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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, 12 Jan 2014 07:28:38 -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/2014/Jan/12/t13895297585ijhmbuwugrcx88.htm/, Retrieved Tue, 10 Feb 2026 11:38:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232993, Retrieved Tue, 10 Feb 2026 11:38:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

336

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

-     [Classical Decomposition] [] [2014-01-12 12:09:27] [69f0adfa1a431ec50764c1a969b4d177]
- RMPD  [Exponential Smoothing] [] [2014-01-12 12:22:23] [7374732ae26351929a6f66a8cd8fe417]
- R PD      [Exponential Smoothing] [] [2014-01-12 12:28:38] [f824ea295e177f9d3dd7528a75f4b680] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232993&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]4 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=232993&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232993&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	4 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=232993&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=232993&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232993&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	103.5	103.55	-0.0499999999999829
4	103.5	103.56	-0.0599999999999881
5	103.5	103.56	-0.0599999999999881
6	103.5	103.56	-0.0599999999999881
7	103.54	103.56	-0.0199999999999818
8	103.71	103.6	0.109999999999999
9	103.76	103.77	-0.00999999999997669
10	103.76	103.82	-0.0599999999999881
11	103.76	103.82	-0.0599999999999881
12	103.82	103.82	0
13	105.11	103.88	1.23000000000002
14	105.58	105.17	0.410000000000011
15	105.91	105.64	0.27000000000001
16	105.92	105.97	-0.0499999999999829
17	105.92	105.98	-0.0599999999999881
18	105.92	105.98	-0.0599999999999881
19	105.96	105.98	-0.019999999999996
20	105.98	106.02	-0.0399999999999778
21	105.98	106.04	-0.0599999999999881
22	105.98	106.04	-0.0599999999999881
23	106.01	106.04	-0.0299999999999869
24	106.01	106.07	-0.0599999999999881
25	106.91	106.07	0.840000000000003
26	107.11	106.97	0.140000000000015
27	107.18	107.17	0.0100000000000193
28	107.2	107.24	-0.039999999999992
29	107.35	107.26	0.0900000000000034
30	107.35	107.41	-0.0599999999999881
31	107.35	107.41	-0.0599999999999881
32	107.52	107.41	0.110000000000014
33	107.56	107.58	-0.0199999999999818
34	107.55	107.62	-0.0699999999999932
35	107.6	107.61	-0.00999999999999091
36	107.6	107.66	-0.0599999999999881
37	110.04	107.66	2.38000000000002
38	110.27	110.1	0.170000000000002
39	110.33	110.33	1.4210854715202e-14
40	110.33	110.39	-0.0599999999999881
41	110.33	110.39	-0.0599999999999881
42	110.33	110.39	-0.0599999999999881
43	110.33	110.39	-0.0599999999999881
44	110.35	110.39	-0.039999999999992
45	110.38	110.41	-0.0299999999999869
46	110.54	110.44	0.100000000000023
47	110.54	110.6	-0.0599999999999881
48	110.54	110.6	-0.0599999999999881
49	110.54	110.6	-0.0599999999999881
50	106.74	110.6	-3.86
51	106.78	106.8	-0.0199999999999818
52	106.75	106.84	-0.0899999999999892
53	106.75	106.81	-0.0599999999999881
54	106.75	106.81	-0.0599999999999881
55	106.82	106.81	0.0100000000000051
56	107.08	106.88	0.200000000000017
57	107.25	107.14	0.110000000000014
58	107.28	107.31	-0.0299999999999869
59	107.28	107.34	-0.0599999999999881
60	107.28	107.34	-0.0599999999999881
61	108.44	107.34	1.10000000000001
62	109.33	108.5	0.830000000000013
63	109.44	109.39	0.0500000000000114
64	109.44	109.5	-0.0599999999999881
65	109.45	109.5	-0.0499999999999829
66	109.45	109.51	-0.0599999999999881
67	109.45	109.51	-0.0599999999999881
68	109.45	109.51	-0.0599999999999881
69	109.46	109.51	-0.0499999999999972
70	109.46	109.52	-0.0599999999999881
71	109.46	109.52	-0.0599999999999881
72	109.46	109.52	-0.0599999999999881
73	110.95	109.52	1.43000000000002
74	110.95	111.01	-0.0599999999999881
75	110.95	111.01	-0.0599999999999881
76	110.95	111.01	-0.0599999999999881
77	110.95	111.01	-0.0599999999999881
78	110.95	111.01	-0.0599999999999881
79	110.95	111.01	-0.0599999999999881
80	110.95	111.01	-0.0599999999999881
81	110.97	111.01	-0.039999999999992
82	110.97	111.03	-0.0599999999999881
83	110.97	111.03	-0.0599999999999881
84	111	111.03	-0.0299999999999869

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 103.5 & 103.55 & -0.0499999999999829 \tabularnewline
4 & 103.5 & 103.56 & -0.0599999999999881 \tabularnewline
5 & 103.5 & 103.56 & -0.0599999999999881 \tabularnewline
6 & 103.5 & 103.56 & -0.0599999999999881 \tabularnewline
7 & 103.54 & 103.56 & -0.0199999999999818 \tabularnewline
8 & 103.71 & 103.6 & 0.109999999999999 \tabularnewline
9 & 103.76 & 103.77 & -0.00999999999997669 \tabularnewline
10 & 103.76 & 103.82 & -0.0599999999999881 \tabularnewline
11 & 103.76 & 103.82 & -0.0599999999999881 \tabularnewline
12 & 103.82 & 103.82 & 0 \tabularnewline
13 & 105.11 & 103.88 & 1.23000000000002 \tabularnewline
14 & 105.58 & 105.17 & 0.410000000000011 \tabularnewline
15 & 105.91 & 105.64 & 0.27000000000001 \tabularnewline
16 & 105.92 & 105.97 & -0.0499999999999829 \tabularnewline
17 & 105.92 & 105.98 & -0.0599999999999881 \tabularnewline
18 & 105.92 & 105.98 & -0.0599999999999881 \tabularnewline
19 & 105.96 & 105.98 & -0.019999999999996 \tabularnewline
20 & 105.98 & 106.02 & -0.0399999999999778 \tabularnewline
21 & 105.98 & 106.04 & -0.0599999999999881 \tabularnewline
22 & 105.98 & 106.04 & -0.0599999999999881 \tabularnewline
23 & 106.01 & 106.04 & -0.0299999999999869 \tabularnewline
24 & 106.01 & 106.07 & -0.0599999999999881 \tabularnewline
25 & 106.91 & 106.07 & 0.840000000000003 \tabularnewline
26 & 107.11 & 106.97 & 0.140000000000015 \tabularnewline
27 & 107.18 & 107.17 & 0.0100000000000193 \tabularnewline
28 & 107.2 & 107.24 & -0.039999999999992 \tabularnewline
29 & 107.35 & 107.26 & 0.0900000000000034 \tabularnewline
30 & 107.35 & 107.41 & -0.0599999999999881 \tabularnewline
31 & 107.35 & 107.41 & -0.0599999999999881 \tabularnewline
32 & 107.52 & 107.41 & 0.110000000000014 \tabularnewline
33 & 107.56 & 107.58 & -0.0199999999999818 \tabularnewline
34 & 107.55 & 107.62 & -0.0699999999999932 \tabularnewline
35 & 107.6 & 107.61 & -0.00999999999999091 \tabularnewline
36 & 107.6 & 107.66 & -0.0599999999999881 \tabularnewline
37 & 110.04 & 107.66 & 2.38000000000002 \tabularnewline
38 & 110.27 & 110.1 & 0.170000000000002 \tabularnewline
39 & 110.33 & 110.33 & 1.4210854715202e-14 \tabularnewline
40 & 110.33 & 110.39 & -0.0599999999999881 \tabularnewline
41 & 110.33 & 110.39 & -0.0599999999999881 \tabularnewline
42 & 110.33 & 110.39 & -0.0599999999999881 \tabularnewline
43 & 110.33 & 110.39 & -0.0599999999999881 \tabularnewline
44 & 110.35 & 110.39 & -0.039999999999992 \tabularnewline
45 & 110.38 & 110.41 & -0.0299999999999869 \tabularnewline
46 & 110.54 & 110.44 & 0.100000000000023 \tabularnewline
47 & 110.54 & 110.6 & -0.0599999999999881 \tabularnewline
48 & 110.54 & 110.6 & -0.0599999999999881 \tabularnewline
49 & 110.54 & 110.6 & -0.0599999999999881 \tabularnewline
50 & 106.74 & 110.6 & -3.86 \tabularnewline
51 & 106.78 & 106.8 & -0.0199999999999818 \tabularnewline
52 & 106.75 & 106.84 & -0.0899999999999892 \tabularnewline
53 & 106.75 & 106.81 & -0.0599999999999881 \tabularnewline
54 & 106.75 & 106.81 & -0.0599999999999881 \tabularnewline
55 & 106.82 & 106.81 & 0.0100000000000051 \tabularnewline
56 & 107.08 & 106.88 & 0.200000000000017 \tabularnewline
57 & 107.25 & 107.14 & 0.110000000000014 \tabularnewline
58 & 107.28 & 107.31 & -0.0299999999999869 \tabularnewline
59 & 107.28 & 107.34 & -0.0599999999999881 \tabularnewline
60 & 107.28 & 107.34 & -0.0599999999999881 \tabularnewline
61 & 108.44 & 107.34 & 1.10000000000001 \tabularnewline
62 & 109.33 & 108.5 & 0.830000000000013 \tabularnewline
63 & 109.44 & 109.39 & 0.0500000000000114 \tabularnewline
64 & 109.44 & 109.5 & -0.0599999999999881 \tabularnewline
65 & 109.45 & 109.5 & -0.0499999999999829 \tabularnewline
66 & 109.45 & 109.51 & -0.0599999999999881 \tabularnewline
67 & 109.45 & 109.51 & -0.0599999999999881 \tabularnewline
68 & 109.45 & 109.51 & -0.0599999999999881 \tabularnewline
69 & 109.46 & 109.51 & -0.0499999999999972 \tabularnewline
70 & 109.46 & 109.52 & -0.0599999999999881 \tabularnewline
71 & 109.46 & 109.52 & -0.0599999999999881 \tabularnewline
72 & 109.46 & 109.52 & -0.0599999999999881 \tabularnewline
73 & 110.95 & 109.52 & 1.43000000000002 \tabularnewline
74 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
75 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
76 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
77 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
78 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
79 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
80 & 110.95 & 111.01 & -0.0599999999999881 \tabularnewline
81 & 110.97 & 111.01 & -0.039999999999992 \tabularnewline
82 & 110.97 & 111.03 & -0.0599999999999881 \tabularnewline
83 & 110.97 & 111.03 & -0.0599999999999881 \tabularnewline
84 & 111 & 111.03 & -0.0299999999999869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232993&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]103.5[/C][C]103.55[/C][C]-0.0499999999999829[/C][/ROW]
[ROW][C]4[/C][C]103.5[/C][C]103.56[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]5[/C][C]103.5[/C][C]103.56[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]6[/C][C]103.5[/C][C]103.56[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]7[/C][C]103.54[/C][C]103.56[/C][C]-0.0199999999999818[/C][/ROW]
[ROW][C]8[/C][C]103.71[/C][C]103.6[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]9[/C][C]103.76[/C][C]103.77[/C][C]-0.00999999999997669[/C][/ROW]
[ROW][C]10[/C][C]103.76[/C][C]103.82[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]11[/C][C]103.76[/C][C]103.82[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]12[/C][C]103.82[/C][C]103.82[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]105.11[/C][C]103.88[/C][C]1.23000000000002[/C][/ROW]
[ROW][C]14[/C][C]105.58[/C][C]105.17[/C][C]0.410000000000011[/C][/ROW]
[ROW][C]15[/C][C]105.91[/C][C]105.64[/C][C]0.27000000000001[/C][/ROW]
[ROW][C]16[/C][C]105.92[/C][C]105.97[/C][C]-0.0499999999999829[/C][/ROW]
[ROW][C]17[/C][C]105.92[/C][C]105.98[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]18[/C][C]105.92[/C][C]105.98[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]19[/C][C]105.96[/C][C]105.98[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]20[/C][C]105.98[/C][C]106.02[/C][C]-0.0399999999999778[/C][/ROW]
[ROW][C]21[/C][C]105.98[/C][C]106.04[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]22[/C][C]105.98[/C][C]106.04[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]23[/C][C]106.01[/C][C]106.04[/C][C]-0.0299999999999869[/C][/ROW]
[ROW][C]24[/C][C]106.01[/C][C]106.07[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]25[/C][C]106.91[/C][C]106.07[/C][C]0.840000000000003[/C][/ROW]
[ROW][C]26[/C][C]107.11[/C][C]106.97[/C][C]0.140000000000015[/C][/ROW]
[ROW][C]27[/C][C]107.18[/C][C]107.17[/C][C]0.0100000000000193[/C][/ROW]
[ROW][C]28[/C][C]107.2[/C][C]107.24[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]29[/C][C]107.35[/C][C]107.26[/C][C]0.0900000000000034[/C][/ROW]
[ROW][C]30[/C][C]107.35[/C][C]107.41[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]31[/C][C]107.35[/C][C]107.41[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]32[/C][C]107.52[/C][C]107.41[/C][C]0.110000000000014[/C][/ROW]
[ROW][C]33[/C][C]107.56[/C][C]107.58[/C][C]-0.0199999999999818[/C][/ROW]
[ROW][C]34[/C][C]107.55[/C][C]107.62[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]35[/C][C]107.6[/C][C]107.61[/C][C]-0.00999999999999091[/C][/ROW]
[ROW][C]36[/C][C]107.6[/C][C]107.66[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]37[/C][C]110.04[/C][C]107.66[/C][C]2.38000000000002[/C][/ROW]
[ROW][C]38[/C][C]110.27[/C][C]110.1[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]39[/C][C]110.33[/C][C]110.33[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]40[/C][C]110.33[/C][C]110.39[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]41[/C][C]110.33[/C][C]110.39[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]42[/C][C]110.33[/C][C]110.39[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]43[/C][C]110.33[/C][C]110.39[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]44[/C][C]110.35[/C][C]110.39[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]45[/C][C]110.38[/C][C]110.41[/C][C]-0.0299999999999869[/C][/ROW]
[ROW][C]46[/C][C]110.54[/C][C]110.44[/C][C]0.100000000000023[/C][/ROW]
[ROW][C]47[/C][C]110.54[/C][C]110.6[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]48[/C][C]110.54[/C][C]110.6[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]49[/C][C]110.54[/C][C]110.6[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]50[/C][C]106.74[/C][C]110.6[/C][C]-3.86[/C][/ROW]
[ROW][C]51[/C][C]106.78[/C][C]106.8[/C][C]-0.0199999999999818[/C][/ROW]
[ROW][C]52[/C][C]106.75[/C][C]106.84[/C][C]-0.0899999999999892[/C][/ROW]
[ROW][C]53[/C][C]106.75[/C][C]106.81[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]54[/C][C]106.75[/C][C]106.81[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]55[/C][C]106.82[/C][C]106.81[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]56[/C][C]107.08[/C][C]106.88[/C][C]0.200000000000017[/C][/ROW]
[ROW][C]57[/C][C]107.25[/C][C]107.14[/C][C]0.110000000000014[/C][/ROW]
[ROW][C]58[/C][C]107.28[/C][C]107.31[/C][C]-0.0299999999999869[/C][/ROW]
[ROW][C]59[/C][C]107.28[/C][C]107.34[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]60[/C][C]107.28[/C][C]107.34[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]61[/C][C]108.44[/C][C]107.34[/C][C]1.10000000000001[/C][/ROW]
[ROW][C]62[/C][C]109.33[/C][C]108.5[/C][C]0.830000000000013[/C][/ROW]
[ROW][C]63[/C][C]109.44[/C][C]109.39[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]64[/C][C]109.44[/C][C]109.5[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]65[/C][C]109.45[/C][C]109.5[/C][C]-0.0499999999999829[/C][/ROW]
[ROW][C]66[/C][C]109.45[/C][C]109.51[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]67[/C][C]109.45[/C][C]109.51[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]68[/C][C]109.45[/C][C]109.51[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]69[/C][C]109.46[/C][C]109.51[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]70[/C][C]109.46[/C][C]109.52[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]71[/C][C]109.46[/C][C]109.52[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]72[/C][C]109.46[/C][C]109.52[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]73[/C][C]110.95[/C][C]109.52[/C][C]1.43000000000002[/C][/ROW]
[ROW][C]74[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]75[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]76[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]77[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]78[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]79[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]80[/C][C]110.95[/C][C]111.01[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]81[/C][C]110.97[/C][C]111.01[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]82[/C][C]110.97[/C][C]111.03[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]83[/C][C]110.97[/C][C]111.03[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]84[/C][C]111[/C][C]111.03[/C][C]-0.0299999999999869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232993&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232993&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	103.5	103.55	-0.0499999999999829
4	103.5	103.56	-0.0599999999999881
5	103.5	103.56	-0.0599999999999881
6	103.5	103.56	-0.0599999999999881
7	103.54	103.56	-0.0199999999999818
8	103.71	103.6	0.109999999999999
9	103.76	103.77	-0.00999999999997669
10	103.76	103.82	-0.0599999999999881
11	103.76	103.82	-0.0599999999999881
12	103.82	103.82	0
13	105.11	103.88	1.23000000000002
14	105.58	105.17	0.410000000000011
15	105.91	105.64	0.27000000000001
16	105.92	105.97	-0.0499999999999829
17	105.92	105.98	-0.0599999999999881
18	105.92	105.98	-0.0599999999999881
19	105.96	105.98	-0.019999999999996
20	105.98	106.02	-0.0399999999999778
21	105.98	106.04	-0.0599999999999881
22	105.98	106.04	-0.0599999999999881
23	106.01	106.04	-0.0299999999999869
24	106.01	106.07	-0.0599999999999881
25	106.91	106.07	0.840000000000003
26	107.11	106.97	0.140000000000015
27	107.18	107.17	0.0100000000000193
28	107.2	107.24	-0.039999999999992
29	107.35	107.26	0.0900000000000034
30	107.35	107.41	-0.0599999999999881
31	107.35	107.41	-0.0599999999999881
32	107.52	107.41	0.110000000000014
33	107.56	107.58	-0.0199999999999818
34	107.55	107.62	-0.0699999999999932
35	107.6	107.61	-0.00999999999999091
36	107.6	107.66	-0.0599999999999881
37	110.04	107.66	2.38000000000002
38	110.27	110.1	0.170000000000002
39	110.33	110.33	1.4210854715202e-14
40	110.33	110.39	-0.0599999999999881
41	110.33	110.39	-0.0599999999999881
42	110.33	110.39	-0.0599999999999881
43	110.33	110.39	-0.0599999999999881
44	110.35	110.39	-0.039999999999992
45	110.38	110.41	-0.0299999999999869
46	110.54	110.44	0.100000000000023
47	110.54	110.6	-0.0599999999999881
48	110.54	110.6	-0.0599999999999881
49	110.54	110.6	-0.0599999999999881
50	106.74	110.6	-3.86
51	106.78	106.8	-0.0199999999999818
52	106.75	106.84	-0.0899999999999892
53	106.75	106.81	-0.0599999999999881
54	106.75	106.81	-0.0599999999999881
55	106.82	106.81	0.0100000000000051
56	107.08	106.88	0.200000000000017
57	107.25	107.14	0.110000000000014
58	107.28	107.31	-0.0299999999999869
59	107.28	107.34	-0.0599999999999881
60	107.28	107.34	-0.0599999999999881
61	108.44	107.34	1.10000000000001
62	109.33	108.5	0.830000000000013
63	109.44	109.39	0.0500000000000114
64	109.44	109.5	-0.0599999999999881
65	109.45	109.5	-0.0499999999999829
66	109.45	109.51	-0.0599999999999881
67	109.45	109.51	-0.0599999999999881
68	109.45	109.51	-0.0599999999999881
69	109.46	109.51	-0.0499999999999972
70	109.46	109.52	-0.0599999999999881
71	109.46	109.52	-0.0599999999999881
72	109.46	109.52	-0.0599999999999881
73	110.95	109.52	1.43000000000002
74	110.95	111.01	-0.0599999999999881
75	110.95	111.01	-0.0599999999999881
76	110.95	111.01	-0.0599999999999881
77	110.95	111.01	-0.0599999999999881
78	110.95	111.01	-0.0599999999999881
79	110.95	111.01	-0.0599999999999881
80	110.95	111.01	-0.0599999999999881
81	110.97	111.01	-0.039999999999992
82	110.97	111.03	-0.0599999999999881
83	110.97	111.03	-0.0599999999999881
84	111	111.03	-0.0299999999999869

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	111.06	109.924024393076	112.195975606924
86	111.12	109.513487890163	112.726512109837
87	111.18	109.212432532648	113.147567467352
88	111.24	108.968048786151	113.511951213848
89	111.3	108.759881322136	113.840118677864
90	111.36	108.577439402787	114.142560597213
91	111.42	108.414491048643	114.425508951357
92	111.48	108.266975780325	114.693024219674
93	111.54	108.132073179227	114.947926820773
94	111.6	108.007729715727	115.192270284273
95	111.66	107.892395140836	115.427604859164
96	111.72	107.784865065297	115.655134934703

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 111.06 & 109.924024393076 & 112.195975606924 \tabularnewline
86 & 111.12 & 109.513487890163 & 112.726512109837 \tabularnewline
87 & 111.18 & 109.212432532648 & 113.147567467352 \tabularnewline
88 & 111.24 & 108.968048786151 & 113.511951213848 \tabularnewline
89 & 111.3 & 108.759881322136 & 113.840118677864 \tabularnewline
90 & 111.36 & 108.577439402787 & 114.142560597213 \tabularnewline
91 & 111.42 & 108.414491048643 & 114.425508951357 \tabularnewline
92 & 111.48 & 108.266975780325 & 114.693024219674 \tabularnewline
93 & 111.54 & 108.132073179227 & 114.947926820773 \tabularnewline
94 & 111.6 & 108.007729715727 & 115.192270284273 \tabularnewline
95 & 111.66 & 107.892395140836 & 115.427604859164 \tabularnewline
96 & 111.72 & 107.784865065297 & 115.655134934703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232993&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]111.06[/C][C]109.924024393076[/C][C]112.195975606924[/C][/ROW]
[ROW][C]86[/C][C]111.12[/C][C]109.513487890163[/C][C]112.726512109837[/C][/ROW]
[ROW][C]87[/C][C]111.18[/C][C]109.212432532648[/C][C]113.147567467352[/C][/ROW]
[ROW][C]88[/C][C]111.24[/C][C]108.968048786151[/C][C]113.511951213848[/C][/ROW]
[ROW][C]89[/C][C]111.3[/C][C]108.759881322136[/C][C]113.840118677864[/C][/ROW]
[ROW][C]90[/C][C]111.36[/C][C]108.577439402787[/C][C]114.142560597213[/C][/ROW]
[ROW][C]91[/C][C]111.42[/C][C]108.414491048643[/C][C]114.425508951357[/C][/ROW]
[ROW][C]92[/C][C]111.48[/C][C]108.266975780325[/C][C]114.693024219674[/C][/ROW]
[ROW][C]93[/C][C]111.54[/C][C]108.132073179227[/C][C]114.947926820773[/C][/ROW]
[ROW][C]94[/C][C]111.6[/C][C]108.007729715727[/C][C]115.192270284273[/C][/ROW]
[ROW][C]95[/C][C]111.66[/C][C]107.892395140836[/C][C]115.427604859164[/C][/ROW]
[ROW][C]96[/C][C]111.72[/C][C]107.784865065297[/C][C]115.655134934703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232993&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232993&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	111.06	109.924024393076	112.195975606924
86	111.12	109.513487890163	112.726512109837
87	111.18	109.212432532648	113.147567467352
88	111.24	108.968048786151	113.511951213848
89	111.3	108.759881322136	113.840118677864
90	111.36	108.577439402787	114.142560597213
91	111.42	108.414491048643	114.425508951357
92	111.48	108.266975780325	114.693024219674
93	111.54	108.132073179227	114.947926820773
94	111.6	108.007729715727	115.192270284273
95	111.66	107.892395140836	115.427604859164
96	111.72	107.784865065297	115.655134934703

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