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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 11 Aug 2012 09:16:22 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/11/t1344691109i4lw7heai5wbs11.htm/, Retrieved Mon, 06 May 2024 22:17:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169213, Retrieved Mon, 06 May 2024 22:17:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Workshop 5] [2010-12-07 13:27:14] [eb6e95800005ec22b7fd76eead8d8a59]
-    D    [Exponential Smoothing] [Berekening 6] [2012-08-11 13:16:22] [0b94335bf72158573fe52322b9537409] [Current]
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Dataseries X:
-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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169213&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169213&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169213&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.882224374780309
beta0.209594426294991
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.882224374780309 \tabularnewline
beta & 0.209594426294991 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169213&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]0.882224374780309[/C][/ROW]
[ROW][C]beta[/C][C]0.209594426294991[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169213&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169213&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
alpha0.882224374780309
beta0.209594426294991
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-30-3
4-7-0.201401059427534-6.79859894057247
5-9-5.01114294483801-3.98885705516199
6-11-8.07963886462007-2.92036113537993
7-13-10.7454836070626-2.25451639293741
8-11-13.24078496232742.24078496232736
9-9-11.35587988495292.35587988495293
10-17-8.93381113346077-8.06618886653923
11-22-17.1978589014891-4.80214109851087
12-25-23.4702447733061-1.5297552266939
13-20-27.13851805135017.13851805135005
14-24-21.8394508968455-2.16054910315448
15-24-25.14375309631261.14375309631256
16-22-25.32142875598083.3214287559808
17-19-22.96374276320983.96374276320976
18-18-19.30645875091521.30645875091523
19-17-17.75191907659060.75191907659061
20-11-16.54757098083485.54757098083479
21-11-10.0865843505449-0.913415649455137
22-12-9.49453666965908-2.50546333034092
23-10-10.77031575855490.770315758554943
24-15-9.01368413212862-5.98631586787138
25-15-14.3248431646673-0.675156835332714
26-15-15.07521102607360.0752110260736458
27-13-15.14967885103242.14967885103235
28-8-12.99650495940424.99650495940415
29-13-7.40789139128263-5.59210860871737
30-9-12.1948437618523.19484376185202
31-7-8.638976210092651.63897621009265
32-4-6.152670973531562.15267097353156
33-4-2.81512278744498-1.18487721255502
34-2-2.641135792945060.641135792945064
350-0.737643638150280.73764363815028
36-21.38738726744903-3.38738726744903
37-3-0.753144086663685-2.24685591333632
381-2.302935460391033.30293546039103
39-21.65417791328506-3.65417791328506
40-1-1.202135232164530.202135232164531
411-0.618938237263811.61893823726381
42-31.51355365812752-4.51355365812752
43-4-2.5987863749633-1.4012136250367
44-9-4.22444161520079-4.77555838479921
45-9-9.710071265308040.710071265308041
46-7-10.22484593815023.22484593815021
47-14-7.92472105478334-6.07527894521666
48-12-14.9527686801422.95276868014199
49-16-13.4700582094906-2.52994179050943
50-20-17.2921383510239-2.70786164897608
51-12-21.77189256213299.77189256213292
52-12-13.43478948930761.43478948930763
53-10-12.18757602548882.18757602548876
54-10-9.87173275328967-0.128267246710328

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -3 & 0 & -3 \tabularnewline
4 & -7 & -0.201401059427534 & -6.79859894057247 \tabularnewline
5 & -9 & -5.01114294483801 & -3.98885705516199 \tabularnewline
6 & -11 & -8.07963886462007 & -2.92036113537993 \tabularnewline
7 & -13 & -10.7454836070626 & -2.25451639293741 \tabularnewline
8 & -11 & -13.2407849623274 & 2.24078496232736 \tabularnewline
9 & -9 & -11.3558798849529 & 2.35587988495293 \tabularnewline
10 & -17 & -8.93381113346077 & -8.06618886653923 \tabularnewline
11 & -22 & -17.1978589014891 & -4.80214109851087 \tabularnewline
12 & -25 & -23.4702447733061 & -1.5297552266939 \tabularnewline
13 & -20 & -27.1385180513501 & 7.13851805135005 \tabularnewline
14 & -24 & -21.8394508968455 & -2.16054910315448 \tabularnewline
15 & -24 & -25.1437530963126 & 1.14375309631256 \tabularnewline
16 & -22 & -25.3214287559808 & 3.3214287559808 \tabularnewline
17 & -19 & -22.9637427632098 & 3.96374276320976 \tabularnewline
18 & -18 & -19.3064587509152 & 1.30645875091523 \tabularnewline
19 & -17 & -17.7519190765906 & 0.75191907659061 \tabularnewline
20 & -11 & -16.5475709808348 & 5.54757098083479 \tabularnewline
21 & -11 & -10.0865843505449 & -0.913415649455137 \tabularnewline
22 & -12 & -9.49453666965908 & -2.50546333034092 \tabularnewline
23 & -10 & -10.7703157585549 & 0.770315758554943 \tabularnewline
24 & -15 & -9.01368413212862 & -5.98631586787138 \tabularnewline
25 & -15 & -14.3248431646673 & -0.675156835332714 \tabularnewline
26 & -15 & -15.0752110260736 & 0.0752110260736458 \tabularnewline
27 & -13 & -15.1496788510324 & 2.14967885103235 \tabularnewline
28 & -8 & -12.9965049594042 & 4.99650495940415 \tabularnewline
29 & -13 & -7.40789139128263 & -5.59210860871737 \tabularnewline
30 & -9 & -12.194843761852 & 3.19484376185202 \tabularnewline
31 & -7 & -8.63897621009265 & 1.63897621009265 \tabularnewline
32 & -4 & -6.15267097353156 & 2.15267097353156 \tabularnewline
33 & -4 & -2.81512278744498 & -1.18487721255502 \tabularnewline
34 & -2 & -2.64113579294506 & 0.641135792945064 \tabularnewline
35 & 0 & -0.73764363815028 & 0.73764363815028 \tabularnewline
36 & -2 & 1.38738726744903 & -3.38738726744903 \tabularnewline
37 & -3 & -0.753144086663685 & -2.24685591333632 \tabularnewline
38 & 1 & -2.30293546039103 & 3.30293546039103 \tabularnewline
39 & -2 & 1.65417791328506 & -3.65417791328506 \tabularnewline
40 & -1 & -1.20213523216453 & 0.202135232164531 \tabularnewline
41 & 1 & -0.61893823726381 & 1.61893823726381 \tabularnewline
42 & -3 & 1.51355365812752 & -4.51355365812752 \tabularnewline
43 & -4 & -2.5987863749633 & -1.4012136250367 \tabularnewline
44 & -9 & -4.22444161520079 & -4.77555838479921 \tabularnewline
45 & -9 & -9.71007126530804 & 0.710071265308041 \tabularnewline
46 & -7 & -10.2248459381502 & 3.22484593815021 \tabularnewline
47 & -14 & -7.92472105478334 & -6.07527894521666 \tabularnewline
48 & -12 & -14.952768680142 & 2.95276868014199 \tabularnewline
49 & -16 & -13.4700582094906 & -2.52994179050943 \tabularnewline
50 & -20 & -17.2921383510239 & -2.70786164897608 \tabularnewline
51 & -12 & -21.7718925621329 & 9.77189256213292 \tabularnewline
52 & -12 & -13.4347894893076 & 1.43478948930763 \tabularnewline
53 & -10 & -12.1875760254888 & 2.18757602548876 \tabularnewline
54 & -10 & -9.87173275328967 & -0.128267246710328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169213&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]-3[/C][C]0[/C][C]-3[/C][/ROW]
[ROW][C]4[/C][C]-7[/C][C]-0.201401059427534[/C][C]-6.79859894057247[/C][/ROW]
[ROW][C]5[/C][C]-9[/C][C]-5.01114294483801[/C][C]-3.98885705516199[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-8.07963886462007[/C][C]-2.92036113537993[/C][/ROW]
[ROW][C]7[/C][C]-13[/C][C]-10.7454836070626[/C][C]-2.25451639293741[/C][/ROW]
[ROW][C]8[/C][C]-11[/C][C]-13.2407849623274[/C][C]2.24078496232736[/C][/ROW]
[ROW][C]9[/C][C]-9[/C][C]-11.3558798849529[/C][C]2.35587988495293[/C][/ROW]
[ROW][C]10[/C][C]-17[/C][C]-8.93381113346077[/C][C]-8.06618886653923[/C][/ROW]
[ROW][C]11[/C][C]-22[/C][C]-17.1978589014891[/C][C]-4.80214109851087[/C][/ROW]
[ROW][C]12[/C][C]-25[/C][C]-23.4702447733061[/C][C]-1.5297552266939[/C][/ROW]
[ROW][C]13[/C][C]-20[/C][C]-27.1385180513501[/C][C]7.13851805135005[/C][/ROW]
[ROW][C]14[/C][C]-24[/C][C]-21.8394508968455[/C][C]-2.16054910315448[/C][/ROW]
[ROW][C]15[/C][C]-24[/C][C]-25.1437530963126[/C][C]1.14375309631256[/C][/ROW]
[ROW][C]16[/C][C]-22[/C][C]-25.3214287559808[/C][C]3.3214287559808[/C][/ROW]
[ROW][C]17[/C][C]-19[/C][C]-22.9637427632098[/C][C]3.96374276320976[/C][/ROW]
[ROW][C]18[/C][C]-18[/C][C]-19.3064587509152[/C][C]1.30645875091523[/C][/ROW]
[ROW][C]19[/C][C]-17[/C][C]-17.7519190765906[/C][C]0.75191907659061[/C][/ROW]
[ROW][C]20[/C][C]-11[/C][C]-16.5475709808348[/C][C]5.54757098083479[/C][/ROW]
[ROW][C]21[/C][C]-11[/C][C]-10.0865843505449[/C][C]-0.913415649455137[/C][/ROW]
[ROW][C]22[/C][C]-12[/C][C]-9.49453666965908[/C][C]-2.50546333034092[/C][/ROW]
[ROW][C]23[/C][C]-10[/C][C]-10.7703157585549[/C][C]0.770315758554943[/C][/ROW]
[ROW][C]24[/C][C]-15[/C][C]-9.01368413212862[/C][C]-5.98631586787138[/C][/ROW]
[ROW][C]25[/C][C]-15[/C][C]-14.3248431646673[/C][C]-0.675156835332714[/C][/ROW]
[ROW][C]26[/C][C]-15[/C][C]-15.0752110260736[/C][C]0.0752110260736458[/C][/ROW]
[ROW][C]27[/C][C]-13[/C][C]-15.1496788510324[/C][C]2.14967885103235[/C][/ROW]
[ROW][C]28[/C][C]-8[/C][C]-12.9965049594042[/C][C]4.99650495940415[/C][/ROW]
[ROW][C]29[/C][C]-13[/C][C]-7.40789139128263[/C][C]-5.59210860871737[/C][/ROW]
[ROW][C]30[/C][C]-9[/C][C]-12.194843761852[/C][C]3.19484376185202[/C][/ROW]
[ROW][C]31[/C][C]-7[/C][C]-8.63897621009265[/C][C]1.63897621009265[/C][/ROW]
[ROW][C]32[/C][C]-4[/C][C]-6.15267097353156[/C][C]2.15267097353156[/C][/ROW]
[ROW][C]33[/C][C]-4[/C][C]-2.81512278744498[/C][C]-1.18487721255502[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C]-2.64113579294506[/C][C]0.641135792945064[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]-0.73764363815028[/C][C]0.73764363815028[/C][/ROW]
[ROW][C]36[/C][C]-2[/C][C]1.38738726744903[/C][C]-3.38738726744903[/C][/ROW]
[ROW][C]37[/C][C]-3[/C][C]-0.753144086663685[/C][C]-2.24685591333632[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]-2.30293546039103[/C][C]3.30293546039103[/C][/ROW]
[ROW][C]39[/C][C]-2[/C][C]1.65417791328506[/C][C]-3.65417791328506[/C][/ROW]
[ROW][C]40[/C][C]-1[/C][C]-1.20213523216453[/C][C]0.202135232164531[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]-0.61893823726381[/C][C]1.61893823726381[/C][/ROW]
[ROW][C]42[/C][C]-3[/C][C]1.51355365812752[/C][C]-4.51355365812752[/C][/ROW]
[ROW][C]43[/C][C]-4[/C][C]-2.5987863749633[/C][C]-1.4012136250367[/C][/ROW]
[ROW][C]44[/C][C]-9[/C][C]-4.22444161520079[/C][C]-4.77555838479921[/C][/ROW]
[ROW][C]45[/C][C]-9[/C][C]-9.71007126530804[/C][C]0.710071265308041[/C][/ROW]
[ROW][C]46[/C][C]-7[/C][C]-10.2248459381502[/C][C]3.22484593815021[/C][/ROW]
[ROW][C]47[/C][C]-14[/C][C]-7.92472105478334[/C][C]-6.07527894521666[/C][/ROW]
[ROW][C]48[/C][C]-12[/C][C]-14.952768680142[/C][C]2.95276868014199[/C][/ROW]
[ROW][C]49[/C][C]-16[/C][C]-13.4700582094906[/C][C]-2.52994179050943[/C][/ROW]
[ROW][C]50[/C][C]-20[/C][C]-17.2921383510239[/C][C]-2.70786164897608[/C][/ROW]
[ROW][C]51[/C][C]-12[/C][C]-21.7718925621329[/C][C]9.77189256213292[/C][/ROW]
[ROW][C]52[/C][C]-12[/C][C]-13.4347894893076[/C][C]1.43478948930763[/C][/ROW]
[ROW][C]53[/C][C]-10[/C][C]-12.1875760254888[/C][C]2.18757602548876[/C][/ROW]
[ROW][C]54[/C][C]-10[/C][C]-9.87173275328967[/C][C]-0.128267246710328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169213&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169213&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
3-30-3
4-7-0.201401059427534-6.79859894057247
5-9-5.01114294483801-3.98885705516199
6-11-8.07963886462007-2.92036113537993
7-13-10.7454836070626-2.25451639293741
8-11-13.24078496232742.24078496232736
9-9-11.35587988495292.35587988495293
10-17-8.93381113346077-8.06618886653923
11-22-17.1978589014891-4.80214109851087
12-25-23.4702447733061-1.5297552266939
13-20-27.13851805135017.13851805135005
14-24-21.8394508968455-2.16054910315448
15-24-25.14375309631261.14375309631256
16-22-25.32142875598083.3214287559808
17-19-22.96374276320983.96374276320976
18-18-19.30645875091521.30645875091523
19-17-17.75191907659060.75191907659061
20-11-16.54757098083485.54757098083479
21-11-10.0865843505449-0.913415649455137
22-12-9.49453666965908-2.50546333034092
23-10-10.77031575855490.770315758554943
24-15-9.01368413212862-5.98631586787138
25-15-14.3248431646673-0.675156835332714
26-15-15.07521102607360.0752110260736458
27-13-15.14967885103242.14967885103235
28-8-12.99650495940424.99650495940415
29-13-7.40789139128263-5.59210860871737
30-9-12.1948437618523.19484376185202
31-7-8.638976210092651.63897621009265
32-4-6.152670973531562.15267097353156
33-4-2.81512278744498-1.18487721255502
34-2-2.641135792945060.641135792945064
350-0.737643638150280.73764363815028
36-21.38738726744903-3.38738726744903
37-3-0.753144086663685-2.24685591333632
381-2.302935460391033.30293546039103
39-21.65417791328506-3.65417791328506
40-1-1.202135232164530.202135232164531
411-0.618938237263811.61893823726381
42-31.51355365812752-4.51355365812752
43-4-2.5987863749633-1.4012136250367
44-9-4.22444161520079-4.77555838479921
45-9-9.710071265308040.710071265308041
46-7-10.22484593815023.22484593815021
47-14-7.92472105478334-6.07527894521666
48-12-14.9527686801422.95276868014199
49-16-13.4700582094906-2.52994179050943
50-20-17.2921383510239-2.70786164897608
51-12-21.77189256213299.77189256213292
52-12-13.43478948930761.43478948930763
53-10-12.18757602548882.18757602548876
54-10-9.87173275328967-0.128267246710328







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
55-9.6227006722979-16.8033347286816-2.44206661591423
56-9.26050809977231-19.7618614876691.24084528812437
57-8.89831552724673-22.72245530550054.925824251007
58-8.53612295472114-25.78641814010098.71417223065866
59-8.17393038219556-28.987432700090712.6395719356996
60-7.81173780966997-32.337649627765216.7141740084252
61-7.44954523714439-35.840635827962120.9415453536734
62-7.08735266461881-39.496129680352625.321424351115
63-6.72516009209322-43.302074728308929.8517545441225
64-6.36296751956764-47.255577127194734.5296420880594
65-6.00077494704205-51.35338525718139.3518353630969
66-5.63858237451647-55.592139146852744.3149743978198

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
55 & -9.6227006722979 & -16.8033347286816 & -2.44206661591423 \tabularnewline
56 & -9.26050809977231 & -19.761861487669 & 1.24084528812437 \tabularnewline
57 & -8.89831552724673 & -22.7224553055005 & 4.925824251007 \tabularnewline
58 & -8.53612295472114 & -25.7864181401009 & 8.71417223065866 \tabularnewline
59 & -8.17393038219556 & -28.9874327000907 & 12.6395719356996 \tabularnewline
60 & -7.81173780966997 & -32.3376496277652 & 16.7141740084252 \tabularnewline
61 & -7.44954523714439 & -35.8406358279621 & 20.9415453536734 \tabularnewline
62 & -7.08735266461881 & -39.4961296803526 & 25.321424351115 \tabularnewline
63 & -6.72516009209322 & -43.3020747283089 & 29.8517545441225 \tabularnewline
64 & -6.36296751956764 & -47.2555771271947 & 34.5296420880594 \tabularnewline
65 & -6.00077494704205 & -51.353385257181 & 39.3518353630969 \tabularnewline
66 & -5.63858237451647 & -55.5921391468527 & 44.3149743978198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169213&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]55[/C][C]-9.6227006722979[/C][C]-16.8033347286816[/C][C]-2.44206661591423[/C][/ROW]
[ROW][C]56[/C][C]-9.26050809977231[/C][C]-19.761861487669[/C][C]1.24084528812437[/C][/ROW]
[ROW][C]57[/C][C]-8.89831552724673[/C][C]-22.7224553055005[/C][C]4.925824251007[/C][/ROW]
[ROW][C]58[/C][C]-8.53612295472114[/C][C]-25.7864181401009[/C][C]8.71417223065866[/C][/ROW]
[ROW][C]59[/C][C]-8.17393038219556[/C][C]-28.9874327000907[/C][C]12.6395719356996[/C][/ROW]
[ROW][C]60[/C][C]-7.81173780966997[/C][C]-32.3376496277652[/C][C]16.7141740084252[/C][/ROW]
[ROW][C]61[/C][C]-7.44954523714439[/C][C]-35.8406358279621[/C][C]20.9415453536734[/C][/ROW]
[ROW][C]62[/C][C]-7.08735266461881[/C][C]-39.4961296803526[/C][C]25.321424351115[/C][/ROW]
[ROW][C]63[/C][C]-6.72516009209322[/C][C]-43.3020747283089[/C][C]29.8517545441225[/C][/ROW]
[ROW][C]64[/C][C]-6.36296751956764[/C][C]-47.2555771271947[/C][C]34.5296420880594[/C][/ROW]
[ROW][C]65[/C][C]-6.00077494704205[/C][C]-51.353385257181[/C][C]39.3518353630969[/C][/ROW]
[ROW][C]66[/C][C]-5.63858237451647[/C][C]-55.5921391468527[/C][C]44.3149743978198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169213&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169213&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
55-9.6227006722979-16.8033347286816-2.44206661591423
56-9.26050809977231-19.7618614876691.24084528812437
57-8.89831552724673-22.72245530550054.925824251007
58-8.53612295472114-25.78641814010098.71417223065866
59-8.17393038219556-28.987432700090712.6395719356996
60-7.81173780966997-32.337649627765216.7141740084252
61-7.44954523714439-35.840635827962120.9415453536734
62-7.08735266461881-39.496129680352625.321424351115
63-6.72516009209322-43.302074728308929.8517545441225
64-6.36296751956764-47.255577127194734.5296420880594
65-6.00077494704205-51.35338525718139.3518353630969
66-5.63858237451647-55.592139146852744.3149743978198



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')