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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 computationSat, 17 Dec 2011 12:53:58 -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/17/t1324145085faelbnzek07kxhf.htm/, Retrieved Fri, 19 Apr 2024 20:08:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156533, Retrieved Fri, 19 Apr 2024 20:08:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
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] [fd45a0bdad9cb518cfd91b75ef7bafe6] [Current]
- R P     [Exponential Smoothing] [] [2011-12-22 14:38:33] [3e69114d76a3312df18b1cf403d3c20a]
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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'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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156533&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156533&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.335957853720046
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.335957853720046 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156533&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]0.335957853720046[/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=156533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156533&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
alpha0.335957853720046
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13164.257172.438913995726-8.18191399572646
14162.401167.845569296834-5.44456929683378
15152.779154.149940381206-1.37094038120634
16156.005153.0480874262582.95691257374165
17153.387146.7802939946046.60670600539603
18153.19145.8102606641037.37973933589694
19148.84160.178933952171-11.3389339521713
20144.211126.13600527122718.0749947287733
21145.953109.31691693940736.6360830605933
22145.542111.0508636729234.4911363270801
23150.271122.88390703883127.3870929611685
24147.489177.207957909464-29.7189579094639
25143.824199.357605098104-55.5336050981041
26134.754180.673800135403-45.9198001354028
27131.736156.085260826708-24.3492608267076
28126.304150.137537417785-23.8335374177853
29125.511137.292898570618-11.7818985706176
30125.495130.658395825784-5.16339582578428
31130.133128.3831163602921.74988363970843
32126.257118.2695670770687.98743292293196
33110.323110.386828064843-0.0638280648428662
3498.41798.36681639235980.0501836076402071
35105.74993.91176699860911.837233001391
36120.665105.090895705815.5741042941998
37124.075125.315089136187-1.24008913618736
38127.245131.255588948316-4.0105889483157
39146.731135.07052550009611.6604744999035
40144.979141.5630175638773.41598243612307
41148.21145.8758650479942.33413495200583
42144.67148.378719396301-3.70871939630055
43142.97151.182858836013-8.21285883601323
44142.524141.8642435870390.659756412960519
45146.142126.17333747518719.9686625248126
46146.522120.95910690156925.5628930984314
47148.128132.90235020866115.2256497913388
48148.798147.7012841817611.09671581823909
49150.181151.896352158812-1.71535215881235
50152.388155.837454984393-3.44945498439318
51155.694170.247155504988-14.5531555049876
52160.662162.458282489093-1.79628248909265
53155.52164.301636310613-8.78163631061335
54158.262159.057350031981-0.795350031980718
55154.338159.849320369733-5.51132036973303
56158.196157.3300986586780.865901341322314
57160.371154.5303760113465.8406239886543
58154.856148.2845248107366.57147518926416
59150.636146.9830868857043.6529131142957
60145.899148.511861442972-2.61286144297247
61141.242149.593336150172-8.35133615017227
62140.834150.153510674526-9.31951067452638
63141.119155.217794758901-14.0987947589012
64139.104156.052669141372-16.9486691413718
65134.437148.166890320289-13.729890320289
66129.425146.563429926174-17.1384299261735
67123.155138.733211154624-15.5782111546239
68119.273137.066682414155-17.7936824141549
69120.472131.301551560905-10.8295515609052
70121.523119.9405399613931.58246003860681
71121.983115.0249549898576.95804501014331
72123.658113.50337618000110.1546238199992
73124.794115.0635987726099.73040122739131
74124.827121.0555662887333.77143371126709
75120.382127.344209891057-6.96220989105748
76117.395128.684239307056-11.2892393070558
77115.79124.837195183141-9.04719518314126
78114.283122.543509041355-8.26050904135543
79117.271118.731948537492-1.46094853749177
80117.448120.337058756076-2.8890587560762
81118.764124.203729676266-5.43972967626601
82120.55122.895569891242-2.34556989124236
83123.554120.2299473971353.32405260286501
84125.412119.6101633513455.80183664865532
85124.182119.4263312272724.75566877272806
86119.828119.7899927260760.0380072739236255
87115.361117.696770660398-2.33577066039764
88114.226117.717758770279-3.49175877027865
89115.214117.979151264022-2.76515126402218
90115.864118.318359868319-2.45435986831882
91114.276120.972615529753-6.69661552975299
92113.469119.870436928151-6.40143692815131
93114.883120.863343823901-5.98034382390092
94114.172121.428212974727-7.25621297472739
95111.225120.877689659491-9.65268965949137
96112.149117.543620170746-5.39462017074642
97115.618112.9035508826582.71444911734156
98118.002109.448722539988.55327746002034
99121.382108.6399837755712.7420162244304
100120.663112.9588479805667.70415201943382
101128.049117.4640926416210.5849073583798

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 164.257 & 172.438913995726 & -8.18191399572646 \tabularnewline
14 & 162.401 & 167.845569296834 & -5.44456929683378 \tabularnewline
15 & 152.779 & 154.149940381206 & -1.37094038120634 \tabularnewline
16 & 156.005 & 153.048087426258 & 2.95691257374165 \tabularnewline
17 & 153.387 & 146.780293994604 & 6.60670600539603 \tabularnewline
18 & 153.19 & 145.810260664103 & 7.37973933589694 \tabularnewline
19 & 148.84 & 160.178933952171 & -11.3389339521713 \tabularnewline
20 & 144.211 & 126.136005271227 & 18.0749947287733 \tabularnewline
21 & 145.953 & 109.316916939407 & 36.6360830605933 \tabularnewline
22 & 145.542 & 111.05086367292 & 34.4911363270801 \tabularnewline
23 & 150.271 & 122.883907038831 & 27.3870929611685 \tabularnewline
24 & 147.489 & 177.207957909464 & -29.7189579094639 \tabularnewline
25 & 143.824 & 199.357605098104 & -55.5336050981041 \tabularnewline
26 & 134.754 & 180.673800135403 & -45.9198001354028 \tabularnewline
27 & 131.736 & 156.085260826708 & -24.3492608267076 \tabularnewline
28 & 126.304 & 150.137537417785 & -23.8335374177853 \tabularnewline
29 & 125.511 & 137.292898570618 & -11.7818985706176 \tabularnewline
30 & 125.495 & 130.658395825784 & -5.16339582578428 \tabularnewline
31 & 130.133 & 128.383116360292 & 1.74988363970843 \tabularnewline
32 & 126.257 & 118.269567077068 & 7.98743292293196 \tabularnewline
33 & 110.323 & 110.386828064843 & -0.0638280648428662 \tabularnewline
34 & 98.417 & 98.3668163923598 & 0.0501836076402071 \tabularnewline
35 & 105.749 & 93.911766998609 & 11.837233001391 \tabularnewline
36 & 120.665 & 105.0908957058 & 15.5741042941998 \tabularnewline
37 & 124.075 & 125.315089136187 & -1.24008913618736 \tabularnewline
38 & 127.245 & 131.255588948316 & -4.0105889483157 \tabularnewline
39 & 146.731 & 135.070525500096 & 11.6604744999035 \tabularnewline
40 & 144.979 & 141.563017563877 & 3.41598243612307 \tabularnewline
41 & 148.21 & 145.875865047994 & 2.33413495200583 \tabularnewline
42 & 144.67 & 148.378719396301 & -3.70871939630055 \tabularnewline
43 & 142.97 & 151.182858836013 & -8.21285883601323 \tabularnewline
44 & 142.524 & 141.864243587039 & 0.659756412960519 \tabularnewline
45 & 146.142 & 126.173337475187 & 19.9686625248126 \tabularnewline
46 & 146.522 & 120.959106901569 & 25.5628930984314 \tabularnewline
47 & 148.128 & 132.902350208661 & 15.2256497913388 \tabularnewline
48 & 148.798 & 147.701284181761 & 1.09671581823909 \tabularnewline
49 & 150.181 & 151.896352158812 & -1.71535215881235 \tabularnewline
50 & 152.388 & 155.837454984393 & -3.44945498439318 \tabularnewline
51 & 155.694 & 170.247155504988 & -14.5531555049876 \tabularnewline
52 & 160.662 & 162.458282489093 & -1.79628248909265 \tabularnewline
53 & 155.52 & 164.301636310613 & -8.78163631061335 \tabularnewline
54 & 158.262 & 159.057350031981 & -0.795350031980718 \tabularnewline
55 & 154.338 & 159.849320369733 & -5.51132036973303 \tabularnewline
56 & 158.196 & 157.330098658678 & 0.865901341322314 \tabularnewline
57 & 160.371 & 154.530376011346 & 5.8406239886543 \tabularnewline
58 & 154.856 & 148.284524810736 & 6.57147518926416 \tabularnewline
59 & 150.636 & 146.983086885704 & 3.6529131142957 \tabularnewline
60 & 145.899 & 148.511861442972 & -2.61286144297247 \tabularnewline
61 & 141.242 & 149.593336150172 & -8.35133615017227 \tabularnewline
62 & 140.834 & 150.153510674526 & -9.31951067452638 \tabularnewline
63 & 141.119 & 155.217794758901 & -14.0987947589012 \tabularnewline
64 & 139.104 & 156.052669141372 & -16.9486691413718 \tabularnewline
65 & 134.437 & 148.166890320289 & -13.729890320289 \tabularnewline
66 & 129.425 & 146.563429926174 & -17.1384299261735 \tabularnewline
67 & 123.155 & 138.733211154624 & -15.5782111546239 \tabularnewline
68 & 119.273 & 137.066682414155 & -17.7936824141549 \tabularnewline
69 & 120.472 & 131.301551560905 & -10.8295515609052 \tabularnewline
70 & 121.523 & 119.940539961393 & 1.58246003860681 \tabularnewline
71 & 121.983 & 115.024954989857 & 6.95804501014331 \tabularnewline
72 & 123.658 & 113.503376180001 & 10.1546238199992 \tabularnewline
73 & 124.794 & 115.063598772609 & 9.73040122739131 \tabularnewline
74 & 124.827 & 121.055566288733 & 3.77143371126709 \tabularnewline
75 & 120.382 & 127.344209891057 & -6.96220989105748 \tabularnewline
76 & 117.395 & 128.684239307056 & -11.2892393070558 \tabularnewline
77 & 115.79 & 124.837195183141 & -9.04719518314126 \tabularnewline
78 & 114.283 & 122.543509041355 & -8.26050904135543 \tabularnewline
79 & 117.271 & 118.731948537492 & -1.46094853749177 \tabularnewline
80 & 117.448 & 120.337058756076 & -2.8890587560762 \tabularnewline
81 & 118.764 & 124.203729676266 & -5.43972967626601 \tabularnewline
82 & 120.55 & 122.895569891242 & -2.34556989124236 \tabularnewline
83 & 123.554 & 120.229947397135 & 3.32405260286501 \tabularnewline
84 & 125.412 & 119.610163351345 & 5.80183664865532 \tabularnewline
85 & 124.182 & 119.426331227272 & 4.75566877272806 \tabularnewline
86 & 119.828 & 119.789992726076 & 0.0380072739236255 \tabularnewline
87 & 115.361 & 117.696770660398 & -2.33577066039764 \tabularnewline
88 & 114.226 & 117.717758770279 & -3.49175877027865 \tabularnewline
89 & 115.214 & 117.979151264022 & -2.76515126402218 \tabularnewline
90 & 115.864 & 118.318359868319 & -2.45435986831882 \tabularnewline
91 & 114.276 & 120.972615529753 & -6.69661552975299 \tabularnewline
92 & 113.469 & 119.870436928151 & -6.40143692815131 \tabularnewline
93 & 114.883 & 120.863343823901 & -5.98034382390092 \tabularnewline
94 & 114.172 & 121.428212974727 & -7.25621297472739 \tabularnewline
95 & 111.225 & 120.877689659491 & -9.65268965949137 \tabularnewline
96 & 112.149 & 117.543620170746 & -5.39462017074642 \tabularnewline
97 & 115.618 & 112.903550882658 & 2.71444911734156 \tabularnewline
98 & 118.002 & 109.44872253998 & 8.55327746002034 \tabularnewline
99 & 121.382 & 108.63998377557 & 12.7420162244304 \tabularnewline
100 & 120.663 & 112.958847980566 & 7.70415201943382 \tabularnewline
101 & 128.049 & 117.46409264162 & 10.5849073583798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156533&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]172.438913995726[/C][C]-8.18191399572646[/C][/ROW]
[ROW][C]14[/C][C]162.401[/C][C]167.845569296834[/C][C]-5.44456929683378[/C][/ROW]
[ROW][C]15[/C][C]152.779[/C][C]154.149940381206[/C][C]-1.37094038120634[/C][/ROW]
[ROW][C]16[/C][C]156.005[/C][C]153.048087426258[/C][C]2.95691257374165[/C][/ROW]
[ROW][C]17[/C][C]153.387[/C][C]146.780293994604[/C][C]6.60670600539603[/C][/ROW]
[ROW][C]18[/C][C]153.19[/C][C]145.810260664103[/C][C]7.37973933589694[/C][/ROW]
[ROW][C]19[/C][C]148.84[/C][C]160.178933952171[/C][C]-11.3389339521713[/C][/ROW]
[ROW][C]20[/C][C]144.211[/C][C]126.136005271227[/C][C]18.0749947287733[/C][/ROW]
[ROW][C]21[/C][C]145.953[/C][C]109.316916939407[/C][C]36.6360830605933[/C][/ROW]
[ROW][C]22[/C][C]145.542[/C][C]111.05086367292[/C][C]34.4911363270801[/C][/ROW]
[ROW][C]23[/C][C]150.271[/C][C]122.883907038831[/C][C]27.3870929611685[/C][/ROW]
[ROW][C]24[/C][C]147.489[/C][C]177.207957909464[/C][C]-29.7189579094639[/C][/ROW]
[ROW][C]25[/C][C]143.824[/C][C]199.357605098104[/C][C]-55.5336050981041[/C][/ROW]
[ROW][C]26[/C][C]134.754[/C][C]180.673800135403[/C][C]-45.9198001354028[/C][/ROW]
[ROW][C]27[/C][C]131.736[/C][C]156.085260826708[/C][C]-24.3492608267076[/C][/ROW]
[ROW][C]28[/C][C]126.304[/C][C]150.137537417785[/C][C]-23.8335374177853[/C][/ROW]
[ROW][C]29[/C][C]125.511[/C][C]137.292898570618[/C][C]-11.7818985706176[/C][/ROW]
[ROW][C]30[/C][C]125.495[/C][C]130.658395825784[/C][C]-5.16339582578428[/C][/ROW]
[ROW][C]31[/C][C]130.133[/C][C]128.383116360292[/C][C]1.74988363970843[/C][/ROW]
[ROW][C]32[/C][C]126.257[/C][C]118.269567077068[/C][C]7.98743292293196[/C][/ROW]
[ROW][C]33[/C][C]110.323[/C][C]110.386828064843[/C][C]-0.0638280648428662[/C][/ROW]
[ROW][C]34[/C][C]98.417[/C][C]98.3668163923598[/C][C]0.0501836076402071[/C][/ROW]
[ROW][C]35[/C][C]105.749[/C][C]93.911766998609[/C][C]11.837233001391[/C][/ROW]
[ROW][C]36[/C][C]120.665[/C][C]105.0908957058[/C][C]15.5741042941998[/C][/ROW]
[ROW][C]37[/C][C]124.075[/C][C]125.315089136187[/C][C]-1.24008913618736[/C][/ROW]
[ROW][C]38[/C][C]127.245[/C][C]131.255588948316[/C][C]-4.0105889483157[/C][/ROW]
[ROW][C]39[/C][C]146.731[/C][C]135.070525500096[/C][C]11.6604744999035[/C][/ROW]
[ROW][C]40[/C][C]144.979[/C][C]141.563017563877[/C][C]3.41598243612307[/C][/ROW]
[ROW][C]41[/C][C]148.21[/C][C]145.875865047994[/C][C]2.33413495200583[/C][/ROW]
[ROW][C]42[/C][C]144.67[/C][C]148.378719396301[/C][C]-3.70871939630055[/C][/ROW]
[ROW][C]43[/C][C]142.97[/C][C]151.182858836013[/C][C]-8.21285883601323[/C][/ROW]
[ROW][C]44[/C][C]142.524[/C][C]141.864243587039[/C][C]0.659756412960519[/C][/ROW]
[ROW][C]45[/C][C]146.142[/C][C]126.173337475187[/C][C]19.9686625248126[/C][/ROW]
[ROW][C]46[/C][C]146.522[/C][C]120.959106901569[/C][C]25.5628930984314[/C][/ROW]
[ROW][C]47[/C][C]148.128[/C][C]132.902350208661[/C][C]15.2256497913388[/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]151.896352158812[/C][C]-1.71535215881235[/C][/ROW]
[ROW][C]50[/C][C]152.388[/C][C]155.837454984393[/C][C]-3.44945498439318[/C][/ROW]
[ROW][C]51[/C][C]155.694[/C][C]170.247155504988[/C][C]-14.5531555049876[/C][/ROW]
[ROW][C]52[/C][C]160.662[/C][C]162.458282489093[/C][C]-1.79628248909265[/C][/ROW]
[ROW][C]53[/C][C]155.52[/C][C]164.301636310613[/C][C]-8.78163631061335[/C][/ROW]
[ROW][C]54[/C][C]158.262[/C][C]159.057350031981[/C][C]-0.795350031980718[/C][/ROW]
[ROW][C]55[/C][C]154.338[/C][C]159.849320369733[/C][C]-5.51132036973303[/C][/ROW]
[ROW][C]56[/C][C]158.196[/C][C]157.330098658678[/C][C]0.865901341322314[/C][/ROW]
[ROW][C]57[/C][C]160.371[/C][C]154.530376011346[/C][C]5.8406239886543[/C][/ROW]
[ROW][C]58[/C][C]154.856[/C][C]148.284524810736[/C][C]6.57147518926416[/C][/ROW]
[ROW][C]59[/C][C]150.636[/C][C]146.983086885704[/C][C]3.6529131142957[/C][/ROW]
[ROW][C]60[/C][C]145.899[/C][C]148.511861442972[/C][C]-2.61286144297247[/C][/ROW]
[ROW][C]61[/C][C]141.242[/C][C]149.593336150172[/C][C]-8.35133615017227[/C][/ROW]
[ROW][C]62[/C][C]140.834[/C][C]150.153510674526[/C][C]-9.31951067452638[/C][/ROW]
[ROW][C]63[/C][C]141.119[/C][C]155.217794758901[/C][C]-14.0987947589012[/C][/ROW]
[ROW][C]64[/C][C]139.104[/C][C]156.052669141372[/C][C]-16.9486691413718[/C][/ROW]
[ROW][C]65[/C][C]134.437[/C][C]148.166890320289[/C][C]-13.729890320289[/C][/ROW]
[ROW][C]66[/C][C]129.425[/C][C]146.563429926174[/C][C]-17.1384299261735[/C][/ROW]
[ROW][C]67[/C][C]123.155[/C][C]138.733211154624[/C][C]-15.5782111546239[/C][/ROW]
[ROW][C]68[/C][C]119.273[/C][C]137.066682414155[/C][C]-17.7936824141549[/C][/ROW]
[ROW][C]69[/C][C]120.472[/C][C]131.301551560905[/C][C]-10.8295515609052[/C][/ROW]
[ROW][C]70[/C][C]121.523[/C][C]119.940539961393[/C][C]1.58246003860681[/C][/ROW]
[ROW][C]71[/C][C]121.983[/C][C]115.024954989857[/C][C]6.95804501014331[/C][/ROW]
[ROW][C]72[/C][C]123.658[/C][C]113.503376180001[/C][C]10.1546238199992[/C][/ROW]
[ROW][C]73[/C][C]124.794[/C][C]115.063598772609[/C][C]9.73040122739131[/C][/ROW]
[ROW][C]74[/C][C]124.827[/C][C]121.055566288733[/C][C]3.77143371126709[/C][/ROW]
[ROW][C]75[/C][C]120.382[/C][C]127.344209891057[/C][C]-6.96220989105748[/C][/ROW]
[ROW][C]76[/C][C]117.395[/C][C]128.684239307056[/C][C]-11.2892393070558[/C][/ROW]
[ROW][C]77[/C][C]115.79[/C][C]124.837195183141[/C][C]-9.04719518314126[/C][/ROW]
[ROW][C]78[/C][C]114.283[/C][C]122.543509041355[/C][C]-8.26050904135543[/C][/ROW]
[ROW][C]79[/C][C]117.271[/C][C]118.731948537492[/C][C]-1.46094853749177[/C][/ROW]
[ROW][C]80[/C][C]117.448[/C][C]120.337058756076[/C][C]-2.8890587560762[/C][/ROW]
[ROW][C]81[/C][C]118.764[/C][C]124.203729676266[/C][C]-5.43972967626601[/C][/ROW]
[ROW][C]82[/C][C]120.55[/C][C]122.895569891242[/C][C]-2.34556989124236[/C][/ROW]
[ROW][C]83[/C][C]123.554[/C][C]120.229947397135[/C][C]3.32405260286501[/C][/ROW]
[ROW][C]84[/C][C]125.412[/C][C]119.610163351345[/C][C]5.80183664865532[/C][/ROW]
[ROW][C]85[/C][C]124.182[/C][C]119.426331227272[/C][C]4.75566877272806[/C][/ROW]
[ROW][C]86[/C][C]119.828[/C][C]119.789992726076[/C][C]0.0380072739236255[/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]-3.49175877027865[/C][/ROW]
[ROW][C]89[/C][C]115.214[/C][C]117.979151264022[/C][C]-2.76515126402218[/C][/ROW]
[ROW][C]90[/C][C]115.864[/C][C]118.318359868319[/C][C]-2.45435986831882[/C][/ROW]
[ROW][C]91[/C][C]114.276[/C][C]120.972615529753[/C][C]-6.69661552975299[/C][/ROW]
[ROW][C]92[/C][C]113.469[/C][C]119.870436928151[/C][C]-6.40143692815131[/C][/ROW]
[ROW][C]93[/C][C]114.883[/C][C]120.863343823901[/C][C]-5.98034382390092[/C][/ROW]
[ROW][C]94[/C][C]114.172[/C][C]121.428212974727[/C][C]-7.25621297472739[/C][/ROW]
[ROW][C]95[/C][C]111.225[/C][C]120.877689659491[/C][C]-9.65268965949137[/C][/ROW]
[ROW][C]96[/C][C]112.149[/C][C]117.543620170746[/C][C]-5.39462017074642[/C][/ROW]
[ROW][C]97[/C][C]115.618[/C][C]112.903550882658[/C][C]2.71444911734156[/C][/ROW]
[ROW][C]98[/C][C]118.002[/C][C]109.44872253998[/C][C]8.55327746002034[/C][/ROW]
[ROW][C]99[/C][C]121.382[/C][C]108.63998377557[/C][C]12.7420162244304[/C][/ROW]
[ROW][C]100[/C][C]120.663[/C][C]112.958847980566[/C][C]7.70415201943382[/C][/ROW]
[ROW][C]101[/C][C]128.049[/C][C]117.46409264162[/C][C]10.5849073583798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156533&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
13164.257172.438913995726-8.18191399572646
14162.401167.845569296834-5.44456929683378
15152.779154.149940381206-1.37094038120634
16156.005153.0480874262582.95691257374165
17153.387146.7802939946046.60670600539603
18153.19145.8102606641037.37973933589694
19148.84160.178933952171-11.3389339521713
20144.211126.13600527122718.0749947287733
21145.953109.31691693940736.6360830605933
22145.542111.0508636729234.4911363270801
23150.271122.88390703883127.3870929611685
24147.489177.207957909464-29.7189579094639
25143.824199.357605098104-55.5336050981041
26134.754180.673800135403-45.9198001354028
27131.736156.085260826708-24.3492608267076
28126.304150.137537417785-23.8335374177853
29125.511137.292898570618-11.7818985706176
30125.495130.658395825784-5.16339582578428
31130.133128.3831163602921.74988363970843
32126.257118.2695670770687.98743292293196
33110.323110.386828064843-0.0638280648428662
3498.41798.36681639235980.0501836076402071
35105.74993.91176699860911.837233001391
36120.665105.090895705815.5741042941998
37124.075125.315089136187-1.24008913618736
38127.245131.255588948316-4.0105889483157
39146.731135.07052550009611.6604744999035
40144.979141.5630175638773.41598243612307
41148.21145.8758650479942.33413495200583
42144.67148.378719396301-3.70871939630055
43142.97151.182858836013-8.21285883601323
44142.524141.8642435870390.659756412960519
45146.142126.17333747518719.9686625248126
46146.522120.95910690156925.5628930984314
47148.128132.90235020866115.2256497913388
48148.798147.7012841817611.09671581823909
49150.181151.896352158812-1.71535215881235
50152.388155.837454984393-3.44945498439318
51155.694170.247155504988-14.5531555049876
52160.662162.458282489093-1.79628248909265
53155.52164.301636310613-8.78163631061335
54158.262159.057350031981-0.795350031980718
55154.338159.849320369733-5.51132036973303
56158.196157.3300986586780.865901341322314
57160.371154.5303760113465.8406239886543
58154.856148.2845248107366.57147518926416
59150.636146.9830868857043.6529131142957
60145.899148.511861442972-2.61286144297247
61141.242149.593336150172-8.35133615017227
62140.834150.153510674526-9.31951067452638
63141.119155.217794758901-14.0987947589012
64139.104156.052669141372-16.9486691413718
65134.437148.166890320289-13.729890320289
66129.425146.563429926174-17.1384299261735
67123.155138.733211154624-15.5782111546239
68119.273137.066682414155-17.7936824141549
69120.472131.301551560905-10.8295515609052
70121.523119.9405399613931.58246003860681
71121.983115.0249549898576.95804501014331
72123.658113.50337618000110.1546238199992
73124.794115.0635987726099.73040122739131
74124.827121.0555662887333.77143371126709
75120.382127.344209891057-6.96220989105748
76117.395128.684239307056-11.2892393070558
77115.79124.837195183141-9.04719518314126
78114.283122.543509041355-8.26050904135543
79117.271118.731948537492-1.46094853749177
80117.448120.337058756076-2.8890587560762
81118.764124.203729676266-5.43972967626601
82120.55122.895569891242-2.34556989124236
83123.554120.2299473971353.32405260286501
84125.412119.6101633513455.80183664865532
85124.182119.4263312272724.75566877272806
86119.828119.7899927260760.0380072739236255
87115.361117.696770660398-2.33577066039764
88114.226117.717758770279-3.49175877027865
89115.214117.979151264022-2.76515126402218
90115.864118.318359868319-2.45435986831882
91114.276120.972615529753-6.69661552975299
92113.469119.870436928151-6.40143692815131
93114.883120.863343823901-5.98034382390092
94114.172121.428212974727-7.25621297472739
95111.225120.877689659491-9.65268965949137
96112.149117.543620170746-5.39462017074642
97115.618112.9035508826582.71444911734156
98118.002109.448722539988.55327746002034
99121.382108.6399837755712.7420162244304
100120.663112.9588479805667.70415201943382
101128.049117.4640926416210.5849073583798







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
102122.49473687318495.4376065267439149.551867219624
103123.15651745374894.6132623753835151.699772532113
104124.50013046485494.5443878041734154.455873125535
105127.9232739404496.6187115535086159.227836327371
106129.65005567756597.052437143052162.247674212078
107129.94595257819396.1046487911647163.787256365222
108132.68231759239297.6414421768107167.723193007973
109135.23937709289899.0386580700021171.440096115793
110134.74983635515797.4252979700818172.074374740233
111133.84905593233295.433560705232172.264551159431
112130.5417855551591.0654713727484170.018099737551
113134.37170279720393.8623398139123174.881065780493

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
102 & 122.494736873184 & 95.4376065267439 & 149.551867219624 \tabularnewline
103 & 123.156517453748 & 94.6132623753835 & 151.699772532113 \tabularnewline
104 & 124.500130464854 & 94.5443878041734 & 154.455873125535 \tabularnewline
105 & 127.92327394044 & 96.6187115535086 & 159.227836327371 \tabularnewline
106 & 129.650055677565 & 97.052437143052 & 162.247674212078 \tabularnewline
107 & 129.945952578193 & 96.1046487911647 & 163.787256365222 \tabularnewline
108 & 132.682317592392 & 97.6414421768107 & 167.723193007973 \tabularnewline
109 & 135.239377092898 & 99.0386580700021 & 171.440096115793 \tabularnewline
110 & 134.749836355157 & 97.4252979700818 & 172.074374740233 \tabularnewline
111 & 133.849055932332 & 95.433560705232 & 172.264551159431 \tabularnewline
112 & 130.54178555515 & 91.0654713727484 & 170.018099737551 \tabularnewline
113 & 134.371702797203 & 93.8623398139123 & 174.881065780493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156533&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]122.494736873184[/C][C]95.4376065267439[/C][C]149.551867219624[/C][/ROW]
[ROW][C]103[/C][C]123.156517453748[/C][C]94.6132623753835[/C][C]151.699772532113[/C][/ROW]
[ROW][C]104[/C][C]124.500130464854[/C][C]94.5443878041734[/C][C]154.455873125535[/C][/ROW]
[ROW][C]105[/C][C]127.92327394044[/C][C]96.6187115535086[/C][C]159.227836327371[/C][/ROW]
[ROW][C]106[/C][C]129.650055677565[/C][C]97.052437143052[/C][C]162.247674212078[/C][/ROW]
[ROW][C]107[/C][C]129.945952578193[/C][C]96.1046487911647[/C][C]163.787256365222[/C][/ROW]
[ROW][C]108[/C][C]132.682317592392[/C][C]97.6414421768107[/C][C]167.723193007973[/C][/ROW]
[ROW][C]109[/C][C]135.239377092898[/C][C]99.0386580700021[/C][C]171.440096115793[/C][/ROW]
[ROW][C]110[/C][C]134.749836355157[/C][C]97.4252979700818[/C][C]172.074374740233[/C][/ROW]
[ROW][C]111[/C][C]133.849055932332[/C][C]95.433560705232[/C][C]172.264551159431[/C][/ROW]
[ROW][C]112[/C][C]130.54178555515[/C][C]91.0654713727484[/C][C]170.018099737551[/C][/ROW]
[ROW][C]113[/C][C]134.371702797203[/C][C]93.8623398139123[/C][C]174.881065780493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156533&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156533&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
102122.49473687318495.4376065267439149.551867219624
103123.15651745374894.6132623753835151.699772532113
104124.50013046485494.5443878041734154.455873125535
105127.9232739404496.6187115535086159.227836327371
106129.65005567756597.052437143052162.247674212078
107129.94595257819396.1046487911647163.787256365222
108132.68231759239297.6414421768107167.723193007973
109135.23937709289899.0386580700021171.440096115793
110134.74983635515797.4252979700818172.074374740233
111133.84905593233295.433560705232172.264551159431
112130.5417855551591.0654713727484170.018099737551
113134.37170279720393.8623398139123174.881065780493



Parameters (Session):
par1 = 12 ;
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')