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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 computationFri, 04 Dec 2009 03:24:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259922348gc6apgi5uewb3bu.htm/, Retrieved Sun, 28 Apr 2024 12:20:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63246, Retrieved Sun, 28 Apr 2024 12:20:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW WS 9 Exponential Smoothing
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [WS 9 Exponential ...] [2009-12-04 10:24:57] [a45cc820faa25ce30779915639528ec2] [Current]
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Dataseries X:
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5
22.2
20.9
22.2
23.5
21.5
24.3
22.8
20.3
23.7
23.3
19.6
18
17.3
16.8
18.2
16.5
16
18.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63246&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63246&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63246&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.317087774037496
beta1
gamma0.738379041593874

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.317087774037496 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.738379041593874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63246&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]0.317087774037496[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.738379041593874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63246&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63246&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
alpha0.317087774037496
beta1
gamma0.738379041593874







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1317.516.4131767360861.08682326391400
1414.514.17716765055870.322832349441292
1514.414.5732869780867-0.173286978086702
1616.617.1319032562038-0.531903256203826
1716.717.3034566455206-0.603456645520573
1816.617.0118877403367-0.411887740336734
1916.916.89213267254770.00786732745228846
2015.715.9393910683414-0.239391068341405
2116.416.10773955752550.292260442474461
2218.418.9064054728083-0.506405472808321
2316.916.55019835966900.349801640331023
2416.515.33810300697771.16189699302232
2518.320.0935234065092-1.79352340650924
2615.115.6275565387011-0.527556538701084
2715.714.72926527132380.970734728676204
2818.117.11842151698620.981578483013802
2916.817.7762601846023-0.976260184602303
3018.917.38212078696921.51787921303081
311918.64310695534360.356893044656434
3218.118.1646179990937-0.0646179990937306
3317.819.4299709565994-1.62997095659941
3421.521.6566019190386-0.1566019190386
3517.119.7409316726321-2.64093167263206
3618.717.13477005926161.56522994073841
371919.997718610579-0.997718610578982
3816.415.84337525349740.5566247465026
3916.915.99376438961810.906235610381929
4018.618.36007926035010.239920739649932
4119.317.43724569787551.86275430212455
4219.419.8534457152028-0.4534457152028
4317.619.8426632968719-2.24266329687188
4418.617.51528445873791.08471554126212
4518.117.90600163418340.193998365816643
4620.421.5809089377904-1.18090893779042
4718.117.92891912762840.171080872371633
4819.619.06399568228590.536004317714077
4919.920.7616097208104-0.861609720810378
5019.217.63426143142991.56573856857007
5117.819.0380416453745-1.23804164537448
5219.220.6175198079932-1.41751980799319
532219.44412852581052.55587147418955
5421.120.60963151754940.490368482450613
5519.519.8658549968483-0.36585499684827
5622.220.38003440053801.81996559946203
5720.921.2286391355478-0.328639135547832
5822.225.1539248642576-2.95392486425764
5923.521.26924129520222.23075870479783
6021.524.3108188211452-2.81081882114518
6124.324.09101077142390.208989228576133
6222.822.23955056811610.56044943188391
6320.321.4533952185358-1.15339521853578
6423.722.97973689673950.720263103260521
6523.325.1663445591757-1.86634455917566
6619.622.7398461236589-3.13984612365891
671818.3892614822285-0.389261482228502
6817.317.7901178246006-0.490117824600606
6916.814.53478671872202.26521328127796
7018.215.47122052203592.72877947796406
7116.515.87035218245090.629647817549079
721615.39282872042860.607171279571432
7318.417.45025339917520.949746600824781

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 17.5 & 16.413176736086 & 1.08682326391400 \tabularnewline
14 & 14.5 & 14.1771676505587 & 0.322832349441292 \tabularnewline
15 & 14.4 & 14.5732869780867 & -0.173286978086702 \tabularnewline
16 & 16.6 & 17.1319032562038 & -0.531903256203826 \tabularnewline
17 & 16.7 & 17.3034566455206 & -0.603456645520573 \tabularnewline
18 & 16.6 & 17.0118877403367 & -0.411887740336734 \tabularnewline
19 & 16.9 & 16.8921326725477 & 0.00786732745228846 \tabularnewline
20 & 15.7 & 15.9393910683414 & -0.239391068341405 \tabularnewline
21 & 16.4 & 16.1077395575255 & 0.292260442474461 \tabularnewline
22 & 18.4 & 18.9064054728083 & -0.506405472808321 \tabularnewline
23 & 16.9 & 16.5501983596690 & 0.349801640331023 \tabularnewline
24 & 16.5 & 15.3381030069777 & 1.16189699302232 \tabularnewline
25 & 18.3 & 20.0935234065092 & -1.79352340650924 \tabularnewline
26 & 15.1 & 15.6275565387011 & -0.527556538701084 \tabularnewline
27 & 15.7 & 14.7292652713238 & 0.970734728676204 \tabularnewline
28 & 18.1 & 17.1184215169862 & 0.981578483013802 \tabularnewline
29 & 16.8 & 17.7762601846023 & -0.976260184602303 \tabularnewline
30 & 18.9 & 17.3821207869692 & 1.51787921303081 \tabularnewline
31 & 19 & 18.6431069553436 & 0.356893044656434 \tabularnewline
32 & 18.1 & 18.1646179990937 & -0.0646179990937306 \tabularnewline
33 & 17.8 & 19.4299709565994 & -1.62997095659941 \tabularnewline
34 & 21.5 & 21.6566019190386 & -0.1566019190386 \tabularnewline
35 & 17.1 & 19.7409316726321 & -2.64093167263206 \tabularnewline
36 & 18.7 & 17.1347700592616 & 1.56522994073841 \tabularnewline
37 & 19 & 19.997718610579 & -0.997718610578982 \tabularnewline
38 & 16.4 & 15.8433752534974 & 0.5566247465026 \tabularnewline
39 & 16.9 & 15.9937643896181 & 0.906235610381929 \tabularnewline
40 & 18.6 & 18.3600792603501 & 0.239920739649932 \tabularnewline
41 & 19.3 & 17.4372456978755 & 1.86275430212455 \tabularnewline
42 & 19.4 & 19.8534457152028 & -0.4534457152028 \tabularnewline
43 & 17.6 & 19.8426632968719 & -2.24266329687188 \tabularnewline
44 & 18.6 & 17.5152844587379 & 1.08471554126212 \tabularnewline
45 & 18.1 & 17.9060016341834 & 0.193998365816643 \tabularnewline
46 & 20.4 & 21.5809089377904 & -1.18090893779042 \tabularnewline
47 & 18.1 & 17.9289191276284 & 0.171080872371633 \tabularnewline
48 & 19.6 & 19.0639956822859 & 0.536004317714077 \tabularnewline
49 & 19.9 & 20.7616097208104 & -0.861609720810378 \tabularnewline
50 & 19.2 & 17.6342614314299 & 1.56573856857007 \tabularnewline
51 & 17.8 & 19.0380416453745 & -1.23804164537448 \tabularnewline
52 & 19.2 & 20.6175198079932 & -1.41751980799319 \tabularnewline
53 & 22 & 19.4441285258105 & 2.55587147418955 \tabularnewline
54 & 21.1 & 20.6096315175494 & 0.490368482450613 \tabularnewline
55 & 19.5 & 19.8658549968483 & -0.36585499684827 \tabularnewline
56 & 22.2 & 20.3800344005380 & 1.81996559946203 \tabularnewline
57 & 20.9 & 21.2286391355478 & -0.328639135547832 \tabularnewline
58 & 22.2 & 25.1539248642576 & -2.95392486425764 \tabularnewline
59 & 23.5 & 21.2692412952022 & 2.23075870479783 \tabularnewline
60 & 21.5 & 24.3108188211452 & -2.81081882114518 \tabularnewline
61 & 24.3 & 24.0910107714239 & 0.208989228576133 \tabularnewline
62 & 22.8 & 22.2395505681161 & 0.56044943188391 \tabularnewline
63 & 20.3 & 21.4533952185358 & -1.15339521853578 \tabularnewline
64 & 23.7 & 22.9797368967395 & 0.720263103260521 \tabularnewline
65 & 23.3 & 25.1663445591757 & -1.86634455917566 \tabularnewline
66 & 19.6 & 22.7398461236589 & -3.13984612365891 \tabularnewline
67 & 18 & 18.3892614822285 & -0.389261482228502 \tabularnewline
68 & 17.3 & 17.7901178246006 & -0.490117824600606 \tabularnewline
69 & 16.8 & 14.5347867187220 & 2.26521328127796 \tabularnewline
70 & 18.2 & 15.4712205220359 & 2.72877947796406 \tabularnewline
71 & 16.5 & 15.8703521824509 & 0.629647817549079 \tabularnewline
72 & 16 & 15.3928287204286 & 0.607171279571432 \tabularnewline
73 & 18.4 & 17.4502533991752 & 0.949746600824781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63246&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]17.5[/C][C]16.413176736086[/C][C]1.08682326391400[/C][/ROW]
[ROW][C]14[/C][C]14.5[/C][C]14.1771676505587[/C][C]0.322832349441292[/C][/ROW]
[ROW][C]15[/C][C]14.4[/C][C]14.5732869780867[/C][C]-0.173286978086702[/C][/ROW]
[ROW][C]16[/C][C]16.6[/C][C]17.1319032562038[/C][C]-0.531903256203826[/C][/ROW]
[ROW][C]17[/C][C]16.7[/C][C]17.3034566455206[/C][C]-0.603456645520573[/C][/ROW]
[ROW][C]18[/C][C]16.6[/C][C]17.0118877403367[/C][C]-0.411887740336734[/C][/ROW]
[ROW][C]19[/C][C]16.9[/C][C]16.8921326725477[/C][C]0.00786732745228846[/C][/ROW]
[ROW][C]20[/C][C]15.7[/C][C]15.9393910683414[/C][C]-0.239391068341405[/C][/ROW]
[ROW][C]21[/C][C]16.4[/C][C]16.1077395575255[/C][C]0.292260442474461[/C][/ROW]
[ROW][C]22[/C][C]18.4[/C][C]18.9064054728083[/C][C]-0.506405472808321[/C][/ROW]
[ROW][C]23[/C][C]16.9[/C][C]16.5501983596690[/C][C]0.349801640331023[/C][/ROW]
[ROW][C]24[/C][C]16.5[/C][C]15.3381030069777[/C][C]1.16189699302232[/C][/ROW]
[ROW][C]25[/C][C]18.3[/C][C]20.0935234065092[/C][C]-1.79352340650924[/C][/ROW]
[ROW][C]26[/C][C]15.1[/C][C]15.6275565387011[/C][C]-0.527556538701084[/C][/ROW]
[ROW][C]27[/C][C]15.7[/C][C]14.7292652713238[/C][C]0.970734728676204[/C][/ROW]
[ROW][C]28[/C][C]18.1[/C][C]17.1184215169862[/C][C]0.981578483013802[/C][/ROW]
[ROW][C]29[/C][C]16.8[/C][C]17.7762601846023[/C][C]-0.976260184602303[/C][/ROW]
[ROW][C]30[/C][C]18.9[/C][C]17.3821207869692[/C][C]1.51787921303081[/C][/ROW]
[ROW][C]31[/C][C]19[/C][C]18.6431069553436[/C][C]0.356893044656434[/C][/ROW]
[ROW][C]32[/C][C]18.1[/C][C]18.1646179990937[/C][C]-0.0646179990937306[/C][/ROW]
[ROW][C]33[/C][C]17.8[/C][C]19.4299709565994[/C][C]-1.62997095659941[/C][/ROW]
[ROW][C]34[/C][C]21.5[/C][C]21.6566019190386[/C][C]-0.1566019190386[/C][/ROW]
[ROW][C]35[/C][C]17.1[/C][C]19.7409316726321[/C][C]-2.64093167263206[/C][/ROW]
[ROW][C]36[/C][C]18.7[/C][C]17.1347700592616[/C][C]1.56522994073841[/C][/ROW]
[ROW][C]37[/C][C]19[/C][C]19.997718610579[/C][C]-0.997718610578982[/C][/ROW]
[ROW][C]38[/C][C]16.4[/C][C]15.8433752534974[/C][C]0.5566247465026[/C][/ROW]
[ROW][C]39[/C][C]16.9[/C][C]15.9937643896181[/C][C]0.906235610381929[/C][/ROW]
[ROW][C]40[/C][C]18.6[/C][C]18.3600792603501[/C][C]0.239920739649932[/C][/ROW]
[ROW][C]41[/C][C]19.3[/C][C]17.4372456978755[/C][C]1.86275430212455[/C][/ROW]
[ROW][C]42[/C][C]19.4[/C][C]19.8534457152028[/C][C]-0.4534457152028[/C][/ROW]
[ROW][C]43[/C][C]17.6[/C][C]19.8426632968719[/C][C]-2.24266329687188[/C][/ROW]
[ROW][C]44[/C][C]18.6[/C][C]17.5152844587379[/C][C]1.08471554126212[/C][/ROW]
[ROW][C]45[/C][C]18.1[/C][C]17.9060016341834[/C][C]0.193998365816643[/C][/ROW]
[ROW][C]46[/C][C]20.4[/C][C]21.5809089377904[/C][C]-1.18090893779042[/C][/ROW]
[ROW][C]47[/C][C]18.1[/C][C]17.9289191276284[/C][C]0.171080872371633[/C][/ROW]
[ROW][C]48[/C][C]19.6[/C][C]19.0639956822859[/C][C]0.536004317714077[/C][/ROW]
[ROW][C]49[/C][C]19.9[/C][C]20.7616097208104[/C][C]-0.861609720810378[/C][/ROW]
[ROW][C]50[/C][C]19.2[/C][C]17.6342614314299[/C][C]1.56573856857007[/C][/ROW]
[ROW][C]51[/C][C]17.8[/C][C]19.0380416453745[/C][C]-1.23804164537448[/C][/ROW]
[ROW][C]52[/C][C]19.2[/C][C]20.6175198079932[/C][C]-1.41751980799319[/C][/ROW]
[ROW][C]53[/C][C]22[/C][C]19.4441285258105[/C][C]2.55587147418955[/C][/ROW]
[ROW][C]54[/C][C]21.1[/C][C]20.6096315175494[/C][C]0.490368482450613[/C][/ROW]
[ROW][C]55[/C][C]19.5[/C][C]19.8658549968483[/C][C]-0.36585499684827[/C][/ROW]
[ROW][C]56[/C][C]22.2[/C][C]20.3800344005380[/C][C]1.81996559946203[/C][/ROW]
[ROW][C]57[/C][C]20.9[/C][C]21.2286391355478[/C][C]-0.328639135547832[/C][/ROW]
[ROW][C]58[/C][C]22.2[/C][C]25.1539248642576[/C][C]-2.95392486425764[/C][/ROW]
[ROW][C]59[/C][C]23.5[/C][C]21.2692412952022[/C][C]2.23075870479783[/C][/ROW]
[ROW][C]60[/C][C]21.5[/C][C]24.3108188211452[/C][C]-2.81081882114518[/C][/ROW]
[ROW][C]61[/C][C]24.3[/C][C]24.0910107714239[/C][C]0.208989228576133[/C][/ROW]
[ROW][C]62[/C][C]22.8[/C][C]22.2395505681161[/C][C]0.56044943188391[/C][/ROW]
[ROW][C]63[/C][C]20.3[/C][C]21.4533952185358[/C][C]-1.15339521853578[/C][/ROW]
[ROW][C]64[/C][C]23.7[/C][C]22.9797368967395[/C][C]0.720263103260521[/C][/ROW]
[ROW][C]65[/C][C]23.3[/C][C]25.1663445591757[/C][C]-1.86634455917566[/C][/ROW]
[ROW][C]66[/C][C]19.6[/C][C]22.7398461236589[/C][C]-3.13984612365891[/C][/ROW]
[ROW][C]67[/C][C]18[/C][C]18.3892614822285[/C][C]-0.389261482228502[/C][/ROW]
[ROW][C]68[/C][C]17.3[/C][C]17.7901178246006[/C][C]-0.490117824600606[/C][/ROW]
[ROW][C]69[/C][C]16.8[/C][C]14.5347867187220[/C][C]2.26521328127796[/C][/ROW]
[ROW][C]70[/C][C]18.2[/C][C]15.4712205220359[/C][C]2.72877947796406[/C][/ROW]
[ROW][C]71[/C][C]16.5[/C][C]15.8703521824509[/C][C]0.629647817549079[/C][/ROW]
[ROW][C]72[/C][C]16[/C][C]15.3928287204286[/C][C]0.607171279571432[/C][/ROW]
[ROW][C]73[/C][C]18.4[/C][C]17.4502533991752[/C][C]0.949746600824781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63246&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63246&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
1317.516.4131767360861.08682326391400
1414.514.17716765055870.322832349441292
1514.414.5732869780867-0.173286978086702
1616.617.1319032562038-0.531903256203826
1716.717.3034566455206-0.603456645520573
1816.617.0118877403367-0.411887740336734
1916.916.89213267254770.00786732745228846
2015.715.9393910683414-0.239391068341405
2116.416.10773955752550.292260442474461
2218.418.9064054728083-0.506405472808321
2316.916.55019835966900.349801640331023
2416.515.33810300697771.16189699302232
2518.320.0935234065092-1.79352340650924
2615.115.6275565387011-0.527556538701084
2715.714.72926527132380.970734728676204
2818.117.11842151698620.981578483013802
2916.817.7762601846023-0.976260184602303
3018.917.38212078696921.51787921303081
311918.64310695534360.356893044656434
3218.118.1646179990937-0.0646179990937306
3317.819.4299709565994-1.62997095659941
3421.521.6566019190386-0.1566019190386
3517.119.7409316726321-2.64093167263206
3618.717.13477005926161.56522994073841
371919.997718610579-0.997718610578982
3816.415.84337525349740.5566247465026
3916.915.99376438961810.906235610381929
4018.618.36007926035010.239920739649932
4119.317.43724569787551.86275430212455
4219.419.8534457152028-0.4534457152028
4317.619.8426632968719-2.24266329687188
4418.617.51528445873791.08471554126212
4518.117.90600163418340.193998365816643
4620.421.5809089377904-1.18090893779042
4718.117.92891912762840.171080872371633
4819.619.06399568228590.536004317714077
4919.920.7616097208104-0.861609720810378
5019.217.63426143142991.56573856857007
5117.819.0380416453745-1.23804164537448
5219.220.6175198079932-1.41751980799319
532219.44412852581052.55587147418955
5421.120.60963151754940.490368482450613
5519.519.8658549968483-0.36585499684827
5622.220.38003440053801.81996559946203
5720.921.2286391355478-0.328639135547832
5822.225.1539248642576-2.95392486425764
5923.521.26924129520222.23075870479783
6021.524.3108188211452-2.81081882114518
6124.324.09101077142390.208989228576133
6222.822.23955056811610.56044943188391
6320.321.4533952185358-1.15339521853578
6423.722.97973689673950.720263103260521
6523.325.1663445591757-1.86634455917566
6619.622.7398461236589-3.13984612365891
671818.3892614822285-0.389261482228502
6817.317.7901178246006-0.490117824600606
6916.814.53478671872202.26521328127796
7018.215.47122052203592.72877947796406
7116.515.87035218245090.629647817549079
721615.39282872042860.607171279571432
7318.417.45025339917520.949746600824781







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7417.002654275103514.847326199248019.1579823509590
7515.984195272769313.346629158550918.6217613869878
7618.919972742985915.020391363901722.8195541220702
7719.989395623153614.580289739605425.3985015067018
7818.790426079938212.273871621838625.3069805380379
7918.771108980354010.773792730427926.7684252302802
8020.449214093014310.071831471403030.8265967146256
8121.01694780898568.5490792629856633.4848163549855
8223.51890468689447.5290359298394239.5087734439493
8322.24967257464685.1257347368564139.3736104124371
8421.77812443227913.0534130236363540.5028358409219
8524.78105184009230.90673692561476248.6553667545698

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 17.0026542751035 & 14.8473261992480 & 19.1579823509590 \tabularnewline
75 & 15.9841952727693 & 13.3466291585509 & 18.6217613869878 \tabularnewline
76 & 18.9199727429859 & 15.0203913639017 & 22.8195541220702 \tabularnewline
77 & 19.9893956231536 & 14.5802897396054 & 25.3985015067018 \tabularnewline
78 & 18.7904260799382 & 12.2738716218386 & 25.3069805380379 \tabularnewline
79 & 18.7711089803540 & 10.7737927304279 & 26.7684252302802 \tabularnewline
80 & 20.4492140930143 & 10.0718314714030 & 30.8265967146256 \tabularnewline
81 & 21.0169478089856 & 8.54907926298566 & 33.4848163549855 \tabularnewline
82 & 23.5189046868944 & 7.52903592983942 & 39.5087734439493 \tabularnewline
83 & 22.2496725746468 & 5.12573473685641 & 39.3736104124371 \tabularnewline
84 & 21.7781244322791 & 3.05341302363635 & 40.5028358409219 \tabularnewline
85 & 24.7810518400923 & 0.906736925614762 & 48.6553667545698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63246&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]74[/C][C]17.0026542751035[/C][C]14.8473261992480[/C][C]19.1579823509590[/C][/ROW]
[ROW][C]75[/C][C]15.9841952727693[/C][C]13.3466291585509[/C][C]18.6217613869878[/C][/ROW]
[ROW][C]76[/C][C]18.9199727429859[/C][C]15.0203913639017[/C][C]22.8195541220702[/C][/ROW]
[ROW][C]77[/C][C]19.9893956231536[/C][C]14.5802897396054[/C][C]25.3985015067018[/C][/ROW]
[ROW][C]78[/C][C]18.7904260799382[/C][C]12.2738716218386[/C][C]25.3069805380379[/C][/ROW]
[ROW][C]79[/C][C]18.7711089803540[/C][C]10.7737927304279[/C][C]26.7684252302802[/C][/ROW]
[ROW][C]80[/C][C]20.4492140930143[/C][C]10.0718314714030[/C][C]30.8265967146256[/C][/ROW]
[ROW][C]81[/C][C]21.0169478089856[/C][C]8.54907926298566[/C][C]33.4848163549855[/C][/ROW]
[ROW][C]82[/C][C]23.5189046868944[/C][C]7.52903592983942[/C][C]39.5087734439493[/C][/ROW]
[ROW][C]83[/C][C]22.2496725746468[/C][C]5.12573473685641[/C][C]39.3736104124371[/C][/ROW]
[ROW][C]84[/C][C]21.7781244322791[/C][C]3.05341302363635[/C][C]40.5028358409219[/C][/ROW]
[ROW][C]85[/C][C]24.7810518400923[/C][C]0.906736925614762[/C][C]48.6553667545698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63246&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63246&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
7417.002654275103514.847326199248019.1579823509590
7515.984195272769313.346629158550918.6217613869878
7618.919972742985915.020391363901722.8195541220702
7719.989395623153614.580289739605425.3985015067018
7818.790426079938212.273871621838625.3069805380379
7918.771108980354010.773792730427926.7684252302802
8020.449214093014310.071831471403030.8265967146256
8121.01694780898568.5490792629856633.4848163549855
8223.51890468689447.5290359298394239.5087734439493
8322.24967257464685.1257347368564139.3736104124371
8421.77812443227913.0534130236363540.5028358409219
8524.78105184009230.90673692561476248.6553667545698



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')