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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 16 Dec 2014 00:05:52 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/16/t14186883583zzh6mlzgi1ivi8.htm/, Retrieved Thu, 16 May 2024 11:29:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269111, Retrieved Thu, 16 May 2024 11:29:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-16 00:05:52] [6993448de96b8662e47595bfdf466bf3] [Current]
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Dataseries X:
4.35
12.7
18.1
17.85


17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6

14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1

17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85


18.95
15.6




17.1
16.1









15.4
15.4

13.35
19.1

7.6


19.1













14.75



19.25

13.6

12.75

9.85




15.25
11.9

16.35
12.4

18.15


17.75

12.35
15.6
19.3

17.1

18.4
19.05
18.55
19.1

12.85
9.5
4.5

13.6
11.7

13.35





17.6
14.05
16.1
13.35
11.85
11.95


13.2


7.7

















14.6




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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=269111&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]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=269111&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269111&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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.452915874331558
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.452915874331558 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269111&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]0.452915874331558[/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=269111&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269111&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
alpha0.452915874331558
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
212.74.358.35
318.18.131847550668519.96815244933149
417.8512.64658203272775.20341796727226
517.115.00329263088742.09670736911261
619.115.95292468218643.14707531781355
716.117.3782850513412-1.27828505134124
813.3516.7993294596681-3.44932945966806
918.415.23707339158493.16292660841509
1014.716.6696130618818-1.96961306188178
1110.615.7775440398647-5.17754403986474
1212.613.4325521541593-0.832552154159254
1316.213.05547606733163.14452393266841
1413.614.4796808736526-0.879680873652612
1514.114.08125944162950.0187405583705083
1614.514.08974733800930.410252661990668
1716.1514.27555728111171.87444271888831
1814.7515.1245221440214-0.374522144021407
1914.814.9548951197054-0.15489511970542
2012.4514.8847406611343-2.43474066113435
2112.6513.7820079658261-1.13200796582609
2217.3513.26930358823374.08069641176632
238.615.1175157714505-6.51751577145047
2418.412.16562941735436.23437058264573
2516.114.98927482070021.1107251792998
2617.7515.49233988642482.25766011357516
2715.2516.5148699907082-1.26486999070822
2817.6515.94199029295091.70800970704914
2916.3516.7155750027858-0.365575002785807
3017.6516.55000028076531.09999971923468
3113.617.048207615367-3.44820761536696
3214.3515.4864596483763-1.1364596483763
3314.7514.9717390330894-0.22173903308941
3418.2514.87130990504433.37869009495572
359.916.4015722834965-6.50157228349653
361613.45690698818692.54309301181312
3718.2514.60871418313873.64128581686131
3816.8516.25791033257350.592089667426471
3918.9516.52607714197872.42392285802133
4015.617.6239102825316-2.02391028253165
4117.116.70724918735020.392750812649805
4216.116.8851322650559-0.785132265055914
4315.416.5295333987622-1.1295333987622
4415.416.0179497918751-0.617949791875121
4513.3515.738070521595-2.388070521595
4619.114.65647547334144.44352452665862
477.616.6690182694467-9.06901826944669
4819.112.56151593061146.53848406938863
4914.7515.5228991597015-0.772899159701483
5019.2515.17284086101524.07715913898484
5113.617.0194509572374-3.41945095723738
5212.7515.4707273372063-2.72072733720633
539.8514.2384667364578-4.38846673645776
5415.2512.250860487542.99913951245997
5511.913.6092183820682-1.70921838206816
5616.3512.83508624413023.51491375586981
5712.414.42704648107-2.02704648106998
5818.1513.50896495178554.64103504821453
5917.7515.6109633984512.13903660154905
6012.3516.5797670310687-4.22976703106874
6115.614.66403839797340.935961602026554
6219.315.08795026529614.21204973470393
6317.116.99565445361750.104345546382497
6418.417.04291420798991.35708579201006
6519.0517.65755990602111.39244009397889
6618.5518.28821812863990.261781871360125
6719.118.40678329379110.693216706208904
6812.8518.7207521443849-5.87075214438495
699.516.061795303927-6.56179530392697
704.513.0898540466642-8.58985404666418
7113.69.19937279073884.4006272092612
7211.711.19248671082860.507513289171419
7313.3511.42234753592851.92765246407146
7417.612.29541193710085.30458806289916
7514.0514.6979440775776-0.647944077577559
7616.114.40447991916361.69552008083644
7713.3515.1724078790223-1.82240787902231
7811.8514.3470104211062-2.4970104211062
7911.9513.2160747630159-1.26607476301588
8013.212.64264940475540.557350595244579
817.712.8950823369098-5.19508233690983
8214.610.54214707806394.05785292193612

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12.7 & 4.35 & 8.35 \tabularnewline
3 & 18.1 & 8.13184755066851 & 9.96815244933149 \tabularnewline
4 & 17.85 & 12.6465820327277 & 5.20341796727226 \tabularnewline
5 & 17.1 & 15.0032926308874 & 2.09670736911261 \tabularnewline
6 & 19.1 & 15.9529246821864 & 3.14707531781355 \tabularnewline
7 & 16.1 & 17.3782850513412 & -1.27828505134124 \tabularnewline
8 & 13.35 & 16.7993294596681 & -3.44932945966806 \tabularnewline
9 & 18.4 & 15.2370733915849 & 3.16292660841509 \tabularnewline
10 & 14.7 & 16.6696130618818 & -1.96961306188178 \tabularnewline
11 & 10.6 & 15.7775440398647 & -5.17754403986474 \tabularnewline
12 & 12.6 & 13.4325521541593 & -0.832552154159254 \tabularnewline
13 & 16.2 & 13.0554760673316 & 3.14452393266841 \tabularnewline
14 & 13.6 & 14.4796808736526 & -0.879680873652612 \tabularnewline
15 & 14.1 & 14.0812594416295 & 0.0187405583705083 \tabularnewline
16 & 14.5 & 14.0897473380093 & 0.410252661990668 \tabularnewline
17 & 16.15 & 14.2755572811117 & 1.87444271888831 \tabularnewline
18 & 14.75 & 15.1245221440214 & -0.374522144021407 \tabularnewline
19 & 14.8 & 14.9548951197054 & -0.15489511970542 \tabularnewline
20 & 12.45 & 14.8847406611343 & -2.43474066113435 \tabularnewline
21 & 12.65 & 13.7820079658261 & -1.13200796582609 \tabularnewline
22 & 17.35 & 13.2693035882337 & 4.08069641176632 \tabularnewline
23 & 8.6 & 15.1175157714505 & -6.51751577145047 \tabularnewline
24 & 18.4 & 12.1656294173543 & 6.23437058264573 \tabularnewline
25 & 16.1 & 14.9892748207002 & 1.1107251792998 \tabularnewline
26 & 17.75 & 15.4923398864248 & 2.25766011357516 \tabularnewline
27 & 15.25 & 16.5148699907082 & -1.26486999070822 \tabularnewline
28 & 17.65 & 15.9419902929509 & 1.70800970704914 \tabularnewline
29 & 16.35 & 16.7155750027858 & -0.365575002785807 \tabularnewline
30 & 17.65 & 16.5500002807653 & 1.09999971923468 \tabularnewline
31 & 13.6 & 17.048207615367 & -3.44820761536696 \tabularnewline
32 & 14.35 & 15.4864596483763 & -1.1364596483763 \tabularnewline
33 & 14.75 & 14.9717390330894 & -0.22173903308941 \tabularnewline
34 & 18.25 & 14.8713099050443 & 3.37869009495572 \tabularnewline
35 & 9.9 & 16.4015722834965 & -6.50157228349653 \tabularnewline
36 & 16 & 13.4569069881869 & 2.54309301181312 \tabularnewline
37 & 18.25 & 14.6087141831387 & 3.64128581686131 \tabularnewline
38 & 16.85 & 16.2579103325735 & 0.592089667426471 \tabularnewline
39 & 18.95 & 16.5260771419787 & 2.42392285802133 \tabularnewline
40 & 15.6 & 17.6239102825316 & -2.02391028253165 \tabularnewline
41 & 17.1 & 16.7072491873502 & 0.392750812649805 \tabularnewline
42 & 16.1 & 16.8851322650559 & -0.785132265055914 \tabularnewline
43 & 15.4 & 16.5295333987622 & -1.1295333987622 \tabularnewline
44 & 15.4 & 16.0179497918751 & -0.617949791875121 \tabularnewline
45 & 13.35 & 15.738070521595 & -2.388070521595 \tabularnewline
46 & 19.1 & 14.6564754733414 & 4.44352452665862 \tabularnewline
47 & 7.6 & 16.6690182694467 & -9.06901826944669 \tabularnewline
48 & 19.1 & 12.5615159306114 & 6.53848406938863 \tabularnewline
49 & 14.75 & 15.5228991597015 & -0.772899159701483 \tabularnewline
50 & 19.25 & 15.1728408610152 & 4.07715913898484 \tabularnewline
51 & 13.6 & 17.0194509572374 & -3.41945095723738 \tabularnewline
52 & 12.75 & 15.4707273372063 & -2.72072733720633 \tabularnewline
53 & 9.85 & 14.2384667364578 & -4.38846673645776 \tabularnewline
54 & 15.25 & 12.25086048754 & 2.99913951245997 \tabularnewline
55 & 11.9 & 13.6092183820682 & -1.70921838206816 \tabularnewline
56 & 16.35 & 12.8350862441302 & 3.51491375586981 \tabularnewline
57 & 12.4 & 14.42704648107 & -2.02704648106998 \tabularnewline
58 & 18.15 & 13.5089649517855 & 4.64103504821453 \tabularnewline
59 & 17.75 & 15.610963398451 & 2.13903660154905 \tabularnewline
60 & 12.35 & 16.5797670310687 & -4.22976703106874 \tabularnewline
61 & 15.6 & 14.6640383979734 & 0.935961602026554 \tabularnewline
62 & 19.3 & 15.0879502652961 & 4.21204973470393 \tabularnewline
63 & 17.1 & 16.9956544536175 & 0.104345546382497 \tabularnewline
64 & 18.4 & 17.0429142079899 & 1.35708579201006 \tabularnewline
65 & 19.05 & 17.6575599060211 & 1.39244009397889 \tabularnewline
66 & 18.55 & 18.2882181286399 & 0.261781871360125 \tabularnewline
67 & 19.1 & 18.4067832937911 & 0.693216706208904 \tabularnewline
68 & 12.85 & 18.7207521443849 & -5.87075214438495 \tabularnewline
69 & 9.5 & 16.061795303927 & -6.56179530392697 \tabularnewline
70 & 4.5 & 13.0898540466642 & -8.58985404666418 \tabularnewline
71 & 13.6 & 9.1993727907388 & 4.4006272092612 \tabularnewline
72 & 11.7 & 11.1924867108286 & 0.507513289171419 \tabularnewline
73 & 13.35 & 11.4223475359285 & 1.92765246407146 \tabularnewline
74 & 17.6 & 12.2954119371008 & 5.30458806289916 \tabularnewline
75 & 14.05 & 14.6979440775776 & -0.647944077577559 \tabularnewline
76 & 16.1 & 14.4044799191636 & 1.69552008083644 \tabularnewline
77 & 13.35 & 15.1724078790223 & -1.82240787902231 \tabularnewline
78 & 11.85 & 14.3470104211062 & -2.4970104211062 \tabularnewline
79 & 11.95 & 13.2160747630159 & -1.26607476301588 \tabularnewline
80 & 13.2 & 12.6426494047554 & 0.557350595244579 \tabularnewline
81 & 7.7 & 12.8950823369098 & -5.19508233690983 \tabularnewline
82 & 14.6 & 10.5421470780639 & 4.05785292193612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269111&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]12.7[/C][C]4.35[/C][C]8.35[/C][/ROW]
[ROW][C]3[/C][C]18.1[/C][C]8.13184755066851[/C][C]9.96815244933149[/C][/ROW]
[ROW][C]4[/C][C]17.85[/C][C]12.6465820327277[/C][C]5.20341796727226[/C][/ROW]
[ROW][C]5[/C][C]17.1[/C][C]15.0032926308874[/C][C]2.09670736911261[/C][/ROW]
[ROW][C]6[/C][C]19.1[/C][C]15.9529246821864[/C][C]3.14707531781355[/C][/ROW]
[ROW][C]7[/C][C]16.1[/C][C]17.3782850513412[/C][C]-1.27828505134124[/C][/ROW]
[ROW][C]8[/C][C]13.35[/C][C]16.7993294596681[/C][C]-3.44932945966806[/C][/ROW]
[ROW][C]9[/C][C]18.4[/C][C]15.2370733915849[/C][C]3.16292660841509[/C][/ROW]
[ROW][C]10[/C][C]14.7[/C][C]16.6696130618818[/C][C]-1.96961306188178[/C][/ROW]
[ROW][C]11[/C][C]10.6[/C][C]15.7775440398647[/C][C]-5.17754403986474[/C][/ROW]
[ROW][C]12[/C][C]12.6[/C][C]13.4325521541593[/C][C]-0.832552154159254[/C][/ROW]
[ROW][C]13[/C][C]16.2[/C][C]13.0554760673316[/C][C]3.14452393266841[/C][/ROW]
[ROW][C]14[/C][C]13.6[/C][C]14.4796808736526[/C][C]-0.879680873652612[/C][/ROW]
[ROW][C]15[/C][C]14.1[/C][C]14.0812594416295[/C][C]0.0187405583705083[/C][/ROW]
[ROW][C]16[/C][C]14.5[/C][C]14.0897473380093[/C][C]0.410252661990668[/C][/ROW]
[ROW][C]17[/C][C]16.15[/C][C]14.2755572811117[/C][C]1.87444271888831[/C][/ROW]
[ROW][C]18[/C][C]14.75[/C][C]15.1245221440214[/C][C]-0.374522144021407[/C][/ROW]
[ROW][C]19[/C][C]14.8[/C][C]14.9548951197054[/C][C]-0.15489511970542[/C][/ROW]
[ROW][C]20[/C][C]12.45[/C][C]14.8847406611343[/C][C]-2.43474066113435[/C][/ROW]
[ROW][C]21[/C][C]12.65[/C][C]13.7820079658261[/C][C]-1.13200796582609[/C][/ROW]
[ROW][C]22[/C][C]17.35[/C][C]13.2693035882337[/C][C]4.08069641176632[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]15.1175157714505[/C][C]-6.51751577145047[/C][/ROW]
[ROW][C]24[/C][C]18.4[/C][C]12.1656294173543[/C][C]6.23437058264573[/C][/ROW]
[ROW][C]25[/C][C]16.1[/C][C]14.9892748207002[/C][C]1.1107251792998[/C][/ROW]
[ROW][C]26[/C][C]17.75[/C][C]15.4923398864248[/C][C]2.25766011357516[/C][/ROW]
[ROW][C]27[/C][C]15.25[/C][C]16.5148699907082[/C][C]-1.26486999070822[/C][/ROW]
[ROW][C]28[/C][C]17.65[/C][C]15.9419902929509[/C][C]1.70800970704914[/C][/ROW]
[ROW][C]29[/C][C]16.35[/C][C]16.7155750027858[/C][C]-0.365575002785807[/C][/ROW]
[ROW][C]30[/C][C]17.65[/C][C]16.5500002807653[/C][C]1.09999971923468[/C][/ROW]
[ROW][C]31[/C][C]13.6[/C][C]17.048207615367[/C][C]-3.44820761536696[/C][/ROW]
[ROW][C]32[/C][C]14.35[/C][C]15.4864596483763[/C][C]-1.1364596483763[/C][/ROW]
[ROW][C]33[/C][C]14.75[/C][C]14.9717390330894[/C][C]-0.22173903308941[/C][/ROW]
[ROW][C]34[/C][C]18.25[/C][C]14.8713099050443[/C][C]3.37869009495572[/C][/ROW]
[ROW][C]35[/C][C]9.9[/C][C]16.4015722834965[/C][C]-6.50157228349653[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]13.4569069881869[/C][C]2.54309301181312[/C][/ROW]
[ROW][C]37[/C][C]18.25[/C][C]14.6087141831387[/C][C]3.64128581686131[/C][/ROW]
[ROW][C]38[/C][C]16.85[/C][C]16.2579103325735[/C][C]0.592089667426471[/C][/ROW]
[ROW][C]39[/C][C]18.95[/C][C]16.5260771419787[/C][C]2.42392285802133[/C][/ROW]
[ROW][C]40[/C][C]15.6[/C][C]17.6239102825316[/C][C]-2.02391028253165[/C][/ROW]
[ROW][C]41[/C][C]17.1[/C][C]16.7072491873502[/C][C]0.392750812649805[/C][/ROW]
[ROW][C]42[/C][C]16.1[/C][C]16.8851322650559[/C][C]-0.785132265055914[/C][/ROW]
[ROW][C]43[/C][C]15.4[/C][C]16.5295333987622[/C][C]-1.1295333987622[/C][/ROW]
[ROW][C]44[/C][C]15.4[/C][C]16.0179497918751[/C][C]-0.617949791875121[/C][/ROW]
[ROW][C]45[/C][C]13.35[/C][C]15.738070521595[/C][C]-2.388070521595[/C][/ROW]
[ROW][C]46[/C][C]19.1[/C][C]14.6564754733414[/C][C]4.44352452665862[/C][/ROW]
[ROW][C]47[/C][C]7.6[/C][C]16.6690182694467[/C][C]-9.06901826944669[/C][/ROW]
[ROW][C]48[/C][C]19.1[/C][C]12.5615159306114[/C][C]6.53848406938863[/C][/ROW]
[ROW][C]49[/C][C]14.75[/C][C]15.5228991597015[/C][C]-0.772899159701483[/C][/ROW]
[ROW][C]50[/C][C]19.25[/C][C]15.1728408610152[/C][C]4.07715913898484[/C][/ROW]
[ROW][C]51[/C][C]13.6[/C][C]17.0194509572374[/C][C]-3.41945095723738[/C][/ROW]
[ROW][C]52[/C][C]12.75[/C][C]15.4707273372063[/C][C]-2.72072733720633[/C][/ROW]
[ROW][C]53[/C][C]9.85[/C][C]14.2384667364578[/C][C]-4.38846673645776[/C][/ROW]
[ROW][C]54[/C][C]15.25[/C][C]12.25086048754[/C][C]2.99913951245997[/C][/ROW]
[ROW][C]55[/C][C]11.9[/C][C]13.6092183820682[/C][C]-1.70921838206816[/C][/ROW]
[ROW][C]56[/C][C]16.35[/C][C]12.8350862441302[/C][C]3.51491375586981[/C][/ROW]
[ROW][C]57[/C][C]12.4[/C][C]14.42704648107[/C][C]-2.02704648106998[/C][/ROW]
[ROW][C]58[/C][C]18.15[/C][C]13.5089649517855[/C][C]4.64103504821453[/C][/ROW]
[ROW][C]59[/C][C]17.75[/C][C]15.610963398451[/C][C]2.13903660154905[/C][/ROW]
[ROW][C]60[/C][C]12.35[/C][C]16.5797670310687[/C][C]-4.22976703106874[/C][/ROW]
[ROW][C]61[/C][C]15.6[/C][C]14.6640383979734[/C][C]0.935961602026554[/C][/ROW]
[ROW][C]62[/C][C]19.3[/C][C]15.0879502652961[/C][C]4.21204973470393[/C][/ROW]
[ROW][C]63[/C][C]17.1[/C][C]16.9956544536175[/C][C]0.104345546382497[/C][/ROW]
[ROW][C]64[/C][C]18.4[/C][C]17.0429142079899[/C][C]1.35708579201006[/C][/ROW]
[ROW][C]65[/C][C]19.05[/C][C]17.6575599060211[/C][C]1.39244009397889[/C][/ROW]
[ROW][C]66[/C][C]18.55[/C][C]18.2882181286399[/C][C]0.261781871360125[/C][/ROW]
[ROW][C]67[/C][C]19.1[/C][C]18.4067832937911[/C][C]0.693216706208904[/C][/ROW]
[ROW][C]68[/C][C]12.85[/C][C]18.7207521443849[/C][C]-5.87075214438495[/C][/ROW]
[ROW][C]69[/C][C]9.5[/C][C]16.061795303927[/C][C]-6.56179530392697[/C][/ROW]
[ROW][C]70[/C][C]4.5[/C][C]13.0898540466642[/C][C]-8.58985404666418[/C][/ROW]
[ROW][C]71[/C][C]13.6[/C][C]9.1993727907388[/C][C]4.4006272092612[/C][/ROW]
[ROW][C]72[/C][C]11.7[/C][C]11.1924867108286[/C][C]0.507513289171419[/C][/ROW]
[ROW][C]73[/C][C]13.35[/C][C]11.4223475359285[/C][C]1.92765246407146[/C][/ROW]
[ROW][C]74[/C][C]17.6[/C][C]12.2954119371008[/C][C]5.30458806289916[/C][/ROW]
[ROW][C]75[/C][C]14.05[/C][C]14.6979440775776[/C][C]-0.647944077577559[/C][/ROW]
[ROW][C]76[/C][C]16.1[/C][C]14.4044799191636[/C][C]1.69552008083644[/C][/ROW]
[ROW][C]77[/C][C]13.35[/C][C]15.1724078790223[/C][C]-1.82240787902231[/C][/ROW]
[ROW][C]78[/C][C]11.85[/C][C]14.3470104211062[/C][C]-2.4970104211062[/C][/ROW]
[ROW][C]79[/C][C]11.95[/C][C]13.2160747630159[/C][C]-1.26607476301588[/C][/ROW]
[ROW][C]80[/C][C]13.2[/C][C]12.6426494047554[/C][C]0.557350595244579[/C][/ROW]
[ROW][C]81[/C][C]7.7[/C][C]12.8950823369098[/C][C]-5.19508233690983[/C][/ROW]
[ROW][C]82[/C][C]14.6[/C][C]10.5421470780639[/C][C]4.05785292193612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269111&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269111&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
212.74.358.35
318.18.131847550668519.96815244933149
417.8512.64658203272775.20341796727226
517.115.00329263088742.09670736911261
619.115.95292468218643.14707531781355
716.117.3782850513412-1.27828505134124
813.3516.7993294596681-3.44932945966806
918.415.23707339158493.16292660841509
1014.716.6696130618818-1.96961306188178
1110.615.7775440398647-5.17754403986474
1212.613.4325521541593-0.832552154159254
1316.213.05547606733163.14452393266841
1413.614.4796808736526-0.879680873652612
1514.114.08125944162950.0187405583705083
1614.514.08974733800930.410252661990668
1716.1514.27555728111171.87444271888831
1814.7515.1245221440214-0.374522144021407
1914.814.9548951197054-0.15489511970542
2012.4514.8847406611343-2.43474066113435
2112.6513.7820079658261-1.13200796582609
2217.3513.26930358823374.08069641176632
238.615.1175157714505-6.51751577145047
2418.412.16562941735436.23437058264573
2516.114.98927482070021.1107251792998
2617.7515.49233988642482.25766011357516
2715.2516.5148699907082-1.26486999070822
2817.6515.94199029295091.70800970704914
2916.3516.7155750027858-0.365575002785807
3017.6516.55000028076531.09999971923468
3113.617.048207615367-3.44820761536696
3214.3515.4864596483763-1.1364596483763
3314.7514.9717390330894-0.22173903308941
3418.2514.87130990504433.37869009495572
359.916.4015722834965-6.50157228349653
361613.45690698818692.54309301181312
3718.2514.60871418313873.64128581686131
3816.8516.25791033257350.592089667426471
3918.9516.52607714197872.42392285802133
4015.617.6239102825316-2.02391028253165
4117.116.70724918735020.392750812649805
4216.116.8851322650559-0.785132265055914
4315.416.5295333987622-1.1295333987622
4415.416.0179497918751-0.617949791875121
4513.3515.738070521595-2.388070521595
4619.114.65647547334144.44352452665862
477.616.6690182694467-9.06901826944669
4819.112.56151593061146.53848406938863
4914.7515.5228991597015-0.772899159701483
5019.2515.17284086101524.07715913898484
5113.617.0194509572374-3.41945095723738
5212.7515.4707273372063-2.72072733720633
539.8514.2384667364578-4.38846673645776
5415.2512.250860487542.99913951245997
5511.913.6092183820682-1.70921838206816
5616.3512.83508624413023.51491375586981
5712.414.42704648107-2.02704648106998
5818.1513.50896495178554.64103504821453
5917.7515.6109633984512.13903660154905
6012.3516.5797670310687-4.22976703106874
6115.614.66403839797340.935961602026554
6219.315.08795026529614.21204973470393
6317.116.99565445361750.104345546382497
6418.417.04291420798991.35708579201006
6519.0517.65755990602111.39244009397889
6618.5518.28821812863990.261781871360125
6719.118.40678329379110.693216706208904
6812.8518.7207521443849-5.87075214438495
699.516.061795303927-6.56179530392697
704.513.0898540466642-8.58985404666418
7113.69.19937279073884.4006272092612
7211.711.19248671082860.507513289171419
7313.3511.42234753592851.92765246407146
7417.612.29541193710085.30458806289916
7514.0514.6979440775776-0.647944077577559
7616.114.40447991916361.69552008083644
7713.3515.1724078790223-1.82240787902231
7811.8514.3470104211062-2.4970104211062
7911.9513.2160747630159-1.26607476301588
8013.212.64264940475540.557350595244579
817.712.8950823369098-5.19508233690983
8214.610.54214707806394.05785292193612







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8312.38001308211145.2619180618572419.4981081023657
8412.38001308211144.5658722776045420.1941538866184
8512.38001308211143.926947584438320.8330785797846
8612.38001308211143.3330336909972921.4269924732256
8712.38001308211142.7757767304520221.9842494337709
8812.38001308211142.2491258705278222.5109002936951
8912.38001308211141.7485317418126823.0114944224102
9012.38001308211141.2704714496041423.4895547146187
9112.38001308211140.81215091662446223.9478752475984
9212.38001308211140.37130978512732124.3887163790956
9312.3800130821114-0.053911265024076724.813937429247
9412.3800130821114-0.46506358039165425.2250897446145

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
83 & 12.3800130821114 & 5.26191806185724 & 19.4981081023657 \tabularnewline
84 & 12.3800130821114 & 4.56587227760454 & 20.1941538866184 \tabularnewline
85 & 12.3800130821114 & 3.9269475844383 & 20.8330785797846 \tabularnewline
86 & 12.3800130821114 & 3.33303369099729 & 21.4269924732256 \tabularnewline
87 & 12.3800130821114 & 2.77577673045202 & 21.9842494337709 \tabularnewline
88 & 12.3800130821114 & 2.24912587052782 & 22.5109002936951 \tabularnewline
89 & 12.3800130821114 & 1.74853174181268 & 23.0114944224102 \tabularnewline
90 & 12.3800130821114 & 1.27047144960414 & 23.4895547146187 \tabularnewline
91 & 12.3800130821114 & 0.812150916624462 & 23.9478752475984 \tabularnewline
92 & 12.3800130821114 & 0.371309785127321 & 24.3887163790956 \tabularnewline
93 & 12.3800130821114 & -0.0539112650240767 & 24.813937429247 \tabularnewline
94 & 12.3800130821114 & -0.465063580391654 & 25.2250897446145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269111&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]83[/C][C]12.3800130821114[/C][C]5.26191806185724[/C][C]19.4981081023657[/C][/ROW]
[ROW][C]84[/C][C]12.3800130821114[/C][C]4.56587227760454[/C][C]20.1941538866184[/C][/ROW]
[ROW][C]85[/C][C]12.3800130821114[/C][C]3.9269475844383[/C][C]20.8330785797846[/C][/ROW]
[ROW][C]86[/C][C]12.3800130821114[/C][C]3.33303369099729[/C][C]21.4269924732256[/C][/ROW]
[ROW][C]87[/C][C]12.3800130821114[/C][C]2.77577673045202[/C][C]21.9842494337709[/C][/ROW]
[ROW][C]88[/C][C]12.3800130821114[/C][C]2.24912587052782[/C][C]22.5109002936951[/C][/ROW]
[ROW][C]89[/C][C]12.3800130821114[/C][C]1.74853174181268[/C][C]23.0114944224102[/C][/ROW]
[ROW][C]90[/C][C]12.3800130821114[/C][C]1.27047144960414[/C][C]23.4895547146187[/C][/ROW]
[ROW][C]91[/C][C]12.3800130821114[/C][C]0.812150916624462[/C][C]23.9478752475984[/C][/ROW]
[ROW][C]92[/C][C]12.3800130821114[/C][C]0.371309785127321[/C][C]24.3887163790956[/C][/ROW]
[ROW][C]93[/C][C]12.3800130821114[/C][C]-0.0539112650240767[/C][C]24.813937429247[/C][/ROW]
[ROW][C]94[/C][C]12.3800130821114[/C][C]-0.465063580391654[/C][C]25.2250897446145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269111&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269111&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
8312.38001308211145.2619180618572419.4981081023657
8412.38001308211144.5658722776045420.1941538866184
8512.38001308211143.926947584438320.8330785797846
8612.38001308211143.3330336909972921.4269924732256
8712.38001308211142.7757767304520221.9842494337709
8812.38001308211142.2491258705278222.5109002936951
8912.38001308211141.7485317418126823.0114944224102
9012.38001308211141.2704714496041423.4895547146187
9112.38001308211140.81215091662446223.9478752475984
9212.38001308211140.37130978512732124.3887163790956
9312.3800130821114-0.053911265024076724.813937429247
9412.3800130821114-0.46506358039165425.2250897446145



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')