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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 14 Jan 2013 21:42:48 -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/2013/Jan/14/t1358217805p7ig6xo8o3mhtzj.htm/, Retrieved Sun, 28 Apr 2024 05:55:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205397, Retrieved Sun, 28 Apr 2024 05:55:14 +0000

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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] [Oef 10 gemiddelde...] [2012-12-21 20:48:06] [c05f3eadce52e4946a2aac59a0f05a38]
- R PD    [Exponential Smoothing] [Opgave 10 oefenin...] [2013-01-15 02:42:48] [3afff8224e6da3a7e2f9dd48a805005a] [Current]

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Dataseries X:

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Histogram

Boxplots

1.01
1.02
1.04
1.06
1.06
1.06
1.06
1.06
1.02
0.98
0.99
0.99
0.94
0.96
0.98
1.01
1.01
1.02
1.04
1.03
1.05
1.08
1.17
1.11
1.11
1.11
1.2
1.21
1.31
1.37
1.37
1.26
1.23
1.17
1.06
0.95
0.92
0.92
0.9
0.93
0.93
0.97
0.96
0.99
0.98
0.96
1
0.99
1.03
1.02
1.07
1.13
1.15
1.16
1.14
1.15
1.15
1.16
1.17
1.22
1.26
1.29
1.36
1.38
1.37
1.37
1.37
1.36
1.38
1.4
1.44
1.42

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=205397&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=205397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205397&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=205397&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=205397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205397&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	1.04	1.03	0.01
4	1.06	1.05	0.01
5	1.06	1.07	-0.01
6	1.06	1.07	-0.01
7	1.06	1.07	-0.01
8	1.06	1.07	-0.01
9	1.02	1.07	-0.05
10	0.98	1.03	-0.05
11	0.99	0.99	0
12	0.99	1	-0.01
13	0.94	1	-0.0600000000000001
14	0.96	0.95	0.01
15	0.98	0.97	0.01
16	1.01	0.99	0.02
17	1.01	1.02	-0.01
18	1.02	1.02	0
19	1.04	1.03	0.01
20	1.03	1.05	-0.02
21	1.05	1.04	0.01
22	1.08	1.06	0.02
23	1.17	1.09	0.0799999999999998
24	1.11	1.18	-0.0699999999999998
25	1.11	1.12	-0.01
26	1.11	1.12	-0.01
27	1.2	1.12	0.0799999999999998
28	1.21	1.21	0
29	1.31	1.22	0.0900000000000001
30	1.37	1.32	0.05
31	1.37	1.38	-0.01
32	1.26	1.38	-0.12
33	1.23	1.27	-0.04
34	1.17	1.24	-0.0700000000000001
35	1.06	1.18	-0.12
36	0.95	1.07	-0.12
37	0.92	0.96	-0.0399999999999999
38	0.92	0.93	-0.01
39	0.9	0.93	-0.03
40	0.93	0.91	0.02
41	0.93	0.94	-0.01
42	0.97	0.94	0.0299999999999999
43	0.96	0.98	-0.02
44	0.99	0.97	0.02
45	0.98	1	-0.02
46	0.96	0.99	-0.03
47	1	0.97	0.03
48	0.99	1.01	-0.02
49	1.03	1	0.03
50	1.02	1.04	-0.02
51	1.07	1.03	0.04
52	1.13	1.08	0.0499999999999998
53	1.15	1.14	0.01
54	1.16	1.16	0
55	1.14	1.17	-0.03
56	1.15	1.15	0
57	1.15	1.16	-0.01
58	1.16	1.16	0
59	1.17	1.17	0
60	1.22	1.18	0.04
61	1.26	1.23	0.03
62	1.29	1.27	0.02
63	1.36	1.3	0.0600000000000001
64	1.38	1.37	0.00999999999999979
65	1.37	1.39	-0.0199999999999998
66	1.37	1.38	-0.01
67	1.37	1.38	-0.01
68	1.36	1.38	-0.02
69	1.38	1.37	0.00999999999999979
70	1.4	1.39	0.01
71	1.44	1.41	0.03
72	1.42	1.45	-0.03

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.04 & 1.03 & 0.01 \tabularnewline
4 & 1.06 & 1.05 & 0.01 \tabularnewline
5 & 1.06 & 1.07 & -0.01 \tabularnewline
6 & 1.06 & 1.07 & -0.01 \tabularnewline
7 & 1.06 & 1.07 & -0.01 \tabularnewline
8 & 1.06 & 1.07 & -0.01 \tabularnewline
9 & 1.02 & 1.07 & -0.05 \tabularnewline
10 & 0.98 & 1.03 & -0.05 \tabularnewline
11 & 0.99 & 0.99 & 0 \tabularnewline
12 & 0.99 & 1 & -0.01 \tabularnewline
13 & 0.94 & 1 & -0.0600000000000001 \tabularnewline
14 & 0.96 & 0.95 & 0.01 \tabularnewline
15 & 0.98 & 0.97 & 0.01 \tabularnewline
16 & 1.01 & 0.99 & 0.02 \tabularnewline
17 & 1.01 & 1.02 & -0.01 \tabularnewline
18 & 1.02 & 1.02 & 0 \tabularnewline
19 & 1.04 & 1.03 & 0.01 \tabularnewline
20 & 1.03 & 1.05 & -0.02 \tabularnewline
21 & 1.05 & 1.04 & 0.01 \tabularnewline
22 & 1.08 & 1.06 & 0.02 \tabularnewline
23 & 1.17 & 1.09 & 0.0799999999999998 \tabularnewline
24 & 1.11 & 1.18 & -0.0699999999999998 \tabularnewline
25 & 1.11 & 1.12 & -0.01 \tabularnewline
26 & 1.11 & 1.12 & -0.01 \tabularnewline
27 & 1.2 & 1.12 & 0.0799999999999998 \tabularnewline
28 & 1.21 & 1.21 & 0 \tabularnewline
29 & 1.31 & 1.22 & 0.0900000000000001 \tabularnewline
30 & 1.37 & 1.32 & 0.05 \tabularnewline
31 & 1.37 & 1.38 & -0.01 \tabularnewline
32 & 1.26 & 1.38 & -0.12 \tabularnewline
33 & 1.23 & 1.27 & -0.04 \tabularnewline
34 & 1.17 & 1.24 & -0.0700000000000001 \tabularnewline
35 & 1.06 & 1.18 & -0.12 \tabularnewline
36 & 0.95 & 1.07 & -0.12 \tabularnewline
37 & 0.92 & 0.96 & -0.0399999999999999 \tabularnewline
38 & 0.92 & 0.93 & -0.01 \tabularnewline
39 & 0.9 & 0.93 & -0.03 \tabularnewline
40 & 0.93 & 0.91 & 0.02 \tabularnewline
41 & 0.93 & 0.94 & -0.01 \tabularnewline
42 & 0.97 & 0.94 & 0.0299999999999999 \tabularnewline
43 & 0.96 & 0.98 & -0.02 \tabularnewline
44 & 0.99 & 0.97 & 0.02 \tabularnewline
45 & 0.98 & 1 & -0.02 \tabularnewline
46 & 0.96 & 0.99 & -0.03 \tabularnewline
47 & 1 & 0.97 & 0.03 \tabularnewline
48 & 0.99 & 1.01 & -0.02 \tabularnewline
49 & 1.03 & 1 & 0.03 \tabularnewline
50 & 1.02 & 1.04 & -0.02 \tabularnewline
51 & 1.07 & 1.03 & 0.04 \tabularnewline
52 & 1.13 & 1.08 & 0.0499999999999998 \tabularnewline
53 & 1.15 & 1.14 & 0.01 \tabularnewline
54 & 1.16 & 1.16 & 0 \tabularnewline
55 & 1.14 & 1.17 & -0.03 \tabularnewline
56 & 1.15 & 1.15 & 0 \tabularnewline
57 & 1.15 & 1.16 & -0.01 \tabularnewline
58 & 1.16 & 1.16 & 0 \tabularnewline
59 & 1.17 & 1.17 & 0 \tabularnewline
60 & 1.22 & 1.18 & 0.04 \tabularnewline
61 & 1.26 & 1.23 & 0.03 \tabularnewline
62 & 1.29 & 1.27 & 0.02 \tabularnewline
63 & 1.36 & 1.3 & 0.0600000000000001 \tabularnewline
64 & 1.38 & 1.37 & 0.00999999999999979 \tabularnewline
65 & 1.37 & 1.39 & -0.0199999999999998 \tabularnewline
66 & 1.37 & 1.38 & -0.01 \tabularnewline
67 & 1.37 & 1.38 & -0.01 \tabularnewline
68 & 1.36 & 1.38 & -0.02 \tabularnewline
69 & 1.38 & 1.37 & 0.00999999999999979 \tabularnewline
70 & 1.4 & 1.39 & 0.01 \tabularnewline
71 & 1.44 & 1.41 & 0.03 \tabularnewline
72 & 1.42 & 1.45 & -0.03 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205397&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]1.04[/C][C]1.03[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]1.06[/C][C]1.05[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]1.06[/C][C]1.07[/C][C]-0.01[/C][/ROW]
[ROW][C]6[/C][C]1.06[/C][C]1.07[/C][C]-0.01[/C][/ROW]
[ROW][C]7[/C][C]1.06[/C][C]1.07[/C][C]-0.01[/C][/ROW]
[ROW][C]8[/C][C]1.06[/C][C]1.07[/C][C]-0.01[/C][/ROW]
[ROW][C]9[/C][C]1.02[/C][C]1.07[/C][C]-0.05[/C][/ROW]
[ROW][C]10[/C][C]0.98[/C][C]1.03[/C][C]-0.05[/C][/ROW]
[ROW][C]11[/C][C]0.99[/C][C]0.99[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.99[/C][C]1[/C][C]-0.01[/C][/ROW]
[ROW][C]13[/C][C]0.94[/C][C]1[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]14[/C][C]0.96[/C][C]0.95[/C][C]0.01[/C][/ROW]
[ROW][C]15[/C][C]0.98[/C][C]0.97[/C][C]0.01[/C][/ROW]
[ROW][C]16[/C][C]1.01[/C][C]0.99[/C][C]0.02[/C][/ROW]
[ROW][C]17[/C][C]1.01[/C][C]1.02[/C][C]-0.01[/C][/ROW]
[ROW][C]18[/C][C]1.02[/C][C]1.02[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]1.04[/C][C]1.03[/C][C]0.01[/C][/ROW]
[ROW][C]20[/C][C]1.03[/C][C]1.05[/C][C]-0.02[/C][/ROW]
[ROW][C]21[/C][C]1.05[/C][C]1.04[/C][C]0.01[/C][/ROW]
[ROW][C]22[/C][C]1.08[/C][C]1.06[/C][C]0.02[/C][/ROW]
[ROW][C]23[/C][C]1.17[/C][C]1.09[/C][C]0.0799999999999998[/C][/ROW]
[ROW][C]24[/C][C]1.11[/C][C]1.18[/C][C]-0.0699999999999998[/C][/ROW]
[ROW][C]25[/C][C]1.11[/C][C]1.12[/C][C]-0.01[/C][/ROW]
[ROW][C]26[/C][C]1.11[/C][C]1.12[/C][C]-0.01[/C][/ROW]
[ROW][C]27[/C][C]1.2[/C][C]1.12[/C][C]0.0799999999999998[/C][/ROW]
[ROW][C]28[/C][C]1.21[/C][C]1.21[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]1.31[/C][C]1.22[/C][C]0.0900000000000001[/C][/ROW]
[ROW][C]30[/C][C]1.37[/C][C]1.32[/C][C]0.05[/C][/ROW]
[ROW][C]31[/C][C]1.37[/C][C]1.38[/C][C]-0.01[/C][/ROW]
[ROW][C]32[/C][C]1.26[/C][C]1.38[/C][C]-0.12[/C][/ROW]
[ROW][C]33[/C][C]1.23[/C][C]1.27[/C][C]-0.04[/C][/ROW]
[ROW][C]34[/C][C]1.17[/C][C]1.24[/C][C]-0.0700000000000001[/C][/ROW]
[ROW][C]35[/C][C]1.06[/C][C]1.18[/C][C]-0.12[/C][/ROW]
[ROW][C]36[/C][C]0.95[/C][C]1.07[/C][C]-0.12[/C][/ROW]
[ROW][C]37[/C][C]0.92[/C][C]0.96[/C][C]-0.0399999999999999[/C][/ROW]
[ROW][C]38[/C][C]0.92[/C][C]0.93[/C][C]-0.01[/C][/ROW]
[ROW][C]39[/C][C]0.9[/C][C]0.93[/C][C]-0.03[/C][/ROW]
[ROW][C]40[/C][C]0.93[/C][C]0.91[/C][C]0.02[/C][/ROW]
[ROW][C]41[/C][C]0.93[/C][C]0.94[/C][C]-0.01[/C][/ROW]
[ROW][C]42[/C][C]0.97[/C][C]0.94[/C][C]0.0299999999999999[/C][/ROW]
[ROW][C]43[/C][C]0.96[/C][C]0.98[/C][C]-0.02[/C][/ROW]
[ROW][C]44[/C][C]0.99[/C][C]0.97[/C][C]0.02[/C][/ROW]
[ROW][C]45[/C][C]0.98[/C][C]1[/C][C]-0.02[/C][/ROW]
[ROW][C]46[/C][C]0.96[/C][C]0.99[/C][C]-0.03[/C][/ROW]
[ROW][C]47[/C][C]1[/C][C]0.97[/C][C]0.03[/C][/ROW]
[ROW][C]48[/C][C]0.99[/C][C]1.01[/C][C]-0.02[/C][/ROW]
[ROW][C]49[/C][C]1.03[/C][C]1[/C][C]0.03[/C][/ROW]
[ROW][C]50[/C][C]1.02[/C][C]1.04[/C][C]-0.02[/C][/ROW]
[ROW][C]51[/C][C]1.07[/C][C]1.03[/C][C]0.04[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.08[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.14[/C][C]0.01[/C][/ROW]
[ROW][C]54[/C][C]1.16[/C][C]1.16[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]1.14[/C][C]1.17[/C][C]-0.03[/C][/ROW]
[ROW][C]56[/C][C]1.15[/C][C]1.15[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]1.15[/C][C]1.16[/C][C]-0.01[/C][/ROW]
[ROW][C]58[/C][C]1.16[/C][C]1.16[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]1.17[/C][C]1.17[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]1.22[/C][C]1.18[/C][C]0.04[/C][/ROW]
[ROW][C]61[/C][C]1.26[/C][C]1.23[/C][C]0.03[/C][/ROW]
[ROW][C]62[/C][C]1.29[/C][C]1.27[/C][C]0.02[/C][/ROW]
[ROW][C]63[/C][C]1.36[/C][C]1.3[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]64[/C][C]1.38[/C][C]1.37[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]65[/C][C]1.37[/C][C]1.39[/C][C]-0.0199999999999998[/C][/ROW]
[ROW][C]66[/C][C]1.37[/C][C]1.38[/C][C]-0.01[/C][/ROW]
[ROW][C]67[/C][C]1.37[/C][C]1.38[/C][C]-0.01[/C][/ROW]
[ROW][C]68[/C][C]1.36[/C][C]1.38[/C][C]-0.02[/C][/ROW]
[ROW][C]69[/C][C]1.38[/C][C]1.37[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]70[/C][C]1.4[/C][C]1.39[/C][C]0.01[/C][/ROW]
[ROW][C]71[/C][C]1.44[/C][C]1.41[/C][C]0.03[/C][/ROW]
[ROW][C]72[/C][C]1.42[/C][C]1.45[/C][C]-0.03[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205397&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	1.04	1.03	0.01
4	1.06	1.05	0.01
5	1.06	1.07	-0.01
6	1.06	1.07	-0.01
7	1.06	1.07	-0.01
8	1.06	1.07	-0.01
9	1.02	1.07	-0.05
10	0.98	1.03	-0.05
11	0.99	0.99	0
12	0.99	1	-0.01
13	0.94	1	-0.0600000000000001
14	0.96	0.95	0.01
15	0.98	0.97	0.01
16	1.01	0.99	0.02
17	1.01	1.02	-0.01
18	1.02	1.02	0
19	1.04	1.03	0.01
20	1.03	1.05	-0.02
21	1.05	1.04	0.01
22	1.08	1.06	0.02
23	1.17	1.09	0.0799999999999998
24	1.11	1.18	-0.0699999999999998
25	1.11	1.12	-0.01
26	1.11	1.12	-0.01
27	1.2	1.12	0.0799999999999998
28	1.21	1.21	0
29	1.31	1.22	0.0900000000000001
30	1.37	1.32	0.05
31	1.37	1.38	-0.01
32	1.26	1.38	-0.12
33	1.23	1.27	-0.04
34	1.17	1.24	-0.0700000000000001
35	1.06	1.18	-0.12
36	0.95	1.07	-0.12
37	0.92	0.96	-0.0399999999999999
38	0.92	0.93	-0.01
39	0.9	0.93	-0.03
40	0.93	0.91	0.02
41	0.93	0.94	-0.01
42	0.97	0.94	0.0299999999999999
43	0.96	0.98	-0.02
44	0.99	0.97	0.02
45	0.98	1	-0.02
46	0.96	0.99	-0.03
47	1	0.97	0.03
48	0.99	1.01	-0.02
49	1.03	1	0.03
50	1.02	1.04	-0.02
51	1.07	1.03	0.04
52	1.13	1.08	0.0499999999999998
53	1.15	1.14	0.01
54	1.16	1.16	0
55	1.14	1.17	-0.03
56	1.15	1.15	0
57	1.15	1.16	-0.01
58	1.16	1.16	0
59	1.17	1.17	0
60	1.22	1.18	0.04
61	1.26	1.23	0.03
62	1.29	1.27	0.02
63	1.36	1.3	0.0600000000000001
64	1.38	1.37	0.00999999999999979
65	1.37	1.39	-0.0199999999999998
66	1.37	1.38	-0.01
67	1.37	1.38	-0.01
68	1.36	1.38	-0.02
69	1.38	1.37	0.00999999999999979
70	1.4	1.39	0.01
71	1.44	1.41	0.03
72	1.42	1.45	-0.03

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.43	1.35120678903569	1.50879321096431
74	1.44	1.32856957243135	1.55143042756865
75	1.45	1.31352615531833	1.58647384468167
76	1.46	1.30241357807138	1.61758642192862
77	1.47	1.29381302411833	1.64618697588167
78	1.48	1.28699683794198	1.67300316205802
79	1.49	1.28153275878819	1.69846724121181
80	1.5	1.2771391448627	1.7228608551373
81	1.51	1.27362036710708	1.74637963289292
82	1.52	1.27083398919464	1.76916601080536
83	1.53	1.26867248320407	1.79132751679593
84	1.54	1.26705231063665	1.81294768936335

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.43 & 1.35120678903569 & 1.50879321096431 \tabularnewline
74 & 1.44 & 1.32856957243135 & 1.55143042756865 \tabularnewline
75 & 1.45 & 1.31352615531833 & 1.58647384468167 \tabularnewline
76 & 1.46 & 1.30241357807138 & 1.61758642192862 \tabularnewline
77 & 1.47 & 1.29381302411833 & 1.64618697588167 \tabularnewline
78 & 1.48 & 1.28699683794198 & 1.67300316205802 \tabularnewline
79 & 1.49 & 1.28153275878819 & 1.69846724121181 \tabularnewline
80 & 1.5 & 1.2771391448627 & 1.7228608551373 \tabularnewline
81 & 1.51 & 1.27362036710708 & 1.74637963289292 \tabularnewline
82 & 1.52 & 1.27083398919464 & 1.76916601080536 \tabularnewline
83 & 1.53 & 1.26867248320407 & 1.79132751679593 \tabularnewline
84 & 1.54 & 1.26705231063665 & 1.81294768936335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205397&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]1.43[/C][C]1.35120678903569[/C][C]1.50879321096431[/C][/ROW]
[ROW][C]74[/C][C]1.44[/C][C]1.32856957243135[/C][C]1.55143042756865[/C][/ROW]
[ROW][C]75[/C][C]1.45[/C][C]1.31352615531833[/C][C]1.58647384468167[/C][/ROW]
[ROW][C]76[/C][C]1.46[/C][C]1.30241357807138[/C][C]1.61758642192862[/C][/ROW]
[ROW][C]77[/C][C]1.47[/C][C]1.29381302411833[/C][C]1.64618697588167[/C][/ROW]
[ROW][C]78[/C][C]1.48[/C][C]1.28699683794198[/C][C]1.67300316205802[/C][/ROW]
[ROW][C]79[/C][C]1.49[/C][C]1.28153275878819[/C][C]1.69846724121181[/C][/ROW]
[ROW][C]80[/C][C]1.5[/C][C]1.2771391448627[/C][C]1.7228608551373[/C][/ROW]
[ROW][C]81[/C][C]1.51[/C][C]1.27362036710708[/C][C]1.74637963289292[/C][/ROW]
[ROW][C]82[/C][C]1.52[/C][C]1.27083398919464[/C][C]1.76916601080536[/C][/ROW]
[ROW][C]83[/C][C]1.53[/C][C]1.26867248320407[/C][C]1.79132751679593[/C][/ROW]
[ROW][C]84[/C][C]1.54[/C][C]1.26705231063665[/C][C]1.81294768936335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205397&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	1.43	1.35120678903569	1.50879321096431
74	1.44	1.32856957243135	1.55143042756865
75	1.45	1.31352615531833	1.58647384468167
76	1.46	1.30241357807138	1.61758642192862
77	1.47	1.29381302411833	1.64618697588167
78	1.48	1.28699683794198	1.67300316205802
79	1.49	1.28153275878819	1.69846724121181
80	1.5	1.2771391448627	1.7228608551373
81	1.51	1.27362036710708	1.74637963289292
82	1.52	1.27083398919464	1.76916601080536
83	1.53	1.26867248320407	1.79132751679593
84	1.54	1.26705231063665	1.81294768936335

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