FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 09:43:03 -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/28/t1211989437k9mxsvmiklz9umw.htm/, Retrieved Sun, 19 May 2024 23:28:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13449, Retrieved Sun, 19 May 2024 23:28:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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...] [2008-05-28 15:43:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13449&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13449&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.726841894609817
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.726841894609817 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13449&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]0.726841894609817[/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=13449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13449&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
alpha0.726841894609817
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.111.107151268115940.00284873188405754
141.121.117971845795790.00202815420421376
151.111.108612659906800.00138734009319519
161.111.109621036808610.000378963191389081
171.121.12031314979929-0.000313149799294088
181.121.12091887273921-0.000918872739211984
191.111.11108433086987-0.00108433086987114
201.121.12112952709936-0.00112952709936343
211.111.11114187281578-0.00114187281578260
221.111.11114524514829-0.00114524514828895
231.11.10197949966158-0.00197949966158073
241.11.10262404971051-0.00262404971051144
251.11.10524493465159-0.0052449346515866
261.111.109958548967974.14510320287942e-05
271.11.098980300412820.00101969958718162
281.11.099446014468680.000553985531318357
291.091.11007628475527-0.0200762847552671
301.11.096151875109700.00384812489030328
311.11.08973699059950.0102630094004992
321.111.108017563413470.00198243658652775
331.131.100288442378790.0297115576212050
341.131.122716459365380.00728354063462477
351.131.119449225124120.0105507748758837
361.131.129025239587640.000974760412356446
371.141.133545974531820.00645402546818485
381.141.14820690228432-0.00820690228431742
391.141.131500621499230.00849937850077342
401.151.137275665978560.0127243340214351
411.151.15111652987460-0.00111652987459743
421.151.15750801079919-0.00750801079919339
431.151.14459128880810.00540871119190034
441.151.15708164873372-0.00708164873372219
451.151.15033880491794-0.000338804917936919
461.141.14479856483514-0.00479856483514229
471.141.133642021678570.00635797832142959
481.141.137554769982700.00244523001730146
491.131.14464100950208-0.0146410095020753
501.121.13996443082180-0.0199644308217972
511.131.119275741725970.0107242582740326
521.131.127822002880360.00217799711963784
531.131.13021660312270-0.000216603122695336
541.121.13551630369265-0.0155163036926533
551.131.120307126229230.009692873770774
561.121.13249955194757-0.0124995519475688
571.121.12366061153668-0.0036606115366804
581.111.11448772366811-0.00448772366811201
591.111.106604613085660.00339538691433972
601.111.107295226924880.00270477307511996
611.111.109902868396789.71316032214453e-05
621.141.114484452438610.0255155475613873
631.151.135235381167960.0147646188320447
641.151.144383865140140.00561613485986179
651.161.148623343466140.0113766565338573
661.151.15817027362885-0.00817027362884626
671.161.155186589729210.00481341027078841
681.131.15777037598931-0.0277703759893106
691.131.14024638911596-0.0102463891159645
701.121.12606074981142-0.00606074981142313
711.121.119187633477980.000812366522019659
721.111.11781215311355-0.00781215311355288
731.111.11206335362500-0.00206335362500409

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.11 & 1.10715126811594 & 0.00284873188405754 \tabularnewline
14 & 1.12 & 1.11797184579579 & 0.00202815420421376 \tabularnewline
15 & 1.11 & 1.10861265990680 & 0.00138734009319519 \tabularnewline
16 & 1.11 & 1.10962103680861 & 0.000378963191389081 \tabularnewline
17 & 1.12 & 1.12031314979929 & -0.000313149799294088 \tabularnewline
18 & 1.12 & 1.12091887273921 & -0.000918872739211984 \tabularnewline
19 & 1.11 & 1.11108433086987 & -0.00108433086987114 \tabularnewline
20 & 1.12 & 1.12112952709936 & -0.00112952709936343 \tabularnewline
21 & 1.11 & 1.11114187281578 & -0.00114187281578260 \tabularnewline
22 & 1.11 & 1.11114524514829 & -0.00114524514828895 \tabularnewline
23 & 1.1 & 1.10197949966158 & -0.00197949966158073 \tabularnewline
24 & 1.1 & 1.10262404971051 & -0.00262404971051144 \tabularnewline
25 & 1.1 & 1.10524493465159 & -0.0052449346515866 \tabularnewline
26 & 1.11 & 1.10995854896797 & 4.14510320287942e-05 \tabularnewline
27 & 1.1 & 1.09898030041282 & 0.00101969958718162 \tabularnewline
28 & 1.1 & 1.09944601446868 & 0.000553985531318357 \tabularnewline
29 & 1.09 & 1.11007628475527 & -0.0200762847552671 \tabularnewline
30 & 1.1 & 1.09615187510970 & 0.00384812489030328 \tabularnewline
31 & 1.1 & 1.0897369905995 & 0.0102630094004992 \tabularnewline
32 & 1.11 & 1.10801756341347 & 0.00198243658652775 \tabularnewline
33 & 1.13 & 1.10028844237879 & 0.0297115576212050 \tabularnewline
34 & 1.13 & 1.12271645936538 & 0.00728354063462477 \tabularnewline
35 & 1.13 & 1.11944922512412 & 0.0105507748758837 \tabularnewline
36 & 1.13 & 1.12902523958764 & 0.000974760412356446 \tabularnewline
37 & 1.14 & 1.13354597453182 & 0.00645402546818485 \tabularnewline
38 & 1.14 & 1.14820690228432 & -0.00820690228431742 \tabularnewline
39 & 1.14 & 1.13150062149923 & 0.00849937850077342 \tabularnewline
40 & 1.15 & 1.13727566597856 & 0.0127243340214351 \tabularnewline
41 & 1.15 & 1.15111652987460 & -0.00111652987459743 \tabularnewline
42 & 1.15 & 1.15750801079919 & -0.00750801079919339 \tabularnewline
43 & 1.15 & 1.1445912888081 & 0.00540871119190034 \tabularnewline
44 & 1.15 & 1.15708164873372 & -0.00708164873372219 \tabularnewline
45 & 1.15 & 1.15033880491794 & -0.000338804917936919 \tabularnewline
46 & 1.14 & 1.14479856483514 & -0.00479856483514229 \tabularnewline
47 & 1.14 & 1.13364202167857 & 0.00635797832142959 \tabularnewline
48 & 1.14 & 1.13755476998270 & 0.00244523001730146 \tabularnewline
49 & 1.13 & 1.14464100950208 & -0.0146410095020753 \tabularnewline
50 & 1.12 & 1.13996443082180 & -0.0199644308217972 \tabularnewline
51 & 1.13 & 1.11927574172597 & 0.0107242582740326 \tabularnewline
52 & 1.13 & 1.12782200288036 & 0.00217799711963784 \tabularnewline
53 & 1.13 & 1.13021660312270 & -0.000216603122695336 \tabularnewline
54 & 1.12 & 1.13551630369265 & -0.0155163036926533 \tabularnewline
55 & 1.13 & 1.12030712622923 & 0.009692873770774 \tabularnewline
56 & 1.12 & 1.13249955194757 & -0.0124995519475688 \tabularnewline
57 & 1.12 & 1.12366061153668 & -0.0036606115366804 \tabularnewline
58 & 1.11 & 1.11448772366811 & -0.00448772366811201 \tabularnewline
59 & 1.11 & 1.10660461308566 & 0.00339538691433972 \tabularnewline
60 & 1.11 & 1.10729522692488 & 0.00270477307511996 \tabularnewline
61 & 1.11 & 1.10990286839678 & 9.71316032214453e-05 \tabularnewline
62 & 1.14 & 1.11448445243861 & 0.0255155475613873 \tabularnewline
63 & 1.15 & 1.13523538116796 & 0.0147646188320447 \tabularnewline
64 & 1.15 & 1.14438386514014 & 0.00561613485986179 \tabularnewline
65 & 1.16 & 1.14862334346614 & 0.0113766565338573 \tabularnewline
66 & 1.15 & 1.15817027362885 & -0.00817027362884626 \tabularnewline
67 & 1.16 & 1.15518658972921 & 0.00481341027078841 \tabularnewline
68 & 1.13 & 1.15777037598931 & -0.0277703759893106 \tabularnewline
69 & 1.13 & 1.14024638911596 & -0.0102463891159645 \tabularnewline
70 & 1.12 & 1.12606074981142 & -0.00606074981142313 \tabularnewline
71 & 1.12 & 1.11918763347798 & 0.000812366522019659 \tabularnewline
72 & 1.11 & 1.11781215311355 & -0.00781215311355288 \tabularnewline
73 & 1.11 & 1.11206335362500 & -0.00206335362500409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13449&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]1.10715126811594[/C][C]0.00284873188405754[/C][/ROW]
[ROW][C]14[/C][C]1.12[/C][C]1.11797184579579[/C][C]0.00202815420421376[/C][/ROW]
[ROW][C]15[/C][C]1.11[/C][C]1.10861265990680[/C][C]0.00138734009319519[/C][/ROW]
[ROW][C]16[/C][C]1.11[/C][C]1.10962103680861[/C][C]0.000378963191389081[/C][/ROW]
[ROW][C]17[/C][C]1.12[/C][C]1.12031314979929[/C][C]-0.000313149799294088[/C][/ROW]
[ROW][C]18[/C][C]1.12[/C][C]1.12091887273921[/C][C]-0.000918872739211984[/C][/ROW]
[ROW][C]19[/C][C]1.11[/C][C]1.11108433086987[/C][C]-0.00108433086987114[/C][/ROW]
[ROW][C]20[/C][C]1.12[/C][C]1.12112952709936[/C][C]-0.00112952709936343[/C][/ROW]
[ROW][C]21[/C][C]1.11[/C][C]1.11114187281578[/C][C]-0.00114187281578260[/C][/ROW]
[ROW][C]22[/C][C]1.11[/C][C]1.11114524514829[/C][C]-0.00114524514828895[/C][/ROW]
[ROW][C]23[/C][C]1.1[/C][C]1.10197949966158[/C][C]-0.00197949966158073[/C][/ROW]
[ROW][C]24[/C][C]1.1[/C][C]1.10262404971051[/C][C]-0.00262404971051144[/C][/ROW]
[ROW][C]25[/C][C]1.1[/C][C]1.10524493465159[/C][C]-0.0052449346515866[/C][/ROW]
[ROW][C]26[/C][C]1.11[/C][C]1.10995854896797[/C][C]4.14510320287942e-05[/C][/ROW]
[ROW][C]27[/C][C]1.1[/C][C]1.09898030041282[/C][C]0.00101969958718162[/C][/ROW]
[ROW][C]28[/C][C]1.1[/C][C]1.09944601446868[/C][C]0.000553985531318357[/C][/ROW]
[ROW][C]29[/C][C]1.09[/C][C]1.11007628475527[/C][C]-0.0200762847552671[/C][/ROW]
[ROW][C]30[/C][C]1.1[/C][C]1.09615187510970[/C][C]0.00384812489030328[/C][/ROW]
[ROW][C]31[/C][C]1.1[/C][C]1.0897369905995[/C][C]0.0102630094004992[/C][/ROW]
[ROW][C]32[/C][C]1.11[/C][C]1.10801756341347[/C][C]0.00198243658652775[/C][/ROW]
[ROW][C]33[/C][C]1.13[/C][C]1.10028844237879[/C][C]0.0297115576212050[/C][/ROW]
[ROW][C]34[/C][C]1.13[/C][C]1.12271645936538[/C][C]0.00728354063462477[/C][/ROW]
[ROW][C]35[/C][C]1.13[/C][C]1.11944922512412[/C][C]0.0105507748758837[/C][/ROW]
[ROW][C]36[/C][C]1.13[/C][C]1.12902523958764[/C][C]0.000974760412356446[/C][/ROW]
[ROW][C]37[/C][C]1.14[/C][C]1.13354597453182[/C][C]0.00645402546818485[/C][/ROW]
[ROW][C]38[/C][C]1.14[/C][C]1.14820690228432[/C][C]-0.00820690228431742[/C][/ROW]
[ROW][C]39[/C][C]1.14[/C][C]1.13150062149923[/C][C]0.00849937850077342[/C][/ROW]
[ROW][C]40[/C][C]1.15[/C][C]1.13727566597856[/C][C]0.0127243340214351[/C][/ROW]
[ROW][C]41[/C][C]1.15[/C][C]1.15111652987460[/C][C]-0.00111652987459743[/C][/ROW]
[ROW][C]42[/C][C]1.15[/C][C]1.15750801079919[/C][C]-0.00750801079919339[/C][/ROW]
[ROW][C]43[/C][C]1.15[/C][C]1.1445912888081[/C][C]0.00540871119190034[/C][/ROW]
[ROW][C]44[/C][C]1.15[/C][C]1.15708164873372[/C][C]-0.00708164873372219[/C][/ROW]
[ROW][C]45[/C][C]1.15[/C][C]1.15033880491794[/C][C]-0.000338804917936919[/C][/ROW]
[ROW][C]46[/C][C]1.14[/C][C]1.14479856483514[/C][C]-0.00479856483514229[/C][/ROW]
[ROW][C]47[/C][C]1.14[/C][C]1.13364202167857[/C][C]0.00635797832142959[/C][/ROW]
[ROW][C]48[/C][C]1.14[/C][C]1.13755476998270[/C][C]0.00244523001730146[/C][/ROW]
[ROW][C]49[/C][C]1.13[/C][C]1.14464100950208[/C][C]-0.0146410095020753[/C][/ROW]
[ROW][C]50[/C][C]1.12[/C][C]1.13996443082180[/C][C]-0.0199644308217972[/C][/ROW]
[ROW][C]51[/C][C]1.13[/C][C]1.11927574172597[/C][C]0.0107242582740326[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.12782200288036[/C][C]0.00217799711963784[/C][/ROW]
[ROW][C]53[/C][C]1.13[/C][C]1.13021660312270[/C][C]-0.000216603122695336[/C][/ROW]
[ROW][C]54[/C][C]1.12[/C][C]1.13551630369265[/C][C]-0.0155163036926533[/C][/ROW]
[ROW][C]55[/C][C]1.13[/C][C]1.12030712622923[/C][C]0.009692873770774[/C][/ROW]
[ROW][C]56[/C][C]1.12[/C][C]1.13249955194757[/C][C]-0.0124995519475688[/C][/ROW]
[ROW][C]57[/C][C]1.12[/C][C]1.12366061153668[/C][C]-0.0036606115366804[/C][/ROW]
[ROW][C]58[/C][C]1.11[/C][C]1.11448772366811[/C][C]-0.00448772366811201[/C][/ROW]
[ROW][C]59[/C][C]1.11[/C][C]1.10660461308566[/C][C]0.00339538691433972[/C][/ROW]
[ROW][C]60[/C][C]1.11[/C][C]1.10729522692488[/C][C]0.00270477307511996[/C][/ROW]
[ROW][C]61[/C][C]1.11[/C][C]1.10990286839678[/C][C]9.71316032214453e-05[/C][/ROW]
[ROW][C]62[/C][C]1.14[/C][C]1.11448445243861[/C][C]0.0255155475613873[/C][/ROW]
[ROW][C]63[/C][C]1.15[/C][C]1.13523538116796[/C][C]0.0147646188320447[/C][/ROW]
[ROW][C]64[/C][C]1.15[/C][C]1.14438386514014[/C][C]0.00561613485986179[/C][/ROW]
[ROW][C]65[/C][C]1.16[/C][C]1.14862334346614[/C][C]0.0113766565338573[/C][/ROW]
[ROW][C]66[/C][C]1.15[/C][C]1.15817027362885[/C][C]-0.00817027362884626[/C][/ROW]
[ROW][C]67[/C][C]1.16[/C][C]1.15518658972921[/C][C]0.00481341027078841[/C][/ROW]
[ROW][C]68[/C][C]1.13[/C][C]1.15777037598931[/C][C]-0.0277703759893106[/C][/ROW]
[ROW][C]69[/C][C]1.13[/C][C]1.14024638911596[/C][C]-0.0102463891159645[/C][/ROW]
[ROW][C]70[/C][C]1.12[/C][C]1.12606074981142[/C][C]-0.00606074981142313[/C][/ROW]
[ROW][C]71[/C][C]1.12[/C][C]1.11918763347798[/C][C]0.000812366522019659[/C][/ROW]
[ROW][C]72[/C][C]1.11[/C][C]1.11781215311355[/C][C]-0.00781215311355288[/C][/ROW]
[ROW][C]73[/C][C]1.11[/C][C]1.11206335362500[/C][C]-0.00206335362500409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13449&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13449&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
131.111.107151268115940.00284873188405754
141.121.117971845795790.00202815420421376
151.111.108612659906800.00138734009319519
161.111.109621036808610.000378963191389081
171.121.12031314979929-0.000313149799294088
181.121.12091887273921-0.000918872739211984
191.111.11108433086987-0.00108433086987114
201.121.12112952709936-0.00112952709936343
211.111.11114187281578-0.00114187281578260
221.111.11114524514829-0.00114524514828895
231.11.10197949966158-0.00197949966158073
241.11.10262404971051-0.00262404971051144
251.11.10524493465159-0.0052449346515866
261.111.109958548967974.14510320287942e-05
271.11.098980300412820.00101969958718162
281.11.099446014468680.000553985531318357
291.091.11007628475527-0.0200762847552671
301.11.096151875109700.00384812489030328
311.11.08973699059950.0102630094004992
321.111.108017563413470.00198243658652775
331.131.100288442378790.0297115576212050
341.131.122716459365380.00728354063462477
351.131.119449225124120.0105507748758837
361.131.129025239587640.000974760412356446
371.141.133545974531820.00645402546818485
381.141.14820690228432-0.00820690228431742
391.141.131500621499230.00849937850077342
401.151.137275665978560.0127243340214351
411.151.15111652987460-0.00111652987459743
421.151.15750801079919-0.00750801079919339
431.151.14459128880810.00540871119190034
441.151.15708164873372-0.00708164873372219
451.151.15033880491794-0.000338804917936919
461.141.14479856483514-0.00479856483514229
471.141.133642021678570.00635797832142959
481.141.137554769982700.00244523001730146
491.131.14464100950208-0.0146410095020753
501.121.13996443082180-0.0199644308217972
511.131.119275741725970.0107242582740326
521.131.127822002880360.00217799711963784
531.131.13021660312270-0.000216603122695336
541.121.13551630369265-0.0155163036926533
551.131.120307126229230.009692873770774
561.121.13249955194757-0.0124995519475688
571.121.12366061153668-0.0036606115366804
581.111.11448772366811-0.00448772366811201
591.111.106604613085660.00339538691433972
601.111.107295226924880.00270477307511996
611.111.109902868396789.71316032214453e-05
621.141.114484452438610.0255155475613873
631.151.135235381167960.0147646188320447
641.151.144383865140140.00561613485986179
651.161.148623343466140.0113766565338573
661.151.15817027362885-0.00817027362884626
671.161.155186589729210.00481341027078841
681.131.15777037598931-0.0277703759893106
691.131.14024638911596-0.0102463891159645
701.121.12606074981142-0.00606074981142313
711.121.119187633477980.000812366522019659
721.111.11781215311355-0.00781215311355288
731.111.11206335362500-0.00206335362500409






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
741.122017852835431.103152999524051.14088270614681
751.121286309310361.0979647482631.14460787035771
761.117204267208431.090150473964021.14425806045283
771.118935236619041.088605049541861.14926542369621
781.114873733782911.081588109748471.14815935781735
791.121375145542151.085375905458681.15737438562563
801.111559818240251.073037645328881.15008199115161
811.119007323118211.078117589381751.15989705685467
821.113412529993901.070285011583211.15654004840458
831.112822067971921.067567285202691.15807685074114
841.108500268141951.061213823121051.15578671316286
851.111.060765658307021.15923434169298

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 1.12201785283543 & 1.10315299952405 & 1.14088270614681 \tabularnewline
75 & 1.12128630931036 & 1.097964748263 & 1.14460787035771 \tabularnewline
76 & 1.11720426720843 & 1.09015047396402 & 1.14425806045283 \tabularnewline
77 & 1.11893523661904 & 1.08860504954186 & 1.14926542369621 \tabularnewline
78 & 1.11487373378291 & 1.08158810974847 & 1.14815935781735 \tabularnewline
79 & 1.12137514554215 & 1.08537590545868 & 1.15737438562563 \tabularnewline
80 & 1.11155981824025 & 1.07303764532888 & 1.15008199115161 \tabularnewline
81 & 1.11900732311821 & 1.07811758938175 & 1.15989705685467 \tabularnewline
82 & 1.11341252999390 & 1.07028501158321 & 1.15654004840458 \tabularnewline
83 & 1.11282206797192 & 1.06756728520269 & 1.15807685074114 \tabularnewline
84 & 1.10850026814195 & 1.06121382312105 & 1.15578671316286 \tabularnewline
85 & 1.11 & 1.06076565830702 & 1.15923434169298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13449&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]1.12201785283543[/C][C]1.10315299952405[/C][C]1.14088270614681[/C][/ROW]
[ROW][C]75[/C][C]1.12128630931036[/C][C]1.097964748263[/C][C]1.14460787035771[/C][/ROW]
[ROW][C]76[/C][C]1.11720426720843[/C][C]1.09015047396402[/C][C]1.14425806045283[/C][/ROW]
[ROW][C]77[/C][C]1.11893523661904[/C][C]1.08860504954186[/C][C]1.14926542369621[/C][/ROW]
[ROW][C]78[/C][C]1.11487373378291[/C][C]1.08158810974847[/C][C]1.14815935781735[/C][/ROW]
[ROW][C]79[/C][C]1.12137514554215[/C][C]1.08537590545868[/C][C]1.15737438562563[/C][/ROW]
[ROW][C]80[/C][C]1.11155981824025[/C][C]1.07303764532888[/C][C]1.15008199115161[/C][/ROW]
[ROW][C]81[/C][C]1.11900732311821[/C][C]1.07811758938175[/C][C]1.15989705685467[/C][/ROW]
[ROW][C]82[/C][C]1.11341252999390[/C][C]1.07028501158321[/C][C]1.15654004840458[/C][/ROW]
[ROW][C]83[/C][C]1.11282206797192[/C][C]1.06756728520269[/C][C]1.15807685074114[/C][/ROW]
[ROW][C]84[/C][C]1.10850026814195[/C][C]1.06121382312105[/C][C]1.15578671316286[/C][/ROW]
[ROW][C]85[/C][C]1.11[/C][C]1.06076565830702[/C][C]1.15923434169298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13449&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13449&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
741.122017852835431.103152999524051.14088270614681
751.121286309310361.0979647482631.14460787035771
761.117204267208431.090150473964021.14425806045283
771.118935236619041.088605049541861.14926542369621
781.114873733782911.081588109748471.14815935781735
791.121375145542151.085375905458681.15737438562563
801.111559818240251.073037645328881.15008199115161
811.119007323118211.078117589381751.15989705685467
821.113412529993901.070285011583211.15654004840458
831.112822067971921.067567285202691.15807685074114
841.108500268141951.061213823121051.15578671316286
851.111.060765658307021.15923434169298


Figures (Output of Computation)

Input Parameters & R Code

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=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')