C][C]1.45[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.51[/C][C]-0.03[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.48[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]1.45[/C][C]1.48[/C][C]-0.03[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.45[/C][C]-0.0700000000000001[/C][/ROW]
[ROW][C]23[/C][C]1.46[/C][C]1.38[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]24[/C][C]1.45[/C][C]1.46[/C][C]-0.01[/C][/ROW]
[ROW][C]25[/C][C]1.41[/C][C]1.45[/C][C]-0.04[/C][/ROW]
[ROW][C]26[/C][C]1.45[/C][C]1.41[/C][C]0.04[/C][/ROW]
[ROW][C]27[/C][C]1.47[/C][C]1.45[/C][C]0.02[/C][/ROW]
[ROW][C]28[/C][C]1.47[/C][C]1.47[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]1.53[/C][C]1.47[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]30[/C][C]1.56[/C][C]1.53[/C][C]0.03[/C][/ROW]
[ROW][C]31[/C][C]1.66[/C][C]1.56[/C][C]0.0999999999999999[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.66[/C][C]0.13[/C][/ROW]
[ROW][C]33[/C][C]1.78[/C][C]1.79[/C][C]-0.01[/C][/ROW]
[ROW][C]34[/C][C]1.46[/C][C]1.78[/C][C]-0.32[/C][/ROW]
[ROW][C]35[/C][C]1.41[/C][C]1.46[/C][C]-0.05[/C][/ROW]
[ROW][C]36[/C][C]1.43[/C][C]1.41[/C][C]0.02[/C][/ROW]
[ROW][C]37[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]1.45[/C][C]1.43[/C][C]0.02[/C][/ROW]
[ROW][C]39[/C][C]1.35[/C][C]1.45[/C][C]-0.0999999999999999[/C][/ROW]
[ROW][C]40[/C][C]1.35[/C][C]1.35[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]1.29[/C][C]1.35[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]42[/C][C]1.29[/C][C]1.29[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]1.26[/C][C]1.29[/C][C]-0.03[/C][/ROW]
[ROW][C]44[/C][C]1.3[/C][C]1.26[/C][C]0.04[/C][/ROW]
[ROW][C]45[/C][C]1.3[/C][C]1.3[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]1.16[/C][C]1.3[/C][C]-0.14[/C][/ROW]
[ROW][C]47[/C][C]1.24[/C][C]1.16[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]48[/C][C]1.15[/C][C]1.24[/C][C]-0.0900000000000001[/C][/ROW]
[ROW][C]49[/C][C]1.21[/C][C]1.15[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]50[/C][C]1.22[/C][C]1.21[/C][C]0.01[/C][/ROW]
[ROW][C]51[/C][C]1.17[/C][C]1.22[/C][C]-0.05[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.17[/C][C]-0.04[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.13[/C][C]0.02[/C][/ROW]
[ROW][C]54[/C][C]1.2[/C][C]1.15[/C][C]0.05[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.2[/C][C]0.03[/C][/ROW]
[ROW][C]56[/C][C]1.25[/C][C]1.23[/C][C]0.02[/C][/ROW]
[ROW][C]57[/C][C]1.38[/C][C]1.25[/C][C]0.13[/C][/ROW]
[ROW][C]58[/C][C]1.28[/C][C]1.38[/C][C]-0.0999999999999999[/C][/ROW]
[ROW][C]59[/C][C]1.26[/C][C]1.28[/C][C]-0.02[/C][/ROW]
[ROW][C]60[/C][C]1.25[/C][C]1.26[/C][C]-0.01[/C][/ROW]
[ROW][C]61[/C][C]1.26[/C][C]1.25[/C][C]0.01[/C][/ROW]
[ROW][C]62[/C][C]1.28[/C][C]1.26[/C][C]0.02[/C][/ROW]
[ROW][C]63[/C][C]1.31[/C][C]1.28[/C][C]0.03[/C][/ROW]
[ROW][C]64[/C][C]1.22[/C][C]1.31[/C][C]-0.0900000000000001[/C][/ROW]
[ROW][C]65[/C][C]1.23[/C][C]1.22[/C][C]0.01[/C][/ROW]
[ROW][C]66[/C][C]1.36[/C][C]1.23[/C][C]0.13[/C][/ROW]
[ROW][C]67[/C][C]1.54[/C][C]1.36[/C][C]0.18[/C][/ROW]
[ROW][C]68[/C][C]1.58[/C][C]1.54[/C][C]0.04[/C][/ROW]
[ROW][C]69[/C][C]1.44[/C][C]1.58[/C][C]-0.14[/C][/ROW]
[ROW][C]70[/C][C]1.29[/C][C]1.44[/C][C]-0.15[/C][/ROW]
[ROW][C]71[/C][C]1.28[/C][C]1.29[/C][C]-0.01[/C][/ROW]
[ROW][C]72[/C][C]1.23[/C][C]1.28[/C][C]-0.05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203380&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203380&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
t	Observed	Fitted	Residuals
3	1.28	1.26	0.02
4	1.34	1.28	0.0600000000000001
5	1.39	1.34	0.0499999999999998
6	1.47	1.39	0.0800000000000001
7	1.57	1.47	0.1
8	1.63	1.57	0.0599999999999998
9	1.72	1.63	0.0900000000000001
10	1.43	1.72	-0.29
11	1.35	1.43	-0.0799999999999998
12	1.41	1.35	0.0599999999999998
13	1.44	1.41	0.03
14	1.43	1.44	-0.01
15	1.43	1.43	0
16	1.42	1.43	-0.01
17	1.45	1.42	0.03
18	1.51	1.45	0.0600000000000001
19	1.48	1.51	-0.03
20	1.48	1.48	0
21	1.45	1.48	-0.03
22	1.38	1.45	-0.0700000000000001
23	1.46	1.38	0.0800000000000001
24	1.45	1.46	-0.01
25	1.41	1.45	-0.04
26	1.45	1.41	0.04
27	1.47	1.45	0.02
28	1.47	1.47	0
29	1.53	1.47	0.0600000000000001
30	1.56	1.53	0.03
31	1.66	1.56	0.0999999999999999
32	1.79	1.66	0.13
33	1.78	1.79	-0.01
34	1.46	1.78	-0.32
35	1.41	1.46	-0.05
36	1.43	1.41	0.02
37	1.43	1.43	0
38	1.45	1.43	0.02
39	1.35	1.45	-0.0999999999999999
40	1.35	1.35	0
41	1.29	1.35	-0.0600000000000001
42	1.29	1.29	0
43	1.26	1.29	-0.03
44	1.3	1.26	0.04
45	1.3	1.3	0
46	1.16	1.3	-0.14
47	1.24	1.16	0.0800000000000001
48	1.15	1.24	-0.0900000000000001
49	1.21	1.15	0.0600000000000001
50	1.22	1.21	0.01
51	1.17	1.22	-0.05
52	1.13	1.17	-0.04
53	1.15	1.13	0.02
54	1.2	1.15	0.05
55	1.23	1.2	0.03
56	1.25	1.23	0.02
57	1.38	1.25	0.13
58	1.28	1.38	-0.0999999999999999
59	1.26	1.28	-0.02
60	1.25	1.26	-0.01
61	1.26	1.25	0.01
62	1.28	1.26	0.02
63	1.31	1.28	0.03
64	1.22	1.31	-0.0900000000000001
65	1.23	1.22	0.01
66	1.36	1.23	0.13
67	1.54	1.36	0.18
68	1.58	1.54	0.04
69	1.44	1.58	-0.14
70	1.29	1.44	-0.15
71	1.28	1.29	-0.01
72	1.23	1.28	-0.05

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.23	1.06600285588858	1.39399714411142
74	1.23	0.998073014607171	1.46192698539283
75	1.23	0.94594861410282	1.51405138589718
76	1.23	0.902005711777154	1.55799428822285
77	1.23	0.863291237651029	1.59670876234897
78	1.23	0.828290677653335	1.63170932234666
79	1.23	0.796104340956354	1.66389565904365
80	1.23	0.766146029214341	1.69385397078566
81	1.23	0.738008567665731	1.72199143233427
82	1.23	0.711395494845033	1.74860450515497
83	1.23	0.686083006292568	1.77391699370743
84	1.23	0.661897228205641	1.79810277179436

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.23 & 1.06600285588858 & 1.39399714411142 \tabularnewline
74 & 1.23 & 0.998073014607171 & 1.46192698539283 \tabularnewline
75 & 1.23 & 0.94594861410282 & 1.51405138589718 \tabularnewline
76 & 1.23 & 0.902005711777154 & 1.55799428822285 \tabularnewline
77 & 1.23 & 0.863291237651029 & 1.59670876234897 \tabularnewline
78 & 1.23 & 0.828290677653335 & 1.63170932234666 \tabularnewline
79 & 1.23 & 0.796104340956354 & 1.66389565904365 \tabularnewline
80 & 1.23 & 0.766146029214341 & 1.69385397078566 \tabularnewline
81 & 1.23 & 0.738008567665731 & 1.72199143233427 \tabularnewline
82 & 1.23 & 0.711395494845033 & 1.74860450515497 \tabularnewline
83 & 1.23 & 0.686083006292568 & 1.77391699370743 \tabularnewline
84 & 1.23 & 0.661897228205641 & 1.79810277179436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203380&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]1.23[/C][C]1.06600285588858[/C][C]1.39399714411142[/C][/ROW]
[ROW][C]74[/C][C]1.23[/C][C]0.998073014607171[/C][C]1.46192698539283[/C][/ROW]
[ROW][C]75[/C][C]1.23[/C][C]0.94594861410282[/C][C]1.51405138589718[/C][/ROW]
[ROW][C]76[/C][C]1.23[/C][C]0.902005711777154[/C][C]1.55799428822285[/C][/ROW]
[ROW][C]77[/C][C]1.23[/C][C]0.863291237651029[/C][C]1.59670876234897[/C][/ROW]
[ROW][C]78[/C][C]1.23[/C][C]0.828290677653335[/C][C]1.63170932234666[/C][/ROW]
[ROW][C]79[/C][C]1.23[/C][C]0.796104340956354[/C][C]1.66389565904365[/C][/ROW]
[ROW][C]80[/C][C]1.23[/C][C]0.766146029214341[/C][C]1.69385397078566[/C][/ROW]
[ROW][C]81[/C][C]1.23[/C][C]0.738008567665731[/C][C]1.72199143233427[/C][/ROW]
[ROW][C]82[/C][C]1.23[/C][C]0.711395494845033[/C][C]1.74860450515497[/C][/ROW]
[ROW][C]83[/C][C]1.23[/C][C]0.686083006292568[/C][C]1.77391699370743[/C][/ROW]
[ROW][C]84[/C][C]1.23[/C][C]0.661897228205641[/C][C]1.79810277179436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203380&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203380&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.23	1.06600285588858	1.39399714411142
74	1.23	0.998073014607171	1.46192698539283
75	1.23	0.94594861410282	1.51405138589718
76	1.23	0.902005711777154	1.55799428822285
77	1.23	0.863291237651029	1.59670876234897
78	1.23	0.828290677653335	1.63170932234666
79	1.23	0.796104340956354	1.66389565904365
80	1.23	0.766146029214341	1.69385397078566
81	1.23	0.738008567665731	1.72199143233427
82	1.23	0.711395494845033	1.74860450515497
83	1.23	0.686083006292568	1.77391699370743
84	1.23	0.661897228205641	1.79810277179436

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code