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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 computationWed, 13 May 2015 22:11:21 +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/13/t1431551508a598botzfext5y2.htm/, Retrieved Fri, 03 May 2024 03:30:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279080, Retrieved Fri, 03 May 2024 03:30:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

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...] [2015-05-13 21:11:21] [b807b9265c4c1efe31f917466850b643] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,05
100,05
100,05
100,05
100,05
108,77
111,32
111,6
108,52
103,13
102,87
102,75
102,75
102,75
102,75
102,75
102,75
115,22
115,53
115,4
111,99
107,93
107,43
106,98
106,98
106,98
106,98
106,98
106,98
113,71
118,77
118,54
116,16
110,52
110,06
109,9
109,9
110,72
110,09
110,07
112,45
113,06
119,83
119,84
113,73
110,5
110,12
109,86
110,36
110,36
110,59
112,52
112,1
115,9
122,96
121,26
114,55
111,57
110,65
109,77
112,38
112,35
112,2
114,46
116,26
119,57
127,77
126,59
120,45
116,38
116,3
115,05
115,05
115,22
115,19
116,07
120,42
121,88
130,74
130,74
124,64
120,5
120,1
119,62

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279080&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279080&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.46523192195286
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.46523192195286 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279080&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]0.46523192195286[/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=279080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279080&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
alpha0.46523192195286
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.75100.899110972271.85088902772962
14102.75101.7519757046610.998024295338823
15102.75102.2362278499160.513772150083639
16102.75102.4544579567790.295542043220848
17102.75102.527441422770.222558577229591
18115.22115.0396690849020.180330915098239
19115.53115.2667828202220.263217179778081
20115.4115.774364629447-0.374364629447186
21111.99112.502036597109-0.512036597109116
22107.93106.7756380743951.15436192560487
23107.43107.1281627681590.301837231840693
24106.98107.069894186851-0.0898941868505858
25106.98107.931379618269-0.951379618268689
26106.98106.986070395633-0.00607039563303147
27106.98106.7208828243820.259117175617561
28106.98106.6858998983090.294100101690944
29106.98106.702718423740.277281576259952
30113.71119.696084810187-5.98608481018722
31118.77117.0962560889031.67374391109654
32118.54117.9127179522680.627282047731939
33116.16114.9469920768591.21300792314148
34110.52110.756530793947-0.236530793946656
35110.06109.9817853458380.0782146541620108
36109.9109.5925890874330.307410912566922
37109.9110.179385655648-0.279385655647715
38110.72110.043332139470.676667860529861
39110.09110.223779414739-0.133779414739081
40110.07110.0112085257980.0587914742022804
41112.45109.8968497203312.5531502796686
42113.06120.872597000984-7.81259700098406
43119.83121.635216439495-1.8052164394954
44119.84120.257924962166-0.417924962165742
45113.73117.073807342929-3.3438073429291
46110.5110.020391180390.479608819610263
47110.12109.7491504151870.370849584813328
48109.86109.6192255369890.240774463010666
49110.36109.8613261690330.498673830967192
50110.36110.597819944505-0.237819944505361
51110.59109.9212255418560.668774458144469
52112.52110.1845385402042.33546145979599
53112.1112.458098535059-0.35809853505944
54115.9116.401298541054-0.501298541054425
55122.96123.970761473298-1.01076147329783
56121.26123.700311623262-2.44031162326175
57114.55117.8749602668-3.32496026679986
58111.57112.788254668884-1.21825466888404
59110.65111.655100711855-1.00510071185488
60109.77110.808693566942-1.03869356694244
61112.38110.5927010521731.78729894782693
62112.35111.53276496830.817235031699923
63112.2111.8252705881340.37472941186617
64114.46112.8374736327051.62252636729478
65116.26113.3332446788132.92675532118737
66119.57118.8134236374630.756576362537359
67127.77126.8960326452670.873967354732713
68126.59126.693468193032-0.103468193031802
69120.45121.213791866189-0.763791866189493
70116.38118.291394377983-1.91139437798266
71116.3116.907275720762-0.607275720761635
72115.05116.187108457547-1.13710845754721
73115.05117.507465365055-2.45746536505469
74115.22115.926727476915-0.706727476914921
75115.19115.254851448787-0.0648514487865128
76116.07116.755955064506-0.685955064506388
77120.42116.8584074730643.56159252693564
78121.88121.5232739764990.356726023501139
79130.74129.6131493123831.12685068761655
80130.74128.9782393249311.76176067506921
81124.64123.8571880654710.782811934529022
82120.5120.92320421439-0.423204214389656
83120.1120.923864233999-0.823864233999331
84119.62119.779079868893-0.159079868892846

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.75 & 100.89911097227 & 1.85088902772962 \tabularnewline
14 & 102.75 & 101.751975704661 & 0.998024295338823 \tabularnewline
15 & 102.75 & 102.236227849916 & 0.513772150083639 \tabularnewline
16 & 102.75 & 102.454457956779 & 0.295542043220848 \tabularnewline
17 & 102.75 & 102.52744142277 & 0.222558577229591 \tabularnewline
18 & 115.22 & 115.039669084902 & 0.180330915098239 \tabularnewline
19 & 115.53 & 115.266782820222 & 0.263217179778081 \tabularnewline
20 & 115.4 & 115.774364629447 & -0.374364629447186 \tabularnewline
21 & 111.99 & 112.502036597109 & -0.512036597109116 \tabularnewline
22 & 107.93 & 106.775638074395 & 1.15436192560487 \tabularnewline
23 & 107.43 & 107.128162768159 & 0.301837231840693 \tabularnewline
24 & 106.98 & 107.069894186851 & -0.0898941868505858 \tabularnewline
25 & 106.98 & 107.931379618269 & -0.951379618268689 \tabularnewline
26 & 106.98 & 106.986070395633 & -0.00607039563303147 \tabularnewline
27 & 106.98 & 106.720882824382 & 0.259117175617561 \tabularnewline
28 & 106.98 & 106.685899898309 & 0.294100101690944 \tabularnewline
29 & 106.98 & 106.70271842374 & 0.277281576259952 \tabularnewline
30 & 113.71 & 119.696084810187 & -5.98608481018722 \tabularnewline
31 & 118.77 & 117.096256088903 & 1.67374391109654 \tabularnewline
32 & 118.54 & 117.912717952268 & 0.627282047731939 \tabularnewline
33 & 116.16 & 114.946992076859 & 1.21300792314148 \tabularnewline
34 & 110.52 & 110.756530793947 & -0.236530793946656 \tabularnewline
35 & 110.06 & 109.981785345838 & 0.0782146541620108 \tabularnewline
36 & 109.9 & 109.592589087433 & 0.307410912566922 \tabularnewline
37 & 109.9 & 110.179385655648 & -0.279385655647715 \tabularnewline
38 & 110.72 & 110.04333213947 & 0.676667860529861 \tabularnewline
39 & 110.09 & 110.223779414739 & -0.133779414739081 \tabularnewline
40 & 110.07 & 110.011208525798 & 0.0587914742022804 \tabularnewline
41 & 112.45 & 109.896849720331 & 2.5531502796686 \tabularnewline
42 & 113.06 & 120.872597000984 & -7.81259700098406 \tabularnewline
43 & 119.83 & 121.635216439495 & -1.8052164394954 \tabularnewline
44 & 119.84 & 120.257924962166 & -0.417924962165742 \tabularnewline
45 & 113.73 & 117.073807342929 & -3.3438073429291 \tabularnewline
46 & 110.5 & 110.02039118039 & 0.479608819610263 \tabularnewline
47 & 110.12 & 109.749150415187 & 0.370849584813328 \tabularnewline
48 & 109.86 & 109.619225536989 & 0.240774463010666 \tabularnewline
49 & 110.36 & 109.861326169033 & 0.498673830967192 \tabularnewline
50 & 110.36 & 110.597819944505 & -0.237819944505361 \tabularnewline
51 & 110.59 & 109.921225541856 & 0.668774458144469 \tabularnewline
52 & 112.52 & 110.184538540204 & 2.33546145979599 \tabularnewline
53 & 112.1 & 112.458098535059 & -0.35809853505944 \tabularnewline
54 & 115.9 & 116.401298541054 & -0.501298541054425 \tabularnewline
55 & 122.96 & 123.970761473298 & -1.01076147329783 \tabularnewline
56 & 121.26 & 123.700311623262 & -2.44031162326175 \tabularnewline
57 & 114.55 & 117.8749602668 & -3.32496026679986 \tabularnewline
58 & 111.57 & 112.788254668884 & -1.21825466888404 \tabularnewline
59 & 110.65 & 111.655100711855 & -1.00510071185488 \tabularnewline
60 & 109.77 & 110.808693566942 & -1.03869356694244 \tabularnewline
61 & 112.38 & 110.592701052173 & 1.78729894782693 \tabularnewline
62 & 112.35 & 111.5327649683 & 0.817235031699923 \tabularnewline
63 & 112.2 & 111.825270588134 & 0.37472941186617 \tabularnewline
64 & 114.46 & 112.837473632705 & 1.62252636729478 \tabularnewline
65 & 116.26 & 113.333244678813 & 2.92675532118737 \tabularnewline
66 & 119.57 & 118.813423637463 & 0.756576362537359 \tabularnewline
67 & 127.77 & 126.896032645267 & 0.873967354732713 \tabularnewline
68 & 126.59 & 126.693468193032 & -0.103468193031802 \tabularnewline
69 & 120.45 & 121.213791866189 & -0.763791866189493 \tabularnewline
70 & 116.38 & 118.291394377983 & -1.91139437798266 \tabularnewline
71 & 116.3 & 116.907275720762 & -0.607275720761635 \tabularnewline
72 & 115.05 & 116.187108457547 & -1.13710845754721 \tabularnewline
73 & 115.05 & 117.507465365055 & -2.45746536505469 \tabularnewline
74 & 115.22 & 115.926727476915 & -0.706727476914921 \tabularnewline
75 & 115.19 & 115.254851448787 & -0.0648514487865128 \tabularnewline
76 & 116.07 & 116.755955064506 & -0.685955064506388 \tabularnewline
77 & 120.42 & 116.858407473064 & 3.56159252693564 \tabularnewline
78 & 121.88 & 121.523273976499 & 0.356726023501139 \tabularnewline
79 & 130.74 & 129.613149312383 & 1.12685068761655 \tabularnewline
80 & 130.74 & 128.978239324931 & 1.76176067506921 \tabularnewline
81 & 124.64 & 123.857188065471 & 0.782811934529022 \tabularnewline
82 & 120.5 & 120.92320421439 & -0.423204214389656 \tabularnewline
83 & 120.1 & 120.923864233999 & -0.823864233999331 \tabularnewline
84 & 119.62 & 119.779079868893 & -0.159079868892846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279080&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]102.75[/C][C]100.89911097227[/C][C]1.85088902772962[/C][/ROW]
[ROW][C]14[/C][C]102.75[/C][C]101.751975704661[/C][C]0.998024295338823[/C][/ROW]
[ROW][C]15[/C][C]102.75[/C][C]102.236227849916[/C][C]0.513772150083639[/C][/ROW]
[ROW][C]16[/C][C]102.75[/C][C]102.454457956779[/C][C]0.295542043220848[/C][/ROW]
[ROW][C]17[/C][C]102.75[/C][C]102.52744142277[/C][C]0.222558577229591[/C][/ROW]
[ROW][C]18[/C][C]115.22[/C][C]115.039669084902[/C][C]0.180330915098239[/C][/ROW]
[ROW][C]19[/C][C]115.53[/C][C]115.266782820222[/C][C]0.263217179778081[/C][/ROW]
[ROW][C]20[/C][C]115.4[/C][C]115.774364629447[/C][C]-0.374364629447186[/C][/ROW]
[ROW][C]21[/C][C]111.99[/C][C]112.502036597109[/C][C]-0.512036597109116[/C][/ROW]
[ROW][C]22[/C][C]107.93[/C][C]106.775638074395[/C][C]1.15436192560487[/C][/ROW]
[ROW][C]23[/C][C]107.43[/C][C]107.128162768159[/C][C]0.301837231840693[/C][/ROW]
[ROW][C]24[/C][C]106.98[/C][C]107.069894186851[/C][C]-0.0898941868505858[/C][/ROW]
[ROW][C]25[/C][C]106.98[/C][C]107.931379618269[/C][C]-0.951379618268689[/C][/ROW]
[ROW][C]26[/C][C]106.98[/C][C]106.986070395633[/C][C]-0.00607039563303147[/C][/ROW]
[ROW][C]27[/C][C]106.98[/C][C]106.720882824382[/C][C]0.259117175617561[/C][/ROW]
[ROW][C]28[/C][C]106.98[/C][C]106.685899898309[/C][C]0.294100101690944[/C][/ROW]
[ROW][C]29[/C][C]106.98[/C][C]106.70271842374[/C][C]0.277281576259952[/C][/ROW]
[ROW][C]30[/C][C]113.71[/C][C]119.696084810187[/C][C]-5.98608481018722[/C][/ROW]
[ROW][C]31[/C][C]118.77[/C][C]117.096256088903[/C][C]1.67374391109654[/C][/ROW]
[ROW][C]32[/C][C]118.54[/C][C]117.912717952268[/C][C]0.627282047731939[/C][/ROW]
[ROW][C]33[/C][C]116.16[/C][C]114.946992076859[/C][C]1.21300792314148[/C][/ROW]
[ROW][C]34[/C][C]110.52[/C][C]110.756530793947[/C][C]-0.236530793946656[/C][/ROW]
[ROW][C]35[/C][C]110.06[/C][C]109.981785345838[/C][C]0.0782146541620108[/C][/ROW]
[ROW][C]36[/C][C]109.9[/C][C]109.592589087433[/C][C]0.307410912566922[/C][/ROW]
[ROW][C]37[/C][C]109.9[/C][C]110.179385655648[/C][C]-0.279385655647715[/C][/ROW]
[ROW][C]38[/C][C]110.72[/C][C]110.04333213947[/C][C]0.676667860529861[/C][/ROW]
[ROW][C]39[/C][C]110.09[/C][C]110.223779414739[/C][C]-0.133779414739081[/C][/ROW]
[ROW][C]40[/C][C]110.07[/C][C]110.011208525798[/C][C]0.0587914742022804[/C][/ROW]
[ROW][C]41[/C][C]112.45[/C][C]109.896849720331[/C][C]2.5531502796686[/C][/ROW]
[ROW][C]42[/C][C]113.06[/C][C]120.872597000984[/C][C]-7.81259700098406[/C][/ROW]
[ROW][C]43[/C][C]119.83[/C][C]121.635216439495[/C][C]-1.8052164394954[/C][/ROW]
[ROW][C]44[/C][C]119.84[/C][C]120.257924962166[/C][C]-0.417924962165742[/C][/ROW]
[ROW][C]45[/C][C]113.73[/C][C]117.073807342929[/C][C]-3.3438073429291[/C][/ROW]
[ROW][C]46[/C][C]110.5[/C][C]110.02039118039[/C][C]0.479608819610263[/C][/ROW]
[ROW][C]47[/C][C]110.12[/C][C]109.749150415187[/C][C]0.370849584813328[/C][/ROW]
[ROW][C]48[/C][C]109.86[/C][C]109.619225536989[/C][C]0.240774463010666[/C][/ROW]
[ROW][C]49[/C][C]110.36[/C][C]109.861326169033[/C][C]0.498673830967192[/C][/ROW]
[ROW][C]50[/C][C]110.36[/C][C]110.597819944505[/C][C]-0.237819944505361[/C][/ROW]
[ROW][C]51[/C][C]110.59[/C][C]109.921225541856[/C][C]0.668774458144469[/C][/ROW]
[ROW][C]52[/C][C]112.52[/C][C]110.184538540204[/C][C]2.33546145979599[/C][/ROW]
[ROW][C]53[/C][C]112.1[/C][C]112.458098535059[/C][C]-0.35809853505944[/C][/ROW]
[ROW][C]54[/C][C]115.9[/C][C]116.401298541054[/C][C]-0.501298541054425[/C][/ROW]
[ROW][C]55[/C][C]122.96[/C][C]123.970761473298[/C][C]-1.01076147329783[/C][/ROW]
[ROW][C]56[/C][C]121.26[/C][C]123.700311623262[/C][C]-2.44031162326175[/C][/ROW]
[ROW][C]57[/C][C]114.55[/C][C]117.8749602668[/C][C]-3.32496026679986[/C][/ROW]
[ROW][C]58[/C][C]111.57[/C][C]112.788254668884[/C][C]-1.21825466888404[/C][/ROW]
[ROW][C]59[/C][C]110.65[/C][C]111.655100711855[/C][C]-1.00510071185488[/C][/ROW]
[ROW][C]60[/C][C]109.77[/C][C]110.808693566942[/C][C]-1.03869356694244[/C][/ROW]
[ROW][C]61[/C][C]112.38[/C][C]110.592701052173[/C][C]1.78729894782693[/C][/ROW]
[ROW][C]62[/C][C]112.35[/C][C]111.5327649683[/C][C]0.817235031699923[/C][/ROW]
[ROW][C]63[/C][C]112.2[/C][C]111.825270588134[/C][C]0.37472941186617[/C][/ROW]
[ROW][C]64[/C][C]114.46[/C][C]112.837473632705[/C][C]1.62252636729478[/C][/ROW]
[ROW][C]65[/C][C]116.26[/C][C]113.333244678813[/C][C]2.92675532118737[/C][/ROW]
[ROW][C]66[/C][C]119.57[/C][C]118.813423637463[/C][C]0.756576362537359[/C][/ROW]
[ROW][C]67[/C][C]127.77[/C][C]126.896032645267[/C][C]0.873967354732713[/C][/ROW]
[ROW][C]68[/C][C]126.59[/C][C]126.693468193032[/C][C]-0.103468193031802[/C][/ROW]
[ROW][C]69[/C][C]120.45[/C][C]121.213791866189[/C][C]-0.763791866189493[/C][/ROW]
[ROW][C]70[/C][C]116.38[/C][C]118.291394377983[/C][C]-1.91139437798266[/C][/ROW]
[ROW][C]71[/C][C]116.3[/C][C]116.907275720762[/C][C]-0.607275720761635[/C][/ROW]
[ROW][C]72[/C][C]115.05[/C][C]116.187108457547[/C][C]-1.13710845754721[/C][/ROW]
[ROW][C]73[/C][C]115.05[/C][C]117.507465365055[/C][C]-2.45746536505469[/C][/ROW]
[ROW][C]74[/C][C]115.22[/C][C]115.926727476915[/C][C]-0.706727476914921[/C][/ROW]
[ROW][C]75[/C][C]115.19[/C][C]115.254851448787[/C][C]-0.0648514487865128[/C][/ROW]
[ROW][C]76[/C][C]116.07[/C][C]116.755955064506[/C][C]-0.685955064506388[/C][/ROW]
[ROW][C]77[/C][C]120.42[/C][C]116.858407473064[/C][C]3.56159252693564[/C][/ROW]
[ROW][C]78[/C][C]121.88[/C][C]121.523273976499[/C][C]0.356726023501139[/C][/ROW]
[ROW][C]79[/C][C]130.74[/C][C]129.613149312383[/C][C]1.12685068761655[/C][/ROW]
[ROW][C]80[/C][C]130.74[/C][C]128.978239324931[/C][C]1.76176067506921[/C][/ROW]
[ROW][C]81[/C][C]124.64[/C][C]123.857188065471[/C][C]0.782811934529022[/C][/ROW]
[ROW][C]82[/C][C]120.5[/C][C]120.92320421439[/C][C]-0.423204214389656[/C][/ROW]
[ROW][C]83[/C][C]120.1[/C][C]120.923864233999[/C][C]-0.823864233999331[/C][/ROW]
[ROW][C]84[/C][C]119.62[/C][C]119.779079868893[/C][C]-0.159079868892846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279080&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279080&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
13102.75100.899110972271.85088902772962
14102.75101.7519757046610.998024295338823
15102.75102.2362278499160.513772150083639
16102.75102.4544579567790.295542043220848
17102.75102.527441422770.222558577229591
18115.22115.0396690849020.180330915098239
19115.53115.2667828202220.263217179778081
20115.4115.774364629447-0.374364629447186
21111.99112.502036597109-0.512036597109116
22107.93106.7756380743951.15436192560487
23107.43107.1281627681590.301837231840693
24106.98107.069894186851-0.0898941868505858
25106.98107.931379618269-0.951379618268689
26106.98106.986070395633-0.00607039563303147
27106.98106.7208828243820.259117175617561
28106.98106.6858998983090.294100101690944
29106.98106.702718423740.277281576259952
30113.71119.696084810187-5.98608481018722
31118.77117.0962560889031.67374391109654
32118.54117.9127179522680.627282047731939
33116.16114.9469920768591.21300792314148
34110.52110.756530793947-0.236530793946656
35110.06109.9817853458380.0782146541620108
36109.9109.5925890874330.307410912566922
37109.9110.179385655648-0.279385655647715
38110.72110.043332139470.676667860529861
39110.09110.223779414739-0.133779414739081
40110.07110.0112085257980.0587914742022804
41112.45109.8968497203312.5531502796686
42113.06120.872597000984-7.81259700098406
43119.83121.635216439495-1.8052164394954
44119.84120.257924962166-0.417924962165742
45113.73117.073807342929-3.3438073429291
46110.5110.020391180390.479608819610263
47110.12109.7491504151870.370849584813328
48109.86109.6192255369890.240774463010666
49110.36109.8613261690330.498673830967192
50110.36110.597819944505-0.237819944505361
51110.59109.9212255418560.668774458144469
52112.52110.1845385402042.33546145979599
53112.1112.458098535059-0.35809853505944
54115.9116.401298541054-0.501298541054425
55122.96123.970761473298-1.01076147329783
56121.26123.700311623262-2.44031162326175
57114.55117.8749602668-3.32496026679986
58111.57112.788254668884-1.21825466888404
59110.65111.655100711855-1.00510071185488
60109.77110.808693566942-1.03869356694244
61112.38110.5927010521731.78729894782693
62112.35111.53276496830.817235031699923
63112.2111.8252705881340.37472941186617
64114.46112.8374736327051.62252636729478
65116.26113.3332446788132.92675532118737
66119.57118.8134236374630.756576362537359
67127.77126.8960326452670.873967354732713
68126.59126.693468193032-0.103468193031802
69120.45121.213791866189-0.763791866189493
70116.38118.291394377983-1.91139437798266
71116.3116.907275720762-0.607275720761635
72115.05116.187108457547-1.13710845754721
73115.05117.507465365055-2.45746536505469
74115.22115.926727476915-0.706727476914921
75115.19115.254851448787-0.0648514487865128
76116.07116.755955064506-0.685955064506388
77120.42116.8584074730643.56159252693564
78121.88121.5232739764990.356726023501139
79130.74129.6131493123831.12685068761655
80130.74128.9782393249311.76176067506921
81124.64123.8571880654710.782811934529022
82120.5120.92320421439-0.423204214389656
83120.1120.923864233999-0.823864233999331
84119.62119.779079868893-0.159079868892846






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85120.868509263729117.520335384587124.216683142872
86121.375526486963117.681695192524125.069357781403
87121.358976580793117.353431353207125.364521808379
88122.604374812822118.293637294872126.915112330771
89125.402776623762120.775824684268130.029728563256
90126.736670109288121.833698206226131.639642012351
91135.388290638539130.046886249151140.729695027927
92134.521184535638128.988943825525140.053425245751
93127.859387982625122.307430729745133.411345235506
94123.805948130828118.169396312596129.442499949061
95123.778757481608117.941719586801129.615795376415
96123.350753492107112.135472498296134.566034485918

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 120.868509263729 & 117.520335384587 & 124.216683142872 \tabularnewline
86 & 121.375526486963 & 117.681695192524 & 125.069357781403 \tabularnewline
87 & 121.358976580793 & 117.353431353207 & 125.364521808379 \tabularnewline
88 & 122.604374812822 & 118.293637294872 & 126.915112330771 \tabularnewline
89 & 125.402776623762 & 120.775824684268 & 130.029728563256 \tabularnewline
90 & 126.736670109288 & 121.833698206226 & 131.639642012351 \tabularnewline
91 & 135.388290638539 & 130.046886249151 & 140.729695027927 \tabularnewline
92 & 134.521184535638 & 128.988943825525 & 140.053425245751 \tabularnewline
93 & 127.859387982625 & 122.307430729745 & 133.411345235506 \tabularnewline
94 & 123.805948130828 & 118.169396312596 & 129.442499949061 \tabularnewline
95 & 123.778757481608 & 117.941719586801 & 129.615795376415 \tabularnewline
96 & 123.350753492107 & 112.135472498296 & 134.566034485918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279080&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]120.868509263729[/C][C]117.520335384587[/C][C]124.216683142872[/C][/ROW]
[ROW][C]86[/C][C]121.375526486963[/C][C]117.681695192524[/C][C]125.069357781403[/C][/ROW]
[ROW][C]87[/C][C]121.358976580793[/C][C]117.353431353207[/C][C]125.364521808379[/C][/ROW]
[ROW][C]88[/C][C]122.604374812822[/C][C]118.293637294872[/C][C]126.915112330771[/C][/ROW]
[ROW][C]89[/C][C]125.402776623762[/C][C]120.775824684268[/C][C]130.029728563256[/C][/ROW]
[ROW][C]90[/C][C]126.736670109288[/C][C]121.833698206226[/C][C]131.639642012351[/C][/ROW]
[ROW][C]91[/C][C]135.388290638539[/C][C]130.046886249151[/C][C]140.729695027927[/C][/ROW]
[ROW][C]92[/C][C]134.521184535638[/C][C]128.988943825525[/C][C]140.053425245751[/C][/ROW]
[ROW][C]93[/C][C]127.859387982625[/C][C]122.307430729745[/C][C]133.411345235506[/C][/ROW]
[ROW][C]94[/C][C]123.805948130828[/C][C]118.169396312596[/C][C]129.442499949061[/C][/ROW]
[ROW][C]95[/C][C]123.778757481608[/C][C]117.941719586801[/C][C]129.615795376415[/C][/ROW]
[ROW][C]96[/C][C]123.350753492107[/C][C]112.135472498296[/C][C]134.566034485918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279080&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279080&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
85120.868509263729117.520335384587124.216683142872
86121.375526486963117.681695192524125.069357781403
87121.358976580793117.353431353207125.364521808379
88122.604374812822118.293637294872126.915112330771
89125.402776623762120.775824684268130.029728563256
90126.736670109288121.833698206226131.639642012351
91135.388290638539130.046886249151140.729695027927
92134.521184535638128.988943825525140.053425245751
93127.859387982625122.307430729745133.411345235506
94123.805948130828118.169396312596129.442499949061
95123.778757481608117.941719586801129.615795376415
96123.350753492107112.135472498296134.566034485918


Figures (Output of Computation)

Input Parameters & R Code

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