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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 16:47:17 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1427989656140ckxc992xxb2c.htm/, Retrieved Thu, 09 May 2024 09:11:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278578, Retrieved Thu, 09 May 2024 09:11:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-02 15:47:17] [1689e0541609f8eb663ad6752b966f5b] [Current]
- RMPD    [Bootstrap Plot - Central Tendency] [] [2015-05-26 19:05:34] [77cae2e8655af67d2d17f40c5b6aa8cb]
- RMPD      [Blocked Bootstrap Plot - Central Tendency] [] [2015-05-26 20:01:38] [77cae2e8655af67d2d17f40c5b6aa8cb]
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Dataseries X:
498.10
498.76
498.88
498.88
498.88
498.88
499.48
501.21
502.05
502.05
502.05
504.10
506.81
516.88
520.43
520.68
520.68
520.68
521.03
521.25
521.25
521.25
521.65
521.65
522.77
518.72
519.27
519.38
521.29
521.29
521.29
523.47
523.86
524.14
524.14
524.14
534.60
534.99
535.39
535.39
535.39
535.39
535.39
535.64
536.08
537.80
537.80
537.80
537.85
544.39
545.15
544.65
544.65
544.65
545.73
548.94
550.94
551.22
551.22
551.22
553.12
565.37
566.73
566.73
566.78
566.78
566.78
566.78
566.93
566.93
566.93
566.93
574.38
574.40
574.40
574.40
574.40
574.40
574.50
574.50
574.67
574.66
574.66
574.94
576.10
583.38
584.15
584.15
584.15
584.15
585.14
585.14
585.67
586.49
586.81
586.85




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278578&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278578&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0022417599933826
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0022417599933826 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278578&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]0.0022417599933826[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278578&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
ParameterValue
alpha1
beta0.0022417599933826
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3498.88499.42-0.539999999999964
4498.88499.538789449604-0.658789449603546
5498.88499.537312601771-0.657312601771366
6498.88499.535839064678-0.655839064677536
7499.48499.5343688309-0.0543688309002732
8501.21500.134246949031.07575305096969
9502.05501.8666585291830.183341470817311
10502.05502.707069536757-0.657069536757092
11502.05502.705596544557-0.655596544556715
12504.1502.7041268544511.39587314554865
13506.81504.7572560670252.05274393297509
14516.88507.471857826259.40814217374952
15520.43517.5629486229882.86705137701233
16520.68521.119375864063-0.43937586406355
17520.68521.368390888829-0.688390888829531
18520.68521.366847681675-0.68684768167509
19521.03521.365307934021-0.335307934020761
20521.25521.714556254109-0.464556254108743
21521.25521.933514830484-0.683514830483659
22521.25521.931982554282-0.681982554281831
23521.65521.930453713075-0.280453713075417
24521.65522.329825003161-0.679825003161454
25522.77522.3283009986670.441699001333063
26518.72523.449291181817-4.72929118181719
27519.27519.388689246049-0.118689246048802
28519.38519.938423173245-0.558423173245274
29521.29520.0471713225161.24282867748377
30521.29521.959957446124-0.669957446123931
31521.29521.958455562324-0.66845556232397
32523.47521.9569570453871.51304295461307
33523.86524.140348924551-0.280348924550935
34524.14524.529720449548-0.389720449547667
35524.14524.808846789835-0.668846789835243
36524.14524.80734739586-0.667347395860133
37534.6524.8058513631669.7941486368336
38534.99535.28780749375-0.297807493749701
39535.39535.677139880824-0.287139880824498
40535.39536.076496182127-0.686496182127144
41535.39536.07495722245-0.684957222450407
42535.39536.073421712752-0.683421712751965
43535.39536.071889645298-0.681889645297701
44535.64536.070361012371-0.430361012371009
45536.08536.319396246271-0.239396246270644
46537.8536.7588595773431.04114042265667
47537.8538.48119356429-0.681193564290311
48537.8538.47966649181-0.679666491810053
49537.85538.47814284266-0.628142842659827
50544.39538.5267346971655.86326530283486
51545.15545.0798787307520.070121269248375
52544.65545.840035925808-1.19003592580771
53544.65545.337368150879-0.687368150878569
54544.65545.335827236457-0.685827236457158
55545.73545.3342897763960.395710223603942
56548.94546.4151768637442.52482313625569
57550.94549.6308369112421.3091630887584
58551.22551.633771740679-0.413771740678726
59551.22551.912844163744-0.692844163744098
60551.22551.911290973416-0.69129097341613
61553.12551.9097412649681.21025873503174
62565.37553.81245437458211.557545625418
63566.73566.0883636179870.641636382013189
64566.73567.449802012758-0.719802012758237
65566.78567.448188389403-0.668188389402985
66566.78567.496690471403-0.716690471403467
67566.78567.495083823377-0.715083823377086
68566.78567.49348077707-0.71348077706989
69566.93567.491881324408-0.561881324407864
70566.93567.640621721334-0.710621721333723
71566.93567.639028677988-0.709028677988385
72566.93567.637439205864-0.707439205863921
73574.38567.6358532969546.74414670304554
74574.4575.100972055223-0.700972055222906
75574.4575.119400644113-0.719400644112966
76574.4575.11778792053-0.717787920529872
77574.4575.116178812286-0.716178812285875
78574.4575.114573311276-0.714573311276354
79574.5575.112971409415-0.61297140941474
80574.5575.211597274632-0.71159727463214
81574.67575.21000204433-0.540002044330436
82574.66575.378791489351-0.718791489351133
83574.66575.367180131347-0.707180131346718
84574.94575.36559480322-0.425594803220065
85576.1575.6446407218170.455359278183096
86583.38576.8056615280296.57433847197069
87584.15584.1003996169990.0496003830012341
88584.15584.870510809153-0.720510809152984
89584.15584.868895596846-0.71889559684621
90584.15584.867284005458-0.717284005457827
91585.14584.865676026870.274323973129526
92585.14585.856290995379-0.716290995378699
93585.67585.854685242882-0.184685242881642
94586.49586.3842712228930.105728777107288
95586.81587.204508241435-0.39450824143546
96586.85587.523623848643-0.673623848642592

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 498.88 & 499.42 & -0.539999999999964 \tabularnewline
4 & 498.88 & 499.538789449604 & -0.658789449603546 \tabularnewline
5 & 498.88 & 499.537312601771 & -0.657312601771366 \tabularnewline
6 & 498.88 & 499.535839064678 & -0.655839064677536 \tabularnewline
7 & 499.48 & 499.5343688309 & -0.0543688309002732 \tabularnewline
8 & 501.21 & 500.13424694903 & 1.07575305096969 \tabularnewline
9 & 502.05 & 501.866658529183 & 0.183341470817311 \tabularnewline
10 & 502.05 & 502.707069536757 & -0.657069536757092 \tabularnewline
11 & 502.05 & 502.705596544557 & -0.655596544556715 \tabularnewline
12 & 504.1 & 502.704126854451 & 1.39587314554865 \tabularnewline
13 & 506.81 & 504.757256067025 & 2.05274393297509 \tabularnewline
14 & 516.88 & 507.47185782625 & 9.40814217374952 \tabularnewline
15 & 520.43 & 517.562948622988 & 2.86705137701233 \tabularnewline
16 & 520.68 & 521.119375864063 & -0.43937586406355 \tabularnewline
17 & 520.68 & 521.368390888829 & -0.688390888829531 \tabularnewline
18 & 520.68 & 521.366847681675 & -0.68684768167509 \tabularnewline
19 & 521.03 & 521.365307934021 & -0.335307934020761 \tabularnewline
20 & 521.25 & 521.714556254109 & -0.464556254108743 \tabularnewline
21 & 521.25 & 521.933514830484 & -0.683514830483659 \tabularnewline
22 & 521.25 & 521.931982554282 & -0.681982554281831 \tabularnewline
23 & 521.65 & 521.930453713075 & -0.280453713075417 \tabularnewline
24 & 521.65 & 522.329825003161 & -0.679825003161454 \tabularnewline
25 & 522.77 & 522.328300998667 & 0.441699001333063 \tabularnewline
26 & 518.72 & 523.449291181817 & -4.72929118181719 \tabularnewline
27 & 519.27 & 519.388689246049 & -0.118689246048802 \tabularnewline
28 & 519.38 & 519.938423173245 & -0.558423173245274 \tabularnewline
29 & 521.29 & 520.047171322516 & 1.24282867748377 \tabularnewline
30 & 521.29 & 521.959957446124 & -0.669957446123931 \tabularnewline
31 & 521.29 & 521.958455562324 & -0.66845556232397 \tabularnewline
32 & 523.47 & 521.956957045387 & 1.51304295461307 \tabularnewline
33 & 523.86 & 524.140348924551 & -0.280348924550935 \tabularnewline
34 & 524.14 & 524.529720449548 & -0.389720449547667 \tabularnewline
35 & 524.14 & 524.808846789835 & -0.668846789835243 \tabularnewline
36 & 524.14 & 524.80734739586 & -0.667347395860133 \tabularnewline
37 & 534.6 & 524.805851363166 & 9.7941486368336 \tabularnewline
38 & 534.99 & 535.28780749375 & -0.297807493749701 \tabularnewline
39 & 535.39 & 535.677139880824 & -0.287139880824498 \tabularnewline
40 & 535.39 & 536.076496182127 & -0.686496182127144 \tabularnewline
41 & 535.39 & 536.07495722245 & -0.684957222450407 \tabularnewline
42 & 535.39 & 536.073421712752 & -0.683421712751965 \tabularnewline
43 & 535.39 & 536.071889645298 & -0.681889645297701 \tabularnewline
44 & 535.64 & 536.070361012371 & -0.430361012371009 \tabularnewline
45 & 536.08 & 536.319396246271 & -0.239396246270644 \tabularnewline
46 & 537.8 & 536.758859577343 & 1.04114042265667 \tabularnewline
47 & 537.8 & 538.48119356429 & -0.681193564290311 \tabularnewline
48 & 537.8 & 538.47966649181 & -0.679666491810053 \tabularnewline
49 & 537.85 & 538.47814284266 & -0.628142842659827 \tabularnewline
50 & 544.39 & 538.526734697165 & 5.86326530283486 \tabularnewline
51 & 545.15 & 545.079878730752 & 0.070121269248375 \tabularnewline
52 & 544.65 & 545.840035925808 & -1.19003592580771 \tabularnewline
53 & 544.65 & 545.337368150879 & -0.687368150878569 \tabularnewline
54 & 544.65 & 545.335827236457 & -0.685827236457158 \tabularnewline
55 & 545.73 & 545.334289776396 & 0.395710223603942 \tabularnewline
56 & 548.94 & 546.415176863744 & 2.52482313625569 \tabularnewline
57 & 550.94 & 549.630836911242 & 1.3091630887584 \tabularnewline
58 & 551.22 & 551.633771740679 & -0.413771740678726 \tabularnewline
59 & 551.22 & 551.912844163744 & -0.692844163744098 \tabularnewline
60 & 551.22 & 551.911290973416 & -0.69129097341613 \tabularnewline
61 & 553.12 & 551.909741264968 & 1.21025873503174 \tabularnewline
62 & 565.37 & 553.812454374582 & 11.557545625418 \tabularnewline
63 & 566.73 & 566.088363617987 & 0.641636382013189 \tabularnewline
64 & 566.73 & 567.449802012758 & -0.719802012758237 \tabularnewline
65 & 566.78 & 567.448188389403 & -0.668188389402985 \tabularnewline
66 & 566.78 & 567.496690471403 & -0.716690471403467 \tabularnewline
67 & 566.78 & 567.495083823377 & -0.715083823377086 \tabularnewline
68 & 566.78 & 567.49348077707 & -0.71348077706989 \tabularnewline
69 & 566.93 & 567.491881324408 & -0.561881324407864 \tabularnewline
70 & 566.93 & 567.640621721334 & -0.710621721333723 \tabularnewline
71 & 566.93 & 567.639028677988 & -0.709028677988385 \tabularnewline
72 & 566.93 & 567.637439205864 & -0.707439205863921 \tabularnewline
73 & 574.38 & 567.635853296954 & 6.74414670304554 \tabularnewline
74 & 574.4 & 575.100972055223 & -0.700972055222906 \tabularnewline
75 & 574.4 & 575.119400644113 & -0.719400644112966 \tabularnewline
76 & 574.4 & 575.11778792053 & -0.717787920529872 \tabularnewline
77 & 574.4 & 575.116178812286 & -0.716178812285875 \tabularnewline
78 & 574.4 & 575.114573311276 & -0.714573311276354 \tabularnewline
79 & 574.5 & 575.112971409415 & -0.61297140941474 \tabularnewline
80 & 574.5 & 575.211597274632 & -0.71159727463214 \tabularnewline
81 & 574.67 & 575.21000204433 & -0.540002044330436 \tabularnewline
82 & 574.66 & 575.378791489351 & -0.718791489351133 \tabularnewline
83 & 574.66 & 575.367180131347 & -0.707180131346718 \tabularnewline
84 & 574.94 & 575.36559480322 & -0.425594803220065 \tabularnewline
85 & 576.1 & 575.644640721817 & 0.455359278183096 \tabularnewline
86 & 583.38 & 576.805661528029 & 6.57433847197069 \tabularnewline
87 & 584.15 & 584.100399616999 & 0.0496003830012341 \tabularnewline
88 & 584.15 & 584.870510809153 & -0.720510809152984 \tabularnewline
89 & 584.15 & 584.868895596846 & -0.71889559684621 \tabularnewline
90 & 584.15 & 584.867284005458 & -0.717284005457827 \tabularnewline
91 & 585.14 & 584.86567602687 & 0.274323973129526 \tabularnewline
92 & 585.14 & 585.856290995379 & -0.716290995378699 \tabularnewline
93 & 585.67 & 585.854685242882 & -0.184685242881642 \tabularnewline
94 & 586.49 & 586.384271222893 & 0.105728777107288 \tabularnewline
95 & 586.81 & 587.204508241435 & -0.39450824143546 \tabularnewline
96 & 586.85 & 587.523623848643 & -0.673623848642592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278578&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]498.88[/C][C]499.42[/C][C]-0.539999999999964[/C][/ROW]
[ROW][C]4[/C][C]498.88[/C][C]499.538789449604[/C][C]-0.658789449603546[/C][/ROW]
[ROW][C]5[/C][C]498.88[/C][C]499.537312601771[/C][C]-0.657312601771366[/C][/ROW]
[ROW][C]6[/C][C]498.88[/C][C]499.535839064678[/C][C]-0.655839064677536[/C][/ROW]
[ROW][C]7[/C][C]499.48[/C][C]499.5343688309[/C][C]-0.0543688309002732[/C][/ROW]
[ROW][C]8[/C][C]501.21[/C][C]500.13424694903[/C][C]1.07575305096969[/C][/ROW]
[ROW][C]9[/C][C]502.05[/C][C]501.866658529183[/C][C]0.183341470817311[/C][/ROW]
[ROW][C]10[/C][C]502.05[/C][C]502.707069536757[/C][C]-0.657069536757092[/C][/ROW]
[ROW][C]11[/C][C]502.05[/C][C]502.705596544557[/C][C]-0.655596544556715[/C][/ROW]
[ROW][C]12[/C][C]504.1[/C][C]502.704126854451[/C][C]1.39587314554865[/C][/ROW]
[ROW][C]13[/C][C]506.81[/C][C]504.757256067025[/C][C]2.05274393297509[/C][/ROW]
[ROW][C]14[/C][C]516.88[/C][C]507.47185782625[/C][C]9.40814217374952[/C][/ROW]
[ROW][C]15[/C][C]520.43[/C][C]517.562948622988[/C][C]2.86705137701233[/C][/ROW]
[ROW][C]16[/C][C]520.68[/C][C]521.119375864063[/C][C]-0.43937586406355[/C][/ROW]
[ROW][C]17[/C][C]520.68[/C][C]521.368390888829[/C][C]-0.688390888829531[/C][/ROW]
[ROW][C]18[/C][C]520.68[/C][C]521.366847681675[/C][C]-0.68684768167509[/C][/ROW]
[ROW][C]19[/C][C]521.03[/C][C]521.365307934021[/C][C]-0.335307934020761[/C][/ROW]
[ROW][C]20[/C][C]521.25[/C][C]521.714556254109[/C][C]-0.464556254108743[/C][/ROW]
[ROW][C]21[/C][C]521.25[/C][C]521.933514830484[/C][C]-0.683514830483659[/C][/ROW]
[ROW][C]22[/C][C]521.25[/C][C]521.931982554282[/C][C]-0.681982554281831[/C][/ROW]
[ROW][C]23[/C][C]521.65[/C][C]521.930453713075[/C][C]-0.280453713075417[/C][/ROW]
[ROW][C]24[/C][C]521.65[/C][C]522.329825003161[/C][C]-0.679825003161454[/C][/ROW]
[ROW][C]25[/C][C]522.77[/C][C]522.328300998667[/C][C]0.441699001333063[/C][/ROW]
[ROW][C]26[/C][C]518.72[/C][C]523.449291181817[/C][C]-4.72929118181719[/C][/ROW]
[ROW][C]27[/C][C]519.27[/C][C]519.388689246049[/C][C]-0.118689246048802[/C][/ROW]
[ROW][C]28[/C][C]519.38[/C][C]519.938423173245[/C][C]-0.558423173245274[/C][/ROW]
[ROW][C]29[/C][C]521.29[/C][C]520.047171322516[/C][C]1.24282867748377[/C][/ROW]
[ROW][C]30[/C][C]521.29[/C][C]521.959957446124[/C][C]-0.669957446123931[/C][/ROW]
[ROW][C]31[/C][C]521.29[/C][C]521.958455562324[/C][C]-0.66845556232397[/C][/ROW]
[ROW][C]32[/C][C]523.47[/C][C]521.956957045387[/C][C]1.51304295461307[/C][/ROW]
[ROW][C]33[/C][C]523.86[/C][C]524.140348924551[/C][C]-0.280348924550935[/C][/ROW]
[ROW][C]34[/C][C]524.14[/C][C]524.529720449548[/C][C]-0.389720449547667[/C][/ROW]
[ROW][C]35[/C][C]524.14[/C][C]524.808846789835[/C][C]-0.668846789835243[/C][/ROW]
[ROW][C]36[/C][C]524.14[/C][C]524.80734739586[/C][C]-0.667347395860133[/C][/ROW]
[ROW][C]37[/C][C]534.6[/C][C]524.805851363166[/C][C]9.7941486368336[/C][/ROW]
[ROW][C]38[/C][C]534.99[/C][C]535.28780749375[/C][C]-0.297807493749701[/C][/ROW]
[ROW][C]39[/C][C]535.39[/C][C]535.677139880824[/C][C]-0.287139880824498[/C][/ROW]
[ROW][C]40[/C][C]535.39[/C][C]536.076496182127[/C][C]-0.686496182127144[/C][/ROW]
[ROW][C]41[/C][C]535.39[/C][C]536.07495722245[/C][C]-0.684957222450407[/C][/ROW]
[ROW][C]42[/C][C]535.39[/C][C]536.073421712752[/C][C]-0.683421712751965[/C][/ROW]
[ROW][C]43[/C][C]535.39[/C][C]536.071889645298[/C][C]-0.681889645297701[/C][/ROW]
[ROW][C]44[/C][C]535.64[/C][C]536.070361012371[/C][C]-0.430361012371009[/C][/ROW]
[ROW][C]45[/C][C]536.08[/C][C]536.319396246271[/C][C]-0.239396246270644[/C][/ROW]
[ROW][C]46[/C][C]537.8[/C][C]536.758859577343[/C][C]1.04114042265667[/C][/ROW]
[ROW][C]47[/C][C]537.8[/C][C]538.48119356429[/C][C]-0.681193564290311[/C][/ROW]
[ROW][C]48[/C][C]537.8[/C][C]538.47966649181[/C][C]-0.679666491810053[/C][/ROW]
[ROW][C]49[/C][C]537.85[/C][C]538.47814284266[/C][C]-0.628142842659827[/C][/ROW]
[ROW][C]50[/C][C]544.39[/C][C]538.526734697165[/C][C]5.86326530283486[/C][/ROW]
[ROW][C]51[/C][C]545.15[/C][C]545.079878730752[/C][C]0.070121269248375[/C][/ROW]
[ROW][C]52[/C][C]544.65[/C][C]545.840035925808[/C][C]-1.19003592580771[/C][/ROW]
[ROW][C]53[/C][C]544.65[/C][C]545.337368150879[/C][C]-0.687368150878569[/C][/ROW]
[ROW][C]54[/C][C]544.65[/C][C]545.335827236457[/C][C]-0.685827236457158[/C][/ROW]
[ROW][C]55[/C][C]545.73[/C][C]545.334289776396[/C][C]0.395710223603942[/C][/ROW]
[ROW][C]56[/C][C]548.94[/C][C]546.415176863744[/C][C]2.52482313625569[/C][/ROW]
[ROW][C]57[/C][C]550.94[/C][C]549.630836911242[/C][C]1.3091630887584[/C][/ROW]
[ROW][C]58[/C][C]551.22[/C][C]551.633771740679[/C][C]-0.413771740678726[/C][/ROW]
[ROW][C]59[/C][C]551.22[/C][C]551.912844163744[/C][C]-0.692844163744098[/C][/ROW]
[ROW][C]60[/C][C]551.22[/C][C]551.911290973416[/C][C]-0.69129097341613[/C][/ROW]
[ROW][C]61[/C][C]553.12[/C][C]551.909741264968[/C][C]1.21025873503174[/C][/ROW]
[ROW][C]62[/C][C]565.37[/C][C]553.812454374582[/C][C]11.557545625418[/C][/ROW]
[ROW][C]63[/C][C]566.73[/C][C]566.088363617987[/C][C]0.641636382013189[/C][/ROW]
[ROW][C]64[/C][C]566.73[/C][C]567.449802012758[/C][C]-0.719802012758237[/C][/ROW]
[ROW][C]65[/C][C]566.78[/C][C]567.448188389403[/C][C]-0.668188389402985[/C][/ROW]
[ROW][C]66[/C][C]566.78[/C][C]567.496690471403[/C][C]-0.716690471403467[/C][/ROW]
[ROW][C]67[/C][C]566.78[/C][C]567.495083823377[/C][C]-0.715083823377086[/C][/ROW]
[ROW][C]68[/C][C]566.78[/C][C]567.49348077707[/C][C]-0.71348077706989[/C][/ROW]
[ROW][C]69[/C][C]566.93[/C][C]567.491881324408[/C][C]-0.561881324407864[/C][/ROW]
[ROW][C]70[/C][C]566.93[/C][C]567.640621721334[/C][C]-0.710621721333723[/C][/ROW]
[ROW][C]71[/C][C]566.93[/C][C]567.639028677988[/C][C]-0.709028677988385[/C][/ROW]
[ROW][C]72[/C][C]566.93[/C][C]567.637439205864[/C][C]-0.707439205863921[/C][/ROW]
[ROW][C]73[/C][C]574.38[/C][C]567.635853296954[/C][C]6.74414670304554[/C][/ROW]
[ROW][C]74[/C][C]574.4[/C][C]575.100972055223[/C][C]-0.700972055222906[/C][/ROW]
[ROW][C]75[/C][C]574.4[/C][C]575.119400644113[/C][C]-0.719400644112966[/C][/ROW]
[ROW][C]76[/C][C]574.4[/C][C]575.11778792053[/C][C]-0.717787920529872[/C][/ROW]
[ROW][C]77[/C][C]574.4[/C][C]575.116178812286[/C][C]-0.716178812285875[/C][/ROW]
[ROW][C]78[/C][C]574.4[/C][C]575.114573311276[/C][C]-0.714573311276354[/C][/ROW]
[ROW][C]79[/C][C]574.5[/C][C]575.112971409415[/C][C]-0.61297140941474[/C][/ROW]
[ROW][C]80[/C][C]574.5[/C][C]575.211597274632[/C][C]-0.71159727463214[/C][/ROW]
[ROW][C]81[/C][C]574.67[/C][C]575.21000204433[/C][C]-0.540002044330436[/C][/ROW]
[ROW][C]82[/C][C]574.66[/C][C]575.378791489351[/C][C]-0.718791489351133[/C][/ROW]
[ROW][C]83[/C][C]574.66[/C][C]575.367180131347[/C][C]-0.707180131346718[/C][/ROW]
[ROW][C]84[/C][C]574.94[/C][C]575.36559480322[/C][C]-0.425594803220065[/C][/ROW]
[ROW][C]85[/C][C]576.1[/C][C]575.644640721817[/C][C]0.455359278183096[/C][/ROW]
[ROW][C]86[/C][C]583.38[/C][C]576.805661528029[/C][C]6.57433847197069[/C][/ROW]
[ROW][C]87[/C][C]584.15[/C][C]584.100399616999[/C][C]0.0496003830012341[/C][/ROW]
[ROW][C]88[/C][C]584.15[/C][C]584.870510809153[/C][C]-0.720510809152984[/C][/ROW]
[ROW][C]89[/C][C]584.15[/C][C]584.868895596846[/C][C]-0.71889559684621[/C][/ROW]
[ROW][C]90[/C][C]584.15[/C][C]584.867284005458[/C][C]-0.717284005457827[/C][/ROW]
[ROW][C]91[/C][C]585.14[/C][C]584.86567602687[/C][C]0.274323973129526[/C][/ROW]
[ROW][C]92[/C][C]585.14[/C][C]585.856290995379[/C][C]-0.716290995378699[/C][/ROW]
[ROW][C]93[/C][C]585.67[/C][C]585.854685242882[/C][C]-0.184685242881642[/C][/ROW]
[ROW][C]94[/C][C]586.49[/C][C]586.384271222893[/C][C]0.105728777107288[/C][/ROW]
[ROW][C]95[/C][C]586.81[/C][C]587.204508241435[/C][C]-0.39450824143546[/C][/ROW]
[ROW][C]96[/C][C]586.85[/C][C]587.523623848643[/C][C]-0.673623848642592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278578&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278578&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
tObservedFittedResiduals
3498.88499.42-0.539999999999964
4498.88499.538789449604-0.658789449603546
5498.88499.537312601771-0.657312601771366
6498.88499.535839064678-0.655839064677536
7499.48499.5343688309-0.0543688309002732
8501.21500.134246949031.07575305096969
9502.05501.8666585291830.183341470817311
10502.05502.707069536757-0.657069536757092
11502.05502.705596544557-0.655596544556715
12504.1502.7041268544511.39587314554865
13506.81504.7572560670252.05274393297509
14516.88507.471857826259.40814217374952
15520.43517.5629486229882.86705137701233
16520.68521.119375864063-0.43937586406355
17520.68521.368390888829-0.688390888829531
18520.68521.366847681675-0.68684768167509
19521.03521.365307934021-0.335307934020761
20521.25521.714556254109-0.464556254108743
21521.25521.933514830484-0.683514830483659
22521.25521.931982554282-0.681982554281831
23521.65521.930453713075-0.280453713075417
24521.65522.329825003161-0.679825003161454
25522.77522.3283009986670.441699001333063
26518.72523.449291181817-4.72929118181719
27519.27519.388689246049-0.118689246048802
28519.38519.938423173245-0.558423173245274
29521.29520.0471713225161.24282867748377
30521.29521.959957446124-0.669957446123931
31521.29521.958455562324-0.66845556232397
32523.47521.9569570453871.51304295461307
33523.86524.140348924551-0.280348924550935
34524.14524.529720449548-0.389720449547667
35524.14524.808846789835-0.668846789835243
36524.14524.80734739586-0.667347395860133
37534.6524.8058513631669.7941486368336
38534.99535.28780749375-0.297807493749701
39535.39535.677139880824-0.287139880824498
40535.39536.076496182127-0.686496182127144
41535.39536.07495722245-0.684957222450407
42535.39536.073421712752-0.683421712751965
43535.39536.071889645298-0.681889645297701
44535.64536.070361012371-0.430361012371009
45536.08536.319396246271-0.239396246270644
46537.8536.7588595773431.04114042265667
47537.8538.48119356429-0.681193564290311
48537.8538.47966649181-0.679666491810053
49537.85538.47814284266-0.628142842659827
50544.39538.5267346971655.86326530283486
51545.15545.0798787307520.070121269248375
52544.65545.840035925808-1.19003592580771
53544.65545.337368150879-0.687368150878569
54544.65545.335827236457-0.685827236457158
55545.73545.3342897763960.395710223603942
56548.94546.4151768637442.52482313625569
57550.94549.6308369112421.3091630887584
58551.22551.633771740679-0.413771740678726
59551.22551.912844163744-0.692844163744098
60551.22551.911290973416-0.69129097341613
61553.12551.9097412649681.21025873503174
62565.37553.81245437458211.557545625418
63566.73566.0883636179870.641636382013189
64566.73567.449802012758-0.719802012758237
65566.78567.448188389403-0.668188389402985
66566.78567.496690471403-0.716690471403467
67566.78567.495083823377-0.715083823377086
68566.78567.49348077707-0.71348077706989
69566.93567.491881324408-0.561881324407864
70566.93567.640621721334-0.710621721333723
71566.93567.639028677988-0.709028677988385
72566.93567.637439205864-0.707439205863921
73574.38567.6358532969546.74414670304554
74574.4575.100972055223-0.700972055222906
75574.4575.119400644113-0.719400644112966
76574.4575.11778792053-0.717787920529872
77574.4575.116178812286-0.716178812285875
78574.4575.114573311276-0.714573311276354
79574.5575.112971409415-0.61297140941474
80574.5575.211597274632-0.71159727463214
81574.67575.21000204433-0.540002044330436
82574.66575.378791489351-0.718791489351133
83574.66575.367180131347-0.707180131346718
84574.94575.36559480322-0.425594803220065
85576.1575.6446407218170.455359278183096
86583.38576.8056615280296.57433847197069
87584.15584.1003996169990.0496003830012341
88584.15584.870510809153-0.720510809152984
89584.15584.868895596846-0.71889559684621
90584.15584.867284005458-0.717284005457827
91585.14584.865676026870.274323973129526
92585.14585.856290995379-0.716290995378699
93585.67585.854685242882-0.184685242881642
94586.49586.3842712228930.105728777107288
95586.81587.204508241435-0.39450824143546
96586.85587.523623848643-0.673623848642592







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97587.562113745648582.94718137102592.177046120277
98588.274227491297581.740408019151594.808046963442
99588.986341236945580.975111476276596.997570997614
100589.698454982593580.437524627871598.959385337315
101590.410568728241580.044947800068600.776189656415
102591.122682473889579.755017150058602.490347797721
103591.834796219538579.542595514993604.126996924083
104592.546909965186579.391323280176605.702496650196
105593.259023710834579.289849877917607.228197543752
106593.971137456482579.229920347136608.712354565828
107594.683251202131579.205309867434610.161192536827
108595.395364947779579.21118780088611.579542094678

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 587.562113745648 & 582.94718137102 & 592.177046120277 \tabularnewline
98 & 588.274227491297 & 581.740408019151 & 594.808046963442 \tabularnewline
99 & 588.986341236945 & 580.975111476276 & 596.997570997614 \tabularnewline
100 & 589.698454982593 & 580.437524627871 & 598.959385337315 \tabularnewline
101 & 590.410568728241 & 580.044947800068 & 600.776189656415 \tabularnewline
102 & 591.122682473889 & 579.755017150058 & 602.490347797721 \tabularnewline
103 & 591.834796219538 & 579.542595514993 & 604.126996924083 \tabularnewline
104 & 592.546909965186 & 579.391323280176 & 605.702496650196 \tabularnewline
105 & 593.259023710834 & 579.289849877917 & 607.228197543752 \tabularnewline
106 & 593.971137456482 & 579.229920347136 & 608.712354565828 \tabularnewline
107 & 594.683251202131 & 579.205309867434 & 610.161192536827 \tabularnewline
108 & 595.395364947779 & 579.21118780088 & 611.579542094678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278578&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]97[/C][C]587.562113745648[/C][C]582.94718137102[/C][C]592.177046120277[/C][/ROW]
[ROW][C]98[/C][C]588.274227491297[/C][C]581.740408019151[/C][C]594.808046963442[/C][/ROW]
[ROW][C]99[/C][C]588.986341236945[/C][C]580.975111476276[/C][C]596.997570997614[/C][/ROW]
[ROW][C]100[/C][C]589.698454982593[/C][C]580.437524627871[/C][C]598.959385337315[/C][/ROW]
[ROW][C]101[/C][C]590.410568728241[/C][C]580.044947800068[/C][C]600.776189656415[/C][/ROW]
[ROW][C]102[/C][C]591.122682473889[/C][C]579.755017150058[/C][C]602.490347797721[/C][/ROW]
[ROW][C]103[/C][C]591.834796219538[/C][C]579.542595514993[/C][C]604.126996924083[/C][/ROW]
[ROW][C]104[/C][C]592.546909965186[/C][C]579.391323280176[/C][C]605.702496650196[/C][/ROW]
[ROW][C]105[/C][C]593.259023710834[/C][C]579.289849877917[/C][C]607.228197543752[/C][/ROW]
[ROW][C]106[/C][C]593.971137456482[/C][C]579.229920347136[/C][C]608.712354565828[/C][/ROW]
[ROW][C]107[/C][C]594.683251202131[/C][C]579.205309867434[/C][C]610.161192536827[/C][/ROW]
[ROW][C]108[/C][C]595.395364947779[/C][C]579.21118780088[/C][C]611.579542094678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278578&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278578&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
tForecast95% Lower Bound95% Upper Bound
97587.562113745648582.94718137102592.177046120277
98588.274227491297581.740408019151594.808046963442
99588.986341236945580.975111476276596.997570997614
100589.698454982593580.437524627871598.959385337315
101590.410568728241580.044947800068600.776189656415
102591.122682473889579.755017150058602.490347797721
103591.834796219538579.542595514993604.126996924083
104592.546909965186579.391323280176605.702496650196
105593.259023710834579.289849877917607.228197543752
106593.971137456482579.229920347136608.712354565828
107594.683251202131579.205309867434610.161192536827
108595.395364947779579.21118780088611.579542094678



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')