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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 30 May 2008 03:00:10 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/30/t1212138054mss0nl614ykkm0q.htm/, Retrieved Tue, 14 May 2024 14:56:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13525, Retrieved Tue, 14 May 2024 14:56:08 +0000
QR Codes:

Original text written by user:Kara Van den Acker
IsPrivate?No (this computation is public)
User-defined keywordsInleiding tot kwantitatief onderzoek
Estimated Impact226

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave10(oefening2)] [2008-05-30 09:00:10] [90941d2aa133223de960c34c4b1bc975] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
107,5
107,5
113,3
107,8
104,5
105,1
104,2
106,6
103,8
107,7
106,4
110
113,2
113,9
112
113,9
113,1
111,7
110,7
113,5
114
112,7
112,2
115,8
118,4
118,8
123,9
118
120,2
118,7
119,8
124,8
121,3
120,2
118,3
129,6
130,2
127,19
133,1
129,12
123,28
123,36
124,13
126,96
127,14
123,7
123,67
130,19
134,01
124,96
129,96
128,32
132,38
126,25
128,91
131,42
129,44
126,86
126,71
131,63
132,78
126,61
132,84
123,14
128,13
125,49
126,48
130,86
127,32
126,56
126,64
129,26
126,47
135,38
135,5
132,22
122,62
125,16
128,5
133,86
128,87
125,07
125,25
132,16
130,24

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 9 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13525&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13525&T=0

As an alternative you can also use a QR Code:  
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 time9 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.208973562504445
beta0.109887621724869
gamma0.279719189082164

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.208973562504445 \tabularnewline
beta & 0.109887621724869 \tabularnewline
gamma & 0.279719189082164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13525&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]0.208973562504445[/C][/ROW]
[ROW][C]beta[/C][C]0.109887621724869[/C][/ROW]
[ROW][C]gamma[/C][C]0.279719189082164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13525&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.208973562504445
beta0.109887621724869
gamma0.279719189082164






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13113.2109.9004444444453.2995555555555
14113.9111.3807919942342.51920800576609
15112110.0017509744641.99824902553620
16113.9112.4388969742261.46110302577384
17113.1112.2806791909870.819320809013234
18111.7111.3738271199350.326172880064505
19110.7110.796410275419-0.0964102754186626
20113.5113.965970795695-0.465970795694773
21114114.468435900229-0.468435900228599
22112.7113.192962218133-0.492962218133187
23112.2112.901042992979-0.701042992979126
24115.8116.528708577351-0.728708577350915
25118.4121.388936070923-2.98893607092288
26118.8121.409624807102-2.60962480710229
27123.9118.7528801849955.14711981500547
28118121.710871602031-3.71087160203068
29120.2120.1927429681450.00725703185524651
30118.7118.851325841396-0.151325841396485
31119.8117.9139076333131.88609236668715
32124.8121.2947995197313.50520048026935
33121.3122.596593046716-1.29659304671632
34120.2121.093616172693-0.893616172692958
35118.3120.613715933197-2.31371593319659
36129.6123.8030074055715.79699259442884
37130.2129.5814310388130.618568961187009
38127.19130.577369667350-3.38736966735038
39133.1129.5939836279673.50601637203326
40129.12130.330964737036-1.21096473703628
41123.28130.297252996741-7.0172529967407
42123.36127.430811708914-4.07081170891371
43124.13126.013130544339-1.88313054433884
44126.96128.766048005480-1.80604800547955
45127.14127.574936543771-0.434936543771229
46123.7126.04045031653-2.34045031652990
47123.67124.610019127134-0.940019127134306
48130.19129.5785779889090.611422011091292
49134.01132.7060526647441.3039473352558
50124.96132.553084430357-7.59308443035728
51129.96131.713746041498-1.75374604149775
52128.32129.684752523245-1.36475252324536
53132.38127.7075224963904.67247750361025
54126.25127.577658615698-1.32765861569837
55128.91126.9220621307031.98793786929713
56131.42130.2946602684411.12533973155871
57129.44129.880499966701-0.440499966701083
58126.86127.784088617249-0.924088617249467
59126.71126.852892655279-0.142892655279169
60131.63132.243001110282-0.613001110281886
61132.78135.151409544114-2.37140954411387
62126.61132.060959281453-5.45095928145291
63132.84132.8096767049960.0303232950044219
64123.14131.128911419740-7.98891141973972
65128.13128.840456227516-0.71045622751592
66125.49125.871687732967-0.381687732967038
67126.48125.7827314061890.697268593811103
68130.86128.3004432407012.55955675929891
69127.32127.478157694923-0.158157694922977
70126.56124.9788579015301.58114209847038
71126.64124.4466804617532.19331953824712
72129.26129.977264682529-0.717264682529446
73126.47132.228703652032-5.75870365203167
74135.38127.4251101528027.95488984719839
75135.5132.1720688734983.32793112650157
76132.22129.4657190110512.75428098894949
77122.62131.339159575819-8.71915957581882
78125.16126.892003326774-1.73200332677361
79128.5126.8510686533861.64893134661386
80133.86130.0930325010313.76696749896905
81128.87129.062774510051-0.192774510051493
82125.07127.081338898747-2.01133889874713
83125.25125.991636727422-0.741636727421522
84132.16130.2552394948921.90476050510765
85130.24131.989686221112-1.74968622111246

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 113.2 & 109.900444444445 & 3.2995555555555 \tabularnewline
14 & 113.9 & 111.380791994234 & 2.51920800576609 \tabularnewline
15 & 112 & 110.001750974464 & 1.99824902553620 \tabularnewline
16 & 113.9 & 112.438896974226 & 1.46110302577384 \tabularnewline
17 & 113.1 & 112.280679190987 & 0.819320809013234 \tabularnewline
18 & 111.7 & 111.373827119935 & 0.326172880064505 \tabularnewline
19 & 110.7 & 110.796410275419 & -0.0964102754186626 \tabularnewline
20 & 113.5 & 113.965970795695 & -0.465970795694773 \tabularnewline
21 & 114 & 114.468435900229 & -0.468435900228599 \tabularnewline
22 & 112.7 & 113.192962218133 & -0.492962218133187 \tabularnewline
23 & 112.2 & 112.901042992979 & -0.701042992979126 \tabularnewline
24 & 115.8 & 116.528708577351 & -0.728708577350915 \tabularnewline
25 & 118.4 & 121.388936070923 & -2.98893607092288 \tabularnewline
26 & 118.8 & 121.409624807102 & -2.60962480710229 \tabularnewline
27 & 123.9 & 118.752880184995 & 5.14711981500547 \tabularnewline
28 & 118 & 121.710871602031 & -3.71087160203068 \tabularnewline
29 & 120.2 & 120.192742968145 & 0.00725703185524651 \tabularnewline
30 & 118.7 & 118.851325841396 & -0.151325841396485 \tabularnewline
31 & 119.8 & 117.913907633313 & 1.88609236668715 \tabularnewline
32 & 124.8 & 121.294799519731 & 3.50520048026935 \tabularnewline
33 & 121.3 & 122.596593046716 & -1.29659304671632 \tabularnewline
34 & 120.2 & 121.093616172693 & -0.893616172692958 \tabularnewline
35 & 118.3 & 120.613715933197 & -2.31371593319659 \tabularnewline
36 & 129.6 & 123.803007405571 & 5.79699259442884 \tabularnewline
37 & 130.2 & 129.581431038813 & 0.618568961187009 \tabularnewline
38 & 127.19 & 130.577369667350 & -3.38736966735038 \tabularnewline
39 & 133.1 & 129.593983627967 & 3.50601637203326 \tabularnewline
40 & 129.12 & 130.330964737036 & -1.21096473703628 \tabularnewline
41 & 123.28 & 130.297252996741 & -7.0172529967407 \tabularnewline
42 & 123.36 & 127.430811708914 & -4.07081170891371 \tabularnewline
43 & 124.13 & 126.013130544339 & -1.88313054433884 \tabularnewline
44 & 126.96 & 128.766048005480 & -1.80604800547955 \tabularnewline
45 & 127.14 & 127.574936543771 & -0.434936543771229 \tabularnewline
46 & 123.7 & 126.04045031653 & -2.34045031652990 \tabularnewline
47 & 123.67 & 124.610019127134 & -0.940019127134306 \tabularnewline
48 & 130.19 & 129.578577988909 & 0.611422011091292 \tabularnewline
49 & 134.01 & 132.706052664744 & 1.3039473352558 \tabularnewline
50 & 124.96 & 132.553084430357 & -7.59308443035728 \tabularnewline
51 & 129.96 & 131.713746041498 & -1.75374604149775 \tabularnewline
52 & 128.32 & 129.684752523245 & -1.36475252324536 \tabularnewline
53 & 132.38 & 127.707522496390 & 4.67247750361025 \tabularnewline
54 & 126.25 & 127.577658615698 & -1.32765861569837 \tabularnewline
55 & 128.91 & 126.922062130703 & 1.98793786929713 \tabularnewline
56 & 131.42 & 130.294660268441 & 1.12533973155871 \tabularnewline
57 & 129.44 & 129.880499966701 & -0.440499966701083 \tabularnewline
58 & 126.86 & 127.784088617249 & -0.924088617249467 \tabularnewline
59 & 126.71 & 126.852892655279 & -0.142892655279169 \tabularnewline
60 & 131.63 & 132.243001110282 & -0.613001110281886 \tabularnewline
61 & 132.78 & 135.151409544114 & -2.37140954411387 \tabularnewline
62 & 126.61 & 132.060959281453 & -5.45095928145291 \tabularnewline
63 & 132.84 & 132.809676704996 & 0.0303232950044219 \tabularnewline
64 & 123.14 & 131.128911419740 & -7.98891141973972 \tabularnewline
65 & 128.13 & 128.840456227516 & -0.71045622751592 \tabularnewline
66 & 125.49 & 125.871687732967 & -0.381687732967038 \tabularnewline
67 & 126.48 & 125.782731406189 & 0.697268593811103 \tabularnewline
68 & 130.86 & 128.300443240701 & 2.55955675929891 \tabularnewline
69 & 127.32 & 127.478157694923 & -0.158157694922977 \tabularnewline
70 & 126.56 & 124.978857901530 & 1.58114209847038 \tabularnewline
71 & 126.64 & 124.446680461753 & 2.19331953824712 \tabularnewline
72 & 129.26 & 129.977264682529 & -0.717264682529446 \tabularnewline
73 & 126.47 & 132.228703652032 & -5.75870365203167 \tabularnewline
74 & 135.38 & 127.425110152802 & 7.95488984719839 \tabularnewline
75 & 135.5 & 132.172068873498 & 3.32793112650157 \tabularnewline
76 & 132.22 & 129.465719011051 & 2.75428098894949 \tabularnewline
77 & 122.62 & 131.339159575819 & -8.71915957581882 \tabularnewline
78 & 125.16 & 126.892003326774 & -1.73200332677361 \tabularnewline
79 & 128.5 & 126.851068653386 & 1.64893134661386 \tabularnewline
80 & 133.86 & 130.093032501031 & 3.76696749896905 \tabularnewline
81 & 128.87 & 129.062774510051 & -0.192774510051493 \tabularnewline
82 & 125.07 & 127.081338898747 & -2.01133889874713 \tabularnewline
83 & 125.25 & 125.991636727422 & -0.741636727421522 \tabularnewline
84 & 132.16 & 130.255239494892 & 1.90476050510765 \tabularnewline
85 & 130.24 & 131.989686221112 & -1.74968622111246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13525&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]113.2[/C][C]109.900444444445[/C][C]3.2995555555555[/C][/ROW]
[ROW][C]14[/C][C]113.9[/C][C]111.380791994234[/C][C]2.51920800576609[/C][/ROW]
[ROW][C]15[/C][C]112[/C][C]110.001750974464[/C][C]1.99824902553620[/C][/ROW]
[ROW][C]16[/C][C]113.9[/C][C]112.438896974226[/C][C]1.46110302577384[/C][/ROW]
[ROW][C]17[/C][C]113.1[/C][C]112.280679190987[/C][C]0.819320809013234[/C][/ROW]
[ROW][C]18[/C][C]111.7[/C][C]111.373827119935[/C][C]0.326172880064505[/C][/ROW]
[ROW][C]19[/C][C]110.7[/C][C]110.796410275419[/C][C]-0.0964102754186626[/C][/ROW]
[ROW][C]20[/C][C]113.5[/C][C]113.965970795695[/C][C]-0.465970795694773[/C][/ROW]
[ROW][C]21[/C][C]114[/C][C]114.468435900229[/C][C]-0.468435900228599[/C][/ROW]
[ROW][C]22[/C][C]112.7[/C][C]113.192962218133[/C][C]-0.492962218133187[/C][/ROW]
[ROW][C]23[/C][C]112.2[/C][C]112.901042992979[/C][C]-0.701042992979126[/C][/ROW]
[ROW][C]24[/C][C]115.8[/C][C]116.528708577351[/C][C]-0.728708577350915[/C][/ROW]
[ROW][C]25[/C][C]118.4[/C][C]121.388936070923[/C][C]-2.98893607092288[/C][/ROW]
[ROW][C]26[/C][C]118.8[/C][C]121.409624807102[/C][C]-2.60962480710229[/C][/ROW]
[ROW][C]27[/C][C]123.9[/C][C]118.752880184995[/C][C]5.14711981500547[/C][/ROW]
[ROW][C]28[/C][C]118[/C][C]121.710871602031[/C][C]-3.71087160203068[/C][/ROW]
[ROW][C]29[/C][C]120.2[/C][C]120.192742968145[/C][C]0.00725703185524651[/C][/ROW]
[ROW][C]30[/C][C]118.7[/C][C]118.851325841396[/C][C]-0.151325841396485[/C][/ROW]
[ROW][C]31[/C][C]119.8[/C][C]117.913907633313[/C][C]1.88609236668715[/C][/ROW]
[ROW][C]32[/C][C]124.8[/C][C]121.294799519731[/C][C]3.50520048026935[/C][/ROW]
[ROW][C]33[/C][C]121.3[/C][C]122.596593046716[/C][C]-1.29659304671632[/C][/ROW]
[ROW][C]34[/C][C]120.2[/C][C]121.093616172693[/C][C]-0.893616172692958[/C][/ROW]
[ROW][C]35[/C][C]118.3[/C][C]120.613715933197[/C][C]-2.31371593319659[/C][/ROW]
[ROW][C]36[/C][C]129.6[/C][C]123.803007405571[/C][C]5.79699259442884[/C][/ROW]
[ROW][C]37[/C][C]130.2[/C][C]129.581431038813[/C][C]0.618568961187009[/C][/ROW]
[ROW][C]38[/C][C]127.19[/C][C]130.577369667350[/C][C]-3.38736966735038[/C][/ROW]
[ROW][C]39[/C][C]133.1[/C][C]129.593983627967[/C][C]3.50601637203326[/C][/ROW]
[ROW][C]40[/C][C]129.12[/C][C]130.330964737036[/C][C]-1.21096473703628[/C][/ROW]
[ROW][C]41[/C][C]123.28[/C][C]130.297252996741[/C][C]-7.0172529967407[/C][/ROW]
[ROW][C]42[/C][C]123.36[/C][C]127.430811708914[/C][C]-4.07081170891371[/C][/ROW]
[ROW][C]43[/C][C]124.13[/C][C]126.013130544339[/C][C]-1.88313054433884[/C][/ROW]
[ROW][C]44[/C][C]126.96[/C][C]128.766048005480[/C][C]-1.80604800547955[/C][/ROW]
[ROW][C]45[/C][C]127.14[/C][C]127.574936543771[/C][C]-0.434936543771229[/C][/ROW]
[ROW][C]46[/C][C]123.7[/C][C]126.04045031653[/C][C]-2.34045031652990[/C][/ROW]
[ROW][C]47[/C][C]123.67[/C][C]124.610019127134[/C][C]-0.940019127134306[/C][/ROW]
[ROW][C]48[/C][C]130.19[/C][C]129.578577988909[/C][C]0.611422011091292[/C][/ROW]
[ROW][C]49[/C][C]134.01[/C][C]132.706052664744[/C][C]1.3039473352558[/C][/ROW]
[ROW][C]50[/C][C]124.96[/C][C]132.553084430357[/C][C]-7.59308443035728[/C][/ROW]
[ROW][C]51[/C][C]129.96[/C][C]131.713746041498[/C][C]-1.75374604149775[/C][/ROW]
[ROW][C]52[/C][C]128.32[/C][C]129.684752523245[/C][C]-1.36475252324536[/C][/ROW]
[ROW][C]53[/C][C]132.38[/C][C]127.707522496390[/C][C]4.67247750361025[/C][/ROW]
[ROW][C]54[/C][C]126.25[/C][C]127.577658615698[/C][C]-1.32765861569837[/C][/ROW]
[ROW][C]55[/C][C]128.91[/C][C]126.922062130703[/C][C]1.98793786929713[/C][/ROW]
[ROW][C]56[/C][C]131.42[/C][C]130.294660268441[/C][C]1.12533973155871[/C][/ROW]
[ROW][C]57[/C][C]129.44[/C][C]129.880499966701[/C][C]-0.440499966701083[/C][/ROW]
[ROW][C]58[/C][C]126.86[/C][C]127.784088617249[/C][C]-0.924088617249467[/C][/ROW]
[ROW][C]59[/C][C]126.71[/C][C]126.852892655279[/C][C]-0.142892655279169[/C][/ROW]
[ROW][C]60[/C][C]131.63[/C][C]132.243001110282[/C][C]-0.613001110281886[/C][/ROW]
[ROW][C]61[/C][C]132.78[/C][C]135.151409544114[/C][C]-2.37140954411387[/C][/ROW]
[ROW][C]62[/C][C]126.61[/C][C]132.060959281453[/C][C]-5.45095928145291[/C][/ROW]
[ROW][C]63[/C][C]132.84[/C][C]132.809676704996[/C][C]0.0303232950044219[/C][/ROW]
[ROW][C]64[/C][C]123.14[/C][C]131.128911419740[/C][C]-7.98891141973972[/C][/ROW]
[ROW][C]65[/C][C]128.13[/C][C]128.840456227516[/C][C]-0.71045622751592[/C][/ROW]
[ROW][C]66[/C][C]125.49[/C][C]125.871687732967[/C][C]-0.381687732967038[/C][/ROW]
[ROW][C]67[/C][C]126.48[/C][C]125.782731406189[/C][C]0.697268593811103[/C][/ROW]
[ROW][C]68[/C][C]130.86[/C][C]128.300443240701[/C][C]2.55955675929891[/C][/ROW]
[ROW][C]69[/C][C]127.32[/C][C]127.478157694923[/C][C]-0.158157694922977[/C][/ROW]
[ROW][C]70[/C][C]126.56[/C][C]124.978857901530[/C][C]1.58114209847038[/C][/ROW]
[ROW][C]71[/C][C]126.64[/C][C]124.446680461753[/C][C]2.19331953824712[/C][/ROW]
[ROW][C]72[/C][C]129.26[/C][C]129.977264682529[/C][C]-0.717264682529446[/C][/ROW]
[ROW][C]73[/C][C]126.47[/C][C]132.228703652032[/C][C]-5.75870365203167[/C][/ROW]
[ROW][C]74[/C][C]135.38[/C][C]127.425110152802[/C][C]7.95488984719839[/C][/ROW]
[ROW][C]75[/C][C]135.5[/C][C]132.172068873498[/C][C]3.32793112650157[/C][/ROW]
[ROW][C]76[/C][C]132.22[/C][C]129.465719011051[/C][C]2.75428098894949[/C][/ROW]
[ROW][C]77[/C][C]122.62[/C][C]131.339159575819[/C][C]-8.71915957581882[/C][/ROW]
[ROW][C]78[/C][C]125.16[/C][C]126.892003326774[/C][C]-1.73200332677361[/C][/ROW]
[ROW][C]79[/C][C]128.5[/C][C]126.851068653386[/C][C]1.64893134661386[/C][/ROW]
[ROW][C]80[/C][C]133.86[/C][C]130.093032501031[/C][C]3.76696749896905[/C][/ROW]
[ROW][C]81[/C][C]128.87[/C][C]129.062774510051[/C][C]-0.192774510051493[/C][/ROW]
[ROW][C]82[/C][C]125.07[/C][C]127.081338898747[/C][C]-2.01133889874713[/C][/ROW]
[ROW][C]83[/C][C]125.25[/C][C]125.991636727422[/C][C]-0.741636727421522[/C][/ROW]
[ROW][C]84[/C][C]132.16[/C][C]130.255239494892[/C][C]1.90476050510765[/C][/ROW]
[ROW][C]85[/C][C]130.24[/C][C]131.989686221112[/C][C]-1.74968622111246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13525&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13525&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13113.2109.9004444444453.2995555555555
14113.9111.3807919942342.51920800576609
15112110.0017509744641.99824902553620
16113.9112.4388969742261.46110302577384
17113.1112.2806791909870.819320809013234
18111.7111.3738271199350.326172880064505
19110.7110.796410275419-0.0964102754186626
20113.5113.965970795695-0.465970795694773
21114114.468435900229-0.468435900228599
22112.7113.192962218133-0.492962218133187
23112.2112.901042992979-0.701042992979126
24115.8116.528708577351-0.728708577350915
25118.4121.388936070923-2.98893607092288
26118.8121.409624807102-2.60962480710229
27123.9118.7528801849955.14711981500547
28118121.710871602031-3.71087160203068
29120.2120.1927429681450.00725703185524651
30118.7118.851325841396-0.151325841396485
31119.8117.9139076333131.88609236668715
32124.8121.2947995197313.50520048026935
33121.3122.596593046716-1.29659304671632
34120.2121.093616172693-0.893616172692958
35118.3120.613715933197-2.31371593319659
36129.6123.8030074055715.79699259442884
37130.2129.5814310388130.618568961187009
38127.19130.577369667350-3.38736966735038
39133.1129.5939836279673.50601637203326
40129.12130.330964737036-1.21096473703628
41123.28130.297252996741-7.0172529967407
42123.36127.430811708914-4.07081170891371
43124.13126.013130544339-1.88313054433884
44126.96128.766048005480-1.80604800547955
45127.14127.574936543771-0.434936543771229
46123.7126.04045031653-2.34045031652990
47123.67124.610019127134-0.940019127134306
48130.19129.5785779889090.611422011091292
49134.01132.7060526647441.3039473352558
50124.96132.553084430357-7.59308443035728
51129.96131.713746041498-1.75374604149775
52128.32129.684752523245-1.36475252324536
53132.38127.7075224963904.67247750361025
54126.25127.577658615698-1.32765861569837
55128.91126.9220621307031.98793786929713
56131.42130.2946602684411.12533973155871
57129.44129.880499966701-0.440499966701083
58126.86127.784088617249-0.924088617249467
59126.71126.852892655279-0.142892655279169
60131.63132.243001110282-0.613001110281886
61132.78135.151409544114-2.37140954411387
62126.61132.060959281453-5.45095928145291
63132.84132.8096767049960.0303232950044219
64123.14131.128911419740-7.98891141973972
65128.13128.840456227516-0.71045622751592
66125.49125.871687732967-0.381687732967038
67126.48125.7827314061890.697268593811103
68130.86128.3004432407012.55955675929891
69127.32127.478157694923-0.158157694922977
70126.56124.9788579015301.58114209847038
71126.64124.4466804617532.19331953824712
72129.26129.977264682529-0.717264682529446
73126.47132.228703652032-5.75870365203167
74135.38127.4251101528027.95488984719839
75135.5132.1720688734983.32793112650157
76132.22129.4657190110512.75428098894949
77122.62131.339159575819-8.71915957581882
78125.16126.892003326774-1.73200332677361
79128.5126.8510686533861.64893134661386
80133.86130.0930325010313.76696749896905
81128.87129.062774510051-0.192774510051493
82125.07127.081338898747-2.01133889874713
83125.25125.991636727422-0.741636727421522
84132.16130.2552394948921.90476050510765
85130.24131.989686221112-1.74968622111246






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
86131.200844084039125.230256164462137.171432003615
87133.221613565442127.092535767388139.350691363496
88129.576421638786123.261217991057135.891625286515
89128.155904512373121.626423390558134.685385634188
90127.097348687425120.325334901273133.869362473577
91128.226724946338121.184173253020135.269276639655
92131.615172763445124.274613461765138.955732065124
93128.857480769471121.192195615821136.522765923121
94126.454287599707118.438460289278134.470114910136
95126.052373491941117.661182869943134.443564113939
96131.060075601273122.26974167811139.850409524436
97131.547696476016122.335489629103140.759903322928

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 131.200844084039 & 125.230256164462 & 137.171432003615 \tabularnewline
87 & 133.221613565442 & 127.092535767388 & 139.350691363496 \tabularnewline
88 & 129.576421638786 & 123.261217991057 & 135.891625286515 \tabularnewline
89 & 128.155904512373 & 121.626423390558 & 134.685385634188 \tabularnewline
90 & 127.097348687425 & 120.325334901273 & 133.869362473577 \tabularnewline
91 & 128.226724946338 & 121.184173253020 & 135.269276639655 \tabularnewline
92 & 131.615172763445 & 124.274613461765 & 138.955732065124 \tabularnewline
93 & 128.857480769471 & 121.192195615821 & 136.522765923121 \tabularnewline
94 & 126.454287599707 & 118.438460289278 & 134.470114910136 \tabularnewline
95 & 126.052373491941 & 117.661182869943 & 134.443564113939 \tabularnewline
96 & 131.060075601273 & 122.26974167811 & 139.850409524436 \tabularnewline
97 & 131.547696476016 & 122.335489629103 & 140.759903322928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13525&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]86[/C][C]131.200844084039[/C][C]125.230256164462[/C][C]137.171432003615[/C][/ROW]
[ROW][C]87[/C][C]133.221613565442[/C][C]127.092535767388[/C][C]139.350691363496[/C][/ROW]
[ROW][C]88[/C][C]129.576421638786[/C][C]123.261217991057[/C][C]135.891625286515[/C][/ROW]
[ROW][C]89[/C][C]128.155904512373[/C][C]121.626423390558[/C][C]134.685385634188[/C][/ROW]
[ROW][C]90[/C][C]127.097348687425[/C][C]120.325334901273[/C][C]133.869362473577[/C][/ROW]
[ROW][C]91[/C][C]128.226724946338[/C][C]121.184173253020[/C][C]135.269276639655[/C][/ROW]
[ROW][C]92[/C][C]131.615172763445[/C][C]124.274613461765[/C][C]138.955732065124[/C][/ROW]
[ROW][C]93[/C][C]128.857480769471[/C][C]121.192195615821[/C][C]136.522765923121[/C][/ROW]
[ROW][C]94[/C][C]126.454287599707[/C][C]118.438460289278[/C][C]134.470114910136[/C][/ROW]
[ROW][C]95[/C][C]126.052373491941[/C][C]117.661182869943[/C][C]134.443564113939[/C][/ROW]
[ROW][C]96[/C][C]131.060075601273[/C][C]122.26974167811[/C][C]139.850409524436[/C][/ROW]
[ROW][C]97[/C][C]131.547696476016[/C][C]122.335489629103[/C][C]140.759903322928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13525&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13525&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
86131.200844084039125.230256164462137.171432003615
87133.221613565442127.092535767388139.350691363496
88129.576421638786123.261217991057135.891625286515
89128.155904512373121.626423390558134.685385634188
90127.097348687425120.325334901273133.869362473577
91128.226724946338121.184173253020135.269276639655
92131.615172763445124.274613461765138.955732065124
93128.857480769471121.192195615821136.522765923121
94126.454287599707118.438460289278134.470114910136
95126.052373491941117.661182869943134.443564113939
96131.060075601273122.26974167811139.850409524436
97131.547696476016122.335489629103140.759903322928


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')