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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

Thu, 22 May 2008 12:05:12 -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/22/t12114795701xewgwgjs7cai27.htm/, Retrieved Tue, 14 May 2024 18:22:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13036, Retrieved Tue, 14 May 2024 18:22:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

229

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

-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-22 18:05:12] [d25fa315f14c5a57000358f8421eb4b7] [Current]

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Dataseries X:

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Histogram

Boxplots

0.73
0.74
0.75
0.74
0.76
0.76
0.78
0.79
0.89
0.88
0.88
0.84
0.76
0.77
0.76
0.77
0.78
0.79
0.78
0.76
0.78
0.76
0.74
0.73
0.72
0.71
0.73
0.75
0.75
0.72
0.72
0.72
0.74
0.78
0.74
0.74
0.75
0.78
0.81
0.75
0.7
0.71
0.71
0.73
0.74
0.74
0.75
0.74
0.74
0.73
0.76
0.8
0.83
0.81
0.83
0.88
0.89
0.93
0.91
0.9
0.86
0.88
0.93
0.98
0.97
1.03
1.06
1.06
1.08
1.09
1.04
1

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13036&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13036&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13036&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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=13036&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=13036&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13036&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
3	0.75	0.74	0.01
4	0.74	0.75	-0.01
5	0.76	0.74	0.02
6	0.76	0.76	0
7	0.78	0.76	0.02
8	0.79	0.78	0.01
9	0.89	0.79	0.1
10	0.88	0.89	-0.01
11	0.88	0.88	0
12	0.84	0.88	-0.04
13	0.76	0.84	-0.08
14	0.77	0.76	0.01
15	0.76	0.77	-0.01
16	0.77	0.76	0.01
17	0.78	0.77	0.01
18	0.79	0.78	0.01
19	0.78	0.79	-0.01
20	0.76	0.78	-0.02
21	0.78	0.76	0.02
22	0.76	0.78	-0.02
23	0.74	0.76	-0.02
24	0.73	0.74	-0.01
25	0.72	0.73	-0.01
26	0.71	0.72	-0.01
27	0.73	0.71	0.02
28	0.75	0.73	0.02
29	0.75	0.75	0
30	0.72	0.75	-0.03
31	0.72	0.72	0
32	0.72	0.72	0
33	0.74	0.72	0.02
34	0.78	0.74	0.04
35	0.74	0.78	-0.04
36	0.74	0.74	0
37	0.75	0.74	0.01
38	0.78	0.75	0.03
39	0.81	0.78	0.03
40	0.75	0.81	-0.06
41	0.7	0.75	-0.05
42	0.71	0.7	0.01
43	0.71	0.71	0
44	0.73	0.71	0.02
45	0.74	0.73	0.01
46	0.74	0.74	0
47	0.75	0.74	0.01
48	0.74	0.75	-0.01
49	0.74	0.74	0
50	0.73	0.74	-0.01
51	0.76	0.73	0.03
52	0.8	0.76	0.04
53	0.83	0.8	0.0299999999999999
54	0.81	0.83	-0.0199999999999999
55	0.83	0.81	0.0199999999999999
56	0.88	0.83	0.05
57	0.89	0.88	0.01
58	0.93	0.89	0.04
59	0.91	0.93	-0.02
60	0.9	0.91	-0.01
61	0.86	0.9	-0.04
62	0.88	0.86	0.02
63	0.93	0.88	0.05
64	0.98	0.93	0.0499999999999999
65	0.97	0.98	-0.01
66	1.03	0.97	0.06
67	1.06	1.03	0.03
68	1.06	1.06	0
69	1.08	1.06	0.02
70	1.09	1.08	0.01
71	1.04	1.09	-0.05
72	1	1.04	-0.04

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.75 & 0.74 & 0.01 \tabularnewline
4 & 0.74 & 0.75 & -0.01 \tabularnewline
5 & 0.76 & 0.74 & 0.02 \tabularnewline
6 & 0.76 & 0.76 & 0 \tabularnewline
7 & 0.78 & 0.76 & 0.02 \tabularnewline
8 & 0.79 & 0.78 & 0.01 \tabularnewline
9 & 0.89 & 0.79 & 0.1 \tabularnewline
10 & 0.88 & 0.89 & -0.01 \tabularnewline
11 & 0.88 & 0.88 & 0 \tabularnewline
12 & 0.84 & 0.88 & -0.04 \tabularnewline
13 & 0.76 & 0.84 & -0.08 \tabularnewline
14 & 0.77 & 0.76 & 0.01 \tabularnewline
15 & 0.76 & 0.77 & -0.01 \tabularnewline
16 & 0.77 & 0.76 & 0.01 \tabularnewline
17 & 0.78 & 0.77 & 0.01 \tabularnewline
18 & 0.79 & 0.78 & 0.01 \tabularnewline
19 & 0.78 & 0.79 & -0.01 \tabularnewline
20 & 0.76 & 0.78 & -0.02 \tabularnewline
21 & 0.78 & 0.76 & 0.02 \tabularnewline
22 & 0.76 & 0.78 & -0.02 \tabularnewline
23 & 0.74 & 0.76 & -0.02 \tabularnewline
24 & 0.73 & 0.74 & -0.01 \tabularnewline
25 & 0.72 & 0.73 & -0.01 \tabularnewline
26 & 0.71 & 0.72 & -0.01 \tabularnewline
27 & 0.73 & 0.71 & 0.02 \tabularnewline
28 & 0.75 & 0.73 & 0.02 \tabularnewline
29 & 0.75 & 0.75 & 0 \tabularnewline
30 & 0.72 & 0.75 & -0.03 \tabularnewline
31 & 0.72 & 0.72 & 0 \tabularnewline
32 & 0.72 & 0.72 & 0 \tabularnewline
33 & 0.74 & 0.72 & 0.02 \tabularnewline
34 & 0.78 & 0.74 & 0.04 \tabularnewline
35 & 0.74 & 0.78 & -0.04 \tabularnewline
36 & 0.74 & 0.74 & 0 \tabularnewline
37 & 0.75 & 0.74 & 0.01 \tabularnewline
38 & 0.78 & 0.75 & 0.03 \tabularnewline
39 & 0.81 & 0.78 & 0.03 \tabularnewline
40 & 0.75 & 0.81 & -0.06 \tabularnewline
41 & 0.7 & 0.75 & -0.05 \tabularnewline
42 & 0.71 & 0.7 & 0.01 \tabularnewline
43 & 0.71 & 0.71 & 0 \tabularnewline
44 & 0.73 & 0.71 & 0.02 \tabularnewline
45 & 0.74 & 0.73 & 0.01 \tabularnewline
46 & 0.74 & 0.74 & 0 \tabularnewline
47 & 0.75 & 0.74 & 0.01 \tabularnewline
48 & 0.74 & 0.75 & -0.01 \tabularnewline
49 & 0.74 & 0.74 & 0 \tabularnewline
50 & 0.73 & 0.74 & -0.01 \tabularnewline
51 & 0.76 & 0.73 & 0.03 \tabularnewline
52 & 0.8 & 0.76 & 0.04 \tabularnewline
53 & 0.83 & 0.8 & 0.0299999999999999 \tabularnewline
54 & 0.81 & 0.83 & -0.0199999999999999 \tabularnewline
55 & 0.83 & 0.81 & 0.0199999999999999 \tabularnewline
56 & 0.88 & 0.83 & 0.05 \tabularnewline
57 & 0.89 & 0.88 & 0.01 \tabularnewline
58 & 0.93 & 0.89 & 0.04 \tabularnewline
59 & 0.91 & 0.93 & -0.02 \tabularnewline
60 & 0.9 & 0.91 & -0.01 \tabularnewline
61 & 0.86 & 0.9 & -0.04 \tabularnewline
62 & 0.88 & 0.86 & 0.02 \tabularnewline
63 & 0.93 & 0.88 & 0.05 \tabularnewline
64 & 0.98 & 0.93 & 0.0499999999999999 \tabularnewline
65 & 0.97 & 0.98 & -0.01 \tabularnewline
66 & 1.03 & 0.97 & 0.06 \tabularnewline
67 & 1.06 & 1.03 & 0.03 \tabularnewline
68 & 1.06 & 1.06 & 0 \tabularnewline
69 & 1.08 & 1.06 & 0.02 \tabularnewline
70 & 1.09 & 1.08 & 0.01 \tabularnewline
71 & 1.04 & 1.09 & -0.05 \tabularnewline
72 & 1 & 1.04 & -0.04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13036&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]0.75[/C][C]0.74[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]0.74[/C][C]0.75[/C][C]-0.01[/C][/ROW]
[ROW][C]5[/C][C]0.76[/C][C]0.74[/C][C]0.02[/C][/ROW]
[ROW][C]6[/C][C]0.76[/C][C]0.76[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.78[/C][C]0.76[/C][C]0.02[/C][/ROW]
[ROW][C]8[/C][C]0.79[/C][C]0.78[/C][C]0.01[/C][/ROW]
[ROW][C]9[/C][C]0.89[/C][C]0.79[/C][C]0.1[/C][/ROW]
[ROW][C]10[/C][C]0.88[/C][C]0.89[/C][C]-0.01[/C][/ROW]
[ROW][C]11[/C][C]0.88[/C][C]0.88[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.84[/C][C]0.88[/C][C]-0.04[/C][/ROW]
[ROW][C]13[/C][C]0.76[/C][C]0.84[/C][C]-0.08[/C][/ROW]
[ROW][C]14[/C][C]0.77[/C][C]0.76[/C][C]0.01[/C][/ROW]
[ROW][C]15[/C][C]0.76[/C][C]0.77[/C][C]-0.01[/C][/ROW]
[ROW][C]16[/C][C]0.77[/C][C]0.76[/C][C]0.01[/C][/ROW]
[ROW][C]17[/C][C]0.78[/C][C]0.77[/C][C]0.01[/C][/ROW]
[ROW][C]18[/C][C]0.79[/C][C]0.78[/C][C]0.01[/C][/ROW]
[ROW][C]19[/C][C]0.78[/C][C]0.79[/C][C]-0.01[/C][/ROW]
[ROW][C]20[/C][C]0.76[/C][C]0.78[/C][C]-0.02[/C][/ROW]
[ROW][C]21[/C][C]0.78[/C][C]0.76[/C][C]0.02[/C][/ROW]
[ROW][C]22[/C][C]0.76[/C][C]0.78[/C][C]-0.02[/C][/ROW]
[ROW][C]23[/C][C]0.74[/C][C]0.76[/C][C]-0.02[/C][/ROW]
[ROW][C]24[/C][C]0.73[/C][C]0.74[/C][C]-0.01[/C][/ROW]
[ROW][C]25[/C][C]0.72[/C][C]0.73[/C][C]-0.01[/C][/ROW]
[ROW][C]26[/C][C]0.71[/C][C]0.72[/C][C]-0.01[/C][/ROW]
[ROW][C]27[/C][C]0.73[/C][C]0.71[/C][C]0.02[/C][/ROW]
[ROW][C]28[/C][C]0.75[/C][C]0.73[/C][C]0.02[/C][/ROW]
[ROW][C]29[/C][C]0.75[/C][C]0.75[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]0.72[/C][C]0.75[/C][C]-0.03[/C][/ROW]
[ROW][C]31[/C][C]0.72[/C][C]0.72[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]0.72[/C][C]0.72[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]0.74[/C][C]0.72[/C][C]0.02[/C][/ROW]
[ROW][C]34[/C][C]0.78[/C][C]0.74[/C][C]0.04[/C][/ROW]
[ROW][C]35[/C][C]0.74[/C][C]0.78[/C][C]-0.04[/C][/ROW]
[ROW][C]36[/C][C]0.74[/C][C]0.74[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]0.75[/C][C]0.74[/C][C]0.01[/C][/ROW]
[ROW][C]38[/C][C]0.78[/C][C]0.75[/C][C]0.03[/C][/ROW]
[ROW][C]39[/C][C]0.81[/C][C]0.78[/C][C]0.03[/C][/ROW]
[ROW][C]40[/C][C]0.75[/C][C]0.81[/C][C]-0.06[/C][/ROW]
[ROW][C]41[/C][C]0.7[/C][C]0.75[/C][C]-0.05[/C][/ROW]
[ROW][C]42[/C][C]0.71[/C][C]0.7[/C][C]0.01[/C][/ROW]
[ROW][C]43[/C][C]0.71[/C][C]0.71[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]0.73[/C][C]0.71[/C][C]0.02[/C][/ROW]
[ROW][C]45[/C][C]0.74[/C][C]0.73[/C][C]0.01[/C][/ROW]
[ROW][C]46[/C][C]0.74[/C][C]0.74[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]0.75[/C][C]0.74[/C][C]0.01[/C][/ROW]
[ROW][C]48[/C][C]0.74[/C][C]0.75[/C][C]-0.01[/C][/ROW]
[ROW][C]49[/C][C]0.74[/C][C]0.74[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.73[/C][C]0.74[/C][C]-0.01[/C][/ROW]
[ROW][C]51[/C][C]0.76[/C][C]0.73[/C][C]0.03[/C][/ROW]
[ROW][C]52[/C][C]0.8[/C][C]0.76[/C][C]0.04[/C][/ROW]
[ROW][C]53[/C][C]0.83[/C][C]0.8[/C][C]0.0299999999999999[/C][/ROW]
[ROW][C]54[/C][C]0.81[/C][C]0.83[/C][C]-0.0199999999999999[/C][/ROW]
[ROW][C]55[/C][C]0.83[/C][C]0.81[/C][C]0.0199999999999999[/C][/ROW]
[ROW][C]56[/C][C]0.88[/C][C]0.83[/C][C]0.05[/C][/ROW]
[ROW][C]57[/C][C]0.89[/C][C]0.88[/C][C]0.01[/C][/ROW]
[ROW][C]58[/C][C]0.93[/C][C]0.89[/C][C]0.04[/C][/ROW]
[ROW][C]59[/C][C]0.91[/C][C]0.93[/C][C]-0.02[/C][/ROW]
[ROW][C]60[/C][C]0.9[/C][C]0.91[/C][C]-0.01[/C][/ROW]
[ROW][C]61[/C][C]0.86[/C][C]0.9[/C][C]-0.04[/C][/ROW]
[ROW][C]62[/C][C]0.88[/C][C]0.86[/C][C]0.02[/C][/ROW]
[ROW][C]63[/C][C]0.93[/C][C]0.88[/C][C]0.05[/C][/ROW]
[ROW][C]64[/C][C]0.98[/C][C]0.93[/C][C]0.0499999999999999[/C][/ROW]
[ROW][C]65[/C][C]0.97[/C][C]0.98[/C][C]-0.01[/C][/ROW]
[ROW][C]66[/C][C]1.03[/C][C]0.97[/C][C]0.06[/C][/ROW]
[ROW][C]67[/C][C]1.06[/C][C]1.03[/C][C]0.03[/C][/ROW]
[ROW][C]68[/C][C]1.06[/C][C]1.06[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]1.08[/C][C]1.06[/C][C]0.02[/C][/ROW]
[ROW][C]70[/C][C]1.09[/C][C]1.08[/C][C]0.01[/C][/ROW]
[ROW][C]71[/C][C]1.04[/C][C]1.09[/C][C]-0.05[/C][/ROW]
[ROW][C]72[/C][C]1[/C][C]1.04[/C][C]-0.04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13036&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13036&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	0.75	0.74	0.01
4	0.74	0.75	-0.01
5	0.76	0.74	0.02
6	0.76	0.76	0
7	0.78	0.76	0.02
8	0.79	0.78	0.01
9	0.89	0.79	0.1
10	0.88	0.89	-0.01
11	0.88	0.88	0
12	0.84	0.88	-0.04
13	0.76	0.84	-0.08
14	0.77	0.76	0.01
15	0.76	0.77	-0.01
16	0.77	0.76	0.01
17	0.78	0.77	0.01
18	0.79	0.78	0.01
19	0.78	0.79	-0.01
20	0.76	0.78	-0.02
21	0.78	0.76	0.02
22	0.76	0.78	-0.02
23	0.74	0.76	-0.02
24	0.73	0.74	-0.01
25	0.72	0.73	-0.01
26	0.71	0.72	-0.01
27	0.73	0.71	0.02
28	0.75	0.73	0.02
29	0.75	0.75	0
30	0.72	0.75	-0.03
31	0.72	0.72	0
32	0.72	0.72	0
33	0.74	0.72	0.02
34	0.78	0.74	0.04
35	0.74	0.78	-0.04
36	0.74	0.74	0
37	0.75	0.74	0.01
38	0.78	0.75	0.03
39	0.81	0.78	0.03
40	0.75	0.81	-0.06
41	0.7	0.75	-0.05
42	0.71	0.7	0.01
43	0.71	0.71	0
44	0.73	0.71	0.02
45	0.74	0.73	0.01
46	0.74	0.74	0
47	0.75	0.74	0.01
48	0.74	0.75	-0.01
49	0.74	0.74	0
50	0.73	0.74	-0.01
51	0.76	0.73	0.03
52	0.8	0.76	0.04
53	0.83	0.8	0.0299999999999999
54	0.81	0.83	-0.0199999999999999
55	0.83	0.81	0.0199999999999999
56	0.88	0.83	0.05
57	0.89	0.88	0.01
58	0.93	0.89	0.04
59	0.91	0.93	-0.02
60	0.9	0.91	-0.01
61	0.86	0.9	-0.04
62	0.88	0.86	0.02
63	0.93	0.88	0.05
64	0.98	0.93	0.0499999999999999
65	0.97	0.98	-0.01
66	1.03	0.97	0.06
67	1.06	1.03	0.03
68	1.06	1.06	0
69	1.08	1.06	0.02
70	1.09	1.08	0.01
71	1.04	1.09	-0.05
72	1	1.04	-0.04

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1	0.942187304387958	1.05781269561204
74	1	0.918240501788102	1.08175949821190
75	1	0.899865473877429	1.10013452612257
76	1	0.884374608775916	1.11562539122408
77	1	0.87072688264897	1.12927311735103
78	1	0.858388395095657	1.14161160490434
79	1	0.847041984788261	1.15295801521174
80	1	0.836481003576205	1.16351899642380
81	1	0.826561913163874	1.17343808683613
82	1	0.817180204191924	1.18281979580808
83	1	0.80825698053583	1.19174301946417
84	1	0.799730947754857	1.20026905224514

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1 & 0.942187304387958 & 1.05781269561204 \tabularnewline
74 & 1 & 0.918240501788102 & 1.08175949821190 \tabularnewline
75 & 1 & 0.899865473877429 & 1.10013452612257 \tabularnewline
76 & 1 & 0.884374608775916 & 1.11562539122408 \tabularnewline
77 & 1 & 0.87072688264897 & 1.12927311735103 \tabularnewline
78 & 1 & 0.858388395095657 & 1.14161160490434 \tabularnewline
79 & 1 & 0.847041984788261 & 1.15295801521174 \tabularnewline
80 & 1 & 0.836481003576205 & 1.16351899642380 \tabularnewline
81 & 1 & 0.826561913163874 & 1.17343808683613 \tabularnewline
82 & 1 & 0.817180204191924 & 1.18281979580808 \tabularnewline
83 & 1 & 0.80825698053583 & 1.19174301946417 \tabularnewline
84 & 1 & 0.799730947754857 & 1.20026905224514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13036&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[/C][C]0.942187304387958[/C][C]1.05781269561204[/C][/ROW]
[ROW][C]74[/C][C]1[/C][C]0.918240501788102[/C][C]1.08175949821190[/C][/ROW]
[ROW][C]75[/C][C]1[/C][C]0.899865473877429[/C][C]1.10013452612257[/C][/ROW]
[ROW][C]76[/C][C]1[/C][C]0.884374608775916[/C][C]1.11562539122408[/C][/ROW]
[ROW][C]77[/C][C]1[/C][C]0.87072688264897[/C][C]1.12927311735103[/C][/ROW]
[ROW][C]78[/C][C]1[/C][C]0.858388395095657[/C][C]1.14161160490434[/C][/ROW]
[ROW][C]79[/C][C]1[/C][C]0.847041984788261[/C][C]1.15295801521174[/C][/ROW]
[ROW][C]80[/C][C]1[/C][C]0.836481003576205[/C][C]1.16351899642380[/C][/ROW]
[ROW][C]81[/C][C]1[/C][C]0.826561913163874[/C][C]1.17343808683613[/C][/ROW]
[ROW][C]82[/C][C]1[/C][C]0.817180204191924[/C][C]1.18281979580808[/C][/ROW]
[ROW][C]83[/C][C]1[/C][C]0.80825698053583[/C][C]1.19174301946417[/C][/ROW]
[ROW][C]84[/C][C]1[/C][C]0.799730947754857[/C][C]1.20026905224514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13036&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13036&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	0.942187304387958	1.05781269561204
74	1	0.918240501788102	1.08175949821190
75	1	0.899865473877429	1.10013452612257
76	1	0.884374608775916	1.11562539122408
77	1	0.87072688264897	1.12927311735103
78	1	0.858388395095657	1.14161160490434
79	1	0.847041984788261	1.15295801521174
80	1	0.836481003576205	1.16351899642380
81	1	0.826561913163874	1.17343808683613
82	1	0.817180204191924	1.18281979580808
83	1	0.80825698053583	1.19174301946417
84	1	0.799730947754857	1.20026905224514

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=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