Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Jan 2013 07:34:03 -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/2013/Jan/12/t1357994218rrdqgqhmelrwuyw.htm/, Retrieved Sun, 28 Apr 2024 02:05:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205209, Retrieved Sun, 28 Apr 2024 02:05:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-12 12:34:03] [2f2dfc06a630b81f17a3d9dd284f5d45] [Current]
Feedback Forum

Post a new message
Dataseries X:
22.24
22.24
22.25
22.24
22.09
22.09
22.08
22.08
22.05
22.05
22.12
22.11
22.43
22.43
22.39
22.35
22.29
22.29
22.29
22.29
22.26
22.24
22.29
22.19
22.14
22.14
22.22
22.12
22.4
22.4
22.13
22.13
22.08
22.03
21.97
22.06
22.06
22.06
22.05
22.04
22.3
22.27
22.18
22.18
22.13
22.1
21.96
21.95
21.94
21.94
21.84
21.72
21.74
21.65
21.67
21.67
21.68
21.6
21.59
21.52
21.16
21.16
21.15
21.25
21.29
21.22
21.24
21.24
21.25
21.12
21.07
21.04
20.89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205209&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205209&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.962988058725841
beta0.0285777275021911
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.962988058725841 \tabularnewline
beta & 0.0285777275021911 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205209&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]0.962988058725841[/C][/ROW]
[ROW][C]beta[/C][C]0.0285777275021911[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205209&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
alpha0.962988058725841
beta0.0285777275021911
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
322.2522.240.0100000000000016
422.2422.2499050806906-0.00990508069056162
522.0922.2403692184452-0.15036921844521
622.0922.091429906418-0.00142990641796814
722.0822.0858780223084-0.0058780223084085
822.0822.07588089247790.00411910752212563
922.0522.0756242371772-0.0256242371772331
1022.0522.04601991683270.00398008316727427
1122.1222.04503373539660.0749662646034466
1222.1122.1144694713943-0.00446947139426257
1322.4322.10728654229110.322713457708865
1422.4322.42405794462310.0059420553769165
1522.3922.4359457945889-0.0459457945888815
1622.3522.3966018359029-0.0466018359029476
1722.2922.3553436342601-0.0653436342600848
1822.2922.2942390471104-0.00423904711040635
1922.2922.291860789099-0.00186078909896992
2022.2922.2917215562179-0.00172155621789116
2122.2622.2916690256938-0.0316690256937697
2222.2422.2619059077611-0.0219059077610879
2322.2922.24094170500560.0490582949943672
2422.1922.2896652668857-0.099665266885701
2522.1422.1924270254498-0.0524270254498447
2622.1422.139235854150.000764145850030928
2722.2222.13728817494320.0827118250568013
2822.1222.2165313625328-0.0965313625328292
2922.422.12050895677160.27949104322839
3022.422.39428323396860.00571676603137306
3122.1322.4045734768989-0.274573476898858
3222.1322.1373912979893-0.00739129798927607
3322.0822.127298958277-0.0472989582769578
3422.0322.0774743504355-0.0474743504355217
3521.9722.0261743474254-0.0561743474253973
3622.0621.96495043258160.0950495674183642
3722.0622.05196910700340.00803089299658311
3822.0622.05541084732910.00458915267090276
3922.0522.0556645263488-0.00566452634881998
4022.0422.0458881470909-0.00588814709091068
4122.322.03573438185990.264265618140087
4222.2722.2930080591073-0.0230080591073083
4322.1822.2730074335549-0.0930074335548881
4422.1822.183038680759-0.00303868075896219
4522.1322.1796251380381-0.0496251380380954
4622.122.1299837089476-0.0299837089476327
4721.9622.0984315895476-0.138431589547626
4821.9521.9586358173613-0.00863581736133412
4921.9421.9435941660805-0.00359416608054275
5021.9421.93330865329180.00669134670824789
5121.8421.933112112427-0.0931121124269723
5221.7221.8342435858996-0.114243585899594
5321.7421.71188171809070.0281182819093111
5421.6521.7273864444083-0.0773864444082761
5521.6721.63916170339340.0308382966066425
5621.6721.65600476587570.0139952341243159
5721.6821.65701330930280.0229866906971665
5821.621.6673131120056-0.0673131120056283
5921.5921.58880282546260.0011971745374133
6021.5221.576300073016-0.0563000730160148
6121.1621.5068787791749-0.346878779174901
6221.1621.14808755359660.0119124464034215
6321.1521.13513582447390.0148641755261316
6421.2521.1254356375130.12456436248705
6521.2921.22480343317780.0651965668222019
6621.2221.268794960737-0.0487949607369558
6721.2421.20167117063720.0383288293628112
6821.2421.21950135981440.0204986401855578
6921.2521.22072541251880.0292745874811651
7021.1221.2312062346228-0.111206234622795
7121.0721.1033453058351-0.0333453058350592
7221.0421.0495458585502-0.00954585855017598
7320.8921.018402292679-0.128402292678999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 22.25 & 22.24 & 0.0100000000000016 \tabularnewline
4 & 22.24 & 22.2499050806906 & -0.00990508069056162 \tabularnewline
5 & 22.09 & 22.2403692184452 & -0.15036921844521 \tabularnewline
6 & 22.09 & 22.091429906418 & -0.00142990641796814 \tabularnewline
7 & 22.08 & 22.0858780223084 & -0.0058780223084085 \tabularnewline
8 & 22.08 & 22.0758808924779 & 0.00411910752212563 \tabularnewline
9 & 22.05 & 22.0756242371772 & -0.0256242371772331 \tabularnewline
10 & 22.05 & 22.0460199168327 & 0.00398008316727427 \tabularnewline
11 & 22.12 & 22.0450337353966 & 0.0749662646034466 \tabularnewline
12 & 22.11 & 22.1144694713943 & -0.00446947139426257 \tabularnewline
13 & 22.43 & 22.1072865422911 & 0.322713457708865 \tabularnewline
14 & 22.43 & 22.4240579446231 & 0.0059420553769165 \tabularnewline
15 & 22.39 & 22.4359457945889 & -0.0459457945888815 \tabularnewline
16 & 22.35 & 22.3966018359029 & -0.0466018359029476 \tabularnewline
17 & 22.29 & 22.3553436342601 & -0.0653436342600848 \tabularnewline
18 & 22.29 & 22.2942390471104 & -0.00423904711040635 \tabularnewline
19 & 22.29 & 22.291860789099 & -0.00186078909896992 \tabularnewline
20 & 22.29 & 22.2917215562179 & -0.00172155621789116 \tabularnewline
21 & 22.26 & 22.2916690256938 & -0.0316690256937697 \tabularnewline
22 & 22.24 & 22.2619059077611 & -0.0219059077610879 \tabularnewline
23 & 22.29 & 22.2409417050056 & 0.0490582949943672 \tabularnewline
24 & 22.19 & 22.2896652668857 & -0.099665266885701 \tabularnewline
25 & 22.14 & 22.1924270254498 & -0.0524270254498447 \tabularnewline
26 & 22.14 & 22.13923585415 & 0.000764145850030928 \tabularnewline
27 & 22.22 & 22.1372881749432 & 0.0827118250568013 \tabularnewline
28 & 22.12 & 22.2165313625328 & -0.0965313625328292 \tabularnewline
29 & 22.4 & 22.1205089567716 & 0.27949104322839 \tabularnewline
30 & 22.4 & 22.3942832339686 & 0.00571676603137306 \tabularnewline
31 & 22.13 & 22.4045734768989 & -0.274573476898858 \tabularnewline
32 & 22.13 & 22.1373912979893 & -0.00739129798927607 \tabularnewline
33 & 22.08 & 22.127298958277 & -0.0472989582769578 \tabularnewline
34 & 22.03 & 22.0774743504355 & -0.0474743504355217 \tabularnewline
35 & 21.97 & 22.0261743474254 & -0.0561743474253973 \tabularnewline
36 & 22.06 & 21.9649504325816 & 0.0950495674183642 \tabularnewline
37 & 22.06 & 22.0519691070034 & 0.00803089299658311 \tabularnewline
38 & 22.06 & 22.0554108473291 & 0.00458915267090276 \tabularnewline
39 & 22.05 & 22.0556645263488 & -0.00566452634881998 \tabularnewline
40 & 22.04 & 22.0458881470909 & -0.00588814709091068 \tabularnewline
41 & 22.3 & 22.0357343818599 & 0.264265618140087 \tabularnewline
42 & 22.27 & 22.2930080591073 & -0.0230080591073083 \tabularnewline
43 & 22.18 & 22.2730074335549 & -0.0930074335548881 \tabularnewline
44 & 22.18 & 22.183038680759 & -0.00303868075896219 \tabularnewline
45 & 22.13 & 22.1796251380381 & -0.0496251380380954 \tabularnewline
46 & 22.1 & 22.1299837089476 & -0.0299837089476327 \tabularnewline
47 & 21.96 & 22.0984315895476 & -0.138431589547626 \tabularnewline
48 & 21.95 & 21.9586358173613 & -0.00863581736133412 \tabularnewline
49 & 21.94 & 21.9435941660805 & -0.00359416608054275 \tabularnewline
50 & 21.94 & 21.9333086532918 & 0.00669134670824789 \tabularnewline
51 & 21.84 & 21.933112112427 & -0.0931121124269723 \tabularnewline
52 & 21.72 & 21.8342435858996 & -0.114243585899594 \tabularnewline
53 & 21.74 & 21.7118817180907 & 0.0281182819093111 \tabularnewline
54 & 21.65 & 21.7273864444083 & -0.0773864444082761 \tabularnewline
55 & 21.67 & 21.6391617033934 & 0.0308382966066425 \tabularnewline
56 & 21.67 & 21.6560047658757 & 0.0139952341243159 \tabularnewline
57 & 21.68 & 21.6570133093028 & 0.0229866906971665 \tabularnewline
58 & 21.6 & 21.6673131120056 & -0.0673131120056283 \tabularnewline
59 & 21.59 & 21.5888028254626 & 0.0011971745374133 \tabularnewline
60 & 21.52 & 21.576300073016 & -0.0563000730160148 \tabularnewline
61 & 21.16 & 21.5068787791749 & -0.346878779174901 \tabularnewline
62 & 21.16 & 21.1480875535966 & 0.0119124464034215 \tabularnewline
63 & 21.15 & 21.1351358244739 & 0.0148641755261316 \tabularnewline
64 & 21.25 & 21.125435637513 & 0.12456436248705 \tabularnewline
65 & 21.29 & 21.2248034331778 & 0.0651965668222019 \tabularnewline
66 & 21.22 & 21.268794960737 & -0.0487949607369558 \tabularnewline
67 & 21.24 & 21.2016711706372 & 0.0383288293628112 \tabularnewline
68 & 21.24 & 21.2195013598144 & 0.0204986401855578 \tabularnewline
69 & 21.25 & 21.2207254125188 & 0.0292745874811651 \tabularnewline
70 & 21.12 & 21.2312062346228 & -0.111206234622795 \tabularnewline
71 & 21.07 & 21.1033453058351 & -0.0333453058350592 \tabularnewline
72 & 21.04 & 21.0495458585502 & -0.00954585855017598 \tabularnewline
73 & 20.89 & 21.018402292679 & -0.128402292678999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205209&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]22.25[/C][C]22.24[/C][C]0.0100000000000016[/C][/ROW]
[ROW][C]4[/C][C]22.24[/C][C]22.2499050806906[/C][C]-0.00990508069056162[/C][/ROW]
[ROW][C]5[/C][C]22.09[/C][C]22.2403692184452[/C][C]-0.15036921844521[/C][/ROW]
[ROW][C]6[/C][C]22.09[/C][C]22.091429906418[/C][C]-0.00142990641796814[/C][/ROW]
[ROW][C]7[/C][C]22.08[/C][C]22.0858780223084[/C][C]-0.0058780223084085[/C][/ROW]
[ROW][C]8[/C][C]22.08[/C][C]22.0758808924779[/C][C]0.00411910752212563[/C][/ROW]
[ROW][C]9[/C][C]22.05[/C][C]22.0756242371772[/C][C]-0.0256242371772331[/C][/ROW]
[ROW][C]10[/C][C]22.05[/C][C]22.0460199168327[/C][C]0.00398008316727427[/C][/ROW]
[ROW][C]11[/C][C]22.12[/C][C]22.0450337353966[/C][C]0.0749662646034466[/C][/ROW]
[ROW][C]12[/C][C]22.11[/C][C]22.1144694713943[/C][C]-0.00446947139426257[/C][/ROW]
[ROW][C]13[/C][C]22.43[/C][C]22.1072865422911[/C][C]0.322713457708865[/C][/ROW]
[ROW][C]14[/C][C]22.43[/C][C]22.4240579446231[/C][C]0.0059420553769165[/C][/ROW]
[ROW][C]15[/C][C]22.39[/C][C]22.4359457945889[/C][C]-0.0459457945888815[/C][/ROW]
[ROW][C]16[/C][C]22.35[/C][C]22.3966018359029[/C][C]-0.0466018359029476[/C][/ROW]
[ROW][C]17[/C][C]22.29[/C][C]22.3553436342601[/C][C]-0.0653436342600848[/C][/ROW]
[ROW][C]18[/C][C]22.29[/C][C]22.2942390471104[/C][C]-0.00423904711040635[/C][/ROW]
[ROW][C]19[/C][C]22.29[/C][C]22.291860789099[/C][C]-0.00186078909896992[/C][/ROW]
[ROW][C]20[/C][C]22.29[/C][C]22.2917215562179[/C][C]-0.00172155621789116[/C][/ROW]
[ROW][C]21[/C][C]22.26[/C][C]22.2916690256938[/C][C]-0.0316690256937697[/C][/ROW]
[ROW][C]22[/C][C]22.24[/C][C]22.2619059077611[/C][C]-0.0219059077610879[/C][/ROW]
[ROW][C]23[/C][C]22.29[/C][C]22.2409417050056[/C][C]0.0490582949943672[/C][/ROW]
[ROW][C]24[/C][C]22.19[/C][C]22.2896652668857[/C][C]-0.099665266885701[/C][/ROW]
[ROW][C]25[/C][C]22.14[/C][C]22.1924270254498[/C][C]-0.0524270254498447[/C][/ROW]
[ROW][C]26[/C][C]22.14[/C][C]22.13923585415[/C][C]0.000764145850030928[/C][/ROW]
[ROW][C]27[/C][C]22.22[/C][C]22.1372881749432[/C][C]0.0827118250568013[/C][/ROW]
[ROW][C]28[/C][C]22.12[/C][C]22.2165313625328[/C][C]-0.0965313625328292[/C][/ROW]
[ROW][C]29[/C][C]22.4[/C][C]22.1205089567716[/C][C]0.27949104322839[/C][/ROW]
[ROW][C]30[/C][C]22.4[/C][C]22.3942832339686[/C][C]0.00571676603137306[/C][/ROW]
[ROW][C]31[/C][C]22.13[/C][C]22.4045734768989[/C][C]-0.274573476898858[/C][/ROW]
[ROW][C]32[/C][C]22.13[/C][C]22.1373912979893[/C][C]-0.00739129798927607[/C][/ROW]
[ROW][C]33[/C][C]22.08[/C][C]22.127298958277[/C][C]-0.0472989582769578[/C][/ROW]
[ROW][C]34[/C][C]22.03[/C][C]22.0774743504355[/C][C]-0.0474743504355217[/C][/ROW]
[ROW][C]35[/C][C]21.97[/C][C]22.0261743474254[/C][C]-0.0561743474253973[/C][/ROW]
[ROW][C]36[/C][C]22.06[/C][C]21.9649504325816[/C][C]0.0950495674183642[/C][/ROW]
[ROW][C]37[/C][C]22.06[/C][C]22.0519691070034[/C][C]0.00803089299658311[/C][/ROW]
[ROW][C]38[/C][C]22.06[/C][C]22.0554108473291[/C][C]0.00458915267090276[/C][/ROW]
[ROW][C]39[/C][C]22.05[/C][C]22.0556645263488[/C][C]-0.00566452634881998[/C][/ROW]
[ROW][C]40[/C][C]22.04[/C][C]22.0458881470909[/C][C]-0.00588814709091068[/C][/ROW]
[ROW][C]41[/C][C]22.3[/C][C]22.0357343818599[/C][C]0.264265618140087[/C][/ROW]
[ROW][C]42[/C][C]22.27[/C][C]22.2930080591073[/C][C]-0.0230080591073083[/C][/ROW]
[ROW][C]43[/C][C]22.18[/C][C]22.2730074335549[/C][C]-0.0930074335548881[/C][/ROW]
[ROW][C]44[/C][C]22.18[/C][C]22.183038680759[/C][C]-0.00303868075896219[/C][/ROW]
[ROW][C]45[/C][C]22.13[/C][C]22.1796251380381[/C][C]-0.0496251380380954[/C][/ROW]
[ROW][C]46[/C][C]22.1[/C][C]22.1299837089476[/C][C]-0.0299837089476327[/C][/ROW]
[ROW][C]47[/C][C]21.96[/C][C]22.0984315895476[/C][C]-0.138431589547626[/C][/ROW]
[ROW][C]48[/C][C]21.95[/C][C]21.9586358173613[/C][C]-0.00863581736133412[/C][/ROW]
[ROW][C]49[/C][C]21.94[/C][C]21.9435941660805[/C][C]-0.00359416608054275[/C][/ROW]
[ROW][C]50[/C][C]21.94[/C][C]21.9333086532918[/C][C]0.00669134670824789[/C][/ROW]
[ROW][C]51[/C][C]21.84[/C][C]21.933112112427[/C][C]-0.0931121124269723[/C][/ROW]
[ROW][C]52[/C][C]21.72[/C][C]21.8342435858996[/C][C]-0.114243585899594[/C][/ROW]
[ROW][C]53[/C][C]21.74[/C][C]21.7118817180907[/C][C]0.0281182819093111[/C][/ROW]
[ROW][C]54[/C][C]21.65[/C][C]21.7273864444083[/C][C]-0.0773864444082761[/C][/ROW]
[ROW][C]55[/C][C]21.67[/C][C]21.6391617033934[/C][C]0.0308382966066425[/C][/ROW]
[ROW][C]56[/C][C]21.67[/C][C]21.6560047658757[/C][C]0.0139952341243159[/C][/ROW]
[ROW][C]57[/C][C]21.68[/C][C]21.6570133093028[/C][C]0.0229866906971665[/C][/ROW]
[ROW][C]58[/C][C]21.6[/C][C]21.6673131120056[/C][C]-0.0673131120056283[/C][/ROW]
[ROW][C]59[/C][C]21.59[/C][C]21.5888028254626[/C][C]0.0011971745374133[/C][/ROW]
[ROW][C]60[/C][C]21.52[/C][C]21.576300073016[/C][C]-0.0563000730160148[/C][/ROW]
[ROW][C]61[/C][C]21.16[/C][C]21.5068787791749[/C][C]-0.346878779174901[/C][/ROW]
[ROW][C]62[/C][C]21.16[/C][C]21.1480875535966[/C][C]0.0119124464034215[/C][/ROW]
[ROW][C]63[/C][C]21.15[/C][C]21.1351358244739[/C][C]0.0148641755261316[/C][/ROW]
[ROW][C]64[/C][C]21.25[/C][C]21.125435637513[/C][C]0.12456436248705[/C][/ROW]
[ROW][C]65[/C][C]21.29[/C][C]21.2248034331778[/C][C]0.0651965668222019[/C][/ROW]
[ROW][C]66[/C][C]21.22[/C][C]21.268794960737[/C][C]-0.0487949607369558[/C][/ROW]
[ROW][C]67[/C][C]21.24[/C][C]21.2016711706372[/C][C]0.0383288293628112[/C][/ROW]
[ROW][C]68[/C][C]21.24[/C][C]21.2195013598144[/C][C]0.0204986401855578[/C][/ROW]
[ROW][C]69[/C][C]21.25[/C][C]21.2207254125188[/C][C]0.0292745874811651[/C][/ROW]
[ROW][C]70[/C][C]21.12[/C][C]21.2312062346228[/C][C]-0.111206234622795[/C][/ROW]
[ROW][C]71[/C][C]21.07[/C][C]21.1033453058351[/C][C]-0.0333453058350592[/C][/ROW]
[ROW][C]72[/C][C]21.04[/C][C]21.0495458585502[/C][C]-0.00954585855017598[/C][/ROW]
[ROW][C]73[/C][C]20.89[/C][C]21.018402292679[/C][C]-0.128402292678999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205209&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205209&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
322.2522.240.0100000000000016
422.2422.2499050806906-0.00990508069056162
522.0922.2403692184452-0.15036921844521
622.0922.091429906418-0.00142990641796814
722.0822.0858780223084-0.0058780223084085
822.0822.07588089247790.00411910752212563
922.0522.0756242371772-0.0256242371772331
1022.0522.04601991683270.00398008316727427
1122.1222.04503373539660.0749662646034466
1222.1122.1144694713943-0.00446947139426257
1322.4322.10728654229110.322713457708865
1422.4322.42405794462310.0059420553769165
1522.3922.4359457945889-0.0459457945888815
1622.3522.3966018359029-0.0466018359029476
1722.2922.3553436342601-0.0653436342600848
1822.2922.2942390471104-0.00423904711040635
1922.2922.291860789099-0.00186078909896992
2022.2922.2917215562179-0.00172155621789116
2122.2622.2916690256938-0.0316690256937697
2222.2422.2619059077611-0.0219059077610879
2322.2922.24094170500560.0490582949943672
2422.1922.2896652668857-0.099665266885701
2522.1422.1924270254498-0.0524270254498447
2622.1422.139235854150.000764145850030928
2722.2222.13728817494320.0827118250568013
2822.1222.2165313625328-0.0965313625328292
2922.422.12050895677160.27949104322839
3022.422.39428323396860.00571676603137306
3122.1322.4045734768989-0.274573476898858
3222.1322.1373912979893-0.00739129798927607
3322.0822.127298958277-0.0472989582769578
3422.0322.0774743504355-0.0474743504355217
3521.9722.0261743474254-0.0561743474253973
3622.0621.96495043258160.0950495674183642
3722.0622.05196910700340.00803089299658311
3822.0622.05541084732910.00458915267090276
3922.0522.0556645263488-0.00566452634881998
4022.0422.0458881470909-0.00588814709091068
4122.322.03573438185990.264265618140087
4222.2722.2930080591073-0.0230080591073083
4322.1822.2730074335549-0.0930074335548881
4422.1822.183038680759-0.00303868075896219
4522.1322.1796251380381-0.0496251380380954
4622.122.1299837089476-0.0299837089476327
4721.9622.0984315895476-0.138431589547626
4821.9521.9586358173613-0.00863581736133412
4921.9421.9435941660805-0.00359416608054275
5021.9421.93330865329180.00669134670824789
5121.8421.933112112427-0.0931121124269723
5221.7221.8342435858996-0.114243585899594
5321.7421.71188171809070.0281182819093111
5421.6521.7273864444083-0.0773864444082761
5521.6721.63916170339340.0308382966066425
5621.6721.65600476587570.0139952341243159
5721.6821.65701330930280.0229866906971665
5821.621.6673131120056-0.0673131120056283
5921.5921.58880282546260.0011971745374133
6021.5221.576300073016-0.0563000730160148
6121.1621.5068787791749-0.346878779174901
6221.1621.14808755359660.0119124464034215
6321.1521.13513582447390.0148641755261316
6421.2521.1254356375130.12456436248705
6521.2921.22480343317780.0651965668222019
6621.2221.268794960737-0.0487949607369558
6721.2421.20167117063720.0383288293628112
6821.2421.21950135981440.0204986401855578
6921.2521.22072541251880.0292745874811651
7021.1221.2312062346228-0.111206234622795
7121.0721.1033453058351-0.0333453058350592
7221.0421.0495458585502-0.00954585855017598
7320.8921.018402292679-0.128402292678999







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7420.869267767618120.680661083537421.0578744516988
7520.843783117120120.578315860281821.1092503739584
7620.818298466622120.490671370311621.1459255629325
7720.792813816124120.410418324078321.1752093081698
7820.767329165626120.334677873636921.1999804576152
7920.74184451512820.261973823887221.2217152063689
8020.7163598646320.191434714156721.2412850151034
8120.69087521413220.122498031243121.2592523970209
8220.66539056363420.05477743954821.27600368772
8320.63990591313619.987995189848121.2918166364239
8420.61442126263819.921944465026721.3068980602493
8520.5889366121419.856466925880321.3214062983996

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 20.8692677676181 & 20.6806610835374 & 21.0578744516988 \tabularnewline
75 & 20.8437831171201 & 20.5783158602818 & 21.1092503739584 \tabularnewline
76 & 20.8182984666221 & 20.4906713703116 & 21.1459255629325 \tabularnewline
77 & 20.7928138161241 & 20.4104183240783 & 21.1752093081698 \tabularnewline
78 & 20.7673291656261 & 20.3346778736369 & 21.1999804576152 \tabularnewline
79 & 20.741844515128 & 20.2619738238872 & 21.2217152063689 \tabularnewline
80 & 20.71635986463 & 20.1914347141567 & 21.2412850151034 \tabularnewline
81 & 20.690875214132 & 20.1224980312431 & 21.2592523970209 \tabularnewline
82 & 20.665390563634 & 20.054777439548 & 21.27600368772 \tabularnewline
83 & 20.639905913136 & 19.9879951898481 & 21.2918166364239 \tabularnewline
84 & 20.614421262638 & 19.9219444650267 & 21.3068980602493 \tabularnewline
85 & 20.58893661214 & 19.8564669258803 & 21.3214062983996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205209&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]20.8692677676181[/C][C]20.6806610835374[/C][C]21.0578744516988[/C][/ROW]
[ROW][C]75[/C][C]20.8437831171201[/C][C]20.5783158602818[/C][C]21.1092503739584[/C][/ROW]
[ROW][C]76[/C][C]20.8182984666221[/C][C]20.4906713703116[/C][C]21.1459255629325[/C][/ROW]
[ROW][C]77[/C][C]20.7928138161241[/C][C]20.4104183240783[/C][C]21.1752093081698[/C][/ROW]
[ROW][C]78[/C][C]20.7673291656261[/C][C]20.3346778736369[/C][C]21.1999804576152[/C][/ROW]
[ROW][C]79[/C][C]20.741844515128[/C][C]20.2619738238872[/C][C]21.2217152063689[/C][/ROW]
[ROW][C]80[/C][C]20.71635986463[/C][C]20.1914347141567[/C][C]21.2412850151034[/C][/ROW]
[ROW][C]81[/C][C]20.690875214132[/C][C]20.1224980312431[/C][C]21.2592523970209[/C][/ROW]
[ROW][C]82[/C][C]20.665390563634[/C][C]20.054777439548[/C][C]21.27600368772[/C][/ROW]
[ROW][C]83[/C][C]20.639905913136[/C][C]19.9879951898481[/C][C]21.2918166364239[/C][/ROW]
[ROW][C]84[/C][C]20.614421262638[/C][C]19.9219444650267[/C][C]21.3068980602493[/C][/ROW]
[ROW][C]85[/C][C]20.58893661214[/C][C]19.8564669258803[/C][C]21.3214062983996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205209&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205209&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
7420.869267767618120.680661083537421.0578744516988
7520.843783117120120.578315860281821.1092503739584
7620.818298466622120.490671370311621.1459255629325
7720.792813816124120.410418324078321.1752093081698
7820.767329165626120.334677873636921.1999804576152
7920.74184451512820.261973823887221.2217152063689
8020.7163598646320.191434714156721.2412850151034
8120.69087521413220.122498031243121.2592523970209
8220.66539056363420.05477743954821.27600368772
8320.63990591313619.987995189848121.2918166364239
8420.61442126263819.921944465026721.3068980602493
8520.5889366121419.856466925880321.3214062983996



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')