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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

Sun, 01 Jun 2008 11:07:05 -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/Jun/01/t1212340062p87uuc6a25dt5gn.htm/, Retrieved Sat, 18 May 2024 13:45:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13715, Retrieved Sat, 18 May 2024 13:45:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

222

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

-     [Bootstrap Plot - Central Tendency] [Raf Mattheussen B...] [2008-05-28 17:41:26] [5082cdd0793c7a78ec5f799f0ca6d0b9]
- RMPD    [Exponential Smoothing] [raf mattheussen s...] [2008-06-01 17:07:05] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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=13715&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=13715&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13715&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=13715&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=13715&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13715&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	14.8	14.67	0.130000000000001
4	14.8	14.8	0
5	14.8	14.8	0
6	14.8	14.8	0
7	14.8	14.8	0
8	14.8	14.8	0
9	14.8	14.8	0
10	14.8	14.8	0
11	14.8	14.8	0
12	14.8	14.8	0
13	14.8	14.8	0
14	15.56	14.8	0.76
15	15.56	15.56	0
16	15.56	15.56	0
17	15.56	15.56	0
18	15.56	15.56	0
19	15.56	15.56	0
20	15.56	15.56	0
21	15.56	15.56	0
22	15.56	15.56	0
23	15.56	15.56	0
24	15.56	15.56	0
25	15.56	15.56	0
26	16.8	15.56	1.24
27	16.8	16.8	0
28	16.8	16.8	0
29	16.8	16.8	0
30	16.8	16.8	0
31	16.8	16.8	0
32	16.8	16.8	0
33	16.8	16.8	0
34	16.8	16.8	0
35	16.8	16.8	0
36	16.8	16.8	0
37	16.8	16.8	0
38	17.43	16.8	0.629999999999999
39	17.43	17.43	0
40	17.43	17.43	0
41	17.43	17.43	0
42	17.43	17.43	0
43	17.43	17.43	0
44	17.43	17.43	0
45	17.43	17.43	0
46	17.43	17.43	0
47	17.43	17.43	0
48	17.43	17.43	0
49	17.43	17.43	0
50	18.61	17.43	1.18
51	18.61	18.61	0
52	18.61	18.61	0
53	18.61	18.61	0
54	18.61	18.61	0
55	18.61	18.61	0
56	18.61	18.61	0
57	18.61	18.61	0
58	18.61	18.61	0
59	18.61	18.61	0
60	18.61	18.61	0
61	18.61	18.61	0
62	20	18.61	1.39
63	20	20	0
64	20	20	0
65	20	20	0
66	20	20	0
67	20	20	0
68	20	20	0
69	20	20	0
70	20	20	0
71	20	20	0
72	20	20	0
73	20	20	0
74	20.61	20	0.61
75	20.61	20.61	0
76	20.61	20.61	0
77	20.61	20.61	0
78	20.61	20.61	0
79	20.61	20.61	0
80	20.61	20.61	0
81	20.61	20.61	0
82	20.61	20.61	0
83	20.61	20.61	0
84	20.61	20.61	0
85	20.61	20.61	0
86	19.47	20.61	-1.14
87	19.47	19.47	0
88	19.47	19.47	0
89	19.47	19.47	0
90	19.47	19.47	0

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14.8 & 14.67 & 0.130000000000001 \tabularnewline
4 & 14.8 & 14.8 & 0 \tabularnewline
5 & 14.8 & 14.8 & 0 \tabularnewline
6 & 14.8 & 14.8 & 0 \tabularnewline
7 & 14.8 & 14.8 & 0 \tabularnewline
8 & 14.8 & 14.8 & 0 \tabularnewline
9 & 14.8 & 14.8 & 0 \tabularnewline
10 & 14.8 & 14.8 & 0 \tabularnewline
11 & 14.8 & 14.8 & 0 \tabularnewline
12 & 14.8 & 14.8 & 0 \tabularnewline
13 & 14.8 & 14.8 & 0 \tabularnewline
14 & 15.56 & 14.8 & 0.76 \tabularnewline
15 & 15.56 & 15.56 & 0 \tabularnewline
16 & 15.56 & 15.56 & 0 \tabularnewline
17 & 15.56 & 15.56 & 0 \tabularnewline
18 & 15.56 & 15.56 & 0 \tabularnewline
19 & 15.56 & 15.56 & 0 \tabularnewline
20 & 15.56 & 15.56 & 0 \tabularnewline
21 & 15.56 & 15.56 & 0 \tabularnewline
22 & 15.56 & 15.56 & 0 \tabularnewline
23 & 15.56 & 15.56 & 0 \tabularnewline
24 & 15.56 & 15.56 & 0 \tabularnewline
25 & 15.56 & 15.56 & 0 \tabularnewline
26 & 16.8 & 15.56 & 1.24 \tabularnewline
27 & 16.8 & 16.8 & 0 \tabularnewline
28 & 16.8 & 16.8 & 0 \tabularnewline
29 & 16.8 & 16.8 & 0 \tabularnewline
30 & 16.8 & 16.8 & 0 \tabularnewline
31 & 16.8 & 16.8 & 0 \tabularnewline
32 & 16.8 & 16.8 & 0 \tabularnewline
33 & 16.8 & 16.8 & 0 \tabularnewline
34 & 16.8 & 16.8 & 0 \tabularnewline
35 & 16.8 & 16.8 & 0 \tabularnewline
36 & 16.8 & 16.8 & 0 \tabularnewline
37 & 16.8 & 16.8 & 0 \tabularnewline
38 & 17.43 & 16.8 & 0.629999999999999 \tabularnewline
39 & 17.43 & 17.43 & 0 \tabularnewline
40 & 17.43 & 17.43 & 0 \tabularnewline
41 & 17.43 & 17.43 & 0 \tabularnewline
42 & 17.43 & 17.43 & 0 \tabularnewline
43 & 17.43 & 17.43 & 0 \tabularnewline
44 & 17.43 & 17.43 & 0 \tabularnewline
45 & 17.43 & 17.43 & 0 \tabularnewline
46 & 17.43 & 17.43 & 0 \tabularnewline
47 & 17.43 & 17.43 & 0 \tabularnewline
48 & 17.43 & 17.43 & 0 \tabularnewline
49 & 17.43 & 17.43 & 0 \tabularnewline
50 & 18.61 & 17.43 & 1.18 \tabularnewline
51 & 18.61 & 18.61 & 0 \tabularnewline
52 & 18.61 & 18.61 & 0 \tabularnewline
53 & 18.61 & 18.61 & 0 \tabularnewline
54 & 18.61 & 18.61 & 0 \tabularnewline
55 & 18.61 & 18.61 & 0 \tabularnewline
56 & 18.61 & 18.61 & 0 \tabularnewline
57 & 18.61 & 18.61 & 0 \tabularnewline
58 & 18.61 & 18.61 & 0 \tabularnewline
59 & 18.61 & 18.61 & 0 \tabularnewline
60 & 18.61 & 18.61 & 0 \tabularnewline
61 & 18.61 & 18.61 & 0 \tabularnewline
62 & 20 & 18.61 & 1.39 \tabularnewline
63 & 20 & 20 & 0 \tabularnewline
64 & 20 & 20 & 0 \tabularnewline
65 & 20 & 20 & 0 \tabularnewline
66 & 20 & 20 & 0 \tabularnewline
67 & 20 & 20 & 0 \tabularnewline
68 & 20 & 20 & 0 \tabularnewline
69 & 20 & 20 & 0 \tabularnewline
70 & 20 & 20 & 0 \tabularnewline
71 & 20 & 20 & 0 \tabularnewline
72 & 20 & 20 & 0 \tabularnewline
73 & 20 & 20 & 0 \tabularnewline
74 & 20.61 & 20 & 0.61 \tabularnewline
75 & 20.61 & 20.61 & 0 \tabularnewline
76 & 20.61 & 20.61 & 0 \tabularnewline
77 & 20.61 & 20.61 & 0 \tabularnewline
78 & 20.61 & 20.61 & 0 \tabularnewline
79 & 20.61 & 20.61 & 0 \tabularnewline
80 & 20.61 & 20.61 & 0 \tabularnewline
81 & 20.61 & 20.61 & 0 \tabularnewline
82 & 20.61 & 20.61 & 0 \tabularnewline
83 & 20.61 & 20.61 & 0 \tabularnewline
84 & 20.61 & 20.61 & 0 \tabularnewline
85 & 20.61 & 20.61 & 0 \tabularnewline
86 & 19.47 & 20.61 & -1.14 \tabularnewline
87 & 19.47 & 19.47 & 0 \tabularnewline
88 & 19.47 & 19.47 & 0 \tabularnewline
89 & 19.47 & 19.47 & 0 \tabularnewline
90 & 19.47 & 19.47 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13715&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]14.8[/C][C]14.67[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]4[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]14.8[/C][C]14.8[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]15.56[/C][C]14.8[/C][C]0.76[/C][/ROW]
[ROW][C]15[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]15.56[/C][C]15.56[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]16.8[/C][C]15.56[/C][C]1.24[/C][/ROW]
[ROW][C]27[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]16.8[/C][C]16.8[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]17.43[/C][C]16.8[/C][C]0.629999999999999[/C][/ROW]
[ROW][C]39[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]17.43[/C][C]17.43[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]18.61[/C][C]17.43[/C][C]1.18[/C][/ROW]
[ROW][C]51[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]18.61[/C][C]18.61[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]20[/C][C]18.61[/C][C]1.39[/C][/ROW]
[ROW][C]63[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]20[/C][C]20[/C][C]0[/C][/ROW]
[ROW][C]74[/C][C]20.61[/C][C]20[/C][C]0.61[/C][/ROW]
[ROW][C]75[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]77[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]82[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]83[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]84[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]85[/C][C]20.61[/C][C]20.61[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]19.47[/C][C]20.61[/C][C]-1.14[/C][/ROW]
[ROW][C]87[/C][C]19.47[/C][C]19.47[/C][C]0[/C][/ROW]
[ROW][C]88[/C][C]19.47[/C][C]19.47[/C][C]0[/C][/ROW]
[ROW][C]89[/C][C]19.47[/C][C]19.47[/C][C]0[/C][/ROW]
[ROW][C]90[/C][C]19.47[/C][C]19.47[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13715&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13715&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	14.8	14.67	0.130000000000001
4	14.8	14.8	0
5	14.8	14.8	0
6	14.8	14.8	0
7	14.8	14.8	0
8	14.8	14.8	0
9	14.8	14.8	0
10	14.8	14.8	0
11	14.8	14.8	0
12	14.8	14.8	0
13	14.8	14.8	0
14	15.56	14.8	0.76
15	15.56	15.56	0
16	15.56	15.56	0
17	15.56	15.56	0
18	15.56	15.56	0
19	15.56	15.56	0
20	15.56	15.56	0
21	15.56	15.56	0
22	15.56	15.56	0
23	15.56	15.56	0
24	15.56	15.56	0
25	15.56	15.56	0
26	16.8	15.56	1.24
27	16.8	16.8	0
28	16.8	16.8	0
29	16.8	16.8	0
30	16.8	16.8	0
31	16.8	16.8	0
32	16.8	16.8	0
33	16.8	16.8	0
34	16.8	16.8	0
35	16.8	16.8	0
36	16.8	16.8	0
37	16.8	16.8	0
38	17.43	16.8	0.629999999999999
39	17.43	17.43	0
40	17.43	17.43	0
41	17.43	17.43	0
42	17.43	17.43	0
43	17.43	17.43	0
44	17.43	17.43	0
45	17.43	17.43	0
46	17.43	17.43	0
47	17.43	17.43	0
48	17.43	17.43	0
49	17.43	17.43	0
50	18.61	17.43	1.18
51	18.61	18.61	0
52	18.61	18.61	0
53	18.61	18.61	0
54	18.61	18.61	0
55	18.61	18.61	0
56	18.61	18.61	0
57	18.61	18.61	0
58	18.61	18.61	0
59	18.61	18.61	0
60	18.61	18.61	0
61	18.61	18.61	0
62	20	18.61	1.39
63	20	20	0
64	20	20	0
65	20	20	0
66	20	20	0
67	20	20	0
68	20	20	0
69	20	20	0
70	20	20	0
71	20	20	0
72	20	20	0
73	20	20	0
74	20.61	20	0.61
75	20.61	20.61	0
76	20.61	20.61	0
77	20.61	20.61	0
78	20.61	20.61	0
79	20.61	20.61	0
80	20.61	20.61	0
81	20.61	20.61	0
82	20.61	20.61	0
83	20.61	20.61	0
84	20.61	20.61	0
85	20.61	20.61	0
86	19.47	20.61	-1.14
87	19.47	19.47	0
88	19.47	19.47	0
89	19.47	19.47	0
90	19.47	19.47	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
91	19.47	18.9036852124955	20.0363147875045
92	19.47	18.6691099469387	20.2708900530613
93	19.47	18.4891140149647	20.4508859850353
94	19.47	18.3373704249910	20.6026295750090
95	19.47	18.2036816384766	20.7363183615234
96	19.47	18.0828177368213	20.8571822631787
97	19.47	17.9716719084847	20.9683280915153
98	19.47	17.8682198938774	21.0717801061226
99	19.47	17.7710556374865	21.1689443625135
100	19.47	17.6791553988516	21.2608446011484
101	19.47	17.5917463366178	21.3482536633822
102	19.47	17.5082280299293	21.4317719700707

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 19.47 & 18.9036852124955 & 20.0363147875045 \tabularnewline
92 & 19.47 & 18.6691099469387 & 20.2708900530613 \tabularnewline
93 & 19.47 & 18.4891140149647 & 20.4508859850353 \tabularnewline
94 & 19.47 & 18.3373704249910 & 20.6026295750090 \tabularnewline
95 & 19.47 & 18.2036816384766 & 20.7363183615234 \tabularnewline
96 & 19.47 & 18.0828177368213 & 20.8571822631787 \tabularnewline
97 & 19.47 & 17.9716719084847 & 20.9683280915153 \tabularnewline
98 & 19.47 & 17.8682198938774 & 21.0717801061226 \tabularnewline
99 & 19.47 & 17.7710556374865 & 21.1689443625135 \tabularnewline
100 & 19.47 & 17.6791553988516 & 21.2608446011484 \tabularnewline
101 & 19.47 & 17.5917463366178 & 21.3482536633822 \tabularnewline
102 & 19.47 & 17.5082280299293 & 21.4317719700707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13715&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]91[/C][C]19.47[/C][C]18.9036852124955[/C][C]20.0363147875045[/C][/ROW]
[ROW][C]92[/C][C]19.47[/C][C]18.6691099469387[/C][C]20.2708900530613[/C][/ROW]
[ROW][C]93[/C][C]19.47[/C][C]18.4891140149647[/C][C]20.4508859850353[/C][/ROW]
[ROW][C]94[/C][C]19.47[/C][C]18.3373704249910[/C][C]20.6026295750090[/C][/ROW]
[ROW][C]95[/C][C]19.47[/C][C]18.2036816384766[/C][C]20.7363183615234[/C][/ROW]
[ROW][C]96[/C][C]19.47[/C][C]18.0828177368213[/C][C]20.8571822631787[/C][/ROW]
[ROW][C]97[/C][C]19.47[/C][C]17.9716719084847[/C][C]20.9683280915153[/C][/ROW]
[ROW][C]98[/C][C]19.47[/C][C]17.8682198938774[/C][C]21.0717801061226[/C][/ROW]
[ROW][C]99[/C][C]19.47[/C][C]17.7710556374865[/C][C]21.1689443625135[/C][/ROW]
[ROW][C]100[/C][C]19.47[/C][C]17.6791553988516[/C][C]21.2608446011484[/C][/ROW]
[ROW][C]101[/C][C]19.47[/C][C]17.5917463366178[/C][C]21.3482536633822[/C][/ROW]
[ROW][C]102[/C][C]19.47[/C][C]17.5082280299293[/C][C]21.4317719700707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13715&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13715&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
91	19.47	18.9036852124955	20.0363147875045
92	19.47	18.6691099469387	20.2708900530613
93	19.47	18.4891140149647	20.4508859850353
94	19.47	18.3373704249910	20.6026295750090
95	19.47	18.2036816384766	20.7363183615234
96	19.47	18.0828177368213	20.8571822631787
97	19.47	17.9716719084847	20.9683280915153
98	19.47	17.8682198938774	21.0717801061226
99	19.47	17.7710556374865	21.1689443625135
100	19.47	17.6791553988516	21.2608446011484
101	19.47	17.5917463366178	21.3482536633822
102	19.47	17.5082280299293	21.4317719700707

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