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 08:55:36 -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/t13868565932undt680zygfnxa.htm/, Retrieved Tue, 07 Dec 2021 11:52:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232249, Retrieved Tue, 07 Dec 2021 11:52:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 13:55:36] [e13de47ca0b629216b947109e84252a5] [Current]
Feedback Forum

Post a new message
Dataseries X:
16.68
16.68
16.69
16.61
16.58
16.6
16.6
16.62
16.62
16.6
16.63
16.66
16.66
16.65
16.5
16.39
16.34
16.35
16.35
16.38
16.36
16.38
16.39
16.41
16.41
16.41
16.45
16.41
16.44
16.47
16.47
16.49
16.54
16.62
16.69
16.72
16.72
16.71
16.89
16.93
16.91
16.93
16.93
16.93
16.95
16.93
16.95
16.95
16.95
16.95
16.92
16.91
16.9
16.96
16.96
16.95
16.92
16.87
16.87
16.88
16.88
16.86
16.88
16.88
16.88
16.88
16.88
16.87
16.92
16.94
17.03
17.02
17.02
17.02
16.99
17.03
16.98
16.89
16.89
16.9
16.89
16.96
16.97
16.97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232249&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]5 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=232249&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232249&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 time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.750204331714779
beta0.0598915504599032
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.750204331714779 \tabularnewline
beta & 0.0598915504599032 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232249&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]0.750204331714779[/C][/ROW]
[ROW][C]beta[/C][C]0.0598915504599032[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232249&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232249&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
alpha0.750204331714779
beta0.0598915504599032
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1316.6616.7628926282051-0.102892628205122
1416.6516.6730531419741-0.0230531419740529
1516.516.5024904523918-0.0024904523918039
1616.3916.38640875000370.00359124999630822
1716.3416.33421759185460.00578240814542497
1816.3516.34518005884590.00481994115405371
1916.3516.3856370432281-0.035637043228089
2016.3816.35580848489880.0241915151012329
2116.3616.35903385008180.000966149918230741
2216.3816.33279552235140.0472044776485738
2316.3916.3954496614015-0.00544966140150649
2416.4116.4196075790588-0.00960757905883369
2516.4116.38492906554170.02507093445832
2616.4116.4126220067224-0.00262200672241519
2716.4516.2650313539820.184968646017968
2816.4116.30203220815590.107967791844089
2916.4416.34431260367340.0956873963266354
3016.4716.44214175227090.0278582477291351
3116.4716.510471316568-0.0404713165680342
3216.4916.5124388938715-0.0224388938715236
3316.5416.49326309608930.0467369039107481
3416.6216.5333516088960.0866483911040028
3516.6916.63465550603270.0553444939673398
3616.7216.7283259079265-0.00832590792650478
3716.7216.7282721140978-0.00827211409779949
3816.7116.7475359078641-0.037535907864136
3916.8916.64254584348820.247454156511818
4016.9316.73193046450990.198069535490077
4116.9116.867527687320.0424723126800011
4216.9316.9348899190364-0.00488991903641889
4316.9316.986510529854-0.0565105298540338
4416.9317.0051564769146-0.0751564769146142
4516.9516.9855495220924-0.0355495220923849
4616.9316.9920169025398-0.0620169025397637
4716.9516.9854329932282-0.0354329932282376
4816.9517.0024795448861-0.0524795448860864
4916.9516.9747134806133-0.0247134806132721
5016.9516.9789927374741-0.0289927374740664
5116.9216.9566447488504-0.0366447488503532
5216.9116.81283992508240.0971600749175963
5316.916.8216118173230.0783881826769708
5416.9616.8934460384680.0665539615320441
5516.9616.9783382193841-0.0183382193840806
5616.9517.0152473049889-0.0652473049889331
5716.9217.0076969103213-0.0876969103212772
5816.8716.9608176388323-0.0908176388323376
5916.8716.9303597763576-0.0603597763576467
6016.8816.914419948326-0.0344199483259899
6116.8816.8979215038932-0.0179215038931844
6216.8616.8973157506047-0.0373157506047228
6316.8816.85752696102820.0224730389718246
6416.8816.78486723743250.0951327625674843
6516.8816.78070881912330.0992911808767474
6616.8816.85948733874220.0205126612578148
6716.8816.8807836764633-0.000783676463338878
6816.8716.9120835500168-0.0420835500167982
6916.9216.91028263906870.0097173609313046
7016.9416.93406109088530.00593890911475015
7117.0316.98650267025560.0434973297443726
7217.0217.0623269614311-0.0423269614310691
7317.0217.0510330239005-0.0310330239005232
7417.0217.0421723827188-0.0221723827188427
7516.9917.0357856291622-0.0457856291621717
7617.0316.9341075530230.0958924469770075
7716.9816.93563145318840.0443685468115618
7816.8916.9551341635159-0.0651341635159035
7916.8916.9046158820597-0.0146158820596689
8016.916.9123584847672-0.0123584847672085
8116.8916.9442689028736-0.0542689028736163
8216.9616.91469759423450.0453024057654545
8316.9717.0034172601571-0.0334172601571261
8416.9716.994011004927-0.0240110049269617

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 16.66 & 16.7628926282051 & -0.102892628205122 \tabularnewline
14 & 16.65 & 16.6730531419741 & -0.0230531419740529 \tabularnewline
15 & 16.5 & 16.5024904523918 & -0.0024904523918039 \tabularnewline
16 & 16.39 & 16.3864087500037 & 0.00359124999630822 \tabularnewline
17 & 16.34 & 16.3342175918546 & 0.00578240814542497 \tabularnewline
18 & 16.35 & 16.3451800588459 & 0.00481994115405371 \tabularnewline
19 & 16.35 & 16.3856370432281 & -0.035637043228089 \tabularnewline
20 & 16.38 & 16.3558084848988 & 0.0241915151012329 \tabularnewline
21 & 16.36 & 16.3590338500818 & 0.000966149918230741 \tabularnewline
22 & 16.38 & 16.3327955223514 & 0.0472044776485738 \tabularnewline
23 & 16.39 & 16.3954496614015 & -0.00544966140150649 \tabularnewline
24 & 16.41 & 16.4196075790588 & -0.00960757905883369 \tabularnewline
25 & 16.41 & 16.3849290655417 & 0.02507093445832 \tabularnewline
26 & 16.41 & 16.4126220067224 & -0.00262200672241519 \tabularnewline
27 & 16.45 & 16.265031353982 & 0.184968646017968 \tabularnewline
28 & 16.41 & 16.3020322081559 & 0.107967791844089 \tabularnewline
29 & 16.44 & 16.3443126036734 & 0.0956873963266354 \tabularnewline
30 & 16.47 & 16.4421417522709 & 0.0278582477291351 \tabularnewline
31 & 16.47 & 16.510471316568 & -0.0404713165680342 \tabularnewline
32 & 16.49 & 16.5124388938715 & -0.0224388938715236 \tabularnewline
33 & 16.54 & 16.4932630960893 & 0.0467369039107481 \tabularnewline
34 & 16.62 & 16.533351608896 & 0.0866483911040028 \tabularnewline
35 & 16.69 & 16.6346555060327 & 0.0553444939673398 \tabularnewline
36 & 16.72 & 16.7283259079265 & -0.00832590792650478 \tabularnewline
37 & 16.72 & 16.7282721140978 & -0.00827211409779949 \tabularnewline
38 & 16.71 & 16.7475359078641 & -0.037535907864136 \tabularnewline
39 & 16.89 & 16.6425458434882 & 0.247454156511818 \tabularnewline
40 & 16.93 & 16.7319304645099 & 0.198069535490077 \tabularnewline
41 & 16.91 & 16.86752768732 & 0.0424723126800011 \tabularnewline
42 & 16.93 & 16.9348899190364 & -0.00488991903641889 \tabularnewline
43 & 16.93 & 16.986510529854 & -0.0565105298540338 \tabularnewline
44 & 16.93 & 17.0051564769146 & -0.0751564769146142 \tabularnewline
45 & 16.95 & 16.9855495220924 & -0.0355495220923849 \tabularnewline
46 & 16.93 & 16.9920169025398 & -0.0620169025397637 \tabularnewline
47 & 16.95 & 16.9854329932282 & -0.0354329932282376 \tabularnewline
48 & 16.95 & 17.0024795448861 & -0.0524795448860864 \tabularnewline
49 & 16.95 & 16.9747134806133 & -0.0247134806132721 \tabularnewline
50 & 16.95 & 16.9789927374741 & -0.0289927374740664 \tabularnewline
51 & 16.92 & 16.9566447488504 & -0.0366447488503532 \tabularnewline
52 & 16.91 & 16.8128399250824 & 0.0971600749175963 \tabularnewline
53 & 16.9 & 16.821611817323 & 0.0783881826769708 \tabularnewline
54 & 16.96 & 16.893446038468 & 0.0665539615320441 \tabularnewline
55 & 16.96 & 16.9783382193841 & -0.0183382193840806 \tabularnewline
56 & 16.95 & 17.0152473049889 & -0.0652473049889331 \tabularnewline
57 & 16.92 & 17.0076969103213 & -0.0876969103212772 \tabularnewline
58 & 16.87 & 16.9608176388323 & -0.0908176388323376 \tabularnewline
59 & 16.87 & 16.9303597763576 & -0.0603597763576467 \tabularnewline
60 & 16.88 & 16.914419948326 & -0.0344199483259899 \tabularnewline
61 & 16.88 & 16.8979215038932 & -0.0179215038931844 \tabularnewline
62 & 16.86 & 16.8973157506047 & -0.0373157506047228 \tabularnewline
63 & 16.88 & 16.8575269610282 & 0.0224730389718246 \tabularnewline
64 & 16.88 & 16.7848672374325 & 0.0951327625674843 \tabularnewline
65 & 16.88 & 16.7807088191233 & 0.0992911808767474 \tabularnewline
66 & 16.88 & 16.8594873387422 & 0.0205126612578148 \tabularnewline
67 & 16.88 & 16.8807836764633 & -0.000783676463338878 \tabularnewline
68 & 16.87 & 16.9120835500168 & -0.0420835500167982 \tabularnewline
69 & 16.92 & 16.9102826390687 & 0.0097173609313046 \tabularnewline
70 & 16.94 & 16.9340610908853 & 0.00593890911475015 \tabularnewline
71 & 17.03 & 16.9865026702556 & 0.0434973297443726 \tabularnewline
72 & 17.02 & 17.0623269614311 & -0.0423269614310691 \tabularnewline
73 & 17.02 & 17.0510330239005 & -0.0310330239005232 \tabularnewline
74 & 17.02 & 17.0421723827188 & -0.0221723827188427 \tabularnewline
75 & 16.99 & 17.0357856291622 & -0.0457856291621717 \tabularnewline
76 & 17.03 & 16.934107553023 & 0.0958924469770075 \tabularnewline
77 & 16.98 & 16.9356314531884 & 0.0443685468115618 \tabularnewline
78 & 16.89 & 16.9551341635159 & -0.0651341635159035 \tabularnewline
79 & 16.89 & 16.9046158820597 & -0.0146158820596689 \tabularnewline
80 & 16.9 & 16.9123584847672 & -0.0123584847672085 \tabularnewline
81 & 16.89 & 16.9442689028736 & -0.0542689028736163 \tabularnewline
82 & 16.96 & 16.9146975942345 & 0.0453024057654545 \tabularnewline
83 & 16.97 & 17.0034172601571 & -0.0334172601571261 \tabularnewline
84 & 16.97 & 16.994011004927 & -0.0240110049269617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232249&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]16.66[/C][C]16.7628926282051[/C][C]-0.102892628205122[/C][/ROW]
[ROW][C]14[/C][C]16.65[/C][C]16.6730531419741[/C][C]-0.0230531419740529[/C][/ROW]
[ROW][C]15[/C][C]16.5[/C][C]16.5024904523918[/C][C]-0.0024904523918039[/C][/ROW]
[ROW][C]16[/C][C]16.39[/C][C]16.3864087500037[/C][C]0.00359124999630822[/C][/ROW]
[ROW][C]17[/C][C]16.34[/C][C]16.3342175918546[/C][C]0.00578240814542497[/C][/ROW]
[ROW][C]18[/C][C]16.35[/C][C]16.3451800588459[/C][C]0.00481994115405371[/C][/ROW]
[ROW][C]19[/C][C]16.35[/C][C]16.3856370432281[/C][C]-0.035637043228089[/C][/ROW]
[ROW][C]20[/C][C]16.38[/C][C]16.3558084848988[/C][C]0.0241915151012329[/C][/ROW]
[ROW][C]21[/C][C]16.36[/C][C]16.3590338500818[/C][C]0.000966149918230741[/C][/ROW]
[ROW][C]22[/C][C]16.38[/C][C]16.3327955223514[/C][C]0.0472044776485738[/C][/ROW]
[ROW][C]23[/C][C]16.39[/C][C]16.3954496614015[/C][C]-0.00544966140150649[/C][/ROW]
[ROW][C]24[/C][C]16.41[/C][C]16.4196075790588[/C][C]-0.00960757905883369[/C][/ROW]
[ROW][C]25[/C][C]16.41[/C][C]16.3849290655417[/C][C]0.02507093445832[/C][/ROW]
[ROW][C]26[/C][C]16.41[/C][C]16.4126220067224[/C][C]-0.00262200672241519[/C][/ROW]
[ROW][C]27[/C][C]16.45[/C][C]16.265031353982[/C][C]0.184968646017968[/C][/ROW]
[ROW][C]28[/C][C]16.41[/C][C]16.3020322081559[/C][C]0.107967791844089[/C][/ROW]
[ROW][C]29[/C][C]16.44[/C][C]16.3443126036734[/C][C]0.0956873963266354[/C][/ROW]
[ROW][C]30[/C][C]16.47[/C][C]16.4421417522709[/C][C]0.0278582477291351[/C][/ROW]
[ROW][C]31[/C][C]16.47[/C][C]16.510471316568[/C][C]-0.0404713165680342[/C][/ROW]
[ROW][C]32[/C][C]16.49[/C][C]16.5124388938715[/C][C]-0.0224388938715236[/C][/ROW]
[ROW][C]33[/C][C]16.54[/C][C]16.4932630960893[/C][C]0.0467369039107481[/C][/ROW]
[ROW][C]34[/C][C]16.62[/C][C]16.533351608896[/C][C]0.0866483911040028[/C][/ROW]
[ROW][C]35[/C][C]16.69[/C][C]16.6346555060327[/C][C]0.0553444939673398[/C][/ROW]
[ROW][C]36[/C][C]16.72[/C][C]16.7283259079265[/C][C]-0.00832590792650478[/C][/ROW]
[ROW][C]37[/C][C]16.72[/C][C]16.7282721140978[/C][C]-0.00827211409779949[/C][/ROW]
[ROW][C]38[/C][C]16.71[/C][C]16.7475359078641[/C][C]-0.037535907864136[/C][/ROW]
[ROW][C]39[/C][C]16.89[/C][C]16.6425458434882[/C][C]0.247454156511818[/C][/ROW]
[ROW][C]40[/C][C]16.93[/C][C]16.7319304645099[/C][C]0.198069535490077[/C][/ROW]
[ROW][C]41[/C][C]16.91[/C][C]16.86752768732[/C][C]0.0424723126800011[/C][/ROW]
[ROW][C]42[/C][C]16.93[/C][C]16.9348899190364[/C][C]-0.00488991903641889[/C][/ROW]
[ROW][C]43[/C][C]16.93[/C][C]16.986510529854[/C][C]-0.0565105298540338[/C][/ROW]
[ROW][C]44[/C][C]16.93[/C][C]17.0051564769146[/C][C]-0.0751564769146142[/C][/ROW]
[ROW][C]45[/C][C]16.95[/C][C]16.9855495220924[/C][C]-0.0355495220923849[/C][/ROW]
[ROW][C]46[/C][C]16.93[/C][C]16.9920169025398[/C][C]-0.0620169025397637[/C][/ROW]
[ROW][C]47[/C][C]16.95[/C][C]16.9854329932282[/C][C]-0.0354329932282376[/C][/ROW]
[ROW][C]48[/C][C]16.95[/C][C]17.0024795448861[/C][C]-0.0524795448860864[/C][/ROW]
[ROW][C]49[/C][C]16.95[/C][C]16.9747134806133[/C][C]-0.0247134806132721[/C][/ROW]
[ROW][C]50[/C][C]16.95[/C][C]16.9789927374741[/C][C]-0.0289927374740664[/C][/ROW]
[ROW][C]51[/C][C]16.92[/C][C]16.9566447488504[/C][C]-0.0366447488503532[/C][/ROW]
[ROW][C]52[/C][C]16.91[/C][C]16.8128399250824[/C][C]0.0971600749175963[/C][/ROW]
[ROW][C]53[/C][C]16.9[/C][C]16.821611817323[/C][C]0.0783881826769708[/C][/ROW]
[ROW][C]54[/C][C]16.96[/C][C]16.893446038468[/C][C]0.0665539615320441[/C][/ROW]
[ROW][C]55[/C][C]16.96[/C][C]16.9783382193841[/C][C]-0.0183382193840806[/C][/ROW]
[ROW][C]56[/C][C]16.95[/C][C]17.0152473049889[/C][C]-0.0652473049889331[/C][/ROW]
[ROW][C]57[/C][C]16.92[/C][C]17.0076969103213[/C][C]-0.0876969103212772[/C][/ROW]
[ROW][C]58[/C][C]16.87[/C][C]16.9608176388323[/C][C]-0.0908176388323376[/C][/ROW]
[ROW][C]59[/C][C]16.87[/C][C]16.9303597763576[/C][C]-0.0603597763576467[/C][/ROW]
[ROW][C]60[/C][C]16.88[/C][C]16.914419948326[/C][C]-0.0344199483259899[/C][/ROW]
[ROW][C]61[/C][C]16.88[/C][C]16.8979215038932[/C][C]-0.0179215038931844[/C][/ROW]
[ROW][C]62[/C][C]16.86[/C][C]16.8973157506047[/C][C]-0.0373157506047228[/C][/ROW]
[ROW][C]63[/C][C]16.88[/C][C]16.8575269610282[/C][C]0.0224730389718246[/C][/ROW]
[ROW][C]64[/C][C]16.88[/C][C]16.7848672374325[/C][C]0.0951327625674843[/C][/ROW]
[ROW][C]65[/C][C]16.88[/C][C]16.7807088191233[/C][C]0.0992911808767474[/C][/ROW]
[ROW][C]66[/C][C]16.88[/C][C]16.8594873387422[/C][C]0.0205126612578148[/C][/ROW]
[ROW][C]67[/C][C]16.88[/C][C]16.8807836764633[/C][C]-0.000783676463338878[/C][/ROW]
[ROW][C]68[/C][C]16.87[/C][C]16.9120835500168[/C][C]-0.0420835500167982[/C][/ROW]
[ROW][C]69[/C][C]16.92[/C][C]16.9102826390687[/C][C]0.0097173609313046[/C][/ROW]
[ROW][C]70[/C][C]16.94[/C][C]16.9340610908853[/C][C]0.00593890911475015[/C][/ROW]
[ROW][C]71[/C][C]17.03[/C][C]16.9865026702556[/C][C]0.0434973297443726[/C][/ROW]
[ROW][C]72[/C][C]17.02[/C][C]17.0623269614311[/C][C]-0.0423269614310691[/C][/ROW]
[ROW][C]73[/C][C]17.02[/C][C]17.0510330239005[/C][C]-0.0310330239005232[/C][/ROW]
[ROW][C]74[/C][C]17.02[/C][C]17.0421723827188[/C][C]-0.0221723827188427[/C][/ROW]
[ROW][C]75[/C][C]16.99[/C][C]17.0357856291622[/C][C]-0.0457856291621717[/C][/ROW]
[ROW][C]76[/C][C]17.03[/C][C]16.934107553023[/C][C]0.0958924469770075[/C][/ROW]
[ROW][C]77[/C][C]16.98[/C][C]16.9356314531884[/C][C]0.0443685468115618[/C][/ROW]
[ROW][C]78[/C][C]16.89[/C][C]16.9551341635159[/C][C]-0.0651341635159035[/C][/ROW]
[ROW][C]79[/C][C]16.89[/C][C]16.9046158820597[/C][C]-0.0146158820596689[/C][/ROW]
[ROW][C]80[/C][C]16.9[/C][C]16.9123584847672[/C][C]-0.0123584847672085[/C][/ROW]
[ROW][C]81[/C][C]16.89[/C][C]16.9442689028736[/C][C]-0.0542689028736163[/C][/ROW]
[ROW][C]82[/C][C]16.96[/C][C]16.9146975942345[/C][C]0.0453024057654545[/C][/ROW]
[ROW][C]83[/C][C]16.97[/C][C]17.0034172601571[/C][C]-0.0334172601571261[/C][/ROW]
[ROW][C]84[/C][C]16.97[/C][C]16.994011004927[/C][C]-0.0240110049269617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232249&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232249&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
1316.6616.7628926282051-0.102892628205122
1416.6516.6730531419741-0.0230531419740529
1516.516.5024904523918-0.0024904523918039
1616.3916.38640875000370.00359124999630822
1716.3416.33421759185460.00578240814542497
1816.3516.34518005884590.00481994115405371
1916.3516.3856370432281-0.035637043228089
2016.3816.35580848489880.0241915151012329
2116.3616.35903385008180.000966149918230741
2216.3816.33279552235140.0472044776485738
2316.3916.3954496614015-0.00544966140150649
2416.4116.4196075790588-0.00960757905883369
2516.4116.38492906554170.02507093445832
2616.4116.4126220067224-0.00262200672241519
2716.4516.2650313539820.184968646017968
2816.4116.30203220815590.107967791844089
2916.4416.34431260367340.0956873963266354
3016.4716.44214175227090.0278582477291351
3116.4716.510471316568-0.0404713165680342
3216.4916.5124388938715-0.0224388938715236
3316.5416.49326309608930.0467369039107481
3416.6216.5333516088960.0866483911040028
3516.6916.63465550603270.0553444939673398
3616.7216.7283259079265-0.00832590792650478
3716.7216.7282721140978-0.00827211409779949
3816.7116.7475359078641-0.037535907864136
3916.8916.64254584348820.247454156511818
4016.9316.73193046450990.198069535490077
4116.9116.867527687320.0424723126800011
4216.9316.9348899190364-0.00488991903641889
4316.9316.986510529854-0.0565105298540338
4416.9317.0051564769146-0.0751564769146142
4516.9516.9855495220924-0.0355495220923849
4616.9316.9920169025398-0.0620169025397637
4716.9516.9854329932282-0.0354329932282376
4816.9517.0024795448861-0.0524795448860864
4916.9516.9747134806133-0.0247134806132721
5016.9516.9789927374741-0.0289927374740664
5116.9216.9566447488504-0.0366447488503532
5216.9116.81283992508240.0971600749175963
5316.916.8216118173230.0783881826769708
5416.9616.8934460384680.0665539615320441
5516.9616.9783382193841-0.0183382193840806
5616.9517.0152473049889-0.0652473049889331
5716.9217.0076969103213-0.0876969103212772
5816.8716.9608176388323-0.0908176388323376
5916.8716.9303597763576-0.0603597763576467
6016.8816.914419948326-0.0344199483259899
6116.8816.8979215038932-0.0179215038931844
6216.8616.8973157506047-0.0373157506047228
6316.8816.85752696102820.0224730389718246
6416.8816.78486723743250.0951327625674843
6516.8816.78070881912330.0992911808767474
6616.8816.85948733874220.0205126612578148
6716.8816.8807836764633-0.000783676463338878
6816.8716.9120835500168-0.0420835500167982
6916.9216.91028263906870.0097173609313046
7016.9416.93406109088530.00593890911475015
7117.0316.98650267025560.0434973297443726
7217.0217.0623269614311-0.0423269614310691
7317.0217.0510330239005-0.0310330239005232
7417.0217.0421723827188-0.0221723827188427
7516.9917.0357856291622-0.0457856291621717
7617.0316.9341075530230.0958924469770075
7716.9816.93563145318840.0443685468115618
7816.8916.9551341635159-0.0651341635159035
7916.8916.9046158820597-0.0146158820596689
8016.916.9123584847672-0.0123584847672085
8116.8916.9442689028736-0.0542689028736163
8216.9616.91469759423450.0453024057654545
8316.9717.0034172601571-0.0334172601571261
8416.9716.994011004927-0.0240110049269617







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8516.99401155467916.865040878910517.1229822304475
8617.006772314651716.842000475703217.1715441536001
8717.008244059515716.811043250960317.2054448680711
8816.975485487503316.747635111492917.2033358635138
8916.887071834579616.62958431554917.1445593536103
9016.838814070512116.552270176131517.1253579648928
9116.845583809491216.530297121879117.1608704971032
9216.861316743986816.51742452674617.2052089612276
9316.889046333540416.516564055876617.2615286112041
9416.924515446718416.523371551892317.3256593415446
9516.957004916372916.527064051470117.3869457812757
9616.973939240202616.515018359514617.4328601208905

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 16.994011554679 & 16.8650408789105 & 17.1229822304475 \tabularnewline
86 & 17.0067723146517 & 16.8420004757032 & 17.1715441536001 \tabularnewline
87 & 17.0082440595157 & 16.8110432509603 & 17.2054448680711 \tabularnewline
88 & 16.9754854875033 & 16.7476351114929 & 17.2033358635138 \tabularnewline
89 & 16.8870718345796 & 16.629584315549 & 17.1445593536103 \tabularnewline
90 & 16.8388140705121 & 16.5522701761315 & 17.1253579648928 \tabularnewline
91 & 16.8455838094912 & 16.5302971218791 & 17.1608704971032 \tabularnewline
92 & 16.8613167439868 & 16.517424526746 & 17.2052089612276 \tabularnewline
93 & 16.8890463335404 & 16.5165640558766 & 17.2615286112041 \tabularnewline
94 & 16.9245154467184 & 16.5233715518923 & 17.3256593415446 \tabularnewline
95 & 16.9570049163729 & 16.5270640514701 & 17.3869457812757 \tabularnewline
96 & 16.9739392402026 & 16.5150183595146 & 17.4328601208905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232249&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]16.994011554679[/C][C]16.8650408789105[/C][C]17.1229822304475[/C][/ROW]
[ROW][C]86[/C][C]17.0067723146517[/C][C]16.8420004757032[/C][C]17.1715441536001[/C][/ROW]
[ROW][C]87[/C][C]17.0082440595157[/C][C]16.8110432509603[/C][C]17.2054448680711[/C][/ROW]
[ROW][C]88[/C][C]16.9754854875033[/C][C]16.7476351114929[/C][C]17.2033358635138[/C][/ROW]
[ROW][C]89[/C][C]16.8870718345796[/C][C]16.629584315549[/C][C]17.1445593536103[/C][/ROW]
[ROW][C]90[/C][C]16.8388140705121[/C][C]16.5522701761315[/C][C]17.1253579648928[/C][/ROW]
[ROW][C]91[/C][C]16.8455838094912[/C][C]16.5302971218791[/C][C]17.1608704971032[/C][/ROW]
[ROW][C]92[/C][C]16.8613167439868[/C][C]16.517424526746[/C][C]17.2052089612276[/C][/ROW]
[ROW][C]93[/C][C]16.8890463335404[/C][C]16.5165640558766[/C][C]17.2615286112041[/C][/ROW]
[ROW][C]94[/C][C]16.9245154467184[/C][C]16.5233715518923[/C][C]17.3256593415446[/C][/ROW]
[ROW][C]95[/C][C]16.9570049163729[/C][C]16.5270640514701[/C][C]17.3869457812757[/C][/ROW]
[ROW][C]96[/C][C]16.9739392402026[/C][C]16.5150183595146[/C][C]17.4328601208905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232249&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232249&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
8516.99401155467916.865040878910517.1229822304475
8617.006772314651716.842000475703217.1715441536001
8717.008244059515716.811043250960317.2054448680711
8816.975485487503316.747635111492917.2033358635138
8916.887071834579616.62958431554917.1445593536103
9016.838814070512116.552270176131517.1253579648928
9116.845583809491216.530297121879117.1608704971032
9216.861316743986816.51742452674617.2052089612276
9316.889046333540416.516564055876617.2615286112041
9416.924515446718416.523371551892317.3256593415446
9516.957004916372916.527064051470117.3869457812757
9616.973939240202616.515018359514617.4328601208905



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')