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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 12:57:14 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t12119146949n46bgk44o210o5.htm/, Retrieved Mon, 20 May 2024 00:01:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13381, Retrieved Mon, 20 May 2024 00:01:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-27 18:57:14] [cd7facba9466f9e80bdffad33137a939] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,08
1,08
1,09
1,1
1,1
1,11
1,1
1,1
1,11
1,11
1,11
1,11
1,11
1,12
1,11
1,11
1,12
1,12
1,11
1,12
1,11
1,11
1,1
1,1
1,1
1,11
1,1
1,1
1,09
1,1
1,1
1,11
1,13
1,13
1,13
1,13
1,14
1,14
1,14
1,15
1,15
1,15
1,15
1,15
1,15
1,14
1,14
1,14
1,13
1,12
1,13
1,13
1,13
1,12
1,13
1,12
1,12
1,11
1,11
1,11
1,11
1,14
1,15
1,15
1,16
1,15
1,16
1,13
1,13
1,12
1,12
1,11
1,11

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13381&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13381&T=0

As an alternative you can also use a QR Code:  
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'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.725335875539957
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.725335875539957 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13381&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]0.725335875539957[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13381&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.725335875539957
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.111.107161848505110.00283815149489031
141.121.117955895546550.00204410445344738
151.111.108613148882050.00138685111795045
161.111.109619081751930.000380918248068518
171.121.12031371194296-0.000313711942956596
181.121.12092549562627-0.000925495626272976
191.111.11108451567403-0.00108451567403356
201.121.12114131201974-0.00114131201973899
211.111.11114455815405-0.00114455815404702
221.111.11114887817193-0.00114887817192821
231.11.10196918656044-0.00196918656044298
241.11.10261579111840-0.00261579111840238
251.11.10525415369942-0.00525415369941795
261.111.109894068097000.00010593190299657
271.11.099063182378040.000936817621960628
281.11.099468923512970.000531076487026549
291.091.10998817743964-0.0199881774396358
301.11.096146490889510.00385350911049098
311.11.089901241460480.0100987585395207
321.111.107929233293560.00207076670644013
331.131.100347720910480.0296522790895171
341.131.122697566390100.00730243360990435
351.131.119282935745690.0107170642543128
361.131.128999133231220.00100086676878486
371.141.133633980442340.00636601955766403
381.141.14851971336284-0.00851971336284119
391.141.131349239097170.00865076090282546
401.151.137225509142560.0127744908574350
411.151.15110383290820-0.0011038329081976
421.151.157903858618-0.00790385861799914
431.151.144479108432760.00552089156723912
441.151.15735536166582-0.00735536166582418
451.151.15029325727767-0.000293257277665715
461.141.14468011981976-0.00468011981976502
471.141.133413849982830.00658615001717289
481.141.137459616071600.00254038392840372
491.131.14472190290522-0.0147219029052230
501.121.14017835130926-0.0201783513092593
511.131.119334199963960.0106658000360418
521.131.127768328555100.00223167144489578
531.131.13017313118788-0.000173131187879427
541.121.13567042413462-0.0156704241346211
551.131.120383911034860.00961608896514443
561.121.13257970368752-0.0125797036875179
571.121.12366297890352-0.00366297890352074
581.111.11456355510224-0.00456355510224449
591.111.106589335319130.00341066468087248
601.111.107269487772430.00273051222757403
611.111.109873005770920.000126994229077804
621.141.114448212130150.0255517878698479
631.151.135251450235110.0147485497648880
641.151.144306653299220.00569334670078137
651.161.14856386364610.0114361363539004
661.151.15821315319504-0.00821315319504445
671.161.155351275372100.00464872462790256
681.131.15779664287646-0.0277966428764622
691.131.14033104205929-0.0103310420592868
701.121.12606722013088-0.00606722013088334
711.121.119164457464910.000835542535094325
721.111.1177711839068-0.00777118390680109
731.111.11204217192436-0.00204217192435752

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.11 & 1.10716184850511 & 0.00283815149489031 \tabularnewline
14 & 1.12 & 1.11795589554655 & 0.00204410445344738 \tabularnewline
15 & 1.11 & 1.10861314888205 & 0.00138685111795045 \tabularnewline
16 & 1.11 & 1.10961908175193 & 0.000380918248068518 \tabularnewline
17 & 1.12 & 1.12031371194296 & -0.000313711942956596 \tabularnewline
18 & 1.12 & 1.12092549562627 & -0.000925495626272976 \tabularnewline
19 & 1.11 & 1.11108451567403 & -0.00108451567403356 \tabularnewline
20 & 1.12 & 1.12114131201974 & -0.00114131201973899 \tabularnewline
21 & 1.11 & 1.11114455815405 & -0.00114455815404702 \tabularnewline
22 & 1.11 & 1.11114887817193 & -0.00114887817192821 \tabularnewline
23 & 1.1 & 1.10196918656044 & -0.00196918656044298 \tabularnewline
24 & 1.1 & 1.10261579111840 & -0.00261579111840238 \tabularnewline
25 & 1.1 & 1.10525415369942 & -0.00525415369941795 \tabularnewline
26 & 1.11 & 1.10989406809700 & 0.00010593190299657 \tabularnewline
27 & 1.1 & 1.09906318237804 & 0.000936817621960628 \tabularnewline
28 & 1.1 & 1.09946892351297 & 0.000531076487026549 \tabularnewline
29 & 1.09 & 1.10998817743964 & -0.0199881774396358 \tabularnewline
30 & 1.1 & 1.09614649088951 & 0.00385350911049098 \tabularnewline
31 & 1.1 & 1.08990124146048 & 0.0100987585395207 \tabularnewline
32 & 1.11 & 1.10792923329356 & 0.00207076670644013 \tabularnewline
33 & 1.13 & 1.10034772091048 & 0.0296522790895171 \tabularnewline
34 & 1.13 & 1.12269756639010 & 0.00730243360990435 \tabularnewline
35 & 1.13 & 1.11928293574569 & 0.0107170642543128 \tabularnewline
36 & 1.13 & 1.12899913323122 & 0.00100086676878486 \tabularnewline
37 & 1.14 & 1.13363398044234 & 0.00636601955766403 \tabularnewline
38 & 1.14 & 1.14851971336284 & -0.00851971336284119 \tabularnewline
39 & 1.14 & 1.13134923909717 & 0.00865076090282546 \tabularnewline
40 & 1.15 & 1.13722550914256 & 0.0127744908574350 \tabularnewline
41 & 1.15 & 1.15110383290820 & -0.0011038329081976 \tabularnewline
42 & 1.15 & 1.157903858618 & -0.00790385861799914 \tabularnewline
43 & 1.15 & 1.14447910843276 & 0.00552089156723912 \tabularnewline
44 & 1.15 & 1.15735536166582 & -0.00735536166582418 \tabularnewline
45 & 1.15 & 1.15029325727767 & -0.000293257277665715 \tabularnewline
46 & 1.14 & 1.14468011981976 & -0.00468011981976502 \tabularnewline
47 & 1.14 & 1.13341384998283 & 0.00658615001717289 \tabularnewline
48 & 1.14 & 1.13745961607160 & 0.00254038392840372 \tabularnewline
49 & 1.13 & 1.14472190290522 & -0.0147219029052230 \tabularnewline
50 & 1.12 & 1.14017835130926 & -0.0201783513092593 \tabularnewline
51 & 1.13 & 1.11933419996396 & 0.0106658000360418 \tabularnewline
52 & 1.13 & 1.12776832855510 & 0.00223167144489578 \tabularnewline
53 & 1.13 & 1.13017313118788 & -0.000173131187879427 \tabularnewline
54 & 1.12 & 1.13567042413462 & -0.0156704241346211 \tabularnewline
55 & 1.13 & 1.12038391103486 & 0.00961608896514443 \tabularnewline
56 & 1.12 & 1.13257970368752 & -0.0125797036875179 \tabularnewline
57 & 1.12 & 1.12366297890352 & -0.00366297890352074 \tabularnewline
58 & 1.11 & 1.11456355510224 & -0.00456355510224449 \tabularnewline
59 & 1.11 & 1.10658933531913 & 0.00341066468087248 \tabularnewline
60 & 1.11 & 1.10726948777243 & 0.00273051222757403 \tabularnewline
61 & 1.11 & 1.10987300577092 & 0.000126994229077804 \tabularnewline
62 & 1.14 & 1.11444821213015 & 0.0255517878698479 \tabularnewline
63 & 1.15 & 1.13525145023511 & 0.0147485497648880 \tabularnewline
64 & 1.15 & 1.14430665329922 & 0.00569334670078137 \tabularnewline
65 & 1.16 & 1.1485638636461 & 0.0114361363539004 \tabularnewline
66 & 1.15 & 1.15821315319504 & -0.00821315319504445 \tabularnewline
67 & 1.16 & 1.15535127537210 & 0.00464872462790256 \tabularnewline
68 & 1.13 & 1.15779664287646 & -0.0277966428764622 \tabularnewline
69 & 1.13 & 1.14033104205929 & -0.0103310420592868 \tabularnewline
70 & 1.12 & 1.12606722013088 & -0.00606722013088334 \tabularnewline
71 & 1.12 & 1.11916445746491 & 0.000835542535094325 \tabularnewline
72 & 1.11 & 1.1177711839068 & -0.00777118390680109 \tabularnewline
73 & 1.11 & 1.11204217192436 & -0.00204217192435752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13381&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]1.11[/C][C]1.10716184850511[/C][C]0.00283815149489031[/C][/ROW]
[ROW][C]14[/C][C]1.12[/C][C]1.11795589554655[/C][C]0.00204410445344738[/C][/ROW]
[ROW][C]15[/C][C]1.11[/C][C]1.10861314888205[/C][C]0.00138685111795045[/C][/ROW]
[ROW][C]16[/C][C]1.11[/C][C]1.10961908175193[/C][C]0.000380918248068518[/C][/ROW]
[ROW][C]17[/C][C]1.12[/C][C]1.12031371194296[/C][C]-0.000313711942956596[/C][/ROW]
[ROW][C]18[/C][C]1.12[/C][C]1.12092549562627[/C][C]-0.000925495626272976[/C][/ROW]
[ROW][C]19[/C][C]1.11[/C][C]1.11108451567403[/C][C]-0.00108451567403356[/C][/ROW]
[ROW][C]20[/C][C]1.12[/C][C]1.12114131201974[/C][C]-0.00114131201973899[/C][/ROW]
[ROW][C]21[/C][C]1.11[/C][C]1.11114455815405[/C][C]-0.00114455815404702[/C][/ROW]
[ROW][C]22[/C][C]1.11[/C][C]1.11114887817193[/C][C]-0.00114887817192821[/C][/ROW]
[ROW][C]23[/C][C]1.1[/C][C]1.10196918656044[/C][C]-0.00196918656044298[/C][/ROW]
[ROW][C]24[/C][C]1.1[/C][C]1.10261579111840[/C][C]-0.00261579111840238[/C][/ROW]
[ROW][C]25[/C][C]1.1[/C][C]1.10525415369942[/C][C]-0.00525415369941795[/C][/ROW]
[ROW][C]26[/C][C]1.11[/C][C]1.10989406809700[/C][C]0.00010593190299657[/C][/ROW]
[ROW][C]27[/C][C]1.1[/C][C]1.09906318237804[/C][C]0.000936817621960628[/C][/ROW]
[ROW][C]28[/C][C]1.1[/C][C]1.09946892351297[/C][C]0.000531076487026549[/C][/ROW]
[ROW][C]29[/C][C]1.09[/C][C]1.10998817743964[/C][C]-0.0199881774396358[/C][/ROW]
[ROW][C]30[/C][C]1.1[/C][C]1.09614649088951[/C][C]0.00385350911049098[/C][/ROW]
[ROW][C]31[/C][C]1.1[/C][C]1.08990124146048[/C][C]0.0100987585395207[/C][/ROW]
[ROW][C]32[/C][C]1.11[/C][C]1.10792923329356[/C][C]0.00207076670644013[/C][/ROW]
[ROW][C]33[/C][C]1.13[/C][C]1.10034772091048[/C][C]0.0296522790895171[/C][/ROW]
[ROW][C]34[/C][C]1.13[/C][C]1.12269756639010[/C][C]0.00730243360990435[/C][/ROW]
[ROW][C]35[/C][C]1.13[/C][C]1.11928293574569[/C][C]0.0107170642543128[/C][/ROW]
[ROW][C]36[/C][C]1.13[/C][C]1.12899913323122[/C][C]0.00100086676878486[/C][/ROW]
[ROW][C]37[/C][C]1.14[/C][C]1.13363398044234[/C][C]0.00636601955766403[/C][/ROW]
[ROW][C]38[/C][C]1.14[/C][C]1.14851971336284[/C][C]-0.00851971336284119[/C][/ROW]
[ROW][C]39[/C][C]1.14[/C][C]1.13134923909717[/C][C]0.00865076090282546[/C][/ROW]
[ROW][C]40[/C][C]1.15[/C][C]1.13722550914256[/C][C]0.0127744908574350[/C][/ROW]
[ROW][C]41[/C][C]1.15[/C][C]1.15110383290820[/C][C]-0.0011038329081976[/C][/ROW]
[ROW][C]42[/C][C]1.15[/C][C]1.157903858618[/C][C]-0.00790385861799914[/C][/ROW]
[ROW][C]43[/C][C]1.15[/C][C]1.14447910843276[/C][C]0.00552089156723912[/C][/ROW]
[ROW][C]44[/C][C]1.15[/C][C]1.15735536166582[/C][C]-0.00735536166582418[/C][/ROW]
[ROW][C]45[/C][C]1.15[/C][C]1.15029325727767[/C][C]-0.000293257277665715[/C][/ROW]
[ROW][C]46[/C][C]1.14[/C][C]1.14468011981976[/C][C]-0.00468011981976502[/C][/ROW]
[ROW][C]47[/C][C]1.14[/C][C]1.13341384998283[/C][C]0.00658615001717289[/C][/ROW]
[ROW][C]48[/C][C]1.14[/C][C]1.13745961607160[/C][C]0.00254038392840372[/C][/ROW]
[ROW][C]49[/C][C]1.13[/C][C]1.14472190290522[/C][C]-0.0147219029052230[/C][/ROW]
[ROW][C]50[/C][C]1.12[/C][C]1.14017835130926[/C][C]-0.0201783513092593[/C][/ROW]
[ROW][C]51[/C][C]1.13[/C][C]1.11933419996396[/C][C]0.0106658000360418[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.12776832855510[/C][C]0.00223167144489578[/C][/ROW]
[ROW][C]53[/C][C]1.13[/C][C]1.13017313118788[/C][C]-0.000173131187879427[/C][/ROW]
[ROW][C]54[/C][C]1.12[/C][C]1.13567042413462[/C][C]-0.0156704241346211[/C][/ROW]
[ROW][C]55[/C][C]1.13[/C][C]1.12038391103486[/C][C]0.00961608896514443[/C][/ROW]
[ROW][C]56[/C][C]1.12[/C][C]1.13257970368752[/C][C]-0.0125797036875179[/C][/ROW]
[ROW][C]57[/C][C]1.12[/C][C]1.12366297890352[/C][C]-0.00366297890352074[/C][/ROW]
[ROW][C]58[/C][C]1.11[/C][C]1.11456355510224[/C][C]-0.00456355510224449[/C][/ROW]
[ROW][C]59[/C][C]1.11[/C][C]1.10658933531913[/C][C]0.00341066468087248[/C][/ROW]
[ROW][C]60[/C][C]1.11[/C][C]1.10726948777243[/C][C]0.00273051222757403[/C][/ROW]
[ROW][C]61[/C][C]1.11[/C][C]1.10987300577092[/C][C]0.000126994229077804[/C][/ROW]
[ROW][C]62[/C][C]1.14[/C][C]1.11444821213015[/C][C]0.0255517878698479[/C][/ROW]
[ROW][C]63[/C][C]1.15[/C][C]1.13525145023511[/C][C]0.0147485497648880[/C][/ROW]
[ROW][C]64[/C][C]1.15[/C][C]1.14430665329922[/C][C]0.00569334670078137[/C][/ROW]
[ROW][C]65[/C][C]1.16[/C][C]1.1485638636461[/C][C]0.0114361363539004[/C][/ROW]
[ROW][C]66[/C][C]1.15[/C][C]1.15821315319504[/C][C]-0.00821315319504445[/C][/ROW]
[ROW][C]67[/C][C]1.16[/C][C]1.15535127537210[/C][C]0.00464872462790256[/C][/ROW]
[ROW][C]68[/C][C]1.13[/C][C]1.15779664287646[/C][C]-0.0277966428764622[/C][/ROW]
[ROW][C]69[/C][C]1.13[/C][C]1.14033104205929[/C][C]-0.0103310420592868[/C][/ROW]
[ROW][C]70[/C][C]1.12[/C][C]1.12606722013088[/C][C]-0.00606722013088334[/C][/ROW]
[ROW][C]71[/C][C]1.12[/C][C]1.11916445746491[/C][C]0.000835542535094325[/C][/ROW]
[ROW][C]72[/C][C]1.11[/C][C]1.1177711839068[/C][C]-0.00777118390680109[/C][/ROW]
[ROW][C]73[/C][C]1.11[/C][C]1.11204217192436[/C][C]-0.00204217192435752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13381&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.111.107161848505110.00283815149489031
141.121.117955895546550.00204410445344738
151.111.108613148882050.00138685111795045
161.111.109619081751930.000380918248068518
171.121.12031371194296-0.000313711942956596
181.121.12092549562627-0.000925495626272976
191.111.11108451567403-0.00108451567403356
201.121.12114131201974-0.00114131201973899
211.111.11114455815405-0.00114455815404702
221.111.11114887817193-0.00114887817192821
231.11.10196918656044-0.00196918656044298
241.11.10261579111840-0.00261579111840238
251.11.10525415369942-0.00525415369941795
261.111.109894068097000.00010593190299657
271.11.099063182378040.000936817621960628
281.11.099468923512970.000531076487026549
291.091.10998817743964-0.0199881774396358
301.11.096146490889510.00385350911049098
311.11.089901241460480.0100987585395207
321.111.107929233293560.00207076670644013
331.131.100347720910480.0296522790895171
341.131.122697566390100.00730243360990435
351.131.119282935745690.0107170642543128
361.131.128999133231220.00100086676878486
371.141.133633980442340.00636601955766403
381.141.14851971336284-0.00851971336284119
391.141.131349239097170.00865076090282546
401.151.137225509142560.0127744908574350
411.151.15110383290820-0.0011038329081976
421.151.157903858618-0.00790385861799914
431.151.144479108432760.00552089156723912
441.151.15735536166582-0.00735536166582418
451.151.15029325727767-0.000293257277665715
461.141.14468011981976-0.00468011981976502
471.141.133413849982830.00658615001717289
481.141.137459616071600.00254038392840372
491.131.14472190290522-0.0147219029052230
501.121.14017835130926-0.0201783513092593
511.131.119334199963960.0106658000360418
521.131.127768328555100.00223167144489578
531.131.13017313118788-0.000173131187879427
541.121.13567042413462-0.0156704241346211
551.131.120383911034860.00961608896514443
561.121.13257970368752-0.0125797036875179
571.121.12366297890352-0.00366297890352074
581.111.11456355510224-0.00456355510224449
591.111.106589335319130.00341066468087248
601.111.107269487772430.00273051222757403
611.111.109873005770920.000126994229077804
621.141.114448212130150.0255517878698479
631.151.135251450235110.0147485497648880
641.151.144306653299220.00569334670078137
651.161.14856386364610.0114361363539004
661.151.15821315319504-0.00821315319504445
671.161.155351275372100.00464872462790256
681.131.15779664287646-0.0277966428764622
691.131.14033104205929-0.0103310420592868
701.121.12606722013088-0.00606722013088334
711.121.119164457464910.000835542535094325
721.111.1177711839068-0.00777118390680109
731.111.11204217192436-0.00204217192435752






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
741.121918214192471.102990596708711.14084583167623
751.121194411458081.097840958075671.1445478648405
761.117162780004271.090052527975421.14427303203312
771.118797176893711.088473853346891.14912050044054
781.114886818358271.081470528941561.14830310777497
791.121308951941511.085407440691271.15721046319175
801.111668202881191.073038480626531.15029792513584
811.119021647556911.078184791125591.15985850398823
821.113470343813421.070406321141991.15653436648485
831.112867704649361.067813752683511.15792165661520
841.108521459649691.061369513881951.15567340541742
851.11NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 1.12191821419247 & 1.10299059670871 & 1.14084583167623 \tabularnewline
75 & 1.12119441145808 & 1.09784095807567 & 1.1445478648405 \tabularnewline
76 & 1.11716278000427 & 1.09005252797542 & 1.14427303203312 \tabularnewline
77 & 1.11879717689371 & 1.08847385334689 & 1.14912050044054 \tabularnewline
78 & 1.11488681835827 & 1.08147052894156 & 1.14830310777497 \tabularnewline
79 & 1.12130895194151 & 1.08540744069127 & 1.15721046319175 \tabularnewline
80 & 1.11166820288119 & 1.07303848062653 & 1.15029792513584 \tabularnewline
81 & 1.11902164755691 & 1.07818479112559 & 1.15985850398823 \tabularnewline
82 & 1.11347034381342 & 1.07040632114199 & 1.15653436648485 \tabularnewline
83 & 1.11286770464936 & 1.06781375268351 & 1.15792165661520 \tabularnewline
84 & 1.10852145964969 & 1.06136951388195 & 1.15567340541742 \tabularnewline
85 & 1.11 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13381&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]74[/C][C]1.12191821419247[/C][C]1.10299059670871[/C][C]1.14084583167623[/C][/ROW]
[ROW][C]75[/C][C]1.12119441145808[/C][C]1.09784095807567[/C][C]1.1445478648405[/C][/ROW]
[ROW][C]76[/C][C]1.11716278000427[/C][C]1.09005252797542[/C][C]1.14427303203312[/C][/ROW]
[ROW][C]77[/C][C]1.11879717689371[/C][C]1.08847385334689[/C][C]1.14912050044054[/C][/ROW]
[ROW][C]78[/C][C]1.11488681835827[/C][C]1.08147052894156[/C][C]1.14830310777497[/C][/ROW]
[ROW][C]79[/C][C]1.12130895194151[/C][C]1.08540744069127[/C][C]1.15721046319175[/C][/ROW]
[ROW][C]80[/C][C]1.11166820288119[/C][C]1.07303848062653[/C][C]1.15029792513584[/C][/ROW]
[ROW][C]81[/C][C]1.11902164755691[/C][C]1.07818479112559[/C][C]1.15985850398823[/C][/ROW]
[ROW][C]82[/C][C]1.11347034381342[/C][C]1.07040632114199[/C][C]1.15653436648485[/C][/ROW]
[ROW][C]83[/C][C]1.11286770464936[/C][C]1.06781375268351[/C][C]1.15792165661520[/C][/ROW]
[ROW][C]84[/C][C]1.10852145964969[/C][C]1.06136951388195[/C][C]1.15567340541742[/C][/ROW]
[ROW][C]85[/C][C]1.11[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13381&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
741.121918214192471.102990596708711.14084583167623
751.121194411458081.097840958075671.1445478648405
761.117162780004271.090052527975421.14427303203312
771.118797176893711.088473853346891.14912050044054
781.114886818358271.081470528941561.14830310777497
791.121308951941511.085407440691271.15721046319175
801.111668202881191.073038480626531.15029792513584
811.119021647556911.078184791125591.15985850398823
821.113470343813421.070406321141991.15653436648485
831.112867704649361.067813752683511.15792165661520
841.108521459649691.061369513881951.15567340541742
851.11NANA


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')