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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 05 Jun 2009 02:35:00 -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/2009/Jun/05/t1244191120dnta3jy0sxo6ckb.htm/, Retrieved Fri, 10 May 2024 10:27:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41758, Retrieved Fri, 10 May 2024 10:27:53 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

-       [Exponential Smoothing] [opgave 10_maandel...] [2009-06-05 08:35:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68

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=41758&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=41758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41758&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	0.999924940543429
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999924940543429 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41758&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]0.999924940543429[/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=41758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41758&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	0.999924940543429
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	3.42	3.42	0
3	3.43	3.42	0.0100000000000002
4	3.47	3.42999924940543	0.0400007505945656
5	3.51	3.4699969975654	0.0400030024346019
6	3.52	3.50999699739638	0.0100030026036242
7	3.52	3.51999924918006	7.50819939554503e-07
8	3.52	3.51999999994364	5.63562529976025e-11
9	3.52	3.52000000000000	4.44089209850063e-15
10	3.52	3.52	0
11	3.52	3.52	0
12	3.52	3.52	0
13	3.52	3.52	0
14	3.52	3.52	0
15	3.58	3.52	0.06
16	3.6	3.57999549643261	0.0200045035673941
17	3.61	3.59999849847283	0.0100015015271664
18	3.61	3.60999924929273	7.50707269681072e-07
19	3.61	3.60999999994365	5.63478153026153e-11
20	3.63	3.61000000000000	0.0200000000000045
21	3.68	3.62999849881087	0.0500015011891315
22	3.69	3.67999624691449	0.0100037530855066
23	3.69	3.68999924912373	7.50876270050327e-07
24	3.69	3.68999999994364	5.63602498004911e-11
25	3.69	3.69000000000000	4.44089209850063e-15
26	3.69	3.69	0
27	3.69	3.69	0
28	3.69	3.69	0
29	3.69	3.69	0
30	3.78	3.69	0.0899999999999999
31	3.79	3.77999324464891	0.0100067553510916
32	3.79	3.78999924889838	7.51101618678973e-07
33	3.8	3.78999999994362	0.0100000000563769
34	3.8	3.79999924940543	7.50594570053664e-07
35	3.8	3.79999999994366	5.63393776076282e-11
36	3.8	3.80000000000000	4.44089209850063e-15
37	3.81	3.8	0.0100000000000002
38	3.95	3.80999924940543	0.140000750594566
39	3.99	3.94998949161974	0.0400105083802593
40	4	3.98999699683298	0.0100030031670157
41	4.06	3.99999924918002	0.0600007508199814
42	4.16	4.05999549637625	0.100004503623751
43	4.19	4.1599924937163	0.0300075062836971
44	4.2	4.18999774765289	0.0100022523471148
45	4.2	4.19999924923637	7.50763625489981e-07
46	4.2	4.19999999994365	5.63522561947138e-11
47	4.2	4.20000000000000	4.44089209850063e-15
48	4.2	4.2	0
49	4.23	4.2	0.0300000000000002
50	4.38	4.2299977482163	0.150002251783697
51	4.43	4.3799887409125	0.050011259087503
52	4.44	4.42999624618207	0.0100037538179301
53	4.44	4.43999924912367	7.50876325561478e-07
54	4.44	4.43999999994364	5.63602498004911e-11
55	4.44	4.44	4.44089209850063e-15
56	4.44	4.44	0
57	4.45	4.44	0.00999999999999979
58	4.45	4.44999924940543	7.50594566056861e-07
59	4.45	4.44999999994366	5.63389335184183e-11
60	4.45	4.45	4.44089209850063e-15
61	4.45	4.45	0
62	4.45	4.45	0
63	4.45	4.45	0
64	4.45	4.45	0
65	4.46	4.45	0.00999999999999979
66	4.46	4.45999924940543	7.50594566056861e-07
67	4.46	4.45999999994366	5.63389335184183e-11
68	4.48	4.46000000000000	0.0200000000000049
69	4.58	4.47999849881087	0.100001501189131
70	4.67	4.57999249394166	0.0900075060583356
71	4.68	4.66999324408551	0.0100067559144916
72	4.68	4.67999924889834	7.51101660867448e-07

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.42 & 3.42 & 0 \tabularnewline
3 & 3.43 & 3.42 & 0.0100000000000002 \tabularnewline
4 & 3.47 & 3.42999924940543 & 0.0400007505945656 \tabularnewline
5 & 3.51 & 3.4699969975654 & 0.0400030024346019 \tabularnewline
6 & 3.52 & 3.50999699739638 & 0.0100030026036242 \tabularnewline
7 & 3.52 & 3.51999924918006 & 7.50819939554503e-07 \tabularnewline
8 & 3.52 & 3.51999999994364 & 5.63562529976025e-11 \tabularnewline
9 & 3.52 & 3.52000000000000 & 4.44089209850063e-15 \tabularnewline
10 & 3.52 & 3.52 & 0 \tabularnewline
11 & 3.52 & 3.52 & 0 \tabularnewline
12 & 3.52 & 3.52 & 0 \tabularnewline
13 & 3.52 & 3.52 & 0 \tabularnewline
14 & 3.52 & 3.52 & 0 \tabularnewline
15 & 3.58 & 3.52 & 0.06 \tabularnewline
16 & 3.6 & 3.57999549643261 & 0.0200045035673941 \tabularnewline
17 & 3.61 & 3.59999849847283 & 0.0100015015271664 \tabularnewline
18 & 3.61 & 3.60999924929273 & 7.50707269681072e-07 \tabularnewline
19 & 3.61 & 3.60999999994365 & 5.63478153026153e-11 \tabularnewline
20 & 3.63 & 3.61000000000000 & 0.0200000000000045 \tabularnewline
21 & 3.68 & 3.62999849881087 & 0.0500015011891315 \tabularnewline
22 & 3.69 & 3.67999624691449 & 0.0100037530855066 \tabularnewline
23 & 3.69 & 3.68999924912373 & 7.50876270050327e-07 \tabularnewline
24 & 3.69 & 3.68999999994364 & 5.63602498004911e-11 \tabularnewline
25 & 3.69 & 3.69000000000000 & 4.44089209850063e-15 \tabularnewline
26 & 3.69 & 3.69 & 0 \tabularnewline
27 & 3.69 & 3.69 & 0 \tabularnewline
28 & 3.69 & 3.69 & 0 \tabularnewline
29 & 3.69 & 3.69 & 0 \tabularnewline
30 & 3.78 & 3.69 & 0.0899999999999999 \tabularnewline
31 & 3.79 & 3.77999324464891 & 0.0100067553510916 \tabularnewline
32 & 3.79 & 3.78999924889838 & 7.51101618678973e-07 \tabularnewline
33 & 3.8 & 3.78999999994362 & 0.0100000000563769 \tabularnewline
34 & 3.8 & 3.79999924940543 & 7.50594570053664e-07 \tabularnewline
35 & 3.8 & 3.79999999994366 & 5.63393776076282e-11 \tabularnewline
36 & 3.8 & 3.80000000000000 & 4.44089209850063e-15 \tabularnewline
37 & 3.81 & 3.8 & 0.0100000000000002 \tabularnewline
38 & 3.95 & 3.80999924940543 & 0.140000750594566 \tabularnewline
39 & 3.99 & 3.94998949161974 & 0.0400105083802593 \tabularnewline
40 & 4 & 3.98999699683298 & 0.0100030031670157 \tabularnewline
41 & 4.06 & 3.99999924918002 & 0.0600007508199814 \tabularnewline
42 & 4.16 & 4.05999549637625 & 0.100004503623751 \tabularnewline
43 & 4.19 & 4.1599924937163 & 0.0300075062836971 \tabularnewline
44 & 4.2 & 4.18999774765289 & 0.0100022523471148 \tabularnewline
45 & 4.2 & 4.19999924923637 & 7.50763625489981e-07 \tabularnewline
46 & 4.2 & 4.19999999994365 & 5.63522561947138e-11 \tabularnewline
47 & 4.2 & 4.20000000000000 & 4.44089209850063e-15 \tabularnewline
48 & 4.2 & 4.2 & 0 \tabularnewline
49 & 4.23 & 4.2 & 0.0300000000000002 \tabularnewline
50 & 4.38 & 4.2299977482163 & 0.150002251783697 \tabularnewline
51 & 4.43 & 4.3799887409125 & 0.050011259087503 \tabularnewline
52 & 4.44 & 4.42999624618207 & 0.0100037538179301 \tabularnewline
53 & 4.44 & 4.43999924912367 & 7.50876325561478e-07 \tabularnewline
54 & 4.44 & 4.43999999994364 & 5.63602498004911e-11 \tabularnewline
55 & 4.44 & 4.44 & 4.44089209850063e-15 \tabularnewline
56 & 4.44 & 4.44 & 0 \tabularnewline
57 & 4.45 & 4.44 & 0.00999999999999979 \tabularnewline
58 & 4.45 & 4.44999924940543 & 7.50594566056861e-07 \tabularnewline
59 & 4.45 & 4.44999999994366 & 5.63389335184183e-11 \tabularnewline
60 & 4.45 & 4.45 & 4.44089209850063e-15 \tabularnewline
61 & 4.45 & 4.45 & 0 \tabularnewline
62 & 4.45 & 4.45 & 0 \tabularnewline
63 & 4.45 & 4.45 & 0 \tabularnewline
64 & 4.45 & 4.45 & 0 \tabularnewline
65 & 4.46 & 4.45 & 0.00999999999999979 \tabularnewline
66 & 4.46 & 4.45999924940543 & 7.50594566056861e-07 \tabularnewline
67 & 4.46 & 4.45999999994366 & 5.63389335184183e-11 \tabularnewline
68 & 4.48 & 4.46000000000000 & 0.0200000000000049 \tabularnewline
69 & 4.58 & 4.47999849881087 & 0.100001501189131 \tabularnewline
70 & 4.67 & 4.57999249394166 & 0.0900075060583356 \tabularnewline
71 & 4.68 & 4.66999324408551 & 0.0100067559144916 \tabularnewline
72 & 4.68 & 4.67999924889834 & 7.51101660867448e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41758&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]2[/C][C]3.42[/C][C]3.42[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]3.43[/C][C]3.42[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]4[/C][C]3.47[/C][C]3.42999924940543[/C][C]0.0400007505945656[/C][/ROW]
[ROW][C]5[/C][C]3.51[/C][C]3.4699969975654[/C][C]0.0400030024346019[/C][/ROW]
[ROW][C]6[/C][C]3.52[/C][C]3.50999699739638[/C][C]0.0100030026036242[/C][/ROW]
[ROW][C]7[/C][C]3.52[/C][C]3.51999924918006[/C][C]7.50819939554503e-07[/C][/ROW]
[ROW][C]8[/C][C]3.52[/C][C]3.51999999994364[/C][C]5.63562529976025e-11[/C][/ROW]
[ROW][C]9[/C][C]3.52[/C][C]3.52000000000000[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]10[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]3.52[/C][C]3.52[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]3.58[/C][C]3.52[/C][C]0.06[/C][/ROW]
[ROW][C]16[/C][C]3.6[/C][C]3.57999549643261[/C][C]0.0200045035673941[/C][/ROW]
[ROW][C]17[/C][C]3.61[/C][C]3.59999849847283[/C][C]0.0100015015271664[/C][/ROW]
[ROW][C]18[/C][C]3.61[/C][C]3.60999924929273[/C][C]7.50707269681072e-07[/C][/ROW]
[ROW][C]19[/C][C]3.61[/C][C]3.60999999994365[/C][C]5.63478153026153e-11[/C][/ROW]
[ROW][C]20[/C][C]3.63[/C][C]3.61000000000000[/C][C]0.0200000000000045[/C][/ROW]
[ROW][C]21[/C][C]3.68[/C][C]3.62999849881087[/C][C]0.0500015011891315[/C][/ROW]
[ROW][C]22[/C][C]3.69[/C][C]3.67999624691449[/C][C]0.0100037530855066[/C][/ROW]
[ROW][C]23[/C][C]3.69[/C][C]3.68999924912373[/C][C]7.50876270050327e-07[/C][/ROW]
[ROW][C]24[/C][C]3.69[/C][C]3.68999999994364[/C][C]5.63602498004911e-11[/C][/ROW]
[ROW][C]25[/C][C]3.69[/C][C]3.69000000000000[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]26[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]3.69[/C][C]3.69[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]3.78[/C][C]3.69[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]31[/C][C]3.79[/C][C]3.77999324464891[/C][C]0.0100067553510916[/C][/ROW]
[ROW][C]32[/C][C]3.79[/C][C]3.78999924889838[/C][C]7.51101618678973e-07[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]3.78999999994362[/C][C]0.0100000000563769[/C][/ROW]
[ROW][C]34[/C][C]3.8[/C][C]3.79999924940543[/C][C]7.50594570053664e-07[/C][/ROW]
[ROW][C]35[/C][C]3.8[/C][C]3.79999999994366[/C][C]5.63393776076282e-11[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.80000000000000[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.8[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]38[/C][C]3.95[/C][C]3.80999924940543[/C][C]0.140000750594566[/C][/ROW]
[ROW][C]39[/C][C]3.99[/C][C]3.94998949161974[/C][C]0.0400105083802593[/C][/ROW]
[ROW][C]40[/C][C]4[/C][C]3.98999699683298[/C][C]0.0100030031670157[/C][/ROW]
[ROW][C]41[/C][C]4.06[/C][C]3.99999924918002[/C][C]0.0600007508199814[/C][/ROW]
[ROW][C]42[/C][C]4.16[/C][C]4.05999549637625[/C][C]0.100004503623751[/C][/ROW]
[ROW][C]43[/C][C]4.19[/C][C]4.1599924937163[/C][C]0.0300075062836971[/C][/ROW]
[ROW][C]44[/C][C]4.2[/C][C]4.18999774765289[/C][C]0.0100022523471148[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]4.19999924923637[/C][C]7.50763625489981e-07[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.19999999994365[/C][C]5.63522561947138e-11[/C][/ROW]
[ROW][C]47[/C][C]4.2[/C][C]4.20000000000000[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]48[/C][C]4.2[/C][C]4.2[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]4.23[/C][C]4.2[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.2299977482163[/C][C]0.150002251783697[/C][/ROW]
[ROW][C]51[/C][C]4.43[/C][C]4.3799887409125[/C][C]0.050011259087503[/C][/ROW]
[ROW][C]52[/C][C]4.44[/C][C]4.42999624618207[/C][C]0.0100037538179301[/C][/ROW]
[ROW][C]53[/C][C]4.44[/C][C]4.43999924912367[/C][C]7.50876325561478e-07[/C][/ROW]
[ROW][C]54[/C][C]4.44[/C][C]4.43999999994364[/C][C]5.63602498004911e-11[/C][/ROW]
[ROW][C]55[/C][C]4.44[/C][C]4.44[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]56[/C][C]4.44[/C][C]4.44[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]4.45[/C][C]4.44[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]58[/C][C]4.45[/C][C]4.44999924940543[/C][C]7.50594566056861e-07[/C][/ROW]
[ROW][C]59[/C][C]4.45[/C][C]4.44999999994366[/C][C]5.63389335184183e-11[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.45[/C][C]4.44089209850063e-15[/C][/ROW]
[ROW][C]61[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]4.45[/C][C]4.45[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]4.46[/C][C]4.45[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]66[/C][C]4.46[/C][C]4.45999924940543[/C][C]7.50594566056861e-07[/C][/ROW]
[ROW][C]67[/C][C]4.46[/C][C]4.45999999994366[/C][C]5.63389335184183e-11[/C][/ROW]
[ROW][C]68[/C][C]4.48[/C][C]4.46000000000000[/C][C]0.0200000000000049[/C][/ROW]
[ROW][C]69[/C][C]4.58[/C][C]4.47999849881087[/C][C]0.100001501189131[/C][/ROW]
[ROW][C]70[/C][C]4.67[/C][C]4.57999249394166[/C][C]0.0900075060583356[/C][/ROW]
[ROW][C]71[/C][C]4.68[/C][C]4.66999324408551[/C][C]0.0100067559144916[/C][/ROW]
[ROW][C]72[/C][C]4.68[/C][C]4.67999924889834[/C][C]7.51101660867448e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41758&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41758&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
2	3.42	3.42	0
3	3.43	3.42	0.0100000000000002
4	3.47	3.42999924940543	0.0400007505945656
5	3.51	3.4699969975654	0.0400030024346019
6	3.52	3.50999699739638	0.0100030026036242
7	3.52	3.51999924918006	7.50819939554503e-07
8	3.52	3.51999999994364	5.63562529976025e-11
9	3.52	3.52000000000000	4.44089209850063e-15
10	3.52	3.52	0
11	3.52	3.52	0
12	3.52	3.52	0
13	3.52	3.52	0
14	3.52	3.52	0
15	3.58	3.52	0.06
16	3.6	3.57999549643261	0.0200045035673941
17	3.61	3.59999849847283	0.0100015015271664
18	3.61	3.60999924929273	7.50707269681072e-07
19	3.61	3.60999999994365	5.63478153026153e-11
20	3.63	3.61000000000000	0.0200000000000045
21	3.68	3.62999849881087	0.0500015011891315
22	3.69	3.67999624691449	0.0100037530855066
23	3.69	3.68999924912373	7.50876270050327e-07
24	3.69	3.68999999994364	5.63602498004911e-11
25	3.69	3.69000000000000	4.44089209850063e-15
26	3.69	3.69	0
27	3.69	3.69	0
28	3.69	3.69	0
29	3.69	3.69	0
30	3.78	3.69	0.0899999999999999
31	3.79	3.77999324464891	0.0100067553510916
32	3.79	3.78999924889838	7.51101618678973e-07
33	3.8	3.78999999994362	0.0100000000563769
34	3.8	3.79999924940543	7.50594570053664e-07
35	3.8	3.79999999994366	5.63393776076282e-11
36	3.8	3.80000000000000	4.44089209850063e-15
37	3.81	3.8	0.0100000000000002
38	3.95	3.80999924940543	0.140000750594566
39	3.99	3.94998949161974	0.0400105083802593
40	4	3.98999699683298	0.0100030031670157
41	4.06	3.99999924918002	0.0600007508199814
42	4.16	4.05999549637625	0.100004503623751
43	4.19	4.1599924937163	0.0300075062836971
44	4.2	4.18999774765289	0.0100022523471148
45	4.2	4.19999924923637	7.50763625489981e-07
46	4.2	4.19999999994365	5.63522561947138e-11
47	4.2	4.20000000000000	4.44089209850063e-15
48	4.2	4.2	0
49	4.23	4.2	0.0300000000000002
50	4.38	4.2299977482163	0.150002251783697
51	4.43	4.3799887409125	0.050011259087503
52	4.44	4.42999624618207	0.0100037538179301
53	4.44	4.43999924912367	7.50876325561478e-07
54	4.44	4.43999999994364	5.63602498004911e-11
55	4.44	4.44	4.44089209850063e-15
56	4.44	4.44	0
57	4.45	4.44	0.00999999999999979
58	4.45	4.44999924940543	7.50594566056861e-07
59	4.45	4.44999999994366	5.63389335184183e-11
60	4.45	4.45	4.44089209850063e-15
61	4.45	4.45	0
62	4.45	4.45	0
63	4.45	4.45	0
64	4.45	4.45	0
65	4.46	4.45	0.00999999999999979
66	4.46	4.45999924940543	7.50594566056861e-07
67	4.46	4.45999999994366	5.63389335184183e-11
68	4.48	4.46000000000000	0.0200000000000049
69	4.58	4.47999849881087	0.100001501189131
70	4.67	4.57999249394166	0.0900075060583356
71	4.68	4.66999324408551	0.0100067559144916
72	4.68	4.67999924889834	7.51101660867448e-07

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	4.67999999994362	4.61489274289132	4.74510725699593
74	4.67999999994362	4.58792788951747	4.77207211036978
75	4.67999999994362	4.56723656564076	4.79276343424649
76	4.67999999994362	4.54979281614324	4.81020718374401
77	4.67999999994362	4.53442448926041	4.82557551062684
78	4.67999999994362	4.52053041692501	4.83946958296223
79	4.67999999994362	4.50775347166052	4.85224652822672
80	4.67999999994362	4.49586096252072	4.86413903736652
81	4.67999999994362	4.48469126050659	4.87530873938066
82	4.67999999994362	4.47412668380495	4.8858733160823
83	4.67999999994362	4.46407839172577	4.89592160816148
84	4.67999999994362	4.45447736362337	4.90552263626387

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.67999999994362 & 4.61489274289132 & 4.74510725699593 \tabularnewline
74 & 4.67999999994362 & 4.58792788951747 & 4.77207211036978 \tabularnewline
75 & 4.67999999994362 & 4.56723656564076 & 4.79276343424649 \tabularnewline
76 & 4.67999999994362 & 4.54979281614324 & 4.81020718374401 \tabularnewline
77 & 4.67999999994362 & 4.53442448926041 & 4.82557551062684 \tabularnewline
78 & 4.67999999994362 & 4.52053041692501 & 4.83946958296223 \tabularnewline
79 & 4.67999999994362 & 4.50775347166052 & 4.85224652822672 \tabularnewline
80 & 4.67999999994362 & 4.49586096252072 & 4.86413903736652 \tabularnewline
81 & 4.67999999994362 & 4.48469126050659 & 4.87530873938066 \tabularnewline
82 & 4.67999999994362 & 4.47412668380495 & 4.8858733160823 \tabularnewline
83 & 4.67999999994362 & 4.46407839172577 & 4.89592160816148 \tabularnewline
84 & 4.67999999994362 & 4.45447736362337 & 4.90552263626387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41758&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]4.67999999994362[/C][C]4.61489274289132[/C][C]4.74510725699593[/C][/ROW]
[ROW][C]74[/C][C]4.67999999994362[/C][C]4.58792788951747[/C][C]4.77207211036978[/C][/ROW]
[ROW][C]75[/C][C]4.67999999994362[/C][C]4.56723656564076[/C][C]4.79276343424649[/C][/ROW]
[ROW][C]76[/C][C]4.67999999994362[/C][C]4.54979281614324[/C][C]4.81020718374401[/C][/ROW]
[ROW][C]77[/C][C]4.67999999994362[/C][C]4.53442448926041[/C][C]4.82557551062684[/C][/ROW]
[ROW][C]78[/C][C]4.67999999994362[/C][C]4.52053041692501[/C][C]4.83946958296223[/C][/ROW]
[ROW][C]79[/C][C]4.67999999994362[/C][C]4.50775347166052[/C][C]4.85224652822672[/C][/ROW]
[ROW][C]80[/C][C]4.67999999994362[/C][C]4.49586096252072[/C][C]4.86413903736652[/C][/ROW]
[ROW][C]81[/C][C]4.67999999994362[/C][C]4.48469126050659[/C][C]4.87530873938066[/C][/ROW]
[ROW][C]82[/C][C]4.67999999994362[/C][C]4.47412668380495[/C][C]4.8858733160823[/C][/ROW]
[ROW][C]83[/C][C]4.67999999994362[/C][C]4.46407839172577[/C][C]4.89592160816148[/C][/ROW]
[ROW][C]84[/C][C]4.67999999994362[/C][C]4.45447736362337[/C][C]4.90552263626387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41758&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41758&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	4.67999999994362	4.61489274289132	4.74510725699593
74	4.67999999994362	4.58792788951747	4.77207211036978
75	4.67999999994362	4.56723656564076	4.79276343424649
76	4.67999999994362	4.54979281614324	4.81020718374401
77	4.67999999994362	4.53442448926041	4.82557551062684
78	4.67999999994362	4.52053041692501	4.83946958296223
79	4.67999999994362	4.50775347166052	4.85224652822672
80	4.67999999994362	4.49586096252072	4.86413903736652
81	4.67999999994362	4.48469126050659	4.87530873938066
82	4.67999999994362	4.47412668380495	4.8858733160823
83	4.67999999994362	4.46407839172577	4.89592160816148
84	4.67999999994362	4.45447736362337	4.90552263626387

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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