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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 25 May 2016 22:43:10 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/May/25/t14642126149ts30zj7nqnnwwm.htm/, Retrieved Mon, 29 Apr 2024 05:39:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295592, Retrieved Mon, 29 Apr 2024 05:39:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-04-26 12:43:13] [abb1dd46b01bd3b5295a6bb2c98eecd5]
- R PD    [Exponential Smoothing] [] [2016-05-25 21:43:10] [705d764c18df8303d824462e41ab6988] [Current]
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Dataseries X:
109.12
109.12
109.73
112.59
112.59
112.29
113.8
114.16
112.29
112.29
110.99
110.99
110.99
110.99
111.98
114.26
114.26
114.44
115.47
115.41
114.63
116.48
115.8
115.18
115.18
115.18
115.18
116.38
122.41
122.47
123.09
123.09
123.09
123.09
121.77
121.52
121.52
121.52
121.52
124.73
125.23
124.62
128.94
129.34
127.17
128.08
124.54
121.21
120.85
119.02
119.13
119.84
125.53
124.16
127.32
127.22
122.57
125.45
125.45
127.32
128.79
128.99
129.8
130.33
131.19
132.02
136.97
139.45
128.31
130.73
129.83
125.46
130.23
130.23
132.65
136.34
139.12
133.94
143.09
142.71
136.09
134.57
134.65
134.35




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295592&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295592&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295592&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.627060828465961
beta0
gamma0.400037464658975

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.627060828465961 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.400037464658975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295592&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]0.627060828465961[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.400037464658975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295592&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295592&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
alpha0.627060828465961
beta0
gamma0.400037464658975







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13110.99110.0221067497330.967893250267252
14110.99110.693263242630.296736757369644
15111.98111.9051451103070.0748548896933841
16114.26114.1452780540480.11472194595153
17114.26114.0278287391470.232171260853107
18114.44114.1643609247760.275639075223566
19115.47116.168685875243-0.698685875243129
20115.41116.125318855673-0.715318855673104
21114.63113.7945557942390.835444205761476
22116.48114.3387102319872.14128976801297
23115.8114.3848188488981.41518115110183
24115.18115.293178499606-0.113178499606292
25115.18115.393627064117-0.21362706411746
26115.18115.214801329573-0.034801329572602
27115.18116.216771259392-1.03677125939164
28116.38117.830500970525-1.4505009705248
29122.41116.7405827198445.66941728015649
30122.47120.2828941929342.18710580706637
31123.09123.435231426943-0.345231426942959
32123.09123.623851250126-0.533851250125778
33123.09121.5148671570381.57513284296165
34123.09122.7156680854660.374331914533713
35121.77121.4485083507480.321491649251712
36121.52121.4221508085340.0978491914658548
37121.52121.638403197227-0.118403197226613
38121.52121.534869780959-0.0148697809585769
39121.52122.436879263399-0.916879263398982
40124.73124.1748532399550.555146760045162
41125.23125.424561661307-0.194561661307432
42124.62124.74173549829-0.121735498289866
43128.94126.0951033700032.84489662999708
44129.34128.2629140368441.07708596315601
45127.17127.40015750051-0.230157500509534
46128.08127.284030604730.795969395269807
47124.54126.207494291929-1.66749429192851
48121.21124.887874239384-3.67787423938367
49120.85122.703698462582-1.8536984625819
50119.02121.527483710461-2.50748371046113
51119.13120.72362228019-1.59362228018979
52119.84122.218083816926-2.37808381692572
53125.53121.4978998280294.03210017197115
54124.16123.4836474282190.676352571781038
55127.32125.7641920419661.55580795803407
56127.22126.859949728950.360050271049815
57122.57125.382454396309-2.81245439630861
58125.45123.7998809627981.65011903720161
59125.45122.9404172721822.50958272781784
60127.32123.9322789331123.3877210668884
61128.79126.4550257605172.33497423948255
62128.99127.7864976526181.20350234738207
63129.8129.4978565999240.302143400075749
64130.33132.246186303389-1.91618630338948
65131.19132.89494006926-1.70494006925958
66132.02130.7110933053391.30890669466095
67136.97133.626611367043.34338863296003
68139.45135.647662245783.80233775422016
69128.31135.646407881477-7.33640788147707
70130.73131.932611243959-1.20261124395861
71129.83129.312469624090.517530375909729
72125.46129.153228951516-3.69322895151639
73130.23127.074859392663.15514060734007
74130.23128.7477911548221.48220884517767
75132.65130.5041173365852.14588266341485
76136.34134.1082755720332.23172442796678
77139.12137.4488624108261.67113758917441
78133.94137.785455573964-3.84545557396413
79143.09137.8255792732985.2644207267021
80142.71141.1024197928761.60758020712433
81136.09137.916509984556-1.82650998455591
82134.57138.656475446989-4.08647544698891
83134.65134.4146138927720.235386107227782
84134.35133.3914108009370.958589199062686

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 110.99 & 110.022106749733 & 0.967893250267252 \tabularnewline
14 & 110.99 & 110.69326324263 & 0.296736757369644 \tabularnewline
15 & 111.98 & 111.905145110307 & 0.0748548896933841 \tabularnewline
16 & 114.26 & 114.145278054048 & 0.11472194595153 \tabularnewline
17 & 114.26 & 114.027828739147 & 0.232171260853107 \tabularnewline
18 & 114.44 & 114.164360924776 & 0.275639075223566 \tabularnewline
19 & 115.47 & 116.168685875243 & -0.698685875243129 \tabularnewline
20 & 115.41 & 116.125318855673 & -0.715318855673104 \tabularnewline
21 & 114.63 & 113.794555794239 & 0.835444205761476 \tabularnewline
22 & 116.48 & 114.338710231987 & 2.14128976801297 \tabularnewline
23 & 115.8 & 114.384818848898 & 1.41518115110183 \tabularnewline
24 & 115.18 & 115.293178499606 & -0.113178499606292 \tabularnewline
25 & 115.18 & 115.393627064117 & -0.21362706411746 \tabularnewline
26 & 115.18 & 115.214801329573 & -0.034801329572602 \tabularnewline
27 & 115.18 & 116.216771259392 & -1.03677125939164 \tabularnewline
28 & 116.38 & 117.830500970525 & -1.4505009705248 \tabularnewline
29 & 122.41 & 116.740582719844 & 5.66941728015649 \tabularnewline
30 & 122.47 & 120.282894192934 & 2.18710580706637 \tabularnewline
31 & 123.09 & 123.435231426943 & -0.345231426942959 \tabularnewline
32 & 123.09 & 123.623851250126 & -0.533851250125778 \tabularnewline
33 & 123.09 & 121.514867157038 & 1.57513284296165 \tabularnewline
34 & 123.09 & 122.715668085466 & 0.374331914533713 \tabularnewline
35 & 121.77 & 121.448508350748 & 0.321491649251712 \tabularnewline
36 & 121.52 & 121.422150808534 & 0.0978491914658548 \tabularnewline
37 & 121.52 & 121.638403197227 & -0.118403197226613 \tabularnewline
38 & 121.52 & 121.534869780959 & -0.0148697809585769 \tabularnewline
39 & 121.52 & 122.436879263399 & -0.916879263398982 \tabularnewline
40 & 124.73 & 124.174853239955 & 0.555146760045162 \tabularnewline
41 & 125.23 & 125.424561661307 & -0.194561661307432 \tabularnewline
42 & 124.62 & 124.74173549829 & -0.121735498289866 \tabularnewline
43 & 128.94 & 126.095103370003 & 2.84489662999708 \tabularnewline
44 & 129.34 & 128.262914036844 & 1.07708596315601 \tabularnewline
45 & 127.17 & 127.40015750051 & -0.230157500509534 \tabularnewline
46 & 128.08 & 127.28403060473 & 0.795969395269807 \tabularnewline
47 & 124.54 & 126.207494291929 & -1.66749429192851 \tabularnewline
48 & 121.21 & 124.887874239384 & -3.67787423938367 \tabularnewline
49 & 120.85 & 122.703698462582 & -1.8536984625819 \tabularnewline
50 & 119.02 & 121.527483710461 & -2.50748371046113 \tabularnewline
51 & 119.13 & 120.72362228019 & -1.59362228018979 \tabularnewline
52 & 119.84 & 122.218083816926 & -2.37808381692572 \tabularnewline
53 & 125.53 & 121.497899828029 & 4.03210017197115 \tabularnewline
54 & 124.16 & 123.483647428219 & 0.676352571781038 \tabularnewline
55 & 127.32 & 125.764192041966 & 1.55580795803407 \tabularnewline
56 & 127.22 & 126.85994972895 & 0.360050271049815 \tabularnewline
57 & 122.57 & 125.382454396309 & -2.81245439630861 \tabularnewline
58 & 125.45 & 123.799880962798 & 1.65011903720161 \tabularnewline
59 & 125.45 & 122.940417272182 & 2.50958272781784 \tabularnewline
60 & 127.32 & 123.932278933112 & 3.3877210668884 \tabularnewline
61 & 128.79 & 126.455025760517 & 2.33497423948255 \tabularnewline
62 & 128.99 & 127.786497652618 & 1.20350234738207 \tabularnewline
63 & 129.8 & 129.497856599924 & 0.302143400075749 \tabularnewline
64 & 130.33 & 132.246186303389 & -1.91618630338948 \tabularnewline
65 & 131.19 & 132.89494006926 & -1.70494006925958 \tabularnewline
66 & 132.02 & 130.711093305339 & 1.30890669466095 \tabularnewline
67 & 136.97 & 133.62661136704 & 3.34338863296003 \tabularnewline
68 & 139.45 & 135.64766224578 & 3.80233775422016 \tabularnewline
69 & 128.31 & 135.646407881477 & -7.33640788147707 \tabularnewline
70 & 130.73 & 131.932611243959 & -1.20261124395861 \tabularnewline
71 & 129.83 & 129.31246962409 & 0.517530375909729 \tabularnewline
72 & 125.46 & 129.153228951516 & -3.69322895151639 \tabularnewline
73 & 130.23 & 127.07485939266 & 3.15514060734007 \tabularnewline
74 & 130.23 & 128.747791154822 & 1.48220884517767 \tabularnewline
75 & 132.65 & 130.504117336585 & 2.14588266341485 \tabularnewline
76 & 136.34 & 134.108275572033 & 2.23172442796678 \tabularnewline
77 & 139.12 & 137.448862410826 & 1.67113758917441 \tabularnewline
78 & 133.94 & 137.785455573964 & -3.84545557396413 \tabularnewline
79 & 143.09 & 137.825579273298 & 5.2644207267021 \tabularnewline
80 & 142.71 & 141.102419792876 & 1.60758020712433 \tabularnewline
81 & 136.09 & 137.916509984556 & -1.82650998455591 \tabularnewline
82 & 134.57 & 138.656475446989 & -4.08647544698891 \tabularnewline
83 & 134.65 & 134.414613892772 & 0.235386107227782 \tabularnewline
84 & 134.35 & 133.391410800937 & 0.958589199062686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295592&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]110.99[/C][C]110.022106749733[/C][C]0.967893250267252[/C][/ROW]
[ROW][C]14[/C][C]110.99[/C][C]110.69326324263[/C][C]0.296736757369644[/C][/ROW]
[ROW][C]15[/C][C]111.98[/C][C]111.905145110307[/C][C]0.0748548896933841[/C][/ROW]
[ROW][C]16[/C][C]114.26[/C][C]114.145278054048[/C][C]0.11472194595153[/C][/ROW]
[ROW][C]17[/C][C]114.26[/C][C]114.027828739147[/C][C]0.232171260853107[/C][/ROW]
[ROW][C]18[/C][C]114.44[/C][C]114.164360924776[/C][C]0.275639075223566[/C][/ROW]
[ROW][C]19[/C][C]115.47[/C][C]116.168685875243[/C][C]-0.698685875243129[/C][/ROW]
[ROW][C]20[/C][C]115.41[/C][C]116.125318855673[/C][C]-0.715318855673104[/C][/ROW]
[ROW][C]21[/C][C]114.63[/C][C]113.794555794239[/C][C]0.835444205761476[/C][/ROW]
[ROW][C]22[/C][C]116.48[/C][C]114.338710231987[/C][C]2.14128976801297[/C][/ROW]
[ROW][C]23[/C][C]115.8[/C][C]114.384818848898[/C][C]1.41518115110183[/C][/ROW]
[ROW][C]24[/C][C]115.18[/C][C]115.293178499606[/C][C]-0.113178499606292[/C][/ROW]
[ROW][C]25[/C][C]115.18[/C][C]115.393627064117[/C][C]-0.21362706411746[/C][/ROW]
[ROW][C]26[/C][C]115.18[/C][C]115.214801329573[/C][C]-0.034801329572602[/C][/ROW]
[ROW][C]27[/C][C]115.18[/C][C]116.216771259392[/C][C]-1.03677125939164[/C][/ROW]
[ROW][C]28[/C][C]116.38[/C][C]117.830500970525[/C][C]-1.4505009705248[/C][/ROW]
[ROW][C]29[/C][C]122.41[/C][C]116.740582719844[/C][C]5.66941728015649[/C][/ROW]
[ROW][C]30[/C][C]122.47[/C][C]120.282894192934[/C][C]2.18710580706637[/C][/ROW]
[ROW][C]31[/C][C]123.09[/C][C]123.435231426943[/C][C]-0.345231426942959[/C][/ROW]
[ROW][C]32[/C][C]123.09[/C][C]123.623851250126[/C][C]-0.533851250125778[/C][/ROW]
[ROW][C]33[/C][C]123.09[/C][C]121.514867157038[/C][C]1.57513284296165[/C][/ROW]
[ROW][C]34[/C][C]123.09[/C][C]122.715668085466[/C][C]0.374331914533713[/C][/ROW]
[ROW][C]35[/C][C]121.77[/C][C]121.448508350748[/C][C]0.321491649251712[/C][/ROW]
[ROW][C]36[/C][C]121.52[/C][C]121.422150808534[/C][C]0.0978491914658548[/C][/ROW]
[ROW][C]37[/C][C]121.52[/C][C]121.638403197227[/C][C]-0.118403197226613[/C][/ROW]
[ROW][C]38[/C][C]121.52[/C][C]121.534869780959[/C][C]-0.0148697809585769[/C][/ROW]
[ROW][C]39[/C][C]121.52[/C][C]122.436879263399[/C][C]-0.916879263398982[/C][/ROW]
[ROW][C]40[/C][C]124.73[/C][C]124.174853239955[/C][C]0.555146760045162[/C][/ROW]
[ROW][C]41[/C][C]125.23[/C][C]125.424561661307[/C][C]-0.194561661307432[/C][/ROW]
[ROW][C]42[/C][C]124.62[/C][C]124.74173549829[/C][C]-0.121735498289866[/C][/ROW]
[ROW][C]43[/C][C]128.94[/C][C]126.095103370003[/C][C]2.84489662999708[/C][/ROW]
[ROW][C]44[/C][C]129.34[/C][C]128.262914036844[/C][C]1.07708596315601[/C][/ROW]
[ROW][C]45[/C][C]127.17[/C][C]127.40015750051[/C][C]-0.230157500509534[/C][/ROW]
[ROW][C]46[/C][C]128.08[/C][C]127.28403060473[/C][C]0.795969395269807[/C][/ROW]
[ROW][C]47[/C][C]124.54[/C][C]126.207494291929[/C][C]-1.66749429192851[/C][/ROW]
[ROW][C]48[/C][C]121.21[/C][C]124.887874239384[/C][C]-3.67787423938367[/C][/ROW]
[ROW][C]49[/C][C]120.85[/C][C]122.703698462582[/C][C]-1.8536984625819[/C][/ROW]
[ROW][C]50[/C][C]119.02[/C][C]121.527483710461[/C][C]-2.50748371046113[/C][/ROW]
[ROW][C]51[/C][C]119.13[/C][C]120.72362228019[/C][C]-1.59362228018979[/C][/ROW]
[ROW][C]52[/C][C]119.84[/C][C]122.218083816926[/C][C]-2.37808381692572[/C][/ROW]
[ROW][C]53[/C][C]125.53[/C][C]121.497899828029[/C][C]4.03210017197115[/C][/ROW]
[ROW][C]54[/C][C]124.16[/C][C]123.483647428219[/C][C]0.676352571781038[/C][/ROW]
[ROW][C]55[/C][C]127.32[/C][C]125.764192041966[/C][C]1.55580795803407[/C][/ROW]
[ROW][C]56[/C][C]127.22[/C][C]126.85994972895[/C][C]0.360050271049815[/C][/ROW]
[ROW][C]57[/C][C]122.57[/C][C]125.382454396309[/C][C]-2.81245439630861[/C][/ROW]
[ROW][C]58[/C][C]125.45[/C][C]123.799880962798[/C][C]1.65011903720161[/C][/ROW]
[ROW][C]59[/C][C]125.45[/C][C]122.940417272182[/C][C]2.50958272781784[/C][/ROW]
[ROW][C]60[/C][C]127.32[/C][C]123.932278933112[/C][C]3.3877210668884[/C][/ROW]
[ROW][C]61[/C][C]128.79[/C][C]126.455025760517[/C][C]2.33497423948255[/C][/ROW]
[ROW][C]62[/C][C]128.99[/C][C]127.786497652618[/C][C]1.20350234738207[/C][/ROW]
[ROW][C]63[/C][C]129.8[/C][C]129.497856599924[/C][C]0.302143400075749[/C][/ROW]
[ROW][C]64[/C][C]130.33[/C][C]132.246186303389[/C][C]-1.91618630338948[/C][/ROW]
[ROW][C]65[/C][C]131.19[/C][C]132.89494006926[/C][C]-1.70494006925958[/C][/ROW]
[ROW][C]66[/C][C]132.02[/C][C]130.711093305339[/C][C]1.30890669466095[/C][/ROW]
[ROW][C]67[/C][C]136.97[/C][C]133.62661136704[/C][C]3.34338863296003[/C][/ROW]
[ROW][C]68[/C][C]139.45[/C][C]135.64766224578[/C][C]3.80233775422016[/C][/ROW]
[ROW][C]69[/C][C]128.31[/C][C]135.646407881477[/C][C]-7.33640788147707[/C][/ROW]
[ROW][C]70[/C][C]130.73[/C][C]131.932611243959[/C][C]-1.20261124395861[/C][/ROW]
[ROW][C]71[/C][C]129.83[/C][C]129.31246962409[/C][C]0.517530375909729[/C][/ROW]
[ROW][C]72[/C][C]125.46[/C][C]129.153228951516[/C][C]-3.69322895151639[/C][/ROW]
[ROW][C]73[/C][C]130.23[/C][C]127.07485939266[/C][C]3.15514060734007[/C][/ROW]
[ROW][C]74[/C][C]130.23[/C][C]128.747791154822[/C][C]1.48220884517767[/C][/ROW]
[ROW][C]75[/C][C]132.65[/C][C]130.504117336585[/C][C]2.14588266341485[/C][/ROW]
[ROW][C]76[/C][C]136.34[/C][C]134.108275572033[/C][C]2.23172442796678[/C][/ROW]
[ROW][C]77[/C][C]139.12[/C][C]137.448862410826[/C][C]1.67113758917441[/C][/ROW]
[ROW][C]78[/C][C]133.94[/C][C]137.785455573964[/C][C]-3.84545557396413[/C][/ROW]
[ROW][C]79[/C][C]143.09[/C][C]137.825579273298[/C][C]5.2644207267021[/C][/ROW]
[ROW][C]80[/C][C]142.71[/C][C]141.102419792876[/C][C]1.60758020712433[/C][/ROW]
[ROW][C]81[/C][C]136.09[/C][C]137.916509984556[/C][C]-1.82650998455591[/C][/ROW]
[ROW][C]82[/C][C]134.57[/C][C]138.656475446989[/C][C]-4.08647544698891[/C][/ROW]
[ROW][C]83[/C][C]134.65[/C][C]134.414613892772[/C][C]0.235386107227782[/C][/ROW]
[ROW][C]84[/C][C]134.35[/C][C]133.391410800937[/C][C]0.958589199062686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295592&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295592&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
13110.99110.0221067497330.967893250267252
14110.99110.693263242630.296736757369644
15111.98111.9051451103070.0748548896933841
16114.26114.1452780540480.11472194595153
17114.26114.0278287391470.232171260853107
18114.44114.1643609247760.275639075223566
19115.47116.168685875243-0.698685875243129
20115.41116.125318855673-0.715318855673104
21114.63113.7945557942390.835444205761476
22116.48114.3387102319872.14128976801297
23115.8114.3848188488981.41518115110183
24115.18115.293178499606-0.113178499606292
25115.18115.393627064117-0.21362706411746
26115.18115.214801329573-0.034801329572602
27115.18116.216771259392-1.03677125939164
28116.38117.830500970525-1.4505009705248
29122.41116.7405827198445.66941728015649
30122.47120.2828941929342.18710580706637
31123.09123.435231426943-0.345231426942959
32123.09123.623851250126-0.533851250125778
33123.09121.5148671570381.57513284296165
34123.09122.7156680854660.374331914533713
35121.77121.4485083507480.321491649251712
36121.52121.4221508085340.0978491914658548
37121.52121.638403197227-0.118403197226613
38121.52121.534869780959-0.0148697809585769
39121.52122.436879263399-0.916879263398982
40124.73124.1748532399550.555146760045162
41125.23125.424561661307-0.194561661307432
42124.62124.74173549829-0.121735498289866
43128.94126.0951033700032.84489662999708
44129.34128.2629140368441.07708596315601
45127.17127.40015750051-0.230157500509534
46128.08127.284030604730.795969395269807
47124.54126.207494291929-1.66749429192851
48121.21124.887874239384-3.67787423938367
49120.85122.703698462582-1.8536984625819
50119.02121.527483710461-2.50748371046113
51119.13120.72362228019-1.59362228018979
52119.84122.218083816926-2.37808381692572
53125.53121.4978998280294.03210017197115
54124.16123.4836474282190.676352571781038
55127.32125.7641920419661.55580795803407
56127.22126.859949728950.360050271049815
57122.57125.382454396309-2.81245439630861
58125.45123.7998809627981.65011903720161
59125.45122.9404172721822.50958272781784
60127.32123.9322789331123.3877210668884
61128.79126.4550257605172.33497423948255
62128.99127.7864976526181.20350234738207
63129.8129.4978565999240.302143400075749
64130.33132.246186303389-1.91618630338948
65131.19132.89494006926-1.70494006925958
66132.02130.7110933053391.30890669466095
67136.97133.626611367043.34338863296003
68139.45135.647662245783.80233775422016
69128.31135.646407881477-7.33640788147707
70130.73131.932611243959-1.20261124395861
71129.83129.312469624090.517530375909729
72125.46129.153228951516-3.69322895151639
73130.23127.074859392663.15514060734007
74130.23128.7477911548221.48220884517767
75132.65130.5041173365852.14588266341485
76136.34134.1082755720332.23172442796678
77139.12137.4488624108261.67113758917441
78133.94137.785455573964-3.84545557396413
79143.09137.8255792732985.2644207267021
80142.71141.1024197928761.60758020712433
81136.09137.916509984556-1.82650998455591
82134.57138.656475446989-4.08647544698891
83134.65134.4146138927720.235386107227782
84134.35133.3914108009370.958589199062686







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85135.309634311507131.972175678913138.6470929441
86134.719864127836130.439172210169139.000556045503
87135.669893782422130.594702011469140.745085553376
88137.992912499062132.185971490292143.799853507833
89139.874945029243133.415401792327146.334488266158
90138.316303656832131.384131903557145.248475410107
91142.202377719024134.605346791889149.799408646159
92141.629281515133.603947294726149.654615735274
93136.945494471941128.724539665822145.16644927806
94138.486569227244129.761941785251147.211196669237
95137.424887902654128.364385294397146.48539051091
96136.335142958118116.678371616098155.991914300138

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 135.309634311507 & 131.972175678913 & 138.6470929441 \tabularnewline
86 & 134.719864127836 & 130.439172210169 & 139.000556045503 \tabularnewline
87 & 135.669893782422 & 130.594702011469 & 140.745085553376 \tabularnewline
88 & 137.992912499062 & 132.185971490292 & 143.799853507833 \tabularnewline
89 & 139.874945029243 & 133.415401792327 & 146.334488266158 \tabularnewline
90 & 138.316303656832 & 131.384131903557 & 145.248475410107 \tabularnewline
91 & 142.202377719024 & 134.605346791889 & 149.799408646159 \tabularnewline
92 & 141.629281515 & 133.603947294726 & 149.654615735274 \tabularnewline
93 & 136.945494471941 & 128.724539665822 & 145.16644927806 \tabularnewline
94 & 138.486569227244 & 129.761941785251 & 147.211196669237 \tabularnewline
95 & 137.424887902654 & 128.364385294397 & 146.48539051091 \tabularnewline
96 & 136.335142958118 & 116.678371616098 & 155.991914300138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295592&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]135.309634311507[/C][C]131.972175678913[/C][C]138.6470929441[/C][/ROW]
[ROW][C]86[/C][C]134.719864127836[/C][C]130.439172210169[/C][C]139.000556045503[/C][/ROW]
[ROW][C]87[/C][C]135.669893782422[/C][C]130.594702011469[/C][C]140.745085553376[/C][/ROW]
[ROW][C]88[/C][C]137.992912499062[/C][C]132.185971490292[/C][C]143.799853507833[/C][/ROW]
[ROW][C]89[/C][C]139.874945029243[/C][C]133.415401792327[/C][C]146.334488266158[/C][/ROW]
[ROW][C]90[/C][C]138.316303656832[/C][C]131.384131903557[/C][C]145.248475410107[/C][/ROW]
[ROW][C]91[/C][C]142.202377719024[/C][C]134.605346791889[/C][C]149.799408646159[/C][/ROW]
[ROW][C]92[/C][C]141.629281515[/C][C]133.603947294726[/C][C]149.654615735274[/C][/ROW]
[ROW][C]93[/C][C]136.945494471941[/C][C]128.724539665822[/C][C]145.16644927806[/C][/ROW]
[ROW][C]94[/C][C]138.486569227244[/C][C]129.761941785251[/C][C]147.211196669237[/C][/ROW]
[ROW][C]95[/C][C]137.424887902654[/C][C]128.364385294397[/C][C]146.48539051091[/C][/ROW]
[ROW][C]96[/C][C]136.335142958118[/C][C]116.678371616098[/C][C]155.991914300138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295592&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295592&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
85135.309634311507131.972175678913138.6470929441
86134.719864127836130.439172210169139.000556045503
87135.669893782422130.594702011469140.745085553376
88137.992912499062132.185971490292143.799853507833
89139.874945029243133.415401792327146.334488266158
90138.316303656832131.384131903557145.248475410107
91142.202377719024134.605346791889149.799408646159
92141.629281515133.603947294726149.654615735274
93136.945494471941128.724539665822145.16644927806
94138.486569227244129.761941785251147.211196669237
95137.424887902654128.364385294397146.48539051091
96136.335142958118116.678371616098155.991914300138



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=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')