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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 05 Jan 2011 21:32:04 +0000
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/Jan/05/t1294263055718vg6pwscaku7n.htm/, Retrieved Thu, 16 May 2024 23:13:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117283, Retrieved Thu, 16 May 2024 23:13:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2010-12-21 19:55:16] [aa10f9161a5c33241da7144d3bd8e782]
-   PD    [Exponential Smoothing] [] [2011-01-05 21:32:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
13.2
13.8
16.2
14.7
13.9
16.0
14.4
12.3
15.9
15.9
15.5
15.1
14.5
15.1
17.4
16.2
15.6
17.2
14.9
13.8
17.5
16.2
17.5
16.6
16.2
16.6
19.6
15.9
18.0
18.3
16.3
14.9
18.2
18.4
18.5
16.0
17.4
17.2
19.6
17.2
18.3
19.3
18.1
16.2
18.4
20.5
19.0
16.5
18.7
19.0
19.2
20.5
19.3
20.6
20.1
16.1
20.4
19.7
15.6
14.4
13.9
14.3
15.3
14.4
13.8
15.7
14.7
12.5
16.2
16.1
16
15.8
15.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117283&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117283&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'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.582791898887054
beta0.00347774327083311
gamma0.116580657647063

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.582791898887054 \tabularnewline
beta & 0.00347774327083311 \tabularnewline
gamma & 0.116580657647063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117283&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]0.582791898887054[/C][/ROW]
[ROW][C]beta[/C][C]0.00347774327083311[/C][/ROW]
[ROW][C]gamma[/C][C]0.116580657647063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117283&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
alpha0.582791898887054
beta0.00347774327083311
gamma0.116580657647063







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314.513.82457264957270.675427350427348
1415.114.84137006604560.258629933954428
1517.417.26995218269420.13004781730579
1616.216.1738612644130.0261387355869864
1715.615.6005992864237-0.000599286423735634
1817.217.16175339118030.0382466088197368
1914.915.6747907539062-0.774790753906244
2013.813.12075951510790.679240484892132
2117.517.1196692547020.380330745297961
2216.217.3368143408135-1.1368143408135
2317.516.24664213197621.25335786802377
2416.616.5644832298790.0355167701209567
2516.216.05550008933470.144499910665335
2616.616.7447002532945-0.144700253294545
2719.618.93324862218880.666751377811167
2815.918.1472558569398-2.24725585693984
291816.24553535225291.75446464774715
3018.318.8327309857767-0.532730985776716
3116.316.9736202258681-0.673620225868053
3214.914.54963497533340.350365024666553
3318.218.3420365847266-0.142036584726583
3418.418.17959630024990.22040369975009
3518.517.99804229962910.501957700370866
361617.8186050821708-1.81860508217076
3717.416.23046302758361.16953697241637
3817.217.5011653171813-0.301165317181258
3919.619.6358627574372-0.0358627574371972
4017.218.29510341128-1.09510341127996
4118.317.25826434278181.04173565721818
4219.319.3161762735339-0.0161762735339046
4318.117.74963824539870.350361754601259
4416.215.97268326050310.227316739496899
4518.419.6696311718359-1.26963117183587
4620.518.86558847060911.63441152939095
471919.5225890848276-0.522589084827615
4816.518.6318972722187-2.13189727221875
4918.717.0045859395441.69541406045605
501918.50937482453880.490625175461176
5119.221.1191723288922-1.91917232889216
5220.518.62624565202931.8737543479707
5319.319.4265125352652-0.126512535265228
5420.620.7527032177003-0.15270321770025
5520.119.1247289732620.975271026738046
5616.117.7075506635883-1.60755066358832
5720.420.2601939889020.139806011097978
5819.720.4195148989846-0.71951489898462
5915.619.5956893368729-3.99568933687291
6014.416.5915255088486-2.19152550884863
6113.915.1043935904871-1.20439359048713
6214.314.84349772677-0.543497726769987
6315.316.7142107939444-1.41421079394438
6414.414.6818796255207-0.281879625520743
6513.814.1060278328726-0.30602783287258
6615.715.30341785088110.396582149118949
6714.714.02863208644260.671367913557376
6812.512.28630781367760.21369218632241
6916.215.96662724813820.233372751861753
7016.116.1201536546898-0.0201536546897678
711615.52745130782050.472548692179469
7215.815.20703727895030.59296272104967
7315.215.388283898882-0.188283898882037

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14.5 & 13.8245726495727 & 0.675427350427348 \tabularnewline
14 & 15.1 & 14.8413700660456 & 0.258629933954428 \tabularnewline
15 & 17.4 & 17.2699521826942 & 0.13004781730579 \tabularnewline
16 & 16.2 & 16.173861264413 & 0.0261387355869864 \tabularnewline
17 & 15.6 & 15.6005992864237 & -0.000599286423735634 \tabularnewline
18 & 17.2 & 17.1617533911803 & 0.0382466088197368 \tabularnewline
19 & 14.9 & 15.6747907539062 & -0.774790753906244 \tabularnewline
20 & 13.8 & 13.1207595151079 & 0.679240484892132 \tabularnewline
21 & 17.5 & 17.119669254702 & 0.380330745297961 \tabularnewline
22 & 16.2 & 17.3368143408135 & -1.1368143408135 \tabularnewline
23 & 17.5 & 16.2466421319762 & 1.25335786802377 \tabularnewline
24 & 16.6 & 16.564483229879 & 0.0355167701209567 \tabularnewline
25 & 16.2 & 16.0555000893347 & 0.144499910665335 \tabularnewline
26 & 16.6 & 16.7447002532945 & -0.144700253294545 \tabularnewline
27 & 19.6 & 18.9332486221888 & 0.666751377811167 \tabularnewline
28 & 15.9 & 18.1472558569398 & -2.24725585693984 \tabularnewline
29 & 18 & 16.2455353522529 & 1.75446464774715 \tabularnewline
30 & 18.3 & 18.8327309857767 & -0.532730985776716 \tabularnewline
31 & 16.3 & 16.9736202258681 & -0.673620225868053 \tabularnewline
32 & 14.9 & 14.5496349753334 & 0.350365024666553 \tabularnewline
33 & 18.2 & 18.3420365847266 & -0.142036584726583 \tabularnewline
34 & 18.4 & 18.1795963002499 & 0.22040369975009 \tabularnewline
35 & 18.5 & 17.9980422996291 & 0.501957700370866 \tabularnewline
36 & 16 & 17.8186050821708 & -1.81860508217076 \tabularnewline
37 & 17.4 & 16.2304630275836 & 1.16953697241637 \tabularnewline
38 & 17.2 & 17.5011653171813 & -0.301165317181258 \tabularnewline
39 & 19.6 & 19.6358627574372 & -0.0358627574371972 \tabularnewline
40 & 17.2 & 18.29510341128 & -1.09510341127996 \tabularnewline
41 & 18.3 & 17.2582643427818 & 1.04173565721818 \tabularnewline
42 & 19.3 & 19.3161762735339 & -0.0161762735339046 \tabularnewline
43 & 18.1 & 17.7496382453987 & 0.350361754601259 \tabularnewline
44 & 16.2 & 15.9726832605031 & 0.227316739496899 \tabularnewline
45 & 18.4 & 19.6696311718359 & -1.26963117183587 \tabularnewline
46 & 20.5 & 18.8655884706091 & 1.63441152939095 \tabularnewline
47 & 19 & 19.5225890848276 & -0.522589084827615 \tabularnewline
48 & 16.5 & 18.6318972722187 & -2.13189727221875 \tabularnewline
49 & 18.7 & 17.004585939544 & 1.69541406045605 \tabularnewline
50 & 19 & 18.5093748245388 & 0.490625175461176 \tabularnewline
51 & 19.2 & 21.1191723288922 & -1.91917232889216 \tabularnewline
52 & 20.5 & 18.6262456520293 & 1.8737543479707 \tabularnewline
53 & 19.3 & 19.4265125352652 & -0.126512535265228 \tabularnewline
54 & 20.6 & 20.7527032177003 & -0.15270321770025 \tabularnewline
55 & 20.1 & 19.124728973262 & 0.975271026738046 \tabularnewline
56 & 16.1 & 17.7075506635883 & -1.60755066358832 \tabularnewline
57 & 20.4 & 20.260193988902 & 0.139806011097978 \tabularnewline
58 & 19.7 & 20.4195148989846 & -0.71951489898462 \tabularnewline
59 & 15.6 & 19.5956893368729 & -3.99568933687291 \tabularnewline
60 & 14.4 & 16.5915255088486 & -2.19152550884863 \tabularnewline
61 & 13.9 & 15.1043935904871 & -1.20439359048713 \tabularnewline
62 & 14.3 & 14.84349772677 & -0.543497726769987 \tabularnewline
63 & 15.3 & 16.7142107939444 & -1.41421079394438 \tabularnewline
64 & 14.4 & 14.6818796255207 & -0.281879625520743 \tabularnewline
65 & 13.8 & 14.1060278328726 & -0.30602783287258 \tabularnewline
66 & 15.7 & 15.3034178508811 & 0.396582149118949 \tabularnewline
67 & 14.7 & 14.0286320864426 & 0.671367913557376 \tabularnewline
68 & 12.5 & 12.2863078136776 & 0.21369218632241 \tabularnewline
69 & 16.2 & 15.9666272481382 & 0.233372751861753 \tabularnewline
70 & 16.1 & 16.1201536546898 & -0.0201536546897678 \tabularnewline
71 & 16 & 15.5274513078205 & 0.472548692179469 \tabularnewline
72 & 15.8 & 15.2070372789503 & 0.59296272104967 \tabularnewline
73 & 15.2 & 15.388283898882 & -0.188283898882037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117283&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]14.5[/C][C]13.8245726495727[/C][C]0.675427350427348[/C][/ROW]
[ROW][C]14[/C][C]15.1[/C][C]14.8413700660456[/C][C]0.258629933954428[/C][/ROW]
[ROW][C]15[/C][C]17.4[/C][C]17.2699521826942[/C][C]0.13004781730579[/C][/ROW]
[ROW][C]16[/C][C]16.2[/C][C]16.173861264413[/C][C]0.0261387355869864[/C][/ROW]
[ROW][C]17[/C][C]15.6[/C][C]15.6005992864237[/C][C]-0.000599286423735634[/C][/ROW]
[ROW][C]18[/C][C]17.2[/C][C]17.1617533911803[/C][C]0.0382466088197368[/C][/ROW]
[ROW][C]19[/C][C]14.9[/C][C]15.6747907539062[/C][C]-0.774790753906244[/C][/ROW]
[ROW][C]20[/C][C]13.8[/C][C]13.1207595151079[/C][C]0.679240484892132[/C][/ROW]
[ROW][C]21[/C][C]17.5[/C][C]17.119669254702[/C][C]0.380330745297961[/C][/ROW]
[ROW][C]22[/C][C]16.2[/C][C]17.3368143408135[/C][C]-1.1368143408135[/C][/ROW]
[ROW][C]23[/C][C]17.5[/C][C]16.2466421319762[/C][C]1.25335786802377[/C][/ROW]
[ROW][C]24[/C][C]16.6[/C][C]16.564483229879[/C][C]0.0355167701209567[/C][/ROW]
[ROW][C]25[/C][C]16.2[/C][C]16.0555000893347[/C][C]0.144499910665335[/C][/ROW]
[ROW][C]26[/C][C]16.6[/C][C]16.7447002532945[/C][C]-0.144700253294545[/C][/ROW]
[ROW][C]27[/C][C]19.6[/C][C]18.9332486221888[/C][C]0.666751377811167[/C][/ROW]
[ROW][C]28[/C][C]15.9[/C][C]18.1472558569398[/C][C]-2.24725585693984[/C][/ROW]
[ROW][C]29[/C][C]18[/C][C]16.2455353522529[/C][C]1.75446464774715[/C][/ROW]
[ROW][C]30[/C][C]18.3[/C][C]18.8327309857767[/C][C]-0.532730985776716[/C][/ROW]
[ROW][C]31[/C][C]16.3[/C][C]16.9736202258681[/C][C]-0.673620225868053[/C][/ROW]
[ROW][C]32[/C][C]14.9[/C][C]14.5496349753334[/C][C]0.350365024666553[/C][/ROW]
[ROW][C]33[/C][C]18.2[/C][C]18.3420365847266[/C][C]-0.142036584726583[/C][/ROW]
[ROW][C]34[/C][C]18.4[/C][C]18.1795963002499[/C][C]0.22040369975009[/C][/ROW]
[ROW][C]35[/C][C]18.5[/C][C]17.9980422996291[/C][C]0.501957700370866[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]17.8186050821708[/C][C]-1.81860508217076[/C][/ROW]
[ROW][C]37[/C][C]17.4[/C][C]16.2304630275836[/C][C]1.16953697241637[/C][/ROW]
[ROW][C]38[/C][C]17.2[/C][C]17.5011653171813[/C][C]-0.301165317181258[/C][/ROW]
[ROW][C]39[/C][C]19.6[/C][C]19.6358627574372[/C][C]-0.0358627574371972[/C][/ROW]
[ROW][C]40[/C][C]17.2[/C][C]18.29510341128[/C][C]-1.09510341127996[/C][/ROW]
[ROW][C]41[/C][C]18.3[/C][C]17.2582643427818[/C][C]1.04173565721818[/C][/ROW]
[ROW][C]42[/C][C]19.3[/C][C]19.3161762735339[/C][C]-0.0161762735339046[/C][/ROW]
[ROW][C]43[/C][C]18.1[/C][C]17.7496382453987[/C][C]0.350361754601259[/C][/ROW]
[ROW][C]44[/C][C]16.2[/C][C]15.9726832605031[/C][C]0.227316739496899[/C][/ROW]
[ROW][C]45[/C][C]18.4[/C][C]19.6696311718359[/C][C]-1.26963117183587[/C][/ROW]
[ROW][C]46[/C][C]20.5[/C][C]18.8655884706091[/C][C]1.63441152939095[/C][/ROW]
[ROW][C]47[/C][C]19[/C][C]19.5225890848276[/C][C]-0.522589084827615[/C][/ROW]
[ROW][C]48[/C][C]16.5[/C][C]18.6318972722187[/C][C]-2.13189727221875[/C][/ROW]
[ROW][C]49[/C][C]18.7[/C][C]17.004585939544[/C][C]1.69541406045605[/C][/ROW]
[ROW][C]50[/C][C]19[/C][C]18.5093748245388[/C][C]0.490625175461176[/C][/ROW]
[ROW][C]51[/C][C]19.2[/C][C]21.1191723288922[/C][C]-1.91917232889216[/C][/ROW]
[ROW][C]52[/C][C]20.5[/C][C]18.6262456520293[/C][C]1.8737543479707[/C][/ROW]
[ROW][C]53[/C][C]19.3[/C][C]19.4265125352652[/C][C]-0.126512535265228[/C][/ROW]
[ROW][C]54[/C][C]20.6[/C][C]20.7527032177003[/C][C]-0.15270321770025[/C][/ROW]
[ROW][C]55[/C][C]20.1[/C][C]19.124728973262[/C][C]0.975271026738046[/C][/ROW]
[ROW][C]56[/C][C]16.1[/C][C]17.7075506635883[/C][C]-1.60755066358832[/C][/ROW]
[ROW][C]57[/C][C]20.4[/C][C]20.260193988902[/C][C]0.139806011097978[/C][/ROW]
[ROW][C]58[/C][C]19.7[/C][C]20.4195148989846[/C][C]-0.71951489898462[/C][/ROW]
[ROW][C]59[/C][C]15.6[/C][C]19.5956893368729[/C][C]-3.99568933687291[/C][/ROW]
[ROW][C]60[/C][C]14.4[/C][C]16.5915255088486[/C][C]-2.19152550884863[/C][/ROW]
[ROW][C]61[/C][C]13.9[/C][C]15.1043935904871[/C][C]-1.20439359048713[/C][/ROW]
[ROW][C]62[/C][C]14.3[/C][C]14.84349772677[/C][C]-0.543497726769987[/C][/ROW]
[ROW][C]63[/C][C]15.3[/C][C]16.7142107939444[/C][C]-1.41421079394438[/C][/ROW]
[ROW][C]64[/C][C]14.4[/C][C]14.6818796255207[/C][C]-0.281879625520743[/C][/ROW]
[ROW][C]65[/C][C]13.8[/C][C]14.1060278328726[/C][C]-0.30602783287258[/C][/ROW]
[ROW][C]66[/C][C]15.7[/C][C]15.3034178508811[/C][C]0.396582149118949[/C][/ROW]
[ROW][C]67[/C][C]14.7[/C][C]14.0286320864426[/C][C]0.671367913557376[/C][/ROW]
[ROW][C]68[/C][C]12.5[/C][C]12.2863078136776[/C][C]0.21369218632241[/C][/ROW]
[ROW][C]69[/C][C]16.2[/C][C]15.9666272481382[/C][C]0.233372751861753[/C][/ROW]
[ROW][C]70[/C][C]16.1[/C][C]16.1201536546898[/C][C]-0.0201536546897678[/C][/ROW]
[ROW][C]71[/C][C]16[/C][C]15.5274513078205[/C][C]0.472548692179469[/C][/ROW]
[ROW][C]72[/C][C]15.8[/C][C]15.2070372789503[/C][C]0.59296272104967[/C][/ROW]
[ROW][C]73[/C][C]15.2[/C][C]15.388283898882[/C][C]-0.188283898882037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117283&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
1314.513.82457264957270.675427350427348
1415.114.84137006604560.258629933954428
1517.417.26995218269420.13004781730579
1616.216.1738612644130.0261387355869864
1715.615.6005992864237-0.000599286423735634
1817.217.16175339118030.0382466088197368
1914.915.6747907539062-0.774790753906244
2013.813.12075951510790.679240484892132
2117.517.1196692547020.380330745297961
2216.217.3368143408135-1.1368143408135
2317.516.24664213197621.25335786802377
2416.616.5644832298790.0355167701209567
2516.216.05550008933470.144499910665335
2616.616.7447002532945-0.144700253294545
2719.618.93324862218880.666751377811167
2815.918.1472558569398-2.24725585693984
291816.24553535225291.75446464774715
3018.318.8327309857767-0.532730985776716
3116.316.9736202258681-0.673620225868053
3214.914.54963497533340.350365024666553
3318.218.3420365847266-0.142036584726583
3418.418.17959630024990.22040369975009
3518.517.99804229962910.501957700370866
361617.8186050821708-1.81860508217076
3717.416.23046302758361.16953697241637
3817.217.5011653171813-0.301165317181258
3919.619.6358627574372-0.0358627574371972
4017.218.29510341128-1.09510341127996
4118.317.25826434278181.04173565721818
4219.319.3161762735339-0.0161762735339046
4318.117.74963824539870.350361754601259
4416.215.97268326050310.227316739496899
4518.419.6696311718359-1.26963117183587
4620.518.86558847060911.63441152939095
471919.5225890848276-0.522589084827615
4816.518.6318972722187-2.13189727221875
4918.717.0045859395441.69541406045605
501918.50937482453880.490625175461176
5119.221.1191723288922-1.91917232889216
5220.518.62624565202931.8737543479707
5319.319.4265125352652-0.126512535265228
5420.620.7527032177003-0.15270321770025
5520.119.1247289732620.975271026738046
5616.117.7075506635883-1.60755066358832
5720.420.2601939889020.139806011097978
5819.720.4195148989846-0.71951489898462
5915.619.5956893368729-3.99568933687291
6014.416.5915255088486-2.19152550884863
6113.915.1043935904871-1.20439359048713
6214.314.84349772677-0.543497726769987
6315.316.7142107939444-1.41421079394438
6414.414.6818796255207-0.281879625520743
6513.814.1060278328726-0.30602783287258
6615.715.30341785088110.396582149118949
6714.714.02863208644260.671367913557376
6812.512.28630781367760.21369218632241
6916.215.96662724813820.233372751861753
7016.116.1201536546898-0.0201536546897678
711615.52745130782050.472548692179469
7215.815.20703727895030.59296272104967
7315.215.388283898882-0.188283898882037







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7415.751361740887513.633511410830417.8692120709446
7517.897220651017615.443790986577420.3506503154578
7616.74777102698613.997499119037819.4980429349343
7716.339209360249813.319381183211219.3590375372884
7817.753931492924114.48507023518521.0227927506631
7916.265389961430212.763632184453919.7671477384065
8014.11218052406210.390627100010817.8337339481133
8117.671129232446713.740677877813321.6015805870801
8217.678053890154313.547943931780221.8081638485284
8317.122839146495312.801024945275721.4446533477149
8416.533704516350812.027121124647221.0402879080543
8516.330997070653511.645755054680621.0162390866264

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 15.7513617408875 & 13.6335114108304 & 17.8692120709446 \tabularnewline
75 & 17.8972206510176 & 15.4437909865774 & 20.3506503154578 \tabularnewline
76 & 16.747771026986 & 13.9974991190378 & 19.4980429349343 \tabularnewline
77 & 16.3392093602498 & 13.3193811832112 & 19.3590375372884 \tabularnewline
78 & 17.7539314929241 & 14.485070235185 & 21.0227927506631 \tabularnewline
79 & 16.2653899614302 & 12.7636321844539 & 19.7671477384065 \tabularnewline
80 & 14.112180524062 & 10.3906271000108 & 17.8337339481133 \tabularnewline
81 & 17.6711292324467 & 13.7406778778133 & 21.6015805870801 \tabularnewline
82 & 17.6780538901543 & 13.5479439317802 & 21.8081638485284 \tabularnewline
83 & 17.1228391464953 & 12.8010249452757 & 21.4446533477149 \tabularnewline
84 & 16.5337045163508 & 12.0271211246472 & 21.0402879080543 \tabularnewline
85 & 16.3309970706535 & 11.6457550546806 & 21.0162390866264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117283&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]15.7513617408875[/C][C]13.6335114108304[/C][C]17.8692120709446[/C][/ROW]
[ROW][C]75[/C][C]17.8972206510176[/C][C]15.4437909865774[/C][C]20.3506503154578[/C][/ROW]
[ROW][C]76[/C][C]16.747771026986[/C][C]13.9974991190378[/C][C]19.4980429349343[/C][/ROW]
[ROW][C]77[/C][C]16.3392093602498[/C][C]13.3193811832112[/C][C]19.3590375372884[/C][/ROW]
[ROW][C]78[/C][C]17.7539314929241[/C][C]14.485070235185[/C][C]21.0227927506631[/C][/ROW]
[ROW][C]79[/C][C]16.2653899614302[/C][C]12.7636321844539[/C][C]19.7671477384065[/C][/ROW]
[ROW][C]80[/C][C]14.112180524062[/C][C]10.3906271000108[/C][C]17.8337339481133[/C][/ROW]
[ROW][C]81[/C][C]17.6711292324467[/C][C]13.7406778778133[/C][C]21.6015805870801[/C][/ROW]
[ROW][C]82[/C][C]17.6780538901543[/C][C]13.5479439317802[/C][C]21.8081638485284[/C][/ROW]
[ROW][C]83[/C][C]17.1228391464953[/C][C]12.8010249452757[/C][C]21.4446533477149[/C][/ROW]
[ROW][C]84[/C][C]16.5337045163508[/C][C]12.0271211246472[/C][C]21.0402879080543[/C][/ROW]
[ROW][C]85[/C][C]16.3309970706535[/C][C]11.6457550546806[/C][C]21.0162390866264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117283&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
7415.751361740887513.633511410830417.8692120709446
7517.897220651017615.443790986577420.3506503154578
7616.74777102698613.997499119037819.4980429349343
7716.339209360249813.319381183211219.3590375372884
7817.753931492924114.48507023518521.0227927506631
7916.265389961430212.763632184453919.7671477384065
8014.11218052406210.390627100010817.8337339481133
8117.671129232446713.740677877813321.6015805870801
8217.678053890154313.547943931780221.8081638485284
8317.122839146495312.801024945275721.4446533477149
8416.533704516350812.027121124647221.0402879080543
8516.330997070653511.645755054680621.0162390866264



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')