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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 17:13:10 +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/Nov/30/t1417367603yosbk50jeexc0ms.htm/, Retrieved Tue, 28 May 2024 16:49:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261550, Retrieved Tue, 28 May 2024 16:49:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 17:13:10] [9458cab04bab2efa06ad058ca673aa95] [Current]
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Dataseries X:
18,3
18,6
18,7
20,1
18,9
20,1
19,8
15,9
19,9
19,6
15,6
14,2
13,6
13,9
15
14,1
13,5
15,3
14,7
12,5
16,1
15,9
15,9
15,7
14,7
15,3
18,4
16,8
16,5
19,3
17,1
15,7
19,1
18,6
18,4
17,1
18,3
19,4
22,3
19,4
21,3
20,3
19,3
17,5
19,9
19,6
19,7
18,1
19,1
20,7
22,5
20
20,2
20,4
19,6
18,1
19,3
21
19,9
17,7
19,4
19,3
21,5
20,9
20,8
20,3
21,4
17,4
21,1
22
20,4
19




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261550&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261550&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 Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.422273769717211
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.422273769717211 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261550&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]0.422273769717211[/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=261550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261550&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
alpha0.422273769717211
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
218.618.30.300000000000001
318.718.42668213091520.273317869084835
420.118.54209709782471.55790290217531
518.919.1999586291796-0.299958629179642
620.119.07329396807671.02670603192326
719.819.50684499456840.293155005431625
815.919.6306366638235-3.73063666382346
919.918.05528665634551.84471334365451
1019.618.83426071401810.765739285981887
1115.619.1576123289302-3.55761232893025
1214.217.6553259596004-3.45532595960045
1313.616.1962324410382-2.59623244103823
1413.915.0999115810989-1.1999115810989
151514.59322039442090.406779605579075
1614.114.7649927519129-0.66499275191288
1713.514.484183755728-0.984183755728004
1815.314.06858877110231.2314112288977
1914.714.5885814328010.111418567198967
2012.514.6356305711886-2.13563057118863
2116.113.73380979916952.36619020083052
2215.914.73298985514211.16701014485789
2315.915.22578762830950.674212371690521
2415.715.51048982809320.189510171906782
2514.715.590515002784-0.890515002784049
2615.315.21447387556870.0855261244313059
2718.415.25058931454163.1494106854584
2816.816.58050283707780.219497162922217
2916.516.6731907315072-0.17319073150718
3019.316.60005682843362.69994317156644
3117.117.7401720095132-0.640172009513165
3215.717.4698441617886-1.7698441617886
3319.116.72248539577812.37751460422187
3418.617.72644745026060.873552549739379
3518.418.09532577848520.304674221514848
3617.118.2239817105399-1.12398171053988
3718.317.7493537165370.550646283462992
3819.417.98187719843571.4181228015643
3922.318.58071325977423.71928674022582
4019.420.1512704922286-0.751270492228578
4121.319.83402866939791.46597133060209
4220.320.4530699094686-0.153069909468609
4319.320.388432501767-1.08843250176703
4417.519.9288160061631-2.42881600616313
4519.918.90319071529110.996809284708874
4619.619.32411712963430.275882870365749
4719.719.4406152293040.259384770695998
4818.119.550146614233-1.45014661423303
4919.118.93778773679820.162212263201802
5020.719.00628572067481.69371427932522
5122.519.72149683422932.77850316577069
522020.8947858402105-0.894785840210503
5320.220.5169412503752-0.31694125037523
5420.420.38310527380040.016894726199606
5519.620.390239473521-0.790239473521037
5618.120.056542072058-1.95654207205796
5719.319.23034567567970.0696543243202754
582119.25975886978761.74024113021245
5919.919.9946170520593-0.0946170520593057
6017.719.9546627528067-2.25466275280669
6119.419.0025778127380.397422187261974
6219.319.17039877792240.129601222077603
6321.519.22512597452912.27487402547094
6420.920.18574560489640.714254395103559
6520.820.48735650085390.312643499146095
6620.320.6193776498159-0.319377649815905
6721.420.48451284566470.915487154335281
6817.420.8710990574536-3.47109905745356
6921.119.40534497340081.69465502659922
702220.12095333985311.87904666014695
7120.420.9144254565078-0.514425456507837
721920.6971970797498-1.69719707974977

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 18.6 & 18.3 & 0.300000000000001 \tabularnewline
3 & 18.7 & 18.4266821309152 & 0.273317869084835 \tabularnewline
4 & 20.1 & 18.5420970978247 & 1.55790290217531 \tabularnewline
5 & 18.9 & 19.1999586291796 & -0.299958629179642 \tabularnewline
6 & 20.1 & 19.0732939680767 & 1.02670603192326 \tabularnewline
7 & 19.8 & 19.5068449945684 & 0.293155005431625 \tabularnewline
8 & 15.9 & 19.6306366638235 & -3.73063666382346 \tabularnewline
9 & 19.9 & 18.0552866563455 & 1.84471334365451 \tabularnewline
10 & 19.6 & 18.8342607140181 & 0.765739285981887 \tabularnewline
11 & 15.6 & 19.1576123289302 & -3.55761232893025 \tabularnewline
12 & 14.2 & 17.6553259596004 & -3.45532595960045 \tabularnewline
13 & 13.6 & 16.1962324410382 & -2.59623244103823 \tabularnewline
14 & 13.9 & 15.0999115810989 & -1.1999115810989 \tabularnewline
15 & 15 & 14.5932203944209 & 0.406779605579075 \tabularnewline
16 & 14.1 & 14.7649927519129 & -0.66499275191288 \tabularnewline
17 & 13.5 & 14.484183755728 & -0.984183755728004 \tabularnewline
18 & 15.3 & 14.0685887711023 & 1.2314112288977 \tabularnewline
19 & 14.7 & 14.588581432801 & 0.111418567198967 \tabularnewline
20 & 12.5 & 14.6356305711886 & -2.13563057118863 \tabularnewline
21 & 16.1 & 13.7338097991695 & 2.36619020083052 \tabularnewline
22 & 15.9 & 14.7329898551421 & 1.16701014485789 \tabularnewline
23 & 15.9 & 15.2257876283095 & 0.674212371690521 \tabularnewline
24 & 15.7 & 15.5104898280932 & 0.189510171906782 \tabularnewline
25 & 14.7 & 15.590515002784 & -0.890515002784049 \tabularnewline
26 & 15.3 & 15.2144738755687 & 0.0855261244313059 \tabularnewline
27 & 18.4 & 15.2505893145416 & 3.1494106854584 \tabularnewline
28 & 16.8 & 16.5805028370778 & 0.219497162922217 \tabularnewline
29 & 16.5 & 16.6731907315072 & -0.17319073150718 \tabularnewline
30 & 19.3 & 16.6000568284336 & 2.69994317156644 \tabularnewline
31 & 17.1 & 17.7401720095132 & -0.640172009513165 \tabularnewline
32 & 15.7 & 17.4698441617886 & -1.7698441617886 \tabularnewline
33 & 19.1 & 16.7224853957781 & 2.37751460422187 \tabularnewline
34 & 18.6 & 17.7264474502606 & 0.873552549739379 \tabularnewline
35 & 18.4 & 18.0953257784852 & 0.304674221514848 \tabularnewline
36 & 17.1 & 18.2239817105399 & -1.12398171053988 \tabularnewline
37 & 18.3 & 17.749353716537 & 0.550646283462992 \tabularnewline
38 & 19.4 & 17.9818771984357 & 1.4181228015643 \tabularnewline
39 & 22.3 & 18.5807132597742 & 3.71928674022582 \tabularnewline
40 & 19.4 & 20.1512704922286 & -0.751270492228578 \tabularnewline
41 & 21.3 & 19.8340286693979 & 1.46597133060209 \tabularnewline
42 & 20.3 & 20.4530699094686 & -0.153069909468609 \tabularnewline
43 & 19.3 & 20.388432501767 & -1.08843250176703 \tabularnewline
44 & 17.5 & 19.9288160061631 & -2.42881600616313 \tabularnewline
45 & 19.9 & 18.9031907152911 & 0.996809284708874 \tabularnewline
46 & 19.6 & 19.3241171296343 & 0.275882870365749 \tabularnewline
47 & 19.7 & 19.440615229304 & 0.259384770695998 \tabularnewline
48 & 18.1 & 19.550146614233 & -1.45014661423303 \tabularnewline
49 & 19.1 & 18.9377877367982 & 0.162212263201802 \tabularnewline
50 & 20.7 & 19.0062857206748 & 1.69371427932522 \tabularnewline
51 & 22.5 & 19.7214968342293 & 2.77850316577069 \tabularnewline
52 & 20 & 20.8947858402105 & -0.894785840210503 \tabularnewline
53 & 20.2 & 20.5169412503752 & -0.31694125037523 \tabularnewline
54 & 20.4 & 20.3831052738004 & 0.016894726199606 \tabularnewline
55 & 19.6 & 20.390239473521 & -0.790239473521037 \tabularnewline
56 & 18.1 & 20.056542072058 & -1.95654207205796 \tabularnewline
57 & 19.3 & 19.2303456756797 & 0.0696543243202754 \tabularnewline
58 & 21 & 19.2597588697876 & 1.74024113021245 \tabularnewline
59 & 19.9 & 19.9946170520593 & -0.0946170520593057 \tabularnewline
60 & 17.7 & 19.9546627528067 & -2.25466275280669 \tabularnewline
61 & 19.4 & 19.002577812738 & 0.397422187261974 \tabularnewline
62 & 19.3 & 19.1703987779224 & 0.129601222077603 \tabularnewline
63 & 21.5 & 19.2251259745291 & 2.27487402547094 \tabularnewline
64 & 20.9 & 20.1857456048964 & 0.714254395103559 \tabularnewline
65 & 20.8 & 20.4873565008539 & 0.312643499146095 \tabularnewline
66 & 20.3 & 20.6193776498159 & -0.319377649815905 \tabularnewline
67 & 21.4 & 20.4845128456647 & 0.915487154335281 \tabularnewline
68 & 17.4 & 20.8710990574536 & -3.47109905745356 \tabularnewline
69 & 21.1 & 19.4053449734008 & 1.69465502659922 \tabularnewline
70 & 22 & 20.1209533398531 & 1.87904666014695 \tabularnewline
71 & 20.4 & 20.9144254565078 & -0.514425456507837 \tabularnewline
72 & 19 & 20.6971970797498 & -1.69719707974977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261550&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]18.6[/C][C]18.3[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]3[/C][C]18.7[/C][C]18.4266821309152[/C][C]0.273317869084835[/C][/ROW]
[ROW][C]4[/C][C]20.1[/C][C]18.5420970978247[/C][C]1.55790290217531[/C][/ROW]
[ROW][C]5[/C][C]18.9[/C][C]19.1999586291796[/C][C]-0.299958629179642[/C][/ROW]
[ROW][C]6[/C][C]20.1[/C][C]19.0732939680767[/C][C]1.02670603192326[/C][/ROW]
[ROW][C]7[/C][C]19.8[/C][C]19.5068449945684[/C][C]0.293155005431625[/C][/ROW]
[ROW][C]8[/C][C]15.9[/C][C]19.6306366638235[/C][C]-3.73063666382346[/C][/ROW]
[ROW][C]9[/C][C]19.9[/C][C]18.0552866563455[/C][C]1.84471334365451[/C][/ROW]
[ROW][C]10[/C][C]19.6[/C][C]18.8342607140181[/C][C]0.765739285981887[/C][/ROW]
[ROW][C]11[/C][C]15.6[/C][C]19.1576123289302[/C][C]-3.55761232893025[/C][/ROW]
[ROW][C]12[/C][C]14.2[/C][C]17.6553259596004[/C][C]-3.45532595960045[/C][/ROW]
[ROW][C]13[/C][C]13.6[/C][C]16.1962324410382[/C][C]-2.59623244103823[/C][/ROW]
[ROW][C]14[/C][C]13.9[/C][C]15.0999115810989[/C][C]-1.1999115810989[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]14.5932203944209[/C][C]0.406779605579075[/C][/ROW]
[ROW][C]16[/C][C]14.1[/C][C]14.7649927519129[/C][C]-0.66499275191288[/C][/ROW]
[ROW][C]17[/C][C]13.5[/C][C]14.484183755728[/C][C]-0.984183755728004[/C][/ROW]
[ROW][C]18[/C][C]15.3[/C][C]14.0685887711023[/C][C]1.2314112288977[/C][/ROW]
[ROW][C]19[/C][C]14.7[/C][C]14.588581432801[/C][C]0.111418567198967[/C][/ROW]
[ROW][C]20[/C][C]12.5[/C][C]14.6356305711886[/C][C]-2.13563057118863[/C][/ROW]
[ROW][C]21[/C][C]16.1[/C][C]13.7338097991695[/C][C]2.36619020083052[/C][/ROW]
[ROW][C]22[/C][C]15.9[/C][C]14.7329898551421[/C][C]1.16701014485789[/C][/ROW]
[ROW][C]23[/C][C]15.9[/C][C]15.2257876283095[/C][C]0.674212371690521[/C][/ROW]
[ROW][C]24[/C][C]15.7[/C][C]15.5104898280932[/C][C]0.189510171906782[/C][/ROW]
[ROW][C]25[/C][C]14.7[/C][C]15.590515002784[/C][C]-0.890515002784049[/C][/ROW]
[ROW][C]26[/C][C]15.3[/C][C]15.2144738755687[/C][C]0.0855261244313059[/C][/ROW]
[ROW][C]27[/C][C]18.4[/C][C]15.2505893145416[/C][C]3.1494106854584[/C][/ROW]
[ROW][C]28[/C][C]16.8[/C][C]16.5805028370778[/C][C]0.219497162922217[/C][/ROW]
[ROW][C]29[/C][C]16.5[/C][C]16.6731907315072[/C][C]-0.17319073150718[/C][/ROW]
[ROW][C]30[/C][C]19.3[/C][C]16.6000568284336[/C][C]2.69994317156644[/C][/ROW]
[ROW][C]31[/C][C]17.1[/C][C]17.7401720095132[/C][C]-0.640172009513165[/C][/ROW]
[ROW][C]32[/C][C]15.7[/C][C]17.4698441617886[/C][C]-1.7698441617886[/C][/ROW]
[ROW][C]33[/C][C]19.1[/C][C]16.7224853957781[/C][C]2.37751460422187[/C][/ROW]
[ROW][C]34[/C][C]18.6[/C][C]17.7264474502606[/C][C]0.873552549739379[/C][/ROW]
[ROW][C]35[/C][C]18.4[/C][C]18.0953257784852[/C][C]0.304674221514848[/C][/ROW]
[ROW][C]36[/C][C]17.1[/C][C]18.2239817105399[/C][C]-1.12398171053988[/C][/ROW]
[ROW][C]37[/C][C]18.3[/C][C]17.749353716537[/C][C]0.550646283462992[/C][/ROW]
[ROW][C]38[/C][C]19.4[/C][C]17.9818771984357[/C][C]1.4181228015643[/C][/ROW]
[ROW][C]39[/C][C]22.3[/C][C]18.5807132597742[/C][C]3.71928674022582[/C][/ROW]
[ROW][C]40[/C][C]19.4[/C][C]20.1512704922286[/C][C]-0.751270492228578[/C][/ROW]
[ROW][C]41[/C][C]21.3[/C][C]19.8340286693979[/C][C]1.46597133060209[/C][/ROW]
[ROW][C]42[/C][C]20.3[/C][C]20.4530699094686[/C][C]-0.153069909468609[/C][/ROW]
[ROW][C]43[/C][C]19.3[/C][C]20.388432501767[/C][C]-1.08843250176703[/C][/ROW]
[ROW][C]44[/C][C]17.5[/C][C]19.9288160061631[/C][C]-2.42881600616313[/C][/ROW]
[ROW][C]45[/C][C]19.9[/C][C]18.9031907152911[/C][C]0.996809284708874[/C][/ROW]
[ROW][C]46[/C][C]19.6[/C][C]19.3241171296343[/C][C]0.275882870365749[/C][/ROW]
[ROW][C]47[/C][C]19.7[/C][C]19.440615229304[/C][C]0.259384770695998[/C][/ROW]
[ROW][C]48[/C][C]18.1[/C][C]19.550146614233[/C][C]-1.45014661423303[/C][/ROW]
[ROW][C]49[/C][C]19.1[/C][C]18.9377877367982[/C][C]0.162212263201802[/C][/ROW]
[ROW][C]50[/C][C]20.7[/C][C]19.0062857206748[/C][C]1.69371427932522[/C][/ROW]
[ROW][C]51[/C][C]22.5[/C][C]19.7214968342293[/C][C]2.77850316577069[/C][/ROW]
[ROW][C]52[/C][C]20[/C][C]20.8947858402105[/C][C]-0.894785840210503[/C][/ROW]
[ROW][C]53[/C][C]20.2[/C][C]20.5169412503752[/C][C]-0.31694125037523[/C][/ROW]
[ROW][C]54[/C][C]20.4[/C][C]20.3831052738004[/C][C]0.016894726199606[/C][/ROW]
[ROW][C]55[/C][C]19.6[/C][C]20.390239473521[/C][C]-0.790239473521037[/C][/ROW]
[ROW][C]56[/C][C]18.1[/C][C]20.056542072058[/C][C]-1.95654207205796[/C][/ROW]
[ROW][C]57[/C][C]19.3[/C][C]19.2303456756797[/C][C]0.0696543243202754[/C][/ROW]
[ROW][C]58[/C][C]21[/C][C]19.2597588697876[/C][C]1.74024113021245[/C][/ROW]
[ROW][C]59[/C][C]19.9[/C][C]19.9946170520593[/C][C]-0.0946170520593057[/C][/ROW]
[ROW][C]60[/C][C]17.7[/C][C]19.9546627528067[/C][C]-2.25466275280669[/C][/ROW]
[ROW][C]61[/C][C]19.4[/C][C]19.002577812738[/C][C]0.397422187261974[/C][/ROW]
[ROW][C]62[/C][C]19.3[/C][C]19.1703987779224[/C][C]0.129601222077603[/C][/ROW]
[ROW][C]63[/C][C]21.5[/C][C]19.2251259745291[/C][C]2.27487402547094[/C][/ROW]
[ROW][C]64[/C][C]20.9[/C][C]20.1857456048964[/C][C]0.714254395103559[/C][/ROW]
[ROW][C]65[/C][C]20.8[/C][C]20.4873565008539[/C][C]0.312643499146095[/C][/ROW]
[ROW][C]66[/C][C]20.3[/C][C]20.6193776498159[/C][C]-0.319377649815905[/C][/ROW]
[ROW][C]67[/C][C]21.4[/C][C]20.4845128456647[/C][C]0.915487154335281[/C][/ROW]
[ROW][C]68[/C][C]17.4[/C][C]20.8710990574536[/C][C]-3.47109905745356[/C][/ROW]
[ROW][C]69[/C][C]21.1[/C][C]19.4053449734008[/C][C]1.69465502659922[/C][/ROW]
[ROW][C]70[/C][C]22[/C][C]20.1209533398531[/C][C]1.87904666014695[/C][/ROW]
[ROW][C]71[/C][C]20.4[/C][C]20.9144254565078[/C][C]-0.514425456507837[/C][/ROW]
[ROW][C]72[/C][C]19[/C][C]20.6971970797498[/C][C]-1.69719707974977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261550&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261550&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
218.618.30.300000000000001
318.718.42668213091520.273317869084835
420.118.54209709782471.55790290217531
518.919.1999586291796-0.299958629179642
620.119.07329396807671.02670603192326
719.819.50684499456840.293155005431625
815.919.6306366638235-3.73063666382346
919.918.05528665634551.84471334365451
1019.618.83426071401810.765739285981887
1115.619.1576123289302-3.55761232893025
1214.217.6553259596004-3.45532595960045
1313.616.1962324410382-2.59623244103823
1413.915.0999115810989-1.1999115810989
151514.59322039442090.406779605579075
1614.114.7649927519129-0.66499275191288
1713.514.484183755728-0.984183755728004
1815.314.06858877110231.2314112288977
1914.714.5885814328010.111418567198967
2012.514.6356305711886-2.13563057118863
2116.113.73380979916952.36619020083052
2215.914.73298985514211.16701014485789
2315.915.22578762830950.674212371690521
2415.715.51048982809320.189510171906782
2514.715.590515002784-0.890515002784049
2615.315.21447387556870.0855261244313059
2718.415.25058931454163.1494106854584
2816.816.58050283707780.219497162922217
2916.516.6731907315072-0.17319073150718
3019.316.60005682843362.69994317156644
3117.117.7401720095132-0.640172009513165
3215.717.4698441617886-1.7698441617886
3319.116.72248539577812.37751460422187
3418.617.72644745026060.873552549739379
3518.418.09532577848520.304674221514848
3617.118.2239817105399-1.12398171053988
3718.317.7493537165370.550646283462992
3819.417.98187719843571.4181228015643
3922.318.58071325977423.71928674022582
4019.420.1512704922286-0.751270492228578
4121.319.83402866939791.46597133060209
4220.320.4530699094686-0.153069909468609
4319.320.388432501767-1.08843250176703
4417.519.9288160061631-2.42881600616313
4519.918.90319071529110.996809284708874
4619.619.32411712963430.275882870365749
4719.719.4406152293040.259384770695998
4818.119.550146614233-1.45014661423303
4919.118.93778773679820.162212263201802
5020.719.00628572067481.69371427932522
5122.519.72149683422932.77850316577069
522020.8947858402105-0.894785840210503
5320.220.5169412503752-0.31694125037523
5420.420.38310527380040.016894726199606
5519.620.390239473521-0.790239473521037
5618.120.056542072058-1.95654207205796
5719.319.23034567567970.0696543243202754
582119.25975886978761.74024113021245
5919.919.9946170520593-0.0946170520593057
6017.719.9546627528067-2.25466275280669
6119.419.0025778127380.397422187261974
6219.319.17039877792240.129601222077603
6321.519.22512597452912.27487402547094
6420.920.18574560489640.714254395103559
6520.820.48735650085390.312643499146095
6620.320.6193776498159-0.319377649815905
6721.420.48451284566470.915487154335281
6817.420.8710990574536-3.47109905745356
6921.119.40534497340081.69465502659922
702220.12095333985311.87904666014695
7120.420.9144254565078-0.514425456507837
721920.6971970797498-1.69719707974977







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7319.980515270930816.832373451645323.1286570902163
7419.980515270930816.563200240114723.3978303017468
7519.980515270930816.313733695032323.6472968468292
7619.980515270930816.080190639460323.8808399024013
7719.980515270930815.859862733241824.1011678086197
7819.980515270930815.650732084457224.3102984574044
7919.980515270930815.451247388880124.5097831529815
8019.980515270930815.260185552268824.7008449895928
8119.980515270930815.076561992361524.8844685495001
8219.980515270930814.899570195071625.0614603467899
8319.980515270930814.72853964556825.2324908962935
8419.980515270930814.562905735821125.3981248060405

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 19.9805152709308 & 16.8323734516453 & 23.1286570902163 \tabularnewline
74 & 19.9805152709308 & 16.5632002401147 & 23.3978303017468 \tabularnewline
75 & 19.9805152709308 & 16.3137336950323 & 23.6472968468292 \tabularnewline
76 & 19.9805152709308 & 16.0801906394603 & 23.8808399024013 \tabularnewline
77 & 19.9805152709308 & 15.8598627332418 & 24.1011678086197 \tabularnewline
78 & 19.9805152709308 & 15.6507320844572 & 24.3102984574044 \tabularnewline
79 & 19.9805152709308 & 15.4512473888801 & 24.5097831529815 \tabularnewline
80 & 19.9805152709308 & 15.2601855522688 & 24.7008449895928 \tabularnewline
81 & 19.9805152709308 & 15.0765619923615 & 24.8844685495001 \tabularnewline
82 & 19.9805152709308 & 14.8995701950716 & 25.0614603467899 \tabularnewline
83 & 19.9805152709308 & 14.728539645568 & 25.2324908962935 \tabularnewline
84 & 19.9805152709308 & 14.5629057358211 & 25.3981248060405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261550&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]19.9805152709308[/C][C]16.8323734516453[/C][C]23.1286570902163[/C][/ROW]
[ROW][C]74[/C][C]19.9805152709308[/C][C]16.5632002401147[/C][C]23.3978303017468[/C][/ROW]
[ROW][C]75[/C][C]19.9805152709308[/C][C]16.3137336950323[/C][C]23.6472968468292[/C][/ROW]
[ROW][C]76[/C][C]19.9805152709308[/C][C]16.0801906394603[/C][C]23.8808399024013[/C][/ROW]
[ROW][C]77[/C][C]19.9805152709308[/C][C]15.8598627332418[/C][C]24.1011678086197[/C][/ROW]
[ROW][C]78[/C][C]19.9805152709308[/C][C]15.6507320844572[/C][C]24.3102984574044[/C][/ROW]
[ROW][C]79[/C][C]19.9805152709308[/C][C]15.4512473888801[/C][C]24.5097831529815[/C][/ROW]
[ROW][C]80[/C][C]19.9805152709308[/C][C]15.2601855522688[/C][C]24.7008449895928[/C][/ROW]
[ROW][C]81[/C][C]19.9805152709308[/C][C]15.0765619923615[/C][C]24.8844685495001[/C][/ROW]
[ROW][C]82[/C][C]19.9805152709308[/C][C]14.8995701950716[/C][C]25.0614603467899[/C][/ROW]
[ROW][C]83[/C][C]19.9805152709308[/C][C]14.728539645568[/C][C]25.2324908962935[/C][/ROW]
[ROW][C]84[/C][C]19.9805152709308[/C][C]14.5629057358211[/C][C]25.3981248060405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261550&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261550&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
7319.980515270930816.832373451645323.1286570902163
7419.980515270930816.563200240114723.3978303017468
7519.980515270930816.313733695032323.6472968468292
7619.980515270930816.080190639460323.8808399024013
7719.980515270930815.859862733241824.1011678086197
7819.980515270930815.650732084457224.3102984574044
7919.980515270930815.451247388880124.5097831529815
8019.980515270930815.260185552268824.7008449895928
8119.980515270930815.076561992361524.8844685495001
8219.980515270930814.899570195071625.0614603467899
8319.980515270930814.72853964556825.2324908962935
8419.980515270930814.562905735821125.3981248060405



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')