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*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 09 Jan 2017 16:10:54 +0000

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/2017/Jan/09/t1483978282hp482a89ho70t08.htm/, Retrieved Wed, 15 May 2024 00:59:09 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 00:59:09 +0200

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No (this computation is public)

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Estimated Impact

Dataseries X:

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1,56
1,56
1,54
1,54
1,54
1,54
1,57
1,58
1,57
1,57
1,57
1,57
1,56
1,58
1,58
1,58
1,58
1,53
1,48
1,48
1,48
1,48
1,48
1,57
1,57
1,57
1,60
1,60
1,65
1,71
1,71
1,71
1,74
1,78
1,84
1,84
1,76
1,72
1,66
1,65
1,66
1,66
1,66
1,61
1,55
1,56
1,55
1,55
1,61
1,54
1,48
1,42
1,42
1,42
1,43
1,46
1,50
1,47
1,43
1,42
1,39
1,37
1,38
1,51
1,47
1,47
1,53
1,55
1,50
1,52
1,53
1,53
1,52
1,60
1,52
1,64
1,63
1,69
1,73
1,69
1,61
1,52
1,55
1,56
1,56
1,56
1,54
1,53
1,54
1,48
1,38
1,34
1,28
1,28
1,30
1,31
1,31
1,31
1,32
1,31
1,27
1,24
1,24
1,24
1,24
1,24
1,24
1,24
1,23
1,26
1,28
1,32
1,40
1,41
1,37
1,33
1,33
1,34
1,34
1,38
1,43
1,39
1,33
1,33
1,34
1,38
1,37
1,38
1,31
1,38
1,30
1,30
1,29
1,31
1,31
1,32
1,31
1,30
1,31
1,33
1,34
1,42
1,42
1,36
1,36
1,34
1,34
1,33
1,31
1,25
1,23
1,17
1,19
1,19
1,19
1,19

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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=&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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1.54	1.56	-0.02
4	1.54	1.54	0
5	1.54	1.54	0
6	1.54	1.54	0
7	1.57	1.54	0.03
8	1.58	1.57	0.01
9	1.57	1.58	-0.01
10	1.57	1.57	0
11	1.57	1.57	0
12	1.57	1.57	0
13	1.56	1.57	-0.01
14	1.58	1.56	0.02
15	1.58	1.58	0
16	1.58	1.58	0
17	1.58	1.58	0
18	1.53	1.58	-0.05
19	1.48	1.53	-0.05
20	1.48	1.48	0
21	1.48	1.48	0
22	1.48	1.48	0
23	1.48	1.48	0
24	1.57	1.48	0.0900000000000001
25	1.57	1.57	0
26	1.57	1.57	0
27	1.6	1.57	0.03
28	1.6	1.6	0
29	1.65	1.6	0.0499999999999998
30	1.71	1.65	0.0600000000000001
31	1.71	1.71	0
32	1.71	1.71	0
33	1.74	1.71	0.03
34	1.78	1.74	0.04
35	1.84	1.78	0.0600000000000001
36	1.84	1.84	0
37	1.76	1.84	-0.0800000000000001
38	1.72	1.76	-0.04
39	1.66	1.72	-0.0600000000000001
40	1.65	1.66	-0.01
41	1.66	1.65	0.01
42	1.66	1.66	0
43	1.66	1.66	0
44	1.61	1.66	-0.0499999999999998
45	1.55	1.61	-0.0600000000000001
46	1.56	1.55	0.01
47	1.55	1.56	-0.01
48	1.55	1.55	0
49	1.61	1.55	0.0600000000000001
50	1.54	1.61	-0.0700000000000001
51	1.48	1.54	-0.0600000000000001
52	1.42	1.48	-0.0600000000000001
53	1.42	1.42	0
54	1.42	1.42	0
55	1.43	1.42	0.01
56	1.46	1.43	0.03
57	1.5	1.46	0.04
58	1.47	1.5	-0.03
59	1.43	1.47	-0.04
60	1.42	1.43	-0.01
61	1.39	1.42	-0.03
62	1.37	1.39	-0.0199999999999998
63	1.38	1.37	0.00999999999999979
64	1.51	1.38	0.13
65	1.47	1.51	-0.04
66	1.47	1.47	0
67	1.53	1.47	0.0600000000000001
68	1.55	1.53	0.02
69	1.5	1.55	-0.05
70	1.52	1.5	0.02
71	1.53	1.52	0.01
72	1.53	1.53	0
73	1.52	1.53	-0.01
74	1.6	1.52	0.0800000000000001
75	1.52	1.6	-0.0800000000000001
76	1.64	1.52	0.12
77	1.63	1.64	-0.01
78	1.69	1.63	0.0600000000000001
79	1.73	1.69	0.04
80	1.69	1.73	-0.04
81	1.61	1.69	-0.0799999999999998
82	1.52	1.61	-0.0900000000000001
83	1.55	1.52	0.03
84	1.56	1.55	0.01
85	1.56	1.56	0
86	1.56	1.56	0
87	1.54	1.56	-0.02
88	1.53	1.54	-0.01
89	1.54	1.53	0.01
90	1.48	1.54	-0.0600000000000001
91	1.38	1.48	-0.1
92	1.34	1.38	-0.0399999999999998
93	1.28	1.34	-0.0600000000000001
94	1.28	1.28	0
95	1.3	1.28	0.02
96	1.31	1.3	0.01
97	1.31	1.31	0
98	1.31	1.31	0
99	1.32	1.31	0.01
100	1.31	1.32	-0.01
101	1.27	1.31	-0.04
102	1.24	1.27	-0.03
103	1.24	1.24	0
104	1.24	1.24	0
105	1.24	1.24	0
106	1.24	1.24	0
107	1.24	1.24	0
108	1.24	1.24	0
109	1.23	1.24	-0.01
110	1.26	1.23	0.03
111	1.28	1.26	0.02
112	1.32	1.28	0.04
113	1.4	1.32	0.0799999999999998
114	1.41	1.4	0.01
115	1.37	1.41	-0.0399999999999998
116	1.33	1.37	-0.04
117	1.33	1.33	0
118	1.34	1.33	0.01
119	1.34	1.34	0
120	1.38	1.34	0.0399999999999998
121	1.43	1.38	0.05
122	1.39	1.43	-0.04
123	1.33	1.39	-0.0599999999999998
124	1.33	1.33	0
125	1.34	1.33	0.01
126	1.38	1.34	0.0399999999999998
127	1.37	1.38	-0.00999999999999979
128	1.38	1.37	0.00999999999999979
129	1.31	1.38	-0.0699999999999998
130	1.38	1.31	0.0699999999999998
131	1.3	1.38	-0.0799999999999998
132	1.3	1.3	0
133	1.29	1.3	-0.01
134	1.31	1.29	0.02
135	1.31	1.31	0
136	1.32	1.31	0.01
137	1.31	1.32	-0.01
138	1.3	1.31	-0.01
139	1.31	1.3	0.01
140	1.33	1.31	0.02
141	1.34	1.33	0.01
142	1.42	1.34	0.0799999999999998
143	1.42	1.42	0
144	1.36	1.42	-0.0599999999999998
145	1.36	1.36	0
146	1.34	1.36	-0.02
147	1.34	1.34	0
148	1.33	1.34	-0.01
149	1.31	1.33	-0.02
150	1.25	1.31	-0.0600000000000001
151	1.23	1.25	-0.02
152	1.17	1.23	-0.0600000000000001
153	1.19	1.17	0.02
154	1.19	1.19	0
155	1.19	1.19	0
156	1.19	1.19	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.54 & 1.56 & -0.02 \tabularnewline
4 & 1.54 & 1.54 & 0 \tabularnewline
5 & 1.54 & 1.54 & 0 \tabularnewline
6 & 1.54 & 1.54 & 0 \tabularnewline
7 & 1.57 & 1.54 & 0.03 \tabularnewline
8 & 1.58 & 1.57 & 0.01 \tabularnewline
9 & 1.57 & 1.58 & -0.01 \tabularnewline
10 & 1.57 & 1.57 & 0 \tabularnewline
11 & 1.57 & 1.57 & 0 \tabularnewline
12 & 1.57 & 1.57 & 0 \tabularnewline
13 & 1.56 & 1.57 & -0.01 \tabularnewline
14 & 1.58 & 1.56 & 0.02 \tabularnewline
15 & 1.58 & 1.58 & 0 \tabularnewline
16 & 1.58 & 1.58 & 0 \tabularnewline
17 & 1.58 & 1.58 & 0 \tabularnewline
18 & 1.53 & 1.58 & -0.05 \tabularnewline
19 & 1.48 & 1.53 & -0.05 \tabularnewline
20 & 1.48 & 1.48 & 0 \tabularnewline
21 & 1.48 & 1.48 & 0 \tabularnewline
22 & 1.48 & 1.48 & 0 \tabularnewline
23 & 1.48 & 1.48 & 0 \tabularnewline
24 & 1.57 & 1.48 & 0.0900000000000001 \tabularnewline
25 & 1.57 & 1.57 & 0 \tabularnewline
26 & 1.57 & 1.57 & 0 \tabularnewline
27 & 1.6 & 1.57 & 0.03 \tabularnewline
28 & 1.6 & 1.6 & 0 \tabularnewline
29 & 1.65 & 1.6 & 0.0499999999999998 \tabularnewline
30 & 1.71 & 1.65 & 0.0600000000000001 \tabularnewline
31 & 1.71 & 1.71 & 0 \tabularnewline
32 & 1.71 & 1.71 & 0 \tabularnewline
33 & 1.74 & 1.71 & 0.03 \tabularnewline
34 & 1.78 & 1.74 & 0.04 \tabularnewline
35 & 1.84 & 1.78 & 0.0600000000000001 \tabularnewline
36 & 1.84 & 1.84 & 0 \tabularnewline
37 & 1.76 & 1.84 & -0.0800000000000001 \tabularnewline
38 & 1.72 & 1.76 & -0.04 \tabularnewline
39 & 1.66 & 1.72 & -0.0600000000000001 \tabularnewline
40 & 1.65 & 1.66 & -0.01 \tabularnewline
41 & 1.66 & 1.65 & 0.01 \tabularnewline
42 & 1.66 & 1.66 & 0 \tabularnewline
43 & 1.66 & 1.66 & 0 \tabularnewline
44 & 1.61 & 1.66 & -0.0499999999999998 \tabularnewline
45 & 1.55 & 1.61 & -0.0600000000000001 \tabularnewline
46 & 1.56 & 1.55 & 0.01 \tabularnewline
47 & 1.55 & 1.56 & -0.01 \tabularnewline
48 & 1.55 & 1.55 & 0 \tabularnewline
49 & 1.61 & 1.55 & 0.0600000000000001 \tabularnewline
50 & 1.54 & 1.61 & -0.0700000000000001 \tabularnewline
51 & 1.48 & 1.54 & -0.0600000000000001 \tabularnewline
52 & 1.42 & 1.48 & -0.0600000000000001 \tabularnewline
53 & 1.42 & 1.42 & 0 \tabularnewline
54 & 1.42 & 1.42 & 0 \tabularnewline
55 & 1.43 & 1.42 & 0.01 \tabularnewline
56 & 1.46 & 1.43 & 0.03 \tabularnewline
57 & 1.5 & 1.46 & 0.04 \tabularnewline
58 & 1.47 & 1.5 & -0.03 \tabularnewline
59 & 1.43 & 1.47 & -0.04 \tabularnewline
60 & 1.42 & 1.43 & -0.01 \tabularnewline
61 & 1.39 & 1.42 & -0.03 \tabularnewline
62 & 1.37 & 1.39 & -0.0199999999999998 \tabularnewline
63 & 1.38 & 1.37 & 0.00999999999999979 \tabularnewline
64 & 1.51 & 1.38 & 0.13 \tabularnewline
65 & 1.47 & 1.51 & -0.04 \tabularnewline
66 & 1.47 & 1.47 & 0 \tabularnewline
67 & 1.53 & 1.47 & 0.0600000000000001 \tabularnewline
68 & 1.55 & 1.53 & 0.02 \tabularnewline
69 & 1.5 & 1.55 & -0.05 \tabularnewline
70 & 1.52 & 1.5 & 0.02 \tabularnewline
71 & 1.53 & 1.52 & 0.01 \tabularnewline
72 & 1.53 & 1.53 & 0 \tabularnewline
73 & 1.52 & 1.53 & -0.01 \tabularnewline
74 & 1.6 & 1.52 & 0.0800000000000001 \tabularnewline
75 & 1.52 & 1.6 & -0.0800000000000001 \tabularnewline
76 & 1.64 & 1.52 & 0.12 \tabularnewline
77 & 1.63 & 1.64 & -0.01 \tabularnewline
78 & 1.69 & 1.63 & 0.0600000000000001 \tabularnewline
79 & 1.73 & 1.69 & 0.04 \tabularnewline
80 & 1.69 & 1.73 & -0.04 \tabularnewline
81 & 1.61 & 1.69 & -0.0799999999999998 \tabularnewline
82 & 1.52 & 1.61 & -0.0900000000000001 \tabularnewline
83 & 1.55 & 1.52 & 0.03 \tabularnewline
84 & 1.56 & 1.55 & 0.01 \tabularnewline
85 & 1.56 & 1.56 & 0 \tabularnewline
86 & 1.56 & 1.56 & 0 \tabularnewline
87 & 1.54 & 1.56 & -0.02 \tabularnewline
88 & 1.53 & 1.54 & -0.01 \tabularnewline
89 & 1.54 & 1.53 & 0.01 \tabularnewline
90 & 1.48 & 1.54 & -0.0600000000000001 \tabularnewline
91 & 1.38 & 1.48 & -0.1 \tabularnewline
92 & 1.34 & 1.38 & -0.0399999999999998 \tabularnewline
93 & 1.28 & 1.34 & -0.0600000000000001 \tabularnewline
94 & 1.28 & 1.28 & 0 \tabularnewline
95 & 1.3 & 1.28 & 0.02 \tabularnewline
96 & 1.31 & 1.3 & 0.01 \tabularnewline
97 & 1.31 & 1.31 & 0 \tabularnewline
98 & 1.31 & 1.31 & 0 \tabularnewline
99 & 1.32 & 1.31 & 0.01 \tabularnewline
100 & 1.31 & 1.32 & -0.01 \tabularnewline
101 & 1.27 & 1.31 & -0.04 \tabularnewline
102 & 1.24 & 1.27 & -0.03 \tabularnewline
103 & 1.24 & 1.24 & 0 \tabularnewline
104 & 1.24 & 1.24 & 0 \tabularnewline
105 & 1.24 & 1.24 & 0 \tabularnewline
106 & 1.24 & 1.24 & 0 \tabularnewline
107 & 1.24 & 1.24 & 0 \tabularnewline
108 & 1.24 & 1.24 & 0 \tabularnewline
109 & 1.23 & 1.24 & -0.01 \tabularnewline
110 & 1.26 & 1.23 & 0.03 \tabularnewline
111 & 1.28 & 1.26 & 0.02 \tabularnewline
112 & 1.32 & 1.28 & 0.04 \tabularnewline
113 & 1.4 & 1.32 & 0.0799999999999998 \tabularnewline
114 & 1.41 & 1.4 & 0.01 \tabularnewline
115 & 1.37 & 1.41 & -0.0399999999999998 \tabularnewline
116 & 1.33 & 1.37 & -0.04 \tabularnewline
117 & 1.33 & 1.33 & 0 \tabularnewline
118 & 1.34 & 1.33 & 0.01 \tabularnewline
119 & 1.34 & 1.34 & 0 \tabularnewline
120 & 1.38 & 1.34 & 0.0399999999999998 \tabularnewline
121 & 1.43 & 1.38 & 0.05 \tabularnewline
122 & 1.39 & 1.43 & -0.04 \tabularnewline
123 & 1.33 & 1.39 & -0.0599999999999998 \tabularnewline
124 & 1.33 & 1.33 & 0 \tabularnewline
125 & 1.34 & 1.33 & 0.01 \tabularnewline
126 & 1.38 & 1.34 & 0.0399999999999998 \tabularnewline
127 & 1.37 & 1.38 & -0.00999999999999979 \tabularnewline
128 & 1.38 & 1.37 & 0.00999999999999979 \tabularnewline
129 & 1.31 & 1.38 & -0.0699999999999998 \tabularnewline
130 & 1.38 & 1.31 & 0.0699999999999998 \tabularnewline
131 & 1.3 & 1.38 & -0.0799999999999998 \tabularnewline
132 & 1.3 & 1.3 & 0 \tabularnewline
133 & 1.29 & 1.3 & -0.01 \tabularnewline
134 & 1.31 & 1.29 & 0.02 \tabularnewline
135 & 1.31 & 1.31 & 0 \tabularnewline
136 & 1.32 & 1.31 & 0.01 \tabularnewline
137 & 1.31 & 1.32 & -0.01 \tabularnewline
138 & 1.3 & 1.31 & -0.01 \tabularnewline
139 & 1.31 & 1.3 & 0.01 \tabularnewline
140 & 1.33 & 1.31 & 0.02 \tabularnewline
141 & 1.34 & 1.33 & 0.01 \tabularnewline
142 & 1.42 & 1.34 & 0.0799999999999998 \tabularnewline
143 & 1.42 & 1.42 & 0 \tabularnewline
144 & 1.36 & 1.42 & -0.0599999999999998 \tabularnewline
145 & 1.36 & 1.36 & 0 \tabularnewline
146 & 1.34 & 1.36 & -0.02 \tabularnewline
147 & 1.34 & 1.34 & 0 \tabularnewline
148 & 1.33 & 1.34 & -0.01 \tabularnewline
149 & 1.31 & 1.33 & -0.02 \tabularnewline
150 & 1.25 & 1.31 & -0.0600000000000001 \tabularnewline
151 & 1.23 & 1.25 & -0.02 \tabularnewline
152 & 1.17 & 1.23 & -0.0600000000000001 \tabularnewline
153 & 1.19 & 1.17 & 0.02 \tabularnewline
154 & 1.19 & 1.19 & 0 \tabularnewline
155 & 1.19 & 1.19 & 0 \tabularnewline
156 & 1.19 & 1.19 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.54[/C][C]1.56[/C][C]-0.02[/C][/ROW]
[ROW][C]4[/C][C]1.54[/C][C]1.54[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]1.54[/C][C]1.54[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]1.54[/C][C]1.54[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]1.57[/C][C]1.54[/C][C]0.03[/C][/ROW]
[ROW][C]8[/C][C]1.58[/C][C]1.57[/C][C]0.01[/C][/ROW]
[ROW][C]9[/C][C]1.57[/C][C]1.58[/C][C]-0.01[/C][/ROW]
[ROW][C]10[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]1.56[/C][C]1.57[/C][C]-0.01[/C][/ROW]
[ROW][C]14[/C][C]1.58[/C][C]1.56[/C][C]0.02[/C][/ROW]
[ROW][C]15[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]1.53[/C][C]1.58[/C][C]-0.05[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.53[/C][C]-0.05[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.48[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]1.48[/C][C]1.48[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]1.48[/C][C]1.48[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]1.48[/C][C]1.48[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]1.57[/C][C]1.48[/C][C]0.0900000000000001[/C][/ROW]
[ROW][C]25[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]1.6[/C][C]1.57[/C][C]0.03[/C][/ROW]
[ROW][C]28[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]1.65[/C][C]1.6[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]30[/C][C]1.71[/C][C]1.65[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]31[/C][C]1.71[/C][C]1.71[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]1.71[/C][C]1.71[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]1.74[/C][C]1.71[/C][C]0.03[/C][/ROW]
[ROW][C]34[/C][C]1.78[/C][C]1.74[/C][C]0.04[/C][/ROW]
[ROW][C]35[/C][C]1.84[/C][C]1.78[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]36[/C][C]1.84[/C][C]1.84[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]1.76[/C][C]1.84[/C][C]-0.0800000000000001[/C][/ROW]
[ROW][C]38[/C][C]1.72[/C][C]1.76[/C][C]-0.04[/C][/ROW]
[ROW][C]39[/C][C]1.66[/C][C]1.72[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]40[/C][C]1.65[/C][C]1.66[/C][C]-0.01[/C][/ROW]
[ROW][C]41[/C][C]1.66[/C][C]1.65[/C][C]0.01[/C][/ROW]
[ROW][C]42[/C][C]1.66[/C][C]1.66[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]1.66[/C][C]1.66[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]1.61[/C][C]1.66[/C][C]-0.0499999999999998[/C][/ROW]
[ROW][C]45[/C][C]1.55[/C][C]1.61[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]46[/C][C]1.56[/C][C]1.55[/C][C]0.01[/C][/ROW]
[ROW][C]47[/C][C]1.55[/C][C]1.56[/C][C]-0.01[/C][/ROW]
[ROW][C]48[/C][C]1.55[/C][C]1.55[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]1.61[/C][C]1.55[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]50[/C][C]1.54[/C][C]1.61[/C][C]-0.0700000000000001[/C][/ROW]
[ROW][C]51[/C][C]1.48[/C][C]1.54[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]52[/C][C]1.42[/C][C]1.48[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]53[/C][C]1.42[/C][C]1.42[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]1.42[/C][C]1.42[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]1.43[/C][C]1.42[/C][C]0.01[/C][/ROW]
[ROW][C]56[/C][C]1.46[/C][C]1.43[/C][C]0.03[/C][/ROW]
[ROW][C]57[/C][C]1.5[/C][C]1.46[/C][C]0.04[/C][/ROW]
[ROW][C]58[/C][C]1.47[/C][C]1.5[/C][C]-0.03[/C][/ROW]
[ROW][C]59[/C][C]1.43[/C][C]1.47[/C][C]-0.04[/C][/ROW]
[ROW][C]60[/C][C]1.42[/C][C]1.43[/C][C]-0.01[/C][/ROW]
[ROW][C]61[/C][C]1.39[/C][C]1.42[/C][C]-0.03[/C][/ROW]
[ROW][C]62[/C][C]1.37[/C][C]1.39[/C][C]-0.0199999999999998[/C][/ROW]
[ROW][C]63[/C][C]1.38[/C][C]1.37[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]64[/C][C]1.51[/C][C]1.38[/C][C]0.13[/C][/ROW]
[ROW][C]65[/C][C]1.47[/C][C]1.51[/C][C]-0.04[/C][/ROW]
[ROW][C]66[/C][C]1.47[/C][C]1.47[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]1.53[/C][C]1.47[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]68[/C][C]1.55[/C][C]1.53[/C][C]0.02[/C][/ROW]
[ROW][C]69[/C][C]1.5[/C][C]1.55[/C][C]-0.05[/C][/ROW]
[ROW][C]70[/C][C]1.52[/C][C]1.5[/C][C]0.02[/C][/ROW]
[ROW][C]71[/C][C]1.53[/C][C]1.52[/C][C]0.01[/C][/ROW]
[ROW][C]72[/C][C]1.53[/C][C]1.53[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]1.52[/C][C]1.53[/C][C]-0.01[/C][/ROW]
[ROW][C]74[/C][C]1.6[/C][C]1.52[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]75[/C][C]1.52[/C][C]1.6[/C][C]-0.0800000000000001[/C][/ROW]
[ROW][C]76[/C][C]1.64[/C][C]1.52[/C][C]0.12[/C][/ROW]
[ROW][C]77[/C][C]1.63[/C][C]1.64[/C][C]-0.01[/C][/ROW]
[ROW][C]78[/C][C]1.69[/C][C]1.63[/C][C]0.0600000000000001[/C][/ROW]
[ROW][C]79[/C][C]1.73[/C][C]1.69[/C][C]0.04[/C][/ROW]
[ROW][C]80[/C][C]1.69[/C][C]1.73[/C][C]-0.04[/C][/ROW]
[ROW][C]81[/C][C]1.61[/C][C]1.69[/C][C]-0.0799999999999998[/C][/ROW]
[ROW][C]82[/C][C]1.52[/C][C]1.61[/C][C]-0.0900000000000001[/C][/ROW]
[ROW][C]83[/C][C]1.55[/C][C]1.52[/C][C]0.03[/C][/ROW]
[ROW][C]84[/C][C]1.56[/C][C]1.55[/C][C]0.01[/C][/ROW]
[ROW][C]85[/C][C]1.56[/C][C]1.56[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]1.56[/C][C]1.56[/C][C]0[/C][/ROW]
[ROW][C]87[/C][C]1.54[/C][C]1.56[/C][C]-0.02[/C][/ROW]
[ROW][C]88[/C][C]1.53[/C][C]1.54[/C][C]-0.01[/C][/ROW]
[ROW][C]89[/C][C]1.54[/C][C]1.53[/C][C]0.01[/C][/ROW]
[ROW][C]90[/C][C]1.48[/C][C]1.54[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]91[/C][C]1.38[/C][C]1.48[/C][C]-0.1[/C][/ROW]
[ROW][C]92[/C][C]1.34[/C][C]1.38[/C][C]-0.0399999999999998[/C][/ROW]
[ROW][C]93[/C][C]1.28[/C][C]1.34[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]94[/C][C]1.28[/C][C]1.28[/C][C]0[/C][/ROW]
[ROW][C]95[/C][C]1.3[/C][C]1.28[/C][C]0.02[/C][/ROW]
[ROW][C]96[/C][C]1.31[/C][C]1.3[/C][C]0.01[/C][/ROW]
[ROW][C]97[/C][C]1.31[/C][C]1.31[/C][C]0[/C][/ROW]
[ROW][C]98[/C][C]1.31[/C][C]1.31[/C][C]0[/C][/ROW]
[ROW][C]99[/C][C]1.32[/C][C]1.31[/C][C]0.01[/C][/ROW]
[ROW][C]100[/C][C]1.31[/C][C]1.32[/C][C]-0.01[/C][/ROW]
[ROW][C]101[/C][C]1.27[/C][C]1.31[/C][C]-0.04[/C][/ROW]
[ROW][C]102[/C][C]1.24[/C][C]1.27[/C][C]-0.03[/C][/ROW]
[ROW][C]103[/C][C]1.24[/C][C]1.24[/C][C]0[/C][/ROW]
[ROW][C]104[/C][C]1.24[/C][C]1.24[/C][C]0[/C][/ROW]
[ROW][C]105[/C][C]1.24[/C][C]1.24[/C][C]0[/C][/ROW]
[ROW][C]106[/C][C]1.24[/C][C]1.24[/C][C]0[/C][/ROW]
[ROW][C]107[/C][C]1.24[/C][C]1.24[/C][C]0[/C][/ROW]
[ROW][C]108[/C][C]1.24[/C][C]1.24[/C][C]0[/C][/ROW]
[ROW][C]109[/C][C]1.23[/C][C]1.24[/C][C]-0.01[/C][/ROW]
[ROW][C]110[/C][C]1.26[/C][C]1.23[/C][C]0.03[/C][/ROW]
[ROW][C]111[/C][C]1.28[/C][C]1.26[/C][C]0.02[/C][/ROW]
[ROW][C]112[/C][C]1.32[/C][C]1.28[/C][C]0.04[/C][/ROW]
[ROW][C]113[/C][C]1.4[/C][C]1.32[/C][C]0.0799999999999998[/C][/ROW]
[ROW][C]114[/C][C]1.41[/C][C]1.4[/C][C]0.01[/C][/ROW]
[ROW][C]115[/C][C]1.37[/C][C]1.41[/C][C]-0.0399999999999998[/C][/ROW]
[ROW][C]116[/C][C]1.33[/C][C]1.37[/C][C]-0.04[/C][/ROW]
[ROW][C]117[/C][C]1.33[/C][C]1.33[/C][C]0[/C][/ROW]
[ROW][C]118[/C][C]1.34[/C][C]1.33[/C][C]0.01[/C][/ROW]
[ROW][C]119[/C][C]1.34[/C][C]1.34[/C][C]0[/C][/ROW]
[ROW][C]120[/C][C]1.38[/C][C]1.34[/C][C]0.0399999999999998[/C][/ROW]
[ROW][C]121[/C][C]1.43[/C][C]1.38[/C][C]0.05[/C][/ROW]
[ROW][C]122[/C][C]1.39[/C][C]1.43[/C][C]-0.04[/C][/ROW]
[ROW][C]123[/C][C]1.33[/C][C]1.39[/C][C]-0.0599999999999998[/C][/ROW]
[ROW][C]124[/C][C]1.33[/C][C]1.33[/C][C]0[/C][/ROW]
[ROW][C]125[/C][C]1.34[/C][C]1.33[/C][C]0.01[/C][/ROW]
[ROW][C]126[/C][C]1.38[/C][C]1.34[/C][C]0.0399999999999998[/C][/ROW]
[ROW][C]127[/C][C]1.37[/C][C]1.38[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]128[/C][C]1.38[/C][C]1.37[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]129[/C][C]1.31[/C][C]1.38[/C][C]-0.0699999999999998[/C][/ROW]
[ROW][C]130[/C][C]1.38[/C][C]1.31[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]131[/C][C]1.3[/C][C]1.38[/C][C]-0.0799999999999998[/C][/ROW]
[ROW][C]132[/C][C]1.3[/C][C]1.3[/C][C]0[/C][/ROW]
[ROW][C]133[/C][C]1.29[/C][C]1.3[/C][C]-0.01[/C][/ROW]
[ROW][C]134[/C][C]1.31[/C][C]1.29[/C][C]0.02[/C][/ROW]
[ROW][C]135[/C][C]1.31[/C][C]1.31[/C][C]0[/C][/ROW]
[ROW][C]136[/C][C]1.32[/C][C]1.31[/C][C]0.01[/C][/ROW]
[ROW][C]137[/C][C]1.31[/C][C]1.32[/C][C]-0.01[/C][/ROW]
[ROW][C]138[/C][C]1.3[/C][C]1.31[/C][C]-0.01[/C][/ROW]
[ROW][C]139[/C][C]1.31[/C][C]1.3[/C][C]0.01[/C][/ROW]
[ROW][C]140[/C][C]1.33[/C][C]1.31[/C][C]0.02[/C][/ROW]
[ROW][C]141[/C][C]1.34[/C][C]1.33[/C][C]0.01[/C][/ROW]
[ROW][C]142[/C][C]1.42[/C][C]1.34[/C][C]0.0799999999999998[/C][/ROW]
[ROW][C]143[/C][C]1.42[/C][C]1.42[/C][C]0[/C][/ROW]
[ROW][C]144[/C][C]1.36[/C][C]1.42[/C][C]-0.0599999999999998[/C][/ROW]
[ROW][C]145[/C][C]1.36[/C][C]1.36[/C][C]0[/C][/ROW]
[ROW][C]146[/C][C]1.34[/C][C]1.36[/C][C]-0.02[/C][/ROW]
[ROW][C]147[/C][C]1.34[/C][C]1.34[/C][C]0[/C][/ROW]
[ROW][C]148[/C][C]1.33[/C][C]1.34[/C][C]-0.01[/C][/ROW]
[ROW][C]149[/C][C]1.31[/C][C]1.33[/C][C]-0.02[/C][/ROW]
[ROW][C]150[/C][C]1.25[/C][C]1.31[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]151[/C][C]1.23[/C][C]1.25[/C][C]-0.02[/C][/ROW]
[ROW][C]152[/C][C]1.17[/C][C]1.23[/C][C]-0.0600000000000001[/C][/ROW]
[ROW][C]153[/C][C]1.19[/C][C]1.17[/C][C]0.02[/C][/ROW]
[ROW][C]154[/C][C]1.19[/C][C]1.19[/C][C]0[/C][/ROW]
[ROW][C]155[/C][C]1.19[/C][C]1.19[/C][C]0[/C][/ROW]
[ROW][C]156[/C][C]1.19[/C][C]1.19[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1.54	1.56	-0.02
4	1.54	1.54	0
5	1.54	1.54	0
6	1.54	1.54	0
7	1.57	1.54	0.03
8	1.58	1.57	0.01
9	1.57	1.58	-0.01
10	1.57	1.57	0
11	1.57	1.57	0
12	1.57	1.57	0
13	1.56	1.57	-0.01
14	1.58	1.56	0.02
15	1.58	1.58	0
16	1.58	1.58	0
17	1.58	1.58	0
18	1.53	1.58	-0.05
19	1.48	1.53	-0.05
20	1.48	1.48	0
21	1.48	1.48	0
22	1.48	1.48	0
23	1.48	1.48	0
24	1.57	1.48	0.0900000000000001
25	1.57	1.57	0
26	1.57	1.57	0
27	1.6	1.57	0.03
28	1.6	1.6	0
29	1.65	1.6	0.0499999999999998
30	1.71	1.65	0.0600000000000001
31	1.71	1.71	0
32	1.71	1.71	0
33	1.74	1.71	0.03
34	1.78	1.74	0.04
35	1.84	1.78	0.0600000000000001
36	1.84	1.84	0
37	1.76	1.84	-0.0800000000000001
38	1.72	1.76	-0.04
39	1.66	1.72	-0.0600000000000001
40	1.65	1.66	-0.01
41	1.66	1.65	0.01
42	1.66	1.66	0
43	1.66	1.66	0
44	1.61	1.66	-0.0499999999999998
45	1.55	1.61	-0.0600000000000001
46	1.56	1.55	0.01
47	1.55	1.56	-0.01
48	1.55	1.55	0
49	1.61	1.55	0.0600000000000001
50	1.54	1.61	-0.0700000000000001
51	1.48	1.54	-0.0600000000000001
52	1.42	1.48	-0.0600000000000001
53	1.42	1.42	0
54	1.42	1.42	0
55	1.43	1.42	0.01
56	1.46	1.43	0.03
57	1.5	1.46	0.04
58	1.47	1.5	-0.03
59	1.43	1.47	-0.04
60	1.42	1.43	-0.01
61	1.39	1.42	-0.03
62	1.37	1.39	-0.0199999999999998
63	1.38	1.37	0.00999999999999979
64	1.51	1.38	0.13
65	1.47	1.51	-0.04
66	1.47	1.47	0
67	1.53	1.47	0.0600000000000001
68	1.55	1.53	0.02
69	1.5	1.55	-0.05
70	1.52	1.5	0.02
71	1.53	1.52	0.01
72	1.53	1.53	0
73	1.52	1.53	-0.01
74	1.6	1.52	0.0800000000000001
75	1.52	1.6	-0.0800000000000001
76	1.64	1.52	0.12
77	1.63	1.64	-0.01
78	1.69	1.63	0.0600000000000001
79	1.73	1.69	0.04
80	1.69	1.73	-0.04
81	1.61	1.69	-0.0799999999999998
82	1.52	1.61	-0.0900000000000001
83	1.55	1.52	0.03
84	1.56	1.55	0.01
85	1.56	1.56	0
86	1.56	1.56	0
87	1.54	1.56	-0.02
88	1.53	1.54	-0.01
89	1.54	1.53	0.01
90	1.48	1.54	-0.0600000000000001
91	1.38	1.48	-0.1
92	1.34	1.38	-0.0399999999999998
93	1.28	1.34	-0.0600000000000001
94	1.28	1.28	0
95	1.3	1.28	0.02
96	1.31	1.3	0.01
97	1.31	1.31	0
98	1.31	1.31	0
99	1.32	1.31	0.01
100	1.31	1.32	-0.01
101	1.27	1.31	-0.04
102	1.24	1.27	-0.03
103	1.24	1.24	0
104	1.24	1.24	0
105	1.24	1.24	0
106	1.24	1.24	0
107	1.24	1.24	0
108	1.24	1.24	0
109	1.23	1.24	-0.01
110	1.26	1.23	0.03
111	1.28	1.26	0.02
112	1.32	1.28	0.04
113	1.4	1.32	0.0799999999999998
114	1.41	1.4	0.01
115	1.37	1.41	-0.0399999999999998
116	1.33	1.37	-0.04
117	1.33	1.33	0
118	1.34	1.33	0.01
119	1.34	1.34	0
120	1.38	1.34	0.0399999999999998
121	1.43	1.38	0.05
122	1.39	1.43	-0.04
123	1.33	1.39	-0.0599999999999998
124	1.33	1.33	0
125	1.34	1.33	0.01
126	1.38	1.34	0.0399999999999998
127	1.37	1.38	-0.00999999999999979
128	1.38	1.37	0.00999999999999979
129	1.31	1.38	-0.0699999999999998
130	1.38	1.31	0.0699999999999998
131	1.3	1.38	-0.0799999999999998
132	1.3	1.3	0
133	1.29	1.3	-0.01
134	1.31	1.29	0.02
135	1.31	1.31	0
136	1.32	1.31	0.01
137	1.31	1.32	-0.01
138	1.3	1.31	-0.01
139	1.31	1.3	0.01
140	1.33	1.31	0.02
141	1.34	1.33	0.01
142	1.42	1.34	0.0799999999999998
143	1.42	1.42	0
144	1.36	1.42	-0.0599999999999998
145	1.36	1.36	0
146	1.34	1.36	-0.02
147	1.34	1.34	0
148	1.33	1.34	-0.01
149	1.31	1.33	-0.02
150	1.25	1.31	-0.0600000000000001
151	1.23	1.25	-0.02
152	1.17	1.23	-0.0600000000000001
153	1.19	1.17	0.02
154	1.19	1.19	0
155	1.19	1.19	0
156	1.19	1.19	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
157	1.19	1.11467013285819	1.26532986714181
158	1.19	1.08346748023629	1.29653251976371
159	1.19	1.05952484278298	1.32047515721702
160	1.19	1.03934026571639	1.34065973428361
161	1.19	1.02155729633489	1.35844270366511
162	1.19	1.00548026311093	1.37451973688907
163	1.19	0.990695905247245	1.38930409475275
164	1.19	0.976934960472589	1.40306503952741
165	1.19	0.964010398574582	1.41598960142542
166	1.19	0.951786043994015	1.42821395600598
167	1.19	0.940159095183308	1.43984090481669
168	1.19	0.929049685565958	1.45095031443404

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
157 & 1.19 & 1.11467013285819 & 1.26532986714181 \tabularnewline
158 & 1.19 & 1.08346748023629 & 1.29653251976371 \tabularnewline
159 & 1.19 & 1.05952484278298 & 1.32047515721702 \tabularnewline
160 & 1.19 & 1.03934026571639 & 1.34065973428361 \tabularnewline
161 & 1.19 & 1.02155729633489 & 1.35844270366511 \tabularnewline
162 & 1.19 & 1.00548026311093 & 1.37451973688907 \tabularnewline
163 & 1.19 & 0.990695905247245 & 1.38930409475275 \tabularnewline
164 & 1.19 & 0.976934960472589 & 1.40306503952741 \tabularnewline
165 & 1.19 & 0.964010398574582 & 1.41598960142542 \tabularnewline
166 & 1.19 & 0.951786043994015 & 1.42821395600598 \tabularnewline
167 & 1.19 & 0.940159095183308 & 1.43984090481669 \tabularnewline
168 & 1.19 & 0.929049685565958 & 1.45095031443404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]157[/C][C]1.19[/C][C]1.11467013285819[/C][C]1.26532986714181[/C][/ROW]
[ROW][C]158[/C][C]1.19[/C][C]1.08346748023629[/C][C]1.29653251976371[/C][/ROW]
[ROW][C]159[/C][C]1.19[/C][C]1.05952484278298[/C][C]1.32047515721702[/C][/ROW]
[ROW][C]160[/C][C]1.19[/C][C]1.03934026571639[/C][C]1.34065973428361[/C][/ROW]
[ROW][C]161[/C][C]1.19[/C][C]1.02155729633489[/C][C]1.35844270366511[/C][/ROW]
[ROW][C]162[/C][C]1.19[/C][C]1.00548026311093[/C][C]1.37451973688907[/C][/ROW]
[ROW][C]163[/C][C]1.19[/C][C]0.990695905247245[/C][C]1.38930409475275[/C][/ROW]
[ROW][C]164[/C][C]1.19[/C][C]0.976934960472589[/C][C]1.40306503952741[/C][/ROW]
[ROW][C]165[/C][C]1.19[/C][C]0.964010398574582[/C][C]1.41598960142542[/C][/ROW]
[ROW][C]166[/C][C]1.19[/C][C]0.951786043994015[/C][C]1.42821395600598[/C][/ROW]
[ROW][C]167[/C][C]1.19[/C][C]0.940159095183308[/C][C]1.43984090481669[/C][/ROW]
[ROW][C]168[/C][C]1.19[/C][C]0.929049685565958[/C][C]1.45095031443404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
157	1.19	1.11467013285819	1.26532986714181
158	1.19	1.08346748023629	1.29653251976371
159	1.19	1.05952484278298	1.32047515721702
160	1.19	1.03934026571639	1.34065973428361
161	1.19	1.02155729633489	1.35844270366511
162	1.19	1.00548026311093	1.37451973688907
163	1.19	0.990695905247245	1.38930409475275
164	1.19	0.976934960472589	1.40306503952741
165	1.19	0.964010398574582	1.41598960142542
166	1.19	0.951786043994015	1.42821395600598
167	1.19	0.940159095183308	1.43984090481669
168	1.19	0.929049685565958	1.45095031443404

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code