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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 28 May 2008 05:39:54 -0600

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/2008/May/28/t1211974899jq508k1b7ut1n1n.htm/, Retrieved Tue, 14 May 2024 13:43:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13422, Retrieved Tue, 14 May 2024 13:43:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

201

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

-       [Exponential Smoothing] [] [2008-05-28 11:39:54] [241f313a0252a611c181f3d02bd5b229] [Current]

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Dataseries X:

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Histogram

Boxplots

3.27
3.27
3.27
3.27
3.27
3.28
3.32
3.34
3.34
3.35
3.35
3.35
3.35
3.35
3.4
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.43
3.47
3.51
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.58
3.6
3.61
3.61
3.61
3.63
3.68
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.78
3.79
3.79
3.8
3.8
3.8
3.8
3.81
3.95
3.99
4
4.06
4.16
4.19
4.2
4.2
4.2
4.2
4.2
4.23
4.38
4.43
4.44
4.44
4.44
4.44
4.44
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.46
4.46
4.46
4.48
4.58
4.67
4.68
4.68

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13422&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13422&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13422&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13422&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	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	3.27	3.27	0
3	3.27	3.27	0
4	3.27	3.27	0
5	3.27	3.27	0
6	3.28	3.27	0.00999999999999979
7	3.32	3.28	0.04
8	3.34	3.32	0.02
9	3.34	3.34	0
10	3.35	3.34	0.0100000000000002
11	3.35	3.35	0
12	3.35	3.35	0
13	3.35	3.35	0
14	3.35	3.35	0
15	3.4	3.35	0.0499999999999998
16	3.42	3.4	0.02
17	3.42	3.42	0
18	3.42	3.42	0
19	3.42	3.42	0
20	3.42	3.42	0
21	3.42	3.42	0
22	3.42	3.42	0
23	3.42	3.42	0
24	3.42	3.42	0
25	3.42	3.42	0
26	3.42	3.42	0
27	3.43	3.42	0.0100000000000002
28	3.47	3.43	0.04
29	3.51	3.47	0.0399999999999996
30	3.52	3.51	0.0100000000000002
31	3.52	3.52	0
32	3.52	3.52	0
33	3.52	3.52	0
34	3.52	3.52	0
35	3.52	3.52	0
36	3.52	3.52	0
37	3.52	3.52	0
38	3.52	3.52	0
39	3.58	3.52	0.06
40	3.6	3.58	0.02
41	3.61	3.6	0.00999999999999979
42	3.61	3.61	0
43	3.61	3.61	0
44	3.63	3.61	0.02
45	3.68	3.63	0.0500000000000003
46	3.69	3.68	0.00999999999999979
47	3.69	3.69	0
48	3.69	3.69	0
49	3.69	3.69	0
50	3.69	3.69	0
51	3.69	3.69	0
52	3.69	3.69	0
53	3.69	3.69	0
54	3.78	3.69	0.0899999999999999
55	3.79	3.78	0.0100000000000002
56	3.79	3.79	0
57	3.8	3.79	0.00999999999999979
58	3.8	3.8	0
59	3.8	3.8	0
60	3.8	3.8	0
61	3.81	3.8	0.0100000000000002
62	3.95	3.81	0.14
63	3.99	3.95	0.04
64	4	3.99	0.00999999999999979
65	4.06	4	0.0599999999999996
66	4.16	4.06	0.100000000000001
67	4.19	4.16	0.0300000000000002
68	4.2	4.19	0.00999999999999979
69	4.2	4.2	0
70	4.2	4.2	0
71	4.2	4.2	0
72	4.2	4.2	0
73	4.23	4.2	0.0300000000000002
74	4.38	4.23	0.149999999999999
75	4.43	4.38	0.0499999999999998
76	4.44	4.43	0.0100000000000007
77	4.44	4.44	0
78	4.44	4.44	0
79	4.44	4.44	0
80	4.44	4.44	0
81	4.45	4.44	0.00999999999999979
82	4.45	4.45	0
83	4.45	4.45	0
84	4.45	4.45	0
85	4.45	4.45	0
86	4.45	4.45	0
87	4.45	4.45	0
88	4.45	4.45	0
89	4.46	4.45	0.00999999999999979
90	4.46	4.46	0
91	4.46	4.46	0
92	4.48	4.46	0.0200000000000005
93	4.58	4.48	0.0999999999999996
94	4.67	4.58	0.0899999999999999
95	4.68	4.67	0.00999999999999979
96	4.68	4.68	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.27 & 3.27 & 0 \tabularnewline
3 & 3.27 & 3.27 & 0 \tabularnewline
4 & 3.27 & 3.27 & 0 \tabularnewline
5 & 3.27 & 3.27 & 0 \tabularnewline
6 & 3.28 & 3.27 & 0.00999999999999979 \tabularnewline
7 & 3.32 & 3.28 & 0.04 \tabularnewline
8 & 3.34 & 3.32 & 0.02 \tabularnewline
9 & 3.34 & 3.34 & 0 \tabularnewline
10 & 3.35 & 3.34 & 0.0100000000000002 \tabularnewline
11 & 3.35 & 3.35 & 0 \tabularnewline
12 & 3.35 & 3.35 & 0 \tabularnewline
13 & 3.35 & 3.35 & 0 \tabularnewline
14 & 3.35 & 3.35 & 0 \tabularnewline
15 & 3.4 & 3.35 & 0.0499999999999998 \tabularnewline
16 & 3.42 & 3.4 & 0.02 \tabularnewline
17 & 3.42 & 3.42 & 0 \tabularnewline
18 & 3.42 & 3.42 & 0 \tabularnewline
19 & 3.42 & 3.42 & 0 \tabularnewline
20 & 3.42 & 3.42 & 0 \tabularnewline
21 & 3.42 & 3.42 & 0 \tabularnewline
22 & 3.42 & 3.42 & 0 \tabularnewline
23 & 3.42 & 3.42 & 0 \tabularnewline
24 & 3.42 & 3.42 & 0 \tabularnewline
25 & 3.42 & 3.42 & 0 \tabularnewline
26 & 3.42 & 3.42 & 0 \tabularnewline
27 & 3.43 & 3.42 & 0.0100000000000002 \tabularnewline
28 & 3.47 & 3.43 & 0.04 \tabularnewline
29 & 3.51 & 3.47 & 0.0399999999999996 \tabularnewline
30 & 3.52 & 3.51 & 0.0100000000000002 \tabularnewline
31 & 3.52 & 3.52 & 0 \tabularnewline
32 & 3.52 & 3.52 & 0 \tabularnewline
33 & 3.52 & 3.52 & 0 \tabularnewline
34 & 3.52 & 3.52 & 0 \tabularnewline
35 & 3.52 & 3.52 & 0 \tabularnewline
36 & 3.52 & 3.52 & 0 \tabularnewline
37 & 3.52 & 3.52 & 0 \tabularnewline
38 & 3.52 & 3.52 & 0 \tabularnewline
39 & 3.58 & 3.52 & 0.06 \tabularnewline
40 & 3.6 & 3.58 & 0.02 \tabularnewline
41 & 3.61 & 3.6 & 0.00999999999999979 \tabularnewline
42 & 3.61 & 3.61 & 0 \tabularnewline
43 & 3.61 & 3.61 & 0 \tabularnewline
44 & 3.63 & 3.61 & 0.02 \tabularnewline
45 & 3.68 & 3.63 & 0.0500000000000003 \tabularnewline
46 & 3.69 & 3.68 & 0.00999999999999979 \tabularnewline
47 & 3.69 & 3.69 & 0 \tabularnewline
48 & 3.69 & 3.69 & 0 \tabularnewline
49 & 3.69 & 3.69 & 0 \tabularnewline
50 & 3.69 & 3.69 & 0 \tabularnewline
51 & 3.69 & 3.69 & 0 \tabularnewline
52 & 3.69 & 3.69 & 0 \tabularnewline
53 & 3.69 & 3.69 & 0 \tabularnewline
54 & 3.78 & 3.69 & 0.0899999999999999 \tabularnewline
55 & 3.79 & 3.78 & 0.0100000000000002 \tabularnewline
56 & 3.79 & 3.79 & 0 \tabularnewline
57 & 3.8 & 3.79 & 0.00999999999999979 \tabularnewline
58 & 3.8 & 3.8 & 0 \tabularnewline
59 & 3.8 & 3.8 & 0 \tabularnewline
60 & 3.8 & 3.8 & 0 \tabularnewline
61 & 3.81 & 3.8 & 0.0100000000000002 \tabularnewline
62 & 3.95 & 3.81 & 0.14 \tabularnewline
63 & 3.99 & 3.95 & 0.04 \tabularnewline
64 & 4 & 3.99 & 0.00999999999999979 \tabularnewline
65 & 4.06 & 4 & 0.0599999999999996 \tabularnewline
66 & 4.16 & 4.06 & 0.100000000000001 \tabularnewline
67 & 4.19 & 4.16 & 0.0300000000000002 \tabularnewline
68 & 4.2 & 4.19 & 0.00999999999999979 \tabularnewline
69 & 4.2 & 4.2 & 0 \tabularnewline
70 & 4.2 & 4.2 & 0 \tabularnewline
71 & 4.2 & 4.2 & 0 \tabularnewline
72 & 4.2 & 4.2 & 0 \tabularnewline
73 & 4.23 & 4.2 & 0.0300000000000002 \tabularnewline
74 & 4.38 & 4.23 & 0.149999999999999 \tabularnewline
75 & 4.43 & 4.38 & 0.0499999999999998 \tabularnewline
76 & 4.44 & 4.43 & 0.0100000000000007 \tabularnewline
77 & 4.44 & 4.44 & 0 \tabularnewline
78 & 4.44 & 4.44 & 0 \tabularnewline
79 & 4.44 & 4.44 & 0 \tabularnewline
80 & 4.44 & 4.44 & 0 \tabularnewline
81 & 4.45 & 4.44 & 0.00999999999999979 \tabularnewline
82 & 4.45 & 4.45 & 0 \tabularnewline
83 & 4.45 & 4.45 & 0 \tabularnewline
84 & 4.45 & 4.45 & 0 \tabularnewline
85 & 4.45 & 4.45 & 0 \tabularnewline
86 & 4.45 & 4.45 & 0 \tabularnewline
87 & 4.45 & 4.45 & 0 \tabularnewline
88 & 4.45 & 4.45 & 0 \tabularnewline
89 & 4.46 & 4.45 & 0.00999999999999979 \tabularnewline
90 & 4.46 & 4.46 & 0 \tabularnewline
91 & 4.46 & 4.46 & 0 \tabularnewline
92 & 4.48 & 4.46 & 0.0200000000000005 \tabularnewline
93 & 4.58 & 4.48 & 0.0999999999999996 \tabularnewline
94 & 4.67 & 4.58 & 0.0899999999999999 \tabularnewline
95 & 4.68 & 4.67 & 0.00999999999999979 \tabularnewline
96 & 4.68 & 4.68 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13422&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]2[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]3.28[/C][C]3.27[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]7[/C][C]3.32[/C][C]3.28[/C][C]0.04[/C][/ROW]
[ROW][C]8[/C][C]3.34[/C][C]3.32[/C][C]0.02[/C][/ROW]
[ROW][C]9[/C][C]3.34[/C][C]3.34[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]3.35[/C][C]3.34[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]11[/C][C]3.35[/C][C]3.35[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]3.35[/C][C]3.35[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]3.35[/C][C]3.35[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]3.35[/C][C]3.35[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]3.4[/C][C]3.35[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]16[/C][C]3.42[/C][C]3.4[/C][C]0.02[/C][/ROW]
[ROW][C]17[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]3.43[/C][C]3.42[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]28[/C][C]3.47[/C][C]3.43[/C][C]0.04[/C][/ROW]
[ROW][C]29[/C][C]3.51[/C][C]3.47[/C][C]0.0399999999999996[/C][/ROW]
[ROW][C]30[/C][C]3.52[/C][C]3.51[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]31[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]3.58[/C][C]3.52[/C][C]0.06[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]3.58[/C][C]0.02[/C][/ROW]
[ROW][C]41[/C][C]3.61[/C][C]3.6[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]42[/C][C]3.61[/C][C]3.61[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]3.61[/C][C]3.61[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]3.63[/C][C]3.61[/C][C]0.02[/C][/ROW]
[ROW][C]45[/C][C]3.68[/C][C]3.63[/C][C]0.0500000000000003[/C][/ROW]
[ROW][C]46[/C][C]3.69[/C][C]3.68[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]47[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]3.78[/C][C]3.69[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]55[/C][C]3.79[/C][C]3.78[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]56[/C][C]3.79[/C][C]3.79[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]3.8[/C][C]3.79[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]58[/C][C]3.8[/C][C]3.8[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]3.8[/C][C]3.8[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]3.8[/C][C]3.8[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]3.81[/C][C]3.8[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]62[/C][C]3.95[/C][C]3.81[/C][C]0.14[/C][/ROW]
[ROW][C]63[/C][C]3.99[/C][C]3.95[/C][C]0.04[/C][/ROW]
[ROW][C]64[/C][C]4[/C][C]3.99[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]65[/C][C]4.06[/C][C]4[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]66[/C][C]4.16[/C][C]4.06[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]67[/C][C]4.19[/C][C]4.16[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]68[/C][C]4.2[/C][C]4.19[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]69[/C][C]4.2[/C][C]4.2[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]4.2[/C][C]4.2[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]4.2[/C][C]4.2[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]4.2[/C][C]4.2[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]4.23[/C][C]4.2[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]74[/C][C]4.38[/C][C]4.23[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]75[/C][C]4.43[/C][C]4.38[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]76[/C][C]4.44[/C][C]4.43[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]77[/C][C]4.44[/C][C]4.44[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]4.44[/C][C]4.44[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]4.44[/C][C]4.44[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]4.44[/C][C]4.44[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]4.45[/C][C]4.44[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]82[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]83[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]84[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]85[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]87[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]88[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]89[/C][C]4.46[/C][C]4.45[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]90[/C][C]4.46[/C][C]4.46[/C][C]0[/C][/ROW]
[ROW][C]91[/C][C]4.46[/C][C]4.46[/C][C]0[/C][/ROW]
[ROW][C]92[/C][C]4.48[/C][C]4.46[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]93[/C][C]4.58[/C][C]4.48[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]94[/C][C]4.67[/C][C]4.58[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]95[/C][C]4.68[/C][C]4.67[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]96[/C][C]4.68[/C][C]4.68[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13422&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13422&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
2	3.27	3.27	0
3	3.27	3.27	0
4	3.27	3.27	0
5	3.27	3.27	0
6	3.28	3.27	0.00999999999999979
7	3.32	3.28	0.04
8	3.34	3.32	0.02
9	3.34	3.34	0
10	3.35	3.34	0.0100000000000002
11	3.35	3.35	0
12	3.35	3.35	0
13	3.35	3.35	0
14	3.35	3.35	0
15	3.4	3.35	0.0499999999999998
16	3.42	3.4	0.02
17	3.42	3.42	0
18	3.42	3.42	0
19	3.42	3.42	0
20	3.42	3.42	0
21	3.42	3.42	0
22	3.42	3.42	0
23	3.42	3.42	0
24	3.42	3.42	0
25	3.42	3.42	0
26	3.42	3.42	0
27	3.43	3.42	0.0100000000000002
28	3.47	3.43	0.04
29	3.51	3.47	0.0399999999999996
30	3.52	3.51	0.0100000000000002
31	3.52	3.52	0
32	3.52	3.52	0
33	3.52	3.52	0
34	3.52	3.52	0
35	3.52	3.52	0
36	3.52	3.52	0
37	3.52	3.52	0
38	3.52	3.52	0
39	3.58	3.52	0.06
40	3.6	3.58	0.02
41	3.61	3.6	0.00999999999999979
42	3.61	3.61	0
43	3.61	3.61	0
44	3.63	3.61	0.02
45	3.68	3.63	0.0500000000000003
46	3.69	3.68	0.00999999999999979
47	3.69	3.69	0
48	3.69	3.69	0
49	3.69	3.69	0
50	3.69	3.69	0
51	3.69	3.69	0
52	3.69	3.69	0
53	3.69	3.69	0
54	3.78	3.69	0.0899999999999999
55	3.79	3.78	0.0100000000000002
56	3.79	3.79	0
57	3.8	3.79	0.00999999999999979
58	3.8	3.8	0
59	3.8	3.8	0
60	3.8	3.8	0
61	3.81	3.8	0.0100000000000002
62	3.95	3.81	0.14
63	3.99	3.95	0.04
64	4	3.99	0.00999999999999979
65	4.06	4	0.0599999999999996
66	4.16	4.06	0.100000000000001
67	4.19	4.16	0.0300000000000002
68	4.2	4.19	0.00999999999999979
69	4.2	4.2	0
70	4.2	4.2	0
71	4.2	4.2	0
72	4.2	4.2	0
73	4.23	4.2	0.0300000000000002
74	4.38	4.23	0.149999999999999
75	4.43	4.38	0.0499999999999998
76	4.44	4.43	0.0100000000000007
77	4.44	4.44	0
78	4.44	4.44	0
79	4.44	4.44	0
80	4.44	4.44	0
81	4.45	4.44	0.00999999999999979
82	4.45	4.45	0
83	4.45	4.45	0
84	4.45	4.45	0
85	4.45	4.45	0
86	4.45	4.45	0
87	4.45	4.45	0
88	4.45	4.45	0
89	4.46	4.45	0.00999999999999979
90	4.46	4.46	0
91	4.46	4.46	0
92	4.48	4.46	0.0200000000000005
93	4.58	4.48	0.0999999999999996
94	4.67	4.58	0.0899999999999999
95	4.68	4.67	0.00999999999999979
96	4.68	4.68	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	4.68	4.62148930680457	4.73851069319543
98	4.68	4.59725338413917	4.76274661586083
99	4.68	4.57865650659944	4.78134349340056
100	4.68	4.56297861360914	4.79702138639086
101	4.68	4.54916611260439	4.81083388739561
102	4.68	4.53667865717466	4.82332134282534
103	4.68	4.52519525676689	4.8348047432331
104	4.68	4.51450676827835	4.84549323172165
105	4.68	4.50446792041371	4.85553207958629
106	4.68	4.49497294202713	4.86502705797287
107	4.68	4.48594198444716	4.87405801555284
108	4.68	4.47731301319888	4.88268698680112

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 4.68 & 4.62148930680457 & 4.73851069319543 \tabularnewline
98 & 4.68 & 4.59725338413917 & 4.76274661586083 \tabularnewline
99 & 4.68 & 4.57865650659944 & 4.78134349340056 \tabularnewline
100 & 4.68 & 4.56297861360914 & 4.79702138639086 \tabularnewline
101 & 4.68 & 4.54916611260439 & 4.81083388739561 \tabularnewline
102 & 4.68 & 4.53667865717466 & 4.82332134282534 \tabularnewline
103 & 4.68 & 4.52519525676689 & 4.8348047432331 \tabularnewline
104 & 4.68 & 4.51450676827835 & 4.84549323172165 \tabularnewline
105 & 4.68 & 4.50446792041371 & 4.85553207958629 \tabularnewline
106 & 4.68 & 4.49497294202713 & 4.86502705797287 \tabularnewline
107 & 4.68 & 4.48594198444716 & 4.87405801555284 \tabularnewline
108 & 4.68 & 4.47731301319888 & 4.88268698680112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13422&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]97[/C][C]4.68[/C][C]4.62148930680457[/C][C]4.73851069319543[/C][/ROW]
[ROW][C]98[/C][C]4.68[/C][C]4.59725338413917[/C][C]4.76274661586083[/C][/ROW]
[ROW][C]99[/C][C]4.68[/C][C]4.57865650659944[/C][C]4.78134349340056[/C][/ROW]
[ROW][C]100[/C][C]4.68[/C][C]4.56297861360914[/C][C]4.79702138639086[/C][/ROW]
[ROW][C]101[/C][C]4.68[/C][C]4.54916611260439[/C][C]4.81083388739561[/C][/ROW]
[ROW][C]102[/C][C]4.68[/C][C]4.53667865717466[/C][C]4.82332134282534[/C][/ROW]
[ROW][C]103[/C][C]4.68[/C][C]4.52519525676689[/C][C]4.8348047432331[/C][/ROW]
[ROW][C]104[/C][C]4.68[/C][C]4.51450676827835[/C][C]4.84549323172165[/C][/ROW]
[ROW][C]105[/C][C]4.68[/C][C]4.50446792041371[/C][C]4.85553207958629[/C][/ROW]
[ROW][C]106[/C][C]4.68[/C][C]4.49497294202713[/C][C]4.86502705797287[/C][/ROW]
[ROW][C]107[/C][C]4.68[/C][C]4.48594198444716[/C][C]4.87405801555284[/C][/ROW]
[ROW][C]108[/C][C]4.68[/C][C]4.47731301319888[/C][C]4.88268698680112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13422&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13422&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
97	4.68	4.62148930680457	4.73851069319543
98	4.68	4.59725338413917	4.76274661586083
99	4.68	4.57865650659944	4.78134349340056
100	4.68	4.56297861360914	4.79702138639086
101	4.68	4.54916611260439	4.81083388739561
102	4.68	4.53667865717466	4.82332134282534
103	4.68	4.52519525676689	4.8348047432331
104	4.68	4.51450676827835	4.84549323172165
105	4.68	4.50446792041371	4.85553207958629
106	4.68	4.49497294202713	4.86502705797287
107	4.68	4.48594198444716	4.87405801555284
108	4.68	4.47731301319888	4.88268698680112

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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