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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 09:47:43 -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/12/t1386860062knqeufxu1fq62az.htm/, Retrieved Sun, 05 Dec 2021 18:35:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232251, Retrieved Sun, 05 Dec 2021 18:35:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 14:47:43] [6bddb01df32adf96be73fb2a4c89eedb] [Current]
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Dataseries X:
16,3
16,37
16,38
16,37
16,42
16,43
16,44
16,53
16,55
16,56
16,6
16,61
16,62
16,64
16,61
16,74
16,87
16,89
16,89
16,99
17,06
17,1
17,11
17,17
17,17
17,21
17,37
17,43
17,44
17,46
17,42
17,47
17,45
17,44
17,46
17,47
17,47
17,56
17,61
17,61
17,6
17,57
17,59
17,59
17,68
17,73
17,75
17,75
17,75
17,85
18,06
18,05
18,16
18,2
18,21
18,33
18,36
18,37
18,4
18,47
18,49
18,5
18,53
18,56
18,6
18,61
18,62
18,61
18,65
18,77
18,78
18,78
18,8
18,85
18,85
18,98
19,06
19,08
19,19
19,21
19,29
19,3
19,36
19,36




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232251&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232251&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0718071265959284
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0718071265959284 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232251&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]0.0718071265959284[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232251&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
beta0.0718071265959284
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
316.3816.44-0.0600000000000023
416.3716.4456915724042-0.0756915724042422
516.4216.4302563780824-0.0102563780823672
616.4316.479519897043-0.0495198970429946
716.4416.485964015527-0.0459640155270051
816.5316.49266347164520.0373365283547962
916.5516.5853445004634-0.0353445004634274
1016.5616.6028065134442-0.0428065134441837
1116.616.6097327007142-0.0097327007141601
1216.6116.6490338234419-0.0390338234418657
1316.6216.6562309167404-0.0362309167404469
1416.6416.6636292787154-0.0236292787153829
1516.6116.6819325281073-0.0719325281072969
1616.7416.64676725995510.0932327400448685
1716.8716.78346203512240.0865379648775857
1816.8916.9196760777217-0.0296760777217351
1916.8916.9375451238519-0.0475451238519007
2016.9916.93413104512440.0558689548755495
2117.0617.038142834240.0218571657600215
2217.117.1097123345087-0.00971233450873399
2317.1117.1490149196751-0.0390149196751288
2417.1717.15621337039890.0137866296011175
2517.1717.217203348656-0.0472033486559837
2617.2117.2138138118233-0.00381381182329221
2717.3717.25353995295490.116460047045116
2817.4317.42190261429640.00809738570357865
2917.4417.4824840642967-0.0424840642967297
3017.4617.4894334057135-0.0294334057134691
3117.4217.5073198774233-0.0873198774232513
3217.4717.46104968793080.00895031206921715
3317.4517.5116923841226-0.0616923841226047
3417.4417.4872624312859-0.0472624312859082
3517.4617.4738686518993-0.0138686518993332
3617.4717.4928727838567-0.022872783856684
3717.4717.5012303549707-0.0312303549706812
3817.5617.49898779291770.0610122070823316
3917.6117.59336890419550.016631095804474
4017.6117.6445631353974-0.0345631353973879
4117.617.6420812559584-0.042081255958351
4217.5717.6290595218844-0.0590595218844392
4317.5917.5948186273198-0.00481862731978566
4417.5917.6144726155378-0.0244726155378139
4517.6817.61271530733580.0672846926642414
4617.7317.70754682777990.022453172220132
4717.7517.75915912556-0.00915912555995746
4817.7517.7785014350714-0.0285014350713659
4917.7517.776454828915-0.0264548289150319
5017.8517.77455518366610.0754448163339454
5118.0617.87997265914360.180027340856444
5218.0518.1028999051992-0.0528999051991583
5318.1618.08910131500960.0708986849903859
5418.218.2041923458582-0.00419234585820405
5518.2118.2438913055484-0.0338913055484262
5618.3318.25145766828040.0785423317195857
5718.3618.3770975674373-0.0170975674373395
5818.3718.4058698402479-0.0358698402478836
5918.418.4132941300882-0.0132941300882301
6018.4718.4423395168060.0276604831940013
6118.4918.5143257366244-0.0243257366244158
6218.518.5325789753751-0.0325789753750847
6318.5318.540239572766-0.0102395727659612
6418.5618.5695042984681-0.0095042984680731
6518.618.59882182210480.001178177895234
6618.6118.638906423674-0.0289064236740444
6718.6218.6468307364498-0.0268307364498419
6818.6118.6549040983609-0.0449040983609308
6918.6518.64167966408520.00832033591474968
7018.7718.68227712349960.0877228765004006
7118.7818.8085762511978-0.0285762511978227
7218.7818.8165242727104-0.0365242727104267
7318.818.8139015696361-0.0139015696360829
7418.8518.83290333786530.0170966621346587
7518.8518.8841310000476-0.0341310000476156
7618.9818.88168015100630.0983198489936505
7719.0619.01874021684990.0412597831500676
7819.0819.1017029633219-0.021702963321907
7919.1919.12014453588710.0698554641128588
8019.2119.2351606560421-0.0251606560421145
8119.2919.25335394162850.036646058371538
8219.319.3359853897812-0.0359853897811853
8319.3619.34340138234160.0165986176584347
8419.3619.4045932813811-0.0445932813810828

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16.38 & 16.44 & -0.0600000000000023 \tabularnewline
4 & 16.37 & 16.4456915724042 & -0.0756915724042422 \tabularnewline
5 & 16.42 & 16.4302563780824 & -0.0102563780823672 \tabularnewline
6 & 16.43 & 16.479519897043 & -0.0495198970429946 \tabularnewline
7 & 16.44 & 16.485964015527 & -0.0459640155270051 \tabularnewline
8 & 16.53 & 16.4926634716452 & 0.0373365283547962 \tabularnewline
9 & 16.55 & 16.5853445004634 & -0.0353445004634274 \tabularnewline
10 & 16.56 & 16.6028065134442 & -0.0428065134441837 \tabularnewline
11 & 16.6 & 16.6097327007142 & -0.0097327007141601 \tabularnewline
12 & 16.61 & 16.6490338234419 & -0.0390338234418657 \tabularnewline
13 & 16.62 & 16.6562309167404 & -0.0362309167404469 \tabularnewline
14 & 16.64 & 16.6636292787154 & -0.0236292787153829 \tabularnewline
15 & 16.61 & 16.6819325281073 & -0.0719325281072969 \tabularnewline
16 & 16.74 & 16.6467672599551 & 0.0932327400448685 \tabularnewline
17 & 16.87 & 16.7834620351224 & 0.0865379648775857 \tabularnewline
18 & 16.89 & 16.9196760777217 & -0.0296760777217351 \tabularnewline
19 & 16.89 & 16.9375451238519 & -0.0475451238519007 \tabularnewline
20 & 16.99 & 16.9341310451244 & 0.0558689548755495 \tabularnewline
21 & 17.06 & 17.03814283424 & 0.0218571657600215 \tabularnewline
22 & 17.1 & 17.1097123345087 & -0.00971233450873399 \tabularnewline
23 & 17.11 & 17.1490149196751 & -0.0390149196751288 \tabularnewline
24 & 17.17 & 17.1562133703989 & 0.0137866296011175 \tabularnewline
25 & 17.17 & 17.217203348656 & -0.0472033486559837 \tabularnewline
26 & 17.21 & 17.2138138118233 & -0.00381381182329221 \tabularnewline
27 & 17.37 & 17.2535399529549 & 0.116460047045116 \tabularnewline
28 & 17.43 & 17.4219026142964 & 0.00809738570357865 \tabularnewline
29 & 17.44 & 17.4824840642967 & -0.0424840642967297 \tabularnewline
30 & 17.46 & 17.4894334057135 & -0.0294334057134691 \tabularnewline
31 & 17.42 & 17.5073198774233 & -0.0873198774232513 \tabularnewline
32 & 17.47 & 17.4610496879308 & 0.00895031206921715 \tabularnewline
33 & 17.45 & 17.5116923841226 & -0.0616923841226047 \tabularnewline
34 & 17.44 & 17.4872624312859 & -0.0472624312859082 \tabularnewline
35 & 17.46 & 17.4738686518993 & -0.0138686518993332 \tabularnewline
36 & 17.47 & 17.4928727838567 & -0.022872783856684 \tabularnewline
37 & 17.47 & 17.5012303549707 & -0.0312303549706812 \tabularnewline
38 & 17.56 & 17.4989877929177 & 0.0610122070823316 \tabularnewline
39 & 17.61 & 17.5933689041955 & 0.016631095804474 \tabularnewline
40 & 17.61 & 17.6445631353974 & -0.0345631353973879 \tabularnewline
41 & 17.6 & 17.6420812559584 & -0.042081255958351 \tabularnewline
42 & 17.57 & 17.6290595218844 & -0.0590595218844392 \tabularnewline
43 & 17.59 & 17.5948186273198 & -0.00481862731978566 \tabularnewline
44 & 17.59 & 17.6144726155378 & -0.0244726155378139 \tabularnewline
45 & 17.68 & 17.6127153073358 & 0.0672846926642414 \tabularnewline
46 & 17.73 & 17.7075468277799 & 0.022453172220132 \tabularnewline
47 & 17.75 & 17.75915912556 & -0.00915912555995746 \tabularnewline
48 & 17.75 & 17.7785014350714 & -0.0285014350713659 \tabularnewline
49 & 17.75 & 17.776454828915 & -0.0264548289150319 \tabularnewline
50 & 17.85 & 17.7745551836661 & 0.0754448163339454 \tabularnewline
51 & 18.06 & 17.8799726591436 & 0.180027340856444 \tabularnewline
52 & 18.05 & 18.1028999051992 & -0.0528999051991583 \tabularnewline
53 & 18.16 & 18.0891013150096 & 0.0708986849903859 \tabularnewline
54 & 18.2 & 18.2041923458582 & -0.00419234585820405 \tabularnewline
55 & 18.21 & 18.2438913055484 & -0.0338913055484262 \tabularnewline
56 & 18.33 & 18.2514576682804 & 0.0785423317195857 \tabularnewline
57 & 18.36 & 18.3770975674373 & -0.0170975674373395 \tabularnewline
58 & 18.37 & 18.4058698402479 & -0.0358698402478836 \tabularnewline
59 & 18.4 & 18.4132941300882 & -0.0132941300882301 \tabularnewline
60 & 18.47 & 18.442339516806 & 0.0276604831940013 \tabularnewline
61 & 18.49 & 18.5143257366244 & -0.0243257366244158 \tabularnewline
62 & 18.5 & 18.5325789753751 & -0.0325789753750847 \tabularnewline
63 & 18.53 & 18.540239572766 & -0.0102395727659612 \tabularnewline
64 & 18.56 & 18.5695042984681 & -0.0095042984680731 \tabularnewline
65 & 18.6 & 18.5988218221048 & 0.001178177895234 \tabularnewline
66 & 18.61 & 18.638906423674 & -0.0289064236740444 \tabularnewline
67 & 18.62 & 18.6468307364498 & -0.0268307364498419 \tabularnewline
68 & 18.61 & 18.6549040983609 & -0.0449040983609308 \tabularnewline
69 & 18.65 & 18.6416796640852 & 0.00832033591474968 \tabularnewline
70 & 18.77 & 18.6822771234996 & 0.0877228765004006 \tabularnewline
71 & 18.78 & 18.8085762511978 & -0.0285762511978227 \tabularnewline
72 & 18.78 & 18.8165242727104 & -0.0365242727104267 \tabularnewline
73 & 18.8 & 18.8139015696361 & -0.0139015696360829 \tabularnewline
74 & 18.85 & 18.8329033378653 & 0.0170966621346587 \tabularnewline
75 & 18.85 & 18.8841310000476 & -0.0341310000476156 \tabularnewline
76 & 18.98 & 18.8816801510063 & 0.0983198489936505 \tabularnewline
77 & 19.06 & 19.0187402168499 & 0.0412597831500676 \tabularnewline
78 & 19.08 & 19.1017029633219 & -0.021702963321907 \tabularnewline
79 & 19.19 & 19.1201445358871 & 0.0698554641128588 \tabularnewline
80 & 19.21 & 19.2351606560421 & -0.0251606560421145 \tabularnewline
81 & 19.29 & 19.2533539416285 & 0.036646058371538 \tabularnewline
82 & 19.3 & 19.3359853897812 & -0.0359853897811853 \tabularnewline
83 & 19.36 & 19.3434013823416 & 0.0165986176584347 \tabularnewline
84 & 19.36 & 19.4045932813811 & -0.0445932813810828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232251&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]16.38[/C][C]16.44[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]4[/C][C]16.37[/C][C]16.4456915724042[/C][C]-0.0756915724042422[/C][/ROW]
[ROW][C]5[/C][C]16.42[/C][C]16.4302563780824[/C][C]-0.0102563780823672[/C][/ROW]
[ROW][C]6[/C][C]16.43[/C][C]16.479519897043[/C][C]-0.0495198970429946[/C][/ROW]
[ROW][C]7[/C][C]16.44[/C][C]16.485964015527[/C][C]-0.0459640155270051[/C][/ROW]
[ROW][C]8[/C][C]16.53[/C][C]16.4926634716452[/C][C]0.0373365283547962[/C][/ROW]
[ROW][C]9[/C][C]16.55[/C][C]16.5853445004634[/C][C]-0.0353445004634274[/C][/ROW]
[ROW][C]10[/C][C]16.56[/C][C]16.6028065134442[/C][C]-0.0428065134441837[/C][/ROW]
[ROW][C]11[/C][C]16.6[/C][C]16.6097327007142[/C][C]-0.0097327007141601[/C][/ROW]
[ROW][C]12[/C][C]16.61[/C][C]16.6490338234419[/C][C]-0.0390338234418657[/C][/ROW]
[ROW][C]13[/C][C]16.62[/C][C]16.6562309167404[/C][C]-0.0362309167404469[/C][/ROW]
[ROW][C]14[/C][C]16.64[/C][C]16.6636292787154[/C][C]-0.0236292787153829[/C][/ROW]
[ROW][C]15[/C][C]16.61[/C][C]16.6819325281073[/C][C]-0.0719325281072969[/C][/ROW]
[ROW][C]16[/C][C]16.74[/C][C]16.6467672599551[/C][C]0.0932327400448685[/C][/ROW]
[ROW][C]17[/C][C]16.87[/C][C]16.7834620351224[/C][C]0.0865379648775857[/C][/ROW]
[ROW][C]18[/C][C]16.89[/C][C]16.9196760777217[/C][C]-0.0296760777217351[/C][/ROW]
[ROW][C]19[/C][C]16.89[/C][C]16.9375451238519[/C][C]-0.0475451238519007[/C][/ROW]
[ROW][C]20[/C][C]16.99[/C][C]16.9341310451244[/C][C]0.0558689548755495[/C][/ROW]
[ROW][C]21[/C][C]17.06[/C][C]17.03814283424[/C][C]0.0218571657600215[/C][/ROW]
[ROW][C]22[/C][C]17.1[/C][C]17.1097123345087[/C][C]-0.00971233450873399[/C][/ROW]
[ROW][C]23[/C][C]17.11[/C][C]17.1490149196751[/C][C]-0.0390149196751288[/C][/ROW]
[ROW][C]24[/C][C]17.17[/C][C]17.1562133703989[/C][C]0.0137866296011175[/C][/ROW]
[ROW][C]25[/C][C]17.17[/C][C]17.217203348656[/C][C]-0.0472033486559837[/C][/ROW]
[ROW][C]26[/C][C]17.21[/C][C]17.2138138118233[/C][C]-0.00381381182329221[/C][/ROW]
[ROW][C]27[/C][C]17.37[/C][C]17.2535399529549[/C][C]0.116460047045116[/C][/ROW]
[ROW][C]28[/C][C]17.43[/C][C]17.4219026142964[/C][C]0.00809738570357865[/C][/ROW]
[ROW][C]29[/C][C]17.44[/C][C]17.4824840642967[/C][C]-0.0424840642967297[/C][/ROW]
[ROW][C]30[/C][C]17.46[/C][C]17.4894334057135[/C][C]-0.0294334057134691[/C][/ROW]
[ROW][C]31[/C][C]17.42[/C][C]17.5073198774233[/C][C]-0.0873198774232513[/C][/ROW]
[ROW][C]32[/C][C]17.47[/C][C]17.4610496879308[/C][C]0.00895031206921715[/C][/ROW]
[ROW][C]33[/C][C]17.45[/C][C]17.5116923841226[/C][C]-0.0616923841226047[/C][/ROW]
[ROW][C]34[/C][C]17.44[/C][C]17.4872624312859[/C][C]-0.0472624312859082[/C][/ROW]
[ROW][C]35[/C][C]17.46[/C][C]17.4738686518993[/C][C]-0.0138686518993332[/C][/ROW]
[ROW][C]36[/C][C]17.47[/C][C]17.4928727838567[/C][C]-0.022872783856684[/C][/ROW]
[ROW][C]37[/C][C]17.47[/C][C]17.5012303549707[/C][C]-0.0312303549706812[/C][/ROW]
[ROW][C]38[/C][C]17.56[/C][C]17.4989877929177[/C][C]0.0610122070823316[/C][/ROW]
[ROW][C]39[/C][C]17.61[/C][C]17.5933689041955[/C][C]0.016631095804474[/C][/ROW]
[ROW][C]40[/C][C]17.61[/C][C]17.6445631353974[/C][C]-0.0345631353973879[/C][/ROW]
[ROW][C]41[/C][C]17.6[/C][C]17.6420812559584[/C][C]-0.042081255958351[/C][/ROW]
[ROW][C]42[/C][C]17.57[/C][C]17.6290595218844[/C][C]-0.0590595218844392[/C][/ROW]
[ROW][C]43[/C][C]17.59[/C][C]17.5948186273198[/C][C]-0.00481862731978566[/C][/ROW]
[ROW][C]44[/C][C]17.59[/C][C]17.6144726155378[/C][C]-0.0244726155378139[/C][/ROW]
[ROW][C]45[/C][C]17.68[/C][C]17.6127153073358[/C][C]0.0672846926642414[/C][/ROW]
[ROW][C]46[/C][C]17.73[/C][C]17.7075468277799[/C][C]0.022453172220132[/C][/ROW]
[ROW][C]47[/C][C]17.75[/C][C]17.75915912556[/C][C]-0.00915912555995746[/C][/ROW]
[ROW][C]48[/C][C]17.75[/C][C]17.7785014350714[/C][C]-0.0285014350713659[/C][/ROW]
[ROW][C]49[/C][C]17.75[/C][C]17.776454828915[/C][C]-0.0264548289150319[/C][/ROW]
[ROW][C]50[/C][C]17.85[/C][C]17.7745551836661[/C][C]0.0754448163339454[/C][/ROW]
[ROW][C]51[/C][C]18.06[/C][C]17.8799726591436[/C][C]0.180027340856444[/C][/ROW]
[ROW][C]52[/C][C]18.05[/C][C]18.1028999051992[/C][C]-0.0528999051991583[/C][/ROW]
[ROW][C]53[/C][C]18.16[/C][C]18.0891013150096[/C][C]0.0708986849903859[/C][/ROW]
[ROW][C]54[/C][C]18.2[/C][C]18.2041923458582[/C][C]-0.00419234585820405[/C][/ROW]
[ROW][C]55[/C][C]18.21[/C][C]18.2438913055484[/C][C]-0.0338913055484262[/C][/ROW]
[ROW][C]56[/C][C]18.33[/C][C]18.2514576682804[/C][C]0.0785423317195857[/C][/ROW]
[ROW][C]57[/C][C]18.36[/C][C]18.3770975674373[/C][C]-0.0170975674373395[/C][/ROW]
[ROW][C]58[/C][C]18.37[/C][C]18.4058698402479[/C][C]-0.0358698402478836[/C][/ROW]
[ROW][C]59[/C][C]18.4[/C][C]18.4132941300882[/C][C]-0.0132941300882301[/C][/ROW]
[ROW][C]60[/C][C]18.47[/C][C]18.442339516806[/C][C]0.0276604831940013[/C][/ROW]
[ROW][C]61[/C][C]18.49[/C][C]18.5143257366244[/C][C]-0.0243257366244158[/C][/ROW]
[ROW][C]62[/C][C]18.5[/C][C]18.5325789753751[/C][C]-0.0325789753750847[/C][/ROW]
[ROW][C]63[/C][C]18.53[/C][C]18.540239572766[/C][C]-0.0102395727659612[/C][/ROW]
[ROW][C]64[/C][C]18.56[/C][C]18.5695042984681[/C][C]-0.0095042984680731[/C][/ROW]
[ROW][C]65[/C][C]18.6[/C][C]18.5988218221048[/C][C]0.001178177895234[/C][/ROW]
[ROW][C]66[/C][C]18.61[/C][C]18.638906423674[/C][C]-0.0289064236740444[/C][/ROW]
[ROW][C]67[/C][C]18.62[/C][C]18.6468307364498[/C][C]-0.0268307364498419[/C][/ROW]
[ROW][C]68[/C][C]18.61[/C][C]18.6549040983609[/C][C]-0.0449040983609308[/C][/ROW]
[ROW][C]69[/C][C]18.65[/C][C]18.6416796640852[/C][C]0.00832033591474968[/C][/ROW]
[ROW][C]70[/C][C]18.77[/C][C]18.6822771234996[/C][C]0.0877228765004006[/C][/ROW]
[ROW][C]71[/C][C]18.78[/C][C]18.8085762511978[/C][C]-0.0285762511978227[/C][/ROW]
[ROW][C]72[/C][C]18.78[/C][C]18.8165242727104[/C][C]-0.0365242727104267[/C][/ROW]
[ROW][C]73[/C][C]18.8[/C][C]18.8139015696361[/C][C]-0.0139015696360829[/C][/ROW]
[ROW][C]74[/C][C]18.85[/C][C]18.8329033378653[/C][C]0.0170966621346587[/C][/ROW]
[ROW][C]75[/C][C]18.85[/C][C]18.8841310000476[/C][C]-0.0341310000476156[/C][/ROW]
[ROW][C]76[/C][C]18.98[/C][C]18.8816801510063[/C][C]0.0983198489936505[/C][/ROW]
[ROW][C]77[/C][C]19.06[/C][C]19.0187402168499[/C][C]0.0412597831500676[/C][/ROW]
[ROW][C]78[/C][C]19.08[/C][C]19.1017029633219[/C][C]-0.021702963321907[/C][/ROW]
[ROW][C]79[/C][C]19.19[/C][C]19.1201445358871[/C][C]0.0698554641128588[/C][/ROW]
[ROW][C]80[/C][C]19.21[/C][C]19.2351606560421[/C][C]-0.0251606560421145[/C][/ROW]
[ROW][C]81[/C][C]19.29[/C][C]19.2533539416285[/C][C]0.036646058371538[/C][/ROW]
[ROW][C]82[/C][C]19.3[/C][C]19.3359853897812[/C][C]-0.0359853897811853[/C][/ROW]
[ROW][C]83[/C][C]19.36[/C][C]19.3434013823416[/C][C]0.0165986176584347[/C][/ROW]
[ROW][C]84[/C][C]19.36[/C][C]19.4045932813811[/C][C]-0.0445932813810828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232251&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232251&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
316.3816.44-0.0600000000000023
416.3716.4456915724042-0.0756915724042422
516.4216.4302563780824-0.0102563780823672
616.4316.479519897043-0.0495198970429946
716.4416.485964015527-0.0459640155270051
816.5316.49266347164520.0373365283547962
916.5516.5853445004634-0.0353445004634274
1016.5616.6028065134442-0.0428065134441837
1116.616.6097327007142-0.0097327007141601
1216.6116.6490338234419-0.0390338234418657
1316.6216.6562309167404-0.0362309167404469
1416.6416.6636292787154-0.0236292787153829
1516.6116.6819325281073-0.0719325281072969
1616.7416.64676725995510.0932327400448685
1716.8716.78346203512240.0865379648775857
1816.8916.9196760777217-0.0296760777217351
1916.8916.9375451238519-0.0475451238519007
2016.9916.93413104512440.0558689548755495
2117.0617.038142834240.0218571657600215
2217.117.1097123345087-0.00971233450873399
2317.1117.1490149196751-0.0390149196751288
2417.1717.15621337039890.0137866296011175
2517.1717.217203348656-0.0472033486559837
2617.2117.2138138118233-0.00381381182329221
2717.3717.25353995295490.116460047045116
2817.4317.42190261429640.00809738570357865
2917.4417.4824840642967-0.0424840642967297
3017.4617.4894334057135-0.0294334057134691
3117.4217.5073198774233-0.0873198774232513
3217.4717.46104968793080.00895031206921715
3317.4517.5116923841226-0.0616923841226047
3417.4417.4872624312859-0.0472624312859082
3517.4617.4738686518993-0.0138686518993332
3617.4717.4928727838567-0.022872783856684
3717.4717.5012303549707-0.0312303549706812
3817.5617.49898779291770.0610122070823316
3917.6117.59336890419550.016631095804474
4017.6117.6445631353974-0.0345631353973879
4117.617.6420812559584-0.042081255958351
4217.5717.6290595218844-0.0590595218844392
4317.5917.5948186273198-0.00481862731978566
4417.5917.6144726155378-0.0244726155378139
4517.6817.61271530733580.0672846926642414
4617.7317.70754682777990.022453172220132
4717.7517.75915912556-0.00915912555995746
4817.7517.7785014350714-0.0285014350713659
4917.7517.776454828915-0.0264548289150319
5017.8517.77455518366610.0754448163339454
5118.0617.87997265914360.180027340856444
5218.0518.1028999051992-0.0528999051991583
5318.1618.08910131500960.0708986849903859
5418.218.2041923458582-0.00419234585820405
5518.2118.2438913055484-0.0338913055484262
5618.3318.25145766828040.0785423317195857
5718.3618.3770975674373-0.0170975674373395
5818.3718.4058698402479-0.0358698402478836
5918.418.4132941300882-0.0132941300882301
6018.4718.4423395168060.0276604831940013
6118.4918.5143257366244-0.0243257366244158
6218.518.5325789753751-0.0325789753750847
6318.5318.540239572766-0.0102395727659612
6418.5618.5695042984681-0.0095042984680731
6518.618.59882182210480.001178177895234
6618.6118.638906423674-0.0289064236740444
6718.6218.6468307364498-0.0268307364498419
6818.6118.6549040983609-0.0449040983609308
6918.6518.64167966408520.00832033591474968
7018.7718.68227712349960.0877228765004006
7118.7818.8085762511978-0.0285762511978227
7218.7818.8165242727104-0.0365242727104267
7318.818.8139015696361-0.0139015696360829
7418.8518.83290333786530.0170966621346587
7518.8518.8841310000476-0.0341310000476156
7618.9818.88168015100630.0983198489936505
7719.0619.01874021684990.0412597831500676
7819.0819.1017029633219-0.021702963321907
7919.1919.12014453588710.0698554641128588
8019.2119.2351606560421-0.0251606560421145
8119.2919.25335394162850.036646058371538
8219.319.3359853897812-0.0359853897811853
8319.3619.34340138234160.0165986176584347
8419.3619.4045932813811-0.0445932813810828







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8519.401391165979619.304822379581319.4979599523779
8619.442782331959219.301225188006419.5843394759121
8719.484173497938919.304632824895719.663714170982
8819.525564663918519.31106295038619.7400663774509
8919.566955829898119.31903852456719.8148731352292
9019.608346995877719.32783489527719.8888590964785
9119.649738161857419.337041344165519.9624349795493
9219.69112932783719.346403431362720.0358552243113
9319.732520493816619.355753801972120.1092871856611
9419.773911659796219.364977607987520.182845711605
9519.815302825775919.373993558459120.2566120930926
9619.856693991755519.382742789689120.3306451938218

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 19.4013911659796 & 19.3048223795813 & 19.4979599523779 \tabularnewline
86 & 19.4427823319592 & 19.3012251880064 & 19.5843394759121 \tabularnewline
87 & 19.4841734979389 & 19.3046328248957 & 19.663714170982 \tabularnewline
88 & 19.5255646639185 & 19.311062950386 & 19.7400663774509 \tabularnewline
89 & 19.5669558298981 & 19.319038524567 & 19.8148731352292 \tabularnewline
90 & 19.6083469958777 & 19.327834895277 & 19.8888590964785 \tabularnewline
91 & 19.6497381618574 & 19.3370413441655 & 19.9624349795493 \tabularnewline
92 & 19.691129327837 & 19.3464034313627 & 20.0358552243113 \tabularnewline
93 & 19.7325204938166 & 19.3557538019721 & 20.1092871856611 \tabularnewline
94 & 19.7739116597962 & 19.3649776079875 & 20.182845711605 \tabularnewline
95 & 19.8153028257759 & 19.3739935584591 & 20.2566120930926 \tabularnewline
96 & 19.8566939917555 & 19.3827427896891 & 20.3306451938218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232251&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]19.4013911659796[/C][C]19.3048223795813[/C][C]19.4979599523779[/C][/ROW]
[ROW][C]86[/C][C]19.4427823319592[/C][C]19.3012251880064[/C][C]19.5843394759121[/C][/ROW]
[ROW][C]87[/C][C]19.4841734979389[/C][C]19.3046328248957[/C][C]19.663714170982[/C][/ROW]
[ROW][C]88[/C][C]19.5255646639185[/C][C]19.311062950386[/C][C]19.7400663774509[/C][/ROW]
[ROW][C]89[/C][C]19.5669558298981[/C][C]19.319038524567[/C][C]19.8148731352292[/C][/ROW]
[ROW][C]90[/C][C]19.6083469958777[/C][C]19.327834895277[/C][C]19.8888590964785[/C][/ROW]
[ROW][C]91[/C][C]19.6497381618574[/C][C]19.3370413441655[/C][C]19.9624349795493[/C][/ROW]
[ROW][C]92[/C][C]19.691129327837[/C][C]19.3464034313627[/C][C]20.0358552243113[/C][/ROW]
[ROW][C]93[/C][C]19.7325204938166[/C][C]19.3557538019721[/C][C]20.1092871856611[/C][/ROW]
[ROW][C]94[/C][C]19.7739116597962[/C][C]19.3649776079875[/C][C]20.182845711605[/C][/ROW]
[ROW][C]95[/C][C]19.8153028257759[/C][C]19.3739935584591[/C][C]20.2566120930926[/C][/ROW]
[ROW][C]96[/C][C]19.8566939917555[/C][C]19.3827427896891[/C][C]20.3306451938218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232251&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232251&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
8519.401391165979619.304822379581319.4979599523779
8619.442782331959219.301225188006419.5843394759121
8719.484173497938919.304632824895719.663714170982
8819.525564663918519.31106295038619.7400663774509
8919.566955829898119.31903852456719.8148731352292
9019.608346995877719.32783489527719.8888590964785
9119.649738161857419.337041344165519.9624349795493
9219.69112932783719.346403431362720.0358552243113
9319.732520493816619.355753801972120.1092871856611
9419.773911659796219.364977607987520.182845711605
9519.815302825775919.373993558459120.2566120930926
9619.856693991755519.382742789689120.3306451938218



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=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')