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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 computationSun, 29 Nov 2009 06:45:21 -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/Nov/29/t12595024104vrvymxh15lfdie.htm/, Retrieved Thu, 25 Apr 2024 22:28:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61599, Retrieved Thu, 25 Apr 2024 22:28:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact203
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] [ws 9 exp smoo] [2009-11-29 13:45:21] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
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Dataseries X:
103,63
103,64
103,66
103,77
103,88
103,91
103,91
103,92
104,05
104,23
104,30
104,31
104,31
104,34
104,55
104,65
104,73
104,75
104,75
104,76
104,94
105,29
105,38
105,43
105,43
105,42
105,52
105,69
105,72
105,74
105,74
105,74
105,95
106,17
106,34
106,37
106,37
106,36
106,44
106,29
106,23
106,23
106,23
106,23
106,34
106,44
106,44
106,48
106,50
106,57
106,40
106,37
106,25
106,21
106,21
106,24
106,19
106,08
106,13
106,09




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=61599&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=61599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61599&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
alpha1
beta0.11626637835925
gamma0.267447016888359

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.11626637835925 \tabularnewline
gamma & 0.267447016888359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61599&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.11626637835925[/C][/ROW]
[ROW][C]gamma[/C][C]0.267447016888359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61599&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
alpha1
beta0.11626637835925
gamma0.267447016888359







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.31103.8884974732470.421502526752732
14104.34104.392354346072-0.0523543460724625
15104.55104.594244401859-0.0442444018589043
16104.65104.679935848224-0.0299358482235448
17104.73104.748532918829-0.0185329188294361
18104.75104.763867595833-0.0138675958332186
19104.75104.827628086965-0.077628086965305
20104.76104.796975461544-0.0369754615441167
21104.94104.9148488199900.0251511800095301
22105.29105.1406887443920.14931125560787
23105.38105.398785558175-0.0187855581754945
24105.43105.4276430129730.00235698702741161
25105.43105.468182114807-0.0381821148070998
26105.42105.494052018153-0.0740520181529405
27105.52105.655248452267-0.135248452267049
28105.69105.6190999172190.0709000827806676
29105.72105.769157465029-0.049157465028685
30105.74105.7303614068390.00963859316080118
31105.74105.797289109625-0.0572891096250885
32105.74105.768805327199-0.0288053271987820
33105.95105.8786717369850.0713282630153458
34106.17106.1402983309690.0297016690309704
35106.34106.2534402290950.0865597709048416
36106.37106.374015231714-0.00401523171397855
37106.37106.393748423012-0.0237484230123073
38106.36106.421571710426-0.0615717104262217
39106.44106.585807201723-0.145807201723457
40106.29106.527351257900-0.237351257900372
41106.23106.321356340546-0.0913563405458433
42106.23106.1873938886050.042606111395429
43106.23106.238392940783-0.00839294078335229
44106.23106.2155128480460.0144871519542136
45106.34106.3309138081400.00908619185990744
46106.44106.485354870176-0.0453548701762827
47106.44106.469367742734-0.0293677427344932
48106.48106.4064509904220.0735490095784854
49106.5106.4452256781890.0547743218106547
50106.57106.5022214093480.0677785906520967
51106.4106.761778007652-0.361778007651651
52106.37106.427916602032-0.0579166020315967
53106.25106.362787415179-0.112787415179270
54106.21106.1663546888680.0436453111324369
55106.21106.177503505870.0324964941300294
56106.24106.1593981021460.0806018978543932
57106.19106.312465538121-0.122465538121318
58106.08106.291407666463-0.211407666462961
59106.13106.0462759294100.0837240705904776
60106.09106.0467091166210.043290883378603

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.31 & 103.888497473247 & 0.421502526752732 \tabularnewline
14 & 104.34 & 104.392354346072 & -0.0523543460724625 \tabularnewline
15 & 104.55 & 104.594244401859 & -0.0442444018589043 \tabularnewline
16 & 104.65 & 104.679935848224 & -0.0299358482235448 \tabularnewline
17 & 104.73 & 104.748532918829 & -0.0185329188294361 \tabularnewline
18 & 104.75 & 104.763867595833 & -0.0138675958332186 \tabularnewline
19 & 104.75 & 104.827628086965 & -0.077628086965305 \tabularnewline
20 & 104.76 & 104.796975461544 & -0.0369754615441167 \tabularnewline
21 & 104.94 & 104.914848819990 & 0.0251511800095301 \tabularnewline
22 & 105.29 & 105.140688744392 & 0.14931125560787 \tabularnewline
23 & 105.38 & 105.398785558175 & -0.0187855581754945 \tabularnewline
24 & 105.43 & 105.427643012973 & 0.00235698702741161 \tabularnewline
25 & 105.43 & 105.468182114807 & -0.0381821148070998 \tabularnewline
26 & 105.42 & 105.494052018153 & -0.0740520181529405 \tabularnewline
27 & 105.52 & 105.655248452267 & -0.135248452267049 \tabularnewline
28 & 105.69 & 105.619099917219 & 0.0709000827806676 \tabularnewline
29 & 105.72 & 105.769157465029 & -0.049157465028685 \tabularnewline
30 & 105.74 & 105.730361406839 & 0.00963859316080118 \tabularnewline
31 & 105.74 & 105.797289109625 & -0.0572891096250885 \tabularnewline
32 & 105.74 & 105.768805327199 & -0.0288053271987820 \tabularnewline
33 & 105.95 & 105.878671736985 & 0.0713282630153458 \tabularnewline
34 & 106.17 & 106.140298330969 & 0.0297016690309704 \tabularnewline
35 & 106.34 & 106.253440229095 & 0.0865597709048416 \tabularnewline
36 & 106.37 & 106.374015231714 & -0.00401523171397855 \tabularnewline
37 & 106.37 & 106.393748423012 & -0.0237484230123073 \tabularnewline
38 & 106.36 & 106.421571710426 & -0.0615717104262217 \tabularnewline
39 & 106.44 & 106.585807201723 & -0.145807201723457 \tabularnewline
40 & 106.29 & 106.527351257900 & -0.237351257900372 \tabularnewline
41 & 106.23 & 106.321356340546 & -0.0913563405458433 \tabularnewline
42 & 106.23 & 106.187393888605 & 0.042606111395429 \tabularnewline
43 & 106.23 & 106.238392940783 & -0.00839294078335229 \tabularnewline
44 & 106.23 & 106.215512848046 & 0.0144871519542136 \tabularnewline
45 & 106.34 & 106.330913808140 & 0.00908619185990744 \tabularnewline
46 & 106.44 & 106.485354870176 & -0.0453548701762827 \tabularnewline
47 & 106.44 & 106.469367742734 & -0.0293677427344932 \tabularnewline
48 & 106.48 & 106.406450990422 & 0.0735490095784854 \tabularnewline
49 & 106.5 & 106.445225678189 & 0.0547743218106547 \tabularnewline
50 & 106.57 & 106.502221409348 & 0.0677785906520967 \tabularnewline
51 & 106.4 & 106.761778007652 & -0.361778007651651 \tabularnewline
52 & 106.37 & 106.427916602032 & -0.0579166020315967 \tabularnewline
53 & 106.25 & 106.362787415179 & -0.112787415179270 \tabularnewline
54 & 106.21 & 106.166354688868 & 0.0436453111324369 \tabularnewline
55 & 106.21 & 106.17750350587 & 0.0324964941300294 \tabularnewline
56 & 106.24 & 106.159398102146 & 0.0806018978543932 \tabularnewline
57 & 106.19 & 106.312465538121 & -0.122465538121318 \tabularnewline
58 & 106.08 & 106.291407666463 & -0.211407666462961 \tabularnewline
59 & 106.13 & 106.046275929410 & 0.0837240705904776 \tabularnewline
60 & 106.09 & 106.046709116621 & 0.043290883378603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61599&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]104.31[/C][C]103.888497473247[/C][C]0.421502526752732[/C][/ROW]
[ROW][C]14[/C][C]104.34[/C][C]104.392354346072[/C][C]-0.0523543460724625[/C][/ROW]
[ROW][C]15[/C][C]104.55[/C][C]104.594244401859[/C][C]-0.0442444018589043[/C][/ROW]
[ROW][C]16[/C][C]104.65[/C][C]104.679935848224[/C][C]-0.0299358482235448[/C][/ROW]
[ROW][C]17[/C][C]104.73[/C][C]104.748532918829[/C][C]-0.0185329188294361[/C][/ROW]
[ROW][C]18[/C][C]104.75[/C][C]104.763867595833[/C][C]-0.0138675958332186[/C][/ROW]
[ROW][C]19[/C][C]104.75[/C][C]104.827628086965[/C][C]-0.077628086965305[/C][/ROW]
[ROW][C]20[/C][C]104.76[/C][C]104.796975461544[/C][C]-0.0369754615441167[/C][/ROW]
[ROW][C]21[/C][C]104.94[/C][C]104.914848819990[/C][C]0.0251511800095301[/C][/ROW]
[ROW][C]22[/C][C]105.29[/C][C]105.140688744392[/C][C]0.14931125560787[/C][/ROW]
[ROW][C]23[/C][C]105.38[/C][C]105.398785558175[/C][C]-0.0187855581754945[/C][/ROW]
[ROW][C]24[/C][C]105.43[/C][C]105.427643012973[/C][C]0.00235698702741161[/C][/ROW]
[ROW][C]25[/C][C]105.43[/C][C]105.468182114807[/C][C]-0.0381821148070998[/C][/ROW]
[ROW][C]26[/C][C]105.42[/C][C]105.494052018153[/C][C]-0.0740520181529405[/C][/ROW]
[ROW][C]27[/C][C]105.52[/C][C]105.655248452267[/C][C]-0.135248452267049[/C][/ROW]
[ROW][C]28[/C][C]105.69[/C][C]105.619099917219[/C][C]0.0709000827806676[/C][/ROW]
[ROW][C]29[/C][C]105.72[/C][C]105.769157465029[/C][C]-0.049157465028685[/C][/ROW]
[ROW][C]30[/C][C]105.74[/C][C]105.730361406839[/C][C]0.00963859316080118[/C][/ROW]
[ROW][C]31[/C][C]105.74[/C][C]105.797289109625[/C][C]-0.0572891096250885[/C][/ROW]
[ROW][C]32[/C][C]105.74[/C][C]105.768805327199[/C][C]-0.0288053271987820[/C][/ROW]
[ROW][C]33[/C][C]105.95[/C][C]105.878671736985[/C][C]0.0713282630153458[/C][/ROW]
[ROW][C]34[/C][C]106.17[/C][C]106.140298330969[/C][C]0.0297016690309704[/C][/ROW]
[ROW][C]35[/C][C]106.34[/C][C]106.253440229095[/C][C]0.0865597709048416[/C][/ROW]
[ROW][C]36[/C][C]106.37[/C][C]106.374015231714[/C][C]-0.00401523171397855[/C][/ROW]
[ROW][C]37[/C][C]106.37[/C][C]106.393748423012[/C][C]-0.0237484230123073[/C][/ROW]
[ROW][C]38[/C][C]106.36[/C][C]106.421571710426[/C][C]-0.0615717104262217[/C][/ROW]
[ROW][C]39[/C][C]106.44[/C][C]106.585807201723[/C][C]-0.145807201723457[/C][/ROW]
[ROW][C]40[/C][C]106.29[/C][C]106.527351257900[/C][C]-0.237351257900372[/C][/ROW]
[ROW][C]41[/C][C]106.23[/C][C]106.321356340546[/C][C]-0.0913563405458433[/C][/ROW]
[ROW][C]42[/C][C]106.23[/C][C]106.187393888605[/C][C]0.042606111395429[/C][/ROW]
[ROW][C]43[/C][C]106.23[/C][C]106.238392940783[/C][C]-0.00839294078335229[/C][/ROW]
[ROW][C]44[/C][C]106.23[/C][C]106.215512848046[/C][C]0.0144871519542136[/C][/ROW]
[ROW][C]45[/C][C]106.34[/C][C]106.330913808140[/C][C]0.00908619185990744[/C][/ROW]
[ROW][C]46[/C][C]106.44[/C][C]106.485354870176[/C][C]-0.0453548701762827[/C][/ROW]
[ROW][C]47[/C][C]106.44[/C][C]106.469367742734[/C][C]-0.0293677427344932[/C][/ROW]
[ROW][C]48[/C][C]106.48[/C][C]106.406450990422[/C][C]0.0735490095784854[/C][/ROW]
[ROW][C]49[/C][C]106.5[/C][C]106.445225678189[/C][C]0.0547743218106547[/C][/ROW]
[ROW][C]50[/C][C]106.57[/C][C]106.502221409348[/C][C]0.0677785906520967[/C][/ROW]
[ROW][C]51[/C][C]106.4[/C][C]106.761778007652[/C][C]-0.361778007651651[/C][/ROW]
[ROW][C]52[/C][C]106.37[/C][C]106.427916602032[/C][C]-0.0579166020315967[/C][/ROW]
[ROW][C]53[/C][C]106.25[/C][C]106.362787415179[/C][C]-0.112787415179270[/C][/ROW]
[ROW][C]54[/C][C]106.21[/C][C]106.166354688868[/C][C]0.0436453111324369[/C][/ROW]
[ROW][C]55[/C][C]106.21[/C][C]106.17750350587[/C][C]0.0324964941300294[/C][/ROW]
[ROW][C]56[/C][C]106.24[/C][C]106.159398102146[/C][C]0.0806018978543932[/C][/ROW]
[ROW][C]57[/C][C]106.19[/C][C]106.312465538121[/C][C]-0.122465538121318[/C][/ROW]
[ROW][C]58[/C][C]106.08[/C][C]106.291407666463[/C][C]-0.211407666462961[/C][/ROW]
[ROW][C]59[/C][C]106.13[/C][C]106.046275929410[/C][C]0.0837240705904776[/C][/ROW]
[ROW][C]60[/C][C]106.09[/C][C]106.046709116621[/C][C]0.043290883378603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61599&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61599&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
13104.31103.8884974732470.421502526752732
14104.34104.392354346072-0.0523543460724625
15104.55104.594244401859-0.0442444018589043
16104.65104.679935848224-0.0299358482235448
17104.73104.748532918829-0.0185329188294361
18104.75104.763867595833-0.0138675958332186
19104.75104.827628086965-0.077628086965305
20104.76104.796975461544-0.0369754615441167
21104.94104.9148488199900.0251511800095301
22105.29105.1406887443920.14931125560787
23105.38105.398785558175-0.0187855581754945
24105.43105.4276430129730.00235698702741161
25105.43105.468182114807-0.0381821148070998
26105.42105.494052018153-0.0740520181529405
27105.52105.655248452267-0.135248452267049
28105.69105.6190999172190.0709000827806676
29105.72105.769157465029-0.049157465028685
30105.74105.7303614068390.00963859316080118
31105.74105.797289109625-0.0572891096250885
32105.74105.768805327199-0.0288053271987820
33105.95105.8786717369850.0713282630153458
34106.17106.1402983309690.0297016690309704
35106.34106.2534402290950.0865597709048416
36106.37106.374015231714-0.00401523171397855
37106.37106.393748423012-0.0237484230123073
38106.36106.421571710426-0.0615717104262217
39106.44106.585807201723-0.145807201723457
40106.29106.527351257900-0.237351257900372
41106.23106.321356340546-0.0913563405458433
42106.23106.1873938886050.042606111395429
43106.23106.238392940783-0.00839294078335229
44106.23106.2155128480460.0144871519542136
45106.34106.3309138081400.00908619185990744
46106.44106.485354870176-0.0453548701762827
47106.44106.469367742734-0.0293677427344932
48106.48106.4064509904220.0735490095784854
49106.5106.4452256781890.0547743218106547
50106.57106.5022214093480.0677785906520967
51106.4106.761778007652-0.361778007651651
52106.37106.427916602032-0.0579166020315967
53106.25106.362787415179-0.112787415179270
54106.21106.1663546888680.0436453111324369
55106.21106.177503505870.0324964941300294
56106.24106.1593981021460.0806018978543932
57106.19106.312465538121-0.122465538121318
58106.08106.291407666463-0.211407666462961
59106.13106.0462759294100.0837240705904776
60106.09106.0467091166210.043290883378603







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61106.002083620089105.783292590353106.220874649825
62105.944746486952105.616917729477106.272575244428
63106.067979280668105.643088719579106.492869841757
64106.070175599673105.552721004287106.587630195059
65106.044063933702105.435349488725106.652778378679
66105.954751405137105.254958096060106.654544714214
67105.911439012840105.119384024476106.703494001204
68105.846322030219104.960827170117106.731816890320
69105.894508539229104.912994651376106.876022427082
70105.985805791561104.905951998179107.065659584942
71105.966854132353104.787776402210107.145931862496
72105.88869103476092.7818340680017118.995548001517

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 106.002083620089 & 105.783292590353 & 106.220874649825 \tabularnewline
62 & 105.944746486952 & 105.616917729477 & 106.272575244428 \tabularnewline
63 & 106.067979280668 & 105.643088719579 & 106.492869841757 \tabularnewline
64 & 106.070175599673 & 105.552721004287 & 106.587630195059 \tabularnewline
65 & 106.044063933702 & 105.435349488725 & 106.652778378679 \tabularnewline
66 & 105.954751405137 & 105.254958096060 & 106.654544714214 \tabularnewline
67 & 105.911439012840 & 105.119384024476 & 106.703494001204 \tabularnewline
68 & 105.846322030219 & 104.960827170117 & 106.731816890320 \tabularnewline
69 & 105.894508539229 & 104.912994651376 & 106.876022427082 \tabularnewline
70 & 105.985805791561 & 104.905951998179 & 107.065659584942 \tabularnewline
71 & 105.966854132353 & 104.787776402210 & 107.145931862496 \tabularnewline
72 & 105.888691034760 & 92.7818340680017 & 118.995548001517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61599&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]106.002083620089[/C][C]105.783292590353[/C][C]106.220874649825[/C][/ROW]
[ROW][C]62[/C][C]105.944746486952[/C][C]105.616917729477[/C][C]106.272575244428[/C][/ROW]
[ROW][C]63[/C][C]106.067979280668[/C][C]105.643088719579[/C][C]106.492869841757[/C][/ROW]
[ROW][C]64[/C][C]106.070175599673[/C][C]105.552721004287[/C][C]106.587630195059[/C][/ROW]
[ROW][C]65[/C][C]106.044063933702[/C][C]105.435349488725[/C][C]106.652778378679[/C][/ROW]
[ROW][C]66[/C][C]105.954751405137[/C][C]105.254958096060[/C][C]106.654544714214[/C][/ROW]
[ROW][C]67[/C][C]105.911439012840[/C][C]105.119384024476[/C][C]106.703494001204[/C][/ROW]
[ROW][C]68[/C][C]105.846322030219[/C][C]104.960827170117[/C][C]106.731816890320[/C][/ROW]
[ROW][C]69[/C][C]105.894508539229[/C][C]104.912994651376[/C][C]106.876022427082[/C][/ROW]
[ROW][C]70[/C][C]105.985805791561[/C][C]104.905951998179[/C][C]107.065659584942[/C][/ROW]
[ROW][C]71[/C][C]105.966854132353[/C][C]104.787776402210[/C][C]107.145931862496[/C][/ROW]
[ROW][C]72[/C][C]105.888691034760[/C][C]92.7818340680017[/C][C]118.995548001517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61599&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61599&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
61106.002083620089105.783292590353106.220874649825
62105.944746486952105.616917729477106.272575244428
63106.067979280668105.643088719579106.492869841757
64106.070175599673105.552721004287106.587630195059
65106.044063933702105.435349488725106.652778378679
66105.954751405137105.254958096060106.654544714214
67105.911439012840105.119384024476106.703494001204
68105.846322030219104.960827170117106.731816890320
69105.894508539229104.912994651376106.876022427082
70105.985805791561104.905951998179107.065659584942
71105.966854132353104.787776402210107.145931862496
72105.88869103476092.7818340680017118.995548001517



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')