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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 10 Dec 2009 10:13:00 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/10/t1260465218205sr33bl7h3etv.htm/, Retrieved Fri, 19 Apr 2024 14:49:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65614, Retrieved Fri, 19 Apr 2024 14:49:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D    [Exponential Smoothing] [workshop 9] [2009-12-04 13:54:20] [3d8acb8ffdb376c5fec19e610f8198c2]
-    D        [Exponential Smoothing] [verbetering] [2009-12-10 17:13:00] [5edea6bc5a9a9483633d9320282a2734] [Current]
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Dataseries X:
102.86
102.55
102.28
102.26
102.57
103.08
102.76
102.51
102.87
103.14
103.12
103.16
102.48
102.57
102.88
102.63
102.38
101.69
101.96
102.19
101.87
101.6
101.63
101.22
101.21
101.49
101.64
101.66
101.77
101.82
101.78
101.28
101.29
101.37
101.12
101.51
102.24
102.94
103.09
103.46
103.64
104.39
104.15
105.21
105.8
105.91
105.39
105.46
104.72
103.14
102.63
102.32
101.93
100.62
100.6
99.63
98.9
98.32
99.22
98.81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65614&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]1 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=65614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65614&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.819828902860289
beta0.380658228872049
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.819828902860289 \tabularnewline
beta & 0.380658228872049 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65614&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]0.819828902860289[/C][/ROW]
[ROW][C]beta[/C][C]0.380658228872049[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65614&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
alpha0.819828902860289
beta0.380658228872049
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.48102.641041747874-0.161041747874194
14102.57102.5455929909790.0244070090205071
15102.88102.8379400825730.0420599174272809
16102.63102.648872734969-0.0188727349688236
17102.38102.424351424615-0.044351424614689
18101.69101.741505230615-0.0515052306153052
19101.96102.078938340214-0.118938340213560
20102.19101.5960918941910.593908105808836
21101.87102.449108102370-0.579108102369659
22101.6102.054102773546-0.454102773545628
23101.63101.3653585162290.264641483771214
24101.22101.479890564252-0.259890564251990
25101.21100.3739034275110.836096572488913
26101.49101.2016617854100.288338214589800
27101.64101.867100895439-0.227100895439463
28101.66101.5216853538810.138314646119412
29101.77101.545072346280.224927653719917
30101.82101.2905035057360.529496494264279
31101.78102.480721223983-0.700721223982526
32101.28101.855579183130-0.575579183130472
33101.29101.378370479508-0.0883704795080575
34101.37101.400813155179-0.0308131551786772
35101.12101.314660205805-0.194660205805420
36101.51100.9410140726380.568985927361908
37102.24100.9509245632531.28907543674656
38102.94102.4336907191310.506309280869218
39103.09103.639610313187-0.549610313187472
40103.46103.4443848039870.0156151960129591
41103.64103.692209483583-0.0522094835825868
42104.39103.4796996996200.910300300379731
43104.15105.109346253215-0.959346253215443
44105.21104.5544022387130.655597761286984
45105.8105.829732951958-0.0297329519584082
46105.91106.589733235301-0.679733235301129
47105.39106.410749210747-1.02074921074669
48105.46105.711338035133-0.251338035132790
49104.72105.116760392585-0.396760392584511
50103.14104.499455246477-1.35945524647687
51102.63102.827331842622-0.197331842621836
52102.32101.9742124481070.345787551893338
53101.93101.5376606013590.392339398641354
54100.62101.064479808940-0.444479808939647
55100.6100.0223256679240.577674332076143
5699.63100.262918510549-0.632918510548976
5798.999.20254370552-0.302543705519966
5898.3298.3732347798924-0.0532347798924491
5999.2297.60113985442481.61886014557516
6098.8198.9661073748992-0.156107374899179

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.48 & 102.641041747874 & -0.161041747874194 \tabularnewline
14 & 102.57 & 102.545592990979 & 0.0244070090205071 \tabularnewline
15 & 102.88 & 102.837940082573 & 0.0420599174272809 \tabularnewline
16 & 102.63 & 102.648872734969 & -0.0188727349688236 \tabularnewline
17 & 102.38 & 102.424351424615 & -0.044351424614689 \tabularnewline
18 & 101.69 & 101.741505230615 & -0.0515052306153052 \tabularnewline
19 & 101.96 & 102.078938340214 & -0.118938340213560 \tabularnewline
20 & 102.19 & 101.596091894191 & 0.593908105808836 \tabularnewline
21 & 101.87 & 102.449108102370 & -0.579108102369659 \tabularnewline
22 & 101.6 & 102.054102773546 & -0.454102773545628 \tabularnewline
23 & 101.63 & 101.365358516229 & 0.264641483771214 \tabularnewline
24 & 101.22 & 101.479890564252 & -0.259890564251990 \tabularnewline
25 & 101.21 & 100.373903427511 & 0.836096572488913 \tabularnewline
26 & 101.49 & 101.201661785410 & 0.288338214589800 \tabularnewline
27 & 101.64 & 101.867100895439 & -0.227100895439463 \tabularnewline
28 & 101.66 & 101.521685353881 & 0.138314646119412 \tabularnewline
29 & 101.77 & 101.54507234628 & 0.224927653719917 \tabularnewline
30 & 101.82 & 101.290503505736 & 0.529496494264279 \tabularnewline
31 & 101.78 & 102.480721223983 & -0.700721223982526 \tabularnewline
32 & 101.28 & 101.855579183130 & -0.575579183130472 \tabularnewline
33 & 101.29 & 101.378370479508 & -0.0883704795080575 \tabularnewline
34 & 101.37 & 101.400813155179 & -0.0308131551786772 \tabularnewline
35 & 101.12 & 101.314660205805 & -0.194660205805420 \tabularnewline
36 & 101.51 & 100.941014072638 & 0.568985927361908 \tabularnewline
37 & 102.24 & 100.950924563253 & 1.28907543674656 \tabularnewline
38 & 102.94 & 102.433690719131 & 0.506309280869218 \tabularnewline
39 & 103.09 & 103.639610313187 & -0.549610313187472 \tabularnewline
40 & 103.46 & 103.444384803987 & 0.0156151960129591 \tabularnewline
41 & 103.64 & 103.692209483583 & -0.0522094835825868 \tabularnewline
42 & 104.39 & 103.479699699620 & 0.910300300379731 \tabularnewline
43 & 104.15 & 105.109346253215 & -0.959346253215443 \tabularnewline
44 & 105.21 & 104.554402238713 & 0.655597761286984 \tabularnewline
45 & 105.8 & 105.829732951958 & -0.0297329519584082 \tabularnewline
46 & 105.91 & 106.589733235301 & -0.679733235301129 \tabularnewline
47 & 105.39 & 106.410749210747 & -1.02074921074669 \tabularnewline
48 & 105.46 & 105.711338035133 & -0.251338035132790 \tabularnewline
49 & 104.72 & 105.116760392585 & -0.396760392584511 \tabularnewline
50 & 103.14 & 104.499455246477 & -1.35945524647687 \tabularnewline
51 & 102.63 & 102.827331842622 & -0.197331842621836 \tabularnewline
52 & 102.32 & 101.974212448107 & 0.345787551893338 \tabularnewline
53 & 101.93 & 101.537660601359 & 0.392339398641354 \tabularnewline
54 & 100.62 & 101.064479808940 & -0.444479808939647 \tabularnewline
55 & 100.6 & 100.022325667924 & 0.577674332076143 \tabularnewline
56 & 99.63 & 100.262918510549 & -0.632918510548976 \tabularnewline
57 & 98.9 & 99.20254370552 & -0.302543705519966 \tabularnewline
58 & 98.32 & 98.3732347798924 & -0.0532347798924491 \tabularnewline
59 & 99.22 & 97.6011398544248 & 1.61886014557516 \tabularnewline
60 & 98.81 & 98.9661073748992 & -0.156107374899179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65614&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]102.48[/C][C]102.641041747874[/C][C]-0.161041747874194[/C][/ROW]
[ROW][C]14[/C][C]102.57[/C][C]102.545592990979[/C][C]0.0244070090205071[/C][/ROW]
[ROW][C]15[/C][C]102.88[/C][C]102.837940082573[/C][C]0.0420599174272809[/C][/ROW]
[ROW][C]16[/C][C]102.63[/C][C]102.648872734969[/C][C]-0.0188727349688236[/C][/ROW]
[ROW][C]17[/C][C]102.38[/C][C]102.424351424615[/C][C]-0.044351424614689[/C][/ROW]
[ROW][C]18[/C][C]101.69[/C][C]101.741505230615[/C][C]-0.0515052306153052[/C][/ROW]
[ROW][C]19[/C][C]101.96[/C][C]102.078938340214[/C][C]-0.118938340213560[/C][/ROW]
[ROW][C]20[/C][C]102.19[/C][C]101.596091894191[/C][C]0.593908105808836[/C][/ROW]
[ROW][C]21[/C][C]101.87[/C][C]102.449108102370[/C][C]-0.579108102369659[/C][/ROW]
[ROW][C]22[/C][C]101.6[/C][C]102.054102773546[/C][C]-0.454102773545628[/C][/ROW]
[ROW][C]23[/C][C]101.63[/C][C]101.365358516229[/C][C]0.264641483771214[/C][/ROW]
[ROW][C]24[/C][C]101.22[/C][C]101.479890564252[/C][C]-0.259890564251990[/C][/ROW]
[ROW][C]25[/C][C]101.21[/C][C]100.373903427511[/C][C]0.836096572488913[/C][/ROW]
[ROW][C]26[/C][C]101.49[/C][C]101.201661785410[/C][C]0.288338214589800[/C][/ROW]
[ROW][C]27[/C][C]101.64[/C][C]101.867100895439[/C][C]-0.227100895439463[/C][/ROW]
[ROW][C]28[/C][C]101.66[/C][C]101.521685353881[/C][C]0.138314646119412[/C][/ROW]
[ROW][C]29[/C][C]101.77[/C][C]101.54507234628[/C][C]0.224927653719917[/C][/ROW]
[ROW][C]30[/C][C]101.82[/C][C]101.290503505736[/C][C]0.529496494264279[/C][/ROW]
[ROW][C]31[/C][C]101.78[/C][C]102.480721223983[/C][C]-0.700721223982526[/C][/ROW]
[ROW][C]32[/C][C]101.28[/C][C]101.855579183130[/C][C]-0.575579183130472[/C][/ROW]
[ROW][C]33[/C][C]101.29[/C][C]101.378370479508[/C][C]-0.0883704795080575[/C][/ROW]
[ROW][C]34[/C][C]101.37[/C][C]101.400813155179[/C][C]-0.0308131551786772[/C][/ROW]
[ROW][C]35[/C][C]101.12[/C][C]101.314660205805[/C][C]-0.194660205805420[/C][/ROW]
[ROW][C]36[/C][C]101.51[/C][C]100.941014072638[/C][C]0.568985927361908[/C][/ROW]
[ROW][C]37[/C][C]102.24[/C][C]100.950924563253[/C][C]1.28907543674656[/C][/ROW]
[ROW][C]38[/C][C]102.94[/C][C]102.433690719131[/C][C]0.506309280869218[/C][/ROW]
[ROW][C]39[/C][C]103.09[/C][C]103.639610313187[/C][C]-0.549610313187472[/C][/ROW]
[ROW][C]40[/C][C]103.46[/C][C]103.444384803987[/C][C]0.0156151960129591[/C][/ROW]
[ROW][C]41[/C][C]103.64[/C][C]103.692209483583[/C][C]-0.0522094835825868[/C][/ROW]
[ROW][C]42[/C][C]104.39[/C][C]103.479699699620[/C][C]0.910300300379731[/C][/ROW]
[ROW][C]43[/C][C]104.15[/C][C]105.109346253215[/C][C]-0.959346253215443[/C][/ROW]
[ROW][C]44[/C][C]105.21[/C][C]104.554402238713[/C][C]0.655597761286984[/C][/ROW]
[ROW][C]45[/C][C]105.8[/C][C]105.829732951958[/C][C]-0.0297329519584082[/C][/ROW]
[ROW][C]46[/C][C]105.91[/C][C]106.589733235301[/C][C]-0.679733235301129[/C][/ROW]
[ROW][C]47[/C][C]105.39[/C][C]106.410749210747[/C][C]-1.02074921074669[/C][/ROW]
[ROW][C]48[/C][C]105.46[/C][C]105.711338035133[/C][C]-0.251338035132790[/C][/ROW]
[ROW][C]49[/C][C]104.72[/C][C]105.116760392585[/C][C]-0.396760392584511[/C][/ROW]
[ROW][C]50[/C][C]103.14[/C][C]104.499455246477[/C][C]-1.35945524647687[/C][/ROW]
[ROW][C]51[/C][C]102.63[/C][C]102.827331842622[/C][C]-0.197331842621836[/C][/ROW]
[ROW][C]52[/C][C]102.32[/C][C]101.974212448107[/C][C]0.345787551893338[/C][/ROW]
[ROW][C]53[/C][C]101.93[/C][C]101.537660601359[/C][C]0.392339398641354[/C][/ROW]
[ROW][C]54[/C][C]100.62[/C][C]101.064479808940[/C][C]-0.444479808939647[/C][/ROW]
[ROW][C]55[/C][C]100.6[/C][C]100.022325667924[/C][C]0.577674332076143[/C][/ROW]
[ROW][C]56[/C][C]99.63[/C][C]100.262918510549[/C][C]-0.632918510548976[/C][/ROW]
[ROW][C]57[/C][C]98.9[/C][C]99.20254370552[/C][C]-0.302543705519966[/C][/ROW]
[ROW][C]58[/C][C]98.32[/C][C]98.3732347798924[/C][C]-0.0532347798924491[/C][/ROW]
[ROW][C]59[/C][C]99.22[/C][C]97.6011398544248[/C][C]1.61886014557516[/C][/ROW]
[ROW][C]60[/C][C]98.81[/C][C]98.9661073748992[/C][C]-0.156107374899179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65614&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
13102.48102.641041747874-0.161041747874194
14102.57102.5455929909790.0244070090205071
15102.88102.8379400825730.0420599174272809
16102.63102.648872734969-0.0188727349688236
17102.38102.424351424615-0.044351424614689
18101.69101.741505230615-0.0515052306153052
19101.96102.078938340214-0.118938340213560
20102.19101.5960918941910.593908105808836
21101.87102.449108102370-0.579108102369659
22101.6102.054102773546-0.454102773545628
23101.63101.3653585162290.264641483771214
24101.22101.479890564252-0.259890564251990
25101.21100.3739034275110.836096572488913
26101.49101.2016617854100.288338214589800
27101.64101.867100895439-0.227100895439463
28101.66101.5216853538810.138314646119412
29101.77101.545072346280.224927653719917
30101.82101.2905035057360.529496494264279
31101.78102.480721223983-0.700721223982526
32101.28101.855579183130-0.575579183130472
33101.29101.378370479508-0.0883704795080575
34101.37101.400813155179-0.0308131551786772
35101.12101.314660205805-0.194660205805420
36101.51100.9410140726380.568985927361908
37102.24100.9509245632531.28907543674656
38102.94102.4336907191310.506309280869218
39103.09103.639610313187-0.549610313187472
40103.46103.4443848039870.0156151960129591
41103.64103.692209483583-0.0522094835825868
42104.39103.4796996996200.910300300379731
43104.15105.109346253215-0.959346253215443
44105.21104.5544022387130.655597761286984
45105.8105.829732951958-0.0297329519584082
46105.91106.589733235301-0.679733235301129
47105.39106.410749210747-1.02074921074669
48105.46105.711338035133-0.251338035132790
49104.72105.116760392585-0.396760392584511
50103.14104.499455246477-1.35945524647687
51102.63102.827331842622-0.197331842621836
52102.32101.9742124481070.345787551893338
53101.93101.5376606013590.392339398641354
54100.62101.064479808940-0.444479808939647
55100.6100.0223256679240.577674332076143
5699.63100.262918510549-0.632918510548976
5798.999.20254370552-0.302543705519966
5898.3298.3732347798924-0.0532347798924491
5999.2297.60113985442481.61886014557516
6098.8198.9661073748992-0.156107374899179







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6198.253304037112497.13128885667499.375319217551
6297.734543561324496.042166674265799.4269204483831
6397.728990286288295.3819957589803100.075984813596
6497.55018273387094.481777828534100.618587639206
6597.155532339927293.3103004670476101.000764212807
6696.420288593716291.7583609879724101.08221619946
6796.24873991361990.6930365262981101.804443300940
6895.944871845842489.4516267574393102.438116934245
6995.802065503317488.3115404178762103.292590588759
7095.69972883430787.1598850147617104.239572653852
7195.718279638863886.069524657624105.367034620104
7295.389133649925183.9709845580115106.807282741839

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 98.2533040371124 & 97.131288856674 & 99.375319217551 \tabularnewline
62 & 97.7345435613244 & 96.0421666742657 & 99.4269204483831 \tabularnewline
63 & 97.7289902862882 & 95.3819957589803 & 100.075984813596 \tabularnewline
64 & 97.550182733870 & 94.481777828534 & 100.618587639206 \tabularnewline
65 & 97.1555323399272 & 93.3103004670476 & 101.000764212807 \tabularnewline
66 & 96.4202885937162 & 91.7583609879724 & 101.08221619946 \tabularnewline
67 & 96.248739913619 & 90.6930365262981 & 101.804443300940 \tabularnewline
68 & 95.9448718458424 & 89.4516267574393 & 102.438116934245 \tabularnewline
69 & 95.8020655033174 & 88.3115404178762 & 103.292590588759 \tabularnewline
70 & 95.699728834307 & 87.1598850147617 & 104.239572653852 \tabularnewline
71 & 95.7182796388638 & 86.069524657624 & 105.367034620104 \tabularnewline
72 & 95.3891336499251 & 83.9709845580115 & 106.807282741839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65614&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]61[/C][C]98.2533040371124[/C][C]97.131288856674[/C][C]99.375319217551[/C][/ROW]
[ROW][C]62[/C][C]97.7345435613244[/C][C]96.0421666742657[/C][C]99.4269204483831[/C][/ROW]
[ROW][C]63[/C][C]97.7289902862882[/C][C]95.3819957589803[/C][C]100.075984813596[/C][/ROW]
[ROW][C]64[/C][C]97.550182733870[/C][C]94.481777828534[/C][C]100.618587639206[/C][/ROW]
[ROW][C]65[/C][C]97.1555323399272[/C][C]93.3103004670476[/C][C]101.000764212807[/C][/ROW]
[ROW][C]66[/C][C]96.4202885937162[/C][C]91.7583609879724[/C][C]101.08221619946[/C][/ROW]
[ROW][C]67[/C][C]96.248739913619[/C][C]90.6930365262981[/C][C]101.804443300940[/C][/ROW]
[ROW][C]68[/C][C]95.9448718458424[/C][C]89.4516267574393[/C][C]102.438116934245[/C][/ROW]
[ROW][C]69[/C][C]95.8020655033174[/C][C]88.3115404178762[/C][C]103.292590588759[/C][/ROW]
[ROW][C]70[/C][C]95.699728834307[/C][C]87.1598850147617[/C][C]104.239572653852[/C][/ROW]
[ROW][C]71[/C][C]95.7182796388638[/C][C]86.069524657624[/C][C]105.367034620104[/C][/ROW]
[ROW][C]72[/C][C]95.3891336499251[/C][C]83.9709845580115[/C][C]106.807282741839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65614&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
6198.253304037112497.13128885667499.375319217551
6297.734543561324496.042166674265799.4269204483831
6397.728990286288295.3819957589803100.075984813596
6497.55018273387094.481777828534100.618587639206
6597.155532339927293.3103004670476101.000764212807
6696.420288593716291.7583609879724101.08221619946
6796.24873991361990.6930365262981101.804443300940
6895.944871845842489.4516267574393102.438116934245
6995.802065503317488.3115404178762103.292590588759
7095.69972883430787.1598850147617104.239572653852
7195.718279638863886.069524657624105.367034620104
7295.389133649925183.9709845580115106.807282741839



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')