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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 31 May 2008 14:00:41 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/31/t1212264079ne0yv2rau316k71.htm/, Retrieved Thu, 16 May 2024 00:00:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13631, Retrieved Thu, 16 May 2024 00:00:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Roze Zalm exp smo...] [2008-05-31 20:00:41] [f12139c84a7390b2232de02c02cfb50d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11.98
11.79
11.66
11.96
11.83
12.36
12.53
12.55
12.53
12.24
12.34
12.05
12.22
12.23
11.92
12.13
12.1
12.15
12.23
12.08
12.02
11.93
12.16
11.87
11.93
11.79
11.43
11.63
11.93
11.89
11.83
11.59
12.04
11.81
11.9
11.72
11.91
11.94
11.91
11.84
12.01
11.89
11.8
11.7
11.5
11.76
11.61
11.27
11.64
11.39
11.54
11.62
11.59
11.44
11.31
11.56
11.4
11.51
11.5
11.24
11.8
11.87
11.86
12.11
11.92
12.61
13.34
13.31
13.47
13.24
13.18
13.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13631&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]5 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=13631&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13631&T=0

As an alternative you can also use a QR Code:  
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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.743882684016797
beta0.0836577071765574
gamma0.526978787215965

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.743882684016797 \tabularnewline
beta & 0.0836577071765574 \tabularnewline
gamma & 0.526978787215965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13631&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]0.743882684016797[/C][/ROW]
[ROW][C]beta[/C][C]0.0836577071765574[/C][/ROW]
[ROW][C]gamma[/C][C]0.526978787215965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13631&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13631&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.743882684016797
beta0.0836577071765574
gamma0.526978787215965






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312.2212.2677376624260-0.0477376624260479
1412.2312.2499093149203-0.0199093149202998
1511.9211.9398216041343-0.0198216041342967
1612.1312.142393883475-0.0123938834750064
1712.112.09586903498250.00413096501746146
1812.1512.13641107176070.0135889282392707
1912.2312.21935783236900.0106421676309836
2012.0812.0817588439362-0.00175884393621395
2112.0212.0331339044428-0.0131339044428191
2211.9311.9476616418300-0.0176616418300206
2312.1612.1645367785168-0.00453677851675138
2411.8711.86081771319910.00918228680085775
2511.9311.86582334564100.0641766543590307
2611.7911.9345837473385-0.144583747338494
2711.4311.5338660984570-0.103866098456965
2811.6311.6530126988605-0.0230126988604606
2911.9311.58814174706230.341858252937712
3011.8911.88786193462150.00213806537845151
3111.8311.9672040385983-0.137204038598309
3211.5911.7198001332662-0.129800133266173
3312.0411.56554871805400.474451281945957
3411.8111.8631490856060-0.0531490856060142
3511.912.0717766206156-0.171776620615592
3611.7211.65846987966010.0615301203398655
3711.9111.72078673296590.189213267034051
3811.9411.87337136490150.0666286350985033
3911.9111.66434807639250.245651923607531
4011.8412.1176907060079-0.277690706007881
4112.0111.95147258221620.0585274177837558
4211.8912.0159250033739-0.125925003373920
4311.811.9945464787100-0.194546478709986
4411.711.7149264244336-0.0149264244335914
4511.511.7431141063731-0.243114106373088
4611.7611.41222137311650.347778626883493
4711.6111.897054413292-0.287054413292001
4811.2711.4243086974453-0.154308697445261
4911.6411.31795095594540.322049044054621
5011.3911.5376824568551-0.147682456855064
5111.5411.17492680996820.365073190031801
5211.6211.61829778739870.00170221260128223
5311.5911.6998938164922-0.109893816492249
5411.4411.6002448918256-0.160244891825604
5511.3111.525086158189-0.215086158189001
5611.5611.24063555986780.319364440132162
5711.411.4890983758269-0.0890983758269428
5811.5111.36476187505690.145238124943145
5911.511.6095962693882-0.109596269388241
6011.2411.2997082882507-0.0597082882507465
6111.811.34384323065560.456156769344426
6211.8711.62448165426710.245518345732901
6311.8611.66574107770480.19425892229523
6412.1111.97517324211490.134826757885129
6511.9212.1906327684804-0.270632768480386
6612.6112.00115079912940.608849200870562
6713.3412.58083911971170.759160880288263
6813.3113.23537791671850.074622083281497
6913.4713.37237751851370.0976224814863382
7013.2413.5591580053409-0.319158005340867
7113.1813.5562223667439-0.376222366743885
7213.313.11925630691820.180743693081755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12.22 & 12.2677376624260 & -0.0477376624260479 \tabularnewline
14 & 12.23 & 12.2499093149203 & -0.0199093149202998 \tabularnewline
15 & 11.92 & 11.9398216041343 & -0.0198216041342967 \tabularnewline
16 & 12.13 & 12.142393883475 & -0.0123938834750064 \tabularnewline
17 & 12.1 & 12.0958690349825 & 0.00413096501746146 \tabularnewline
18 & 12.15 & 12.1364110717607 & 0.0135889282392707 \tabularnewline
19 & 12.23 & 12.2193578323690 & 0.0106421676309836 \tabularnewline
20 & 12.08 & 12.0817588439362 & -0.00175884393621395 \tabularnewline
21 & 12.02 & 12.0331339044428 & -0.0131339044428191 \tabularnewline
22 & 11.93 & 11.9476616418300 & -0.0176616418300206 \tabularnewline
23 & 12.16 & 12.1645367785168 & -0.00453677851675138 \tabularnewline
24 & 11.87 & 11.8608177131991 & 0.00918228680085775 \tabularnewline
25 & 11.93 & 11.8658233456410 & 0.0641766543590307 \tabularnewline
26 & 11.79 & 11.9345837473385 & -0.144583747338494 \tabularnewline
27 & 11.43 & 11.5338660984570 & -0.103866098456965 \tabularnewline
28 & 11.63 & 11.6530126988605 & -0.0230126988604606 \tabularnewline
29 & 11.93 & 11.5881417470623 & 0.341858252937712 \tabularnewline
30 & 11.89 & 11.8878619346215 & 0.00213806537845151 \tabularnewline
31 & 11.83 & 11.9672040385983 & -0.137204038598309 \tabularnewline
32 & 11.59 & 11.7198001332662 & -0.129800133266173 \tabularnewline
33 & 12.04 & 11.5655487180540 & 0.474451281945957 \tabularnewline
34 & 11.81 & 11.8631490856060 & -0.0531490856060142 \tabularnewline
35 & 11.9 & 12.0717766206156 & -0.171776620615592 \tabularnewline
36 & 11.72 & 11.6584698796601 & 0.0615301203398655 \tabularnewline
37 & 11.91 & 11.7207867329659 & 0.189213267034051 \tabularnewline
38 & 11.94 & 11.8733713649015 & 0.0666286350985033 \tabularnewline
39 & 11.91 & 11.6643480763925 & 0.245651923607531 \tabularnewline
40 & 11.84 & 12.1176907060079 & -0.277690706007881 \tabularnewline
41 & 12.01 & 11.9514725822162 & 0.0585274177837558 \tabularnewline
42 & 11.89 & 12.0159250033739 & -0.125925003373920 \tabularnewline
43 & 11.8 & 11.9945464787100 & -0.194546478709986 \tabularnewline
44 & 11.7 & 11.7149264244336 & -0.0149264244335914 \tabularnewline
45 & 11.5 & 11.7431141063731 & -0.243114106373088 \tabularnewline
46 & 11.76 & 11.4122213731165 & 0.347778626883493 \tabularnewline
47 & 11.61 & 11.897054413292 & -0.287054413292001 \tabularnewline
48 & 11.27 & 11.4243086974453 & -0.154308697445261 \tabularnewline
49 & 11.64 & 11.3179509559454 & 0.322049044054621 \tabularnewline
50 & 11.39 & 11.5376824568551 & -0.147682456855064 \tabularnewline
51 & 11.54 & 11.1749268099682 & 0.365073190031801 \tabularnewline
52 & 11.62 & 11.6182977873987 & 0.00170221260128223 \tabularnewline
53 & 11.59 & 11.6998938164922 & -0.109893816492249 \tabularnewline
54 & 11.44 & 11.6002448918256 & -0.160244891825604 \tabularnewline
55 & 11.31 & 11.525086158189 & -0.215086158189001 \tabularnewline
56 & 11.56 & 11.2406355598678 & 0.319364440132162 \tabularnewline
57 & 11.4 & 11.4890983758269 & -0.0890983758269428 \tabularnewline
58 & 11.51 & 11.3647618750569 & 0.145238124943145 \tabularnewline
59 & 11.5 & 11.6095962693882 & -0.109596269388241 \tabularnewline
60 & 11.24 & 11.2997082882507 & -0.0597082882507465 \tabularnewline
61 & 11.8 & 11.3438432306556 & 0.456156769344426 \tabularnewline
62 & 11.87 & 11.6244816542671 & 0.245518345732901 \tabularnewline
63 & 11.86 & 11.6657410777048 & 0.19425892229523 \tabularnewline
64 & 12.11 & 11.9751732421149 & 0.134826757885129 \tabularnewline
65 & 11.92 & 12.1906327684804 & -0.270632768480386 \tabularnewline
66 & 12.61 & 12.0011507991294 & 0.608849200870562 \tabularnewline
67 & 13.34 & 12.5808391197117 & 0.759160880288263 \tabularnewline
68 & 13.31 & 13.2353779167185 & 0.074622083281497 \tabularnewline
69 & 13.47 & 13.3723775185137 & 0.0976224814863382 \tabularnewline
70 & 13.24 & 13.5591580053409 & -0.319158005340867 \tabularnewline
71 & 13.18 & 13.5562223667439 & -0.376222366743885 \tabularnewline
72 & 13.3 & 13.1192563069182 & 0.180743693081755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13631&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]12.22[/C][C]12.2677376624260[/C][C]-0.0477376624260479[/C][/ROW]
[ROW][C]14[/C][C]12.23[/C][C]12.2499093149203[/C][C]-0.0199093149202998[/C][/ROW]
[ROW][C]15[/C][C]11.92[/C][C]11.9398216041343[/C][C]-0.0198216041342967[/C][/ROW]
[ROW][C]16[/C][C]12.13[/C][C]12.142393883475[/C][C]-0.0123938834750064[/C][/ROW]
[ROW][C]17[/C][C]12.1[/C][C]12.0958690349825[/C][C]0.00413096501746146[/C][/ROW]
[ROW][C]18[/C][C]12.15[/C][C]12.1364110717607[/C][C]0.0135889282392707[/C][/ROW]
[ROW][C]19[/C][C]12.23[/C][C]12.2193578323690[/C][C]0.0106421676309836[/C][/ROW]
[ROW][C]20[/C][C]12.08[/C][C]12.0817588439362[/C][C]-0.00175884393621395[/C][/ROW]
[ROW][C]21[/C][C]12.02[/C][C]12.0331339044428[/C][C]-0.0131339044428191[/C][/ROW]
[ROW][C]22[/C][C]11.93[/C][C]11.9476616418300[/C][C]-0.0176616418300206[/C][/ROW]
[ROW][C]23[/C][C]12.16[/C][C]12.1645367785168[/C][C]-0.00453677851675138[/C][/ROW]
[ROW][C]24[/C][C]11.87[/C][C]11.8608177131991[/C][C]0.00918228680085775[/C][/ROW]
[ROW][C]25[/C][C]11.93[/C][C]11.8658233456410[/C][C]0.0641766543590307[/C][/ROW]
[ROW][C]26[/C][C]11.79[/C][C]11.9345837473385[/C][C]-0.144583747338494[/C][/ROW]
[ROW][C]27[/C][C]11.43[/C][C]11.5338660984570[/C][C]-0.103866098456965[/C][/ROW]
[ROW][C]28[/C][C]11.63[/C][C]11.6530126988605[/C][C]-0.0230126988604606[/C][/ROW]
[ROW][C]29[/C][C]11.93[/C][C]11.5881417470623[/C][C]0.341858252937712[/C][/ROW]
[ROW][C]30[/C][C]11.89[/C][C]11.8878619346215[/C][C]0.00213806537845151[/C][/ROW]
[ROW][C]31[/C][C]11.83[/C][C]11.9672040385983[/C][C]-0.137204038598309[/C][/ROW]
[ROW][C]32[/C][C]11.59[/C][C]11.7198001332662[/C][C]-0.129800133266173[/C][/ROW]
[ROW][C]33[/C][C]12.04[/C][C]11.5655487180540[/C][C]0.474451281945957[/C][/ROW]
[ROW][C]34[/C][C]11.81[/C][C]11.8631490856060[/C][C]-0.0531490856060142[/C][/ROW]
[ROW][C]35[/C][C]11.9[/C][C]12.0717766206156[/C][C]-0.171776620615592[/C][/ROW]
[ROW][C]36[/C][C]11.72[/C][C]11.6584698796601[/C][C]0.0615301203398655[/C][/ROW]
[ROW][C]37[/C][C]11.91[/C][C]11.7207867329659[/C][C]0.189213267034051[/C][/ROW]
[ROW][C]38[/C][C]11.94[/C][C]11.8733713649015[/C][C]0.0666286350985033[/C][/ROW]
[ROW][C]39[/C][C]11.91[/C][C]11.6643480763925[/C][C]0.245651923607531[/C][/ROW]
[ROW][C]40[/C][C]11.84[/C][C]12.1176907060079[/C][C]-0.277690706007881[/C][/ROW]
[ROW][C]41[/C][C]12.01[/C][C]11.9514725822162[/C][C]0.0585274177837558[/C][/ROW]
[ROW][C]42[/C][C]11.89[/C][C]12.0159250033739[/C][C]-0.125925003373920[/C][/ROW]
[ROW][C]43[/C][C]11.8[/C][C]11.9945464787100[/C][C]-0.194546478709986[/C][/ROW]
[ROW][C]44[/C][C]11.7[/C][C]11.7149264244336[/C][C]-0.0149264244335914[/C][/ROW]
[ROW][C]45[/C][C]11.5[/C][C]11.7431141063731[/C][C]-0.243114106373088[/C][/ROW]
[ROW][C]46[/C][C]11.76[/C][C]11.4122213731165[/C][C]0.347778626883493[/C][/ROW]
[ROW][C]47[/C][C]11.61[/C][C]11.897054413292[/C][C]-0.287054413292001[/C][/ROW]
[ROW][C]48[/C][C]11.27[/C][C]11.4243086974453[/C][C]-0.154308697445261[/C][/ROW]
[ROW][C]49[/C][C]11.64[/C][C]11.3179509559454[/C][C]0.322049044054621[/C][/ROW]
[ROW][C]50[/C][C]11.39[/C][C]11.5376824568551[/C][C]-0.147682456855064[/C][/ROW]
[ROW][C]51[/C][C]11.54[/C][C]11.1749268099682[/C][C]0.365073190031801[/C][/ROW]
[ROW][C]52[/C][C]11.62[/C][C]11.6182977873987[/C][C]0.00170221260128223[/C][/ROW]
[ROW][C]53[/C][C]11.59[/C][C]11.6998938164922[/C][C]-0.109893816492249[/C][/ROW]
[ROW][C]54[/C][C]11.44[/C][C]11.6002448918256[/C][C]-0.160244891825604[/C][/ROW]
[ROW][C]55[/C][C]11.31[/C][C]11.525086158189[/C][C]-0.215086158189001[/C][/ROW]
[ROW][C]56[/C][C]11.56[/C][C]11.2406355598678[/C][C]0.319364440132162[/C][/ROW]
[ROW][C]57[/C][C]11.4[/C][C]11.4890983758269[/C][C]-0.0890983758269428[/C][/ROW]
[ROW][C]58[/C][C]11.51[/C][C]11.3647618750569[/C][C]0.145238124943145[/C][/ROW]
[ROW][C]59[/C][C]11.5[/C][C]11.6095962693882[/C][C]-0.109596269388241[/C][/ROW]
[ROW][C]60[/C][C]11.24[/C][C]11.2997082882507[/C][C]-0.0597082882507465[/C][/ROW]
[ROW][C]61[/C][C]11.8[/C][C]11.3438432306556[/C][C]0.456156769344426[/C][/ROW]
[ROW][C]62[/C][C]11.87[/C][C]11.6244816542671[/C][C]0.245518345732901[/C][/ROW]
[ROW][C]63[/C][C]11.86[/C][C]11.6657410777048[/C][C]0.19425892229523[/C][/ROW]
[ROW][C]64[/C][C]12.11[/C][C]11.9751732421149[/C][C]0.134826757885129[/C][/ROW]
[ROW][C]65[/C][C]11.92[/C][C]12.1906327684804[/C][C]-0.270632768480386[/C][/ROW]
[ROW][C]66[/C][C]12.61[/C][C]12.0011507991294[/C][C]0.608849200870562[/C][/ROW]
[ROW][C]67[/C][C]13.34[/C][C]12.5808391197117[/C][C]0.759160880288263[/C][/ROW]
[ROW][C]68[/C][C]13.31[/C][C]13.2353779167185[/C][C]0.074622083281497[/C][/ROW]
[ROW][C]69[/C][C]13.47[/C][C]13.3723775185137[/C][C]0.0976224814863382[/C][/ROW]
[ROW][C]70[/C][C]13.24[/C][C]13.5591580053409[/C][C]-0.319158005340867[/C][/ROW]
[ROW][C]71[/C][C]13.18[/C][C]13.5562223667439[/C][C]-0.376222366743885[/C][/ROW]
[ROW][C]72[/C][C]13.3[/C][C]13.1192563069182[/C][C]0.180743693081755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13631&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13631&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312.2212.2677376624260-0.0477376624260479
1412.2312.2499093149203-0.0199093149202998
1511.9211.9398216041343-0.0198216041342967
1612.1312.142393883475-0.0123938834750064
1712.112.09586903498250.00413096501746146
1812.1512.13641107176070.0135889282392707
1912.2312.21935783236900.0106421676309836
2012.0812.0817588439362-0.00175884393621395
2112.0212.0331339044428-0.0131339044428191
2211.9311.9476616418300-0.0176616418300206
2312.1612.1645367785168-0.00453677851675138
2411.8711.86081771319910.00918228680085775
2511.9311.86582334564100.0641766543590307
2611.7911.9345837473385-0.144583747338494
2711.4311.5338660984570-0.103866098456965
2811.6311.6530126988605-0.0230126988604606
2911.9311.58814174706230.341858252937712
3011.8911.88786193462150.00213806537845151
3111.8311.9672040385983-0.137204038598309
3211.5911.7198001332662-0.129800133266173
3312.0411.56554871805400.474451281945957
3411.8111.8631490856060-0.0531490856060142
3511.912.0717766206156-0.171776620615592
3611.7211.65846987966010.0615301203398655
3711.9111.72078673296590.189213267034051
3811.9411.87337136490150.0666286350985033
3911.9111.66434807639250.245651923607531
4011.8412.1176907060079-0.277690706007881
4112.0111.95147258221620.0585274177837558
4211.8912.0159250033739-0.125925003373920
4311.811.9945464787100-0.194546478709986
4411.711.7149264244336-0.0149264244335914
4511.511.7431141063731-0.243114106373088
4611.7611.41222137311650.347778626883493
4711.6111.897054413292-0.287054413292001
4811.2711.4243086974453-0.154308697445261
4911.6411.31795095594540.322049044054621
5011.3911.5376824568551-0.147682456855064
5111.5411.17492680996820.365073190031801
5211.6211.61829778739870.00170221260128223
5311.5911.6998938164922-0.109893816492249
5411.4411.6002448918256-0.160244891825604
5511.3111.525086158189-0.215086158189001
5611.5611.24063555986780.319364440132162
5711.411.4890983758269-0.0890983758269428
5811.5111.36476187505690.145238124943145
5911.511.6095962693882-0.109596269388241
6011.2411.2997082882507-0.0597082882507465
6111.811.34384323065560.456156769344426
6211.8711.62448165426710.245518345732901
6311.8611.66574107770480.19425892229523
6412.1111.97517324211490.134826757885129
6511.9212.1906327684804-0.270632768480386
6612.6112.00115079912940.608849200870562
6713.3412.58083911971170.759160880288263
6813.3113.23537791671850.074622083281497
6913.4713.37237751851370.0976224814863382
7013.2413.5591580053409-0.319158005340867
7113.1813.5562223667439-0.376222366743885
7213.313.11925630691820.180743693081755






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313.554421138256413.16276404044313.9460782360697
7413.535565583354113.006030336311314.0651008303969
7513.429566850165012.7799668619314.0791668384001
7613.658272333997612.882631946613414.4339127213818
7713.767438211279012.873567780294114.6613086422640
7813.974872707557612.957548501956714.9921969131586
7914.152956286811613.013140242199515.2927723314236
8014.121542377717312.874422636586315.3686621188483
8114.178535066214512.816551649228615.5405184832005
8214.200698664684712.726267907098915.6751294222704
8314.423127900741912.814501119089516.0317546823943
8414.33780453499019.642263306738619.0333457632416

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 13.5544211382564 & 13.162764040443 & 13.9460782360697 \tabularnewline
74 & 13.5355655833541 & 13.0060303363113 & 14.0651008303969 \tabularnewline
75 & 13.4295668501650 & 12.77996686193 & 14.0791668384001 \tabularnewline
76 & 13.6582723339976 & 12.8826319466134 & 14.4339127213818 \tabularnewline
77 & 13.7674382112790 & 12.8735677802941 & 14.6613086422640 \tabularnewline
78 & 13.9748727075576 & 12.9575485019567 & 14.9921969131586 \tabularnewline
79 & 14.1529562868116 & 13.0131402421995 & 15.2927723314236 \tabularnewline
80 & 14.1215423777173 & 12.8744226365863 & 15.3686621188483 \tabularnewline
81 & 14.1785350662145 & 12.8165516492286 & 15.5405184832005 \tabularnewline
82 & 14.2006986646847 & 12.7262679070989 & 15.6751294222704 \tabularnewline
83 & 14.4231279007419 & 12.8145011190895 & 16.0317546823943 \tabularnewline
84 & 14.3378045349901 & 9.6422633067386 & 19.0333457632416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13631&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]13.5544211382564[/C][C]13.162764040443[/C][C]13.9460782360697[/C][/ROW]
[ROW][C]74[/C][C]13.5355655833541[/C][C]13.0060303363113[/C][C]14.0651008303969[/C][/ROW]
[ROW][C]75[/C][C]13.4295668501650[/C][C]12.77996686193[/C][C]14.0791668384001[/C][/ROW]
[ROW][C]76[/C][C]13.6582723339976[/C][C]12.8826319466134[/C][C]14.4339127213818[/C][/ROW]
[ROW][C]77[/C][C]13.7674382112790[/C][C]12.8735677802941[/C][C]14.6613086422640[/C][/ROW]
[ROW][C]78[/C][C]13.9748727075576[/C][C]12.9575485019567[/C][C]14.9921969131586[/C][/ROW]
[ROW][C]79[/C][C]14.1529562868116[/C][C]13.0131402421995[/C][C]15.2927723314236[/C][/ROW]
[ROW][C]80[/C][C]14.1215423777173[/C][C]12.8744226365863[/C][C]15.3686621188483[/C][/ROW]
[ROW][C]81[/C][C]14.1785350662145[/C][C]12.8165516492286[/C][C]15.5405184832005[/C][/ROW]
[ROW][C]82[/C][C]14.2006986646847[/C][C]12.7262679070989[/C][C]15.6751294222704[/C][/ROW]
[ROW][C]83[/C][C]14.4231279007419[/C][C]12.8145011190895[/C][C]16.0317546823943[/C][/ROW]
[ROW][C]84[/C][C]14.3378045349901[/C][C]9.6422633067386[/C][C]19.0333457632416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13631&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13631&T=3

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313.554421138256413.16276404044313.9460782360697
7413.535565583354113.006030336311314.0651008303969
7513.429566850165012.7799668619314.0791668384001
7613.658272333997612.882631946613414.4339127213818
7713.767438211279012.873567780294114.6613086422640
7813.974872707557612.957548501956714.9921969131586
7914.152956286811613.013140242199515.2927723314236
8014.121542377717312.874422636586315.3686621188483
8114.178535066214512.816551649228615.5405184832005
8214.200698664684712.726267907098915.6751294222704
8314.423127900741912.814501119089516.0317546823943
8414.33780453499019.642263306738619.0333457632416


Figures (Output of Computation)

Input Parameters & R Code

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=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')