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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 06:41:58 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t1211892205z5lbz2onfjquyhh.htm/, Retrieved Sun, 19 May 2024 22:24:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13346, Retrieved Sun, 19 May 2024 22:24:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2008-05-27 12:41:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
77.5 
77.7 
76.6 
77
76.5 
77.6 
77.8 
76.9 
76.9 
77
77
76.3 
76.5 
77.1 
76.4 
75.4 
75.4 
75.5 
75.5 
75.8 
75.7 
75.9 
76.1 
76
76
75.89 
74.87 
74.9 
74.79 
74.64 
74.09 
74.33 
73.93 
73.78 
72.85 
71.51 
71.5 
71.5 
71.31 
70.85 
70.62 
70.07 
68.83 
68.82 
68.4 
68.21 
67.75 
67.7 
67.42 
66.27 
64.8 
62.69 
62.75 
62.31 
62.4 
61.75 
61.69 
60.39 
59.9 
59.62 
58.97 
58.54 
58.32 
56.03 
53.63 
53.61 
53.48 
53.48 
52.81 
52.8 
52.57 
52.36




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13346&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]5 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=13346&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13346&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0938618268174845
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0938618268174845 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13346&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]0.0938618268174845[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13346&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13346&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
beta0.0938618268174845
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
376.677.9-1.30000000000001
47776.67797962513730.322020374862731
576.577.1082050457943-0.608205045794335
677.676.55111780911651.04888219088352
777.877.74956780766910.0504321923308737
876.977.9543014653717-1.05430146537171
976.976.9553428038156-0.0553428038155772
107776.95014822714820.0498517728517527
117777.0548274056182-0.0548274056181981
1276.377.0496812051672-0.749681205167207
1376.576.27931475771950.220685242280524
1477.176.50002867771160.599971322288397
1576.477.1563430820597-0.756343082059672
1675.476.3853513386768-0.985351338676793
1775.475.29286446197150.107135538028459
1875.575.3029203992880.19707960071203
1975.575.42141865063930.0785813493607463
2075.875.4287944396440.371205560355961
2175.775.7636364716639-0.0636364716638553
2275.975.65766343618130.242336563818739
2376.175.8804095887660.219590411234023
247676.101020745916-0.101020745915989
257675.99153875415790.0084612458421418
2675.8975.9923329421497-0.102332942149744
2774.8775.872727785256-1.00272778525596
2874.974.75860992353120.141390076468809
2974.7974.8018810544024-0.0118810544024228
3074.6474.6907658769317-0.0507658769316919
3174.0974.5360008989829-0.446000898982888
3274.3373.94413843984210.385861560157878
3373.9374.2203561107772-0.290356110777168
3473.7873.793102755792-0.0131027557920191
3572.8573.641872907197-0.791872907197032
3671.5172.6375462695202-1.12754626952024
3771.571.19171271684180.308287283158165
3871.571.21064912442370.289350875576346
3971.3171.23780812619650.0721918738035043
4070.8571.054584187353-0.204584187353078
4170.6270.57538154179010.0446184582098681
4270.0770.3495695117875-0.279569511787514
4368.8369.7733286066886-0.943328606688638
4468.8268.44478606037570.375213939624331
4568.468.4700043261962-0.0700043261961696
4668.2168.04343359225430.166566407745705
4767.7567.8690678195717-0.119067819571711
4867.767.39789189651160.30210810348845
4967.4267.37624831500130.0437516849986537
5066.2767.1003549280817-0.830354928081661
5164.865.872416297625-1.07241629762501
5262.6964.3017573448211-1.61175734482109
5362.7562.04047485604970.709525143950323
5462.3162.16707218223380.142927817766207
5562.461.74048764831240.659512351687631
5661.7561.8923906824505-0.142390682450461
5761.6961.22902563287390.46097436712612
5860.3961.2122935290884-0.822293529088363
5959.959.83511155626790.064888443732059
6059.6259.3512021041360.268797895864026
6158.9759.0964319656865-0.126431965686464
6258.5458.4345648304190.105435169580993
6358.3258.01446116804670.305538831953314
6456.0357.8231396009775-1.79313960097751
6553.6355.364832242291-1.73483224229098
6653.6152.80199771880770.808002281192316
6753.4852.85783828899310.62216171100691
6853.4852.78623552376410.693764476235913
6952.8152.8513535248847-0.0413535248846557
7052.852.17747200749360.622527992506349
7152.5752.22590362211530.344096377884689
7252.3652.02820113674490.331798863255145

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 76.6 & 77.9 & -1.30000000000001 \tabularnewline
4 & 77 & 76.6779796251373 & 0.322020374862731 \tabularnewline
5 & 76.5 & 77.1082050457943 & -0.608205045794335 \tabularnewline
6 & 77.6 & 76.5511178091165 & 1.04888219088352 \tabularnewline
7 & 77.8 & 77.7495678076691 & 0.0504321923308737 \tabularnewline
8 & 76.9 & 77.9543014653717 & -1.05430146537171 \tabularnewline
9 & 76.9 & 76.9553428038156 & -0.0553428038155772 \tabularnewline
10 & 77 & 76.9501482271482 & 0.0498517728517527 \tabularnewline
11 & 77 & 77.0548274056182 & -0.0548274056181981 \tabularnewline
12 & 76.3 & 77.0496812051672 & -0.749681205167207 \tabularnewline
13 & 76.5 & 76.2793147577195 & 0.220685242280524 \tabularnewline
14 & 77.1 & 76.5000286777116 & 0.599971322288397 \tabularnewline
15 & 76.4 & 77.1563430820597 & -0.756343082059672 \tabularnewline
16 & 75.4 & 76.3853513386768 & -0.985351338676793 \tabularnewline
17 & 75.4 & 75.2928644619715 & 0.107135538028459 \tabularnewline
18 & 75.5 & 75.302920399288 & 0.19707960071203 \tabularnewline
19 & 75.5 & 75.4214186506393 & 0.0785813493607463 \tabularnewline
20 & 75.8 & 75.428794439644 & 0.371205560355961 \tabularnewline
21 & 75.7 & 75.7636364716639 & -0.0636364716638553 \tabularnewline
22 & 75.9 & 75.6576634361813 & 0.242336563818739 \tabularnewline
23 & 76.1 & 75.880409588766 & 0.219590411234023 \tabularnewline
24 & 76 & 76.101020745916 & -0.101020745915989 \tabularnewline
25 & 76 & 75.9915387541579 & 0.0084612458421418 \tabularnewline
26 & 75.89 & 75.9923329421497 & -0.102332942149744 \tabularnewline
27 & 74.87 & 75.872727785256 & -1.00272778525596 \tabularnewline
28 & 74.9 & 74.7586099235312 & 0.141390076468809 \tabularnewline
29 & 74.79 & 74.8018810544024 & -0.0118810544024228 \tabularnewline
30 & 74.64 & 74.6907658769317 & -0.0507658769316919 \tabularnewline
31 & 74.09 & 74.5360008989829 & -0.446000898982888 \tabularnewline
32 & 74.33 & 73.9441384398421 & 0.385861560157878 \tabularnewline
33 & 73.93 & 74.2203561107772 & -0.290356110777168 \tabularnewline
34 & 73.78 & 73.793102755792 & -0.0131027557920191 \tabularnewline
35 & 72.85 & 73.641872907197 & -0.791872907197032 \tabularnewline
36 & 71.51 & 72.6375462695202 & -1.12754626952024 \tabularnewline
37 & 71.5 & 71.1917127168418 & 0.308287283158165 \tabularnewline
38 & 71.5 & 71.2106491244237 & 0.289350875576346 \tabularnewline
39 & 71.31 & 71.2378081261965 & 0.0721918738035043 \tabularnewline
40 & 70.85 & 71.054584187353 & -0.204584187353078 \tabularnewline
41 & 70.62 & 70.5753815417901 & 0.0446184582098681 \tabularnewline
42 & 70.07 & 70.3495695117875 & -0.279569511787514 \tabularnewline
43 & 68.83 & 69.7733286066886 & -0.943328606688638 \tabularnewline
44 & 68.82 & 68.4447860603757 & 0.375213939624331 \tabularnewline
45 & 68.4 & 68.4700043261962 & -0.0700043261961696 \tabularnewline
46 & 68.21 & 68.0434335922543 & 0.166566407745705 \tabularnewline
47 & 67.75 & 67.8690678195717 & -0.119067819571711 \tabularnewline
48 & 67.7 & 67.3978918965116 & 0.30210810348845 \tabularnewline
49 & 67.42 & 67.3762483150013 & 0.0437516849986537 \tabularnewline
50 & 66.27 & 67.1003549280817 & -0.830354928081661 \tabularnewline
51 & 64.8 & 65.872416297625 & -1.07241629762501 \tabularnewline
52 & 62.69 & 64.3017573448211 & -1.61175734482109 \tabularnewline
53 & 62.75 & 62.0404748560497 & 0.709525143950323 \tabularnewline
54 & 62.31 & 62.1670721822338 & 0.142927817766207 \tabularnewline
55 & 62.4 & 61.7404876483124 & 0.659512351687631 \tabularnewline
56 & 61.75 & 61.8923906824505 & -0.142390682450461 \tabularnewline
57 & 61.69 & 61.2290256328739 & 0.46097436712612 \tabularnewline
58 & 60.39 & 61.2122935290884 & -0.822293529088363 \tabularnewline
59 & 59.9 & 59.8351115562679 & 0.064888443732059 \tabularnewline
60 & 59.62 & 59.351202104136 & 0.268797895864026 \tabularnewline
61 & 58.97 & 59.0964319656865 & -0.126431965686464 \tabularnewline
62 & 58.54 & 58.434564830419 & 0.105435169580993 \tabularnewline
63 & 58.32 & 58.0144611680467 & 0.305538831953314 \tabularnewline
64 & 56.03 & 57.8231396009775 & -1.79313960097751 \tabularnewline
65 & 53.63 & 55.364832242291 & -1.73483224229098 \tabularnewline
66 & 53.61 & 52.8019977188077 & 0.808002281192316 \tabularnewline
67 & 53.48 & 52.8578382889931 & 0.62216171100691 \tabularnewline
68 & 53.48 & 52.7862355237641 & 0.693764476235913 \tabularnewline
69 & 52.81 & 52.8513535248847 & -0.0413535248846557 \tabularnewline
70 & 52.8 & 52.1774720074936 & 0.622527992506349 \tabularnewline
71 & 52.57 & 52.2259036221153 & 0.344096377884689 \tabularnewline
72 & 52.36 & 52.0282011367449 & 0.331798863255145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13346&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]76.6[/C][C]77.9[/C][C]-1.30000000000001[/C][/ROW]
[ROW][C]4[/C][C]77[/C][C]76.6779796251373[/C][C]0.322020374862731[/C][/ROW]
[ROW][C]5[/C][C]76.5[/C][C]77.1082050457943[/C][C]-0.608205045794335[/C][/ROW]
[ROW][C]6[/C][C]77.6[/C][C]76.5511178091165[/C][C]1.04888219088352[/C][/ROW]
[ROW][C]7[/C][C]77.8[/C][C]77.7495678076691[/C][C]0.0504321923308737[/C][/ROW]
[ROW][C]8[/C][C]76.9[/C][C]77.9543014653717[/C][C]-1.05430146537171[/C][/ROW]
[ROW][C]9[/C][C]76.9[/C][C]76.9553428038156[/C][C]-0.0553428038155772[/C][/ROW]
[ROW][C]10[/C][C]77[/C][C]76.9501482271482[/C][C]0.0498517728517527[/C][/ROW]
[ROW][C]11[/C][C]77[/C][C]77.0548274056182[/C][C]-0.0548274056181981[/C][/ROW]
[ROW][C]12[/C][C]76.3[/C][C]77.0496812051672[/C][C]-0.749681205167207[/C][/ROW]
[ROW][C]13[/C][C]76.5[/C][C]76.2793147577195[/C][C]0.220685242280524[/C][/ROW]
[ROW][C]14[/C][C]77.1[/C][C]76.5000286777116[/C][C]0.599971322288397[/C][/ROW]
[ROW][C]15[/C][C]76.4[/C][C]77.1563430820597[/C][C]-0.756343082059672[/C][/ROW]
[ROW][C]16[/C][C]75.4[/C][C]76.3853513386768[/C][C]-0.985351338676793[/C][/ROW]
[ROW][C]17[/C][C]75.4[/C][C]75.2928644619715[/C][C]0.107135538028459[/C][/ROW]
[ROW][C]18[/C][C]75.5[/C][C]75.302920399288[/C][C]0.19707960071203[/C][/ROW]
[ROW][C]19[/C][C]75.5[/C][C]75.4214186506393[/C][C]0.0785813493607463[/C][/ROW]
[ROW][C]20[/C][C]75.8[/C][C]75.428794439644[/C][C]0.371205560355961[/C][/ROW]
[ROW][C]21[/C][C]75.7[/C][C]75.7636364716639[/C][C]-0.0636364716638553[/C][/ROW]
[ROW][C]22[/C][C]75.9[/C][C]75.6576634361813[/C][C]0.242336563818739[/C][/ROW]
[ROW][C]23[/C][C]76.1[/C][C]75.880409588766[/C][C]0.219590411234023[/C][/ROW]
[ROW][C]24[/C][C]76[/C][C]76.101020745916[/C][C]-0.101020745915989[/C][/ROW]
[ROW][C]25[/C][C]76[/C][C]75.9915387541579[/C][C]0.0084612458421418[/C][/ROW]
[ROW][C]26[/C][C]75.89[/C][C]75.9923329421497[/C][C]-0.102332942149744[/C][/ROW]
[ROW][C]27[/C][C]74.87[/C][C]75.872727785256[/C][C]-1.00272778525596[/C][/ROW]
[ROW][C]28[/C][C]74.9[/C][C]74.7586099235312[/C][C]0.141390076468809[/C][/ROW]
[ROW][C]29[/C][C]74.79[/C][C]74.8018810544024[/C][C]-0.0118810544024228[/C][/ROW]
[ROW][C]30[/C][C]74.64[/C][C]74.6907658769317[/C][C]-0.0507658769316919[/C][/ROW]
[ROW][C]31[/C][C]74.09[/C][C]74.5360008989829[/C][C]-0.446000898982888[/C][/ROW]
[ROW][C]32[/C][C]74.33[/C][C]73.9441384398421[/C][C]0.385861560157878[/C][/ROW]
[ROW][C]33[/C][C]73.93[/C][C]74.2203561107772[/C][C]-0.290356110777168[/C][/ROW]
[ROW][C]34[/C][C]73.78[/C][C]73.793102755792[/C][C]-0.0131027557920191[/C][/ROW]
[ROW][C]35[/C][C]72.85[/C][C]73.641872907197[/C][C]-0.791872907197032[/C][/ROW]
[ROW][C]36[/C][C]71.51[/C][C]72.6375462695202[/C][C]-1.12754626952024[/C][/ROW]
[ROW][C]37[/C][C]71.5[/C][C]71.1917127168418[/C][C]0.308287283158165[/C][/ROW]
[ROW][C]38[/C][C]71.5[/C][C]71.2106491244237[/C][C]0.289350875576346[/C][/ROW]
[ROW][C]39[/C][C]71.31[/C][C]71.2378081261965[/C][C]0.0721918738035043[/C][/ROW]
[ROW][C]40[/C][C]70.85[/C][C]71.054584187353[/C][C]-0.204584187353078[/C][/ROW]
[ROW][C]41[/C][C]70.62[/C][C]70.5753815417901[/C][C]0.0446184582098681[/C][/ROW]
[ROW][C]42[/C][C]70.07[/C][C]70.3495695117875[/C][C]-0.279569511787514[/C][/ROW]
[ROW][C]43[/C][C]68.83[/C][C]69.7733286066886[/C][C]-0.943328606688638[/C][/ROW]
[ROW][C]44[/C][C]68.82[/C][C]68.4447860603757[/C][C]0.375213939624331[/C][/ROW]
[ROW][C]45[/C][C]68.4[/C][C]68.4700043261962[/C][C]-0.0700043261961696[/C][/ROW]
[ROW][C]46[/C][C]68.21[/C][C]68.0434335922543[/C][C]0.166566407745705[/C][/ROW]
[ROW][C]47[/C][C]67.75[/C][C]67.8690678195717[/C][C]-0.119067819571711[/C][/ROW]
[ROW][C]48[/C][C]67.7[/C][C]67.3978918965116[/C][C]0.30210810348845[/C][/ROW]
[ROW][C]49[/C][C]67.42[/C][C]67.3762483150013[/C][C]0.0437516849986537[/C][/ROW]
[ROW][C]50[/C][C]66.27[/C][C]67.1003549280817[/C][C]-0.830354928081661[/C][/ROW]
[ROW][C]51[/C][C]64.8[/C][C]65.872416297625[/C][C]-1.07241629762501[/C][/ROW]
[ROW][C]52[/C][C]62.69[/C][C]64.3017573448211[/C][C]-1.61175734482109[/C][/ROW]
[ROW][C]53[/C][C]62.75[/C][C]62.0404748560497[/C][C]0.709525143950323[/C][/ROW]
[ROW][C]54[/C][C]62.31[/C][C]62.1670721822338[/C][C]0.142927817766207[/C][/ROW]
[ROW][C]55[/C][C]62.4[/C][C]61.7404876483124[/C][C]0.659512351687631[/C][/ROW]
[ROW][C]56[/C][C]61.75[/C][C]61.8923906824505[/C][C]-0.142390682450461[/C][/ROW]
[ROW][C]57[/C][C]61.69[/C][C]61.2290256328739[/C][C]0.46097436712612[/C][/ROW]
[ROW][C]58[/C][C]60.39[/C][C]61.2122935290884[/C][C]-0.822293529088363[/C][/ROW]
[ROW][C]59[/C][C]59.9[/C][C]59.8351115562679[/C][C]0.064888443732059[/C][/ROW]
[ROW][C]60[/C][C]59.62[/C][C]59.351202104136[/C][C]0.268797895864026[/C][/ROW]
[ROW][C]61[/C][C]58.97[/C][C]59.0964319656865[/C][C]-0.126431965686464[/C][/ROW]
[ROW][C]62[/C][C]58.54[/C][C]58.434564830419[/C][C]0.105435169580993[/C][/ROW]
[ROW][C]63[/C][C]58.32[/C][C]58.0144611680467[/C][C]0.305538831953314[/C][/ROW]
[ROW][C]64[/C][C]56.03[/C][C]57.8231396009775[/C][C]-1.79313960097751[/C][/ROW]
[ROW][C]65[/C][C]53.63[/C][C]55.364832242291[/C][C]-1.73483224229098[/C][/ROW]
[ROW][C]66[/C][C]53.61[/C][C]52.8019977188077[/C][C]0.808002281192316[/C][/ROW]
[ROW][C]67[/C][C]53.48[/C][C]52.8578382889931[/C][C]0.62216171100691[/C][/ROW]
[ROW][C]68[/C][C]53.48[/C][C]52.7862355237641[/C][C]0.693764476235913[/C][/ROW]
[ROW][C]69[/C][C]52.81[/C][C]52.8513535248847[/C][C]-0.0413535248846557[/C][/ROW]
[ROW][C]70[/C][C]52.8[/C][C]52.1774720074936[/C][C]0.622527992506349[/C][/ROW]
[ROW][C]71[/C][C]52.57[/C][C]52.2259036221153[/C][C]0.344096377884689[/C][/ROW]
[ROW][C]72[/C][C]52.36[/C][C]52.0282011367449[/C][C]0.331798863255145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13346&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13346&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
376.677.9-1.30000000000001
47776.67797962513730.322020374862731
576.577.1082050457943-0.608205045794335
677.676.55111780911651.04888219088352
777.877.74956780766910.0504321923308737
876.977.9543014653717-1.05430146537171
976.976.9553428038156-0.0553428038155772
107776.95014822714820.0498517728517527
117777.0548274056182-0.0548274056181981
1276.377.0496812051672-0.749681205167207
1376.576.27931475771950.220685242280524
1477.176.50002867771160.599971322288397
1576.477.1563430820597-0.756343082059672
1675.476.3853513386768-0.985351338676793
1775.475.29286446197150.107135538028459
1875.575.3029203992880.19707960071203
1975.575.42141865063930.0785813493607463
2075.875.4287944396440.371205560355961
2175.775.7636364716639-0.0636364716638553
2275.975.65766343618130.242336563818739
2376.175.8804095887660.219590411234023
247676.101020745916-0.101020745915989
257675.99153875415790.0084612458421418
2675.8975.9923329421497-0.102332942149744
2774.8775.872727785256-1.00272778525596
2874.974.75860992353120.141390076468809
2974.7974.8018810544024-0.0118810544024228
3074.6474.6907658769317-0.0507658769316919
3174.0974.5360008989829-0.446000898982888
3274.3373.94413843984210.385861560157878
3373.9374.2203561107772-0.290356110777168
3473.7873.793102755792-0.0131027557920191
3572.8573.641872907197-0.791872907197032
3671.5172.6375462695202-1.12754626952024
3771.571.19171271684180.308287283158165
3871.571.21064912442370.289350875576346
3971.3171.23780812619650.0721918738035043
4070.8571.054584187353-0.204584187353078
4170.6270.57538154179010.0446184582098681
4270.0770.3495695117875-0.279569511787514
4368.8369.7733286066886-0.943328606688638
4468.8268.44478606037570.375213939624331
4568.468.4700043261962-0.0700043261961696
4668.2168.04343359225430.166566407745705
4767.7567.8690678195717-0.119067819571711
4867.767.39789189651160.30210810348845
4967.4267.37624831500130.0437516849986537
5066.2767.1003549280817-0.830354928081661
5164.865.872416297625-1.07241629762501
5262.6964.3017573448211-1.61175734482109
5362.7562.04047485604970.709525143950323
5462.3162.16707218223380.142927817766207
5562.461.74048764831240.659512351687631
5661.7561.8923906824505-0.142390682450461
5761.6961.22902563287390.46097436712612
5860.3961.2122935290884-0.822293529088363
5959.959.83511155626790.064888443732059
6059.6259.3512021041360.268797895864026
6158.9759.0964319656865-0.126431965686464
6258.5458.4345648304190.105435169580993
6358.3258.01446116804670.305538831953314
6456.0357.8231396009775-1.79313960097751
6553.6355.364832242291-1.73483224229098
6653.6152.80199771880770.808002281192316
6753.4852.85783828899310.62216171100691
6853.4852.78623552376410.693764476235913
6952.8152.8513535248847-0.0413535248846557
7052.852.17747200749360.622527992506349
7152.5752.22590362211530.344096377884689
7252.3652.02820113674490.331798863255145







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7351.849344384185950.643708447719153.0549803206528
7451.338688768371949.551851016600153.1255265201436
7550.828033152557848.538206688526553.1178596165892
7650.317377536743847.555002095248953.0797529782386
7749.806721920929746.584821937976753.0286219038828
7849.296066305115745.619290365202652.9728422450287
7948.785410689301644.653769933851652.9170514447516
8048.274755073487643.685466089856552.8640440571186
8147.764099457673542.71259995181652.815598963531
8247.253443841859441.733997420785452.7728902629335
8346.742788226045440.748865486855952.7367109652349
8446.232132610231339.756661808947152.7076034115155

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 51.8493443841859 & 50.6437084477191 & 53.0549803206528 \tabularnewline
74 & 51.3386887683719 & 49.5518510166001 & 53.1255265201436 \tabularnewline
75 & 50.8280331525578 & 48.5382066885265 & 53.1178596165892 \tabularnewline
76 & 50.3173775367438 & 47.5550020952489 & 53.0797529782386 \tabularnewline
77 & 49.8067219209297 & 46.5848219379767 & 53.0286219038828 \tabularnewline
78 & 49.2960663051157 & 45.6192903652026 & 52.9728422450287 \tabularnewline
79 & 48.7854106893016 & 44.6537699338516 & 52.9170514447516 \tabularnewline
80 & 48.2747550734876 & 43.6854660898565 & 52.8640440571186 \tabularnewline
81 & 47.7640994576735 & 42.712599951816 & 52.815598963531 \tabularnewline
82 & 47.2534438418594 & 41.7339974207854 & 52.7728902629335 \tabularnewline
83 & 46.7427882260454 & 40.7488654868559 & 52.7367109652349 \tabularnewline
84 & 46.2321326102313 & 39.7566618089471 & 52.7076034115155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13346&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]73[/C][C]51.8493443841859[/C][C]50.6437084477191[/C][C]53.0549803206528[/C][/ROW]
[ROW][C]74[/C][C]51.3386887683719[/C][C]49.5518510166001[/C][C]53.1255265201436[/C][/ROW]
[ROW][C]75[/C][C]50.8280331525578[/C][C]48.5382066885265[/C][C]53.1178596165892[/C][/ROW]
[ROW][C]76[/C][C]50.3173775367438[/C][C]47.5550020952489[/C][C]53.0797529782386[/C][/ROW]
[ROW][C]77[/C][C]49.8067219209297[/C][C]46.5848219379767[/C][C]53.0286219038828[/C][/ROW]
[ROW][C]78[/C][C]49.2960663051157[/C][C]45.6192903652026[/C][C]52.9728422450287[/C][/ROW]
[ROW][C]79[/C][C]48.7854106893016[/C][C]44.6537699338516[/C][C]52.9170514447516[/C][/ROW]
[ROW][C]80[/C][C]48.2747550734876[/C][C]43.6854660898565[/C][C]52.8640440571186[/C][/ROW]
[ROW][C]81[/C][C]47.7640994576735[/C][C]42.712599951816[/C][C]52.815598963531[/C][/ROW]
[ROW][C]82[/C][C]47.2534438418594[/C][C]41.7339974207854[/C][C]52.7728902629335[/C][/ROW]
[ROW][C]83[/C][C]46.7427882260454[/C][C]40.7488654868559[/C][C]52.7367109652349[/C][/ROW]
[ROW][C]84[/C][C]46.2321326102313[/C][C]39.7566618089471[/C][C]52.7076034115155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13346&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13346&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
7351.849344384185950.643708447719153.0549803206528
7451.338688768371949.551851016600153.1255265201436
7550.828033152557848.538206688526553.1178596165892
7650.317377536743847.555002095248953.0797529782386
7749.806721920929746.584821937976753.0286219038828
7849.296066305115745.619290365202652.9728422450287
7948.785410689301644.653769933851652.9170514447516
8048.274755073487643.685466089856552.8640440571186
8147.764099457673542.71259995181652.815598963531
8247.253443841859441.733997420785452.7728902629335
8346.742788226045440.748865486855952.7367109652349
8446.232132610231339.756661808947152.7076034115155



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
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=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')