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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Dec 2011 09:38:33 -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/2011/Dec/22/t1324564723rrc38mmipffgwuf.htm/, Retrieved Thu, 02 May 2024 15:55:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159514, Retrieved Thu, 02 May 2024 15:55:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Deel 2 Exponentia...] [2011-12-17 17:53:58] [845a0512200c8372fa3331a361537afe]
- R P     [Exponential Smoothing] [] [2011-12-22 14:38:33] [7079f287d9c11563cf2e6921d61ac78d] [Current]
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Dataseries X:
183.046
175.714
175.768
171.029
170.465
170.102
156.389
124.291
99.360
86.675
85.056
128.236
164.257
162.401
152.779
156.005
153.387
153.190
148.840
144.211
145.953
145.542
150.271
147.489
143.824
134.754
131.736
126.304
125.511
125.495
130.133
126.257
110.323
98.417
105.749
120.665
124.075
127.245
146.731
144.979
148.210
144.670
142.970
142.524
146.142
146.522
148.128
148.798
150.181
152.388
155.694
160.662
155.520
158.262
154.338
158.196
160.371
154.856
150.636
145.899
141.242
140.834
141.119
139.104
134.437
129.425
123.155
119.273
120.472
121.523
121.983
123.658
124.794
124.827
120.382
117.395
115.790
114.283
117.271
117.448
118.764
120.550
123.554
125.412
124.182
119.828
115.361
114.226
115.214
115.864
114.276
113.469
114.883
114.172
111.225
112.149
115.618
118.002
121.382
120.663
128.049




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159514&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159514&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 time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.335957853720076
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.335957853720076 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159514&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]0.335957853720076[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159514&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
alpha0.335957853720076
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13164.257172.438913995727-8.18191399572657
14162.401167.845569296834-5.44456929683361
15152.779154.149940381206-1.37094038120605
16156.005153.0480874262582.9569125737419
17153.387146.7802939946046.60670600539612
18153.19145.8102606641037.3797393358968
19148.84160.178933952172-11.3389339521716
20144.211126.13600527122718.0749947287734
21145.953109.31691693940736.6360830605928
22145.542111.05086367292134.4911363270787
23150.271122.88390703883327.3870929611666
24147.489177.207957909466-29.718957909466
25143.824199.357605098105-55.5336050981048
26134.754180.673800135402-45.9198001354017
27131.736156.085260826705-24.3492608267054
28126.304150.137537417783-23.8335374177829
29125.511137.292898570615-11.781898570615
30125.495130.658395825782-5.16339582578206
31130.133128.383116360291.74988363970962
32126.257118.2695670770677.9874329229333
33110.323110.386828064841-0.0638280648412461
3498.41798.36681639235810.0501836076418556
35105.74993.911766998607711.8372330013923
36120.665105.09089570580115.5741042941986
37124.075125.315089136191-1.24008913619055
38127.245131.255588948319-4.01058894831877
39146.731135.07052550009811.6604744999016
40144.979141.5630175638793.41598243612148
41148.21145.8758650479952.33413495200517
42144.67148.3787193963-3.70871939630049
43142.97151.182858836013-8.21285883601263
44142.524141.8642435870380.659756412961883
45146.142126.17333747518619.968662524814
46146.522120.95910690156825.5628930984322
47148.128132.90235020866115.2256497913394
48148.798147.7012841817611.09671581823909
49150.181151.896352158814-1.71535215881354
50152.388155.837454984395-3.44945498439509
51155.694170.247155504989-14.5531555049891
52160.662162.458282489094-1.79628248909358
53155.52164.301636310614-8.78163631061406
54158.262159.057350031981-0.795350031981002
55154.338159.849320369733-5.51132036973326
56158.196157.3300986586770.865901341322797
57160.371154.5303760113445.84062398865569
58154.856148.2845248107346.57147518926595
59150.636146.9830868857033.65291311429735
60145.899148.511861442971-2.61286144297145
61141.242149.593336150172-8.35133615017193
62140.834150.153510674527-9.31951067452664
63141.119155.217794758902-14.098794758902
64139.104156.052669141372-16.9486691413722
65134.437148.166890320289-13.7298903202893
66129.425146.563429926173-17.1384299261734
67123.155138.733211154624-15.5782111546236
68119.273137.066682414154-17.793682414154
69120.472131.301551560903-10.8295515609034
70121.523119.9405399613911.58246003860914
71121.983115.0249549898556.9580450101455
72123.658113.50337617999910.1546238200007
73124.794115.0635987726089.73040122739185
74124.827121.0555662887333.77143371126675
75120.382127.344209891059-6.9622098910585
76117.395128.684239307057-11.2892393070569
77115.79124.837195183142-9.04719518314222
78114.283122.543509041356-8.26050904135629
79117.271118.731948537492-1.4609485374924
80117.448120.337058756077-2.88905875607681
81118.764124.203729676266-5.43972967626604
82120.55122.895569891241-2.34556989124138
83123.554120.2299473971333.32405260286667
84125.412119.6101633513435.80183664865716
85124.182119.426331227274.75566877272959
86119.828119.7899927260760.0380072739244781
87115.361117.696770660398-2.33577066039764
88114.226117.717758770279-3.49175877027928
89115.214117.979151264023-2.76515126402307
90115.864118.31835986832-2.45435986831986
91114.276120.972615529754-6.69661552975387
92113.469119.870436928152-6.40143692815198
93114.883120.863343823901-5.98034382390135
94114.172121.428212974727-7.25621297472722
95111.225120.87768965949-9.6526896594904
96112.149117.543620170745-5.39462017074469
97115.618112.9035508826562.71444911734356
98118.002109.4487225399788.55327746002187
99121.382108.63998377556912.7420162244311
100120.663112.9588479805667.70415201943355
101128.049117.46409264162110.5849073583789

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 164.257 & 172.438913995727 & -8.18191399572657 \tabularnewline
14 & 162.401 & 167.845569296834 & -5.44456929683361 \tabularnewline
15 & 152.779 & 154.149940381206 & -1.37094038120605 \tabularnewline
16 & 156.005 & 153.048087426258 & 2.9569125737419 \tabularnewline
17 & 153.387 & 146.780293994604 & 6.60670600539612 \tabularnewline
18 & 153.19 & 145.810260664103 & 7.3797393358968 \tabularnewline
19 & 148.84 & 160.178933952172 & -11.3389339521716 \tabularnewline
20 & 144.211 & 126.136005271227 & 18.0749947287734 \tabularnewline
21 & 145.953 & 109.316916939407 & 36.6360830605928 \tabularnewline
22 & 145.542 & 111.050863672921 & 34.4911363270787 \tabularnewline
23 & 150.271 & 122.883907038833 & 27.3870929611666 \tabularnewline
24 & 147.489 & 177.207957909466 & -29.718957909466 \tabularnewline
25 & 143.824 & 199.357605098105 & -55.5336050981048 \tabularnewline
26 & 134.754 & 180.673800135402 & -45.9198001354017 \tabularnewline
27 & 131.736 & 156.085260826705 & -24.3492608267054 \tabularnewline
28 & 126.304 & 150.137537417783 & -23.8335374177829 \tabularnewline
29 & 125.511 & 137.292898570615 & -11.781898570615 \tabularnewline
30 & 125.495 & 130.658395825782 & -5.16339582578206 \tabularnewline
31 & 130.133 & 128.38311636029 & 1.74988363970962 \tabularnewline
32 & 126.257 & 118.269567077067 & 7.9874329229333 \tabularnewline
33 & 110.323 & 110.386828064841 & -0.0638280648412461 \tabularnewline
34 & 98.417 & 98.3668163923581 & 0.0501836076418556 \tabularnewline
35 & 105.749 & 93.9117669986077 & 11.8372330013923 \tabularnewline
36 & 120.665 & 105.090895705801 & 15.5741042941986 \tabularnewline
37 & 124.075 & 125.315089136191 & -1.24008913619055 \tabularnewline
38 & 127.245 & 131.255588948319 & -4.01058894831877 \tabularnewline
39 & 146.731 & 135.070525500098 & 11.6604744999016 \tabularnewline
40 & 144.979 & 141.563017563879 & 3.41598243612148 \tabularnewline
41 & 148.21 & 145.875865047995 & 2.33413495200517 \tabularnewline
42 & 144.67 & 148.3787193963 & -3.70871939630049 \tabularnewline
43 & 142.97 & 151.182858836013 & -8.21285883601263 \tabularnewline
44 & 142.524 & 141.864243587038 & 0.659756412961883 \tabularnewline
45 & 146.142 & 126.173337475186 & 19.968662524814 \tabularnewline
46 & 146.522 & 120.959106901568 & 25.5628930984322 \tabularnewline
47 & 148.128 & 132.902350208661 & 15.2256497913394 \tabularnewline
48 & 148.798 & 147.701284181761 & 1.09671581823909 \tabularnewline
49 & 150.181 & 151.896352158814 & -1.71535215881354 \tabularnewline
50 & 152.388 & 155.837454984395 & -3.44945498439509 \tabularnewline
51 & 155.694 & 170.247155504989 & -14.5531555049891 \tabularnewline
52 & 160.662 & 162.458282489094 & -1.79628248909358 \tabularnewline
53 & 155.52 & 164.301636310614 & -8.78163631061406 \tabularnewline
54 & 158.262 & 159.057350031981 & -0.795350031981002 \tabularnewline
55 & 154.338 & 159.849320369733 & -5.51132036973326 \tabularnewline
56 & 158.196 & 157.330098658677 & 0.865901341322797 \tabularnewline
57 & 160.371 & 154.530376011344 & 5.84062398865569 \tabularnewline
58 & 154.856 & 148.284524810734 & 6.57147518926595 \tabularnewline
59 & 150.636 & 146.983086885703 & 3.65291311429735 \tabularnewline
60 & 145.899 & 148.511861442971 & -2.61286144297145 \tabularnewline
61 & 141.242 & 149.593336150172 & -8.35133615017193 \tabularnewline
62 & 140.834 & 150.153510674527 & -9.31951067452664 \tabularnewline
63 & 141.119 & 155.217794758902 & -14.098794758902 \tabularnewline
64 & 139.104 & 156.052669141372 & -16.9486691413722 \tabularnewline
65 & 134.437 & 148.166890320289 & -13.7298903202893 \tabularnewline
66 & 129.425 & 146.563429926173 & -17.1384299261734 \tabularnewline
67 & 123.155 & 138.733211154624 & -15.5782111546236 \tabularnewline
68 & 119.273 & 137.066682414154 & -17.793682414154 \tabularnewline
69 & 120.472 & 131.301551560903 & -10.8295515609034 \tabularnewline
70 & 121.523 & 119.940539961391 & 1.58246003860914 \tabularnewline
71 & 121.983 & 115.024954989855 & 6.9580450101455 \tabularnewline
72 & 123.658 & 113.503376179999 & 10.1546238200007 \tabularnewline
73 & 124.794 & 115.063598772608 & 9.73040122739185 \tabularnewline
74 & 124.827 & 121.055566288733 & 3.77143371126675 \tabularnewline
75 & 120.382 & 127.344209891059 & -6.9622098910585 \tabularnewline
76 & 117.395 & 128.684239307057 & -11.2892393070569 \tabularnewline
77 & 115.79 & 124.837195183142 & -9.04719518314222 \tabularnewline
78 & 114.283 & 122.543509041356 & -8.26050904135629 \tabularnewline
79 & 117.271 & 118.731948537492 & -1.4609485374924 \tabularnewline
80 & 117.448 & 120.337058756077 & -2.88905875607681 \tabularnewline
81 & 118.764 & 124.203729676266 & -5.43972967626604 \tabularnewline
82 & 120.55 & 122.895569891241 & -2.34556989124138 \tabularnewline
83 & 123.554 & 120.229947397133 & 3.32405260286667 \tabularnewline
84 & 125.412 & 119.610163351343 & 5.80183664865716 \tabularnewline
85 & 124.182 & 119.42633122727 & 4.75566877272959 \tabularnewline
86 & 119.828 & 119.789992726076 & 0.0380072739244781 \tabularnewline
87 & 115.361 & 117.696770660398 & -2.33577066039764 \tabularnewline
88 & 114.226 & 117.717758770279 & -3.49175877027928 \tabularnewline
89 & 115.214 & 117.979151264023 & -2.76515126402307 \tabularnewline
90 & 115.864 & 118.31835986832 & -2.45435986831986 \tabularnewline
91 & 114.276 & 120.972615529754 & -6.69661552975387 \tabularnewline
92 & 113.469 & 119.870436928152 & -6.40143692815198 \tabularnewline
93 & 114.883 & 120.863343823901 & -5.98034382390135 \tabularnewline
94 & 114.172 & 121.428212974727 & -7.25621297472722 \tabularnewline
95 & 111.225 & 120.87768965949 & -9.6526896594904 \tabularnewline
96 & 112.149 & 117.543620170745 & -5.39462017074469 \tabularnewline
97 & 115.618 & 112.903550882656 & 2.71444911734356 \tabularnewline
98 & 118.002 & 109.448722539978 & 8.55327746002187 \tabularnewline
99 & 121.382 & 108.639983775569 & 12.7420162244311 \tabularnewline
100 & 120.663 & 112.958847980566 & 7.70415201943355 \tabularnewline
101 & 128.049 & 117.464092641621 & 10.5849073583789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159514&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]164.257[/C][C]172.438913995727[/C][C]-8.18191399572657[/C][/ROW]
[ROW][C]14[/C][C]162.401[/C][C]167.845569296834[/C][C]-5.44456929683361[/C][/ROW]
[ROW][C]15[/C][C]152.779[/C][C]154.149940381206[/C][C]-1.37094038120605[/C][/ROW]
[ROW][C]16[/C][C]156.005[/C][C]153.048087426258[/C][C]2.9569125737419[/C][/ROW]
[ROW][C]17[/C][C]153.387[/C][C]146.780293994604[/C][C]6.60670600539612[/C][/ROW]
[ROW][C]18[/C][C]153.19[/C][C]145.810260664103[/C][C]7.3797393358968[/C][/ROW]
[ROW][C]19[/C][C]148.84[/C][C]160.178933952172[/C][C]-11.3389339521716[/C][/ROW]
[ROW][C]20[/C][C]144.211[/C][C]126.136005271227[/C][C]18.0749947287734[/C][/ROW]
[ROW][C]21[/C][C]145.953[/C][C]109.316916939407[/C][C]36.6360830605928[/C][/ROW]
[ROW][C]22[/C][C]145.542[/C][C]111.050863672921[/C][C]34.4911363270787[/C][/ROW]
[ROW][C]23[/C][C]150.271[/C][C]122.883907038833[/C][C]27.3870929611666[/C][/ROW]
[ROW][C]24[/C][C]147.489[/C][C]177.207957909466[/C][C]-29.718957909466[/C][/ROW]
[ROW][C]25[/C][C]143.824[/C][C]199.357605098105[/C][C]-55.5336050981048[/C][/ROW]
[ROW][C]26[/C][C]134.754[/C][C]180.673800135402[/C][C]-45.9198001354017[/C][/ROW]
[ROW][C]27[/C][C]131.736[/C][C]156.085260826705[/C][C]-24.3492608267054[/C][/ROW]
[ROW][C]28[/C][C]126.304[/C][C]150.137537417783[/C][C]-23.8335374177829[/C][/ROW]
[ROW][C]29[/C][C]125.511[/C][C]137.292898570615[/C][C]-11.781898570615[/C][/ROW]
[ROW][C]30[/C][C]125.495[/C][C]130.658395825782[/C][C]-5.16339582578206[/C][/ROW]
[ROW][C]31[/C][C]130.133[/C][C]128.38311636029[/C][C]1.74988363970962[/C][/ROW]
[ROW][C]32[/C][C]126.257[/C][C]118.269567077067[/C][C]7.9874329229333[/C][/ROW]
[ROW][C]33[/C][C]110.323[/C][C]110.386828064841[/C][C]-0.0638280648412461[/C][/ROW]
[ROW][C]34[/C][C]98.417[/C][C]98.3668163923581[/C][C]0.0501836076418556[/C][/ROW]
[ROW][C]35[/C][C]105.749[/C][C]93.9117669986077[/C][C]11.8372330013923[/C][/ROW]
[ROW][C]36[/C][C]120.665[/C][C]105.090895705801[/C][C]15.5741042941986[/C][/ROW]
[ROW][C]37[/C][C]124.075[/C][C]125.315089136191[/C][C]-1.24008913619055[/C][/ROW]
[ROW][C]38[/C][C]127.245[/C][C]131.255588948319[/C][C]-4.01058894831877[/C][/ROW]
[ROW][C]39[/C][C]146.731[/C][C]135.070525500098[/C][C]11.6604744999016[/C][/ROW]
[ROW][C]40[/C][C]144.979[/C][C]141.563017563879[/C][C]3.41598243612148[/C][/ROW]
[ROW][C]41[/C][C]148.21[/C][C]145.875865047995[/C][C]2.33413495200517[/C][/ROW]
[ROW][C]42[/C][C]144.67[/C][C]148.3787193963[/C][C]-3.70871939630049[/C][/ROW]
[ROW][C]43[/C][C]142.97[/C][C]151.182858836013[/C][C]-8.21285883601263[/C][/ROW]
[ROW][C]44[/C][C]142.524[/C][C]141.864243587038[/C][C]0.659756412961883[/C][/ROW]
[ROW][C]45[/C][C]146.142[/C][C]126.173337475186[/C][C]19.968662524814[/C][/ROW]
[ROW][C]46[/C][C]146.522[/C][C]120.959106901568[/C][C]25.5628930984322[/C][/ROW]
[ROW][C]47[/C][C]148.128[/C][C]132.902350208661[/C][C]15.2256497913394[/C][/ROW]
[ROW][C]48[/C][C]148.798[/C][C]147.701284181761[/C][C]1.09671581823909[/C][/ROW]
[ROW][C]49[/C][C]150.181[/C][C]151.896352158814[/C][C]-1.71535215881354[/C][/ROW]
[ROW][C]50[/C][C]152.388[/C][C]155.837454984395[/C][C]-3.44945498439509[/C][/ROW]
[ROW][C]51[/C][C]155.694[/C][C]170.247155504989[/C][C]-14.5531555049891[/C][/ROW]
[ROW][C]52[/C][C]160.662[/C][C]162.458282489094[/C][C]-1.79628248909358[/C][/ROW]
[ROW][C]53[/C][C]155.52[/C][C]164.301636310614[/C][C]-8.78163631061406[/C][/ROW]
[ROW][C]54[/C][C]158.262[/C][C]159.057350031981[/C][C]-0.795350031981002[/C][/ROW]
[ROW][C]55[/C][C]154.338[/C][C]159.849320369733[/C][C]-5.51132036973326[/C][/ROW]
[ROW][C]56[/C][C]158.196[/C][C]157.330098658677[/C][C]0.865901341322797[/C][/ROW]
[ROW][C]57[/C][C]160.371[/C][C]154.530376011344[/C][C]5.84062398865569[/C][/ROW]
[ROW][C]58[/C][C]154.856[/C][C]148.284524810734[/C][C]6.57147518926595[/C][/ROW]
[ROW][C]59[/C][C]150.636[/C][C]146.983086885703[/C][C]3.65291311429735[/C][/ROW]
[ROW][C]60[/C][C]145.899[/C][C]148.511861442971[/C][C]-2.61286144297145[/C][/ROW]
[ROW][C]61[/C][C]141.242[/C][C]149.593336150172[/C][C]-8.35133615017193[/C][/ROW]
[ROW][C]62[/C][C]140.834[/C][C]150.153510674527[/C][C]-9.31951067452664[/C][/ROW]
[ROW][C]63[/C][C]141.119[/C][C]155.217794758902[/C][C]-14.098794758902[/C][/ROW]
[ROW][C]64[/C][C]139.104[/C][C]156.052669141372[/C][C]-16.9486691413722[/C][/ROW]
[ROW][C]65[/C][C]134.437[/C][C]148.166890320289[/C][C]-13.7298903202893[/C][/ROW]
[ROW][C]66[/C][C]129.425[/C][C]146.563429926173[/C][C]-17.1384299261734[/C][/ROW]
[ROW][C]67[/C][C]123.155[/C][C]138.733211154624[/C][C]-15.5782111546236[/C][/ROW]
[ROW][C]68[/C][C]119.273[/C][C]137.066682414154[/C][C]-17.793682414154[/C][/ROW]
[ROW][C]69[/C][C]120.472[/C][C]131.301551560903[/C][C]-10.8295515609034[/C][/ROW]
[ROW][C]70[/C][C]121.523[/C][C]119.940539961391[/C][C]1.58246003860914[/C][/ROW]
[ROW][C]71[/C][C]121.983[/C][C]115.024954989855[/C][C]6.9580450101455[/C][/ROW]
[ROW][C]72[/C][C]123.658[/C][C]113.503376179999[/C][C]10.1546238200007[/C][/ROW]
[ROW][C]73[/C][C]124.794[/C][C]115.063598772608[/C][C]9.73040122739185[/C][/ROW]
[ROW][C]74[/C][C]124.827[/C][C]121.055566288733[/C][C]3.77143371126675[/C][/ROW]
[ROW][C]75[/C][C]120.382[/C][C]127.344209891059[/C][C]-6.9622098910585[/C][/ROW]
[ROW][C]76[/C][C]117.395[/C][C]128.684239307057[/C][C]-11.2892393070569[/C][/ROW]
[ROW][C]77[/C][C]115.79[/C][C]124.837195183142[/C][C]-9.04719518314222[/C][/ROW]
[ROW][C]78[/C][C]114.283[/C][C]122.543509041356[/C][C]-8.26050904135629[/C][/ROW]
[ROW][C]79[/C][C]117.271[/C][C]118.731948537492[/C][C]-1.4609485374924[/C][/ROW]
[ROW][C]80[/C][C]117.448[/C][C]120.337058756077[/C][C]-2.88905875607681[/C][/ROW]
[ROW][C]81[/C][C]118.764[/C][C]124.203729676266[/C][C]-5.43972967626604[/C][/ROW]
[ROW][C]82[/C][C]120.55[/C][C]122.895569891241[/C][C]-2.34556989124138[/C][/ROW]
[ROW][C]83[/C][C]123.554[/C][C]120.229947397133[/C][C]3.32405260286667[/C][/ROW]
[ROW][C]84[/C][C]125.412[/C][C]119.610163351343[/C][C]5.80183664865716[/C][/ROW]
[ROW][C]85[/C][C]124.182[/C][C]119.42633122727[/C][C]4.75566877272959[/C][/ROW]
[ROW][C]86[/C][C]119.828[/C][C]119.789992726076[/C][C]0.0380072739244781[/C][/ROW]
[ROW][C]87[/C][C]115.361[/C][C]117.696770660398[/C][C]-2.33577066039764[/C][/ROW]
[ROW][C]88[/C][C]114.226[/C][C]117.717758770279[/C][C]-3.49175877027928[/C][/ROW]
[ROW][C]89[/C][C]115.214[/C][C]117.979151264023[/C][C]-2.76515126402307[/C][/ROW]
[ROW][C]90[/C][C]115.864[/C][C]118.31835986832[/C][C]-2.45435986831986[/C][/ROW]
[ROW][C]91[/C][C]114.276[/C][C]120.972615529754[/C][C]-6.69661552975387[/C][/ROW]
[ROW][C]92[/C][C]113.469[/C][C]119.870436928152[/C][C]-6.40143692815198[/C][/ROW]
[ROW][C]93[/C][C]114.883[/C][C]120.863343823901[/C][C]-5.98034382390135[/C][/ROW]
[ROW][C]94[/C][C]114.172[/C][C]121.428212974727[/C][C]-7.25621297472722[/C][/ROW]
[ROW][C]95[/C][C]111.225[/C][C]120.87768965949[/C][C]-9.6526896594904[/C][/ROW]
[ROW][C]96[/C][C]112.149[/C][C]117.543620170745[/C][C]-5.39462017074469[/C][/ROW]
[ROW][C]97[/C][C]115.618[/C][C]112.903550882656[/C][C]2.71444911734356[/C][/ROW]
[ROW][C]98[/C][C]118.002[/C][C]109.448722539978[/C][C]8.55327746002187[/C][/ROW]
[ROW][C]99[/C][C]121.382[/C][C]108.639983775569[/C][C]12.7420162244311[/C][/ROW]
[ROW][C]100[/C][C]120.663[/C][C]112.958847980566[/C][C]7.70415201943355[/C][/ROW]
[ROW][C]101[/C][C]128.049[/C][C]117.464092641621[/C][C]10.5849073583789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159514&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
13164.257172.438913995727-8.18191399572657
14162.401167.845569296834-5.44456929683361
15152.779154.149940381206-1.37094038120605
16156.005153.0480874262582.9569125737419
17153.387146.7802939946046.60670600539612
18153.19145.8102606641037.3797393358968
19148.84160.178933952172-11.3389339521716
20144.211126.13600527122718.0749947287734
21145.953109.31691693940736.6360830605928
22145.542111.05086367292134.4911363270787
23150.271122.88390703883327.3870929611666
24147.489177.207957909466-29.718957909466
25143.824199.357605098105-55.5336050981048
26134.754180.673800135402-45.9198001354017
27131.736156.085260826705-24.3492608267054
28126.304150.137537417783-23.8335374177829
29125.511137.292898570615-11.781898570615
30125.495130.658395825782-5.16339582578206
31130.133128.383116360291.74988363970962
32126.257118.2695670770677.9874329229333
33110.323110.386828064841-0.0638280648412461
3498.41798.36681639235810.0501836076418556
35105.74993.911766998607711.8372330013923
36120.665105.09089570580115.5741042941986
37124.075125.315089136191-1.24008913619055
38127.245131.255588948319-4.01058894831877
39146.731135.07052550009811.6604744999016
40144.979141.5630175638793.41598243612148
41148.21145.8758650479952.33413495200517
42144.67148.3787193963-3.70871939630049
43142.97151.182858836013-8.21285883601263
44142.524141.8642435870380.659756412961883
45146.142126.17333747518619.968662524814
46146.522120.95910690156825.5628930984322
47148.128132.90235020866115.2256497913394
48148.798147.7012841817611.09671581823909
49150.181151.896352158814-1.71535215881354
50152.388155.837454984395-3.44945498439509
51155.694170.247155504989-14.5531555049891
52160.662162.458282489094-1.79628248909358
53155.52164.301636310614-8.78163631061406
54158.262159.057350031981-0.795350031981002
55154.338159.849320369733-5.51132036973326
56158.196157.3300986586770.865901341322797
57160.371154.5303760113445.84062398865569
58154.856148.2845248107346.57147518926595
59150.636146.9830868857033.65291311429735
60145.899148.511861442971-2.61286144297145
61141.242149.593336150172-8.35133615017193
62140.834150.153510674527-9.31951067452664
63141.119155.217794758902-14.098794758902
64139.104156.052669141372-16.9486691413722
65134.437148.166890320289-13.7298903202893
66129.425146.563429926173-17.1384299261734
67123.155138.733211154624-15.5782111546236
68119.273137.066682414154-17.793682414154
69120.472131.301551560903-10.8295515609034
70121.523119.9405399613911.58246003860914
71121.983115.0249549898556.9580450101455
72123.658113.50337617999910.1546238200007
73124.794115.0635987726089.73040122739185
74124.827121.0555662887333.77143371126675
75120.382127.344209891059-6.9622098910585
76117.395128.684239307057-11.2892393070569
77115.79124.837195183142-9.04719518314222
78114.283122.543509041356-8.26050904135629
79117.271118.731948537492-1.4609485374924
80117.448120.337058756077-2.88905875607681
81118.764124.203729676266-5.43972967626604
82120.55122.895569891241-2.34556989124138
83123.554120.2299473971333.32405260286667
84125.412119.6101633513435.80183664865716
85124.182119.426331227274.75566877272959
86119.828119.7899927260760.0380072739244781
87115.361117.696770660398-2.33577066039764
88114.226117.717758770279-3.49175877027928
89115.214117.979151264023-2.76515126402307
90115.864118.31835986832-2.45435986831986
91114.276120.972615529754-6.69661552975387
92113.469119.870436928152-6.40143692815198
93114.883120.863343823901-5.98034382390135
94114.172121.428212974727-7.25621297472722
95111.225120.87768965949-9.6526896594904
96112.149117.543620170745-5.39462017074469
97115.618112.9035508826562.71444911734356
98118.002109.4487225399788.55327746002187
99121.382108.63998377556912.7420162244311
100120.663112.9588479805667.70415201943355
101128.049117.46409264162110.5849073583789







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
102122.49473687318595.4376065267452149.551867219626
103123.1565174537594.613262375385151.699772532115
104124.50013046485694.544387804175154.455873125538
105127.92327394044296.6187115535104159.227836327374
106129.65005567756797.0524371430538162.247674212081
107129.94595257819696.1046487911662163.787256365225
108132.68231759239497.6414421768116167.723193007977
109135.23937709289999.0386580700022171.440096115796
110134.74983635515897.4252979700808172.074374740235
111133.84905593233295.4335607052303172.264551159433
112130.5417855551591.0654713727464170.018099737553
113134.37170279720393.8623398139101174.881065780495

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
102 & 122.494736873185 & 95.4376065267452 & 149.551867219626 \tabularnewline
103 & 123.15651745375 & 94.613262375385 & 151.699772532115 \tabularnewline
104 & 124.500130464856 & 94.544387804175 & 154.455873125538 \tabularnewline
105 & 127.923273940442 & 96.6187115535104 & 159.227836327374 \tabularnewline
106 & 129.650055677567 & 97.0524371430538 & 162.247674212081 \tabularnewline
107 & 129.945952578196 & 96.1046487911662 & 163.787256365225 \tabularnewline
108 & 132.682317592394 & 97.6414421768116 & 167.723193007977 \tabularnewline
109 & 135.239377092899 & 99.0386580700022 & 171.440096115796 \tabularnewline
110 & 134.749836355158 & 97.4252979700808 & 172.074374740235 \tabularnewline
111 & 133.849055932332 & 95.4335607052303 & 172.264551159433 \tabularnewline
112 & 130.54178555515 & 91.0654713727464 & 170.018099737553 \tabularnewline
113 & 134.371702797203 & 93.8623398139101 & 174.881065780495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159514&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]102[/C][C]122.494736873185[/C][C]95.4376065267452[/C][C]149.551867219626[/C][/ROW]
[ROW][C]103[/C][C]123.15651745375[/C][C]94.613262375385[/C][C]151.699772532115[/C][/ROW]
[ROW][C]104[/C][C]124.500130464856[/C][C]94.544387804175[/C][C]154.455873125538[/C][/ROW]
[ROW][C]105[/C][C]127.923273940442[/C][C]96.6187115535104[/C][C]159.227836327374[/C][/ROW]
[ROW][C]106[/C][C]129.650055677567[/C][C]97.0524371430538[/C][C]162.247674212081[/C][/ROW]
[ROW][C]107[/C][C]129.945952578196[/C][C]96.1046487911662[/C][C]163.787256365225[/C][/ROW]
[ROW][C]108[/C][C]132.682317592394[/C][C]97.6414421768116[/C][C]167.723193007977[/C][/ROW]
[ROW][C]109[/C][C]135.239377092899[/C][C]99.0386580700022[/C][C]171.440096115796[/C][/ROW]
[ROW][C]110[/C][C]134.749836355158[/C][C]97.4252979700808[/C][C]172.074374740235[/C][/ROW]
[ROW][C]111[/C][C]133.849055932332[/C][C]95.4335607052303[/C][C]172.264551159433[/C][/ROW]
[ROW][C]112[/C][C]130.54178555515[/C][C]91.0654713727464[/C][C]170.018099737553[/C][/ROW]
[ROW][C]113[/C][C]134.371702797203[/C][C]93.8623398139101[/C][C]174.881065780495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159514&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
102122.49473687318595.4376065267452149.551867219626
103123.1565174537594.613262375385151.699772532115
104124.50013046485694.544387804175154.455873125538
105127.92327394044296.6187115535104159.227836327374
106129.65005567756797.0524371430538162.247674212081
107129.94595257819696.1046487911662163.787256365225
108132.68231759239497.6414421768116167.723193007977
109135.23937709289999.0386580700022171.440096115796
110134.74983635515897.4252979700808172.074374740235
111133.84905593233295.4335607052303172.264551159433
112130.5417855551591.0654713727464170.018099737553
113134.37170279720393.8623398139101174.881065780495



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