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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Dec 2011 12:43:02 -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/2011/Dec/21/t13244894225dc3sls07mwgn12.htm/, Retrieved Tue, 07 May 2024 08:44:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158909, Retrieved Tue, 07 May 2024 08:44:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords KDGP2W102
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2011-12-21 17:43:02] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
121
117,7
115,4
114,3
109,5
108,1
108,2
99,1
101,2
98,1
95,5
97,9
98,2
98,7
95,6
95,8
94,4
96,5
103,3
104,3
104,5
102,3
103,8
103,1
102,2
106,3
102,1
94
102,6
102,6
106,7
107,9
109,3
105,9
109,1
108,5
111,7
109,8
109,1
108,5
108,5
106,2
117,1
109,8
115,2
115,9
119,2
121
118,6
117,6
114,6
110,6
102,5
101,6
107,4
105,8
102,8
104
100,4
100,6
107,9
106,9
106,5
103
90,5
90,6
94,4
89,4
92,5
94,4
91,7
93,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158909&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158909&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.796318697062541
beta-2.78911008871896e-17
gamma0.367371436777521

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.796318697062541 \tabularnewline
beta & -2.78911008871896e-17 \tabularnewline
gamma & 0.367371436777521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158909&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]0.796318697062541[/C][/ROW]
[ROW][C]beta[/C][C]-2.78911008871896e-17[/C][/ROW]
[ROW][C]gamma[/C][C]0.367371436777521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158909&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
alpha0.796318697062541
beta-2.78911008871896e-17
gamma0.367371436777521







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1398.2106.17658499612-7.97658499611995
1498.799.7219179747456-1.02191797474561
1595.694.87952304236560.720476957634361
1695.894.77347095858391.02652904141605
1794.493.13439301583821.26560698416182
1896.595.11954673127271.38045326872734
19103.3100.7871335521452.51286644785489
20104.395.14888454277699.1511154572231
21104.5105.66605545652-1.16605545652004
22102.3102.553282777383-0.253282777382651
23103.8100.4672815979353.3327184020645
24103.1106.314312900511-3.21431290051127
25102.2103.583915685599-1.38391568559902
26106.3102.9321588481513.36784115184898
27102.1101.4875690552460.612430944754237
2894101.312282065882-7.3122820658818
29102.693.05322171070529.54677828929481
30102.6101.7464948431230.853505156877119
31106.7107.408618567622-0.708618567622409
32107.999.40424090278428.49575909721582
33109.3108.7166894056870.583310594313076
34105.9106.998548764447-1.09854876444717
35109.1104.4623640555594.6376359444412
36108.5111.004768842139-2.5047688421391
37111.7109.0047750555652.69522494443497
38109.8112.070322479174-2.27032247917398
39109.1105.7736272768733.32637272312687
40108.5107.0882681545861.41173184541412
41108.5106.8917932823771.60820671762262
42106.2108.680682086522-2.48068208652209
43117.1111.7956019561465.30439804385381
44109.8108.6901589603141.10984103968623
45115.2111.5946448033733.60535519662668
46115.9112.0732968976423.82670310235848
47119.2113.8189900073285.38100999267223
48121120.6719755805750.328024419425361
49118.6121.421163479054-2.82116347905405
50117.6119.799872802393-2.19987280239262
51114.6113.7192921834050.880707816595248
52110.6112.894208991271-2.29420899127084
53102.5109.741199783456-7.24119978345614
54101.6104.142905832621-2.54290583262053
55107.4107.517392139358-0.117392139358316
56105.8100.3262562804755.47374371952471
57102.8106.759415600285-3.9594156002853
58104101.3983173805652.60168261943527
59100.4102.334972906023-1.93497290602268
60100.6102.568902787315-1.96890278731514
61107.9101.1108715058456.78912849415542
62106.9107.053950474574-0.153950474574259
63106.5103.1596239860673.34037601393297
64103104.143157892151-1.14315789215127
6590.5101.586602195639-11.0866021956387
6690.693.1614988228925-2.56149882289255
6794.496.0464987826765-1.64649878267649
6889.488.76176162679170.638238373208324
6992.590.3367652802062.16323471979403
7094.490.46279730742923.93720269257076
7191.792.2090590546208-0.509059054620749
7293.393.3665695783184-0.0665695783183935

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.2 & 106.17658499612 & -7.97658499611995 \tabularnewline
14 & 98.7 & 99.7219179747456 & -1.02191797474561 \tabularnewline
15 & 95.6 & 94.8795230423656 & 0.720476957634361 \tabularnewline
16 & 95.8 & 94.7734709585839 & 1.02652904141605 \tabularnewline
17 & 94.4 & 93.1343930158382 & 1.26560698416182 \tabularnewline
18 & 96.5 & 95.1195467312727 & 1.38045326872734 \tabularnewline
19 & 103.3 & 100.787133552145 & 2.51286644785489 \tabularnewline
20 & 104.3 & 95.1488845427769 & 9.1511154572231 \tabularnewline
21 & 104.5 & 105.66605545652 & -1.16605545652004 \tabularnewline
22 & 102.3 & 102.553282777383 & -0.253282777382651 \tabularnewline
23 & 103.8 & 100.467281597935 & 3.3327184020645 \tabularnewline
24 & 103.1 & 106.314312900511 & -3.21431290051127 \tabularnewline
25 & 102.2 & 103.583915685599 & -1.38391568559902 \tabularnewline
26 & 106.3 & 102.932158848151 & 3.36784115184898 \tabularnewline
27 & 102.1 & 101.487569055246 & 0.612430944754237 \tabularnewline
28 & 94 & 101.312282065882 & -7.3122820658818 \tabularnewline
29 & 102.6 & 93.0532217107052 & 9.54677828929481 \tabularnewline
30 & 102.6 & 101.746494843123 & 0.853505156877119 \tabularnewline
31 & 106.7 & 107.408618567622 & -0.708618567622409 \tabularnewline
32 & 107.9 & 99.4042409027842 & 8.49575909721582 \tabularnewline
33 & 109.3 & 108.716689405687 & 0.583310594313076 \tabularnewline
34 & 105.9 & 106.998548764447 & -1.09854876444717 \tabularnewline
35 & 109.1 & 104.462364055559 & 4.6376359444412 \tabularnewline
36 & 108.5 & 111.004768842139 & -2.5047688421391 \tabularnewline
37 & 111.7 & 109.004775055565 & 2.69522494443497 \tabularnewline
38 & 109.8 & 112.070322479174 & -2.27032247917398 \tabularnewline
39 & 109.1 & 105.773627276873 & 3.32637272312687 \tabularnewline
40 & 108.5 & 107.088268154586 & 1.41173184541412 \tabularnewline
41 & 108.5 & 106.891793282377 & 1.60820671762262 \tabularnewline
42 & 106.2 & 108.680682086522 & -2.48068208652209 \tabularnewline
43 & 117.1 & 111.795601956146 & 5.30439804385381 \tabularnewline
44 & 109.8 & 108.690158960314 & 1.10984103968623 \tabularnewline
45 & 115.2 & 111.594644803373 & 3.60535519662668 \tabularnewline
46 & 115.9 & 112.073296897642 & 3.82670310235848 \tabularnewline
47 & 119.2 & 113.818990007328 & 5.38100999267223 \tabularnewline
48 & 121 & 120.671975580575 & 0.328024419425361 \tabularnewline
49 & 118.6 & 121.421163479054 & -2.82116347905405 \tabularnewline
50 & 117.6 & 119.799872802393 & -2.19987280239262 \tabularnewline
51 & 114.6 & 113.719292183405 & 0.880707816595248 \tabularnewline
52 & 110.6 & 112.894208991271 & -2.29420899127084 \tabularnewline
53 & 102.5 & 109.741199783456 & -7.24119978345614 \tabularnewline
54 & 101.6 & 104.142905832621 & -2.54290583262053 \tabularnewline
55 & 107.4 & 107.517392139358 & -0.117392139358316 \tabularnewline
56 & 105.8 & 100.326256280475 & 5.47374371952471 \tabularnewline
57 & 102.8 & 106.759415600285 & -3.9594156002853 \tabularnewline
58 & 104 & 101.398317380565 & 2.60168261943527 \tabularnewline
59 & 100.4 & 102.334972906023 & -1.93497290602268 \tabularnewline
60 & 100.6 & 102.568902787315 & -1.96890278731514 \tabularnewline
61 & 107.9 & 101.110871505845 & 6.78912849415542 \tabularnewline
62 & 106.9 & 107.053950474574 & -0.153950474574259 \tabularnewline
63 & 106.5 & 103.159623986067 & 3.34037601393297 \tabularnewline
64 & 103 & 104.143157892151 & -1.14315789215127 \tabularnewline
65 & 90.5 & 101.586602195639 & -11.0866021956387 \tabularnewline
66 & 90.6 & 93.1614988228925 & -2.56149882289255 \tabularnewline
67 & 94.4 & 96.0464987826765 & -1.64649878267649 \tabularnewline
68 & 89.4 & 88.7617616267917 & 0.638238373208324 \tabularnewline
69 & 92.5 & 90.336765280206 & 2.16323471979403 \tabularnewline
70 & 94.4 & 90.4627973074292 & 3.93720269257076 \tabularnewline
71 & 91.7 & 92.2090590546208 & -0.509059054620749 \tabularnewline
72 & 93.3 & 93.3665695783184 & -0.0665695783183935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158909&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]98.2[/C][C]106.17658499612[/C][C]-7.97658499611995[/C][/ROW]
[ROW][C]14[/C][C]98.7[/C][C]99.7219179747456[/C][C]-1.02191797474561[/C][/ROW]
[ROW][C]15[/C][C]95.6[/C][C]94.8795230423656[/C][C]0.720476957634361[/C][/ROW]
[ROW][C]16[/C][C]95.8[/C][C]94.7734709585839[/C][C]1.02652904141605[/C][/ROW]
[ROW][C]17[/C][C]94.4[/C][C]93.1343930158382[/C][C]1.26560698416182[/C][/ROW]
[ROW][C]18[/C][C]96.5[/C][C]95.1195467312727[/C][C]1.38045326872734[/C][/ROW]
[ROW][C]19[/C][C]103.3[/C][C]100.787133552145[/C][C]2.51286644785489[/C][/ROW]
[ROW][C]20[/C][C]104.3[/C][C]95.1488845427769[/C][C]9.1511154572231[/C][/ROW]
[ROW][C]21[/C][C]104.5[/C][C]105.66605545652[/C][C]-1.16605545652004[/C][/ROW]
[ROW][C]22[/C][C]102.3[/C][C]102.553282777383[/C][C]-0.253282777382651[/C][/ROW]
[ROW][C]23[/C][C]103.8[/C][C]100.467281597935[/C][C]3.3327184020645[/C][/ROW]
[ROW][C]24[/C][C]103.1[/C][C]106.314312900511[/C][C]-3.21431290051127[/C][/ROW]
[ROW][C]25[/C][C]102.2[/C][C]103.583915685599[/C][C]-1.38391568559902[/C][/ROW]
[ROW][C]26[/C][C]106.3[/C][C]102.932158848151[/C][C]3.36784115184898[/C][/ROW]
[ROW][C]27[/C][C]102.1[/C][C]101.487569055246[/C][C]0.612430944754237[/C][/ROW]
[ROW][C]28[/C][C]94[/C][C]101.312282065882[/C][C]-7.3122820658818[/C][/ROW]
[ROW][C]29[/C][C]102.6[/C][C]93.0532217107052[/C][C]9.54677828929481[/C][/ROW]
[ROW][C]30[/C][C]102.6[/C][C]101.746494843123[/C][C]0.853505156877119[/C][/ROW]
[ROW][C]31[/C][C]106.7[/C][C]107.408618567622[/C][C]-0.708618567622409[/C][/ROW]
[ROW][C]32[/C][C]107.9[/C][C]99.4042409027842[/C][C]8.49575909721582[/C][/ROW]
[ROW][C]33[/C][C]109.3[/C][C]108.716689405687[/C][C]0.583310594313076[/C][/ROW]
[ROW][C]34[/C][C]105.9[/C][C]106.998548764447[/C][C]-1.09854876444717[/C][/ROW]
[ROW][C]35[/C][C]109.1[/C][C]104.462364055559[/C][C]4.6376359444412[/C][/ROW]
[ROW][C]36[/C][C]108.5[/C][C]111.004768842139[/C][C]-2.5047688421391[/C][/ROW]
[ROW][C]37[/C][C]111.7[/C][C]109.004775055565[/C][C]2.69522494443497[/C][/ROW]
[ROW][C]38[/C][C]109.8[/C][C]112.070322479174[/C][C]-2.27032247917398[/C][/ROW]
[ROW][C]39[/C][C]109.1[/C][C]105.773627276873[/C][C]3.32637272312687[/C][/ROW]
[ROW][C]40[/C][C]108.5[/C][C]107.088268154586[/C][C]1.41173184541412[/C][/ROW]
[ROW][C]41[/C][C]108.5[/C][C]106.891793282377[/C][C]1.60820671762262[/C][/ROW]
[ROW][C]42[/C][C]106.2[/C][C]108.680682086522[/C][C]-2.48068208652209[/C][/ROW]
[ROW][C]43[/C][C]117.1[/C][C]111.795601956146[/C][C]5.30439804385381[/C][/ROW]
[ROW][C]44[/C][C]109.8[/C][C]108.690158960314[/C][C]1.10984103968623[/C][/ROW]
[ROW][C]45[/C][C]115.2[/C][C]111.594644803373[/C][C]3.60535519662668[/C][/ROW]
[ROW][C]46[/C][C]115.9[/C][C]112.073296897642[/C][C]3.82670310235848[/C][/ROW]
[ROW][C]47[/C][C]119.2[/C][C]113.818990007328[/C][C]5.38100999267223[/C][/ROW]
[ROW][C]48[/C][C]121[/C][C]120.671975580575[/C][C]0.328024419425361[/C][/ROW]
[ROW][C]49[/C][C]118.6[/C][C]121.421163479054[/C][C]-2.82116347905405[/C][/ROW]
[ROW][C]50[/C][C]117.6[/C][C]119.799872802393[/C][C]-2.19987280239262[/C][/ROW]
[ROW][C]51[/C][C]114.6[/C][C]113.719292183405[/C][C]0.880707816595248[/C][/ROW]
[ROW][C]52[/C][C]110.6[/C][C]112.894208991271[/C][C]-2.29420899127084[/C][/ROW]
[ROW][C]53[/C][C]102.5[/C][C]109.741199783456[/C][C]-7.24119978345614[/C][/ROW]
[ROW][C]54[/C][C]101.6[/C][C]104.142905832621[/C][C]-2.54290583262053[/C][/ROW]
[ROW][C]55[/C][C]107.4[/C][C]107.517392139358[/C][C]-0.117392139358316[/C][/ROW]
[ROW][C]56[/C][C]105.8[/C][C]100.326256280475[/C][C]5.47374371952471[/C][/ROW]
[ROW][C]57[/C][C]102.8[/C][C]106.759415600285[/C][C]-3.9594156002853[/C][/ROW]
[ROW][C]58[/C][C]104[/C][C]101.398317380565[/C][C]2.60168261943527[/C][/ROW]
[ROW][C]59[/C][C]100.4[/C][C]102.334972906023[/C][C]-1.93497290602268[/C][/ROW]
[ROW][C]60[/C][C]100.6[/C][C]102.568902787315[/C][C]-1.96890278731514[/C][/ROW]
[ROW][C]61[/C][C]107.9[/C][C]101.110871505845[/C][C]6.78912849415542[/C][/ROW]
[ROW][C]62[/C][C]106.9[/C][C]107.053950474574[/C][C]-0.153950474574259[/C][/ROW]
[ROW][C]63[/C][C]106.5[/C][C]103.159623986067[/C][C]3.34037601393297[/C][/ROW]
[ROW][C]64[/C][C]103[/C][C]104.143157892151[/C][C]-1.14315789215127[/C][/ROW]
[ROW][C]65[/C][C]90.5[/C][C]101.586602195639[/C][C]-11.0866021956387[/C][/ROW]
[ROW][C]66[/C][C]90.6[/C][C]93.1614988228925[/C][C]-2.56149882289255[/C][/ROW]
[ROW][C]67[/C][C]94.4[/C][C]96.0464987826765[/C][C]-1.64649878267649[/C][/ROW]
[ROW][C]68[/C][C]89.4[/C][C]88.7617616267917[/C][C]0.638238373208324[/C][/ROW]
[ROW][C]69[/C][C]92.5[/C][C]90.336765280206[/C][C]2.16323471979403[/C][/ROW]
[ROW][C]70[/C][C]94.4[/C][C]90.4627973074292[/C][C]3.93720269257076[/C][/ROW]
[ROW][C]71[/C][C]91.7[/C][C]92.2090590546208[/C][C]-0.509059054620749[/C][/ROW]
[ROW][C]72[/C][C]93.3[/C][C]93.3665695783184[/C][C]-0.0665695783183935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158909&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158909&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
1398.2106.17658499612-7.97658499611995
1498.799.7219179747456-1.02191797474561
1595.694.87952304236560.720476957634361
1695.894.77347095858391.02652904141605
1794.493.13439301583821.26560698416182
1896.595.11954673127271.38045326872734
19103.3100.7871335521452.51286644785489
20104.395.14888454277699.1511154572231
21104.5105.66605545652-1.16605545652004
22102.3102.553282777383-0.253282777382651
23103.8100.4672815979353.3327184020645
24103.1106.314312900511-3.21431290051127
25102.2103.583915685599-1.38391568559902
26106.3102.9321588481513.36784115184898
27102.1101.4875690552460.612430944754237
2894101.312282065882-7.3122820658818
29102.693.05322171070529.54677828929481
30102.6101.7464948431230.853505156877119
31106.7107.408618567622-0.708618567622409
32107.999.40424090278428.49575909721582
33109.3108.7166894056870.583310594313076
34105.9106.998548764447-1.09854876444717
35109.1104.4623640555594.6376359444412
36108.5111.004768842139-2.5047688421391
37111.7109.0047750555652.69522494443497
38109.8112.070322479174-2.27032247917398
39109.1105.7736272768733.32637272312687
40108.5107.0882681545861.41173184541412
41108.5106.8917932823771.60820671762262
42106.2108.680682086522-2.48068208652209
43117.1111.7956019561465.30439804385381
44109.8108.6901589603141.10984103968623
45115.2111.5946448033733.60535519662668
46115.9112.0732968976423.82670310235848
47119.2113.8189900073285.38100999267223
48121120.6719755805750.328024419425361
49118.6121.421163479054-2.82116347905405
50117.6119.799872802393-2.19987280239262
51114.6113.7192921834050.880707816595248
52110.6112.894208991271-2.29420899127084
53102.5109.741199783456-7.24119978345614
54101.6104.142905832621-2.54290583262053
55107.4107.517392139358-0.117392139358316
56105.8100.3262562804755.47374371952471
57102.8106.759415600285-3.9594156002853
58104101.3983173805652.60168261943527
59100.4102.334972906023-1.93497290602268
60100.6102.568902787315-1.96890278731514
61107.9101.1108715058456.78912849415542
62106.9107.053950474574-0.153950474574259
63106.5103.1596239860673.34037601393297
64103104.143157892151-1.14315789215127
6590.5101.586602195639-11.0866021956387
6690.693.1614988228925-2.56149882289255
6794.496.0464987826765-1.64649878267649
6889.488.76176162679170.638238373208324
6992.590.3367652802062.16323471979403
7094.490.46279730742923.93720269257076
7191.792.2090590546208-0.509059054620749
7293.393.3665695783184-0.0665695783183935







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7393.953265098036687.2846012321298100.621928963943
7493.895424586578384.8368028998942102.954046273262
7590.736471981293980.0047417261879101.4682022364
7688.931865422448876.7080504394529101.155680405445
7786.725414316167473.2578305224916100.192998109843
7887.671306097910572.6818712339061102.660740961915
7992.462174935673775.4493348575727109.475015013775
8086.778085279082369.5654800117065103.990690546458
8187.905794368453469.3328422451932106.478746491714
8286.473910268631467.0935280502794105.854292486983
8384.842845955263664.748123300052104.937568610475
8486.274213793478762.8350813737332109.713346213224

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 93.9532650980366 & 87.2846012321298 & 100.621928963943 \tabularnewline
74 & 93.8954245865783 & 84.8368028998942 & 102.954046273262 \tabularnewline
75 & 90.7364719812939 & 80.0047417261879 & 101.4682022364 \tabularnewline
76 & 88.9318654224488 & 76.7080504394529 & 101.155680405445 \tabularnewline
77 & 86.7254143161674 & 73.2578305224916 & 100.192998109843 \tabularnewline
78 & 87.6713060979105 & 72.6818712339061 & 102.660740961915 \tabularnewline
79 & 92.4621749356737 & 75.4493348575727 & 109.475015013775 \tabularnewline
80 & 86.7780852790823 & 69.5654800117065 & 103.990690546458 \tabularnewline
81 & 87.9057943684534 & 69.3328422451932 & 106.478746491714 \tabularnewline
82 & 86.4739102686314 & 67.0935280502794 & 105.854292486983 \tabularnewline
83 & 84.8428459552636 & 64.748123300052 & 104.937568610475 \tabularnewline
84 & 86.2742137934787 & 62.8350813737332 & 109.713346213224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158909&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]73[/C][C]93.9532650980366[/C][C]87.2846012321298[/C][C]100.621928963943[/C][/ROW]
[ROW][C]74[/C][C]93.8954245865783[/C][C]84.8368028998942[/C][C]102.954046273262[/C][/ROW]
[ROW][C]75[/C][C]90.7364719812939[/C][C]80.0047417261879[/C][C]101.4682022364[/C][/ROW]
[ROW][C]76[/C][C]88.9318654224488[/C][C]76.7080504394529[/C][C]101.155680405445[/C][/ROW]
[ROW][C]77[/C][C]86.7254143161674[/C][C]73.2578305224916[/C][C]100.192998109843[/C][/ROW]
[ROW][C]78[/C][C]87.6713060979105[/C][C]72.6818712339061[/C][C]102.660740961915[/C][/ROW]
[ROW][C]79[/C][C]92.4621749356737[/C][C]75.4493348575727[/C][C]109.475015013775[/C][/ROW]
[ROW][C]80[/C][C]86.7780852790823[/C][C]69.5654800117065[/C][C]103.990690546458[/C][/ROW]
[ROW][C]81[/C][C]87.9057943684534[/C][C]69.3328422451932[/C][C]106.478746491714[/C][/ROW]
[ROW][C]82[/C][C]86.4739102686314[/C][C]67.0935280502794[/C][C]105.854292486983[/C][/ROW]
[ROW][C]83[/C][C]84.8428459552636[/C][C]64.748123300052[/C][C]104.937568610475[/C][/ROW]
[ROW][C]84[/C][C]86.2742137934787[/C][C]62.8350813737332[/C][C]109.713346213224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158909&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158909&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
7393.953265098036687.2846012321298100.621928963943
7493.895424586578384.8368028998942102.954046273262
7590.736471981293980.0047417261879101.4682022364
7688.931865422448876.7080504394529101.155680405445
7786.725414316167473.2578305224916100.192998109843
7887.671306097910572.6818712339061102.660740961915
7992.462174935673775.4493348575727109.475015013775
8086.778085279082369.5654800117065103.990690546458
8187.905794368453469.3328422451932106.478746491714
8286.473910268631467.0935280502794105.854292486983
8384.842845955263664.748123300052104.937568610475
8486.274213793478762.8350813737332109.713346213224



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')