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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, 15 Jan 2012 14:07:05 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/15/t1326654449kgf8u3vyz4bqjsm.htm/, Retrieved Fri, 03 May 2024 10:18:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161119, Retrieved Fri, 03 May 2024 10:18:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

108

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

-       [Exponential Smoothing] [] [2012-01-15 19:07:05] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161119&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161119&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161119&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	'Gwilym Jenkins' @ jenkins.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161119&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=161119&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161119&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	14.87	14.76	0.109999999999998
4	14.94	14.92	0.0199999999999996
5	15.01	14.99	0.0199999999999996
6	15.03	15.06	-0.0300000000000011
7	15.04	15.08	-0.0400000000000009
8	15.05	15.09	-0.0399999999999991
9	15.06	15.1	-0.0400000000000009
10	15.11	15.11	-1.77635683940025e-15
11	15.23	15.16	0.0700000000000003
12	15.23	15.28	-0.0500000000000007
13	15.25	15.28	-0.0300000000000011
14	15.33	15.3	0.0299999999999994
15	15.38	15.38	0
16	15.52	15.43	0.0899999999999981
17	15.59	15.57	0.0199999999999996
18	15.66	15.64	0.0199999999999996
19	15.67	15.71	-0.0400000000000009
20	15.72	15.72	0
21	15.75	15.77	-0.0200000000000014
22	15.77	15.8	-0.0300000000000011
23	15.79	15.82	-0.0300000000000011
24	15.79	15.84	-0.0500000000000007
25	16.49	15.84	0.649999999999999
26	16.67	16.54	0.130000000000003
27	16.64	16.72	-0.0800000000000018
28	16.66	16.69	-0.0300000000000011
29	16.73	16.71	0.0199999999999996
30	16.76	16.78	-0.0199999999999996
31	16.76	16.81	-0.0500000000000007
32	16.76	16.81	-0.0500000000000007
33	16.76	16.81	-0.0500000000000007
34	16.79	16.81	-0.0200000000000031
35	16.8	16.84	-0.0399999999999991
36	16.81	16.85	-0.0400000000000027
37	16.91	16.86	0.0500000000000007
38	17.03	16.96	0.0700000000000003
39	17.12	17.08	0.0399999999999991
40	17.2	17.17	0.0299999999999976
41	17.25	17.25	0
42	17.25	17.3	-0.0500000000000007
43	17.3	17.3	0
44	17.27	17.35	-0.0800000000000018
45	17.31	17.32	-0.0100000000000016
46	17.33	17.36	-0.0300000000000011
47	17.35	17.38	-0.0299999999999976
48	17.36	17.4	-0.0400000000000027
49	17.39	17.41	-0.0199999999999996
50	17.42	17.44	-0.0199999999999996
51	17.54	17.47	0.0699999999999967
52	17.59	17.59	0
53	17.64	17.64	0
54	17.63	17.69	-0.0600000000000023
55	17.67	17.68	-0.00999999999999801
56	17.7	17.72	-0.0200000000000031
57	17.78	17.75	0.0300000000000011
58	17.87	17.83	0.0399999999999991
59	17.9	17.92	-0.0200000000000031
60	17.91	17.95	-0.0399999999999991
61	17.93	17.96	-0.0300000000000011
62	17.97	17.98	-0.0100000000000016
63	18.08	18.02	0.0599999999999987
64	18.08	18.13	-0.0500000000000007
65	18.09	18.13	-0.0399999999999991
66	18.09	18.14	-0.0500000000000007
67	18.12	18.14	-0.0199999999999996
68	18.13	18.17	-0.0400000000000027
69	18.15	18.18	-0.0300000000000011
70	18.17	18.2	-0.0299999999999976
71	18.19	18.22	-0.0300000000000011
72	18.2	18.24	-0.0400000000000027
73	18.21	18.25	-0.0399999999999991
74	18.39	18.26	0.129999999999999
75	18.48	18.44	0.0399999999999991
76	18.48	18.53	-0.0500000000000007
77	18.5	18.53	-0.0300000000000011
78	18.52	18.55	-0.0300000000000011
79	18.48	18.57	-0.0899999999999999
80	18.53	18.53	0
81	18.62	18.58	0.0399999999999991
82	18.65	18.67	-0.0200000000000031
83	18.7	18.7	0
84	18.72	18.75	-0.0300000000000011

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14.87 & 14.76 & 0.109999999999998 \tabularnewline
4 & 14.94 & 14.92 & 0.0199999999999996 \tabularnewline
5 & 15.01 & 14.99 & 0.0199999999999996 \tabularnewline
6 & 15.03 & 15.06 & -0.0300000000000011 \tabularnewline
7 & 15.04 & 15.08 & -0.0400000000000009 \tabularnewline
8 & 15.05 & 15.09 & -0.0399999999999991 \tabularnewline
9 & 15.06 & 15.1 & -0.0400000000000009 \tabularnewline
10 & 15.11 & 15.11 & -1.77635683940025e-15 \tabularnewline
11 & 15.23 & 15.16 & 0.0700000000000003 \tabularnewline
12 & 15.23 & 15.28 & -0.0500000000000007 \tabularnewline
13 & 15.25 & 15.28 & -0.0300000000000011 \tabularnewline
14 & 15.33 & 15.3 & 0.0299999999999994 \tabularnewline
15 & 15.38 & 15.38 & 0 \tabularnewline
16 & 15.52 & 15.43 & 0.0899999999999981 \tabularnewline
17 & 15.59 & 15.57 & 0.0199999999999996 \tabularnewline
18 & 15.66 & 15.64 & 0.0199999999999996 \tabularnewline
19 & 15.67 & 15.71 & -0.0400000000000009 \tabularnewline
20 & 15.72 & 15.72 & 0 \tabularnewline
21 & 15.75 & 15.77 & -0.0200000000000014 \tabularnewline
22 & 15.77 & 15.8 & -0.0300000000000011 \tabularnewline
23 & 15.79 & 15.82 & -0.0300000000000011 \tabularnewline
24 & 15.79 & 15.84 & -0.0500000000000007 \tabularnewline
25 & 16.49 & 15.84 & 0.649999999999999 \tabularnewline
26 & 16.67 & 16.54 & 0.130000000000003 \tabularnewline
27 & 16.64 & 16.72 & -0.0800000000000018 \tabularnewline
28 & 16.66 & 16.69 & -0.0300000000000011 \tabularnewline
29 & 16.73 & 16.71 & 0.0199999999999996 \tabularnewline
30 & 16.76 & 16.78 & -0.0199999999999996 \tabularnewline
31 & 16.76 & 16.81 & -0.0500000000000007 \tabularnewline
32 & 16.76 & 16.81 & -0.0500000000000007 \tabularnewline
33 & 16.76 & 16.81 & -0.0500000000000007 \tabularnewline
34 & 16.79 & 16.81 & -0.0200000000000031 \tabularnewline
35 & 16.8 & 16.84 & -0.0399999999999991 \tabularnewline
36 & 16.81 & 16.85 & -0.0400000000000027 \tabularnewline
37 & 16.91 & 16.86 & 0.0500000000000007 \tabularnewline
38 & 17.03 & 16.96 & 0.0700000000000003 \tabularnewline
39 & 17.12 & 17.08 & 0.0399999999999991 \tabularnewline
40 & 17.2 & 17.17 & 0.0299999999999976 \tabularnewline
41 & 17.25 & 17.25 & 0 \tabularnewline
42 & 17.25 & 17.3 & -0.0500000000000007 \tabularnewline
43 & 17.3 & 17.3 & 0 \tabularnewline
44 & 17.27 & 17.35 & -0.0800000000000018 \tabularnewline
45 & 17.31 & 17.32 & -0.0100000000000016 \tabularnewline
46 & 17.33 & 17.36 & -0.0300000000000011 \tabularnewline
47 & 17.35 & 17.38 & -0.0299999999999976 \tabularnewline
48 & 17.36 & 17.4 & -0.0400000000000027 \tabularnewline
49 & 17.39 & 17.41 & -0.0199999999999996 \tabularnewline
50 & 17.42 & 17.44 & -0.0199999999999996 \tabularnewline
51 & 17.54 & 17.47 & 0.0699999999999967 \tabularnewline
52 & 17.59 & 17.59 & 0 \tabularnewline
53 & 17.64 & 17.64 & 0 \tabularnewline
54 & 17.63 & 17.69 & -0.0600000000000023 \tabularnewline
55 & 17.67 & 17.68 & -0.00999999999999801 \tabularnewline
56 & 17.7 & 17.72 & -0.0200000000000031 \tabularnewline
57 & 17.78 & 17.75 & 0.0300000000000011 \tabularnewline
58 & 17.87 & 17.83 & 0.0399999999999991 \tabularnewline
59 & 17.9 & 17.92 & -0.0200000000000031 \tabularnewline
60 & 17.91 & 17.95 & -0.0399999999999991 \tabularnewline
61 & 17.93 & 17.96 & -0.0300000000000011 \tabularnewline
62 & 17.97 & 17.98 & -0.0100000000000016 \tabularnewline
63 & 18.08 & 18.02 & 0.0599999999999987 \tabularnewline
64 & 18.08 & 18.13 & -0.0500000000000007 \tabularnewline
65 & 18.09 & 18.13 & -0.0399999999999991 \tabularnewline
66 & 18.09 & 18.14 & -0.0500000000000007 \tabularnewline
67 & 18.12 & 18.14 & -0.0199999999999996 \tabularnewline
68 & 18.13 & 18.17 & -0.0400000000000027 \tabularnewline
69 & 18.15 & 18.18 & -0.0300000000000011 \tabularnewline
70 & 18.17 & 18.2 & -0.0299999999999976 \tabularnewline
71 & 18.19 & 18.22 & -0.0300000000000011 \tabularnewline
72 & 18.2 & 18.24 & -0.0400000000000027 \tabularnewline
73 & 18.21 & 18.25 & -0.0399999999999991 \tabularnewline
74 & 18.39 & 18.26 & 0.129999999999999 \tabularnewline
75 & 18.48 & 18.44 & 0.0399999999999991 \tabularnewline
76 & 18.48 & 18.53 & -0.0500000000000007 \tabularnewline
77 & 18.5 & 18.53 & -0.0300000000000011 \tabularnewline
78 & 18.52 & 18.55 & -0.0300000000000011 \tabularnewline
79 & 18.48 & 18.57 & -0.0899999999999999 \tabularnewline
80 & 18.53 & 18.53 & 0 \tabularnewline
81 & 18.62 & 18.58 & 0.0399999999999991 \tabularnewline
82 & 18.65 & 18.67 & -0.0200000000000031 \tabularnewline
83 & 18.7 & 18.7 & 0 \tabularnewline
84 & 18.72 & 18.75 & -0.0300000000000011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161119&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]14.87[/C][C]14.76[/C][C]0.109999999999998[/C][/ROW]
[ROW][C]4[/C][C]14.94[/C][C]14.92[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]5[/C][C]15.01[/C][C]14.99[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]6[/C][C]15.03[/C][C]15.06[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]7[/C][C]15.04[/C][C]15.08[/C][C]-0.0400000000000009[/C][/ROW]
[ROW][C]8[/C][C]15.05[/C][C]15.09[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]9[/C][C]15.06[/C][C]15.1[/C][C]-0.0400000000000009[/C][/ROW]
[ROW][C]10[/C][C]15.11[/C][C]15.11[/C][C]-1.77635683940025e-15[/C][/ROW]
[ROW][C]11[/C][C]15.23[/C][C]15.16[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]12[/C][C]15.23[/C][C]15.28[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]13[/C][C]15.25[/C][C]15.28[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]14[/C][C]15.33[/C][C]15.3[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]15[/C][C]15.38[/C][C]15.38[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]15.52[/C][C]15.43[/C][C]0.0899999999999981[/C][/ROW]
[ROW][C]17[/C][C]15.59[/C][C]15.57[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]18[/C][C]15.66[/C][C]15.64[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]19[/C][C]15.67[/C][C]15.71[/C][C]-0.0400000000000009[/C][/ROW]
[ROW][C]20[/C][C]15.72[/C][C]15.72[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]15.75[/C][C]15.77[/C][C]-0.0200000000000014[/C][/ROW]
[ROW][C]22[/C][C]15.77[/C][C]15.8[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]23[/C][C]15.79[/C][C]15.82[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]24[/C][C]15.79[/C][C]15.84[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]25[/C][C]16.49[/C][C]15.84[/C][C]0.649999999999999[/C][/ROW]
[ROW][C]26[/C][C]16.67[/C][C]16.54[/C][C]0.130000000000003[/C][/ROW]
[ROW][C]27[/C][C]16.64[/C][C]16.72[/C][C]-0.0800000000000018[/C][/ROW]
[ROW][C]28[/C][C]16.66[/C][C]16.69[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]29[/C][C]16.73[/C][C]16.71[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]30[/C][C]16.76[/C][C]16.78[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]31[/C][C]16.76[/C][C]16.81[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]32[/C][C]16.76[/C][C]16.81[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]33[/C][C]16.76[/C][C]16.81[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]34[/C][C]16.79[/C][C]16.81[/C][C]-0.0200000000000031[/C][/ROW]
[ROW][C]35[/C][C]16.8[/C][C]16.84[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]36[/C][C]16.81[/C][C]16.85[/C][C]-0.0400000000000027[/C][/ROW]
[ROW][C]37[/C][C]16.91[/C][C]16.86[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]38[/C][C]17.03[/C][C]16.96[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]39[/C][C]17.12[/C][C]17.08[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]40[/C][C]17.2[/C][C]17.17[/C][C]0.0299999999999976[/C][/ROW]
[ROW][C]41[/C][C]17.25[/C][C]17.25[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]17.25[/C][C]17.3[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]43[/C][C]17.3[/C][C]17.3[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]17.27[/C][C]17.35[/C][C]-0.0800000000000018[/C][/ROW]
[ROW][C]45[/C][C]17.31[/C][C]17.32[/C][C]-0.0100000000000016[/C][/ROW]
[ROW][C]46[/C][C]17.33[/C][C]17.36[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]47[/C][C]17.35[/C][C]17.38[/C][C]-0.0299999999999976[/C][/ROW]
[ROW][C]48[/C][C]17.36[/C][C]17.4[/C][C]-0.0400000000000027[/C][/ROW]
[ROW][C]49[/C][C]17.39[/C][C]17.41[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]50[/C][C]17.42[/C][C]17.44[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]51[/C][C]17.54[/C][C]17.47[/C][C]0.0699999999999967[/C][/ROW]
[ROW][C]52[/C][C]17.59[/C][C]17.59[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]17.64[/C][C]17.64[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]17.63[/C][C]17.69[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]55[/C][C]17.67[/C][C]17.68[/C][C]-0.00999999999999801[/C][/ROW]
[ROW][C]56[/C][C]17.7[/C][C]17.72[/C][C]-0.0200000000000031[/C][/ROW]
[ROW][C]57[/C][C]17.78[/C][C]17.75[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]58[/C][C]17.87[/C][C]17.83[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]59[/C][C]17.9[/C][C]17.92[/C][C]-0.0200000000000031[/C][/ROW]
[ROW][C]60[/C][C]17.91[/C][C]17.95[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]61[/C][C]17.93[/C][C]17.96[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]62[/C][C]17.97[/C][C]17.98[/C][C]-0.0100000000000016[/C][/ROW]
[ROW][C]63[/C][C]18.08[/C][C]18.02[/C][C]0.0599999999999987[/C][/ROW]
[ROW][C]64[/C][C]18.08[/C][C]18.13[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]65[/C][C]18.09[/C][C]18.13[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]66[/C][C]18.09[/C][C]18.14[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]67[/C][C]18.12[/C][C]18.14[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]68[/C][C]18.13[/C][C]18.17[/C][C]-0.0400000000000027[/C][/ROW]
[ROW][C]69[/C][C]18.15[/C][C]18.18[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]70[/C][C]18.17[/C][C]18.2[/C][C]-0.0299999999999976[/C][/ROW]
[ROW][C]71[/C][C]18.19[/C][C]18.22[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]72[/C][C]18.2[/C][C]18.24[/C][C]-0.0400000000000027[/C][/ROW]
[ROW][C]73[/C][C]18.21[/C][C]18.25[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]74[/C][C]18.39[/C][C]18.26[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]75[/C][C]18.48[/C][C]18.44[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]76[/C][C]18.48[/C][C]18.53[/C][C]-0.0500000000000007[/C][/ROW]
[ROW][C]77[/C][C]18.5[/C][C]18.53[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]78[/C][C]18.52[/C][C]18.55[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]79[/C][C]18.48[/C][C]18.57[/C][C]-0.0899999999999999[/C][/ROW]
[ROW][C]80[/C][C]18.53[/C][C]18.53[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]18.62[/C][C]18.58[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]82[/C][C]18.65[/C][C]18.67[/C][C]-0.0200000000000031[/C][/ROW]
[ROW][C]83[/C][C]18.7[/C][C]18.7[/C][C]0[/C][/ROW]
[ROW][C]84[/C][C]18.72[/C][C]18.75[/C][C]-0.0300000000000011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161119&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161119&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	14.87	14.76	0.109999999999998
4	14.94	14.92	0.0199999999999996
5	15.01	14.99	0.0199999999999996
6	15.03	15.06	-0.0300000000000011
7	15.04	15.08	-0.0400000000000009
8	15.05	15.09	-0.0399999999999991
9	15.06	15.1	-0.0400000000000009
10	15.11	15.11	-1.77635683940025e-15
11	15.23	15.16	0.0700000000000003
12	15.23	15.28	-0.0500000000000007
13	15.25	15.28	-0.0300000000000011
14	15.33	15.3	0.0299999999999994
15	15.38	15.38	0
16	15.52	15.43	0.0899999999999981
17	15.59	15.57	0.0199999999999996
18	15.66	15.64	0.0199999999999996
19	15.67	15.71	-0.0400000000000009
20	15.72	15.72	0
21	15.75	15.77	-0.0200000000000014
22	15.77	15.8	-0.0300000000000011
23	15.79	15.82	-0.0300000000000011
24	15.79	15.84	-0.0500000000000007
25	16.49	15.84	0.649999999999999
26	16.67	16.54	0.130000000000003
27	16.64	16.72	-0.0800000000000018
28	16.66	16.69	-0.0300000000000011
29	16.73	16.71	0.0199999999999996
30	16.76	16.78	-0.0199999999999996
31	16.76	16.81	-0.0500000000000007
32	16.76	16.81	-0.0500000000000007
33	16.76	16.81	-0.0500000000000007
34	16.79	16.81	-0.0200000000000031
35	16.8	16.84	-0.0399999999999991
36	16.81	16.85	-0.0400000000000027
37	16.91	16.86	0.0500000000000007
38	17.03	16.96	0.0700000000000003
39	17.12	17.08	0.0399999999999991
40	17.2	17.17	0.0299999999999976
41	17.25	17.25	0
42	17.25	17.3	-0.0500000000000007
43	17.3	17.3	0
44	17.27	17.35	-0.0800000000000018
45	17.31	17.32	-0.0100000000000016
46	17.33	17.36	-0.0300000000000011
47	17.35	17.38	-0.0299999999999976
48	17.36	17.4	-0.0400000000000027
49	17.39	17.41	-0.0199999999999996
50	17.42	17.44	-0.0199999999999996
51	17.54	17.47	0.0699999999999967
52	17.59	17.59	0
53	17.64	17.64	0
54	17.63	17.69	-0.0600000000000023
55	17.67	17.68	-0.00999999999999801
56	17.7	17.72	-0.0200000000000031
57	17.78	17.75	0.0300000000000011
58	17.87	17.83	0.0399999999999991
59	17.9	17.92	-0.0200000000000031
60	17.91	17.95	-0.0399999999999991
61	17.93	17.96	-0.0300000000000011
62	17.97	17.98	-0.0100000000000016
63	18.08	18.02	0.0599999999999987
64	18.08	18.13	-0.0500000000000007
65	18.09	18.13	-0.0399999999999991
66	18.09	18.14	-0.0500000000000007
67	18.12	18.14	-0.0199999999999996
68	18.13	18.17	-0.0400000000000027
69	18.15	18.18	-0.0300000000000011
70	18.17	18.2	-0.0299999999999976
71	18.19	18.22	-0.0300000000000011
72	18.2	18.24	-0.0400000000000027
73	18.21	18.25	-0.0399999999999991
74	18.39	18.26	0.129999999999999
75	18.48	18.44	0.0399999999999991
76	18.48	18.53	-0.0500000000000007
77	18.5	18.53	-0.0300000000000011
78	18.52	18.55	-0.0300000000000011
79	18.48	18.57	-0.0899999999999999
80	18.53	18.53	0
81	18.62	18.58	0.0399999999999991
82	18.65	18.67	-0.0200000000000031
83	18.7	18.7	0
84	18.72	18.75	-0.0300000000000011

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	18.77	18.6025829172346	18.9374170827654
86	18.82	18.5832364909802	19.0567635090198
87	18.87	18.5800251065953	19.1599748934047
88	18.92	18.5851658344692	19.2548341655308
89	18.97	18.5956440223418	19.3443559776582
90	19.02	18.6099135729994	19.4300864270006
91	19.07	18.6270560337788	19.5129439662212
92	19.12	18.6464729819604	19.5935270180396
93	19.17	18.6677487517038	19.6722512482962
94	19.22	18.6905806992404	19.7494193007596
95	19.27	18.7147403529713	19.8252596470287
96	19.32	18.7400502131907	19.8999497868093

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 18.77 & 18.6025829172346 & 18.9374170827654 \tabularnewline
86 & 18.82 & 18.5832364909802 & 19.0567635090198 \tabularnewline
87 & 18.87 & 18.5800251065953 & 19.1599748934047 \tabularnewline
88 & 18.92 & 18.5851658344692 & 19.2548341655308 \tabularnewline
89 & 18.97 & 18.5956440223418 & 19.3443559776582 \tabularnewline
90 & 19.02 & 18.6099135729994 & 19.4300864270006 \tabularnewline
91 & 19.07 & 18.6270560337788 & 19.5129439662212 \tabularnewline
92 & 19.12 & 18.6464729819604 & 19.5935270180396 \tabularnewline
93 & 19.17 & 18.6677487517038 & 19.6722512482962 \tabularnewline
94 & 19.22 & 18.6905806992404 & 19.7494193007596 \tabularnewline
95 & 19.27 & 18.7147403529713 & 19.8252596470287 \tabularnewline
96 & 19.32 & 18.7400502131907 & 19.8999497868093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161119&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]85[/C][C]18.77[/C][C]18.6025829172346[/C][C]18.9374170827654[/C][/ROW]
[ROW][C]86[/C][C]18.82[/C][C]18.5832364909802[/C][C]19.0567635090198[/C][/ROW]
[ROW][C]87[/C][C]18.87[/C][C]18.5800251065953[/C][C]19.1599748934047[/C][/ROW]
[ROW][C]88[/C][C]18.92[/C][C]18.5851658344692[/C][C]19.2548341655308[/C][/ROW]
[ROW][C]89[/C][C]18.97[/C][C]18.5956440223418[/C][C]19.3443559776582[/C][/ROW]
[ROW][C]90[/C][C]19.02[/C][C]18.6099135729994[/C][C]19.4300864270006[/C][/ROW]
[ROW][C]91[/C][C]19.07[/C][C]18.6270560337788[/C][C]19.5129439662212[/C][/ROW]
[ROW][C]92[/C][C]19.12[/C][C]18.6464729819604[/C][C]19.5935270180396[/C][/ROW]
[ROW][C]93[/C][C]19.17[/C][C]18.6677487517038[/C][C]19.6722512482962[/C][/ROW]
[ROW][C]94[/C][C]19.22[/C][C]18.6905806992404[/C][C]19.7494193007596[/C][/ROW]
[ROW][C]95[/C][C]19.27[/C][C]18.7147403529713[/C][C]19.8252596470287[/C][/ROW]
[ROW][C]96[/C][C]19.32[/C][C]18.7400502131907[/C][C]19.8999497868093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161119&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161119&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
85	18.77	18.6025829172346	18.9374170827654
86	18.82	18.5832364909802	19.0567635090198
87	18.87	18.5800251065953	19.1599748934047
88	18.92	18.5851658344692	19.2548341655308
89	18.97	18.5956440223418	19.3443559776582
90	19.02	18.6099135729994	19.4300864270006
91	19.07	18.6270560337788	19.5129439662212
92	19.12	18.6464729819604	19.5935270180396
93	19.17	18.6677487517038	19.6722512482962
94	19.22	18.6905806992404	19.7494193007596
95	19.27	18.7147403529713	19.8252596470287
96	19.32	18.7400502131907	19.8999497868093

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