Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 10:37:58 -0400
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/May/26/t13695792622adimobirkkft5m.htm/, Retrieved Thu, 31 Oct 2024 23:45:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210624, Retrieved Thu, 31 Oct 2024 23:45:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2013-05-26 14:37:58] [86531c41dade6c5b3fb1cb68f8179a3e] [Current]
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Dataseries X:
2,27
2,35
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
3,07
3,07
3,07
3,07
3,07
3,07
3,07
3,07
3,07
3,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210624&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210624&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.947716105380562
beta0.0144218697861163
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.947716105380562 \tabularnewline
beta & 0.0144218697861163 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210624&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]0.947716105380562[/C][/ROW]
[ROW][C]beta[/C][C]0.0144218697861163[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210624&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
alpha0.947716105380562
beta0.0144218697861163
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.542.527067307692310.0129326923076927
142.542.54079138296584-0.000791382965836807
152.542.5414981145768-0.00149811457680427
162.542.54151458927014-0.00151458927013604
172.542.54149474947008-0.00149474947008255
182.542.54147328217406-0.00147328217406217
192.542.56853535653108-0.0285353565310769
202.542.523310250537010.0166897494629867
212.542.532423818657430.00757618134257276
222.542.54092052818057-0.000920528180572422
232.542.5413521876156-0.00135218761560152
242.542.54135627497038-0.00135627497037838
252.542.54133795132627-0.00133795132626569
262.662.541318706392450.118681293607547
272.662.656665749564260.00333425043574342
282.662.66274211420981-0.00274211420980919
292.662.66302233144508-0.00302233144507991
302.662.6629956735561-0.00299567355610142
312.662.69003666872951-0.0300366687295139
322.662.644789940941320.0152100590586781
332.662.6538821544210.0061178455790003
342.662.66235781514301-0.00235781514300548
352.662.66276872945899-0.00276872945898887
362.662.66275237111334-0.00275237111333571
372.662.66271389687209-0.00271389687209034
382.662.6626747921854-0.00267479218539712
392.662.66263618901309-0.00263618901309393
402.662.66259813968383-0.00259813968383149
412.662.66256063936372-0.00256063936371875
422.662.66252368029625-0.00252368029625316
432.662.68957058801147-0.0295705880114734
442.662.644330539669870.0156694603301335
452.662.65342938139930.00657061860069685
462.662.66191157710045-0.00191157710045298
472.662.66232893219999-0.00232893219999086
482.662.66231892168139-0.00231892168139236
492.662.662286703646-0.00228670364599992
502.932.662253764866040.267746235133963
512.932.921794903389230.0082050966107694
522.932.93547687085862-0.00547687085861925
532.932.93611736041888-0.00611736041887578
542.932.93606723661473-0.00606723661472897
552.932.9630650232716-0.0330650232715963
562.932.917774645313780.0122253546862154
572.932.926823782135960.00317621786404043
582.932.9352569849507-0.00525698495069671
592.932.93562605401789-0.00562605401789407
602.932.93556845438972-0.00556845438971854
612.932.93548933412284-0.00548933412283814
622.932.93541017007616-0.00541017007616373
633.072.93533208574190.134667914258103
643.073.069848877213770.000151122786228974
653.073.07688400448543-0.00688400448543236
663.073.07715773887841-0.00715773887840854
673.073.10415755329456-0.0341575532945573
683.073.058852348832240.0111476511677564
693.073.067885980589630.00211401941036948
703.073.07630385478252-0.00630385478252338
713.073.07665781396212-0.0066578139621245
723.073.07658532240213-0.00658532240213106

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.54 & 2.52706730769231 & 0.0129326923076927 \tabularnewline
14 & 2.54 & 2.54079138296584 & -0.000791382965836807 \tabularnewline
15 & 2.54 & 2.5414981145768 & -0.00149811457680427 \tabularnewline
16 & 2.54 & 2.54151458927014 & -0.00151458927013604 \tabularnewline
17 & 2.54 & 2.54149474947008 & -0.00149474947008255 \tabularnewline
18 & 2.54 & 2.54147328217406 & -0.00147328217406217 \tabularnewline
19 & 2.54 & 2.56853535653108 & -0.0285353565310769 \tabularnewline
20 & 2.54 & 2.52331025053701 & 0.0166897494629867 \tabularnewline
21 & 2.54 & 2.53242381865743 & 0.00757618134257276 \tabularnewline
22 & 2.54 & 2.54092052818057 & -0.000920528180572422 \tabularnewline
23 & 2.54 & 2.5413521876156 & -0.00135218761560152 \tabularnewline
24 & 2.54 & 2.54135627497038 & -0.00135627497037838 \tabularnewline
25 & 2.54 & 2.54133795132627 & -0.00133795132626569 \tabularnewline
26 & 2.66 & 2.54131870639245 & 0.118681293607547 \tabularnewline
27 & 2.66 & 2.65666574956426 & 0.00333425043574342 \tabularnewline
28 & 2.66 & 2.66274211420981 & -0.00274211420980919 \tabularnewline
29 & 2.66 & 2.66302233144508 & -0.00302233144507991 \tabularnewline
30 & 2.66 & 2.6629956735561 & -0.00299567355610142 \tabularnewline
31 & 2.66 & 2.69003666872951 & -0.0300366687295139 \tabularnewline
32 & 2.66 & 2.64478994094132 & 0.0152100590586781 \tabularnewline
33 & 2.66 & 2.653882154421 & 0.0061178455790003 \tabularnewline
34 & 2.66 & 2.66235781514301 & -0.00235781514300548 \tabularnewline
35 & 2.66 & 2.66276872945899 & -0.00276872945898887 \tabularnewline
36 & 2.66 & 2.66275237111334 & -0.00275237111333571 \tabularnewline
37 & 2.66 & 2.66271389687209 & -0.00271389687209034 \tabularnewline
38 & 2.66 & 2.6626747921854 & -0.00267479218539712 \tabularnewline
39 & 2.66 & 2.66263618901309 & -0.00263618901309393 \tabularnewline
40 & 2.66 & 2.66259813968383 & -0.00259813968383149 \tabularnewline
41 & 2.66 & 2.66256063936372 & -0.00256063936371875 \tabularnewline
42 & 2.66 & 2.66252368029625 & -0.00252368029625316 \tabularnewline
43 & 2.66 & 2.68957058801147 & -0.0295705880114734 \tabularnewline
44 & 2.66 & 2.64433053966987 & 0.0156694603301335 \tabularnewline
45 & 2.66 & 2.6534293813993 & 0.00657061860069685 \tabularnewline
46 & 2.66 & 2.66191157710045 & -0.00191157710045298 \tabularnewline
47 & 2.66 & 2.66232893219999 & -0.00232893219999086 \tabularnewline
48 & 2.66 & 2.66231892168139 & -0.00231892168139236 \tabularnewline
49 & 2.66 & 2.662286703646 & -0.00228670364599992 \tabularnewline
50 & 2.93 & 2.66225376486604 & 0.267746235133963 \tabularnewline
51 & 2.93 & 2.92179490338923 & 0.0082050966107694 \tabularnewline
52 & 2.93 & 2.93547687085862 & -0.00547687085861925 \tabularnewline
53 & 2.93 & 2.93611736041888 & -0.00611736041887578 \tabularnewline
54 & 2.93 & 2.93606723661473 & -0.00606723661472897 \tabularnewline
55 & 2.93 & 2.9630650232716 & -0.0330650232715963 \tabularnewline
56 & 2.93 & 2.91777464531378 & 0.0122253546862154 \tabularnewline
57 & 2.93 & 2.92682378213596 & 0.00317621786404043 \tabularnewline
58 & 2.93 & 2.9352569849507 & -0.00525698495069671 \tabularnewline
59 & 2.93 & 2.93562605401789 & -0.00562605401789407 \tabularnewline
60 & 2.93 & 2.93556845438972 & -0.00556845438971854 \tabularnewline
61 & 2.93 & 2.93548933412284 & -0.00548933412283814 \tabularnewline
62 & 2.93 & 2.93541017007616 & -0.00541017007616373 \tabularnewline
63 & 3.07 & 2.9353320857419 & 0.134667914258103 \tabularnewline
64 & 3.07 & 3.06984887721377 & 0.000151122786228974 \tabularnewline
65 & 3.07 & 3.07688400448543 & -0.00688400448543236 \tabularnewline
66 & 3.07 & 3.07715773887841 & -0.00715773887840854 \tabularnewline
67 & 3.07 & 3.10415755329456 & -0.0341575532945573 \tabularnewline
68 & 3.07 & 3.05885234883224 & 0.0111476511677564 \tabularnewline
69 & 3.07 & 3.06788598058963 & 0.00211401941036948 \tabularnewline
70 & 3.07 & 3.07630385478252 & -0.00630385478252338 \tabularnewline
71 & 3.07 & 3.07665781396212 & -0.0066578139621245 \tabularnewline
72 & 3.07 & 3.07658532240213 & -0.00658532240213106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210624&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]2.54[/C][C]2.52706730769231[/C][C]0.0129326923076927[/C][/ROW]
[ROW][C]14[/C][C]2.54[/C][C]2.54079138296584[/C][C]-0.000791382965836807[/C][/ROW]
[ROW][C]15[/C][C]2.54[/C][C]2.5414981145768[/C][C]-0.00149811457680427[/C][/ROW]
[ROW][C]16[/C][C]2.54[/C][C]2.54151458927014[/C][C]-0.00151458927013604[/C][/ROW]
[ROW][C]17[/C][C]2.54[/C][C]2.54149474947008[/C][C]-0.00149474947008255[/C][/ROW]
[ROW][C]18[/C][C]2.54[/C][C]2.54147328217406[/C][C]-0.00147328217406217[/C][/ROW]
[ROW][C]19[/C][C]2.54[/C][C]2.56853535653108[/C][C]-0.0285353565310769[/C][/ROW]
[ROW][C]20[/C][C]2.54[/C][C]2.52331025053701[/C][C]0.0166897494629867[/C][/ROW]
[ROW][C]21[/C][C]2.54[/C][C]2.53242381865743[/C][C]0.00757618134257276[/C][/ROW]
[ROW][C]22[/C][C]2.54[/C][C]2.54092052818057[/C][C]-0.000920528180572422[/C][/ROW]
[ROW][C]23[/C][C]2.54[/C][C]2.5413521876156[/C][C]-0.00135218761560152[/C][/ROW]
[ROW][C]24[/C][C]2.54[/C][C]2.54135627497038[/C][C]-0.00135627497037838[/C][/ROW]
[ROW][C]25[/C][C]2.54[/C][C]2.54133795132627[/C][C]-0.00133795132626569[/C][/ROW]
[ROW][C]26[/C][C]2.66[/C][C]2.54131870639245[/C][C]0.118681293607547[/C][/ROW]
[ROW][C]27[/C][C]2.66[/C][C]2.65666574956426[/C][C]0.00333425043574342[/C][/ROW]
[ROW][C]28[/C][C]2.66[/C][C]2.66274211420981[/C][C]-0.00274211420980919[/C][/ROW]
[ROW][C]29[/C][C]2.66[/C][C]2.66302233144508[/C][C]-0.00302233144507991[/C][/ROW]
[ROW][C]30[/C][C]2.66[/C][C]2.6629956735561[/C][C]-0.00299567355610142[/C][/ROW]
[ROW][C]31[/C][C]2.66[/C][C]2.69003666872951[/C][C]-0.0300366687295139[/C][/ROW]
[ROW][C]32[/C][C]2.66[/C][C]2.64478994094132[/C][C]0.0152100590586781[/C][/ROW]
[ROW][C]33[/C][C]2.66[/C][C]2.653882154421[/C][C]0.0061178455790003[/C][/ROW]
[ROW][C]34[/C][C]2.66[/C][C]2.66235781514301[/C][C]-0.00235781514300548[/C][/ROW]
[ROW][C]35[/C][C]2.66[/C][C]2.66276872945899[/C][C]-0.00276872945898887[/C][/ROW]
[ROW][C]36[/C][C]2.66[/C][C]2.66275237111334[/C][C]-0.00275237111333571[/C][/ROW]
[ROW][C]37[/C][C]2.66[/C][C]2.66271389687209[/C][C]-0.00271389687209034[/C][/ROW]
[ROW][C]38[/C][C]2.66[/C][C]2.6626747921854[/C][C]-0.00267479218539712[/C][/ROW]
[ROW][C]39[/C][C]2.66[/C][C]2.66263618901309[/C][C]-0.00263618901309393[/C][/ROW]
[ROW][C]40[/C][C]2.66[/C][C]2.66259813968383[/C][C]-0.00259813968383149[/C][/ROW]
[ROW][C]41[/C][C]2.66[/C][C]2.66256063936372[/C][C]-0.00256063936371875[/C][/ROW]
[ROW][C]42[/C][C]2.66[/C][C]2.66252368029625[/C][C]-0.00252368029625316[/C][/ROW]
[ROW][C]43[/C][C]2.66[/C][C]2.68957058801147[/C][C]-0.0295705880114734[/C][/ROW]
[ROW][C]44[/C][C]2.66[/C][C]2.64433053966987[/C][C]0.0156694603301335[/C][/ROW]
[ROW][C]45[/C][C]2.66[/C][C]2.6534293813993[/C][C]0.00657061860069685[/C][/ROW]
[ROW][C]46[/C][C]2.66[/C][C]2.66191157710045[/C][C]-0.00191157710045298[/C][/ROW]
[ROW][C]47[/C][C]2.66[/C][C]2.66232893219999[/C][C]-0.00232893219999086[/C][/ROW]
[ROW][C]48[/C][C]2.66[/C][C]2.66231892168139[/C][C]-0.00231892168139236[/C][/ROW]
[ROW][C]49[/C][C]2.66[/C][C]2.662286703646[/C][C]-0.00228670364599992[/C][/ROW]
[ROW][C]50[/C][C]2.93[/C][C]2.66225376486604[/C][C]0.267746235133963[/C][/ROW]
[ROW][C]51[/C][C]2.93[/C][C]2.92179490338923[/C][C]0.0082050966107694[/C][/ROW]
[ROW][C]52[/C][C]2.93[/C][C]2.93547687085862[/C][C]-0.00547687085861925[/C][/ROW]
[ROW][C]53[/C][C]2.93[/C][C]2.93611736041888[/C][C]-0.00611736041887578[/C][/ROW]
[ROW][C]54[/C][C]2.93[/C][C]2.93606723661473[/C][C]-0.00606723661472897[/C][/ROW]
[ROW][C]55[/C][C]2.93[/C][C]2.9630650232716[/C][C]-0.0330650232715963[/C][/ROW]
[ROW][C]56[/C][C]2.93[/C][C]2.91777464531378[/C][C]0.0122253546862154[/C][/ROW]
[ROW][C]57[/C][C]2.93[/C][C]2.92682378213596[/C][C]0.00317621786404043[/C][/ROW]
[ROW][C]58[/C][C]2.93[/C][C]2.9352569849507[/C][C]-0.00525698495069671[/C][/ROW]
[ROW][C]59[/C][C]2.93[/C][C]2.93562605401789[/C][C]-0.00562605401789407[/C][/ROW]
[ROW][C]60[/C][C]2.93[/C][C]2.93556845438972[/C][C]-0.00556845438971854[/C][/ROW]
[ROW][C]61[/C][C]2.93[/C][C]2.93548933412284[/C][C]-0.00548933412283814[/C][/ROW]
[ROW][C]62[/C][C]2.93[/C][C]2.93541017007616[/C][C]-0.00541017007616373[/C][/ROW]
[ROW][C]63[/C][C]3.07[/C][C]2.9353320857419[/C][C]0.134667914258103[/C][/ROW]
[ROW][C]64[/C][C]3.07[/C][C]3.06984887721377[/C][C]0.000151122786228974[/C][/ROW]
[ROW][C]65[/C][C]3.07[/C][C]3.07688400448543[/C][C]-0.00688400448543236[/C][/ROW]
[ROW][C]66[/C][C]3.07[/C][C]3.07715773887841[/C][C]-0.00715773887840854[/C][/ROW]
[ROW][C]67[/C][C]3.07[/C][C]3.10415755329456[/C][C]-0.0341575532945573[/C][/ROW]
[ROW][C]68[/C][C]3.07[/C][C]3.05885234883224[/C][C]0.0111476511677564[/C][/ROW]
[ROW][C]69[/C][C]3.07[/C][C]3.06788598058963[/C][C]0.00211401941036948[/C][/ROW]
[ROW][C]70[/C][C]3.07[/C][C]3.07630385478252[/C][C]-0.00630385478252338[/C][/ROW]
[ROW][C]71[/C][C]3.07[/C][C]3.07665781396212[/C][C]-0.0066578139621245[/C][/ROW]
[ROW][C]72[/C][C]3.07[/C][C]3.07658532240213[/C][C]-0.00658532240213106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210624&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
132.542.527067307692310.0129326923076927
142.542.54079138296584-0.000791382965836807
152.542.5414981145768-0.00149811457680427
162.542.54151458927014-0.00151458927013604
172.542.54149474947008-0.00149474947008255
182.542.54147328217406-0.00147328217406217
192.542.56853535653108-0.0285353565310769
202.542.523310250537010.0166897494629867
212.542.532423818657430.00757618134257276
222.542.54092052818057-0.000920528180572422
232.542.5413521876156-0.00135218761560152
242.542.54135627497038-0.00135627497037838
252.542.54133795132627-0.00133795132626569
262.662.541318706392450.118681293607547
272.662.656665749564260.00333425043574342
282.662.66274211420981-0.00274211420980919
292.662.66302233144508-0.00302233144507991
302.662.6629956735561-0.00299567355610142
312.662.69003666872951-0.0300366687295139
322.662.644789940941320.0152100590586781
332.662.6538821544210.0061178455790003
342.662.66235781514301-0.00235781514300548
352.662.66276872945899-0.00276872945898887
362.662.66275237111334-0.00275237111333571
372.662.66271389687209-0.00271389687209034
382.662.6626747921854-0.00267479218539712
392.662.66263618901309-0.00263618901309393
402.662.66259813968383-0.00259813968383149
412.662.66256063936372-0.00256063936371875
422.662.66252368029625-0.00252368029625316
432.662.68957058801147-0.0295705880114734
442.662.644330539669870.0156694603301335
452.662.65342938139930.00657061860069685
462.662.66191157710045-0.00191157710045298
472.662.66232893219999-0.00232893219999086
482.662.66231892168139-0.00231892168139236
492.662.662286703646-0.00228670364599992
502.932.662253764866040.267746235133963
512.932.921794903389230.0082050966107694
522.932.93547687085862-0.00547687085861925
532.932.93611736041888-0.00611736041887578
542.932.93606723661473-0.00606723661472897
552.932.9630650232716-0.0330650232715963
562.932.917774645313780.0122253546862154
572.932.926823782135960.00317621786404043
582.932.9352569849507-0.00525698495069671
592.932.93562605401789-0.00562605401789407
602.932.93556845438972-0.00556845438971854
612.932.93548933412284-0.00548933412283814
622.932.93541017007616-0.00541017007616373
633.072.93533208574190.134667914258103
643.073.069848877213770.000151122786228974
653.073.07688400448543-0.00688400448543236
663.073.07715773887841-0.00715773887840854
673.073.10415755329456-0.0341575532945573
683.073.058852348832240.0111476511677564
693.073.067885980589630.00211401941036948
703.073.07630385478252-0.00630385478252338
713.073.07665781396212-0.0066578139621245
723.073.07658532240213-0.00658532240213106







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733.076491525139532.992369648650033.16061340162902
743.082638743976542.9659468402833.19933064767009
753.088785962813562.94615075201873.23142117360842
763.094933181650582.929819454383073.26004690891809
773.10108040048762.915681201395223.28647959957997
783.107227619324612.903074716945773.31138052170345
793.140458171494962.918688425081153.36222791790878
803.127438723665312.888931395551973.36594605177866
813.125669275835672.871124924330663.38021362734067
823.131816494672682.861805923957573.40182706538779
833.13796371350972.852960145595893.42296728142351
843.144110932346722.844512122142733.4437097425507

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3.07649152513953 & 2.99236964865003 & 3.16061340162902 \tabularnewline
74 & 3.08263874397654 & 2.965946840283 & 3.19933064767009 \tabularnewline
75 & 3.08878596281356 & 2.9461507520187 & 3.23142117360842 \tabularnewline
76 & 3.09493318165058 & 2.92981945438307 & 3.26004690891809 \tabularnewline
77 & 3.1010804004876 & 2.91568120139522 & 3.28647959957997 \tabularnewline
78 & 3.10722761932461 & 2.90307471694577 & 3.31138052170345 \tabularnewline
79 & 3.14045817149496 & 2.91868842508115 & 3.36222791790878 \tabularnewline
80 & 3.12743872366531 & 2.88893139555197 & 3.36594605177866 \tabularnewline
81 & 3.12566927583567 & 2.87112492433066 & 3.38021362734067 \tabularnewline
82 & 3.13181649467268 & 2.86180592395757 & 3.40182706538779 \tabularnewline
83 & 3.1379637135097 & 2.85296014559589 & 3.42296728142351 \tabularnewline
84 & 3.14411093234672 & 2.84451212214273 & 3.4437097425507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210624&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]3.07649152513953[/C][C]2.99236964865003[/C][C]3.16061340162902[/C][/ROW]
[ROW][C]74[/C][C]3.08263874397654[/C][C]2.965946840283[/C][C]3.19933064767009[/C][/ROW]
[ROW][C]75[/C][C]3.08878596281356[/C][C]2.9461507520187[/C][C]3.23142117360842[/C][/ROW]
[ROW][C]76[/C][C]3.09493318165058[/C][C]2.92981945438307[/C][C]3.26004690891809[/C][/ROW]
[ROW][C]77[/C][C]3.1010804004876[/C][C]2.91568120139522[/C][C]3.28647959957997[/C][/ROW]
[ROW][C]78[/C][C]3.10722761932461[/C][C]2.90307471694577[/C][C]3.31138052170345[/C][/ROW]
[ROW][C]79[/C][C]3.14045817149496[/C][C]2.91868842508115[/C][C]3.36222791790878[/C][/ROW]
[ROW][C]80[/C][C]3.12743872366531[/C][C]2.88893139555197[/C][C]3.36594605177866[/C][/ROW]
[ROW][C]81[/C][C]3.12566927583567[/C][C]2.87112492433066[/C][C]3.38021362734067[/C][/ROW]
[ROW][C]82[/C][C]3.13181649467268[/C][C]2.86180592395757[/C][C]3.40182706538779[/C][/ROW]
[ROW][C]83[/C][C]3.1379637135097[/C][C]2.85296014559589[/C][C]3.42296728142351[/C][/ROW]
[ROW][C]84[/C][C]3.14411093234672[/C][C]2.84451212214273[/C][C]3.4437097425507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210624&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210624&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
733.076491525139532.992369648650033.16061340162902
743.082638743976542.9659468402833.19933064767009
753.088785962813562.94615075201873.23142117360842
763.094933181650582.929819454383073.26004690891809
773.10108040048762.915681201395223.28647959957997
783.107227619324612.903074716945773.31138052170345
793.140458171494962.918688425081153.36222791790878
803.127438723665312.888931395551973.36594605177866
813.125669275835672.871124924330663.38021362734067
823.131816494672682.861805923957573.40182706538779
833.13796371350972.852960145595893.42296728142351
843.144110932346722.844512122142733.4437097425507



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):
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')