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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 09:58:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293616610vstam1sk29xvqyx.htm/, Retrieved Fri, 03 May 2024 08:30:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116666, Retrieved Fri, 03 May 2024 08:30:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefening 2] [2010-12-29 09:58:39] [2d936dc014887261753404b7df36ea79] [Current]
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Dataseries X:
7.24
7.52
7.57
7.59
7.58
7.55
7.52
7.55
7.62
7.64
7.68
7.69
7.7
7.6
7.51
7.66
7.69
7.66
7.7
7.72
7.74
7.76
7.72
7.73
7.75
8.1
8.22
8.32
8.07
8.18
8.33
8.34
8.25
8.36
8.36
8.34
8.41
8.39
8.43
8.44
8.49
8.47
8.53
8.52
8.51
8.53
8.54
8.53
8.47
8.63
8.67
8.73
8.57
8.55
8.63
8.65
8.44
8.62
8.37
8.59
8.84
8.72
8.8
8.69
8.68
8.57
8.85
8.85
8.85
8.93
8.75
8.78
8.77
9.03
9.01
9.07
8.99
9.02
8.99
8.98
8.94
8.94
8.75
8.86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116666&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116666&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116666&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.508302927087735
beta0.00202277055986297
gamma0.695819962431208

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.508302927087735 \tabularnewline
beta & 0.00202277055986297 \tabularnewline
gamma & 0.695819962431208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116666&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]0.508302927087735[/C][/ROW]
[ROW][C]beta[/C][C]0.00202277055986297[/C][/ROW]
[ROW][C]gamma[/C][C]0.695819962431208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116666&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116666&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
alpha0.508302927087735
beta0.00202277055986297
gamma0.695819962431208







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.77.656367521367520.0436324786324764
147.67.573127613309670.0268723866903322
157.517.493896131115180.016103868884815
167.667.651290870812170.0087091291878334
177.697.688269130563610.00173086943638712
187.667.66503543343643-0.00503543343643376
197.77.63085722742050.0691427725795046
207.727.68278844521140.0372115547885983
217.747.78019385838409-0.0401938583840913
227.767.78862921360613-0.0286292136061261
237.727.81583014229573-0.0958301422957293
247.737.7771074449082-0.0471074449081987
257.757.77511363066171-0.0251136306617079
268.17.651111245702130.448888754297865
278.227.783057112061570.436942887938426
288.328.152617728548590.167382271451412
298.078.26880781850052-0.198807818500519
308.188.142063854297020.037936145702977
318.338.155890303684840.174109696315156
328.348.251143019747130.0888569802528707
338.258.34926135188351-0.0992613518835128
348.368.332512753967470.0274872460325319
358.368.36618749438794-0.00618749438794453
368.348.3907334932471-0.0507334932471029
378.418.39545107238710.0145489276128981
388.398.45485147158106-0.0648514715810631
398.438.322116891979280.107883108020722
408.448.432393926758580.00760607324141915
418.498.342123399627330.147876600372667
428.478.47299410548398-0.00299410548397638
438.538.512959048897180.0170409511028193
448.528.499398074633620.0206019253663836
458.518.498583112037150.011416887962854
468.538.5816935876789-0.0516935876789084
478.548.56375400659804-0.0237540065980433
488.538.56426695004882-0.0342669500488242
498.478.59984339308978-0.129843393089779
508.638.55868844847690.0713115515231078
518.678.554409233288730.115590766711268
528.738.63444913556050.095550864439497
538.578.6371158404428-0.0671158404428027
548.558.6071099272806-0.0571099272806013
558.638.626389106697070.00361089330293574
568.658.607172931590560.0428270684094407
578.448.6144884359516-0.174488435951602
588.628.581295256324810.0387047436751864
598.378.61874211865705-0.248742118657054
608.598.500942461162440.0890575388375634
618.848.566278418076820.273721581923178
628.728.79926647691246-0.0792664769124567
638.88.733630625875930.0663693741240738
648.698.78177748913779-0.0917774891377867
658.688.63336109084340.0466389091565969
668.578.66450739598698-0.0945073959869767
678.858.685420452474490.164579547525509
688.858.761476299037830.0885237009621651
698.858.717749842982880.132250157017118
708.938.913809550138680.0161904498613161
718.758.84184064575374-0.0918406457537433
728.788.91990134564693-0.139901345646926
738.778.93233560799874-0.162335607998738
749.038.822756619668460.207243380331539
759.018.95272676437290.0572732356271057
769.078.942278896341290.127721103658713
778.998.953152793140770.0368472068592318
789.028.931382872157130.0886171278428716
798.999.13456072744822-0.144560727448217
808.989.0276805956285-0.0476805956284974
818.948.929763417917450.0102365820825447
828.949.02405207516776-0.0840520751677634
838.758.86402219194334-0.11402219194334
848.868.91419556014425-0.054195560144251

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.7 & 7.65636752136752 & 0.0436324786324764 \tabularnewline
14 & 7.6 & 7.57312761330967 & 0.0268723866903322 \tabularnewline
15 & 7.51 & 7.49389613111518 & 0.016103868884815 \tabularnewline
16 & 7.66 & 7.65129087081217 & 0.0087091291878334 \tabularnewline
17 & 7.69 & 7.68826913056361 & 0.00173086943638712 \tabularnewline
18 & 7.66 & 7.66503543343643 & -0.00503543343643376 \tabularnewline
19 & 7.7 & 7.6308572274205 & 0.0691427725795046 \tabularnewline
20 & 7.72 & 7.6827884452114 & 0.0372115547885983 \tabularnewline
21 & 7.74 & 7.78019385838409 & -0.0401938583840913 \tabularnewline
22 & 7.76 & 7.78862921360613 & -0.0286292136061261 \tabularnewline
23 & 7.72 & 7.81583014229573 & -0.0958301422957293 \tabularnewline
24 & 7.73 & 7.7771074449082 & -0.0471074449081987 \tabularnewline
25 & 7.75 & 7.77511363066171 & -0.0251136306617079 \tabularnewline
26 & 8.1 & 7.65111124570213 & 0.448888754297865 \tabularnewline
27 & 8.22 & 7.78305711206157 & 0.436942887938426 \tabularnewline
28 & 8.32 & 8.15261772854859 & 0.167382271451412 \tabularnewline
29 & 8.07 & 8.26880781850052 & -0.198807818500519 \tabularnewline
30 & 8.18 & 8.14206385429702 & 0.037936145702977 \tabularnewline
31 & 8.33 & 8.15589030368484 & 0.174109696315156 \tabularnewline
32 & 8.34 & 8.25114301974713 & 0.0888569802528707 \tabularnewline
33 & 8.25 & 8.34926135188351 & -0.0992613518835128 \tabularnewline
34 & 8.36 & 8.33251275396747 & 0.0274872460325319 \tabularnewline
35 & 8.36 & 8.36618749438794 & -0.00618749438794453 \tabularnewline
36 & 8.34 & 8.3907334932471 & -0.0507334932471029 \tabularnewline
37 & 8.41 & 8.3954510723871 & 0.0145489276128981 \tabularnewline
38 & 8.39 & 8.45485147158106 & -0.0648514715810631 \tabularnewline
39 & 8.43 & 8.32211689197928 & 0.107883108020722 \tabularnewline
40 & 8.44 & 8.43239392675858 & 0.00760607324141915 \tabularnewline
41 & 8.49 & 8.34212339962733 & 0.147876600372667 \tabularnewline
42 & 8.47 & 8.47299410548398 & -0.00299410548397638 \tabularnewline
43 & 8.53 & 8.51295904889718 & 0.0170409511028193 \tabularnewline
44 & 8.52 & 8.49939807463362 & 0.0206019253663836 \tabularnewline
45 & 8.51 & 8.49858311203715 & 0.011416887962854 \tabularnewline
46 & 8.53 & 8.5816935876789 & -0.0516935876789084 \tabularnewline
47 & 8.54 & 8.56375400659804 & -0.0237540065980433 \tabularnewline
48 & 8.53 & 8.56426695004882 & -0.0342669500488242 \tabularnewline
49 & 8.47 & 8.59984339308978 & -0.129843393089779 \tabularnewline
50 & 8.63 & 8.5586884484769 & 0.0713115515231078 \tabularnewline
51 & 8.67 & 8.55440923328873 & 0.115590766711268 \tabularnewline
52 & 8.73 & 8.6344491355605 & 0.095550864439497 \tabularnewline
53 & 8.57 & 8.6371158404428 & -0.0671158404428027 \tabularnewline
54 & 8.55 & 8.6071099272806 & -0.0571099272806013 \tabularnewline
55 & 8.63 & 8.62638910669707 & 0.00361089330293574 \tabularnewline
56 & 8.65 & 8.60717293159056 & 0.0428270684094407 \tabularnewline
57 & 8.44 & 8.6144884359516 & -0.174488435951602 \tabularnewline
58 & 8.62 & 8.58129525632481 & 0.0387047436751864 \tabularnewline
59 & 8.37 & 8.61874211865705 & -0.248742118657054 \tabularnewline
60 & 8.59 & 8.50094246116244 & 0.0890575388375634 \tabularnewline
61 & 8.84 & 8.56627841807682 & 0.273721581923178 \tabularnewline
62 & 8.72 & 8.79926647691246 & -0.0792664769124567 \tabularnewline
63 & 8.8 & 8.73363062587593 & 0.0663693741240738 \tabularnewline
64 & 8.69 & 8.78177748913779 & -0.0917774891377867 \tabularnewline
65 & 8.68 & 8.6333610908434 & 0.0466389091565969 \tabularnewline
66 & 8.57 & 8.66450739598698 & -0.0945073959869767 \tabularnewline
67 & 8.85 & 8.68542045247449 & 0.164579547525509 \tabularnewline
68 & 8.85 & 8.76147629903783 & 0.0885237009621651 \tabularnewline
69 & 8.85 & 8.71774984298288 & 0.132250157017118 \tabularnewline
70 & 8.93 & 8.91380955013868 & 0.0161904498613161 \tabularnewline
71 & 8.75 & 8.84184064575374 & -0.0918406457537433 \tabularnewline
72 & 8.78 & 8.91990134564693 & -0.139901345646926 \tabularnewline
73 & 8.77 & 8.93233560799874 & -0.162335607998738 \tabularnewline
74 & 9.03 & 8.82275661966846 & 0.207243380331539 \tabularnewline
75 & 9.01 & 8.9527267643729 & 0.0572732356271057 \tabularnewline
76 & 9.07 & 8.94227889634129 & 0.127721103658713 \tabularnewline
77 & 8.99 & 8.95315279314077 & 0.0368472068592318 \tabularnewline
78 & 9.02 & 8.93138287215713 & 0.0886171278428716 \tabularnewline
79 & 8.99 & 9.13456072744822 & -0.144560727448217 \tabularnewline
80 & 8.98 & 9.0276805956285 & -0.0476805956284974 \tabularnewline
81 & 8.94 & 8.92976341791745 & 0.0102365820825447 \tabularnewline
82 & 8.94 & 9.02405207516776 & -0.0840520751677634 \tabularnewline
83 & 8.75 & 8.86402219194334 & -0.11402219194334 \tabularnewline
84 & 8.86 & 8.91419556014425 & -0.054195560144251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116666&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]7.7[/C][C]7.65636752136752[/C][C]0.0436324786324764[/C][/ROW]
[ROW][C]14[/C][C]7.6[/C][C]7.57312761330967[/C][C]0.0268723866903322[/C][/ROW]
[ROW][C]15[/C][C]7.51[/C][C]7.49389613111518[/C][C]0.016103868884815[/C][/ROW]
[ROW][C]16[/C][C]7.66[/C][C]7.65129087081217[/C][C]0.0087091291878334[/C][/ROW]
[ROW][C]17[/C][C]7.69[/C][C]7.68826913056361[/C][C]0.00173086943638712[/C][/ROW]
[ROW][C]18[/C][C]7.66[/C][C]7.66503543343643[/C][C]-0.00503543343643376[/C][/ROW]
[ROW][C]19[/C][C]7.7[/C][C]7.6308572274205[/C][C]0.0691427725795046[/C][/ROW]
[ROW][C]20[/C][C]7.72[/C][C]7.6827884452114[/C][C]0.0372115547885983[/C][/ROW]
[ROW][C]21[/C][C]7.74[/C][C]7.78019385838409[/C][C]-0.0401938583840913[/C][/ROW]
[ROW][C]22[/C][C]7.76[/C][C]7.78862921360613[/C][C]-0.0286292136061261[/C][/ROW]
[ROW][C]23[/C][C]7.72[/C][C]7.81583014229573[/C][C]-0.0958301422957293[/C][/ROW]
[ROW][C]24[/C][C]7.73[/C][C]7.7771074449082[/C][C]-0.0471074449081987[/C][/ROW]
[ROW][C]25[/C][C]7.75[/C][C]7.77511363066171[/C][C]-0.0251136306617079[/C][/ROW]
[ROW][C]26[/C][C]8.1[/C][C]7.65111124570213[/C][C]0.448888754297865[/C][/ROW]
[ROW][C]27[/C][C]8.22[/C][C]7.78305711206157[/C][C]0.436942887938426[/C][/ROW]
[ROW][C]28[/C][C]8.32[/C][C]8.15261772854859[/C][C]0.167382271451412[/C][/ROW]
[ROW][C]29[/C][C]8.07[/C][C]8.26880781850052[/C][C]-0.198807818500519[/C][/ROW]
[ROW][C]30[/C][C]8.18[/C][C]8.14206385429702[/C][C]0.037936145702977[/C][/ROW]
[ROW][C]31[/C][C]8.33[/C][C]8.15589030368484[/C][C]0.174109696315156[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.25114301974713[/C][C]0.0888569802528707[/C][/ROW]
[ROW][C]33[/C][C]8.25[/C][C]8.34926135188351[/C][C]-0.0992613518835128[/C][/ROW]
[ROW][C]34[/C][C]8.36[/C][C]8.33251275396747[/C][C]0.0274872460325319[/C][/ROW]
[ROW][C]35[/C][C]8.36[/C][C]8.36618749438794[/C][C]-0.00618749438794453[/C][/ROW]
[ROW][C]36[/C][C]8.34[/C][C]8.3907334932471[/C][C]-0.0507334932471029[/C][/ROW]
[ROW][C]37[/C][C]8.41[/C][C]8.3954510723871[/C][C]0.0145489276128981[/C][/ROW]
[ROW][C]38[/C][C]8.39[/C][C]8.45485147158106[/C][C]-0.0648514715810631[/C][/ROW]
[ROW][C]39[/C][C]8.43[/C][C]8.32211689197928[/C][C]0.107883108020722[/C][/ROW]
[ROW][C]40[/C][C]8.44[/C][C]8.43239392675858[/C][C]0.00760607324141915[/C][/ROW]
[ROW][C]41[/C][C]8.49[/C][C]8.34212339962733[/C][C]0.147876600372667[/C][/ROW]
[ROW][C]42[/C][C]8.47[/C][C]8.47299410548398[/C][C]-0.00299410548397638[/C][/ROW]
[ROW][C]43[/C][C]8.53[/C][C]8.51295904889718[/C][C]0.0170409511028193[/C][/ROW]
[ROW][C]44[/C][C]8.52[/C][C]8.49939807463362[/C][C]0.0206019253663836[/C][/ROW]
[ROW][C]45[/C][C]8.51[/C][C]8.49858311203715[/C][C]0.011416887962854[/C][/ROW]
[ROW][C]46[/C][C]8.53[/C][C]8.5816935876789[/C][C]-0.0516935876789084[/C][/ROW]
[ROW][C]47[/C][C]8.54[/C][C]8.56375400659804[/C][C]-0.0237540065980433[/C][/ROW]
[ROW][C]48[/C][C]8.53[/C][C]8.56426695004882[/C][C]-0.0342669500488242[/C][/ROW]
[ROW][C]49[/C][C]8.47[/C][C]8.59984339308978[/C][C]-0.129843393089779[/C][/ROW]
[ROW][C]50[/C][C]8.63[/C][C]8.5586884484769[/C][C]0.0713115515231078[/C][/ROW]
[ROW][C]51[/C][C]8.67[/C][C]8.55440923328873[/C][C]0.115590766711268[/C][/ROW]
[ROW][C]52[/C][C]8.73[/C][C]8.6344491355605[/C][C]0.095550864439497[/C][/ROW]
[ROW][C]53[/C][C]8.57[/C][C]8.6371158404428[/C][C]-0.0671158404428027[/C][/ROW]
[ROW][C]54[/C][C]8.55[/C][C]8.6071099272806[/C][C]-0.0571099272806013[/C][/ROW]
[ROW][C]55[/C][C]8.63[/C][C]8.62638910669707[/C][C]0.00361089330293574[/C][/ROW]
[ROW][C]56[/C][C]8.65[/C][C]8.60717293159056[/C][C]0.0428270684094407[/C][/ROW]
[ROW][C]57[/C][C]8.44[/C][C]8.6144884359516[/C][C]-0.174488435951602[/C][/ROW]
[ROW][C]58[/C][C]8.62[/C][C]8.58129525632481[/C][C]0.0387047436751864[/C][/ROW]
[ROW][C]59[/C][C]8.37[/C][C]8.61874211865705[/C][C]-0.248742118657054[/C][/ROW]
[ROW][C]60[/C][C]8.59[/C][C]8.50094246116244[/C][C]0.0890575388375634[/C][/ROW]
[ROW][C]61[/C][C]8.84[/C][C]8.56627841807682[/C][C]0.273721581923178[/C][/ROW]
[ROW][C]62[/C][C]8.72[/C][C]8.79926647691246[/C][C]-0.0792664769124567[/C][/ROW]
[ROW][C]63[/C][C]8.8[/C][C]8.73363062587593[/C][C]0.0663693741240738[/C][/ROW]
[ROW][C]64[/C][C]8.69[/C][C]8.78177748913779[/C][C]-0.0917774891377867[/C][/ROW]
[ROW][C]65[/C][C]8.68[/C][C]8.6333610908434[/C][C]0.0466389091565969[/C][/ROW]
[ROW][C]66[/C][C]8.57[/C][C]8.66450739598698[/C][C]-0.0945073959869767[/C][/ROW]
[ROW][C]67[/C][C]8.85[/C][C]8.68542045247449[/C][C]0.164579547525509[/C][/ROW]
[ROW][C]68[/C][C]8.85[/C][C]8.76147629903783[/C][C]0.0885237009621651[/C][/ROW]
[ROW][C]69[/C][C]8.85[/C][C]8.71774984298288[/C][C]0.132250157017118[/C][/ROW]
[ROW][C]70[/C][C]8.93[/C][C]8.91380955013868[/C][C]0.0161904498613161[/C][/ROW]
[ROW][C]71[/C][C]8.75[/C][C]8.84184064575374[/C][C]-0.0918406457537433[/C][/ROW]
[ROW][C]72[/C][C]8.78[/C][C]8.91990134564693[/C][C]-0.139901345646926[/C][/ROW]
[ROW][C]73[/C][C]8.77[/C][C]8.93233560799874[/C][C]-0.162335607998738[/C][/ROW]
[ROW][C]74[/C][C]9.03[/C][C]8.82275661966846[/C][C]0.207243380331539[/C][/ROW]
[ROW][C]75[/C][C]9.01[/C][C]8.9527267643729[/C][C]0.0572732356271057[/C][/ROW]
[ROW][C]76[/C][C]9.07[/C][C]8.94227889634129[/C][C]0.127721103658713[/C][/ROW]
[ROW][C]77[/C][C]8.99[/C][C]8.95315279314077[/C][C]0.0368472068592318[/C][/ROW]
[ROW][C]78[/C][C]9.02[/C][C]8.93138287215713[/C][C]0.0886171278428716[/C][/ROW]
[ROW][C]79[/C][C]8.99[/C][C]9.13456072744822[/C][C]-0.144560727448217[/C][/ROW]
[ROW][C]80[/C][C]8.98[/C][C]9.0276805956285[/C][C]-0.0476805956284974[/C][/ROW]
[ROW][C]81[/C][C]8.94[/C][C]8.92976341791745[/C][C]0.0102365820825447[/C][/ROW]
[ROW][C]82[/C][C]8.94[/C][C]9.02405207516776[/C][C]-0.0840520751677634[/C][/ROW]
[ROW][C]83[/C][C]8.75[/C][C]8.86402219194334[/C][C]-0.11402219194334[/C][/ROW]
[ROW][C]84[/C][C]8.86[/C][C]8.91419556014425[/C][C]-0.054195560144251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116666&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116666&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
137.77.656367521367520.0436324786324764
147.67.573127613309670.0268723866903322
157.517.493896131115180.016103868884815
167.667.651290870812170.0087091291878334
177.697.688269130563610.00173086943638712
187.667.66503543343643-0.00503543343643376
197.77.63085722742050.0691427725795046
207.727.68278844521140.0372115547885983
217.747.78019385838409-0.0401938583840913
227.767.78862921360613-0.0286292136061261
237.727.81583014229573-0.0958301422957293
247.737.7771074449082-0.0471074449081987
257.757.77511363066171-0.0251136306617079
268.17.651111245702130.448888754297865
278.227.783057112061570.436942887938426
288.328.152617728548590.167382271451412
298.078.26880781850052-0.198807818500519
308.188.142063854297020.037936145702977
318.338.155890303684840.174109696315156
328.348.251143019747130.0888569802528707
338.258.34926135188351-0.0992613518835128
348.368.332512753967470.0274872460325319
358.368.36618749438794-0.00618749438794453
368.348.3907334932471-0.0507334932471029
378.418.39545107238710.0145489276128981
388.398.45485147158106-0.0648514715810631
398.438.322116891979280.107883108020722
408.448.432393926758580.00760607324141915
418.498.342123399627330.147876600372667
428.478.47299410548398-0.00299410548397638
438.538.512959048897180.0170409511028193
448.528.499398074633620.0206019253663836
458.518.498583112037150.011416887962854
468.538.5816935876789-0.0516935876789084
478.548.56375400659804-0.0237540065980433
488.538.56426695004882-0.0342669500488242
498.478.59984339308978-0.129843393089779
508.638.55868844847690.0713115515231078
518.678.554409233288730.115590766711268
528.738.63444913556050.095550864439497
538.578.6371158404428-0.0671158404428027
548.558.6071099272806-0.0571099272806013
558.638.626389106697070.00361089330293574
568.658.607172931590560.0428270684094407
578.448.6144884359516-0.174488435951602
588.628.581295256324810.0387047436751864
598.378.61874211865705-0.248742118657054
608.598.500942461162440.0890575388375634
618.848.566278418076820.273721581923178
628.728.79926647691246-0.0792664769124567
638.88.733630625875930.0663693741240738
648.698.78177748913779-0.0917774891377867
658.688.63336109084340.0466389091565969
668.578.66450739598698-0.0945073959869767
678.858.685420452474490.164579547525509
688.858.761476299037830.0885237009621651
698.858.717749842982880.132250157017118
708.938.913809550138680.0161904498613161
718.758.84184064575374-0.0918406457537433
728.788.91990134564693-0.139901345646926
738.778.93233560799874-0.162335607998738
749.038.822756619668460.207243380331539
759.018.95272676437290.0572732356271057
769.078.942278896341290.127721103658713
778.998.953152793140770.0368472068592318
789.028.931382872157130.0886171278428716
798.999.13456072744822-0.144560727448217
808.989.0276805956285-0.0476805956284974
818.948.929763417917450.0102365820825447
828.949.02405207516776-0.0840520751677634
838.758.86402219194334-0.11402219194334
848.868.91419556014425-0.054195560144251







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
858.962437698989148.724315088516629.20056030946165
869.061905188387178.79467494114179.32913543563264
879.03509592984998.74152978622229.32866207347758
889.01945223123578.701631960596359.33727250187503
898.933996678517838.593558642799559.2744347142361
908.910853995974338.549127309408169.27258068254051
918.988763238341138.606854527852769.3706719488295
928.988211724538448.587060408738149.38936304033874
938.93409723620338.514513322397319.35368115000928
948.990664002863058.553354923718169.42797308200795
958.862931322175218.408521586377139.3173410579733
968.991475424900228.520521379936529.46242946986393

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 8.96243769898914 & 8.72431508851662 & 9.20056030946165 \tabularnewline
86 & 9.06190518838717 & 8.7946749411417 & 9.32913543563264 \tabularnewline
87 & 9.0350959298499 & 8.7415297862222 & 9.32866207347758 \tabularnewline
88 & 9.0194522312357 & 8.70163196059635 & 9.33727250187503 \tabularnewline
89 & 8.93399667851783 & 8.59355864279955 & 9.2744347142361 \tabularnewline
90 & 8.91085399597433 & 8.54912730940816 & 9.27258068254051 \tabularnewline
91 & 8.98876323834113 & 8.60685452785276 & 9.3706719488295 \tabularnewline
92 & 8.98821172453844 & 8.58706040873814 & 9.38936304033874 \tabularnewline
93 & 8.9340972362033 & 8.51451332239731 & 9.35368115000928 \tabularnewline
94 & 8.99066400286305 & 8.55335492371816 & 9.42797308200795 \tabularnewline
95 & 8.86293132217521 & 8.40852158637713 & 9.3173410579733 \tabularnewline
96 & 8.99147542490022 & 8.52052137993652 & 9.46242946986393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116666&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]85[/C][C]8.96243769898914[/C][C]8.72431508851662[/C][C]9.20056030946165[/C][/ROW]
[ROW][C]86[/C][C]9.06190518838717[/C][C]8.7946749411417[/C][C]9.32913543563264[/C][/ROW]
[ROW][C]87[/C][C]9.0350959298499[/C][C]8.7415297862222[/C][C]9.32866207347758[/C][/ROW]
[ROW][C]88[/C][C]9.0194522312357[/C][C]8.70163196059635[/C][C]9.33727250187503[/C][/ROW]
[ROW][C]89[/C][C]8.93399667851783[/C][C]8.59355864279955[/C][C]9.2744347142361[/C][/ROW]
[ROW][C]90[/C][C]8.91085399597433[/C][C]8.54912730940816[/C][C]9.27258068254051[/C][/ROW]
[ROW][C]91[/C][C]8.98876323834113[/C][C]8.60685452785276[/C][C]9.3706719488295[/C][/ROW]
[ROW][C]92[/C][C]8.98821172453844[/C][C]8.58706040873814[/C][C]9.38936304033874[/C][/ROW]
[ROW][C]93[/C][C]8.9340972362033[/C][C]8.51451332239731[/C][C]9.35368115000928[/C][/ROW]
[ROW][C]94[/C][C]8.99066400286305[/C][C]8.55335492371816[/C][C]9.42797308200795[/C][/ROW]
[ROW][C]95[/C][C]8.86293132217521[/C][C]8.40852158637713[/C][C]9.3173410579733[/C][/ROW]
[ROW][C]96[/C][C]8.99147542490022[/C][C]8.52052137993652[/C][C]9.46242946986393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116666&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116666&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
858.962437698989148.724315088516629.20056030946165
869.061905188387178.79467494114179.32913543563264
879.03509592984998.74152978622229.32866207347758
889.01945223123578.701631960596359.33727250187503
898.933996678517838.593558642799559.2744347142361
908.910853995974338.549127309408169.27258068254051
918.988763238341138.606854527852769.3706719488295
928.988211724538448.587060408738149.38936304033874
938.93409723620338.514513322397319.35368115000928
948.990664002863058.553354923718169.42797308200795
958.862931322175218.408521586377139.3173410579733
968.991475424900228.520521379936529.46242946986393



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')