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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 computationTue, 26 May 2015 06:50:45 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/26/t1432619463xf4bpm5pdr3xrka.htm/, Retrieved Tue, 30 Apr 2024 14:47:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279379, Retrieved Tue, 30 Apr 2024 14:47:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-05-26 05:50:45] [b43493158838656c32486372ca9c54cf] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,8
100,66
101,44
102,17
102,75
104,28
104,96
105,16
105,29
105,15
105,23
104,45
104,6
105,1
105,94
106,2
106,89
107,57
107,42
107,2
107,08
107,17
107,23
106,61
106,97
108,23
109,8
111,93
113,51
115,27
115,58
115,55
115,44
114,93
115,09
113,78
114,51
114,85
116,12
115,47
115,93
116,6
116,98
117,37
117,48
117,18
117,03
114,95
115,64
116,02
116,07
114,5
114,36
116
116,16
116,42
116,78
115,74
115,44
113,52
113,37
114,35
114,11
113,47
114,33
115,76
116,2
116,48
116,53
116,45
116,23
114,46
115,08
115,57
116,17
115,21
114,97
114,24
114,16
117,2
117,71
117,14
116,67
114,71
115,92
117,74
118,38
118,59
119,66
121,2
121,4
122,66
122,95
122,9
123,29
122,02

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279379&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279379&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0479897513800168
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0479897513800168 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279379&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0479897513800168[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279379&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
alpha1
beta0.0479897513800168
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3101.44100.520.920000000000002
4102.17101.344150571270.825849428730393
5102.75102.1137828800320.636217119968279
6104.28102.7243147814431.5556852185573
7104.96104.3289717283070.631028271693154
8105.16105.0392546181790.120745381820853
9105.29105.2450491590330.0449508409669903
10105.15105.377206338715-0.227206338715348
11105.23105.2263027630080.00369723699157021
12104.45105.306480192492-0.856480192492455
13104.6104.4853779209930.114622079007162
14105.1104.6408786060670.459121393932961
15105.94105.1629117276150.777088272384873
16106.2106.0402040006070.159795999392799
17106.89106.307872570890.5821274291104
18107.57107.0258087214840.54419127851591
19107.42107.731924325643-0.311924325643233
20107.2107.566955154806-0.366955154806249
21107.08107.329345068159-0.249345068159485
22107.17107.197379060331-0.0273790603306594
23107.23107.286065146032-0.0560651460323811
24106.61107.343374593613-0.733374593613206
25106.97106.6881801291970.281819870802721
26108.23107.0617045947311.16829540526895
27109.8108.3777708007681.42222919923167
28111.93110.0160232264451.91397677355515
29113.51112.2378744959551.27212550404511
30115.27113.8789234826181.39107651738179
31115.58115.705680898838-0.125680898837928
32115.55116.009649503749-0.459649503749475
33115.44115.957591038343-0.517591038342587
34114.93115.822751973096-0.892751973095997
35115.09115.269909027863-0.179909027863118
36113.78115.421275238345-1.64127523834495
37114.51114.0325108477110.477489152289408
38114.85114.7854254334160.0645745665843691
39116.12115.1285243508110.991475649188544
40115.47116.446105020715-0.97610502071538
41115.93115.749261983450.180738016549554
42116.6116.217935555930.382064444070409
43116.98116.9062707336120.0737292663883409
44117.37117.2898089827750.0801910172249336
45117.48117.683657329755-0.203657329754606
46117.18117.783883865133-0.603883865132957
47117.03117.454903628583-0.42490362858284
48114.95117.284512609087-2.33451260908667
49115.64115.0924799293830.547520070616912
50116.02115.8087552814480.211244718552436
51116.07116.198892862971-0.128892862971242
52114.5116.242707326523-1.74270732652258
53114.36114.589075235195-0.229075235194642
54116114.438081971611.56191802838967
55116.16116.1530380294690.00696197053127889
56116.42116.3133721327040.106627867296382
57116.78116.5784891775450.201510822454637
58115.74116.948159631815-1.20815963181535
59115.44115.850180351457-0.410180351457143
60113.52115.53049589837-2.01049589836975
61113.37113.514012700056-0.144012700056436
62114.35113.3571015663850.992898433614812
63114.11114.38475051536-0.274750515359955
64113.47114.131565306436-0.661565306436302
65114.33113.4598169518590.870183048141229
66115.76114.3615768199941.39842318000582
67116.2115.8586868007270.341313199273287
68116.48116.3150663363030.16493366369744
69116.53116.602981461818-0.0729814618175908
70116.45116.64947909961-0.199479099609619
71116.23116.559906147214-0.329906147213833
72114.46116.32407403323-1.86407403323032
73115.08114.4646175838220.615382416178363
74115.57115.1141496329780.455850367022322
75116.17115.6260257787580.543974221242451
76115.21116.252130966392-1.04213096639214
77114.97115.24211936041-0.272119360409548
78114.24114.989060419958-0.749060419957814
79114.16114.223113196635-0.0631131966354275
80117.2114.140084410023.05991558997992
81117.71117.3269289984270.38307100157293
82117.14117.855312480553-0.715312480553436
83116.67117.250984812453-0.580984812452655
84114.71116.753103495747-2.0431034957475
85115.92114.6950554669431.22494453305708
86117.74115.9638402505391.77615974946134
87118.38117.8690777153260.510922284673512
88118.59118.5335967487420.056403251257521
89119.66118.7463035267470.913696473252642
90121.2119.8601515933361.33984840666446
91121.4121.464450585258-0.0644505852582853
92122.66121.6613576176950.998642382304553
93122.95122.96928221734-0.0192822173397786
94122.9123.258356868524-0.358356868523586
95123.29123.1911594114980.0988405885021706
96122.02123.585902746766-1.56590274676631

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 101.44 & 100.52 & 0.920000000000002 \tabularnewline
4 & 102.17 & 101.34415057127 & 0.825849428730393 \tabularnewline
5 & 102.75 & 102.113782880032 & 0.636217119968279 \tabularnewline
6 & 104.28 & 102.724314781443 & 1.5556852185573 \tabularnewline
7 & 104.96 & 104.328971728307 & 0.631028271693154 \tabularnewline
8 & 105.16 & 105.039254618179 & 0.120745381820853 \tabularnewline
9 & 105.29 & 105.245049159033 & 0.0449508409669903 \tabularnewline
10 & 105.15 & 105.377206338715 & -0.227206338715348 \tabularnewline
11 & 105.23 & 105.226302763008 & 0.00369723699157021 \tabularnewline
12 & 104.45 & 105.306480192492 & -0.856480192492455 \tabularnewline
13 & 104.6 & 104.485377920993 & 0.114622079007162 \tabularnewline
14 & 105.1 & 104.640878606067 & 0.459121393932961 \tabularnewline
15 & 105.94 & 105.162911727615 & 0.777088272384873 \tabularnewline
16 & 106.2 & 106.040204000607 & 0.159795999392799 \tabularnewline
17 & 106.89 & 106.30787257089 & 0.5821274291104 \tabularnewline
18 & 107.57 & 107.025808721484 & 0.54419127851591 \tabularnewline
19 & 107.42 & 107.731924325643 & -0.311924325643233 \tabularnewline
20 & 107.2 & 107.566955154806 & -0.366955154806249 \tabularnewline
21 & 107.08 & 107.329345068159 & -0.249345068159485 \tabularnewline
22 & 107.17 & 107.197379060331 & -0.0273790603306594 \tabularnewline
23 & 107.23 & 107.286065146032 & -0.0560651460323811 \tabularnewline
24 & 106.61 & 107.343374593613 & -0.733374593613206 \tabularnewline
25 & 106.97 & 106.688180129197 & 0.281819870802721 \tabularnewline
26 & 108.23 & 107.061704594731 & 1.16829540526895 \tabularnewline
27 & 109.8 & 108.377770800768 & 1.42222919923167 \tabularnewline
28 & 111.93 & 110.016023226445 & 1.91397677355515 \tabularnewline
29 & 113.51 & 112.237874495955 & 1.27212550404511 \tabularnewline
30 & 115.27 & 113.878923482618 & 1.39107651738179 \tabularnewline
31 & 115.58 & 115.705680898838 & -0.125680898837928 \tabularnewline
32 & 115.55 & 116.009649503749 & -0.459649503749475 \tabularnewline
33 & 115.44 & 115.957591038343 & -0.517591038342587 \tabularnewline
34 & 114.93 & 115.822751973096 & -0.892751973095997 \tabularnewline
35 & 115.09 & 115.269909027863 & -0.179909027863118 \tabularnewline
36 & 113.78 & 115.421275238345 & -1.64127523834495 \tabularnewline
37 & 114.51 & 114.032510847711 & 0.477489152289408 \tabularnewline
38 & 114.85 & 114.785425433416 & 0.0645745665843691 \tabularnewline
39 & 116.12 & 115.128524350811 & 0.991475649188544 \tabularnewline
40 & 115.47 & 116.446105020715 & -0.97610502071538 \tabularnewline
41 & 115.93 & 115.74926198345 & 0.180738016549554 \tabularnewline
42 & 116.6 & 116.21793555593 & 0.382064444070409 \tabularnewline
43 & 116.98 & 116.906270733612 & 0.0737292663883409 \tabularnewline
44 & 117.37 & 117.289808982775 & 0.0801910172249336 \tabularnewline
45 & 117.48 & 117.683657329755 & -0.203657329754606 \tabularnewline
46 & 117.18 & 117.783883865133 & -0.603883865132957 \tabularnewline
47 & 117.03 & 117.454903628583 & -0.42490362858284 \tabularnewline
48 & 114.95 & 117.284512609087 & -2.33451260908667 \tabularnewline
49 & 115.64 & 115.092479929383 & 0.547520070616912 \tabularnewline
50 & 116.02 & 115.808755281448 & 0.211244718552436 \tabularnewline
51 & 116.07 & 116.198892862971 & -0.128892862971242 \tabularnewline
52 & 114.5 & 116.242707326523 & -1.74270732652258 \tabularnewline
53 & 114.36 & 114.589075235195 & -0.229075235194642 \tabularnewline
54 & 116 & 114.43808197161 & 1.56191802838967 \tabularnewline
55 & 116.16 & 116.153038029469 & 0.00696197053127889 \tabularnewline
56 & 116.42 & 116.313372132704 & 0.106627867296382 \tabularnewline
57 & 116.78 & 116.578489177545 & 0.201510822454637 \tabularnewline
58 & 115.74 & 116.948159631815 & -1.20815963181535 \tabularnewline
59 & 115.44 & 115.850180351457 & -0.410180351457143 \tabularnewline
60 & 113.52 & 115.53049589837 & -2.01049589836975 \tabularnewline
61 & 113.37 & 113.514012700056 & -0.144012700056436 \tabularnewline
62 & 114.35 & 113.357101566385 & 0.992898433614812 \tabularnewline
63 & 114.11 & 114.38475051536 & -0.274750515359955 \tabularnewline
64 & 113.47 & 114.131565306436 & -0.661565306436302 \tabularnewline
65 & 114.33 & 113.459816951859 & 0.870183048141229 \tabularnewline
66 & 115.76 & 114.361576819994 & 1.39842318000582 \tabularnewline
67 & 116.2 & 115.858686800727 & 0.341313199273287 \tabularnewline
68 & 116.48 & 116.315066336303 & 0.16493366369744 \tabularnewline
69 & 116.53 & 116.602981461818 & -0.0729814618175908 \tabularnewline
70 & 116.45 & 116.64947909961 & -0.199479099609619 \tabularnewline
71 & 116.23 & 116.559906147214 & -0.329906147213833 \tabularnewline
72 & 114.46 & 116.32407403323 & -1.86407403323032 \tabularnewline
73 & 115.08 & 114.464617583822 & 0.615382416178363 \tabularnewline
74 & 115.57 & 115.114149632978 & 0.455850367022322 \tabularnewline
75 & 116.17 & 115.626025778758 & 0.543974221242451 \tabularnewline
76 & 115.21 & 116.252130966392 & -1.04213096639214 \tabularnewline
77 & 114.97 & 115.24211936041 & -0.272119360409548 \tabularnewline
78 & 114.24 & 114.989060419958 & -0.749060419957814 \tabularnewline
79 & 114.16 & 114.223113196635 & -0.0631131966354275 \tabularnewline
80 & 117.2 & 114.14008441002 & 3.05991558997992 \tabularnewline
81 & 117.71 & 117.326928998427 & 0.38307100157293 \tabularnewline
82 & 117.14 & 117.855312480553 & -0.715312480553436 \tabularnewline
83 & 116.67 & 117.250984812453 & -0.580984812452655 \tabularnewline
84 & 114.71 & 116.753103495747 & -2.0431034957475 \tabularnewline
85 & 115.92 & 114.695055466943 & 1.22494453305708 \tabularnewline
86 & 117.74 & 115.963840250539 & 1.77615974946134 \tabularnewline
87 & 118.38 & 117.869077715326 & 0.510922284673512 \tabularnewline
88 & 118.59 & 118.533596748742 & 0.056403251257521 \tabularnewline
89 & 119.66 & 118.746303526747 & 0.913696473252642 \tabularnewline
90 & 121.2 & 119.860151593336 & 1.33984840666446 \tabularnewline
91 & 121.4 & 121.464450585258 & -0.0644505852582853 \tabularnewline
92 & 122.66 & 121.661357617695 & 0.998642382304553 \tabularnewline
93 & 122.95 & 122.96928221734 & -0.0192822173397786 \tabularnewline
94 & 122.9 & 123.258356868524 & -0.358356868523586 \tabularnewline
95 & 123.29 & 123.191159411498 & 0.0988405885021706 \tabularnewline
96 & 122.02 & 123.585902746766 & -1.56590274676631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279379&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]3[/C][C]101.44[/C][C]100.52[/C][C]0.920000000000002[/C][/ROW]
[ROW][C]4[/C][C]102.17[/C][C]101.34415057127[/C][C]0.825849428730393[/C][/ROW]
[ROW][C]5[/C][C]102.75[/C][C]102.113782880032[/C][C]0.636217119968279[/C][/ROW]
[ROW][C]6[/C][C]104.28[/C][C]102.724314781443[/C][C]1.5556852185573[/C][/ROW]
[ROW][C]7[/C][C]104.96[/C][C]104.328971728307[/C][C]0.631028271693154[/C][/ROW]
[ROW][C]8[/C][C]105.16[/C][C]105.039254618179[/C][C]0.120745381820853[/C][/ROW]
[ROW][C]9[/C][C]105.29[/C][C]105.245049159033[/C][C]0.0449508409669903[/C][/ROW]
[ROW][C]10[/C][C]105.15[/C][C]105.377206338715[/C][C]-0.227206338715348[/C][/ROW]
[ROW][C]11[/C][C]105.23[/C][C]105.226302763008[/C][C]0.00369723699157021[/C][/ROW]
[ROW][C]12[/C][C]104.45[/C][C]105.306480192492[/C][C]-0.856480192492455[/C][/ROW]
[ROW][C]13[/C][C]104.6[/C][C]104.485377920993[/C][C]0.114622079007162[/C][/ROW]
[ROW][C]14[/C][C]105.1[/C][C]104.640878606067[/C][C]0.459121393932961[/C][/ROW]
[ROW][C]15[/C][C]105.94[/C][C]105.162911727615[/C][C]0.777088272384873[/C][/ROW]
[ROW][C]16[/C][C]106.2[/C][C]106.040204000607[/C][C]0.159795999392799[/C][/ROW]
[ROW][C]17[/C][C]106.89[/C][C]106.30787257089[/C][C]0.5821274291104[/C][/ROW]
[ROW][C]18[/C][C]107.57[/C][C]107.025808721484[/C][C]0.54419127851591[/C][/ROW]
[ROW][C]19[/C][C]107.42[/C][C]107.731924325643[/C][C]-0.311924325643233[/C][/ROW]
[ROW][C]20[/C][C]107.2[/C][C]107.566955154806[/C][C]-0.366955154806249[/C][/ROW]
[ROW][C]21[/C][C]107.08[/C][C]107.329345068159[/C][C]-0.249345068159485[/C][/ROW]
[ROW][C]22[/C][C]107.17[/C][C]107.197379060331[/C][C]-0.0273790603306594[/C][/ROW]
[ROW][C]23[/C][C]107.23[/C][C]107.286065146032[/C][C]-0.0560651460323811[/C][/ROW]
[ROW][C]24[/C][C]106.61[/C][C]107.343374593613[/C][C]-0.733374593613206[/C][/ROW]
[ROW][C]25[/C][C]106.97[/C][C]106.688180129197[/C][C]0.281819870802721[/C][/ROW]
[ROW][C]26[/C][C]108.23[/C][C]107.061704594731[/C][C]1.16829540526895[/C][/ROW]
[ROW][C]27[/C][C]109.8[/C][C]108.377770800768[/C][C]1.42222919923167[/C][/ROW]
[ROW][C]28[/C][C]111.93[/C][C]110.016023226445[/C][C]1.91397677355515[/C][/ROW]
[ROW][C]29[/C][C]113.51[/C][C]112.237874495955[/C][C]1.27212550404511[/C][/ROW]
[ROW][C]30[/C][C]115.27[/C][C]113.878923482618[/C][C]1.39107651738179[/C][/ROW]
[ROW][C]31[/C][C]115.58[/C][C]115.705680898838[/C][C]-0.125680898837928[/C][/ROW]
[ROW][C]32[/C][C]115.55[/C][C]116.009649503749[/C][C]-0.459649503749475[/C][/ROW]
[ROW][C]33[/C][C]115.44[/C][C]115.957591038343[/C][C]-0.517591038342587[/C][/ROW]
[ROW][C]34[/C][C]114.93[/C][C]115.822751973096[/C][C]-0.892751973095997[/C][/ROW]
[ROW][C]35[/C][C]115.09[/C][C]115.269909027863[/C][C]-0.179909027863118[/C][/ROW]
[ROW][C]36[/C][C]113.78[/C][C]115.421275238345[/C][C]-1.64127523834495[/C][/ROW]
[ROW][C]37[/C][C]114.51[/C][C]114.032510847711[/C][C]0.477489152289408[/C][/ROW]
[ROW][C]38[/C][C]114.85[/C][C]114.785425433416[/C][C]0.0645745665843691[/C][/ROW]
[ROW][C]39[/C][C]116.12[/C][C]115.128524350811[/C][C]0.991475649188544[/C][/ROW]
[ROW][C]40[/C][C]115.47[/C][C]116.446105020715[/C][C]-0.97610502071538[/C][/ROW]
[ROW][C]41[/C][C]115.93[/C][C]115.74926198345[/C][C]0.180738016549554[/C][/ROW]
[ROW][C]42[/C][C]116.6[/C][C]116.21793555593[/C][C]0.382064444070409[/C][/ROW]
[ROW][C]43[/C][C]116.98[/C][C]116.906270733612[/C][C]0.0737292663883409[/C][/ROW]
[ROW][C]44[/C][C]117.37[/C][C]117.289808982775[/C][C]0.0801910172249336[/C][/ROW]
[ROW][C]45[/C][C]117.48[/C][C]117.683657329755[/C][C]-0.203657329754606[/C][/ROW]
[ROW][C]46[/C][C]117.18[/C][C]117.783883865133[/C][C]-0.603883865132957[/C][/ROW]
[ROW][C]47[/C][C]117.03[/C][C]117.454903628583[/C][C]-0.42490362858284[/C][/ROW]
[ROW][C]48[/C][C]114.95[/C][C]117.284512609087[/C][C]-2.33451260908667[/C][/ROW]
[ROW][C]49[/C][C]115.64[/C][C]115.092479929383[/C][C]0.547520070616912[/C][/ROW]
[ROW][C]50[/C][C]116.02[/C][C]115.808755281448[/C][C]0.211244718552436[/C][/ROW]
[ROW][C]51[/C][C]116.07[/C][C]116.198892862971[/C][C]-0.128892862971242[/C][/ROW]
[ROW][C]52[/C][C]114.5[/C][C]116.242707326523[/C][C]-1.74270732652258[/C][/ROW]
[ROW][C]53[/C][C]114.36[/C][C]114.589075235195[/C][C]-0.229075235194642[/C][/ROW]
[ROW][C]54[/C][C]116[/C][C]114.43808197161[/C][C]1.56191802838967[/C][/ROW]
[ROW][C]55[/C][C]116.16[/C][C]116.153038029469[/C][C]0.00696197053127889[/C][/ROW]
[ROW][C]56[/C][C]116.42[/C][C]116.313372132704[/C][C]0.106627867296382[/C][/ROW]
[ROW][C]57[/C][C]116.78[/C][C]116.578489177545[/C][C]0.201510822454637[/C][/ROW]
[ROW][C]58[/C][C]115.74[/C][C]116.948159631815[/C][C]-1.20815963181535[/C][/ROW]
[ROW][C]59[/C][C]115.44[/C][C]115.850180351457[/C][C]-0.410180351457143[/C][/ROW]
[ROW][C]60[/C][C]113.52[/C][C]115.53049589837[/C][C]-2.01049589836975[/C][/ROW]
[ROW][C]61[/C][C]113.37[/C][C]113.514012700056[/C][C]-0.144012700056436[/C][/ROW]
[ROW][C]62[/C][C]114.35[/C][C]113.357101566385[/C][C]0.992898433614812[/C][/ROW]
[ROW][C]63[/C][C]114.11[/C][C]114.38475051536[/C][C]-0.274750515359955[/C][/ROW]
[ROW][C]64[/C][C]113.47[/C][C]114.131565306436[/C][C]-0.661565306436302[/C][/ROW]
[ROW][C]65[/C][C]114.33[/C][C]113.459816951859[/C][C]0.870183048141229[/C][/ROW]
[ROW][C]66[/C][C]115.76[/C][C]114.361576819994[/C][C]1.39842318000582[/C][/ROW]
[ROW][C]67[/C][C]116.2[/C][C]115.858686800727[/C][C]0.341313199273287[/C][/ROW]
[ROW][C]68[/C][C]116.48[/C][C]116.315066336303[/C][C]0.16493366369744[/C][/ROW]
[ROW][C]69[/C][C]116.53[/C][C]116.602981461818[/C][C]-0.0729814618175908[/C][/ROW]
[ROW][C]70[/C][C]116.45[/C][C]116.64947909961[/C][C]-0.199479099609619[/C][/ROW]
[ROW][C]71[/C][C]116.23[/C][C]116.559906147214[/C][C]-0.329906147213833[/C][/ROW]
[ROW][C]72[/C][C]114.46[/C][C]116.32407403323[/C][C]-1.86407403323032[/C][/ROW]
[ROW][C]73[/C][C]115.08[/C][C]114.464617583822[/C][C]0.615382416178363[/C][/ROW]
[ROW][C]74[/C][C]115.57[/C][C]115.114149632978[/C][C]0.455850367022322[/C][/ROW]
[ROW][C]75[/C][C]116.17[/C][C]115.626025778758[/C][C]0.543974221242451[/C][/ROW]
[ROW][C]76[/C][C]115.21[/C][C]116.252130966392[/C][C]-1.04213096639214[/C][/ROW]
[ROW][C]77[/C][C]114.97[/C][C]115.24211936041[/C][C]-0.272119360409548[/C][/ROW]
[ROW][C]78[/C][C]114.24[/C][C]114.989060419958[/C][C]-0.749060419957814[/C][/ROW]
[ROW][C]79[/C][C]114.16[/C][C]114.223113196635[/C][C]-0.0631131966354275[/C][/ROW]
[ROW][C]80[/C][C]117.2[/C][C]114.14008441002[/C][C]3.05991558997992[/C][/ROW]
[ROW][C]81[/C][C]117.71[/C][C]117.326928998427[/C][C]0.38307100157293[/C][/ROW]
[ROW][C]82[/C][C]117.14[/C][C]117.855312480553[/C][C]-0.715312480553436[/C][/ROW]
[ROW][C]83[/C][C]116.67[/C][C]117.250984812453[/C][C]-0.580984812452655[/C][/ROW]
[ROW][C]84[/C][C]114.71[/C][C]116.753103495747[/C][C]-2.0431034957475[/C][/ROW]
[ROW][C]85[/C][C]115.92[/C][C]114.695055466943[/C][C]1.22494453305708[/C][/ROW]
[ROW][C]86[/C][C]117.74[/C][C]115.963840250539[/C][C]1.77615974946134[/C][/ROW]
[ROW][C]87[/C][C]118.38[/C][C]117.869077715326[/C][C]0.510922284673512[/C][/ROW]
[ROW][C]88[/C][C]118.59[/C][C]118.533596748742[/C][C]0.056403251257521[/C][/ROW]
[ROW][C]89[/C][C]119.66[/C][C]118.746303526747[/C][C]0.913696473252642[/C][/ROW]
[ROW][C]90[/C][C]121.2[/C][C]119.860151593336[/C][C]1.33984840666446[/C][/ROW]
[ROW][C]91[/C][C]121.4[/C][C]121.464450585258[/C][C]-0.0644505852582853[/C][/ROW]
[ROW][C]92[/C][C]122.66[/C][C]121.661357617695[/C][C]0.998642382304553[/C][/ROW]
[ROW][C]93[/C][C]122.95[/C][C]122.96928221734[/C][C]-0.0192822173397786[/C][/ROW]
[ROW][C]94[/C][C]122.9[/C][C]123.258356868524[/C][C]-0.358356868523586[/C][/ROW]
[ROW][C]95[/C][C]123.29[/C][C]123.191159411498[/C][C]0.0988405885021706[/C][/ROW]
[ROW][C]96[/C][C]122.02[/C][C]123.585902746766[/C][C]-1.56590274676631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279379&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
3101.44100.520.920000000000002
4102.17101.344150571270.825849428730393
5102.75102.1137828800320.636217119968279
6104.28102.7243147814431.5556852185573
7104.96104.3289717283070.631028271693154
8105.16105.0392546181790.120745381820853
9105.29105.2450491590330.0449508409669903
10105.15105.377206338715-0.227206338715348
11105.23105.2263027630080.00369723699157021
12104.45105.306480192492-0.856480192492455
13104.6104.4853779209930.114622079007162
14105.1104.6408786060670.459121393932961
15105.94105.1629117276150.777088272384873
16106.2106.0402040006070.159795999392799
17106.89106.307872570890.5821274291104
18107.57107.0258087214840.54419127851591
19107.42107.731924325643-0.311924325643233
20107.2107.566955154806-0.366955154806249
21107.08107.329345068159-0.249345068159485
22107.17107.197379060331-0.0273790603306594
23107.23107.286065146032-0.0560651460323811
24106.61107.343374593613-0.733374593613206
25106.97106.6881801291970.281819870802721
26108.23107.0617045947311.16829540526895
27109.8108.3777708007681.42222919923167
28111.93110.0160232264451.91397677355515
29113.51112.2378744959551.27212550404511
30115.27113.8789234826181.39107651738179
31115.58115.705680898838-0.125680898837928
32115.55116.009649503749-0.459649503749475
33115.44115.957591038343-0.517591038342587
34114.93115.822751973096-0.892751973095997
35115.09115.269909027863-0.179909027863118
36113.78115.421275238345-1.64127523834495
37114.51114.0325108477110.477489152289408
38114.85114.7854254334160.0645745665843691
39116.12115.1285243508110.991475649188544
40115.47116.446105020715-0.97610502071538
41115.93115.749261983450.180738016549554
42116.6116.217935555930.382064444070409
43116.98116.9062707336120.0737292663883409
44117.37117.2898089827750.0801910172249336
45117.48117.683657329755-0.203657329754606
46117.18117.783883865133-0.603883865132957
47117.03117.454903628583-0.42490362858284
48114.95117.284512609087-2.33451260908667
49115.64115.0924799293830.547520070616912
50116.02115.8087552814480.211244718552436
51116.07116.198892862971-0.128892862971242
52114.5116.242707326523-1.74270732652258
53114.36114.589075235195-0.229075235194642
54116114.438081971611.56191802838967
55116.16116.1530380294690.00696197053127889
56116.42116.3133721327040.106627867296382
57116.78116.5784891775450.201510822454637
58115.74116.948159631815-1.20815963181535
59115.44115.850180351457-0.410180351457143
60113.52115.53049589837-2.01049589836975
61113.37113.514012700056-0.144012700056436
62114.35113.3571015663850.992898433614812
63114.11114.38475051536-0.274750515359955
64113.47114.131565306436-0.661565306436302
65114.33113.4598169518590.870183048141229
66115.76114.3615768199941.39842318000582
67116.2115.8586868007270.341313199273287
68116.48116.3150663363030.16493366369744
69116.53116.602981461818-0.0729814618175908
70116.45116.64947909961-0.199479099609619
71116.23116.559906147214-0.329906147213833
72114.46116.32407403323-1.86407403323032
73115.08114.4646175838220.615382416178363
74115.57115.1141496329780.455850367022322
75116.17115.6260257787580.543974221242451
76115.21116.252130966392-1.04213096639214
77114.97115.24211936041-0.272119360409548
78114.24114.989060419958-0.749060419957814
79114.16114.223113196635-0.0631131966354275
80117.2114.140084410023.05991558997992
81117.71117.3269289984270.38307100157293
82117.14117.855312480553-0.715312480553436
83116.67117.250984812453-0.580984812452655
84114.71116.753103495747-2.0431034957475
85115.92114.6950554669431.22494453305708
86117.74115.9638402505391.77615974946134
87118.38117.8690777153260.510922284673512
88118.59118.5335967487420.056403251257521
89119.66118.7463035267470.913696473252642
90121.2119.8601515933361.33984840666446
91121.4121.464450585258-0.0644505852582853
92122.66121.6613576176950.998642382304553
93122.95122.96928221734-0.0192822173397786
94122.9123.258356868524-0.358356868523586
95123.29123.1911594114980.0988405885021706
96122.02123.585902746766-1.56590274676631






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97122.240755463264120.442661407915124.038849518612
98122.461510926527119.856890833964125.066131019091
99122.682266389791119.416136762506125.948396017077
100122.903021853055119.043137795607126.762905910502
101123.123777316318118.708775122795127.538779509842
102123.344532779582118.398512864944128.29055269422
103123.565288242846118.103951155961129.02662532973
104123.78604370611117.81977136329129.752316048929
105124.006799169373117.542387855848130.471210482899
106124.227554632637117.269270460519131.185838804755
107124.448310095901116.998571000112131.89804919169
108124.669065559164116.728902619105132.609228499224

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 122.240755463264 & 120.442661407915 & 124.038849518612 \tabularnewline
98 & 122.461510926527 & 119.856890833964 & 125.066131019091 \tabularnewline
99 & 122.682266389791 & 119.416136762506 & 125.948396017077 \tabularnewline
100 & 122.903021853055 & 119.043137795607 & 126.762905910502 \tabularnewline
101 & 123.123777316318 & 118.708775122795 & 127.538779509842 \tabularnewline
102 & 123.344532779582 & 118.398512864944 & 128.29055269422 \tabularnewline
103 & 123.565288242846 & 118.103951155961 & 129.02662532973 \tabularnewline
104 & 123.78604370611 & 117.81977136329 & 129.752316048929 \tabularnewline
105 & 124.006799169373 & 117.542387855848 & 130.471210482899 \tabularnewline
106 & 124.227554632637 & 117.269270460519 & 131.185838804755 \tabularnewline
107 & 124.448310095901 & 116.998571000112 & 131.89804919169 \tabularnewline
108 & 124.669065559164 & 116.728902619105 & 132.609228499224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279379&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]97[/C][C]122.240755463264[/C][C]120.442661407915[/C][C]124.038849518612[/C][/ROW]
[ROW][C]98[/C][C]122.461510926527[/C][C]119.856890833964[/C][C]125.066131019091[/C][/ROW]
[ROW][C]99[/C][C]122.682266389791[/C][C]119.416136762506[/C][C]125.948396017077[/C][/ROW]
[ROW][C]100[/C][C]122.903021853055[/C][C]119.043137795607[/C][C]126.762905910502[/C][/ROW]
[ROW][C]101[/C][C]123.123777316318[/C][C]118.708775122795[/C][C]127.538779509842[/C][/ROW]
[ROW][C]102[/C][C]123.344532779582[/C][C]118.398512864944[/C][C]128.29055269422[/C][/ROW]
[ROW][C]103[/C][C]123.565288242846[/C][C]118.103951155961[/C][C]129.02662532973[/C][/ROW]
[ROW][C]104[/C][C]123.78604370611[/C][C]117.81977136329[/C][C]129.752316048929[/C][/ROW]
[ROW][C]105[/C][C]124.006799169373[/C][C]117.542387855848[/C][C]130.471210482899[/C][/ROW]
[ROW][C]106[/C][C]124.227554632637[/C][C]117.269270460519[/C][C]131.185838804755[/C][/ROW]
[ROW][C]107[/C][C]124.448310095901[/C][C]116.998571000112[/C][C]131.89804919169[/C][/ROW]
[ROW][C]108[/C][C]124.669065559164[/C][C]116.728902619105[/C][C]132.609228499224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279379&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279379&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
97122.240755463264120.442661407915124.038849518612
98122.461510926527119.856890833964125.066131019091
99122.682266389791119.416136762506125.948396017077
100122.903021853055119.043137795607126.762905910502
101123.123777316318118.708775122795127.538779509842
102123.344532779582118.398512864944128.29055269422
103123.565288242846118.103951155961129.02662532973
104123.78604370611117.81977136329129.752316048929
105124.006799169373117.542387855848130.471210482899
106124.227554632637117.269270460519131.185838804755
107124.448310095901116.998571000112131.89804919169
108124.669065559164116.728902619105132.609228499224


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')