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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 04:09:53 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t1386839438yzzo62m28zbj1ts.htm/, Retrieved Tue, 07 Dec 2021 12:21:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232228, Retrieved Tue, 07 Dec 2021 12:21:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 09:09:53] [0e26096743f9a17ea293f422aff92055] [Current]
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Dataseries X:
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12
-16
-20
-12
-12
-10
-10
-13
-16
-14
-17
-24
-25
-23
-17
-24
-20
-19
-18
-16
-12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232228&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232228&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232228&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.672918133004308
beta0.000555793245723121
gamma0.637515631536196

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.672918133004308 \tabularnewline
beta & 0.000555793245723121 \tabularnewline
gamma & 0.637515631536196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232228&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]0.672918133004308[/C][/ROW]
[ROW][C]beta[/C][C]0.000555793245723121[/C][/ROW]
[ROW][C]gamma[/C][C]0.637515631536196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232228&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232228&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.672918133004308
beta0.000555793245723121
gamma0.637515631536196







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-1-3.315972222222222.31597222222222
1410.3588839660528380.641116033947162
15-1-1.051394498723680.051394498723683
1622.26651194373964-0.26651194373964
1722.74539370010986-0.745393700109863
1811.61008179264361-0.610081792643613
19-1-0.392737784646734-0.607262215353266
20-2-0.768887135355842-1.23111286464416
21-2-1.73196400726557-0.268035992734427
22-11.82793076504975-2.82793076504975
23-8-1.5024983957644-6.4975016042356
24-4-15.179678401998311.1796784019983
25-6-0.182789466243487-5.81721053375651
26-3-2.33275771023544-0.667242289764563
27-3-4.749529758551251.74952975855125
28-7-0.357678912625815-6.64232108737419
29-9-4.2739074614952-4.7260925385048
30-11-8.06603377218554-2.93396622781446
31-13-11.6392637129066-1.36073628709338
32-11-12.66002077125931.66002077125926
33-9-11.48319562887852.48319562887853
34-17-6.6111218279153-10.3888781720847
35-22-15.8028414737891-6.19715852621092
36-25-25.59997443853810.599974438538055
37-20-21.27860627326641.27860627326635
38-24-17.5892046954795-6.41079530452054
39-24-23.3785253318144-0.621474668185574
40-22-22.3444726548260.344472654826045
41-19-21.16941553074272.1694155307427
42-18-19.95498278421061.95498278421062
43-17-19.91571938687772.91571938687772
44-11-17.43270350252696.43270350252687
45-11-12.87463964073221.87463964073215
46-12-11.0984183870019-0.901581612998061
47-10-13.03062120421373.03062120421375
48-15-15.19613942757480.196139427574831
49-15-11.0004244164532-3.99957558354681
50-15-12.4635871083448-2.53641289165524
51-13-14.43451602098541.43451602098541
52-8-11.81070028976793.81070028976789
53-13-7.9164921345838-5.0835078654162
54-9-11.62398227690122.6239822769012
55-7-10.93053991900673.93053991900674
56-4-7.027228051768993.02722805176899
57-4-5.708446599942711.70844659994271
58-2-4.6202485717322.620248571732
590-3.35858046904623.3585804690462
60-2-5.89030650960423.8903065096042
61-3-0.0780794910445088-2.92192050895549
621-0.5050374400714791.50503744007148
63-21.07906039549226-3.07906039549226
64-11.16684631602017-2.16684631602017
651-0.8124430565232791.81244305652328
66-31.73374116228469-4.73374116228469
67-4-2.24817105544584-1.75182894455416
68-9-2.35576407044059-6.64423592955941
69-9-7.82247273576299-1.17752726423701
70-7-8.489644031381291.48964403138129
71-14-7.83872020004599-6.16127979995401
72-12-16.67311468638594.67311468638589
73-16-11.7617705703687-4.23822942963125
74-20-12.1590450487251-7.84095495127493
75-12-17.83106236172485.83106236172479
76-12-11.5650983745286-0.43490162547141
77-10-11.55634217437381.55634217437383
78-10-10.55476976033310.554769760333111
79-13-10.3614492461854-2.63855075381461
80-16-12.0915187359623-3.90848126403771
81-14-14.58196983370670.581969833706687
82-17-13.5129259044651-3.4870740955349
83-24-17.8120966933916-6.18790330660837
84-25-24.4110323931857-0.588967606814276
85-23-24.90661020259741.90661020259737
86-17-21.9256317068594.92563170685898
87-24-16.1566016808587-7.84339831914125
88-20-20.40482879181980.404828791819835
89-19-19.42129591089190.421295910891939
90-18-19.39829581165311.39829581165311
91-16-19.30883782470893.3088378247089
92-12-17.30499895078755.30499895078745

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -1 & -3.31597222222222 & 2.31597222222222 \tabularnewline
14 & 1 & 0.358883966052838 & 0.641116033947162 \tabularnewline
15 & -1 & -1.05139449872368 & 0.051394498723683 \tabularnewline
16 & 2 & 2.26651194373964 & -0.26651194373964 \tabularnewline
17 & 2 & 2.74539370010986 & -0.745393700109863 \tabularnewline
18 & 1 & 1.61008179264361 & -0.610081792643613 \tabularnewline
19 & -1 & -0.392737784646734 & -0.607262215353266 \tabularnewline
20 & -2 & -0.768887135355842 & -1.23111286464416 \tabularnewline
21 & -2 & -1.73196400726557 & -0.268035992734427 \tabularnewline
22 & -1 & 1.82793076504975 & -2.82793076504975 \tabularnewline
23 & -8 & -1.5024983957644 & -6.4975016042356 \tabularnewline
24 & -4 & -15.1796784019983 & 11.1796784019983 \tabularnewline
25 & -6 & -0.182789466243487 & -5.81721053375651 \tabularnewline
26 & -3 & -2.33275771023544 & -0.667242289764563 \tabularnewline
27 & -3 & -4.74952975855125 & 1.74952975855125 \tabularnewline
28 & -7 & -0.357678912625815 & -6.64232108737419 \tabularnewline
29 & -9 & -4.2739074614952 & -4.7260925385048 \tabularnewline
30 & -11 & -8.06603377218554 & -2.93396622781446 \tabularnewline
31 & -13 & -11.6392637129066 & -1.36073628709338 \tabularnewline
32 & -11 & -12.6600207712593 & 1.66002077125926 \tabularnewline
33 & -9 & -11.4831956288785 & 2.48319562887853 \tabularnewline
34 & -17 & -6.6111218279153 & -10.3888781720847 \tabularnewline
35 & -22 & -15.8028414737891 & -6.19715852621092 \tabularnewline
36 & -25 & -25.5999744385381 & 0.599974438538055 \tabularnewline
37 & -20 & -21.2786062732664 & 1.27860627326635 \tabularnewline
38 & -24 & -17.5892046954795 & -6.41079530452054 \tabularnewline
39 & -24 & -23.3785253318144 & -0.621474668185574 \tabularnewline
40 & -22 & -22.344472654826 & 0.344472654826045 \tabularnewline
41 & -19 & -21.1694155307427 & 2.1694155307427 \tabularnewline
42 & -18 & -19.9549827842106 & 1.95498278421062 \tabularnewline
43 & -17 & -19.9157193868777 & 2.91571938687772 \tabularnewline
44 & -11 & -17.4327035025269 & 6.43270350252687 \tabularnewline
45 & -11 & -12.8746396407322 & 1.87463964073215 \tabularnewline
46 & -12 & -11.0984183870019 & -0.901581612998061 \tabularnewline
47 & -10 & -13.0306212042137 & 3.03062120421375 \tabularnewline
48 & -15 & -15.1961394275748 & 0.196139427574831 \tabularnewline
49 & -15 & -11.0004244164532 & -3.99957558354681 \tabularnewline
50 & -15 & -12.4635871083448 & -2.53641289165524 \tabularnewline
51 & -13 & -14.4345160209854 & 1.43451602098541 \tabularnewline
52 & -8 & -11.8107002897679 & 3.81070028976789 \tabularnewline
53 & -13 & -7.9164921345838 & -5.0835078654162 \tabularnewline
54 & -9 & -11.6239822769012 & 2.6239822769012 \tabularnewline
55 & -7 & -10.9305399190067 & 3.93053991900674 \tabularnewline
56 & -4 & -7.02722805176899 & 3.02722805176899 \tabularnewline
57 & -4 & -5.70844659994271 & 1.70844659994271 \tabularnewline
58 & -2 & -4.620248571732 & 2.620248571732 \tabularnewline
59 & 0 & -3.3585804690462 & 3.3585804690462 \tabularnewline
60 & -2 & -5.8903065096042 & 3.8903065096042 \tabularnewline
61 & -3 & -0.0780794910445088 & -2.92192050895549 \tabularnewline
62 & 1 & -0.505037440071479 & 1.50503744007148 \tabularnewline
63 & -2 & 1.07906039549226 & -3.07906039549226 \tabularnewline
64 & -1 & 1.16684631602017 & -2.16684631602017 \tabularnewline
65 & 1 & -0.812443056523279 & 1.81244305652328 \tabularnewline
66 & -3 & 1.73374116228469 & -4.73374116228469 \tabularnewline
67 & -4 & -2.24817105544584 & -1.75182894455416 \tabularnewline
68 & -9 & -2.35576407044059 & -6.64423592955941 \tabularnewline
69 & -9 & -7.82247273576299 & -1.17752726423701 \tabularnewline
70 & -7 & -8.48964403138129 & 1.48964403138129 \tabularnewline
71 & -14 & -7.83872020004599 & -6.16127979995401 \tabularnewline
72 & -12 & -16.6731146863859 & 4.67311468638589 \tabularnewline
73 & -16 & -11.7617705703687 & -4.23822942963125 \tabularnewline
74 & -20 & -12.1590450487251 & -7.84095495127493 \tabularnewline
75 & -12 & -17.8310623617248 & 5.83106236172479 \tabularnewline
76 & -12 & -11.5650983745286 & -0.43490162547141 \tabularnewline
77 & -10 & -11.5563421743738 & 1.55634217437383 \tabularnewline
78 & -10 & -10.5547697603331 & 0.554769760333111 \tabularnewline
79 & -13 & -10.3614492461854 & -2.63855075381461 \tabularnewline
80 & -16 & -12.0915187359623 & -3.90848126403771 \tabularnewline
81 & -14 & -14.5819698337067 & 0.581969833706687 \tabularnewline
82 & -17 & -13.5129259044651 & -3.4870740955349 \tabularnewline
83 & -24 & -17.8120966933916 & -6.18790330660837 \tabularnewline
84 & -25 & -24.4110323931857 & -0.588967606814276 \tabularnewline
85 & -23 & -24.9066102025974 & 1.90661020259737 \tabularnewline
86 & -17 & -21.925631706859 & 4.92563170685898 \tabularnewline
87 & -24 & -16.1566016808587 & -7.84339831914125 \tabularnewline
88 & -20 & -20.4048287918198 & 0.404828791819835 \tabularnewline
89 & -19 & -19.4212959108919 & 0.421295910891939 \tabularnewline
90 & -18 & -19.3982958116531 & 1.39829581165311 \tabularnewline
91 & -16 & -19.3088378247089 & 3.3088378247089 \tabularnewline
92 & -12 & -17.3049989507875 & 5.30499895078745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232228&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]-1[/C][C]-3.31597222222222[/C][C]2.31597222222222[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]0.358883966052838[/C][C]0.641116033947162[/C][/ROW]
[ROW][C]15[/C][C]-1[/C][C]-1.05139449872368[/C][C]0.051394498723683[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]2.26651194373964[/C][C]-0.26651194373964[/C][/ROW]
[ROW][C]17[/C][C]2[/C][C]2.74539370010986[/C][C]-0.745393700109863[/C][/ROW]
[ROW][C]18[/C][C]1[/C][C]1.61008179264361[/C][C]-0.610081792643613[/C][/ROW]
[ROW][C]19[/C][C]-1[/C][C]-0.392737784646734[/C][C]-0.607262215353266[/C][/ROW]
[ROW][C]20[/C][C]-2[/C][C]-0.768887135355842[/C][C]-1.23111286464416[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-1.73196400726557[/C][C]-0.268035992734427[/C][/ROW]
[ROW][C]22[/C][C]-1[/C][C]1.82793076504975[/C][C]-2.82793076504975[/C][/ROW]
[ROW][C]23[/C][C]-8[/C][C]-1.5024983957644[/C][C]-6.4975016042356[/C][/ROW]
[ROW][C]24[/C][C]-4[/C][C]-15.1796784019983[/C][C]11.1796784019983[/C][/ROW]
[ROW][C]25[/C][C]-6[/C][C]-0.182789466243487[/C][C]-5.81721053375651[/C][/ROW]
[ROW][C]26[/C][C]-3[/C][C]-2.33275771023544[/C][C]-0.667242289764563[/C][/ROW]
[ROW][C]27[/C][C]-3[/C][C]-4.74952975855125[/C][C]1.74952975855125[/C][/ROW]
[ROW][C]28[/C][C]-7[/C][C]-0.357678912625815[/C][C]-6.64232108737419[/C][/ROW]
[ROW][C]29[/C][C]-9[/C][C]-4.2739074614952[/C][C]-4.7260925385048[/C][/ROW]
[ROW][C]30[/C][C]-11[/C][C]-8.06603377218554[/C][C]-2.93396622781446[/C][/ROW]
[ROW][C]31[/C][C]-13[/C][C]-11.6392637129066[/C][C]-1.36073628709338[/C][/ROW]
[ROW][C]32[/C][C]-11[/C][C]-12.6600207712593[/C][C]1.66002077125926[/C][/ROW]
[ROW][C]33[/C][C]-9[/C][C]-11.4831956288785[/C][C]2.48319562887853[/C][/ROW]
[ROW][C]34[/C][C]-17[/C][C]-6.6111218279153[/C][C]-10.3888781720847[/C][/ROW]
[ROW][C]35[/C][C]-22[/C][C]-15.8028414737891[/C][C]-6.19715852621092[/C][/ROW]
[ROW][C]36[/C][C]-25[/C][C]-25.5999744385381[/C][C]0.599974438538055[/C][/ROW]
[ROW][C]37[/C][C]-20[/C][C]-21.2786062732664[/C][C]1.27860627326635[/C][/ROW]
[ROW][C]38[/C][C]-24[/C][C]-17.5892046954795[/C][C]-6.41079530452054[/C][/ROW]
[ROW][C]39[/C][C]-24[/C][C]-23.3785253318144[/C][C]-0.621474668185574[/C][/ROW]
[ROW][C]40[/C][C]-22[/C][C]-22.344472654826[/C][C]0.344472654826045[/C][/ROW]
[ROW][C]41[/C][C]-19[/C][C]-21.1694155307427[/C][C]2.1694155307427[/C][/ROW]
[ROW][C]42[/C][C]-18[/C][C]-19.9549827842106[/C][C]1.95498278421062[/C][/ROW]
[ROW][C]43[/C][C]-17[/C][C]-19.9157193868777[/C][C]2.91571938687772[/C][/ROW]
[ROW][C]44[/C][C]-11[/C][C]-17.4327035025269[/C][C]6.43270350252687[/C][/ROW]
[ROW][C]45[/C][C]-11[/C][C]-12.8746396407322[/C][C]1.87463964073215[/C][/ROW]
[ROW][C]46[/C][C]-12[/C][C]-11.0984183870019[/C][C]-0.901581612998061[/C][/ROW]
[ROW][C]47[/C][C]-10[/C][C]-13.0306212042137[/C][C]3.03062120421375[/C][/ROW]
[ROW][C]48[/C][C]-15[/C][C]-15.1961394275748[/C][C]0.196139427574831[/C][/ROW]
[ROW][C]49[/C][C]-15[/C][C]-11.0004244164532[/C][C]-3.99957558354681[/C][/ROW]
[ROW][C]50[/C][C]-15[/C][C]-12.4635871083448[/C][C]-2.53641289165524[/C][/ROW]
[ROW][C]51[/C][C]-13[/C][C]-14.4345160209854[/C][C]1.43451602098541[/C][/ROW]
[ROW][C]52[/C][C]-8[/C][C]-11.8107002897679[/C][C]3.81070028976789[/C][/ROW]
[ROW][C]53[/C][C]-13[/C][C]-7.9164921345838[/C][C]-5.0835078654162[/C][/ROW]
[ROW][C]54[/C][C]-9[/C][C]-11.6239822769012[/C][C]2.6239822769012[/C][/ROW]
[ROW][C]55[/C][C]-7[/C][C]-10.9305399190067[/C][C]3.93053991900674[/C][/ROW]
[ROW][C]56[/C][C]-4[/C][C]-7.02722805176899[/C][C]3.02722805176899[/C][/ROW]
[ROW][C]57[/C][C]-4[/C][C]-5.70844659994271[/C][C]1.70844659994271[/C][/ROW]
[ROW][C]58[/C][C]-2[/C][C]-4.620248571732[/C][C]2.620248571732[/C][/ROW]
[ROW][C]59[/C][C]0[/C][C]-3.3585804690462[/C][C]3.3585804690462[/C][/ROW]
[ROW][C]60[/C][C]-2[/C][C]-5.8903065096042[/C][C]3.8903065096042[/C][/ROW]
[ROW][C]61[/C][C]-3[/C][C]-0.0780794910445088[/C][C]-2.92192050895549[/C][/ROW]
[ROW][C]62[/C][C]1[/C][C]-0.505037440071479[/C][C]1.50503744007148[/C][/ROW]
[ROW][C]63[/C][C]-2[/C][C]1.07906039549226[/C][C]-3.07906039549226[/C][/ROW]
[ROW][C]64[/C][C]-1[/C][C]1.16684631602017[/C][C]-2.16684631602017[/C][/ROW]
[ROW][C]65[/C][C]1[/C][C]-0.812443056523279[/C][C]1.81244305652328[/C][/ROW]
[ROW][C]66[/C][C]-3[/C][C]1.73374116228469[/C][C]-4.73374116228469[/C][/ROW]
[ROW][C]67[/C][C]-4[/C][C]-2.24817105544584[/C][C]-1.75182894455416[/C][/ROW]
[ROW][C]68[/C][C]-9[/C][C]-2.35576407044059[/C][C]-6.64423592955941[/C][/ROW]
[ROW][C]69[/C][C]-9[/C][C]-7.82247273576299[/C][C]-1.17752726423701[/C][/ROW]
[ROW][C]70[/C][C]-7[/C][C]-8.48964403138129[/C][C]1.48964403138129[/C][/ROW]
[ROW][C]71[/C][C]-14[/C][C]-7.83872020004599[/C][C]-6.16127979995401[/C][/ROW]
[ROW][C]72[/C][C]-12[/C][C]-16.6731146863859[/C][C]4.67311468638589[/C][/ROW]
[ROW][C]73[/C][C]-16[/C][C]-11.7617705703687[/C][C]-4.23822942963125[/C][/ROW]
[ROW][C]74[/C][C]-20[/C][C]-12.1590450487251[/C][C]-7.84095495127493[/C][/ROW]
[ROW][C]75[/C][C]-12[/C][C]-17.8310623617248[/C][C]5.83106236172479[/C][/ROW]
[ROW][C]76[/C][C]-12[/C][C]-11.5650983745286[/C][C]-0.43490162547141[/C][/ROW]
[ROW][C]77[/C][C]-10[/C][C]-11.5563421743738[/C][C]1.55634217437383[/C][/ROW]
[ROW][C]78[/C][C]-10[/C][C]-10.5547697603331[/C][C]0.554769760333111[/C][/ROW]
[ROW][C]79[/C][C]-13[/C][C]-10.3614492461854[/C][C]-2.63855075381461[/C][/ROW]
[ROW][C]80[/C][C]-16[/C][C]-12.0915187359623[/C][C]-3.90848126403771[/C][/ROW]
[ROW][C]81[/C][C]-14[/C][C]-14.5819698337067[/C][C]0.581969833706687[/C][/ROW]
[ROW][C]82[/C][C]-17[/C][C]-13.5129259044651[/C][C]-3.4870740955349[/C][/ROW]
[ROW][C]83[/C][C]-24[/C][C]-17.8120966933916[/C][C]-6.18790330660837[/C][/ROW]
[ROW][C]84[/C][C]-25[/C][C]-24.4110323931857[/C][C]-0.588967606814276[/C][/ROW]
[ROW][C]85[/C][C]-23[/C][C]-24.9066102025974[/C][C]1.90661020259737[/C][/ROW]
[ROW][C]86[/C][C]-17[/C][C]-21.925631706859[/C][C]4.92563170685898[/C][/ROW]
[ROW][C]87[/C][C]-24[/C][C]-16.1566016808587[/C][C]-7.84339831914125[/C][/ROW]
[ROW][C]88[/C][C]-20[/C][C]-20.4048287918198[/C][C]0.404828791819835[/C][/ROW]
[ROW][C]89[/C][C]-19[/C][C]-19.4212959108919[/C][C]0.421295910891939[/C][/ROW]
[ROW][C]90[/C][C]-18[/C][C]-19.3982958116531[/C][C]1.39829581165311[/C][/ROW]
[ROW][C]91[/C][C]-16[/C][C]-19.3088378247089[/C][C]3.3088378247089[/C][/ROW]
[ROW][C]92[/C][C]-12[/C][C]-17.3049989507875[/C][C]5.30499895078745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232228&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232228&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-1-3.315972222222222.31597222222222
1410.3588839660528380.641116033947162
15-1-1.051394498723680.051394498723683
1622.26651194373964-0.26651194373964
1722.74539370010986-0.745393700109863
1811.61008179264361-0.610081792643613
19-1-0.392737784646734-0.607262215353266
20-2-0.768887135355842-1.23111286464416
21-2-1.73196400726557-0.268035992734427
22-11.82793076504975-2.82793076504975
23-8-1.5024983957644-6.4975016042356
24-4-15.179678401998311.1796784019983
25-6-0.182789466243487-5.81721053375651
26-3-2.33275771023544-0.667242289764563
27-3-4.749529758551251.74952975855125
28-7-0.357678912625815-6.64232108737419
29-9-4.2739074614952-4.7260925385048
30-11-8.06603377218554-2.93396622781446
31-13-11.6392637129066-1.36073628709338
32-11-12.66002077125931.66002077125926
33-9-11.48319562887852.48319562887853
34-17-6.6111218279153-10.3888781720847
35-22-15.8028414737891-6.19715852621092
36-25-25.59997443853810.599974438538055
37-20-21.27860627326641.27860627326635
38-24-17.5892046954795-6.41079530452054
39-24-23.3785253318144-0.621474668185574
40-22-22.3444726548260.344472654826045
41-19-21.16941553074272.1694155307427
42-18-19.95498278421061.95498278421062
43-17-19.91571938687772.91571938687772
44-11-17.43270350252696.43270350252687
45-11-12.87463964073221.87463964073215
46-12-11.0984183870019-0.901581612998061
47-10-13.03062120421373.03062120421375
48-15-15.19613942757480.196139427574831
49-15-11.0004244164532-3.99957558354681
50-15-12.4635871083448-2.53641289165524
51-13-14.43451602098541.43451602098541
52-8-11.81070028976793.81070028976789
53-13-7.9164921345838-5.0835078654162
54-9-11.62398227690122.6239822769012
55-7-10.93053991900673.93053991900674
56-4-7.027228051768993.02722805176899
57-4-5.708446599942711.70844659994271
58-2-4.6202485717322.620248571732
590-3.35858046904623.3585804690462
60-2-5.89030650960423.8903065096042
61-3-0.0780794910445088-2.92192050895549
621-0.5050374400714791.50503744007148
63-21.07906039549226-3.07906039549226
64-11.16684631602017-2.16684631602017
651-0.8124430565232791.81244305652328
66-31.73374116228469-4.73374116228469
67-4-2.24817105544584-1.75182894455416
68-9-2.35576407044059-6.64423592955941
69-9-7.82247273576299-1.17752726423701
70-7-8.489644031381291.48964403138129
71-14-7.83872020004599-6.16127979995401
72-12-16.67311468638594.67311468638589
73-16-11.7617705703687-4.23822942963125
74-20-12.1590450487251-7.84095495127493
75-12-17.83106236172485.83106236172479
76-12-11.5650983745286-0.43490162547141
77-10-11.55634217437381.55634217437383
78-10-10.55476976033310.554769760333111
79-13-10.3614492461854-2.63855075381461
80-16-12.0915187359623-3.90848126403771
81-14-14.58196983370670.581969833706687
82-17-13.5129259044651-3.4870740955349
83-24-17.8120966933916-6.18790330660837
84-25-24.4110323931857-0.588967606814276
85-23-24.90661020259741.90661020259737
86-17-21.9256317068594.92563170685898
87-24-16.1566016808587-7.84339831914125
88-20-20.40482879181980.404828791819835
89-19-19.42129591089190.421295910891939
90-18-19.39829581165311.39829581165311
91-16-19.30883782470893.3088378247089
92-12-17.30499895078755.30499895078745







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
93-12.6591298881084-20.1979042478038-5.12035552841304
94-12.8303436325297-21.9186239455532-3.74206331950624
95-15.34503461024-25.7560475241959-4.93402169628412
96-16.6090739077772-28.193985961188-5.02416185436642
97-16.1842719729353-28.8357480575538-3.5327958883168
98-13.8537979956961-27.4897132674061-0.21788272398612
99-14.0607903999903-28.61569396262050.494113162639907
100-11.3070803207642-26.72722818904924.11306754752067
101-10.5886282169451-26.82886925221425.65161281832403
102-10.6416573775057-27.66336820305236.3800534480408
103-11.0915305494995-28.86118467708186.67812357808291
104-10.8960454348288-29.38418622667797.5920953570202

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
93 & -12.6591298881084 & -20.1979042478038 & -5.12035552841304 \tabularnewline
94 & -12.8303436325297 & -21.9186239455532 & -3.74206331950624 \tabularnewline
95 & -15.34503461024 & -25.7560475241959 & -4.93402169628412 \tabularnewline
96 & -16.6090739077772 & -28.193985961188 & -5.02416185436642 \tabularnewline
97 & -16.1842719729353 & -28.8357480575538 & -3.5327958883168 \tabularnewline
98 & -13.8537979956961 & -27.4897132674061 & -0.21788272398612 \tabularnewline
99 & -14.0607903999903 & -28.6156939626205 & 0.494113162639907 \tabularnewline
100 & -11.3070803207642 & -26.7272281890492 & 4.11306754752067 \tabularnewline
101 & -10.5886282169451 & -26.8288692522142 & 5.65161281832403 \tabularnewline
102 & -10.6416573775057 & -27.6633682030523 & 6.3800534480408 \tabularnewline
103 & -11.0915305494995 & -28.8611846770818 & 6.67812357808291 \tabularnewline
104 & -10.8960454348288 & -29.3841862266779 & 7.5920953570202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232228&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]93[/C][C]-12.6591298881084[/C][C]-20.1979042478038[/C][C]-5.12035552841304[/C][/ROW]
[ROW][C]94[/C][C]-12.8303436325297[/C][C]-21.9186239455532[/C][C]-3.74206331950624[/C][/ROW]
[ROW][C]95[/C][C]-15.34503461024[/C][C]-25.7560475241959[/C][C]-4.93402169628412[/C][/ROW]
[ROW][C]96[/C][C]-16.6090739077772[/C][C]-28.193985961188[/C][C]-5.02416185436642[/C][/ROW]
[ROW][C]97[/C][C]-16.1842719729353[/C][C]-28.8357480575538[/C][C]-3.5327958883168[/C][/ROW]
[ROW][C]98[/C][C]-13.8537979956961[/C][C]-27.4897132674061[/C][C]-0.21788272398612[/C][/ROW]
[ROW][C]99[/C][C]-14.0607903999903[/C][C]-28.6156939626205[/C][C]0.494113162639907[/C][/ROW]
[ROW][C]100[/C][C]-11.3070803207642[/C][C]-26.7272281890492[/C][C]4.11306754752067[/C][/ROW]
[ROW][C]101[/C][C]-10.5886282169451[/C][C]-26.8288692522142[/C][C]5.65161281832403[/C][/ROW]
[ROW][C]102[/C][C]-10.6416573775057[/C][C]-27.6633682030523[/C][C]6.3800534480408[/C][/ROW]
[ROW][C]103[/C][C]-11.0915305494995[/C][C]-28.8611846770818[/C][C]6.67812357808291[/C][/ROW]
[ROW][C]104[/C][C]-10.8960454348288[/C][C]-29.3841862266779[/C][C]7.5920953570202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232228&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232228&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
93-12.6591298881084-20.1979042478038-5.12035552841304
94-12.8303436325297-21.9186239455532-3.74206331950624
95-15.34503461024-25.7560475241959-4.93402169628412
96-16.6090739077772-28.193985961188-5.02416185436642
97-16.1842719729353-28.8357480575538-3.5327958883168
98-13.8537979956961-27.4897132674061-0.21788272398612
99-14.0607903999903-28.61569396262050.494113162639907
100-11.3070803207642-26.72722818904924.11306754752067
101-10.5886282169451-26.82886925221425.65161281832403
102-10.6416573775057-27.66336820305236.3800534480408
103-11.0915305494995-28.86118467708186.67812357808291
104-10.8960454348288-29.38418622667797.5920953570202



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=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')