Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 10:45:21 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t1386863178p26ymulqhvz0tyj.htm/, Retrieved Sun, 05 Dec 2021 18:30:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232256, Retrieved Sun, 05 Dec 2021 18:30:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2013-12-04 17:53:18] [690d16d4043299b57a561aafa34f3099]
- RMP     [Exponential Smoothing] [] [2013-12-12 15:45:21] [180e98ae07f6df0eca7781798569558e] [Current]
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Dataseries X:
25
24
25
27
24
26
24
24
21
23
24
23
22
25
26
22
24
22
23
25
24
24
21
22
21
21
20
20
22
21
23
22
24
21
22
20
23
21
21
21
22
24
21
23
25
23
24
25
28
26
25
24
25
26
24
21
22
25
27
26
24
27
23
23
23
25
26
22
23
27
25
24
21
24
22
26
22
25
20
21
23
24
24
18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232256&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232256&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.251311204357706
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.251311204357706 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232256&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]0.251311204357706[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232256&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
alpha0.251311204357706
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22425-1
32524.74868879564230.251311204357705
42724.8118461170782.18815388292198
52425.3617537047151-1.36175370471513
62625.01952974114460.980470258855398
72425.2659329027345-1.26593290273446
82424.9477897803122-0.947789780312217
92124.709599589144-3.70959958914403
102323.7773356487114-0.777335648711389
112423.58198249064360.418017509356449
122323.6870349743625-0.687034974362529
132223.5143753875196-1.51437538751962
142523.13379588503241.8662041149676
152623.60279388874222.39720611125779
162224.2052386436561-2.20523864365606
172423.65103746422270.3489625357773
182223.7387356593646-1.73873565936461
192323.30177190675-0.301771906750002
202523.22593324542331.77406675457666
212423.6717760981270.328223901873034
222423.75426244220570.245737557794335
232123.8160190438109-2.81601904381088
242223.1083219064165-1.10832190641653
252122.829788193299-1.82978819329896
262122.3699419187215-1.36994191872149
272022.0256601652275-2.02566016522749
282021.5165890694847-1.51658906948474
292221.13545324391680.864546756083204
302121.3527235304116-0.352723530411613
312321.26408015517861.73591984482143
322221.70033626204910.299663737950915
332421.77564511693592.22435488306414
342122.3346504215177-1.33465042151765
352221.99923781668950.000762183310467179
362021.9994293618952-1.99942936189523
372321.49695036092921.50304963907082
382121.8746835759335-0.874683575933481
392121.6548657930337-0.654865793033732
402121.4902906818938-0.490290681893761
412221.36707514014170.632924859858321
422421.52613624894062.47386375105939
432122.1478459276362-1.14784592763622
442321.85937938514491.14062061485513
452522.14603012557932.85396987442066
462322.86326473192060.136735268079391
472422.89762783681981.10237216318018
482523.1746663127991.82533368720096
492823.63339312008424.3666068799158
502624.73077035403251.26922964596751
512525.0497419849671-0.0497419849670884
522425.0372412668179-1.03724126681787
532524.77657091484440.223429085155644
542624.83272114732341.16727885267664
552425.1260714016108-1.12607140161081
562124.8430770414792-3.84307704147923
572223.8772687217456-1.87726872174563
582523.40549005838071.59450994161931
592723.80620827216943.19379172783063
602624.60884391775821.39115608224184
612424.9584570282359-0.958457028235909
622724.71758603814482.28241396185517
632325.2911822397415-2.2911822397415
642324.7153824716691-1.71538247166908
652324.2842876367798-1.28428763677982
662523.9615317640391.03846823596103
672624.22251046710561.77748953289444
682224.6692135023505-2.66921350235048
692323.9984102423869-0.998410242386932
702723.74749856192963.2525014380704
712524.56488861550620.435111384493755
722424.6742369815731-0.67423698157312
732124.5047936737115-3.50479367371148
742423.62399975454580.376000245454225
752223.7184928290697-1.71849282906967
762623.28661632651612.71338367348391
772223.9685200453839-1.96852004538387
782523.47380890197621.52619109802384
792023.8573578249005-3.85735782490054
802122.8879605842862-1.88796058428617
812322.41349493606930.586505063930669
822422.56089023004761.43910976995236
832422.92255463953731.07744536046269
841823.1933287307048-5.19332873070481

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 24 & 25 & -1 \tabularnewline
3 & 25 & 24.7486887956423 & 0.251311204357705 \tabularnewline
4 & 27 & 24.811846117078 & 2.18815388292198 \tabularnewline
5 & 24 & 25.3617537047151 & -1.36175370471513 \tabularnewline
6 & 26 & 25.0195297411446 & 0.980470258855398 \tabularnewline
7 & 24 & 25.2659329027345 & -1.26593290273446 \tabularnewline
8 & 24 & 24.9477897803122 & -0.947789780312217 \tabularnewline
9 & 21 & 24.709599589144 & -3.70959958914403 \tabularnewline
10 & 23 & 23.7773356487114 & -0.777335648711389 \tabularnewline
11 & 24 & 23.5819824906436 & 0.418017509356449 \tabularnewline
12 & 23 & 23.6870349743625 & -0.687034974362529 \tabularnewline
13 & 22 & 23.5143753875196 & -1.51437538751962 \tabularnewline
14 & 25 & 23.1337958850324 & 1.8662041149676 \tabularnewline
15 & 26 & 23.6027938887422 & 2.39720611125779 \tabularnewline
16 & 22 & 24.2052386436561 & -2.20523864365606 \tabularnewline
17 & 24 & 23.6510374642227 & 0.3489625357773 \tabularnewline
18 & 22 & 23.7387356593646 & -1.73873565936461 \tabularnewline
19 & 23 & 23.30177190675 & -0.301771906750002 \tabularnewline
20 & 25 & 23.2259332454233 & 1.77406675457666 \tabularnewline
21 & 24 & 23.671776098127 & 0.328223901873034 \tabularnewline
22 & 24 & 23.7542624422057 & 0.245737557794335 \tabularnewline
23 & 21 & 23.8160190438109 & -2.81601904381088 \tabularnewline
24 & 22 & 23.1083219064165 & -1.10832190641653 \tabularnewline
25 & 21 & 22.829788193299 & -1.82978819329896 \tabularnewline
26 & 21 & 22.3699419187215 & -1.36994191872149 \tabularnewline
27 & 20 & 22.0256601652275 & -2.02566016522749 \tabularnewline
28 & 20 & 21.5165890694847 & -1.51658906948474 \tabularnewline
29 & 22 & 21.1354532439168 & 0.864546756083204 \tabularnewline
30 & 21 & 21.3527235304116 & -0.352723530411613 \tabularnewline
31 & 23 & 21.2640801551786 & 1.73591984482143 \tabularnewline
32 & 22 & 21.7003362620491 & 0.299663737950915 \tabularnewline
33 & 24 & 21.7756451169359 & 2.22435488306414 \tabularnewline
34 & 21 & 22.3346504215177 & -1.33465042151765 \tabularnewline
35 & 22 & 21.9992378166895 & 0.000762183310467179 \tabularnewline
36 & 20 & 21.9994293618952 & -1.99942936189523 \tabularnewline
37 & 23 & 21.4969503609292 & 1.50304963907082 \tabularnewline
38 & 21 & 21.8746835759335 & -0.874683575933481 \tabularnewline
39 & 21 & 21.6548657930337 & -0.654865793033732 \tabularnewline
40 & 21 & 21.4902906818938 & -0.490290681893761 \tabularnewline
41 & 22 & 21.3670751401417 & 0.632924859858321 \tabularnewline
42 & 24 & 21.5261362489406 & 2.47386375105939 \tabularnewline
43 & 21 & 22.1478459276362 & -1.14784592763622 \tabularnewline
44 & 23 & 21.8593793851449 & 1.14062061485513 \tabularnewline
45 & 25 & 22.1460301255793 & 2.85396987442066 \tabularnewline
46 & 23 & 22.8632647319206 & 0.136735268079391 \tabularnewline
47 & 24 & 22.8976278368198 & 1.10237216318018 \tabularnewline
48 & 25 & 23.174666312799 & 1.82533368720096 \tabularnewline
49 & 28 & 23.6333931200842 & 4.3666068799158 \tabularnewline
50 & 26 & 24.7307703540325 & 1.26922964596751 \tabularnewline
51 & 25 & 25.0497419849671 & -0.0497419849670884 \tabularnewline
52 & 24 & 25.0372412668179 & -1.03724126681787 \tabularnewline
53 & 25 & 24.7765709148444 & 0.223429085155644 \tabularnewline
54 & 26 & 24.8327211473234 & 1.16727885267664 \tabularnewline
55 & 24 & 25.1260714016108 & -1.12607140161081 \tabularnewline
56 & 21 & 24.8430770414792 & -3.84307704147923 \tabularnewline
57 & 22 & 23.8772687217456 & -1.87726872174563 \tabularnewline
58 & 25 & 23.4054900583807 & 1.59450994161931 \tabularnewline
59 & 27 & 23.8062082721694 & 3.19379172783063 \tabularnewline
60 & 26 & 24.6088439177582 & 1.39115608224184 \tabularnewline
61 & 24 & 24.9584570282359 & -0.958457028235909 \tabularnewline
62 & 27 & 24.7175860381448 & 2.28241396185517 \tabularnewline
63 & 23 & 25.2911822397415 & -2.2911822397415 \tabularnewline
64 & 23 & 24.7153824716691 & -1.71538247166908 \tabularnewline
65 & 23 & 24.2842876367798 & -1.28428763677982 \tabularnewline
66 & 25 & 23.961531764039 & 1.03846823596103 \tabularnewline
67 & 26 & 24.2225104671056 & 1.77748953289444 \tabularnewline
68 & 22 & 24.6692135023505 & -2.66921350235048 \tabularnewline
69 & 23 & 23.9984102423869 & -0.998410242386932 \tabularnewline
70 & 27 & 23.7474985619296 & 3.2525014380704 \tabularnewline
71 & 25 & 24.5648886155062 & 0.435111384493755 \tabularnewline
72 & 24 & 24.6742369815731 & -0.67423698157312 \tabularnewline
73 & 21 & 24.5047936737115 & -3.50479367371148 \tabularnewline
74 & 24 & 23.6239997545458 & 0.376000245454225 \tabularnewline
75 & 22 & 23.7184928290697 & -1.71849282906967 \tabularnewline
76 & 26 & 23.2866163265161 & 2.71338367348391 \tabularnewline
77 & 22 & 23.9685200453839 & -1.96852004538387 \tabularnewline
78 & 25 & 23.4738089019762 & 1.52619109802384 \tabularnewline
79 & 20 & 23.8573578249005 & -3.85735782490054 \tabularnewline
80 & 21 & 22.8879605842862 & -1.88796058428617 \tabularnewline
81 & 23 & 22.4134949360693 & 0.586505063930669 \tabularnewline
82 & 24 & 22.5608902300476 & 1.43910976995236 \tabularnewline
83 & 24 & 22.9225546395373 & 1.07744536046269 \tabularnewline
84 & 18 & 23.1933287307048 & -5.19332873070481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232256&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]24[/C][C]25[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]25[/C][C]24.7486887956423[/C][C]0.251311204357705[/C][/ROW]
[ROW][C]4[/C][C]27[/C][C]24.811846117078[/C][C]2.18815388292198[/C][/ROW]
[ROW][C]5[/C][C]24[/C][C]25.3617537047151[/C][C]-1.36175370471513[/C][/ROW]
[ROW][C]6[/C][C]26[/C][C]25.0195297411446[/C][C]0.980470258855398[/C][/ROW]
[ROW][C]7[/C][C]24[/C][C]25.2659329027345[/C][C]-1.26593290273446[/C][/ROW]
[ROW][C]8[/C][C]24[/C][C]24.9477897803122[/C][C]-0.947789780312217[/C][/ROW]
[ROW][C]9[/C][C]21[/C][C]24.709599589144[/C][C]-3.70959958914403[/C][/ROW]
[ROW][C]10[/C][C]23[/C][C]23.7773356487114[/C][C]-0.777335648711389[/C][/ROW]
[ROW][C]11[/C][C]24[/C][C]23.5819824906436[/C][C]0.418017509356449[/C][/ROW]
[ROW][C]12[/C][C]23[/C][C]23.6870349743625[/C][C]-0.687034974362529[/C][/ROW]
[ROW][C]13[/C][C]22[/C][C]23.5143753875196[/C][C]-1.51437538751962[/C][/ROW]
[ROW][C]14[/C][C]25[/C][C]23.1337958850324[/C][C]1.8662041149676[/C][/ROW]
[ROW][C]15[/C][C]26[/C][C]23.6027938887422[/C][C]2.39720611125779[/C][/ROW]
[ROW][C]16[/C][C]22[/C][C]24.2052386436561[/C][C]-2.20523864365606[/C][/ROW]
[ROW][C]17[/C][C]24[/C][C]23.6510374642227[/C][C]0.3489625357773[/C][/ROW]
[ROW][C]18[/C][C]22[/C][C]23.7387356593646[/C][C]-1.73873565936461[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]23.30177190675[/C][C]-0.301771906750002[/C][/ROW]
[ROW][C]20[/C][C]25[/C][C]23.2259332454233[/C][C]1.77406675457666[/C][/ROW]
[ROW][C]21[/C][C]24[/C][C]23.671776098127[/C][C]0.328223901873034[/C][/ROW]
[ROW][C]22[/C][C]24[/C][C]23.7542624422057[/C][C]0.245737557794335[/C][/ROW]
[ROW][C]23[/C][C]21[/C][C]23.8160190438109[/C][C]-2.81601904381088[/C][/ROW]
[ROW][C]24[/C][C]22[/C][C]23.1083219064165[/C][C]-1.10832190641653[/C][/ROW]
[ROW][C]25[/C][C]21[/C][C]22.829788193299[/C][C]-1.82978819329896[/C][/ROW]
[ROW][C]26[/C][C]21[/C][C]22.3699419187215[/C][C]-1.36994191872149[/C][/ROW]
[ROW][C]27[/C][C]20[/C][C]22.0256601652275[/C][C]-2.02566016522749[/C][/ROW]
[ROW][C]28[/C][C]20[/C][C]21.5165890694847[/C][C]-1.51658906948474[/C][/ROW]
[ROW][C]29[/C][C]22[/C][C]21.1354532439168[/C][C]0.864546756083204[/C][/ROW]
[ROW][C]30[/C][C]21[/C][C]21.3527235304116[/C][C]-0.352723530411613[/C][/ROW]
[ROW][C]31[/C][C]23[/C][C]21.2640801551786[/C][C]1.73591984482143[/C][/ROW]
[ROW][C]32[/C][C]22[/C][C]21.7003362620491[/C][C]0.299663737950915[/C][/ROW]
[ROW][C]33[/C][C]24[/C][C]21.7756451169359[/C][C]2.22435488306414[/C][/ROW]
[ROW][C]34[/C][C]21[/C][C]22.3346504215177[/C][C]-1.33465042151765[/C][/ROW]
[ROW][C]35[/C][C]22[/C][C]21.9992378166895[/C][C]0.000762183310467179[/C][/ROW]
[ROW][C]36[/C][C]20[/C][C]21.9994293618952[/C][C]-1.99942936189523[/C][/ROW]
[ROW][C]37[/C][C]23[/C][C]21.4969503609292[/C][C]1.50304963907082[/C][/ROW]
[ROW][C]38[/C][C]21[/C][C]21.8746835759335[/C][C]-0.874683575933481[/C][/ROW]
[ROW][C]39[/C][C]21[/C][C]21.6548657930337[/C][C]-0.654865793033732[/C][/ROW]
[ROW][C]40[/C][C]21[/C][C]21.4902906818938[/C][C]-0.490290681893761[/C][/ROW]
[ROW][C]41[/C][C]22[/C][C]21.3670751401417[/C][C]0.632924859858321[/C][/ROW]
[ROW][C]42[/C][C]24[/C][C]21.5261362489406[/C][C]2.47386375105939[/C][/ROW]
[ROW][C]43[/C][C]21[/C][C]22.1478459276362[/C][C]-1.14784592763622[/C][/ROW]
[ROW][C]44[/C][C]23[/C][C]21.8593793851449[/C][C]1.14062061485513[/C][/ROW]
[ROW][C]45[/C][C]25[/C][C]22.1460301255793[/C][C]2.85396987442066[/C][/ROW]
[ROW][C]46[/C][C]23[/C][C]22.8632647319206[/C][C]0.136735268079391[/C][/ROW]
[ROW][C]47[/C][C]24[/C][C]22.8976278368198[/C][C]1.10237216318018[/C][/ROW]
[ROW][C]48[/C][C]25[/C][C]23.174666312799[/C][C]1.82533368720096[/C][/ROW]
[ROW][C]49[/C][C]28[/C][C]23.6333931200842[/C][C]4.3666068799158[/C][/ROW]
[ROW][C]50[/C][C]26[/C][C]24.7307703540325[/C][C]1.26922964596751[/C][/ROW]
[ROW][C]51[/C][C]25[/C][C]25.0497419849671[/C][C]-0.0497419849670884[/C][/ROW]
[ROW][C]52[/C][C]24[/C][C]25.0372412668179[/C][C]-1.03724126681787[/C][/ROW]
[ROW][C]53[/C][C]25[/C][C]24.7765709148444[/C][C]0.223429085155644[/C][/ROW]
[ROW][C]54[/C][C]26[/C][C]24.8327211473234[/C][C]1.16727885267664[/C][/ROW]
[ROW][C]55[/C][C]24[/C][C]25.1260714016108[/C][C]-1.12607140161081[/C][/ROW]
[ROW][C]56[/C][C]21[/C][C]24.8430770414792[/C][C]-3.84307704147923[/C][/ROW]
[ROW][C]57[/C][C]22[/C][C]23.8772687217456[/C][C]-1.87726872174563[/C][/ROW]
[ROW][C]58[/C][C]25[/C][C]23.4054900583807[/C][C]1.59450994161931[/C][/ROW]
[ROW][C]59[/C][C]27[/C][C]23.8062082721694[/C][C]3.19379172783063[/C][/ROW]
[ROW][C]60[/C][C]26[/C][C]24.6088439177582[/C][C]1.39115608224184[/C][/ROW]
[ROW][C]61[/C][C]24[/C][C]24.9584570282359[/C][C]-0.958457028235909[/C][/ROW]
[ROW][C]62[/C][C]27[/C][C]24.7175860381448[/C][C]2.28241396185517[/C][/ROW]
[ROW][C]63[/C][C]23[/C][C]25.2911822397415[/C][C]-2.2911822397415[/C][/ROW]
[ROW][C]64[/C][C]23[/C][C]24.7153824716691[/C][C]-1.71538247166908[/C][/ROW]
[ROW][C]65[/C][C]23[/C][C]24.2842876367798[/C][C]-1.28428763677982[/C][/ROW]
[ROW][C]66[/C][C]25[/C][C]23.961531764039[/C][C]1.03846823596103[/C][/ROW]
[ROW][C]67[/C][C]26[/C][C]24.2225104671056[/C][C]1.77748953289444[/C][/ROW]
[ROW][C]68[/C][C]22[/C][C]24.6692135023505[/C][C]-2.66921350235048[/C][/ROW]
[ROW][C]69[/C][C]23[/C][C]23.9984102423869[/C][C]-0.998410242386932[/C][/ROW]
[ROW][C]70[/C][C]27[/C][C]23.7474985619296[/C][C]3.2525014380704[/C][/ROW]
[ROW][C]71[/C][C]25[/C][C]24.5648886155062[/C][C]0.435111384493755[/C][/ROW]
[ROW][C]72[/C][C]24[/C][C]24.6742369815731[/C][C]-0.67423698157312[/C][/ROW]
[ROW][C]73[/C][C]21[/C][C]24.5047936737115[/C][C]-3.50479367371148[/C][/ROW]
[ROW][C]74[/C][C]24[/C][C]23.6239997545458[/C][C]0.376000245454225[/C][/ROW]
[ROW][C]75[/C][C]22[/C][C]23.7184928290697[/C][C]-1.71849282906967[/C][/ROW]
[ROW][C]76[/C][C]26[/C][C]23.2866163265161[/C][C]2.71338367348391[/C][/ROW]
[ROW][C]77[/C][C]22[/C][C]23.9685200453839[/C][C]-1.96852004538387[/C][/ROW]
[ROW][C]78[/C][C]25[/C][C]23.4738089019762[/C][C]1.52619109802384[/C][/ROW]
[ROW][C]79[/C][C]20[/C][C]23.8573578249005[/C][C]-3.85735782490054[/C][/ROW]
[ROW][C]80[/C][C]21[/C][C]22.8879605842862[/C][C]-1.88796058428617[/C][/ROW]
[ROW][C]81[/C][C]23[/C][C]22.4134949360693[/C][C]0.586505063930669[/C][/ROW]
[ROW][C]82[/C][C]24[/C][C]22.5608902300476[/C][C]1.43910976995236[/C][/ROW]
[ROW][C]83[/C][C]24[/C][C]22.9225546395373[/C][C]1.07744536046269[/C][/ROW]
[ROW][C]84[/C][C]18[/C][C]23.1933287307048[/C][C]-5.19332873070481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232256&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232256&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
22425-1
32524.74868879564230.251311204357705
42724.8118461170782.18815388292198
52425.3617537047151-1.36175370471513
62625.01952974114460.980470258855398
72425.2659329027345-1.26593290273446
82424.9477897803122-0.947789780312217
92124.709599589144-3.70959958914403
102323.7773356487114-0.777335648711389
112423.58198249064360.418017509356449
122323.6870349743625-0.687034974362529
132223.5143753875196-1.51437538751962
142523.13379588503241.8662041149676
152623.60279388874222.39720611125779
162224.2052386436561-2.20523864365606
172423.65103746422270.3489625357773
182223.7387356593646-1.73873565936461
192323.30177190675-0.301771906750002
202523.22593324542331.77406675457666
212423.6717760981270.328223901873034
222423.75426244220570.245737557794335
232123.8160190438109-2.81601904381088
242223.1083219064165-1.10832190641653
252122.829788193299-1.82978819329896
262122.3699419187215-1.36994191872149
272022.0256601652275-2.02566016522749
282021.5165890694847-1.51658906948474
292221.13545324391680.864546756083204
302121.3527235304116-0.352723530411613
312321.26408015517861.73591984482143
322221.70033626204910.299663737950915
332421.77564511693592.22435488306414
342122.3346504215177-1.33465042151765
352221.99923781668950.000762183310467179
362021.9994293618952-1.99942936189523
372321.49695036092921.50304963907082
382121.8746835759335-0.874683575933481
392121.6548657930337-0.654865793033732
402121.4902906818938-0.490290681893761
412221.36707514014170.632924859858321
422421.52613624894062.47386375105939
432122.1478459276362-1.14784592763622
442321.85937938514491.14062061485513
452522.14603012557932.85396987442066
462322.86326473192060.136735268079391
472422.89762783681981.10237216318018
482523.1746663127991.82533368720096
492823.63339312008424.3666068799158
502624.73077035403251.26922964596751
512525.0497419849671-0.0497419849670884
522425.0372412668179-1.03724126681787
532524.77657091484440.223429085155644
542624.83272114732341.16727885267664
552425.1260714016108-1.12607140161081
562124.8430770414792-3.84307704147923
572223.8772687217456-1.87726872174563
582523.40549005838071.59450994161931
592723.80620827216943.19379172783063
602624.60884391775821.39115608224184
612424.9584570282359-0.958457028235909
622724.71758603814482.28241396185517
632325.2911822397415-2.2911822397415
642324.7153824716691-1.71538247166908
652324.2842876367798-1.28428763677982
662523.9615317640391.03846823596103
672624.22251046710561.77748953289444
682224.6692135023505-2.66921350235048
692323.9984102423869-0.998410242386932
702723.74749856192963.2525014380704
712524.56488861550620.435111384493755
722424.6742369815731-0.67423698157312
732124.5047936737115-3.50479367371148
742423.62399975454580.376000245454225
752223.7184928290697-1.71849282906967
762623.28661632651612.71338367348391
772223.9685200453839-1.96852004538387
782523.47380890197621.52619109802384
792023.8573578249005-3.85735782490054
802122.8879605842862-1.88796058428617
812322.41349493606930.586505063930669
822422.56089023004761.43910976995236
832422.92255463953731.07744536046269
841823.1933287307048-5.19332873070481







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8521.888187032765918.245805078119325.5305689874125
8621.888187032765918.132544465148725.6438296003831
8721.888187032765918.022600933885125.7537731316468
8821.888187032765917.915699061730225.8606750038017
8921.888187032765917.811599553980925.9647745115509
9021.888187032765917.710092938044126.0662811274877
9121.888187032765917.610994605891526.1653794596404
9221.888187032765917.514140868323326.2622331972085
9321.888187032765917.419385779539526.3569882859923
9421.888187032765917.326598555820526.4497755097113
9521.888187032765917.235661457858926.5407126076729
9621.888187032765917.146468038843326.6299060266885

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 21.8881870327659 & 18.2458050781193 & 25.5305689874125 \tabularnewline
86 & 21.8881870327659 & 18.1325444651487 & 25.6438296003831 \tabularnewline
87 & 21.8881870327659 & 18.0226009338851 & 25.7537731316468 \tabularnewline
88 & 21.8881870327659 & 17.9156990617302 & 25.8606750038017 \tabularnewline
89 & 21.8881870327659 & 17.8115995539809 & 25.9647745115509 \tabularnewline
90 & 21.8881870327659 & 17.7100929380441 & 26.0662811274877 \tabularnewline
91 & 21.8881870327659 & 17.6109946058915 & 26.1653794596404 \tabularnewline
92 & 21.8881870327659 & 17.5141408683233 & 26.2622331972085 \tabularnewline
93 & 21.8881870327659 & 17.4193857795395 & 26.3569882859923 \tabularnewline
94 & 21.8881870327659 & 17.3265985558205 & 26.4497755097113 \tabularnewline
95 & 21.8881870327659 & 17.2356614578589 & 26.5407126076729 \tabularnewline
96 & 21.8881870327659 & 17.1464680388433 & 26.6299060266885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232256&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]21.8881870327659[/C][C]18.2458050781193[/C][C]25.5305689874125[/C][/ROW]
[ROW][C]86[/C][C]21.8881870327659[/C][C]18.1325444651487[/C][C]25.6438296003831[/C][/ROW]
[ROW][C]87[/C][C]21.8881870327659[/C][C]18.0226009338851[/C][C]25.7537731316468[/C][/ROW]
[ROW][C]88[/C][C]21.8881870327659[/C][C]17.9156990617302[/C][C]25.8606750038017[/C][/ROW]
[ROW][C]89[/C][C]21.8881870327659[/C][C]17.8115995539809[/C][C]25.9647745115509[/C][/ROW]
[ROW][C]90[/C][C]21.8881870327659[/C][C]17.7100929380441[/C][C]26.0662811274877[/C][/ROW]
[ROW][C]91[/C][C]21.8881870327659[/C][C]17.6109946058915[/C][C]26.1653794596404[/C][/ROW]
[ROW][C]92[/C][C]21.8881870327659[/C][C]17.5141408683233[/C][C]26.2622331972085[/C][/ROW]
[ROW][C]93[/C][C]21.8881870327659[/C][C]17.4193857795395[/C][C]26.3569882859923[/C][/ROW]
[ROW][C]94[/C][C]21.8881870327659[/C][C]17.3265985558205[/C][C]26.4497755097113[/C][/ROW]
[ROW][C]95[/C][C]21.8881870327659[/C][C]17.2356614578589[/C][C]26.5407126076729[/C][/ROW]
[ROW][C]96[/C][C]21.8881870327659[/C][C]17.1464680388433[/C][C]26.6299060266885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232256&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232256&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
8521.888187032765918.245805078119325.5305689874125
8621.888187032765918.132544465148725.6438296003831
8721.888187032765918.022600933885125.7537731316468
8821.888187032765917.915699061730225.8606750038017
8921.888187032765917.811599553980925.9647745115509
9021.888187032765917.710092938044126.0662811274877
9121.888187032765917.610994605891526.1653794596404
9221.888187032765917.514140868323326.2622331972085
9321.888187032765917.419385779539526.3569882859923
9421.888187032765917.326598555820526.4497755097113
9521.888187032765917.235661457858926.5407126076729
9621.888187032765917.146468038843326.6299060266885



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=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')