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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 computationSun, 29 Dec 2013 16:25:33 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/29/t13883525425003uvi7gha4hjl.htm/, Retrieved Fri, 29 Mar 2024 12:54:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232662, Retrieved Fri, 29 Mar 2024 12:54:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2013-12-09 08:54:13] [862476833f28e78bdb10134cb7564890]
- RMP   [Exponential Smoothing] [] [2013-12-29 21:06:21] [862476833f28e78bdb10134cb7564890]
- R  D      [Exponential Smoothing] [] [2013-12-29 21:25:33] [52cb9535ca11c6f6481093732e3934f7] [Current]
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Dataseries X:
6,35
6,33
6,36
6,37
6,33
6,34
6,42
6,42
6,48
6,47
6,5
6,52
6,49
6,51
6,52
6,54
6,59
6,6
6,59
6,58
6,55
6,57
6,61
6,61
6,64
6,59
6,67
6,58
6,66
6,7
6,65
6,65
6,73
6,74
6,74
6,71
6,78
6,83
6,8
6,84
6,81
6,75
6,8
6,84
6,8
6,84
6,79
6,8
6,68
6,82
6,85
6,85
6,85
6,92
6,91
6,94
6,99
7,05
6,98
6,91
6,98
7,06
7,05
6,95
7,09
7,15
7,1
7,2
7,26
7,26
7,24
7,26
7,26
7,3
7,21
7,23
7,33
7,33
7,31
7,3
7,35
7,4
7,43
7,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232662&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232662&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232662&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.595010884943598
beta0.107134386406202
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.595010884943598 \tabularnewline
beta & 0.107134386406202 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232662&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]0.595010884943598[/C][/ROW]
[ROW][C]beta[/C][C]0.107134386406202[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232662&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232662&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
alpha0.595010884943598
beta0.107134386406202
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.366.310.0499999999999998
46.376.322937850550350.0470621494496477
56.336.33712767775654-0.00712767775654122
66.346.318619606077030.0213803939229722
76.426.318437064641880.101562935358124
86.426.372438251823790.0475617481762063
96.486.397340022027630.0826599779723693
106.476.448394874378670.0216051256213339
116.56.464498668063680.0355013319363158
126.526.491133928146570.0288660718534279
136.496.51566123651103-0.0256612365110334
146.516.506108398454390.00389160154561008
156.526.514387895245140.00561210475486096
166.546.524048860110160.0159511398898431
176.596.540878486794580.0491215132054226
186.66.580576152832630.0194238471673698
196.596.60384157933079-0.0138415793307898
206.586.60643136790932-0.026431367909316
216.556.5998451979337-0.0498451979337045
226.576.57615010596422-0.00615010596422216
236.616.57806202390510.0319379760949046
246.616.604672687508130.00532731249186913
256.646.615789312145470.0242106878545254
266.596.63968508822813-0.0496850882281308
276.676.616444841292590.053555158707411
286.586.65804759894627-0.0780475989462692
296.666.616370051226040.0436299487739626
306.76.649873209067270.0501267909327261
316.656.69043744744469-0.0404374474446882
326.656.67453724757842-0.0245372475784222
336.736.666533685227980.0634663147720209
346.746.71493893209210.0250610679078989
356.746.74209018502727-0.00209018502726632
366.716.75295290572791-0.0429529057279074
376.786.736763781479930.0432362185200654
386.836.774614265759550.0553857342404518
396.86.82322447013659-0.0232244701365936
406.846.823580277240570.0164197227594283
416.816.84857150435944-0.0385715043594361
426.756.83838356878682-0.0883835687868171
436.86.792922802560570.00707719743942636
446.846.804713375244150.0352866247558499
456.86.83553824986906-0.035538249869064
466.846.821956127411160.0180438725888381
476.796.84140617803081-0.0514061780308115
486.86.81625574786669-0.0162557478666949
496.686.81098396530791-0.130983965307911
506.826.729097924196620.0909020758033803
516.856.785031147947180.0649688520528189
526.856.829675333917640.0203246660823639
536.856.849051362012510.00094863798749234
546.926.85695891448070.063041085519302
556.916.905830774087790.00416922591220725
566.946.919939008412380.0200609915876182
576.996.944781826793520.045218173206484
587.056.987475925441960.0625240745580422
596.987.04445289130711-0.0644528913071136
606.917.02176855821097-0.111768558210973
616.986.963806075677030.016193924322975
627.066.983014963056540.0769850369434639
637.057.043302722023070.00669727797693387
646.957.06219542485242-0.112195424852418
657.097.003193651661560.0868063483384418
667.157.068133668066630.0818663319333748
677.17.13535298245465-0.035352982454655
687.27.130571913179910.0694280868200927
697.267.192562492234440.0674375077655576
707.267.257667534955620.00233246504438434
717.247.28418305420373-0.0441830542037298
727.267.28020483463727-0.0202048346372745
737.267.28920593677855-0.0292059367785482
747.37.290989519841590.00901048015841077
757.217.31608667016973-0.106086670169733
767.237.26593714897635-0.0359371489763518
777.337.255236502437610.074763497562393
787.337.315169828900260.0148301710997352
797.317.34038753970323-0.0303875397032298
807.37.33676313244952-0.0367631324495186
817.357.327001670838180.0229983291618163
827.47.354264983775730.0457350162242705
837.437.397972303112740.032027696887261
847.427.43556525984413-0.0155652598441263

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.36 & 6.31 & 0.0499999999999998 \tabularnewline
4 & 6.37 & 6.32293785055035 & 0.0470621494496477 \tabularnewline
5 & 6.33 & 6.33712767775654 & -0.00712767775654122 \tabularnewline
6 & 6.34 & 6.31861960607703 & 0.0213803939229722 \tabularnewline
7 & 6.42 & 6.31843706464188 & 0.101562935358124 \tabularnewline
8 & 6.42 & 6.37243825182379 & 0.0475617481762063 \tabularnewline
9 & 6.48 & 6.39734002202763 & 0.0826599779723693 \tabularnewline
10 & 6.47 & 6.44839487437867 & 0.0216051256213339 \tabularnewline
11 & 6.5 & 6.46449866806368 & 0.0355013319363158 \tabularnewline
12 & 6.52 & 6.49113392814657 & 0.0288660718534279 \tabularnewline
13 & 6.49 & 6.51566123651103 & -0.0256612365110334 \tabularnewline
14 & 6.51 & 6.50610839845439 & 0.00389160154561008 \tabularnewline
15 & 6.52 & 6.51438789524514 & 0.00561210475486096 \tabularnewline
16 & 6.54 & 6.52404886011016 & 0.0159511398898431 \tabularnewline
17 & 6.59 & 6.54087848679458 & 0.0491215132054226 \tabularnewline
18 & 6.6 & 6.58057615283263 & 0.0194238471673698 \tabularnewline
19 & 6.59 & 6.60384157933079 & -0.0138415793307898 \tabularnewline
20 & 6.58 & 6.60643136790932 & -0.026431367909316 \tabularnewline
21 & 6.55 & 6.5998451979337 & -0.0498451979337045 \tabularnewline
22 & 6.57 & 6.57615010596422 & -0.00615010596422216 \tabularnewline
23 & 6.61 & 6.5780620239051 & 0.0319379760949046 \tabularnewline
24 & 6.61 & 6.60467268750813 & 0.00532731249186913 \tabularnewline
25 & 6.64 & 6.61578931214547 & 0.0242106878545254 \tabularnewline
26 & 6.59 & 6.63968508822813 & -0.0496850882281308 \tabularnewline
27 & 6.67 & 6.61644484129259 & 0.053555158707411 \tabularnewline
28 & 6.58 & 6.65804759894627 & -0.0780475989462692 \tabularnewline
29 & 6.66 & 6.61637005122604 & 0.0436299487739626 \tabularnewline
30 & 6.7 & 6.64987320906727 & 0.0501267909327261 \tabularnewline
31 & 6.65 & 6.69043744744469 & -0.0404374474446882 \tabularnewline
32 & 6.65 & 6.67453724757842 & -0.0245372475784222 \tabularnewline
33 & 6.73 & 6.66653368522798 & 0.0634663147720209 \tabularnewline
34 & 6.74 & 6.7149389320921 & 0.0250610679078989 \tabularnewline
35 & 6.74 & 6.74209018502727 & -0.00209018502726632 \tabularnewline
36 & 6.71 & 6.75295290572791 & -0.0429529057279074 \tabularnewline
37 & 6.78 & 6.73676378147993 & 0.0432362185200654 \tabularnewline
38 & 6.83 & 6.77461426575955 & 0.0553857342404518 \tabularnewline
39 & 6.8 & 6.82322447013659 & -0.0232244701365936 \tabularnewline
40 & 6.84 & 6.82358027724057 & 0.0164197227594283 \tabularnewline
41 & 6.81 & 6.84857150435944 & -0.0385715043594361 \tabularnewline
42 & 6.75 & 6.83838356878682 & -0.0883835687868171 \tabularnewline
43 & 6.8 & 6.79292280256057 & 0.00707719743942636 \tabularnewline
44 & 6.84 & 6.80471337524415 & 0.0352866247558499 \tabularnewline
45 & 6.8 & 6.83553824986906 & -0.035538249869064 \tabularnewline
46 & 6.84 & 6.82195612741116 & 0.0180438725888381 \tabularnewline
47 & 6.79 & 6.84140617803081 & -0.0514061780308115 \tabularnewline
48 & 6.8 & 6.81625574786669 & -0.0162557478666949 \tabularnewline
49 & 6.68 & 6.81098396530791 & -0.130983965307911 \tabularnewline
50 & 6.82 & 6.72909792419662 & 0.0909020758033803 \tabularnewline
51 & 6.85 & 6.78503114794718 & 0.0649688520528189 \tabularnewline
52 & 6.85 & 6.82967533391764 & 0.0203246660823639 \tabularnewline
53 & 6.85 & 6.84905136201251 & 0.00094863798749234 \tabularnewline
54 & 6.92 & 6.8569589144807 & 0.063041085519302 \tabularnewline
55 & 6.91 & 6.90583077408779 & 0.00416922591220725 \tabularnewline
56 & 6.94 & 6.91993900841238 & 0.0200609915876182 \tabularnewline
57 & 6.99 & 6.94478182679352 & 0.045218173206484 \tabularnewline
58 & 7.05 & 6.98747592544196 & 0.0625240745580422 \tabularnewline
59 & 6.98 & 7.04445289130711 & -0.0644528913071136 \tabularnewline
60 & 6.91 & 7.02176855821097 & -0.111768558210973 \tabularnewline
61 & 6.98 & 6.96380607567703 & 0.016193924322975 \tabularnewline
62 & 7.06 & 6.98301496305654 & 0.0769850369434639 \tabularnewline
63 & 7.05 & 7.04330272202307 & 0.00669727797693387 \tabularnewline
64 & 6.95 & 7.06219542485242 & -0.112195424852418 \tabularnewline
65 & 7.09 & 7.00319365166156 & 0.0868063483384418 \tabularnewline
66 & 7.15 & 7.06813366806663 & 0.0818663319333748 \tabularnewline
67 & 7.1 & 7.13535298245465 & -0.035352982454655 \tabularnewline
68 & 7.2 & 7.13057191317991 & 0.0694280868200927 \tabularnewline
69 & 7.26 & 7.19256249223444 & 0.0674375077655576 \tabularnewline
70 & 7.26 & 7.25766753495562 & 0.00233246504438434 \tabularnewline
71 & 7.24 & 7.28418305420373 & -0.0441830542037298 \tabularnewline
72 & 7.26 & 7.28020483463727 & -0.0202048346372745 \tabularnewline
73 & 7.26 & 7.28920593677855 & -0.0292059367785482 \tabularnewline
74 & 7.3 & 7.29098951984159 & 0.00901048015841077 \tabularnewline
75 & 7.21 & 7.31608667016973 & -0.106086670169733 \tabularnewline
76 & 7.23 & 7.26593714897635 & -0.0359371489763518 \tabularnewline
77 & 7.33 & 7.25523650243761 & 0.074763497562393 \tabularnewline
78 & 7.33 & 7.31516982890026 & 0.0148301710997352 \tabularnewline
79 & 7.31 & 7.34038753970323 & -0.0303875397032298 \tabularnewline
80 & 7.3 & 7.33676313244952 & -0.0367631324495186 \tabularnewline
81 & 7.35 & 7.32700167083818 & 0.0229983291618163 \tabularnewline
82 & 7.4 & 7.35426498377573 & 0.0457350162242705 \tabularnewline
83 & 7.43 & 7.39797230311274 & 0.032027696887261 \tabularnewline
84 & 7.42 & 7.43556525984413 & -0.0155652598441263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232662&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]6.36[/C][C]6.31[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]4[/C][C]6.37[/C][C]6.32293785055035[/C][C]0.0470621494496477[/C][/ROW]
[ROW][C]5[/C][C]6.33[/C][C]6.33712767775654[/C][C]-0.00712767775654122[/C][/ROW]
[ROW][C]6[/C][C]6.34[/C][C]6.31861960607703[/C][C]0.0213803939229722[/C][/ROW]
[ROW][C]7[/C][C]6.42[/C][C]6.31843706464188[/C][C]0.101562935358124[/C][/ROW]
[ROW][C]8[/C][C]6.42[/C][C]6.37243825182379[/C][C]0.0475617481762063[/C][/ROW]
[ROW][C]9[/C][C]6.48[/C][C]6.39734002202763[/C][C]0.0826599779723693[/C][/ROW]
[ROW][C]10[/C][C]6.47[/C][C]6.44839487437867[/C][C]0.0216051256213339[/C][/ROW]
[ROW][C]11[/C][C]6.5[/C][C]6.46449866806368[/C][C]0.0355013319363158[/C][/ROW]
[ROW][C]12[/C][C]6.52[/C][C]6.49113392814657[/C][C]0.0288660718534279[/C][/ROW]
[ROW][C]13[/C][C]6.49[/C][C]6.51566123651103[/C][C]-0.0256612365110334[/C][/ROW]
[ROW][C]14[/C][C]6.51[/C][C]6.50610839845439[/C][C]0.00389160154561008[/C][/ROW]
[ROW][C]15[/C][C]6.52[/C][C]6.51438789524514[/C][C]0.00561210475486096[/C][/ROW]
[ROW][C]16[/C][C]6.54[/C][C]6.52404886011016[/C][C]0.0159511398898431[/C][/ROW]
[ROW][C]17[/C][C]6.59[/C][C]6.54087848679458[/C][C]0.0491215132054226[/C][/ROW]
[ROW][C]18[/C][C]6.6[/C][C]6.58057615283263[/C][C]0.0194238471673698[/C][/ROW]
[ROW][C]19[/C][C]6.59[/C][C]6.60384157933079[/C][C]-0.0138415793307898[/C][/ROW]
[ROW][C]20[/C][C]6.58[/C][C]6.60643136790932[/C][C]-0.026431367909316[/C][/ROW]
[ROW][C]21[/C][C]6.55[/C][C]6.5998451979337[/C][C]-0.0498451979337045[/C][/ROW]
[ROW][C]22[/C][C]6.57[/C][C]6.57615010596422[/C][C]-0.00615010596422216[/C][/ROW]
[ROW][C]23[/C][C]6.61[/C][C]6.5780620239051[/C][C]0.0319379760949046[/C][/ROW]
[ROW][C]24[/C][C]6.61[/C][C]6.60467268750813[/C][C]0.00532731249186913[/C][/ROW]
[ROW][C]25[/C][C]6.64[/C][C]6.61578931214547[/C][C]0.0242106878545254[/C][/ROW]
[ROW][C]26[/C][C]6.59[/C][C]6.63968508822813[/C][C]-0.0496850882281308[/C][/ROW]
[ROW][C]27[/C][C]6.67[/C][C]6.61644484129259[/C][C]0.053555158707411[/C][/ROW]
[ROW][C]28[/C][C]6.58[/C][C]6.65804759894627[/C][C]-0.0780475989462692[/C][/ROW]
[ROW][C]29[/C][C]6.66[/C][C]6.61637005122604[/C][C]0.0436299487739626[/C][/ROW]
[ROW][C]30[/C][C]6.7[/C][C]6.64987320906727[/C][C]0.0501267909327261[/C][/ROW]
[ROW][C]31[/C][C]6.65[/C][C]6.69043744744469[/C][C]-0.0404374474446882[/C][/ROW]
[ROW][C]32[/C][C]6.65[/C][C]6.67453724757842[/C][C]-0.0245372475784222[/C][/ROW]
[ROW][C]33[/C][C]6.73[/C][C]6.66653368522798[/C][C]0.0634663147720209[/C][/ROW]
[ROW][C]34[/C][C]6.74[/C][C]6.7149389320921[/C][C]0.0250610679078989[/C][/ROW]
[ROW][C]35[/C][C]6.74[/C][C]6.74209018502727[/C][C]-0.00209018502726632[/C][/ROW]
[ROW][C]36[/C][C]6.71[/C][C]6.75295290572791[/C][C]-0.0429529057279074[/C][/ROW]
[ROW][C]37[/C][C]6.78[/C][C]6.73676378147993[/C][C]0.0432362185200654[/C][/ROW]
[ROW][C]38[/C][C]6.83[/C][C]6.77461426575955[/C][C]0.0553857342404518[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.82322447013659[/C][C]-0.0232244701365936[/C][/ROW]
[ROW][C]40[/C][C]6.84[/C][C]6.82358027724057[/C][C]0.0164197227594283[/C][/ROW]
[ROW][C]41[/C][C]6.81[/C][C]6.84857150435944[/C][C]-0.0385715043594361[/C][/ROW]
[ROW][C]42[/C][C]6.75[/C][C]6.83838356878682[/C][C]-0.0883835687868171[/C][/ROW]
[ROW][C]43[/C][C]6.8[/C][C]6.79292280256057[/C][C]0.00707719743942636[/C][/ROW]
[ROW][C]44[/C][C]6.84[/C][C]6.80471337524415[/C][C]0.0352866247558499[/C][/ROW]
[ROW][C]45[/C][C]6.8[/C][C]6.83553824986906[/C][C]-0.035538249869064[/C][/ROW]
[ROW][C]46[/C][C]6.84[/C][C]6.82195612741116[/C][C]0.0180438725888381[/C][/ROW]
[ROW][C]47[/C][C]6.79[/C][C]6.84140617803081[/C][C]-0.0514061780308115[/C][/ROW]
[ROW][C]48[/C][C]6.8[/C][C]6.81625574786669[/C][C]-0.0162557478666949[/C][/ROW]
[ROW][C]49[/C][C]6.68[/C][C]6.81098396530791[/C][C]-0.130983965307911[/C][/ROW]
[ROW][C]50[/C][C]6.82[/C][C]6.72909792419662[/C][C]0.0909020758033803[/C][/ROW]
[ROW][C]51[/C][C]6.85[/C][C]6.78503114794718[/C][C]0.0649688520528189[/C][/ROW]
[ROW][C]52[/C][C]6.85[/C][C]6.82967533391764[/C][C]0.0203246660823639[/C][/ROW]
[ROW][C]53[/C][C]6.85[/C][C]6.84905136201251[/C][C]0.00094863798749234[/C][/ROW]
[ROW][C]54[/C][C]6.92[/C][C]6.8569589144807[/C][C]0.063041085519302[/C][/ROW]
[ROW][C]55[/C][C]6.91[/C][C]6.90583077408779[/C][C]0.00416922591220725[/C][/ROW]
[ROW][C]56[/C][C]6.94[/C][C]6.91993900841238[/C][C]0.0200609915876182[/C][/ROW]
[ROW][C]57[/C][C]6.99[/C][C]6.94478182679352[/C][C]0.045218173206484[/C][/ROW]
[ROW][C]58[/C][C]7.05[/C][C]6.98747592544196[/C][C]0.0625240745580422[/C][/ROW]
[ROW][C]59[/C][C]6.98[/C][C]7.04445289130711[/C][C]-0.0644528913071136[/C][/ROW]
[ROW][C]60[/C][C]6.91[/C][C]7.02176855821097[/C][C]-0.111768558210973[/C][/ROW]
[ROW][C]61[/C][C]6.98[/C][C]6.96380607567703[/C][C]0.016193924322975[/C][/ROW]
[ROW][C]62[/C][C]7.06[/C][C]6.98301496305654[/C][C]0.0769850369434639[/C][/ROW]
[ROW][C]63[/C][C]7.05[/C][C]7.04330272202307[/C][C]0.00669727797693387[/C][/ROW]
[ROW][C]64[/C][C]6.95[/C][C]7.06219542485242[/C][C]-0.112195424852418[/C][/ROW]
[ROW][C]65[/C][C]7.09[/C][C]7.00319365166156[/C][C]0.0868063483384418[/C][/ROW]
[ROW][C]66[/C][C]7.15[/C][C]7.06813366806663[/C][C]0.0818663319333748[/C][/ROW]
[ROW][C]67[/C][C]7.1[/C][C]7.13535298245465[/C][C]-0.035352982454655[/C][/ROW]
[ROW][C]68[/C][C]7.2[/C][C]7.13057191317991[/C][C]0.0694280868200927[/C][/ROW]
[ROW][C]69[/C][C]7.26[/C][C]7.19256249223444[/C][C]0.0674375077655576[/C][/ROW]
[ROW][C]70[/C][C]7.26[/C][C]7.25766753495562[/C][C]0.00233246504438434[/C][/ROW]
[ROW][C]71[/C][C]7.24[/C][C]7.28418305420373[/C][C]-0.0441830542037298[/C][/ROW]
[ROW][C]72[/C][C]7.26[/C][C]7.28020483463727[/C][C]-0.0202048346372745[/C][/ROW]
[ROW][C]73[/C][C]7.26[/C][C]7.28920593677855[/C][C]-0.0292059367785482[/C][/ROW]
[ROW][C]74[/C][C]7.3[/C][C]7.29098951984159[/C][C]0.00901048015841077[/C][/ROW]
[ROW][C]75[/C][C]7.21[/C][C]7.31608667016973[/C][C]-0.106086670169733[/C][/ROW]
[ROW][C]76[/C][C]7.23[/C][C]7.26593714897635[/C][C]-0.0359371489763518[/C][/ROW]
[ROW][C]77[/C][C]7.33[/C][C]7.25523650243761[/C][C]0.074763497562393[/C][/ROW]
[ROW][C]78[/C][C]7.33[/C][C]7.31516982890026[/C][C]0.0148301710997352[/C][/ROW]
[ROW][C]79[/C][C]7.31[/C][C]7.34038753970323[/C][C]-0.0303875397032298[/C][/ROW]
[ROW][C]80[/C][C]7.3[/C][C]7.33676313244952[/C][C]-0.0367631324495186[/C][/ROW]
[ROW][C]81[/C][C]7.35[/C][C]7.32700167083818[/C][C]0.0229983291618163[/C][/ROW]
[ROW][C]82[/C][C]7.4[/C][C]7.35426498377573[/C][C]0.0457350162242705[/C][/ROW]
[ROW][C]83[/C][C]7.43[/C][C]7.39797230311274[/C][C]0.032027696887261[/C][/ROW]
[ROW][C]84[/C][C]7.42[/C][C]7.43556525984413[/C][C]-0.0155652598441263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232662&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232662&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
36.366.310.0499999999999998
46.376.322937850550350.0470621494496477
56.336.33712767775654-0.00712767775654122
66.346.318619606077030.0213803939229722
76.426.318437064641880.101562935358124
86.426.372438251823790.0475617481762063
96.486.397340022027630.0826599779723693
106.476.448394874378670.0216051256213339
116.56.464498668063680.0355013319363158
126.526.491133928146570.0288660718534279
136.496.51566123651103-0.0256612365110334
146.516.506108398454390.00389160154561008
156.526.514387895245140.00561210475486096
166.546.524048860110160.0159511398898431
176.596.540878486794580.0491215132054226
186.66.580576152832630.0194238471673698
196.596.60384157933079-0.0138415793307898
206.586.60643136790932-0.026431367909316
216.556.5998451979337-0.0498451979337045
226.576.57615010596422-0.00615010596422216
236.616.57806202390510.0319379760949046
246.616.604672687508130.00532731249186913
256.646.615789312145470.0242106878545254
266.596.63968508822813-0.0496850882281308
276.676.616444841292590.053555158707411
286.586.65804759894627-0.0780475989462692
296.666.616370051226040.0436299487739626
306.76.649873209067270.0501267909327261
316.656.69043744744469-0.0404374474446882
326.656.67453724757842-0.0245372475784222
336.736.666533685227980.0634663147720209
346.746.71493893209210.0250610679078989
356.746.74209018502727-0.00209018502726632
366.716.75295290572791-0.0429529057279074
376.786.736763781479930.0432362185200654
386.836.774614265759550.0553857342404518
396.86.82322447013659-0.0232244701365936
406.846.823580277240570.0164197227594283
416.816.84857150435944-0.0385715043594361
426.756.83838356878682-0.0883835687868171
436.86.792922802560570.00707719743942636
446.846.804713375244150.0352866247558499
456.86.83553824986906-0.035538249869064
466.846.821956127411160.0180438725888381
476.796.84140617803081-0.0514061780308115
486.86.81625574786669-0.0162557478666949
496.686.81098396530791-0.130983965307911
506.826.729097924196620.0909020758033803
516.856.785031147947180.0649688520528189
526.856.829675333917640.0203246660823639
536.856.849051362012510.00094863798749234
546.926.85695891448070.063041085519302
556.916.905830774087790.00416922591220725
566.946.919939008412380.0200609915876182
576.996.944781826793520.045218173206484
587.056.987475925441960.0625240745580422
596.987.04445289130711-0.0644528913071136
606.917.02176855821097-0.111768558210973
616.986.963806075677030.016193924322975
627.066.983014963056540.0769850369434639
637.057.043302722023070.00669727797693387
646.957.06219542485242-0.112195424852418
657.097.003193651661560.0868063483384418
667.157.068133668066630.0818663319333748
677.17.13535298245465-0.035352982454655
687.27.130571913179910.0694280868200927
697.267.192562492234440.0674375077655576
707.267.257667534955620.00233246504438434
717.247.28418305420373-0.0441830542037298
727.267.28020483463727-0.0202048346372745
737.267.28920593677855-0.0292059367785482
747.37.290989519841590.00901048015841077
757.217.31608667016973-0.106086670169733
767.237.26593714897635-0.0359371489763518
777.337.255236502437610.074763497562393
787.337.315169828900260.0148301710997352
797.317.34038753970323-0.0303875397032298
807.37.33676313244952-0.0367631324495186
817.357.327001670838180.0229983291618163
827.47.354264983775730.0457350162242705
837.437.397972303112740.032027696887261
847.427.43556525984413-0.0155652598441263







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
857.443847664257467.345071479265497.54262384924942
867.461391567705017.343108960689687.57967417472035
877.478935471152577.340790996581127.61707994572402
887.496479374600137.338001012544397.65495773665588
897.514023278047697.334678482752247.69336807334314
907.531567181495257.330791975717287.73234238727322
917.549111084942817.326326281762257.77189588812336
927.566654988390377.321275678463727.81203429831702
937.584198891837937.31564016602127.85275761765465
947.601742795285497.309423255626677.89406233494431
957.619286698733047.302630619960397.9359427775057
967.63683060218067.295269245458617.9783919589026

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 7.44384766425746 & 7.34507147926549 & 7.54262384924942 \tabularnewline
86 & 7.46139156770501 & 7.34310896068968 & 7.57967417472035 \tabularnewline
87 & 7.47893547115257 & 7.34079099658112 & 7.61707994572402 \tabularnewline
88 & 7.49647937460013 & 7.33800101254439 & 7.65495773665588 \tabularnewline
89 & 7.51402327804769 & 7.33467848275224 & 7.69336807334314 \tabularnewline
90 & 7.53156718149525 & 7.33079197571728 & 7.73234238727322 \tabularnewline
91 & 7.54911108494281 & 7.32632628176225 & 7.77189588812336 \tabularnewline
92 & 7.56665498839037 & 7.32127567846372 & 7.81203429831702 \tabularnewline
93 & 7.58419889183793 & 7.3156401660212 & 7.85275761765465 \tabularnewline
94 & 7.60174279528549 & 7.30942325562667 & 7.89406233494431 \tabularnewline
95 & 7.61928669873304 & 7.30263061996039 & 7.9359427775057 \tabularnewline
96 & 7.6368306021806 & 7.29526924545861 & 7.9783919589026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232662&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]7.44384766425746[/C][C]7.34507147926549[/C][C]7.54262384924942[/C][/ROW]
[ROW][C]86[/C][C]7.46139156770501[/C][C]7.34310896068968[/C][C]7.57967417472035[/C][/ROW]
[ROW][C]87[/C][C]7.47893547115257[/C][C]7.34079099658112[/C][C]7.61707994572402[/C][/ROW]
[ROW][C]88[/C][C]7.49647937460013[/C][C]7.33800101254439[/C][C]7.65495773665588[/C][/ROW]
[ROW][C]89[/C][C]7.51402327804769[/C][C]7.33467848275224[/C][C]7.69336807334314[/C][/ROW]
[ROW][C]90[/C][C]7.53156718149525[/C][C]7.33079197571728[/C][C]7.73234238727322[/C][/ROW]
[ROW][C]91[/C][C]7.54911108494281[/C][C]7.32632628176225[/C][C]7.77189588812336[/C][/ROW]
[ROW][C]92[/C][C]7.56665498839037[/C][C]7.32127567846372[/C][C]7.81203429831702[/C][/ROW]
[ROW][C]93[/C][C]7.58419889183793[/C][C]7.3156401660212[/C][C]7.85275761765465[/C][/ROW]
[ROW][C]94[/C][C]7.60174279528549[/C][C]7.30942325562667[/C][C]7.89406233494431[/C][/ROW]
[ROW][C]95[/C][C]7.61928669873304[/C][C]7.30263061996039[/C][C]7.9359427775057[/C][/ROW]
[ROW][C]96[/C][C]7.6368306021806[/C][C]7.29526924545861[/C][C]7.9783919589026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232662&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232662&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
857.443847664257467.345071479265497.54262384924942
867.461391567705017.343108960689687.57967417472035
877.478935471152577.340790996581127.61707994572402
887.496479374600137.338001012544397.65495773665588
897.514023278047697.334678482752247.69336807334314
907.531567181495257.330791975717287.73234238727322
917.549111084942817.326326281762257.77189588812336
927.566654988390377.321275678463727.81203429831702
937.584198891837937.31564016602127.85275761765465
947.601742795285497.309423255626677.89406233494431
957.619286698733047.302630619960397.9359427775057
967.63683060218067.295269245458617.9783919589026



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')