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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 06:12:20 -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/19/t1324293274dbzwcqzi52vketz.htm/, Retrieved Wed, 15 May 2024 18:16:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157278, Retrieved Wed, 15 May 2024 18:16:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-19 11:12:20] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
18,94
18,97
19
19,08
19,18
19,24
19,23
19,25
19,3
19,33
19,35
19,35
19,31
19,47
19,7
19,76
19,9
19,97
20,1
20,26
20,44
20,43
20,57
20,6
20,69
20,93
20,98
21,11
21,14
21,16
21,32
21,32
21,48
21,58
21,74
21,75
21,81
21,89
22,21
22,37
22,47
22,51
22,55
22,61
22,58
22,85
22,93
22,98
23,01
23,11
23,18
23,18
23,21
23,22
23,12
23,15
23,16
23,21
23,21
23,22
23,25
23,39
23,41
23,45
23,46
23,44
23,54
23,62
23,86
24,07
24,13
24,12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157278&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157278&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.128424512863716
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.128424512863716 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157278&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.128424512863716[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157278&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
alpha1
beta0.128424512863716
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
319193.5527136788005e-15
419.0819.030.0500000000000007
519.1819.11642122564320.0635787743568166
619.2419.22458629876840.0154137012315694
719.2319.2865657958405-0.0565657958405197
819.2519.269301361065-0.0193013610649544
919.319.28682259317260.0131774068274204
1019.3319.3385148952252-0.00851489522520055
1119.3519.3674213739538-0.0174213739538125
1219.3519.3851840424904-0.035184042490382
1319.3119.380665548973-0.0706655489729826
1419.4719.33159036026990.138409639730124
1519.719.50936555082790.190634449172141
1619.7619.7638476870978-0.00384768709783145
1719.919.82335354975660.0766464502433521
1819.9719.9731968327919-0.00319683279187899
1920.120.04278628109790.0572137189021262
2020.2620.1801339250770.0798660749229967
2120.4420.35039068684330.0896093131566751
2220.4320.5418987192335-0.111898719233526
2320.5720.51752818072590.0524718192741176
2420.620.6642668485552-0.0642668485552349
2520.6920.68601340983620.00398659016375547
2620.9320.7765253857360.153474614263988
2720.9821.0362352883098-0.0562352883098107
2821.1121.07901329880290.0309867011971257
2921.1421.2129927508094-0.072992750809366
3021.1621.2336186923441-0.0736186923440911
3121.3221.24416424764210.075835752357861
3221.3221.4139034171964-0.0939034171963513
3321.4821.40184391658670.0781560834133295
3421.5821.57188107352640.00811892647363521
3521.7421.67292374270370.0670762572962857
3621.7521.8415379783717-0.0915379783717114
3721.8121.8397822580908-0.0297822580907976
3821.8921.8959574861035-0.005957486103501
3922.2121.97519239885280.234807601147232
4022.3722.32534745064680.0446525493531986
4122.4722.4910819325456-0.0210819325456093
4222.5122.5883744956282-0.0783744956282106
4322.5522.6183092892062-0.0683092892062191
4422.6122.6495367020158-0.0395367020158446
4522.5822.7044592203192-0.124459220319224
4622.8522.65847560557830.191524394421677
4722.9322.9530720326335-0.0230720326334506
4822.9823.0301090180817-0.0501090180817236
4923.0123.0736737918445-0.0636737918444972
5023.1123.09549651614470.0145034838553144
5123.1823.1973591189936-0.0173591189936282
5223.1823.2651297825931-0.0851297825931283
5323.2123.2541970317334-0.0441970317334111
5423.2223.278521049463-0.0585210494630282
5523.1223.2810055121935-0.161005512193462
5623.1523.1603284577216-0.0103284577216485
5723.1623.1890020305701-0.0290020305701084
5823.2123.19527745892210.0147225410779157
5923.2123.2471681940881-0.0371681940881317
6023.2223.2423948868683-0.0223948868683408
6123.2523.24951883443160.000481165568366748
6223.3923.27958062788540.110419372114642
6323.4123.4337611819599-0.0237611819598982
6423.4523.4507096637416-0.000709663741634614
6523.4623.4906185255213-0.0306185255213158
6623.4423.4966863562966-0.0566863562966375
6723.5423.46940643860320.0705935613967767
6823.6223.57847238233690.0415276176630854
6923.8623.66380554640570.196194453594309
7024.0723.92900172353510.140998276464899
7124.1324.1571093585047-0.0271093585047311
7224.1224.2136278523447-0.09362785234471

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 19 & 19 & 3.5527136788005e-15 \tabularnewline
4 & 19.08 & 19.03 & 0.0500000000000007 \tabularnewline
5 & 19.18 & 19.1164212256432 & 0.0635787743568166 \tabularnewline
6 & 19.24 & 19.2245862987684 & 0.0154137012315694 \tabularnewline
7 & 19.23 & 19.2865657958405 & -0.0565657958405197 \tabularnewline
8 & 19.25 & 19.269301361065 & -0.0193013610649544 \tabularnewline
9 & 19.3 & 19.2868225931726 & 0.0131774068274204 \tabularnewline
10 & 19.33 & 19.3385148952252 & -0.00851489522520055 \tabularnewline
11 & 19.35 & 19.3674213739538 & -0.0174213739538125 \tabularnewline
12 & 19.35 & 19.3851840424904 & -0.035184042490382 \tabularnewline
13 & 19.31 & 19.380665548973 & -0.0706655489729826 \tabularnewline
14 & 19.47 & 19.3315903602699 & 0.138409639730124 \tabularnewline
15 & 19.7 & 19.5093655508279 & 0.190634449172141 \tabularnewline
16 & 19.76 & 19.7638476870978 & -0.00384768709783145 \tabularnewline
17 & 19.9 & 19.8233535497566 & 0.0766464502433521 \tabularnewline
18 & 19.97 & 19.9731968327919 & -0.00319683279187899 \tabularnewline
19 & 20.1 & 20.0427862810979 & 0.0572137189021262 \tabularnewline
20 & 20.26 & 20.180133925077 & 0.0798660749229967 \tabularnewline
21 & 20.44 & 20.3503906868433 & 0.0896093131566751 \tabularnewline
22 & 20.43 & 20.5418987192335 & -0.111898719233526 \tabularnewline
23 & 20.57 & 20.5175281807259 & 0.0524718192741176 \tabularnewline
24 & 20.6 & 20.6642668485552 & -0.0642668485552349 \tabularnewline
25 & 20.69 & 20.6860134098362 & 0.00398659016375547 \tabularnewline
26 & 20.93 & 20.776525385736 & 0.153474614263988 \tabularnewline
27 & 20.98 & 21.0362352883098 & -0.0562352883098107 \tabularnewline
28 & 21.11 & 21.0790132988029 & 0.0309867011971257 \tabularnewline
29 & 21.14 & 21.2129927508094 & -0.072992750809366 \tabularnewline
30 & 21.16 & 21.2336186923441 & -0.0736186923440911 \tabularnewline
31 & 21.32 & 21.2441642476421 & 0.075835752357861 \tabularnewline
32 & 21.32 & 21.4139034171964 & -0.0939034171963513 \tabularnewline
33 & 21.48 & 21.4018439165867 & 0.0781560834133295 \tabularnewline
34 & 21.58 & 21.5718810735264 & 0.00811892647363521 \tabularnewline
35 & 21.74 & 21.6729237427037 & 0.0670762572962857 \tabularnewline
36 & 21.75 & 21.8415379783717 & -0.0915379783717114 \tabularnewline
37 & 21.81 & 21.8397822580908 & -0.0297822580907976 \tabularnewline
38 & 21.89 & 21.8959574861035 & -0.005957486103501 \tabularnewline
39 & 22.21 & 21.9751923988528 & 0.234807601147232 \tabularnewline
40 & 22.37 & 22.3253474506468 & 0.0446525493531986 \tabularnewline
41 & 22.47 & 22.4910819325456 & -0.0210819325456093 \tabularnewline
42 & 22.51 & 22.5883744956282 & -0.0783744956282106 \tabularnewline
43 & 22.55 & 22.6183092892062 & -0.0683092892062191 \tabularnewline
44 & 22.61 & 22.6495367020158 & -0.0395367020158446 \tabularnewline
45 & 22.58 & 22.7044592203192 & -0.124459220319224 \tabularnewline
46 & 22.85 & 22.6584756055783 & 0.191524394421677 \tabularnewline
47 & 22.93 & 22.9530720326335 & -0.0230720326334506 \tabularnewline
48 & 22.98 & 23.0301090180817 & -0.0501090180817236 \tabularnewline
49 & 23.01 & 23.0736737918445 & -0.0636737918444972 \tabularnewline
50 & 23.11 & 23.0954965161447 & 0.0145034838553144 \tabularnewline
51 & 23.18 & 23.1973591189936 & -0.0173591189936282 \tabularnewline
52 & 23.18 & 23.2651297825931 & -0.0851297825931283 \tabularnewline
53 & 23.21 & 23.2541970317334 & -0.0441970317334111 \tabularnewline
54 & 23.22 & 23.278521049463 & -0.0585210494630282 \tabularnewline
55 & 23.12 & 23.2810055121935 & -0.161005512193462 \tabularnewline
56 & 23.15 & 23.1603284577216 & -0.0103284577216485 \tabularnewline
57 & 23.16 & 23.1890020305701 & -0.0290020305701084 \tabularnewline
58 & 23.21 & 23.1952774589221 & 0.0147225410779157 \tabularnewline
59 & 23.21 & 23.2471681940881 & -0.0371681940881317 \tabularnewline
60 & 23.22 & 23.2423948868683 & -0.0223948868683408 \tabularnewline
61 & 23.25 & 23.2495188344316 & 0.000481165568366748 \tabularnewline
62 & 23.39 & 23.2795806278854 & 0.110419372114642 \tabularnewline
63 & 23.41 & 23.4337611819599 & -0.0237611819598982 \tabularnewline
64 & 23.45 & 23.4507096637416 & -0.000709663741634614 \tabularnewline
65 & 23.46 & 23.4906185255213 & -0.0306185255213158 \tabularnewline
66 & 23.44 & 23.4966863562966 & -0.0566863562966375 \tabularnewline
67 & 23.54 & 23.4694064386032 & 0.0705935613967767 \tabularnewline
68 & 23.62 & 23.5784723823369 & 0.0415276176630854 \tabularnewline
69 & 23.86 & 23.6638055464057 & 0.196194453594309 \tabularnewline
70 & 24.07 & 23.9290017235351 & 0.140998276464899 \tabularnewline
71 & 24.13 & 24.1571093585047 & -0.0271093585047311 \tabularnewline
72 & 24.12 & 24.2136278523447 & -0.09362785234471 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157278&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]19[/C][C]19[/C][C]3.5527136788005e-15[/C][/ROW]
[ROW][C]4[/C][C]19.08[/C][C]19.03[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]5[/C][C]19.18[/C][C]19.1164212256432[/C][C]0.0635787743568166[/C][/ROW]
[ROW][C]6[/C][C]19.24[/C][C]19.2245862987684[/C][C]0.0154137012315694[/C][/ROW]
[ROW][C]7[/C][C]19.23[/C][C]19.2865657958405[/C][C]-0.0565657958405197[/C][/ROW]
[ROW][C]8[/C][C]19.25[/C][C]19.269301361065[/C][C]-0.0193013610649544[/C][/ROW]
[ROW][C]9[/C][C]19.3[/C][C]19.2868225931726[/C][C]0.0131774068274204[/C][/ROW]
[ROW][C]10[/C][C]19.33[/C][C]19.3385148952252[/C][C]-0.00851489522520055[/C][/ROW]
[ROW][C]11[/C][C]19.35[/C][C]19.3674213739538[/C][C]-0.0174213739538125[/C][/ROW]
[ROW][C]12[/C][C]19.35[/C][C]19.3851840424904[/C][C]-0.035184042490382[/C][/ROW]
[ROW][C]13[/C][C]19.31[/C][C]19.380665548973[/C][C]-0.0706655489729826[/C][/ROW]
[ROW][C]14[/C][C]19.47[/C][C]19.3315903602699[/C][C]0.138409639730124[/C][/ROW]
[ROW][C]15[/C][C]19.7[/C][C]19.5093655508279[/C][C]0.190634449172141[/C][/ROW]
[ROW][C]16[/C][C]19.76[/C][C]19.7638476870978[/C][C]-0.00384768709783145[/C][/ROW]
[ROW][C]17[/C][C]19.9[/C][C]19.8233535497566[/C][C]0.0766464502433521[/C][/ROW]
[ROW][C]18[/C][C]19.97[/C][C]19.9731968327919[/C][C]-0.00319683279187899[/C][/ROW]
[ROW][C]19[/C][C]20.1[/C][C]20.0427862810979[/C][C]0.0572137189021262[/C][/ROW]
[ROW][C]20[/C][C]20.26[/C][C]20.180133925077[/C][C]0.0798660749229967[/C][/ROW]
[ROW][C]21[/C][C]20.44[/C][C]20.3503906868433[/C][C]0.0896093131566751[/C][/ROW]
[ROW][C]22[/C][C]20.43[/C][C]20.5418987192335[/C][C]-0.111898719233526[/C][/ROW]
[ROW][C]23[/C][C]20.57[/C][C]20.5175281807259[/C][C]0.0524718192741176[/C][/ROW]
[ROW][C]24[/C][C]20.6[/C][C]20.6642668485552[/C][C]-0.0642668485552349[/C][/ROW]
[ROW][C]25[/C][C]20.69[/C][C]20.6860134098362[/C][C]0.00398659016375547[/C][/ROW]
[ROW][C]26[/C][C]20.93[/C][C]20.776525385736[/C][C]0.153474614263988[/C][/ROW]
[ROW][C]27[/C][C]20.98[/C][C]21.0362352883098[/C][C]-0.0562352883098107[/C][/ROW]
[ROW][C]28[/C][C]21.11[/C][C]21.0790132988029[/C][C]0.0309867011971257[/C][/ROW]
[ROW][C]29[/C][C]21.14[/C][C]21.2129927508094[/C][C]-0.072992750809366[/C][/ROW]
[ROW][C]30[/C][C]21.16[/C][C]21.2336186923441[/C][C]-0.0736186923440911[/C][/ROW]
[ROW][C]31[/C][C]21.32[/C][C]21.2441642476421[/C][C]0.075835752357861[/C][/ROW]
[ROW][C]32[/C][C]21.32[/C][C]21.4139034171964[/C][C]-0.0939034171963513[/C][/ROW]
[ROW][C]33[/C][C]21.48[/C][C]21.4018439165867[/C][C]0.0781560834133295[/C][/ROW]
[ROW][C]34[/C][C]21.58[/C][C]21.5718810735264[/C][C]0.00811892647363521[/C][/ROW]
[ROW][C]35[/C][C]21.74[/C][C]21.6729237427037[/C][C]0.0670762572962857[/C][/ROW]
[ROW][C]36[/C][C]21.75[/C][C]21.8415379783717[/C][C]-0.0915379783717114[/C][/ROW]
[ROW][C]37[/C][C]21.81[/C][C]21.8397822580908[/C][C]-0.0297822580907976[/C][/ROW]
[ROW][C]38[/C][C]21.89[/C][C]21.8959574861035[/C][C]-0.005957486103501[/C][/ROW]
[ROW][C]39[/C][C]22.21[/C][C]21.9751923988528[/C][C]0.234807601147232[/C][/ROW]
[ROW][C]40[/C][C]22.37[/C][C]22.3253474506468[/C][C]0.0446525493531986[/C][/ROW]
[ROW][C]41[/C][C]22.47[/C][C]22.4910819325456[/C][C]-0.0210819325456093[/C][/ROW]
[ROW][C]42[/C][C]22.51[/C][C]22.5883744956282[/C][C]-0.0783744956282106[/C][/ROW]
[ROW][C]43[/C][C]22.55[/C][C]22.6183092892062[/C][C]-0.0683092892062191[/C][/ROW]
[ROW][C]44[/C][C]22.61[/C][C]22.6495367020158[/C][C]-0.0395367020158446[/C][/ROW]
[ROW][C]45[/C][C]22.58[/C][C]22.7044592203192[/C][C]-0.124459220319224[/C][/ROW]
[ROW][C]46[/C][C]22.85[/C][C]22.6584756055783[/C][C]0.191524394421677[/C][/ROW]
[ROW][C]47[/C][C]22.93[/C][C]22.9530720326335[/C][C]-0.0230720326334506[/C][/ROW]
[ROW][C]48[/C][C]22.98[/C][C]23.0301090180817[/C][C]-0.0501090180817236[/C][/ROW]
[ROW][C]49[/C][C]23.01[/C][C]23.0736737918445[/C][C]-0.0636737918444972[/C][/ROW]
[ROW][C]50[/C][C]23.11[/C][C]23.0954965161447[/C][C]0.0145034838553144[/C][/ROW]
[ROW][C]51[/C][C]23.18[/C][C]23.1973591189936[/C][C]-0.0173591189936282[/C][/ROW]
[ROW][C]52[/C][C]23.18[/C][C]23.2651297825931[/C][C]-0.0851297825931283[/C][/ROW]
[ROW][C]53[/C][C]23.21[/C][C]23.2541970317334[/C][C]-0.0441970317334111[/C][/ROW]
[ROW][C]54[/C][C]23.22[/C][C]23.278521049463[/C][C]-0.0585210494630282[/C][/ROW]
[ROW][C]55[/C][C]23.12[/C][C]23.2810055121935[/C][C]-0.161005512193462[/C][/ROW]
[ROW][C]56[/C][C]23.15[/C][C]23.1603284577216[/C][C]-0.0103284577216485[/C][/ROW]
[ROW][C]57[/C][C]23.16[/C][C]23.1890020305701[/C][C]-0.0290020305701084[/C][/ROW]
[ROW][C]58[/C][C]23.21[/C][C]23.1952774589221[/C][C]0.0147225410779157[/C][/ROW]
[ROW][C]59[/C][C]23.21[/C][C]23.2471681940881[/C][C]-0.0371681940881317[/C][/ROW]
[ROW][C]60[/C][C]23.22[/C][C]23.2423948868683[/C][C]-0.0223948868683408[/C][/ROW]
[ROW][C]61[/C][C]23.25[/C][C]23.2495188344316[/C][C]0.000481165568366748[/C][/ROW]
[ROW][C]62[/C][C]23.39[/C][C]23.2795806278854[/C][C]0.110419372114642[/C][/ROW]
[ROW][C]63[/C][C]23.41[/C][C]23.4337611819599[/C][C]-0.0237611819598982[/C][/ROW]
[ROW][C]64[/C][C]23.45[/C][C]23.4507096637416[/C][C]-0.000709663741634614[/C][/ROW]
[ROW][C]65[/C][C]23.46[/C][C]23.4906185255213[/C][C]-0.0306185255213158[/C][/ROW]
[ROW][C]66[/C][C]23.44[/C][C]23.4966863562966[/C][C]-0.0566863562966375[/C][/ROW]
[ROW][C]67[/C][C]23.54[/C][C]23.4694064386032[/C][C]0.0705935613967767[/C][/ROW]
[ROW][C]68[/C][C]23.62[/C][C]23.5784723823369[/C][C]0.0415276176630854[/C][/ROW]
[ROW][C]69[/C][C]23.86[/C][C]23.6638055464057[/C][C]0.196194453594309[/C][/ROW]
[ROW][C]70[/C][C]24.07[/C][C]23.9290017235351[/C][C]0.140998276464899[/C][/ROW]
[ROW][C]71[/C][C]24.13[/C][C]24.1571093585047[/C][C]-0.0271093585047311[/C][/ROW]
[ROW][C]72[/C][C]24.12[/C][C]24.2136278523447[/C][C]-0.09362785234471[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157278&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
319193.5527136788005e-15
419.0819.030.0500000000000007
519.1819.11642122564320.0635787743568166
619.2419.22458629876840.0154137012315694
719.2319.2865657958405-0.0565657958405197
819.2519.269301361065-0.0193013610649544
919.319.28682259317260.0131774068274204
1019.3319.3385148952252-0.00851489522520055
1119.3519.3674213739538-0.0174213739538125
1219.3519.3851840424904-0.035184042490382
1319.3119.380665548973-0.0706655489729826
1419.4719.33159036026990.138409639730124
1519.719.50936555082790.190634449172141
1619.7619.7638476870978-0.00384768709783145
1719.919.82335354975660.0766464502433521
1819.9719.9731968327919-0.00319683279187899
1920.120.04278628109790.0572137189021262
2020.2620.1801339250770.0798660749229967
2120.4420.35039068684330.0896093131566751
2220.4320.5418987192335-0.111898719233526
2320.5720.51752818072590.0524718192741176
2420.620.6642668485552-0.0642668485552349
2520.6920.68601340983620.00398659016375547
2620.9320.7765253857360.153474614263988
2720.9821.0362352883098-0.0562352883098107
2821.1121.07901329880290.0309867011971257
2921.1421.2129927508094-0.072992750809366
3021.1621.2336186923441-0.0736186923440911
3121.3221.24416424764210.075835752357861
3221.3221.4139034171964-0.0939034171963513
3321.4821.40184391658670.0781560834133295
3421.5821.57188107352640.00811892647363521
3521.7421.67292374270370.0670762572962857
3621.7521.8415379783717-0.0915379783717114
3721.8121.8397822580908-0.0297822580907976
3821.8921.8959574861035-0.005957486103501
3922.2121.97519239885280.234807601147232
4022.3722.32534745064680.0446525493531986
4122.4722.4910819325456-0.0210819325456093
4222.5122.5883744956282-0.0783744956282106
4322.5522.6183092892062-0.0683092892062191
4422.6122.6495367020158-0.0395367020158446
4522.5822.7044592203192-0.124459220319224
4622.8522.65847560557830.191524394421677
4722.9322.9530720326335-0.0230720326334506
4822.9823.0301090180817-0.0501090180817236
4923.0123.0736737918445-0.0636737918444972
5023.1123.09549651614470.0145034838553144
5123.1823.1973591189936-0.0173591189936282
5223.1823.2651297825931-0.0851297825931283
5323.2123.2541970317334-0.0441970317334111
5423.2223.278521049463-0.0585210494630282
5523.1223.2810055121935-0.161005512193462
5623.1523.1603284577216-0.0103284577216485
5723.1623.1890020305701-0.0290020305701084
5823.2123.19527745892210.0147225410779157
5923.2123.2471681940881-0.0371681940881317
6023.2223.2423948868683-0.0223948868683408
6123.2523.24951883443160.000481165568366748
6223.3923.27958062788540.110419372114642
6323.4123.4337611819599-0.0237611819598982
6423.4523.4507096637416-0.000709663741634614
6523.4623.4906185255213-0.0306185255213158
6623.4423.4966863562966-0.0566863562966375
6723.5423.46940643860320.0705935613967767
6823.6223.57847238233690.0415276176630854
6923.8623.66380554640570.196194453594309
7024.0723.92900172353510.140998276464899
7124.1324.1571093585047-0.0271093585047311
7224.1224.2136278523447-0.09362785234471







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7324.191603741016924.033337228087624.3498702539461
7424.263207482033724.024579477185524.501835486882
7524.334811223050624.02414847604824.6454739700532
7624.406414964067524.026180065915324.7866498622196
7724.478018705084324.028606570716924.9274308394517
7824.549622446101224.030473484595225.0687714076072
7924.621226187118124.031278777133825.2111735971024
8024.692829928134924.030738990962525.3549208653074
8124.764433669151824.028688286920425.5001790513832
8224.836037410168724.025028928499125.6470458918383
8324.907641151185524.019704715224325.7955775871468
8424.979244892202424.012685750709625.9458040336952

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 24.1916037410169 & 24.0333372280876 & 24.3498702539461 \tabularnewline
74 & 24.2632074820337 & 24.0245794771855 & 24.501835486882 \tabularnewline
75 & 24.3348112230506 & 24.024148476048 & 24.6454739700532 \tabularnewline
76 & 24.4064149640675 & 24.0261800659153 & 24.7866498622196 \tabularnewline
77 & 24.4780187050843 & 24.0286065707169 & 24.9274308394517 \tabularnewline
78 & 24.5496224461012 & 24.0304734845952 & 25.0687714076072 \tabularnewline
79 & 24.6212261871181 & 24.0312787771338 & 25.2111735971024 \tabularnewline
80 & 24.6928299281349 & 24.0307389909625 & 25.3549208653074 \tabularnewline
81 & 24.7644336691518 & 24.0286882869204 & 25.5001790513832 \tabularnewline
82 & 24.8360374101687 & 24.0250289284991 & 25.6470458918383 \tabularnewline
83 & 24.9076411511855 & 24.0197047152243 & 25.7955775871468 \tabularnewline
84 & 24.9792448922024 & 24.0126857507096 & 25.9458040336952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157278&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]24.1916037410169[/C][C]24.0333372280876[/C][C]24.3498702539461[/C][/ROW]
[ROW][C]74[/C][C]24.2632074820337[/C][C]24.0245794771855[/C][C]24.501835486882[/C][/ROW]
[ROW][C]75[/C][C]24.3348112230506[/C][C]24.024148476048[/C][C]24.6454739700532[/C][/ROW]
[ROW][C]76[/C][C]24.4064149640675[/C][C]24.0261800659153[/C][C]24.7866498622196[/C][/ROW]
[ROW][C]77[/C][C]24.4780187050843[/C][C]24.0286065707169[/C][C]24.9274308394517[/C][/ROW]
[ROW][C]78[/C][C]24.5496224461012[/C][C]24.0304734845952[/C][C]25.0687714076072[/C][/ROW]
[ROW][C]79[/C][C]24.6212261871181[/C][C]24.0312787771338[/C][C]25.2111735971024[/C][/ROW]
[ROW][C]80[/C][C]24.6928299281349[/C][C]24.0307389909625[/C][C]25.3549208653074[/C][/ROW]
[ROW][C]81[/C][C]24.7644336691518[/C][C]24.0286882869204[/C][C]25.5001790513832[/C][/ROW]
[ROW][C]82[/C][C]24.8360374101687[/C][C]24.0250289284991[/C][C]25.6470458918383[/C][/ROW]
[ROW][C]83[/C][C]24.9076411511855[/C][C]24.0197047152243[/C][C]25.7955775871468[/C][/ROW]
[ROW][C]84[/C][C]24.9792448922024[/C][C]24.0126857507096[/C][C]25.9458040336952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157278&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157278&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
7324.191603741016924.033337228087624.3498702539461
7424.263207482033724.024579477185524.501835486882
7524.334811223050624.02414847604824.6454739700532
7624.406414964067524.026180065915324.7866498622196
7724.478018705084324.028606570716924.9274308394517
7824.549622446101224.030473484595225.0687714076072
7924.621226187118124.031278777133825.2111735971024
8024.692829928134924.030738990962525.3549208653074
8124.764433669151824.028688286920425.5001790513832
8224.836037410168724.025028928499125.6470458918383
8324.907641151185524.019704715224325.7955775871468
8424.979244892202424.012685750709625.9458040336952



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