Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 05:08:00 -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/2012/Dec/17/t13557389002i3dstjqmpcymji.htm/, Retrieved Thu, 28 Mar 2024 17:32:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200740, Retrieved Thu, 28 Mar 2024 17:32:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 10:08:00] [4580e6b2a2a2b9b99b0ce0e7252c310b] [Current]
Feedback Forum

Post a new message
Dataseries X:
1,33
1,32
1,32
1,4
1,43
1,43
1,45
1,45
1,33
1,27
1,27
1,29
1,25
1,26
1,32
1,36
1,4
1,41
1,42
1,39
1,38
1,41
1,47
1,44
1,47
1,45
1,47
1,49
1,54
1,61
1,63
1,55
1,53
1,41
1,26
1,19
1,17
1,21
1,24
1,26
1,32
1,39
1,35
1,41
1,37
1,32
1,38
1,38
1,41
1,4
1,45
1,49
1,51
1,48
1,47
1,46
1,46
1,45
1,47
1,53
1,55
1,55
1,6
1,65
1,68
1,63
1,62
1,63
1,66
1,63
1,6
1,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200740&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200740&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0281561480639734
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0281561480639734 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200740&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0281561480639734[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200740&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0281561480639734
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.321.310.01
41.41.310281561480640.0897184385193601
51.431.392807687119660.0371923128803406
61.431.423854879387960.0061451206120402
71.451.424027902313780.0259720976862166
81.451.444759176541770.00524082345823151
91.331.44490673794304-0.114906737943036
101.271.32167140681596-0.0516714068159634
111.271.260216539034980.0097834609650207
121.291.260492003610490.0295079963895115
131.251.2813228351259-0.0313228351259027
141.261.240440904742310.0195590952576856
151.321.250991613524390.0690083864756128
161.361.312934623871650.0470653761283497
171.41.354259803570610.0457401964293931
181.411.395547671313750.0144523286862519
191.421.405954593220110.0140454067798927
201.391.41635005777302-0.0263500577730207
211.381.38560814164487-0.00560814164486945
221.411.375450237978350.0345497620216473
231.471.406423026193410.0635769738065908
241.441.46821310888137-0.0282131088813669
251.471.437418736410360.0325812635896419
261.451.4683360992921-0.0183360992920996
271.471.447819825365520.0221801746344845
281.491.468444333646610.0215556663533913
291.541.489051258180070.0509487418199277
301.611.540485778498430.0695142215015725
311.631.612443031211580.0175569687884223
321.551.63293736782434-0.0829373678243388
331.531.55060217101584-0.0206021710158406
341.411.53002209323828-0.120022093238279
351.261.40664273341011-0.146642733410114
361.191.25251383889571-0.0625138388957134
371.171.18075368999172-0.0107536899917182
381.211.160450907504080.0495490924959225
391.241.201846019088830.0381539809111719
401.261.232920288224590.0270797117754069
411.321.253682748598870.066317251401129
421.391.315549986948520.0744500130514827
431.351.38764621253936-0.0376462125393593
441.411.346586240205050.0634137597949465
451.371.40837172741513-0.038371727415133
461.321.36729132737656-0.0472913273765623
471.381.315959785760810.064040214239194
481.381.377762911514970.00223708848502668
491.411.377825899309590.0321741006904102
501.41.40873179805245-0.00873179805245416
511.451.398485944253620.0515140557463754
521.491.44993638163460.0400636183654046
531.511.491064418805270.0189355811947298
541.481.51159757183307-0.0315975718330663
551.471.48070790592207-0.0107079059220725
561.461.47040641253748-0.0104064125374757
571.461.46011340804526-0.000113408045255614
581.451.46011021491154-0.0101102149115417
591.471.449825550203530.0201744497964662
601.531.470393584999110.0596064150008877
611.551.532071872045440.01792812795456
621.551.55257665907064-0.00257665907063842
631.61.552504110276340.047495889723665
641.651.603841411579820.046158588420175
651.681.655141059629810.0248589403701929
661.631.68584099163558-0.055840991635584
671.621.63426872440705-0.014268724407053
681.631.623866972089960.00613302791003556
691.661.634039654531880.0259603454681203
701.631.66477059786267-0.034770597862672
711.61.63379159176098-0.0337915917609775
721.61.60284015070004-0.0028401507000384

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.32 & 1.31 & 0.01 \tabularnewline
4 & 1.4 & 1.31028156148064 & 0.0897184385193601 \tabularnewline
5 & 1.43 & 1.39280768711966 & 0.0371923128803406 \tabularnewline
6 & 1.43 & 1.42385487938796 & 0.0061451206120402 \tabularnewline
7 & 1.45 & 1.42402790231378 & 0.0259720976862166 \tabularnewline
8 & 1.45 & 1.44475917654177 & 0.00524082345823151 \tabularnewline
9 & 1.33 & 1.44490673794304 & -0.114906737943036 \tabularnewline
10 & 1.27 & 1.32167140681596 & -0.0516714068159634 \tabularnewline
11 & 1.27 & 1.26021653903498 & 0.0097834609650207 \tabularnewline
12 & 1.29 & 1.26049200361049 & 0.0295079963895115 \tabularnewline
13 & 1.25 & 1.2813228351259 & -0.0313228351259027 \tabularnewline
14 & 1.26 & 1.24044090474231 & 0.0195590952576856 \tabularnewline
15 & 1.32 & 1.25099161352439 & 0.0690083864756128 \tabularnewline
16 & 1.36 & 1.31293462387165 & 0.0470653761283497 \tabularnewline
17 & 1.4 & 1.35425980357061 & 0.0457401964293931 \tabularnewline
18 & 1.41 & 1.39554767131375 & 0.0144523286862519 \tabularnewline
19 & 1.42 & 1.40595459322011 & 0.0140454067798927 \tabularnewline
20 & 1.39 & 1.41635005777302 & -0.0263500577730207 \tabularnewline
21 & 1.38 & 1.38560814164487 & -0.00560814164486945 \tabularnewline
22 & 1.41 & 1.37545023797835 & 0.0345497620216473 \tabularnewline
23 & 1.47 & 1.40642302619341 & 0.0635769738065908 \tabularnewline
24 & 1.44 & 1.46821310888137 & -0.0282131088813669 \tabularnewline
25 & 1.47 & 1.43741873641036 & 0.0325812635896419 \tabularnewline
26 & 1.45 & 1.4683360992921 & -0.0183360992920996 \tabularnewline
27 & 1.47 & 1.44781982536552 & 0.0221801746344845 \tabularnewline
28 & 1.49 & 1.46844433364661 & 0.0215556663533913 \tabularnewline
29 & 1.54 & 1.48905125818007 & 0.0509487418199277 \tabularnewline
30 & 1.61 & 1.54048577849843 & 0.0695142215015725 \tabularnewline
31 & 1.63 & 1.61244303121158 & 0.0175569687884223 \tabularnewline
32 & 1.55 & 1.63293736782434 & -0.0829373678243388 \tabularnewline
33 & 1.53 & 1.55060217101584 & -0.0206021710158406 \tabularnewline
34 & 1.41 & 1.53002209323828 & -0.120022093238279 \tabularnewline
35 & 1.26 & 1.40664273341011 & -0.146642733410114 \tabularnewline
36 & 1.19 & 1.25251383889571 & -0.0625138388957134 \tabularnewline
37 & 1.17 & 1.18075368999172 & -0.0107536899917182 \tabularnewline
38 & 1.21 & 1.16045090750408 & 0.0495490924959225 \tabularnewline
39 & 1.24 & 1.20184601908883 & 0.0381539809111719 \tabularnewline
40 & 1.26 & 1.23292028822459 & 0.0270797117754069 \tabularnewline
41 & 1.32 & 1.25368274859887 & 0.066317251401129 \tabularnewline
42 & 1.39 & 1.31554998694852 & 0.0744500130514827 \tabularnewline
43 & 1.35 & 1.38764621253936 & -0.0376462125393593 \tabularnewline
44 & 1.41 & 1.34658624020505 & 0.0634137597949465 \tabularnewline
45 & 1.37 & 1.40837172741513 & -0.038371727415133 \tabularnewline
46 & 1.32 & 1.36729132737656 & -0.0472913273765623 \tabularnewline
47 & 1.38 & 1.31595978576081 & 0.064040214239194 \tabularnewline
48 & 1.38 & 1.37776291151497 & 0.00223708848502668 \tabularnewline
49 & 1.41 & 1.37782589930959 & 0.0321741006904102 \tabularnewline
50 & 1.4 & 1.40873179805245 & -0.00873179805245416 \tabularnewline
51 & 1.45 & 1.39848594425362 & 0.0515140557463754 \tabularnewline
52 & 1.49 & 1.4499363816346 & 0.0400636183654046 \tabularnewline
53 & 1.51 & 1.49106441880527 & 0.0189355811947298 \tabularnewline
54 & 1.48 & 1.51159757183307 & -0.0315975718330663 \tabularnewline
55 & 1.47 & 1.48070790592207 & -0.0107079059220725 \tabularnewline
56 & 1.46 & 1.47040641253748 & -0.0104064125374757 \tabularnewline
57 & 1.46 & 1.46011340804526 & -0.000113408045255614 \tabularnewline
58 & 1.45 & 1.46011021491154 & -0.0101102149115417 \tabularnewline
59 & 1.47 & 1.44982555020353 & 0.0201744497964662 \tabularnewline
60 & 1.53 & 1.47039358499911 & 0.0596064150008877 \tabularnewline
61 & 1.55 & 1.53207187204544 & 0.01792812795456 \tabularnewline
62 & 1.55 & 1.55257665907064 & -0.00257665907063842 \tabularnewline
63 & 1.6 & 1.55250411027634 & 0.047495889723665 \tabularnewline
64 & 1.65 & 1.60384141157982 & 0.046158588420175 \tabularnewline
65 & 1.68 & 1.65514105962981 & 0.0248589403701929 \tabularnewline
66 & 1.63 & 1.68584099163558 & -0.055840991635584 \tabularnewline
67 & 1.62 & 1.63426872440705 & -0.014268724407053 \tabularnewline
68 & 1.63 & 1.62386697208996 & 0.00613302791003556 \tabularnewline
69 & 1.66 & 1.63403965453188 & 0.0259603454681203 \tabularnewline
70 & 1.63 & 1.66477059786267 & -0.034770597862672 \tabularnewline
71 & 1.6 & 1.63379159176098 & -0.0337915917609775 \tabularnewline
72 & 1.6 & 1.60284015070004 & -0.0028401507000384 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200740&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1.32[/C][C]1.31[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]1.4[/C][C]1.31028156148064[/C][C]0.0897184385193601[/C][/ROW]
[ROW][C]5[/C][C]1.43[/C][C]1.39280768711966[/C][C]0.0371923128803406[/C][/ROW]
[ROW][C]6[/C][C]1.43[/C][C]1.42385487938796[/C][C]0.0061451206120402[/C][/ROW]
[ROW][C]7[/C][C]1.45[/C][C]1.42402790231378[/C][C]0.0259720976862166[/C][/ROW]
[ROW][C]8[/C][C]1.45[/C][C]1.44475917654177[/C][C]0.00524082345823151[/C][/ROW]
[ROW][C]9[/C][C]1.33[/C][C]1.44490673794304[/C][C]-0.114906737943036[/C][/ROW]
[ROW][C]10[/C][C]1.27[/C][C]1.32167140681596[/C][C]-0.0516714068159634[/C][/ROW]
[ROW][C]11[/C][C]1.27[/C][C]1.26021653903498[/C][C]0.0097834609650207[/C][/ROW]
[ROW][C]12[/C][C]1.29[/C][C]1.26049200361049[/C][C]0.0295079963895115[/C][/ROW]
[ROW][C]13[/C][C]1.25[/C][C]1.2813228351259[/C][C]-0.0313228351259027[/C][/ROW]
[ROW][C]14[/C][C]1.26[/C][C]1.24044090474231[/C][C]0.0195590952576856[/C][/ROW]
[ROW][C]15[/C][C]1.32[/C][C]1.25099161352439[/C][C]0.0690083864756128[/C][/ROW]
[ROW][C]16[/C][C]1.36[/C][C]1.31293462387165[/C][C]0.0470653761283497[/C][/ROW]
[ROW][C]17[/C][C]1.4[/C][C]1.35425980357061[/C][C]0.0457401964293931[/C][/ROW]
[ROW][C]18[/C][C]1.41[/C][C]1.39554767131375[/C][C]0.0144523286862519[/C][/ROW]
[ROW][C]19[/C][C]1.42[/C][C]1.40595459322011[/C][C]0.0140454067798927[/C][/ROW]
[ROW][C]20[/C][C]1.39[/C][C]1.41635005777302[/C][C]-0.0263500577730207[/C][/ROW]
[ROW][C]21[/C][C]1.38[/C][C]1.38560814164487[/C][C]-0.00560814164486945[/C][/ROW]
[ROW][C]22[/C][C]1.41[/C][C]1.37545023797835[/C][C]0.0345497620216473[/C][/ROW]
[ROW][C]23[/C][C]1.47[/C][C]1.40642302619341[/C][C]0.0635769738065908[/C][/ROW]
[ROW][C]24[/C][C]1.44[/C][C]1.46821310888137[/C][C]-0.0282131088813669[/C][/ROW]
[ROW][C]25[/C][C]1.47[/C][C]1.43741873641036[/C][C]0.0325812635896419[/C][/ROW]
[ROW][C]26[/C][C]1.45[/C][C]1.4683360992921[/C][C]-0.0183360992920996[/C][/ROW]
[ROW][C]27[/C][C]1.47[/C][C]1.44781982536552[/C][C]0.0221801746344845[/C][/ROW]
[ROW][C]28[/C][C]1.49[/C][C]1.46844433364661[/C][C]0.0215556663533913[/C][/ROW]
[ROW][C]29[/C][C]1.54[/C][C]1.48905125818007[/C][C]0.0509487418199277[/C][/ROW]
[ROW][C]30[/C][C]1.61[/C][C]1.54048577849843[/C][C]0.0695142215015725[/C][/ROW]
[ROW][C]31[/C][C]1.63[/C][C]1.61244303121158[/C][C]0.0175569687884223[/C][/ROW]
[ROW][C]32[/C][C]1.55[/C][C]1.63293736782434[/C][C]-0.0829373678243388[/C][/ROW]
[ROW][C]33[/C][C]1.53[/C][C]1.55060217101584[/C][C]-0.0206021710158406[/C][/ROW]
[ROW][C]34[/C][C]1.41[/C][C]1.53002209323828[/C][C]-0.120022093238279[/C][/ROW]
[ROW][C]35[/C][C]1.26[/C][C]1.40664273341011[/C][C]-0.146642733410114[/C][/ROW]
[ROW][C]36[/C][C]1.19[/C][C]1.25251383889571[/C][C]-0.0625138388957134[/C][/ROW]
[ROW][C]37[/C][C]1.17[/C][C]1.18075368999172[/C][C]-0.0107536899917182[/C][/ROW]
[ROW][C]38[/C][C]1.21[/C][C]1.16045090750408[/C][C]0.0495490924959225[/C][/ROW]
[ROW][C]39[/C][C]1.24[/C][C]1.20184601908883[/C][C]0.0381539809111719[/C][/ROW]
[ROW][C]40[/C][C]1.26[/C][C]1.23292028822459[/C][C]0.0270797117754069[/C][/ROW]
[ROW][C]41[/C][C]1.32[/C][C]1.25368274859887[/C][C]0.066317251401129[/C][/ROW]
[ROW][C]42[/C][C]1.39[/C][C]1.31554998694852[/C][C]0.0744500130514827[/C][/ROW]
[ROW][C]43[/C][C]1.35[/C][C]1.38764621253936[/C][C]-0.0376462125393593[/C][/ROW]
[ROW][C]44[/C][C]1.41[/C][C]1.34658624020505[/C][C]0.0634137597949465[/C][/ROW]
[ROW][C]45[/C][C]1.37[/C][C]1.40837172741513[/C][C]-0.038371727415133[/C][/ROW]
[ROW][C]46[/C][C]1.32[/C][C]1.36729132737656[/C][C]-0.0472913273765623[/C][/ROW]
[ROW][C]47[/C][C]1.38[/C][C]1.31595978576081[/C][C]0.064040214239194[/C][/ROW]
[ROW][C]48[/C][C]1.38[/C][C]1.37776291151497[/C][C]0.00223708848502668[/C][/ROW]
[ROW][C]49[/C][C]1.41[/C][C]1.37782589930959[/C][C]0.0321741006904102[/C][/ROW]
[ROW][C]50[/C][C]1.4[/C][C]1.40873179805245[/C][C]-0.00873179805245416[/C][/ROW]
[ROW][C]51[/C][C]1.45[/C][C]1.39848594425362[/C][C]0.0515140557463754[/C][/ROW]
[ROW][C]52[/C][C]1.49[/C][C]1.4499363816346[/C][C]0.0400636183654046[/C][/ROW]
[ROW][C]53[/C][C]1.51[/C][C]1.49106441880527[/C][C]0.0189355811947298[/C][/ROW]
[ROW][C]54[/C][C]1.48[/C][C]1.51159757183307[/C][C]-0.0315975718330663[/C][/ROW]
[ROW][C]55[/C][C]1.47[/C][C]1.48070790592207[/C][C]-0.0107079059220725[/C][/ROW]
[ROW][C]56[/C][C]1.46[/C][C]1.47040641253748[/C][C]-0.0104064125374757[/C][/ROW]
[ROW][C]57[/C][C]1.46[/C][C]1.46011340804526[/C][C]-0.000113408045255614[/C][/ROW]
[ROW][C]58[/C][C]1.45[/C][C]1.46011021491154[/C][C]-0.0101102149115417[/C][/ROW]
[ROW][C]59[/C][C]1.47[/C][C]1.44982555020353[/C][C]0.0201744497964662[/C][/ROW]
[ROW][C]60[/C][C]1.53[/C][C]1.47039358499911[/C][C]0.0596064150008877[/C][/ROW]
[ROW][C]61[/C][C]1.55[/C][C]1.53207187204544[/C][C]0.01792812795456[/C][/ROW]
[ROW][C]62[/C][C]1.55[/C][C]1.55257665907064[/C][C]-0.00257665907063842[/C][/ROW]
[ROW][C]63[/C][C]1.6[/C][C]1.55250411027634[/C][C]0.047495889723665[/C][/ROW]
[ROW][C]64[/C][C]1.65[/C][C]1.60384141157982[/C][C]0.046158588420175[/C][/ROW]
[ROW][C]65[/C][C]1.68[/C][C]1.65514105962981[/C][C]0.0248589403701929[/C][/ROW]
[ROW][C]66[/C][C]1.63[/C][C]1.68584099163558[/C][C]-0.055840991635584[/C][/ROW]
[ROW][C]67[/C][C]1.62[/C][C]1.63426872440705[/C][C]-0.014268724407053[/C][/ROW]
[ROW][C]68[/C][C]1.63[/C][C]1.62386697208996[/C][C]0.00613302791003556[/C][/ROW]
[ROW][C]69[/C][C]1.66[/C][C]1.63403965453188[/C][C]0.0259603454681203[/C][/ROW]
[ROW][C]70[/C][C]1.63[/C][C]1.66477059786267[/C][C]-0.034770597862672[/C][/ROW]
[ROW][C]71[/C][C]1.6[/C][C]1.63379159176098[/C][C]-0.0337915917609775[/C][/ROW]
[ROW][C]72[/C][C]1.6[/C][C]1.60284015070004[/C][C]-0.0028401507000384[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200740&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
31.321.310.01
41.41.310281561480640.0897184385193601
51.431.392807687119660.0371923128803406
61.431.423854879387960.0061451206120402
71.451.424027902313780.0259720976862166
81.451.444759176541770.00524082345823151
91.331.44490673794304-0.114906737943036
101.271.32167140681596-0.0516714068159634
111.271.260216539034980.0097834609650207
121.291.260492003610490.0295079963895115
131.251.2813228351259-0.0313228351259027
141.261.240440904742310.0195590952576856
151.321.250991613524390.0690083864756128
161.361.312934623871650.0470653761283497
171.41.354259803570610.0457401964293931
181.411.395547671313750.0144523286862519
191.421.405954593220110.0140454067798927
201.391.41635005777302-0.0263500577730207
211.381.38560814164487-0.00560814164486945
221.411.375450237978350.0345497620216473
231.471.406423026193410.0635769738065908
241.441.46821310888137-0.0282131088813669
251.471.437418736410360.0325812635896419
261.451.4683360992921-0.0183360992920996
271.471.447819825365520.0221801746344845
281.491.468444333646610.0215556663533913
291.541.489051258180070.0509487418199277
301.611.540485778498430.0695142215015725
311.631.612443031211580.0175569687884223
321.551.63293736782434-0.0829373678243388
331.531.55060217101584-0.0206021710158406
341.411.53002209323828-0.120022093238279
351.261.40664273341011-0.146642733410114
361.191.25251383889571-0.0625138388957134
371.171.18075368999172-0.0107536899917182
381.211.160450907504080.0495490924959225
391.241.201846019088830.0381539809111719
401.261.232920288224590.0270797117754069
411.321.253682748598870.066317251401129
421.391.315549986948520.0744500130514827
431.351.38764621253936-0.0376462125393593
441.411.346586240205050.0634137597949465
451.371.40837172741513-0.038371727415133
461.321.36729132737656-0.0472913273765623
471.381.315959785760810.064040214239194
481.381.377762911514970.00223708848502668
491.411.377825899309590.0321741006904102
501.41.40873179805245-0.00873179805245416
511.451.398485944253620.0515140557463754
521.491.44993638163460.0400636183654046
531.511.491064418805270.0189355811947298
541.481.51159757183307-0.0315975718330663
551.471.48070790592207-0.0107079059220725
561.461.47040641253748-0.0104064125374757
571.461.46011340804526-0.000113408045255614
581.451.46011021491154-0.0101102149115417
591.471.449825550203530.0201744497964662
601.531.470393584999110.0596064150008877
611.551.532071872045440.01792812795456
621.551.55257665907064-0.00257665907063842
631.61.552504110276340.047495889723665
641.651.603841411579820.046158588420175
651.681.655141059629810.0248589403701929
661.631.68584099163558-0.055840991635584
671.621.63426872440705-0.014268724407053
681.631.623866972089960.00613302791003556
691.661.634039654531880.0259603454681203
701.631.66477059786267-0.034770597862672
711.61.63379159176098-0.0337915917609775
721.61.60284015070004-0.0028401507000384







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.60276018299641.511474732779451.69404563321336
741.605520365992811.474593190600741.73644754138487
751.608280548989211.445677080882891.77088401709554
761.611040731985621.420672316776581.80140914719465
771.613800914982021.398032811225141.8295690187389
781.616561097978421.376977451948841.85614474400801
791.619321280974831.357049108636851.88159345331281
801.622081463971231.337954390729871.9062085372126
811.624841646967641.319492600992381.9301906929429
821.627601829964041.301519872311541.95368378761654
831.630362012960441.283929312757561.97679471316333
841.633122195956851.26663922199511.99960516991859

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.6027601829964 & 1.51147473277945 & 1.69404563321336 \tabularnewline
74 & 1.60552036599281 & 1.47459319060074 & 1.73644754138487 \tabularnewline
75 & 1.60828054898921 & 1.44567708088289 & 1.77088401709554 \tabularnewline
76 & 1.61104073198562 & 1.42067231677658 & 1.80140914719465 \tabularnewline
77 & 1.61380091498202 & 1.39803281122514 & 1.8295690187389 \tabularnewline
78 & 1.61656109797842 & 1.37697745194884 & 1.85614474400801 \tabularnewline
79 & 1.61932128097483 & 1.35704910863685 & 1.88159345331281 \tabularnewline
80 & 1.62208146397123 & 1.33795439072987 & 1.9062085372126 \tabularnewline
81 & 1.62484164696764 & 1.31949260099238 & 1.9301906929429 \tabularnewline
82 & 1.62760182996404 & 1.30151987231154 & 1.95368378761654 \tabularnewline
83 & 1.63036201296044 & 1.28392931275756 & 1.97679471316333 \tabularnewline
84 & 1.63312219595685 & 1.2666392219951 & 1.99960516991859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200740&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]1.6027601829964[/C][C]1.51147473277945[/C][C]1.69404563321336[/C][/ROW]
[ROW][C]74[/C][C]1.60552036599281[/C][C]1.47459319060074[/C][C]1.73644754138487[/C][/ROW]
[ROW][C]75[/C][C]1.60828054898921[/C][C]1.44567708088289[/C][C]1.77088401709554[/C][/ROW]
[ROW][C]76[/C][C]1.61104073198562[/C][C]1.42067231677658[/C][C]1.80140914719465[/C][/ROW]
[ROW][C]77[/C][C]1.61380091498202[/C][C]1.39803281122514[/C][C]1.8295690187389[/C][/ROW]
[ROW][C]78[/C][C]1.61656109797842[/C][C]1.37697745194884[/C][C]1.85614474400801[/C][/ROW]
[ROW][C]79[/C][C]1.61932128097483[/C][C]1.35704910863685[/C][C]1.88159345331281[/C][/ROW]
[ROW][C]80[/C][C]1.62208146397123[/C][C]1.33795439072987[/C][C]1.9062085372126[/C][/ROW]
[ROW][C]81[/C][C]1.62484164696764[/C][C]1.31949260099238[/C][C]1.9301906929429[/C][/ROW]
[ROW][C]82[/C][C]1.62760182996404[/C][C]1.30151987231154[/C][C]1.95368378761654[/C][/ROW]
[ROW][C]83[/C][C]1.63036201296044[/C][C]1.28392931275756[/C][C]1.97679471316333[/C][/ROW]
[ROW][C]84[/C][C]1.63312219595685[/C][C]1.2666392219951[/C][C]1.99960516991859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200740&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
731.60276018299641.511474732779451.69404563321336
741.605520365992811.474593190600741.73644754138487
751.608280548989211.445677080882891.77088401709554
761.611040731985621.420672316776581.80140914719465
771.613800914982021.398032811225141.8295690187389
781.616561097978421.376977451948841.85614474400801
791.619321280974831.357049108636851.88159345331281
801.622081463971231.337954390729871.9062085372126
811.624841646967641.319492600992381.9301906929429
821.627601829964041.301519872311541.95368378761654
831.630362012960441.283929312757561.97679471316333
841.633122195956851.26663922199511.99960516991859



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')