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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Jan 2014 00:19:14 -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/2014/Jan/13/t13895904472jp328z3sigzo05.htm/, Retrieved Sun, 19 May 2024 10:23:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233104, Retrieved Sun, 19 May 2024 10:23:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKarel De Grote-Hogeschool Valérie Weyts
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2014-01-13 05:19:14] [feb2df3f24188fb89c42f3077ec68a56] [Current]
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Dataseries X:
100.17
101.13
99.25
99.69
101.04
99.79
100.35
101.45
100.4
100.52
102.52
101.23
102.14
101.06
100.31
101.18
101.28
101.99
101.34
100.5
103.74
104.19
102.23
103.32
104.67
103.22
102.64
105.26
103.63
102.71
104.34
102.92
105.92
107.39
105.68
105.86
107.05
106.77
105.88
106.23
107.53
105.51
107.37
105.61
108.38
109.6
106.62
105.69
107.06
105.67
106.24
107.9
105.91
106.44
107.69
105.9
108.59
111.36
109.36
109.21
111.3
109.21
110.95
110.89
111.04
108.96
110.5
109.02
112.87
112.73
113.28
113.53
112.99
112.68
114.26
114.28
114.28
114.2
113.64
114.2
116.68
116.73
118.71
117.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233104&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233104&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.521025975142054
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.521025975142054 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233104&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]0.521025975142054[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233104&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
alpha0.521025975142054
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101.13100.170.959999999999994
399.25100.670184936136-1.42018493613637
499.6999.9302316949039-0.240231694903855
5101.0499.80506474180651.23493525819346
699.79100.448498088944-0.658498088944086
7100.35100.1054034800230.244596519977179
8101.45100.232844620361.21715537963972
9100.4100.867014188936-0.46701418893646
10100.52100.623687665741-0.103687665740679
11102.52100.5696636985881.95033630141207
12101.23101.585839571886-0.355839571886094
13102.14101.400437911950.739562088049979
14101.06101.785768970054-0.725768970054347
15100.31101.407624484704-1.09762448470394
16101.18100.8357336172210.344266382778727
17101.28101.0151053450170.264894654982811
18101.99101.153122340940.836877659060463
19101.34101.589157339326-0.249157339326104
20100.5101.45933989364-0.959339893639921
21103.74100.9594988900642.78050110993649
22104.19102.4082121922521.78178780774827
23102.23103.33656992228-1.10656992227999
24103.32102.7600182494610.559981750538796
25104.67103.0517832870971.61821671290258
26103.22103.894916227929-0.674916227928662
27102.64103.543267342133-0.903267342132935
28105.26103.0726415943842.18735840561585
29103.63104.212312140655-0.582312140655333
30102.71103.908912389733-1.19891238973334
31104.34103.2842478927631.05575210723738
32102.92103.834322163944-0.914322163944249
33105.92103.3579365668812.56206343311879
34107.39104.6928381654982.69716183450227
35105.68106.098129540435-0.418129540435203
36105.86105.880273188894-0.0202731888942651
37107.05105.8697103308811.18028966911861
38106.77106.4846719066840.285328093315997
39105.88106.633335254739-0.753335254739397
40106.23106.24082801903-0.0108280190299013
41107.53106.2351863398561.294813660144
42105.51106.90981788976-1.39981788975977
43107.37106.1804764087261.1895235912736
44105.61106.800249097824-1.19024909782421
45108.38106.1800984009682.19990159903159
46109.6107.326304276822.27369572317959
47106.62108.510958808166-1.89095880816636
48105.69107.525720151188-1.83572015118803
49107.06106.5692622693270.490737730672635
50105.67106.82494937399-1.15494937399008
51106.24106.2231907501670.0168092498328036
52107.9106.2319488059531.66805119404727
53105.91107.101046805918-1.19104680591809
54106.44106.480480482425-0.0404804824247833
55107.69106.4593890995951.23061090040481
56105.9107.100569343999-1.20056934399904
57108.59106.4750415308162.11495846918372
58111.36107.5769898296083.78301017039232
59109.36109.548036392609-0.188036392608652
60109.21109.450064547788-0.24006454778754
61111.3109.3249846826791.9750153173205
62109.21110.354018964307-1.14401896430691
63110.95109.7579553678481.1920446321521
64110.89110.3790415847280.510958415272199
65111.04110.6452641913020.394735808697973
66108.96110.850931800952-1.89093180095239
67110.5109.8657072154340.634292784565957
68109.02110.196190232038-1.1761902320381
69112.87109.5833645694383.28663543056211
70112.73111.2957869995831.43421300041706
71113.28112.0430492266871.23695077331335
72113.53112.6875327095550.842467290445043
73112.99113.126480051084-0.136480051084376
74112.68113.055370399381-0.375370399380685
75114.26112.8597926710041.4002073289961
76114.28113.5893370599950.690662940004856
77114.28113.9491903918060.330809608194343
78114.2114.1215507905010.0784492094985296
79113.64114.16242486638-0.522424866379566
80114.2113.8902279409360.309772059064301
81116.68114.0516272300812.62837276991857
82116.73115.4210777155651.30892228443493
83118.71116.1030602251982.60693977480204
84117.8117.4613435635010.338656436499207

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101.13 & 100.17 & 0.959999999999994 \tabularnewline
3 & 99.25 & 100.670184936136 & -1.42018493613637 \tabularnewline
4 & 99.69 & 99.9302316949039 & -0.240231694903855 \tabularnewline
5 & 101.04 & 99.8050647418065 & 1.23493525819346 \tabularnewline
6 & 99.79 & 100.448498088944 & -0.658498088944086 \tabularnewline
7 & 100.35 & 100.105403480023 & 0.244596519977179 \tabularnewline
8 & 101.45 & 100.23284462036 & 1.21715537963972 \tabularnewline
9 & 100.4 & 100.867014188936 & -0.46701418893646 \tabularnewline
10 & 100.52 & 100.623687665741 & -0.103687665740679 \tabularnewline
11 & 102.52 & 100.569663698588 & 1.95033630141207 \tabularnewline
12 & 101.23 & 101.585839571886 & -0.355839571886094 \tabularnewline
13 & 102.14 & 101.40043791195 & 0.739562088049979 \tabularnewline
14 & 101.06 & 101.785768970054 & -0.725768970054347 \tabularnewline
15 & 100.31 & 101.407624484704 & -1.09762448470394 \tabularnewline
16 & 101.18 & 100.835733617221 & 0.344266382778727 \tabularnewline
17 & 101.28 & 101.015105345017 & 0.264894654982811 \tabularnewline
18 & 101.99 & 101.15312234094 & 0.836877659060463 \tabularnewline
19 & 101.34 & 101.589157339326 & -0.249157339326104 \tabularnewline
20 & 100.5 & 101.45933989364 & -0.959339893639921 \tabularnewline
21 & 103.74 & 100.959498890064 & 2.78050110993649 \tabularnewline
22 & 104.19 & 102.408212192252 & 1.78178780774827 \tabularnewline
23 & 102.23 & 103.33656992228 & -1.10656992227999 \tabularnewline
24 & 103.32 & 102.760018249461 & 0.559981750538796 \tabularnewline
25 & 104.67 & 103.051783287097 & 1.61821671290258 \tabularnewline
26 & 103.22 & 103.894916227929 & -0.674916227928662 \tabularnewline
27 & 102.64 & 103.543267342133 & -0.903267342132935 \tabularnewline
28 & 105.26 & 103.072641594384 & 2.18735840561585 \tabularnewline
29 & 103.63 & 104.212312140655 & -0.582312140655333 \tabularnewline
30 & 102.71 & 103.908912389733 & -1.19891238973334 \tabularnewline
31 & 104.34 & 103.284247892763 & 1.05575210723738 \tabularnewline
32 & 102.92 & 103.834322163944 & -0.914322163944249 \tabularnewline
33 & 105.92 & 103.357936566881 & 2.56206343311879 \tabularnewline
34 & 107.39 & 104.692838165498 & 2.69716183450227 \tabularnewline
35 & 105.68 & 106.098129540435 & -0.418129540435203 \tabularnewline
36 & 105.86 & 105.880273188894 & -0.0202731888942651 \tabularnewline
37 & 107.05 & 105.869710330881 & 1.18028966911861 \tabularnewline
38 & 106.77 & 106.484671906684 & 0.285328093315997 \tabularnewline
39 & 105.88 & 106.633335254739 & -0.753335254739397 \tabularnewline
40 & 106.23 & 106.24082801903 & -0.0108280190299013 \tabularnewline
41 & 107.53 & 106.235186339856 & 1.294813660144 \tabularnewline
42 & 105.51 & 106.90981788976 & -1.39981788975977 \tabularnewline
43 & 107.37 & 106.180476408726 & 1.1895235912736 \tabularnewline
44 & 105.61 & 106.800249097824 & -1.19024909782421 \tabularnewline
45 & 108.38 & 106.180098400968 & 2.19990159903159 \tabularnewline
46 & 109.6 & 107.32630427682 & 2.27369572317959 \tabularnewline
47 & 106.62 & 108.510958808166 & -1.89095880816636 \tabularnewline
48 & 105.69 & 107.525720151188 & -1.83572015118803 \tabularnewline
49 & 107.06 & 106.569262269327 & 0.490737730672635 \tabularnewline
50 & 105.67 & 106.82494937399 & -1.15494937399008 \tabularnewline
51 & 106.24 & 106.223190750167 & 0.0168092498328036 \tabularnewline
52 & 107.9 & 106.231948805953 & 1.66805119404727 \tabularnewline
53 & 105.91 & 107.101046805918 & -1.19104680591809 \tabularnewline
54 & 106.44 & 106.480480482425 & -0.0404804824247833 \tabularnewline
55 & 107.69 & 106.459389099595 & 1.23061090040481 \tabularnewline
56 & 105.9 & 107.100569343999 & -1.20056934399904 \tabularnewline
57 & 108.59 & 106.475041530816 & 2.11495846918372 \tabularnewline
58 & 111.36 & 107.576989829608 & 3.78301017039232 \tabularnewline
59 & 109.36 & 109.548036392609 & -0.188036392608652 \tabularnewline
60 & 109.21 & 109.450064547788 & -0.24006454778754 \tabularnewline
61 & 111.3 & 109.324984682679 & 1.9750153173205 \tabularnewline
62 & 109.21 & 110.354018964307 & -1.14401896430691 \tabularnewline
63 & 110.95 & 109.757955367848 & 1.1920446321521 \tabularnewline
64 & 110.89 & 110.379041584728 & 0.510958415272199 \tabularnewline
65 & 111.04 & 110.645264191302 & 0.394735808697973 \tabularnewline
66 & 108.96 & 110.850931800952 & -1.89093180095239 \tabularnewline
67 & 110.5 & 109.865707215434 & 0.634292784565957 \tabularnewline
68 & 109.02 & 110.196190232038 & -1.1761902320381 \tabularnewline
69 & 112.87 & 109.583364569438 & 3.28663543056211 \tabularnewline
70 & 112.73 & 111.295786999583 & 1.43421300041706 \tabularnewline
71 & 113.28 & 112.043049226687 & 1.23695077331335 \tabularnewline
72 & 113.53 & 112.687532709555 & 0.842467290445043 \tabularnewline
73 & 112.99 & 113.126480051084 & -0.136480051084376 \tabularnewline
74 & 112.68 & 113.055370399381 & -0.375370399380685 \tabularnewline
75 & 114.26 & 112.859792671004 & 1.4002073289961 \tabularnewline
76 & 114.28 & 113.589337059995 & 0.690662940004856 \tabularnewline
77 & 114.28 & 113.949190391806 & 0.330809608194343 \tabularnewline
78 & 114.2 & 114.121550790501 & 0.0784492094985296 \tabularnewline
79 & 113.64 & 114.16242486638 & -0.522424866379566 \tabularnewline
80 & 114.2 & 113.890227940936 & 0.309772059064301 \tabularnewline
81 & 116.68 & 114.051627230081 & 2.62837276991857 \tabularnewline
82 & 116.73 & 115.421077715565 & 1.30892228443493 \tabularnewline
83 & 118.71 & 116.103060225198 & 2.60693977480204 \tabularnewline
84 & 117.8 & 117.461343563501 & 0.338656436499207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233104&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]2[/C][C]101.13[/C][C]100.17[/C][C]0.959999999999994[/C][/ROW]
[ROW][C]3[/C][C]99.25[/C][C]100.670184936136[/C][C]-1.42018493613637[/C][/ROW]
[ROW][C]4[/C][C]99.69[/C][C]99.9302316949039[/C][C]-0.240231694903855[/C][/ROW]
[ROW][C]5[/C][C]101.04[/C][C]99.8050647418065[/C][C]1.23493525819346[/C][/ROW]
[ROW][C]6[/C][C]99.79[/C][C]100.448498088944[/C][C]-0.658498088944086[/C][/ROW]
[ROW][C]7[/C][C]100.35[/C][C]100.105403480023[/C][C]0.244596519977179[/C][/ROW]
[ROW][C]8[/C][C]101.45[/C][C]100.23284462036[/C][C]1.21715537963972[/C][/ROW]
[ROW][C]9[/C][C]100.4[/C][C]100.867014188936[/C][C]-0.46701418893646[/C][/ROW]
[ROW][C]10[/C][C]100.52[/C][C]100.623687665741[/C][C]-0.103687665740679[/C][/ROW]
[ROW][C]11[/C][C]102.52[/C][C]100.569663698588[/C][C]1.95033630141207[/C][/ROW]
[ROW][C]12[/C][C]101.23[/C][C]101.585839571886[/C][C]-0.355839571886094[/C][/ROW]
[ROW][C]13[/C][C]102.14[/C][C]101.40043791195[/C][C]0.739562088049979[/C][/ROW]
[ROW][C]14[/C][C]101.06[/C][C]101.785768970054[/C][C]-0.725768970054347[/C][/ROW]
[ROW][C]15[/C][C]100.31[/C][C]101.407624484704[/C][C]-1.09762448470394[/C][/ROW]
[ROW][C]16[/C][C]101.18[/C][C]100.835733617221[/C][C]0.344266382778727[/C][/ROW]
[ROW][C]17[/C][C]101.28[/C][C]101.015105345017[/C][C]0.264894654982811[/C][/ROW]
[ROW][C]18[/C][C]101.99[/C][C]101.15312234094[/C][C]0.836877659060463[/C][/ROW]
[ROW][C]19[/C][C]101.34[/C][C]101.589157339326[/C][C]-0.249157339326104[/C][/ROW]
[ROW][C]20[/C][C]100.5[/C][C]101.45933989364[/C][C]-0.959339893639921[/C][/ROW]
[ROW][C]21[/C][C]103.74[/C][C]100.959498890064[/C][C]2.78050110993649[/C][/ROW]
[ROW][C]22[/C][C]104.19[/C][C]102.408212192252[/C][C]1.78178780774827[/C][/ROW]
[ROW][C]23[/C][C]102.23[/C][C]103.33656992228[/C][C]-1.10656992227999[/C][/ROW]
[ROW][C]24[/C][C]103.32[/C][C]102.760018249461[/C][C]0.559981750538796[/C][/ROW]
[ROW][C]25[/C][C]104.67[/C][C]103.051783287097[/C][C]1.61821671290258[/C][/ROW]
[ROW][C]26[/C][C]103.22[/C][C]103.894916227929[/C][C]-0.674916227928662[/C][/ROW]
[ROW][C]27[/C][C]102.64[/C][C]103.543267342133[/C][C]-0.903267342132935[/C][/ROW]
[ROW][C]28[/C][C]105.26[/C][C]103.072641594384[/C][C]2.18735840561585[/C][/ROW]
[ROW][C]29[/C][C]103.63[/C][C]104.212312140655[/C][C]-0.582312140655333[/C][/ROW]
[ROW][C]30[/C][C]102.71[/C][C]103.908912389733[/C][C]-1.19891238973334[/C][/ROW]
[ROW][C]31[/C][C]104.34[/C][C]103.284247892763[/C][C]1.05575210723738[/C][/ROW]
[ROW][C]32[/C][C]102.92[/C][C]103.834322163944[/C][C]-0.914322163944249[/C][/ROW]
[ROW][C]33[/C][C]105.92[/C][C]103.357936566881[/C][C]2.56206343311879[/C][/ROW]
[ROW][C]34[/C][C]107.39[/C][C]104.692838165498[/C][C]2.69716183450227[/C][/ROW]
[ROW][C]35[/C][C]105.68[/C][C]106.098129540435[/C][C]-0.418129540435203[/C][/ROW]
[ROW][C]36[/C][C]105.86[/C][C]105.880273188894[/C][C]-0.0202731888942651[/C][/ROW]
[ROW][C]37[/C][C]107.05[/C][C]105.869710330881[/C][C]1.18028966911861[/C][/ROW]
[ROW][C]38[/C][C]106.77[/C][C]106.484671906684[/C][C]0.285328093315997[/C][/ROW]
[ROW][C]39[/C][C]105.88[/C][C]106.633335254739[/C][C]-0.753335254739397[/C][/ROW]
[ROW][C]40[/C][C]106.23[/C][C]106.24082801903[/C][C]-0.0108280190299013[/C][/ROW]
[ROW][C]41[/C][C]107.53[/C][C]106.235186339856[/C][C]1.294813660144[/C][/ROW]
[ROW][C]42[/C][C]105.51[/C][C]106.90981788976[/C][C]-1.39981788975977[/C][/ROW]
[ROW][C]43[/C][C]107.37[/C][C]106.180476408726[/C][C]1.1895235912736[/C][/ROW]
[ROW][C]44[/C][C]105.61[/C][C]106.800249097824[/C][C]-1.19024909782421[/C][/ROW]
[ROW][C]45[/C][C]108.38[/C][C]106.180098400968[/C][C]2.19990159903159[/C][/ROW]
[ROW][C]46[/C][C]109.6[/C][C]107.32630427682[/C][C]2.27369572317959[/C][/ROW]
[ROW][C]47[/C][C]106.62[/C][C]108.510958808166[/C][C]-1.89095880816636[/C][/ROW]
[ROW][C]48[/C][C]105.69[/C][C]107.525720151188[/C][C]-1.83572015118803[/C][/ROW]
[ROW][C]49[/C][C]107.06[/C][C]106.569262269327[/C][C]0.490737730672635[/C][/ROW]
[ROW][C]50[/C][C]105.67[/C][C]106.82494937399[/C][C]-1.15494937399008[/C][/ROW]
[ROW][C]51[/C][C]106.24[/C][C]106.223190750167[/C][C]0.0168092498328036[/C][/ROW]
[ROW][C]52[/C][C]107.9[/C][C]106.231948805953[/C][C]1.66805119404727[/C][/ROW]
[ROW][C]53[/C][C]105.91[/C][C]107.101046805918[/C][C]-1.19104680591809[/C][/ROW]
[ROW][C]54[/C][C]106.44[/C][C]106.480480482425[/C][C]-0.0404804824247833[/C][/ROW]
[ROW][C]55[/C][C]107.69[/C][C]106.459389099595[/C][C]1.23061090040481[/C][/ROW]
[ROW][C]56[/C][C]105.9[/C][C]107.100569343999[/C][C]-1.20056934399904[/C][/ROW]
[ROW][C]57[/C][C]108.59[/C][C]106.475041530816[/C][C]2.11495846918372[/C][/ROW]
[ROW][C]58[/C][C]111.36[/C][C]107.576989829608[/C][C]3.78301017039232[/C][/ROW]
[ROW][C]59[/C][C]109.36[/C][C]109.548036392609[/C][C]-0.188036392608652[/C][/ROW]
[ROW][C]60[/C][C]109.21[/C][C]109.450064547788[/C][C]-0.24006454778754[/C][/ROW]
[ROW][C]61[/C][C]111.3[/C][C]109.324984682679[/C][C]1.9750153173205[/C][/ROW]
[ROW][C]62[/C][C]109.21[/C][C]110.354018964307[/C][C]-1.14401896430691[/C][/ROW]
[ROW][C]63[/C][C]110.95[/C][C]109.757955367848[/C][C]1.1920446321521[/C][/ROW]
[ROW][C]64[/C][C]110.89[/C][C]110.379041584728[/C][C]0.510958415272199[/C][/ROW]
[ROW][C]65[/C][C]111.04[/C][C]110.645264191302[/C][C]0.394735808697973[/C][/ROW]
[ROW][C]66[/C][C]108.96[/C][C]110.850931800952[/C][C]-1.89093180095239[/C][/ROW]
[ROW][C]67[/C][C]110.5[/C][C]109.865707215434[/C][C]0.634292784565957[/C][/ROW]
[ROW][C]68[/C][C]109.02[/C][C]110.196190232038[/C][C]-1.1761902320381[/C][/ROW]
[ROW][C]69[/C][C]112.87[/C][C]109.583364569438[/C][C]3.28663543056211[/C][/ROW]
[ROW][C]70[/C][C]112.73[/C][C]111.295786999583[/C][C]1.43421300041706[/C][/ROW]
[ROW][C]71[/C][C]113.28[/C][C]112.043049226687[/C][C]1.23695077331335[/C][/ROW]
[ROW][C]72[/C][C]113.53[/C][C]112.687532709555[/C][C]0.842467290445043[/C][/ROW]
[ROW][C]73[/C][C]112.99[/C][C]113.126480051084[/C][C]-0.136480051084376[/C][/ROW]
[ROW][C]74[/C][C]112.68[/C][C]113.055370399381[/C][C]-0.375370399380685[/C][/ROW]
[ROW][C]75[/C][C]114.26[/C][C]112.859792671004[/C][C]1.4002073289961[/C][/ROW]
[ROW][C]76[/C][C]114.28[/C][C]113.589337059995[/C][C]0.690662940004856[/C][/ROW]
[ROW][C]77[/C][C]114.28[/C][C]113.949190391806[/C][C]0.330809608194343[/C][/ROW]
[ROW][C]78[/C][C]114.2[/C][C]114.121550790501[/C][C]0.0784492094985296[/C][/ROW]
[ROW][C]79[/C][C]113.64[/C][C]114.16242486638[/C][C]-0.522424866379566[/C][/ROW]
[ROW][C]80[/C][C]114.2[/C][C]113.890227940936[/C][C]0.309772059064301[/C][/ROW]
[ROW][C]81[/C][C]116.68[/C][C]114.051627230081[/C][C]2.62837276991857[/C][/ROW]
[ROW][C]82[/C][C]116.73[/C][C]115.421077715565[/C][C]1.30892228443493[/C][/ROW]
[ROW][C]83[/C][C]118.71[/C][C]116.103060225198[/C][C]2.60693977480204[/C][/ROW]
[ROW][C]84[/C][C]117.8[/C][C]117.461343563501[/C][C]0.338656436499207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233104&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
2101.13100.170.959999999999994
399.25100.670184936136-1.42018493613637
499.6999.9302316949039-0.240231694903855
5101.0499.80506474180651.23493525819346
699.79100.448498088944-0.658498088944086
7100.35100.1054034800230.244596519977179
8101.45100.232844620361.21715537963972
9100.4100.867014188936-0.46701418893646
10100.52100.623687665741-0.103687665740679
11102.52100.5696636985881.95033630141207
12101.23101.585839571886-0.355839571886094
13102.14101.400437911950.739562088049979
14101.06101.785768970054-0.725768970054347
15100.31101.407624484704-1.09762448470394
16101.18100.8357336172210.344266382778727
17101.28101.0151053450170.264894654982811
18101.99101.153122340940.836877659060463
19101.34101.589157339326-0.249157339326104
20100.5101.45933989364-0.959339893639921
21103.74100.9594988900642.78050110993649
22104.19102.4082121922521.78178780774827
23102.23103.33656992228-1.10656992227999
24103.32102.7600182494610.559981750538796
25104.67103.0517832870971.61821671290258
26103.22103.894916227929-0.674916227928662
27102.64103.543267342133-0.903267342132935
28105.26103.0726415943842.18735840561585
29103.63104.212312140655-0.582312140655333
30102.71103.908912389733-1.19891238973334
31104.34103.2842478927631.05575210723738
32102.92103.834322163944-0.914322163944249
33105.92103.3579365668812.56206343311879
34107.39104.6928381654982.69716183450227
35105.68106.098129540435-0.418129540435203
36105.86105.880273188894-0.0202731888942651
37107.05105.8697103308811.18028966911861
38106.77106.4846719066840.285328093315997
39105.88106.633335254739-0.753335254739397
40106.23106.24082801903-0.0108280190299013
41107.53106.2351863398561.294813660144
42105.51106.90981788976-1.39981788975977
43107.37106.1804764087261.1895235912736
44105.61106.800249097824-1.19024909782421
45108.38106.1800984009682.19990159903159
46109.6107.326304276822.27369572317959
47106.62108.510958808166-1.89095880816636
48105.69107.525720151188-1.83572015118803
49107.06106.5692622693270.490737730672635
50105.67106.82494937399-1.15494937399008
51106.24106.2231907501670.0168092498328036
52107.9106.2319488059531.66805119404727
53105.91107.101046805918-1.19104680591809
54106.44106.480480482425-0.0404804824247833
55107.69106.4593890995951.23061090040481
56105.9107.100569343999-1.20056934399904
57108.59106.4750415308162.11495846918372
58111.36107.5769898296083.78301017039232
59109.36109.548036392609-0.188036392608652
60109.21109.450064547788-0.24006454778754
61111.3109.3249846826791.9750153173205
62109.21110.354018964307-1.14401896430691
63110.95109.7579553678481.1920446321521
64110.89110.3790415847280.510958415272199
65111.04110.6452641913020.394735808697973
66108.96110.850931800952-1.89093180095239
67110.5109.8657072154340.634292784565957
68109.02110.196190232038-1.1761902320381
69112.87109.5833645694383.28663543056211
70112.73111.2957869995831.43421300041706
71113.28112.0430492266871.23695077331335
72113.53112.6875327095550.842467290445043
73112.99113.126480051084-0.136480051084376
74112.68113.055370399381-0.375370399380685
75114.26112.8597926710041.4002073289961
76114.28113.5893370599950.690662940004856
77114.28113.9491903918060.330809608194343
78114.2114.1215507905010.0784492094985296
79113.64114.16242486638-0.522424866379566
80114.2113.8902279409360.309772059064301
81116.68114.0516272300812.62837276991857
82116.73115.4210777155651.30892228443493
83118.71116.1030602251982.60693977480204
84117.8117.4613435635010.338656436499207







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85117.637792363566115.083044513531120.192540213601
86117.637792363566114.757074199944120.518510527188
87117.637792363566114.464412824465120.811171902667
88117.637792363566114.19655156116121.079033165972
89117.637792363566113.948085217855121.327499509277
90117.637792363566113.715326381295121.560258345837
91117.637792363566113.495626270441121.779958456691
92117.637792363566113.287006169785121.988578557347
93117.637792363566113.087941699538122.187643027594
94117.637792363566112.897228934403122.378355792729
95117.637792363566112.713897341646122.561687385485
96117.637792363566112.537150958032122.7384337691

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 117.637792363566 & 115.083044513531 & 120.192540213601 \tabularnewline
86 & 117.637792363566 & 114.757074199944 & 120.518510527188 \tabularnewline
87 & 117.637792363566 & 114.464412824465 & 120.811171902667 \tabularnewline
88 & 117.637792363566 & 114.19655156116 & 121.079033165972 \tabularnewline
89 & 117.637792363566 & 113.948085217855 & 121.327499509277 \tabularnewline
90 & 117.637792363566 & 113.715326381295 & 121.560258345837 \tabularnewline
91 & 117.637792363566 & 113.495626270441 & 121.779958456691 \tabularnewline
92 & 117.637792363566 & 113.287006169785 & 121.988578557347 \tabularnewline
93 & 117.637792363566 & 113.087941699538 & 122.187643027594 \tabularnewline
94 & 117.637792363566 & 112.897228934403 & 122.378355792729 \tabularnewline
95 & 117.637792363566 & 112.713897341646 & 122.561687385485 \tabularnewline
96 & 117.637792363566 & 112.537150958032 & 122.7384337691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233104&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]117.637792363566[/C][C]115.083044513531[/C][C]120.192540213601[/C][/ROW]
[ROW][C]86[/C][C]117.637792363566[/C][C]114.757074199944[/C][C]120.518510527188[/C][/ROW]
[ROW][C]87[/C][C]117.637792363566[/C][C]114.464412824465[/C][C]120.811171902667[/C][/ROW]
[ROW][C]88[/C][C]117.637792363566[/C][C]114.19655156116[/C][C]121.079033165972[/C][/ROW]
[ROW][C]89[/C][C]117.637792363566[/C][C]113.948085217855[/C][C]121.327499509277[/C][/ROW]
[ROW][C]90[/C][C]117.637792363566[/C][C]113.715326381295[/C][C]121.560258345837[/C][/ROW]
[ROW][C]91[/C][C]117.637792363566[/C][C]113.495626270441[/C][C]121.779958456691[/C][/ROW]
[ROW][C]92[/C][C]117.637792363566[/C][C]113.287006169785[/C][C]121.988578557347[/C][/ROW]
[ROW][C]93[/C][C]117.637792363566[/C][C]113.087941699538[/C][C]122.187643027594[/C][/ROW]
[ROW][C]94[/C][C]117.637792363566[/C][C]112.897228934403[/C][C]122.378355792729[/C][/ROW]
[ROW][C]95[/C][C]117.637792363566[/C][C]112.713897341646[/C][C]122.561687385485[/C][/ROW]
[ROW][C]96[/C][C]117.637792363566[/C][C]112.537150958032[/C][C]122.7384337691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233104&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
85117.637792363566115.083044513531120.192540213601
86117.637792363566114.757074199944120.518510527188
87117.637792363566114.464412824465120.811171902667
88117.637792363566114.19655156116121.079033165972
89117.637792363566113.948085217855121.327499509277
90117.637792363566113.715326381295121.560258345837
91117.637792363566113.495626270441121.779958456691
92117.637792363566113.287006169785121.988578557347
93117.637792363566113.087941699538122.187643027594
94117.637792363566112.897228934403122.378355792729
95117.637792363566112.713897341646122.561687385485
96117.637792363566112.537150958032122.7384337691



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')