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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 07 Jan 2013 05:52:57 -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/2013/Jan/07/t1357555993kg3v8mn7kwg9o5f.htm/, Retrieved Tue, 30 Apr 2024 23:29:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205037, Retrieved Tue, 30 Apr 2024 23:29:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

158

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

-       [Exponential Smoothing] [Prijs per 150 cl ...] [2013-01-07 10:52:57] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Boxplots

1,26
1,27
1,24
1,25
1,27
1,25
1,26
1,27
1,26
1,26
1,28
1,27
1,28
1,27
1,26
1,27
1,27
1,28
1,27
1,26
1,3
1,31
1,28
1,29
1,31
1,29
1,29
1,32
1,3
1,29
1,31
1,29
1,33
1,35
1,32
1,33
1,34
1,34
1,33
1,33
1,35
1,32
1,35
1,32
1,36
1,37
1,34
1,32
1,34
1,32
1,33
1,35
1,33
1,33
1,35
1,33
1,36
1,39
1,37
1,37
1,39
1,37
1,39
1,39
1,39
1,37
1,38
1,37
1,41
1,41
1,42
1,42

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205037&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205037&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.28568753838882
beta	0.0196112628231865
gamma	0.740858537204665

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.28568753838882 \tabularnewline
beta & 0.0196112628231865 \tabularnewline
gamma & 0.740858537204665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205037&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]0.28568753838882[/C][/ROW]
[ROW][C]beta[/C][C]0.0196112628231865[/C][/ROW]
[ROW][C]gamma[/C][C]0.740858537204665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205037&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	0.28568753838882
beta	0.0196112628231865
gamma	0.740858537204665

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.28	1.27180854393392	0.00819145606607807
14	1.27	1.265615650886	0.00438434911399632
15	1.26	1.25708954295794	0.0029104570420575
16	1.27	1.2656306516226	0.00436934837739966
17	1.27	1.26629009944361	0.0037099005563892
18	1.28	1.27800602959912	0.00199397040088023
19	1.27	1.27506691559079	-0.00506691559079053
20	1.26	1.28437842907306	-0.0243784290730562
21	1.3	1.26786957467032	0.0321304253296768
22	1.31	1.27689497699757	0.0331050230024257
23	1.28	1.3076503456443	-0.0276503456443047
24	1.29	1.28989556331847	0.000104436681525266
25	1.31	1.30437947859955	0.005620521400447
26	1.29	1.29535654456512	-0.00535654456512247
27	1.29	1.28315698831128	0.00684301168872059
28	1.32	1.29388040288874	0.0261195971112598
29	1.3	1.30060906787353	-0.000609067873531322
30	1.29	1.31062923768122	-0.020629237681222
31	1.31	1.29743253941617	0.012567460583834
32	1.29	1.30168362692955	-0.0116836269295466
33	1.33	1.31937867304122	0.0106213269587783
34	1.35	1.32278397742074	0.0272160225792641
35	1.32	1.31948667072914	0.000513329270857232
36	1.33	1.32484010414548	0.00515989585452448
37	1.34	1.34444703687685	-0.00444703687685122
38	1.34	1.3265225938193	0.0134774061806977
39	1.33	1.32634040797365	0.00365959202635424
40	1.33	1.34714349224861	-0.0171434922486087
41	1.35	1.3271290513252	0.0228709486748044
42	1.32	1.33339164098667	-0.0133916409866677
43	1.35	1.34032647974595	0.00967352025405122
44	1.32	1.33078240051498	-0.0107824005149784
45	1.36	1.36165113206319	-0.00165113206318668
46	1.37	1.37063156014866	-0.000631560148660393
47	1.34	1.34477641230697	-0.00477641230696579
48	1.32	1.35119011408384	-0.031190114083844
49	1.34	1.35524386564322	-0.0152438656432203
50	1.32	1.34338002355838	-0.0233800235583757
51	1.33	1.32702266468358	0.00297733531641975
52	1.35	1.33612007519864	0.0138799248013597
53	1.33	1.34581764909372	-0.0158176490937159
54	1.33	1.32138909676379	0.00861090323620584
55	1.35	1.3464453531992	0.00355464680079964
56	1.33	1.32391988691366	0.00608011308634282
57	1.36	1.36421690967426	-0.00421690967425614
58	1.39	1.37268032532496	0.0173196746750386
59	1.37	1.34936064448812	0.0206393555118805
60	1.37	1.34876914471614	0.0212308552838638
61	1.39	1.37684665161855	0.0131533483814537
62	1.37	1.36870740753079	0.00129259246921376
63	1.39	1.37393723807847	0.0160627619215308
64	1.39	1.39355733053073	-0.00355733053072682
65	1.39	1.38261435275164	0.00738564724835511
66	1.37	1.37800378456366	-0.00800378456365758
67	1.38	1.39680317917066	-0.0168031791706651
68	1.37	1.36943470936787	0.000565290632125404
69	1.41	1.40403931012215	0.00596068987785259
70	1.41	1.42784857859323	-0.0178485785932341
71	1.42	1.39568874981488	0.0243112501851155
72	1.42	1.39644326334738	0.0235567366526159

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.28 & 1.27180854393392 & 0.00819145606607807 \tabularnewline
14 & 1.27 & 1.265615650886 & 0.00438434911399632 \tabularnewline
15 & 1.26 & 1.25708954295794 & 0.0029104570420575 \tabularnewline
16 & 1.27 & 1.2656306516226 & 0.00436934837739966 \tabularnewline
17 & 1.27 & 1.26629009944361 & 0.0037099005563892 \tabularnewline
18 & 1.28 & 1.27800602959912 & 0.00199397040088023 \tabularnewline
19 & 1.27 & 1.27506691559079 & -0.00506691559079053 \tabularnewline
20 & 1.26 & 1.28437842907306 & -0.0243784290730562 \tabularnewline
21 & 1.3 & 1.26786957467032 & 0.0321304253296768 \tabularnewline
22 & 1.31 & 1.27689497699757 & 0.0331050230024257 \tabularnewline
23 & 1.28 & 1.3076503456443 & -0.0276503456443047 \tabularnewline
24 & 1.29 & 1.28989556331847 & 0.000104436681525266 \tabularnewline
25 & 1.31 & 1.30437947859955 & 0.005620521400447 \tabularnewline
26 & 1.29 & 1.29535654456512 & -0.00535654456512247 \tabularnewline
27 & 1.29 & 1.28315698831128 & 0.00684301168872059 \tabularnewline
28 & 1.32 & 1.29388040288874 & 0.0261195971112598 \tabularnewline
29 & 1.3 & 1.30060906787353 & -0.000609067873531322 \tabularnewline
30 & 1.29 & 1.31062923768122 & -0.020629237681222 \tabularnewline
31 & 1.31 & 1.29743253941617 & 0.012567460583834 \tabularnewline
32 & 1.29 & 1.30168362692955 & -0.0116836269295466 \tabularnewline
33 & 1.33 & 1.31937867304122 & 0.0106213269587783 \tabularnewline
34 & 1.35 & 1.32278397742074 & 0.0272160225792641 \tabularnewline
35 & 1.32 & 1.31948667072914 & 0.000513329270857232 \tabularnewline
36 & 1.33 & 1.32484010414548 & 0.00515989585452448 \tabularnewline
37 & 1.34 & 1.34444703687685 & -0.00444703687685122 \tabularnewline
38 & 1.34 & 1.3265225938193 & 0.0134774061806977 \tabularnewline
39 & 1.33 & 1.32634040797365 & 0.00365959202635424 \tabularnewline
40 & 1.33 & 1.34714349224861 & -0.0171434922486087 \tabularnewline
41 & 1.35 & 1.3271290513252 & 0.0228709486748044 \tabularnewline
42 & 1.32 & 1.33339164098667 & -0.0133916409866677 \tabularnewline
43 & 1.35 & 1.34032647974595 & 0.00967352025405122 \tabularnewline
44 & 1.32 & 1.33078240051498 & -0.0107824005149784 \tabularnewline
45 & 1.36 & 1.36165113206319 & -0.00165113206318668 \tabularnewline
46 & 1.37 & 1.37063156014866 & -0.000631560148660393 \tabularnewline
47 & 1.34 & 1.34477641230697 & -0.00477641230696579 \tabularnewline
48 & 1.32 & 1.35119011408384 & -0.031190114083844 \tabularnewline
49 & 1.34 & 1.35524386564322 & -0.0152438656432203 \tabularnewline
50 & 1.32 & 1.34338002355838 & -0.0233800235583757 \tabularnewline
51 & 1.33 & 1.32702266468358 & 0.00297733531641975 \tabularnewline
52 & 1.35 & 1.33612007519864 & 0.0138799248013597 \tabularnewline
53 & 1.33 & 1.34581764909372 & -0.0158176490937159 \tabularnewline
54 & 1.33 & 1.32138909676379 & 0.00861090323620584 \tabularnewline
55 & 1.35 & 1.3464453531992 & 0.00355464680079964 \tabularnewline
56 & 1.33 & 1.32391988691366 & 0.00608011308634282 \tabularnewline
57 & 1.36 & 1.36421690967426 & -0.00421690967425614 \tabularnewline
58 & 1.39 & 1.37268032532496 & 0.0173196746750386 \tabularnewline
59 & 1.37 & 1.34936064448812 & 0.0206393555118805 \tabularnewline
60 & 1.37 & 1.34876914471614 & 0.0212308552838638 \tabularnewline
61 & 1.39 & 1.37684665161855 & 0.0131533483814537 \tabularnewline
62 & 1.37 & 1.36870740753079 & 0.00129259246921376 \tabularnewline
63 & 1.39 & 1.37393723807847 & 0.0160627619215308 \tabularnewline
64 & 1.39 & 1.39355733053073 & -0.00355733053072682 \tabularnewline
65 & 1.39 & 1.38261435275164 & 0.00738564724835511 \tabularnewline
66 & 1.37 & 1.37800378456366 & -0.00800378456365758 \tabularnewline
67 & 1.38 & 1.39680317917066 & -0.0168031791706651 \tabularnewline
68 & 1.37 & 1.36943470936787 & 0.000565290632125404 \tabularnewline
69 & 1.41 & 1.40403931012215 & 0.00596068987785259 \tabularnewline
70 & 1.41 & 1.42784857859323 & -0.0178485785932341 \tabularnewline
71 & 1.42 & 1.39568874981488 & 0.0243112501851155 \tabularnewline
72 & 1.42 & 1.39644326334738 & 0.0235567366526159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205037&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]13[/C][C]1.28[/C][C]1.27180854393392[/C][C]0.00819145606607807[/C][/ROW]
[ROW][C]14[/C][C]1.27[/C][C]1.265615650886[/C][C]0.00438434911399632[/C][/ROW]
[ROW][C]15[/C][C]1.26[/C][C]1.25708954295794[/C][C]0.0029104570420575[/C][/ROW]
[ROW][C]16[/C][C]1.27[/C][C]1.2656306516226[/C][C]0.00436934837739966[/C][/ROW]
[ROW][C]17[/C][C]1.27[/C][C]1.26629009944361[/C][C]0.0037099005563892[/C][/ROW]
[ROW][C]18[/C][C]1.28[/C][C]1.27800602959912[/C][C]0.00199397040088023[/C][/ROW]
[ROW][C]19[/C][C]1.27[/C][C]1.27506691559079[/C][C]-0.00506691559079053[/C][/ROW]
[ROW][C]20[/C][C]1.26[/C][C]1.28437842907306[/C][C]-0.0243784290730562[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]1.26786957467032[/C][C]0.0321304253296768[/C][/ROW]
[ROW][C]22[/C][C]1.31[/C][C]1.27689497699757[/C][C]0.0331050230024257[/C][/ROW]
[ROW][C]23[/C][C]1.28[/C][C]1.3076503456443[/C][C]-0.0276503456443047[/C][/ROW]
[ROW][C]24[/C][C]1.29[/C][C]1.28989556331847[/C][C]0.000104436681525266[/C][/ROW]
[ROW][C]25[/C][C]1.31[/C][C]1.30437947859955[/C][C]0.005620521400447[/C][/ROW]
[ROW][C]26[/C][C]1.29[/C][C]1.29535654456512[/C][C]-0.00535654456512247[/C][/ROW]
[ROW][C]27[/C][C]1.29[/C][C]1.28315698831128[/C][C]0.00684301168872059[/C][/ROW]
[ROW][C]28[/C][C]1.32[/C][C]1.29388040288874[/C][C]0.0261195971112598[/C][/ROW]
[ROW][C]29[/C][C]1.3[/C][C]1.30060906787353[/C][C]-0.000609067873531322[/C][/ROW]
[ROW][C]30[/C][C]1.29[/C][C]1.31062923768122[/C][C]-0.020629237681222[/C][/ROW]
[ROW][C]31[/C][C]1.31[/C][C]1.29743253941617[/C][C]0.012567460583834[/C][/ROW]
[ROW][C]32[/C][C]1.29[/C][C]1.30168362692955[/C][C]-0.0116836269295466[/C][/ROW]
[ROW][C]33[/C][C]1.33[/C][C]1.31937867304122[/C][C]0.0106213269587783[/C][/ROW]
[ROW][C]34[/C][C]1.35[/C][C]1.32278397742074[/C][C]0.0272160225792641[/C][/ROW]
[ROW][C]35[/C][C]1.32[/C][C]1.31948667072914[/C][C]0.000513329270857232[/C][/ROW]
[ROW][C]36[/C][C]1.33[/C][C]1.32484010414548[/C][C]0.00515989585452448[/C][/ROW]
[ROW][C]37[/C][C]1.34[/C][C]1.34444703687685[/C][C]-0.00444703687685122[/C][/ROW]
[ROW][C]38[/C][C]1.34[/C][C]1.3265225938193[/C][C]0.0134774061806977[/C][/ROW]
[ROW][C]39[/C][C]1.33[/C][C]1.32634040797365[/C][C]0.00365959202635424[/C][/ROW]
[ROW][C]40[/C][C]1.33[/C][C]1.34714349224861[/C][C]-0.0171434922486087[/C][/ROW]
[ROW][C]41[/C][C]1.35[/C][C]1.3271290513252[/C][C]0.0228709486748044[/C][/ROW]
[ROW][C]42[/C][C]1.32[/C][C]1.33339164098667[/C][C]-0.0133916409866677[/C][/ROW]
[ROW][C]43[/C][C]1.35[/C][C]1.34032647974595[/C][C]0.00967352025405122[/C][/ROW]
[ROW][C]44[/C][C]1.32[/C][C]1.33078240051498[/C][C]-0.0107824005149784[/C][/ROW]
[ROW][C]45[/C][C]1.36[/C][C]1.36165113206319[/C][C]-0.00165113206318668[/C][/ROW]
[ROW][C]46[/C][C]1.37[/C][C]1.37063156014866[/C][C]-0.000631560148660393[/C][/ROW]
[ROW][C]47[/C][C]1.34[/C][C]1.34477641230697[/C][C]-0.00477641230696579[/C][/ROW]
[ROW][C]48[/C][C]1.32[/C][C]1.35119011408384[/C][C]-0.031190114083844[/C][/ROW]
[ROW][C]49[/C][C]1.34[/C][C]1.35524386564322[/C][C]-0.0152438656432203[/C][/ROW]
[ROW][C]50[/C][C]1.32[/C][C]1.34338002355838[/C][C]-0.0233800235583757[/C][/ROW]
[ROW][C]51[/C][C]1.33[/C][C]1.32702266468358[/C][C]0.00297733531641975[/C][/ROW]
[ROW][C]52[/C][C]1.35[/C][C]1.33612007519864[/C][C]0.0138799248013597[/C][/ROW]
[ROW][C]53[/C][C]1.33[/C][C]1.34581764909372[/C][C]-0.0158176490937159[/C][/ROW]
[ROW][C]54[/C][C]1.33[/C][C]1.32138909676379[/C][C]0.00861090323620584[/C][/ROW]
[ROW][C]55[/C][C]1.35[/C][C]1.3464453531992[/C][C]0.00355464680079964[/C][/ROW]
[ROW][C]56[/C][C]1.33[/C][C]1.32391988691366[/C][C]0.00608011308634282[/C][/ROW]
[ROW][C]57[/C][C]1.36[/C][C]1.36421690967426[/C][C]-0.00421690967425614[/C][/ROW]
[ROW][C]58[/C][C]1.39[/C][C]1.37268032532496[/C][C]0.0173196746750386[/C][/ROW]
[ROW][C]59[/C][C]1.37[/C][C]1.34936064448812[/C][C]0.0206393555118805[/C][/ROW]
[ROW][C]60[/C][C]1.37[/C][C]1.34876914471614[/C][C]0.0212308552838638[/C][/ROW]
[ROW][C]61[/C][C]1.39[/C][C]1.37684665161855[/C][C]0.0131533483814537[/C][/ROW]
[ROW][C]62[/C][C]1.37[/C][C]1.36870740753079[/C][C]0.00129259246921376[/C][/ROW]
[ROW][C]63[/C][C]1.39[/C][C]1.37393723807847[/C][C]0.0160627619215308[/C][/ROW]
[ROW][C]64[/C][C]1.39[/C][C]1.39355733053073[/C][C]-0.00355733053072682[/C][/ROW]
[ROW][C]65[/C][C]1.39[/C][C]1.38261435275164[/C][C]0.00738564724835511[/C][/ROW]
[ROW][C]66[/C][C]1.37[/C][C]1.37800378456366[/C][C]-0.00800378456365758[/C][/ROW]
[ROW][C]67[/C][C]1.38[/C][C]1.39680317917066[/C][C]-0.0168031791706651[/C][/ROW]
[ROW][C]68[/C][C]1.37[/C][C]1.36943470936787[/C][C]0.000565290632125404[/C][/ROW]
[ROW][C]69[/C][C]1.41[/C][C]1.40403931012215[/C][C]0.00596068987785259[/C][/ROW]
[ROW][C]70[/C][C]1.41[/C][C]1.42784857859323[/C][C]-0.0178485785932341[/C][/ROW]
[ROW][C]71[/C][C]1.42[/C][C]1.39568874981488[/C][C]0.0243112501851155[/C][/ROW]
[ROW][C]72[/C][C]1.42[/C][C]1.39644326334738[/C][C]0.0235567366526159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205037&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
13	1.28	1.27180854393392	0.00819145606607807
14	1.27	1.265615650886	0.00438434911399632
15	1.26	1.25708954295794	0.0029104570420575
16	1.27	1.2656306516226	0.00436934837739966
17	1.27	1.26629009944361	0.0037099005563892
18	1.28	1.27800602959912	0.00199397040088023
19	1.27	1.27506691559079	-0.00506691559079053
20	1.26	1.28437842907306	-0.0243784290730562
21	1.3	1.26786957467032	0.0321304253296768
22	1.31	1.27689497699757	0.0331050230024257
23	1.28	1.3076503456443	-0.0276503456443047
24	1.29	1.28989556331847	0.000104436681525266
25	1.31	1.30437947859955	0.005620521400447
26	1.29	1.29535654456512	-0.00535654456512247
27	1.29	1.28315698831128	0.00684301168872059
28	1.32	1.29388040288874	0.0261195971112598
29	1.3	1.30060906787353	-0.000609067873531322
30	1.29	1.31062923768122	-0.020629237681222
31	1.31	1.29743253941617	0.012567460583834
32	1.29	1.30168362692955	-0.0116836269295466
33	1.33	1.31937867304122	0.0106213269587783
34	1.35	1.32278397742074	0.0272160225792641
35	1.32	1.31948667072914	0.000513329270857232
36	1.33	1.32484010414548	0.00515989585452448
37	1.34	1.34444703687685	-0.00444703687685122
38	1.34	1.3265225938193	0.0134774061806977
39	1.33	1.32634040797365	0.00365959202635424
40	1.33	1.34714349224861	-0.0171434922486087
41	1.35	1.3271290513252	0.0228709486748044
42	1.32	1.33339164098667	-0.0133916409866677
43	1.35	1.34032647974595	0.00967352025405122
44	1.32	1.33078240051498	-0.0107824005149784
45	1.36	1.36165113206319	-0.00165113206318668
46	1.37	1.37063156014866	-0.000631560148660393
47	1.34	1.34477641230697	-0.00477641230696579
48	1.32	1.35119011408384	-0.031190114083844
49	1.34	1.35524386564322	-0.0152438656432203
50	1.32	1.34338002355838	-0.0233800235583757
51	1.33	1.32702266468358	0.00297733531641975
52	1.35	1.33612007519864	0.0138799248013597
53	1.33	1.34581764909372	-0.0158176490937159
54	1.33	1.32138909676379	0.00861090323620584
55	1.35	1.3464453531992	0.00355464680079964
56	1.33	1.32391988691366	0.00608011308634282
57	1.36	1.36421690967426	-0.00421690967425614
58	1.39	1.37268032532496	0.0173196746750386
59	1.37	1.34936064448812	0.0206393555118805
60	1.37	1.34876914471614	0.0212308552838638
61	1.39	1.37684665161855	0.0131533483814537
62	1.37	1.36870740753079	0.00129259246921376
63	1.39	1.37393723807847	0.0160627619215308
64	1.39	1.39355733053073	-0.00355733053072682
65	1.39	1.38261435275164	0.00738564724835511
66	1.37	1.37800378456366	-0.00800378456365758
67	1.38	1.39680317917066	-0.0168031791706651
68	1.37	1.36943470936787	0.000565290632125404
69	1.41	1.40403931012215	0.00596068987785259
70	1.41	1.42784857859323	-0.0178485785932341
71	1.42	1.39568874981488	0.0243112501851155
72	1.42	1.39644326334738	0.0235567366526159

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.42158362633113	1.39784418803856	1.44532306462369
74	1.40310200955454	1.3779326588225	1.42827136028658
75	1.41619041624024	1.38953551296069	1.4428453195198
76	1.42098090113768	1.39289214565379	1.44906965662158
77	1.41681348897774	1.38737105945094	1.44625591850453
78	1.40166484886862	1.37099023804947	1.43233945968778
79	1.41849214563176	1.38629282359191	1.45069146767161
80	1.40492806015067	1.37155233671297	1.43830378358838
81	1.44333170560191	1.40812255748498	1.47854085371884
82	1.45315972766973	1.41649306877227	1.48982638656719
83	1.44842818866301	1.41053130860397	1.48632506872204
84	1.44170921480102	-9.67109662079829	12.5545150504003

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.42158362633113 & 1.39784418803856 & 1.44532306462369 \tabularnewline
74 & 1.40310200955454 & 1.3779326588225 & 1.42827136028658 \tabularnewline
75 & 1.41619041624024 & 1.38953551296069 & 1.4428453195198 \tabularnewline
76 & 1.42098090113768 & 1.39289214565379 & 1.44906965662158 \tabularnewline
77 & 1.41681348897774 & 1.38737105945094 & 1.44625591850453 \tabularnewline
78 & 1.40166484886862 & 1.37099023804947 & 1.43233945968778 \tabularnewline
79 & 1.41849214563176 & 1.38629282359191 & 1.45069146767161 \tabularnewline
80 & 1.40492806015067 & 1.37155233671297 & 1.43830378358838 \tabularnewline
81 & 1.44333170560191 & 1.40812255748498 & 1.47854085371884 \tabularnewline
82 & 1.45315972766973 & 1.41649306877227 & 1.48982638656719 \tabularnewline
83 & 1.44842818866301 & 1.41053130860397 & 1.48632506872204 \tabularnewline
84 & 1.44170921480102 & -9.67109662079829 & 12.5545150504003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205037&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]1.42158362633113[/C][C]1.39784418803856[/C][C]1.44532306462369[/C][/ROW]
[ROW][C]74[/C][C]1.40310200955454[/C][C]1.3779326588225[/C][C]1.42827136028658[/C][/ROW]
[ROW][C]75[/C][C]1.41619041624024[/C][C]1.38953551296069[/C][C]1.4428453195198[/C][/ROW]
[ROW][C]76[/C][C]1.42098090113768[/C][C]1.39289214565379[/C][C]1.44906965662158[/C][/ROW]
[ROW][C]77[/C][C]1.41681348897774[/C][C]1.38737105945094[/C][C]1.44625591850453[/C][/ROW]
[ROW][C]78[/C][C]1.40166484886862[/C][C]1.37099023804947[/C][C]1.43233945968778[/C][/ROW]
[ROW][C]79[/C][C]1.41849214563176[/C][C]1.38629282359191[/C][C]1.45069146767161[/C][/ROW]
[ROW][C]80[/C][C]1.40492806015067[/C][C]1.37155233671297[/C][C]1.43830378358838[/C][/ROW]
[ROW][C]81[/C][C]1.44333170560191[/C][C]1.40812255748498[/C][C]1.47854085371884[/C][/ROW]
[ROW][C]82[/C][C]1.45315972766973[/C][C]1.41649306877227[/C][C]1.48982638656719[/C][/ROW]
[ROW][C]83[/C][C]1.44842818866301[/C][C]1.41053130860397[/C][C]1.48632506872204[/C][/ROW]
[ROW][C]84[/C][C]1.44170921480102[/C][C]-9.67109662079829[/C][C]12.5545150504003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205037&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.42158362633113	1.39784418803856	1.44532306462369
74	1.40310200955454	1.3779326588225	1.42827136028658
75	1.41619041624024	1.38953551296069	1.4428453195198
76	1.42098090113768	1.39289214565379	1.44906965662158
77	1.41681348897774	1.38737105945094	1.44625591850453
78	1.40166484886862	1.37099023804947	1.43233945968778
79	1.41849214563176	1.38629282359191	1.45069146767161
80	1.40492806015067	1.37155233671297	1.43830378358838
81	1.44333170560191	1.40812255748498	1.47854085371884
82	1.45315972766973	1.41649306877227	1.48982638656719
83	1.44842818866301	1.41053130860397	1.48632506872204
84	1.44170921480102	-9.67109662079829	12.5545150504003

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 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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