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 12:29:31 -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/t13580119088nsxipvlv7n7l77.htm/, Retrieved Sun, 28 Apr 2024 03:34:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205248, Retrieved Sun, 28 Apr 2024 03:34:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [spreidingsgrafiek...] [2012-11-26 10:45:18] [358bea9e1e2ce3473e10ce6560281f41]
- RMPD    [Exponential Smoothing] [wijn] [2013-01-12 17:29:31] [e1d4b4fa710e50a76527d953f5a9b7a9] [Current]
Feedback Forum

Post a new message
Dataseries X:
23,15
23,18
23,32
23,37
23,43
23,65
23,76
23,81
23,85
23,83
23,85
23,71
23,74
23,87
24,13
24,23
24,27
24,41
24,39
24,34
24,31
24,34
24,41
24,39
24,54
24,9
25,63
26,7
27,12
27,68
27,84
27,84
27,77
27,8
27,82
27,72
27,87
27,83
28,07
28,05
28,15
28,3
28,41
28,43
28,43
28,29
28,19
27,53
27,92
27,98
27,92
27,89
27,95
28,02
27,97
27,81
27,78
27,56
27,52
27,18
27,18
27,26
27,38
27,31
27,43
27,4
27,32
27,31
27,34
27,3
27,3
26,94




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=205248&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=205248&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205248&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
alpha1
beta0.363567034461946
gamma0.0331063466428148

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.363567034461946 \tabularnewline
gamma & 0.0331063466428148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205248&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]0.363567034461946[/C][/ROW]
[ROW][C]gamma[/C][C]0.0331063466428148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205248&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205248&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
beta0.363567034461946
gamma0.0331063466428148







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323.7423.34551282051280.394487179487182
1423.8724.0209050514619-0.15090505146193
1524.1324.2331242827499-0.103124282749924
1624.2324.2964650264229-0.0664650264228541
1724.2724.3081338672042-0.0381338672041913
1824.4124.4271863168589-0.0171863168588686
1924.3924.4296879386052-0.0396879386051658
2024.3424.4348420457959-0.0948420457959074
2124.3124.3311939377969-0.021193937796923
2224.3424.22640518735020.113594812649808
2324.4124.33645451651550.0735454834844518
2424.3924.27735989651070.11264010348928
2524.5424.47706212489780.0629378751021861
2624.924.75952759483740.140472405162619
2725.6325.30768206393940.322317936060575
2826.725.99569957344020.704300426559801
2927.1227.2575933242282-0.137593324228156
3027.6827.7204855940434-0.0404855940434388
3127.8428.1345163666786-0.294516366678632
3227.8428.2270232579781-0.387023257978104
3327.7728.0671476931405-0.297147693140541
3427.827.8220312542149-0.0220312542148946
3527.8227.8827714164545-0.0627714164545132
3627.7227.7241164653918-0.00411646539183153
3727.8727.80136985427690.0686301457231373
3827.8328.0859048461654-0.25590484616545
3928.0728.089949613474-0.0199496134739654
4028.0528.1635299249979-0.113529924997913
4128.1528.03808752017710.111912479822934
4228.328.27169187525220.0283081247477597
4328.4128.3007337762180.109266223782036
4428.4328.4900427064986-0.0600427064985816
4528.4328.4690464910892-0.0390464910891595
4628.2928.3877671407844-0.0977671407843985
4728.1928.2509722313416-0.0609722313415944
4827.5327.9729714046749-0.442971404674864
4927.9227.33067160472580.589328395274212
5027.9828.0445153150532-0.0645153150531819
5127.9228.2181430066153-0.298143006615252
5227.8927.8905813711879-0.000581371187912794
5327.9527.79620333712250.153796662877468
5428.0228.00503540042170.0149645995782954
5527.9727.94922603551230.0207739644877023
5627.8127.9463620975084-0.136362097508439
5727.7827.71761866743760.0623813325623814
5827.5627.6432151301898-0.0832151301897817
5927.5227.43171085208430.0882891479156811
6027.1827.2679765424339-0.0879765424338537
6127.1827.0747411717990.105258828201027
6227.2627.22259314515230.0374068548477133
6327.3827.4532763777712-0.0732763777711547
6427.3127.3874688357421-0.0774688357421169
6527.4327.22513705420150.204862945798535
6627.427.5125351345432-0.112535134543251
6727.3227.31037106940460.00962893059541869
6827.3127.27345516447950.0365448355204698
6927.3427.25757499528790.0824250047120572
7027.327.25045867648330.049541323516717
7127.327.26722026855760.0327797314424174
7226.9427.1233045649752-0.18330456497522

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 23.74 & 23.3455128205128 & 0.394487179487182 \tabularnewline
14 & 23.87 & 24.0209050514619 & -0.15090505146193 \tabularnewline
15 & 24.13 & 24.2331242827499 & -0.103124282749924 \tabularnewline
16 & 24.23 & 24.2964650264229 & -0.0664650264228541 \tabularnewline
17 & 24.27 & 24.3081338672042 & -0.0381338672041913 \tabularnewline
18 & 24.41 & 24.4271863168589 & -0.0171863168588686 \tabularnewline
19 & 24.39 & 24.4296879386052 & -0.0396879386051658 \tabularnewline
20 & 24.34 & 24.4348420457959 & -0.0948420457959074 \tabularnewline
21 & 24.31 & 24.3311939377969 & -0.021193937796923 \tabularnewline
22 & 24.34 & 24.2264051873502 & 0.113594812649808 \tabularnewline
23 & 24.41 & 24.3364545165155 & 0.0735454834844518 \tabularnewline
24 & 24.39 & 24.2773598965107 & 0.11264010348928 \tabularnewline
25 & 24.54 & 24.4770621248978 & 0.0629378751021861 \tabularnewline
26 & 24.9 & 24.7595275948374 & 0.140472405162619 \tabularnewline
27 & 25.63 & 25.3076820639394 & 0.322317936060575 \tabularnewline
28 & 26.7 & 25.9956995734402 & 0.704300426559801 \tabularnewline
29 & 27.12 & 27.2575933242282 & -0.137593324228156 \tabularnewline
30 & 27.68 & 27.7204855940434 & -0.0404855940434388 \tabularnewline
31 & 27.84 & 28.1345163666786 & -0.294516366678632 \tabularnewline
32 & 27.84 & 28.2270232579781 & -0.387023257978104 \tabularnewline
33 & 27.77 & 28.0671476931405 & -0.297147693140541 \tabularnewline
34 & 27.8 & 27.8220312542149 & -0.0220312542148946 \tabularnewline
35 & 27.82 & 27.8827714164545 & -0.0627714164545132 \tabularnewline
36 & 27.72 & 27.7241164653918 & -0.00411646539183153 \tabularnewline
37 & 27.87 & 27.8013698542769 & 0.0686301457231373 \tabularnewline
38 & 27.83 & 28.0859048461654 & -0.25590484616545 \tabularnewline
39 & 28.07 & 28.089949613474 & -0.0199496134739654 \tabularnewline
40 & 28.05 & 28.1635299249979 & -0.113529924997913 \tabularnewline
41 & 28.15 & 28.0380875201771 & 0.111912479822934 \tabularnewline
42 & 28.3 & 28.2716918752522 & 0.0283081247477597 \tabularnewline
43 & 28.41 & 28.300733776218 & 0.109266223782036 \tabularnewline
44 & 28.43 & 28.4900427064986 & -0.0600427064985816 \tabularnewline
45 & 28.43 & 28.4690464910892 & -0.0390464910891595 \tabularnewline
46 & 28.29 & 28.3877671407844 & -0.0977671407843985 \tabularnewline
47 & 28.19 & 28.2509722313416 & -0.0609722313415944 \tabularnewline
48 & 27.53 & 27.9729714046749 & -0.442971404674864 \tabularnewline
49 & 27.92 & 27.3306716047258 & 0.589328395274212 \tabularnewline
50 & 27.98 & 28.0445153150532 & -0.0645153150531819 \tabularnewline
51 & 27.92 & 28.2181430066153 & -0.298143006615252 \tabularnewline
52 & 27.89 & 27.8905813711879 & -0.000581371187912794 \tabularnewline
53 & 27.95 & 27.7962033371225 & 0.153796662877468 \tabularnewline
54 & 28.02 & 28.0050354004217 & 0.0149645995782954 \tabularnewline
55 & 27.97 & 27.9492260355123 & 0.0207739644877023 \tabularnewline
56 & 27.81 & 27.9463620975084 & -0.136362097508439 \tabularnewline
57 & 27.78 & 27.7176186674376 & 0.0623813325623814 \tabularnewline
58 & 27.56 & 27.6432151301898 & -0.0832151301897817 \tabularnewline
59 & 27.52 & 27.4317108520843 & 0.0882891479156811 \tabularnewline
60 & 27.18 & 27.2679765424339 & -0.0879765424338537 \tabularnewline
61 & 27.18 & 27.074741171799 & 0.105258828201027 \tabularnewline
62 & 27.26 & 27.2225931451523 & 0.0374068548477133 \tabularnewline
63 & 27.38 & 27.4532763777712 & -0.0732763777711547 \tabularnewline
64 & 27.31 & 27.3874688357421 & -0.0774688357421169 \tabularnewline
65 & 27.43 & 27.2251370542015 & 0.204862945798535 \tabularnewline
66 & 27.4 & 27.5125351345432 & -0.112535134543251 \tabularnewline
67 & 27.32 & 27.3103710694046 & 0.00962893059541869 \tabularnewline
68 & 27.31 & 27.2734551644795 & 0.0365448355204698 \tabularnewline
69 & 27.34 & 27.2575749952879 & 0.0824250047120572 \tabularnewline
70 & 27.3 & 27.2504586764833 & 0.049541323516717 \tabularnewline
71 & 27.3 & 27.2672202685576 & 0.0327797314424174 \tabularnewline
72 & 26.94 & 27.1233045649752 & -0.18330456497522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205248&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]23.74[/C][C]23.3455128205128[/C][C]0.394487179487182[/C][/ROW]
[ROW][C]14[/C][C]23.87[/C][C]24.0209050514619[/C][C]-0.15090505146193[/C][/ROW]
[ROW][C]15[/C][C]24.13[/C][C]24.2331242827499[/C][C]-0.103124282749924[/C][/ROW]
[ROW][C]16[/C][C]24.23[/C][C]24.2964650264229[/C][C]-0.0664650264228541[/C][/ROW]
[ROW][C]17[/C][C]24.27[/C][C]24.3081338672042[/C][C]-0.0381338672041913[/C][/ROW]
[ROW][C]18[/C][C]24.41[/C][C]24.4271863168589[/C][C]-0.0171863168588686[/C][/ROW]
[ROW][C]19[/C][C]24.39[/C][C]24.4296879386052[/C][C]-0.0396879386051658[/C][/ROW]
[ROW][C]20[/C][C]24.34[/C][C]24.4348420457959[/C][C]-0.0948420457959074[/C][/ROW]
[ROW][C]21[/C][C]24.31[/C][C]24.3311939377969[/C][C]-0.021193937796923[/C][/ROW]
[ROW][C]22[/C][C]24.34[/C][C]24.2264051873502[/C][C]0.113594812649808[/C][/ROW]
[ROW][C]23[/C][C]24.41[/C][C]24.3364545165155[/C][C]0.0735454834844518[/C][/ROW]
[ROW][C]24[/C][C]24.39[/C][C]24.2773598965107[/C][C]0.11264010348928[/C][/ROW]
[ROW][C]25[/C][C]24.54[/C][C]24.4770621248978[/C][C]0.0629378751021861[/C][/ROW]
[ROW][C]26[/C][C]24.9[/C][C]24.7595275948374[/C][C]0.140472405162619[/C][/ROW]
[ROW][C]27[/C][C]25.63[/C][C]25.3076820639394[/C][C]0.322317936060575[/C][/ROW]
[ROW][C]28[/C][C]26.7[/C][C]25.9956995734402[/C][C]0.704300426559801[/C][/ROW]
[ROW][C]29[/C][C]27.12[/C][C]27.2575933242282[/C][C]-0.137593324228156[/C][/ROW]
[ROW][C]30[/C][C]27.68[/C][C]27.7204855940434[/C][C]-0.0404855940434388[/C][/ROW]
[ROW][C]31[/C][C]27.84[/C][C]28.1345163666786[/C][C]-0.294516366678632[/C][/ROW]
[ROW][C]32[/C][C]27.84[/C][C]28.2270232579781[/C][C]-0.387023257978104[/C][/ROW]
[ROW][C]33[/C][C]27.77[/C][C]28.0671476931405[/C][C]-0.297147693140541[/C][/ROW]
[ROW][C]34[/C][C]27.8[/C][C]27.8220312542149[/C][C]-0.0220312542148946[/C][/ROW]
[ROW][C]35[/C][C]27.82[/C][C]27.8827714164545[/C][C]-0.0627714164545132[/C][/ROW]
[ROW][C]36[/C][C]27.72[/C][C]27.7241164653918[/C][C]-0.00411646539183153[/C][/ROW]
[ROW][C]37[/C][C]27.87[/C][C]27.8013698542769[/C][C]0.0686301457231373[/C][/ROW]
[ROW][C]38[/C][C]27.83[/C][C]28.0859048461654[/C][C]-0.25590484616545[/C][/ROW]
[ROW][C]39[/C][C]28.07[/C][C]28.089949613474[/C][C]-0.0199496134739654[/C][/ROW]
[ROW][C]40[/C][C]28.05[/C][C]28.1635299249979[/C][C]-0.113529924997913[/C][/ROW]
[ROW][C]41[/C][C]28.15[/C][C]28.0380875201771[/C][C]0.111912479822934[/C][/ROW]
[ROW][C]42[/C][C]28.3[/C][C]28.2716918752522[/C][C]0.0283081247477597[/C][/ROW]
[ROW][C]43[/C][C]28.41[/C][C]28.300733776218[/C][C]0.109266223782036[/C][/ROW]
[ROW][C]44[/C][C]28.43[/C][C]28.4900427064986[/C][C]-0.0600427064985816[/C][/ROW]
[ROW][C]45[/C][C]28.43[/C][C]28.4690464910892[/C][C]-0.0390464910891595[/C][/ROW]
[ROW][C]46[/C][C]28.29[/C][C]28.3877671407844[/C][C]-0.0977671407843985[/C][/ROW]
[ROW][C]47[/C][C]28.19[/C][C]28.2509722313416[/C][C]-0.0609722313415944[/C][/ROW]
[ROW][C]48[/C][C]27.53[/C][C]27.9729714046749[/C][C]-0.442971404674864[/C][/ROW]
[ROW][C]49[/C][C]27.92[/C][C]27.3306716047258[/C][C]0.589328395274212[/C][/ROW]
[ROW][C]50[/C][C]27.98[/C][C]28.0445153150532[/C][C]-0.0645153150531819[/C][/ROW]
[ROW][C]51[/C][C]27.92[/C][C]28.2181430066153[/C][C]-0.298143006615252[/C][/ROW]
[ROW][C]52[/C][C]27.89[/C][C]27.8905813711879[/C][C]-0.000581371187912794[/C][/ROW]
[ROW][C]53[/C][C]27.95[/C][C]27.7962033371225[/C][C]0.153796662877468[/C][/ROW]
[ROW][C]54[/C][C]28.02[/C][C]28.0050354004217[/C][C]0.0149645995782954[/C][/ROW]
[ROW][C]55[/C][C]27.97[/C][C]27.9492260355123[/C][C]0.0207739644877023[/C][/ROW]
[ROW][C]56[/C][C]27.81[/C][C]27.9463620975084[/C][C]-0.136362097508439[/C][/ROW]
[ROW][C]57[/C][C]27.78[/C][C]27.7176186674376[/C][C]0.0623813325623814[/C][/ROW]
[ROW][C]58[/C][C]27.56[/C][C]27.6432151301898[/C][C]-0.0832151301897817[/C][/ROW]
[ROW][C]59[/C][C]27.52[/C][C]27.4317108520843[/C][C]0.0882891479156811[/C][/ROW]
[ROW][C]60[/C][C]27.18[/C][C]27.2679765424339[/C][C]-0.0879765424338537[/C][/ROW]
[ROW][C]61[/C][C]27.18[/C][C]27.074741171799[/C][C]0.105258828201027[/C][/ROW]
[ROW][C]62[/C][C]27.26[/C][C]27.2225931451523[/C][C]0.0374068548477133[/C][/ROW]
[ROW][C]63[/C][C]27.38[/C][C]27.4532763777712[/C][C]-0.0732763777711547[/C][/ROW]
[ROW][C]64[/C][C]27.31[/C][C]27.3874688357421[/C][C]-0.0774688357421169[/C][/ROW]
[ROW][C]65[/C][C]27.43[/C][C]27.2251370542015[/C][C]0.204862945798535[/C][/ROW]
[ROW][C]66[/C][C]27.4[/C][C]27.5125351345432[/C][C]-0.112535134543251[/C][/ROW]
[ROW][C]67[/C][C]27.32[/C][C]27.3103710694046[/C][C]0.00962893059541869[/C][/ROW]
[ROW][C]68[/C][C]27.31[/C][C]27.2734551644795[/C][C]0.0365448355204698[/C][/ROW]
[ROW][C]69[/C][C]27.34[/C][C]27.2575749952879[/C][C]0.0824250047120572[/C][/ROW]
[ROW][C]70[/C][C]27.3[/C][C]27.2504586764833[/C][C]0.049541323516717[/C][/ROW]
[ROW][C]71[/C][C]27.3[/C][C]27.2672202685576[/C][C]0.0327797314424174[/C][/ROW]
[ROW][C]72[/C][C]26.94[/C][C]27.1233045649752[/C][C]-0.18330456497522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205248&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205248&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
1323.7423.34551282051280.394487179487182
1423.8724.0209050514619-0.15090505146193
1524.1324.2331242827499-0.103124282749924
1624.2324.2964650264229-0.0664650264228541
1724.2724.3081338672042-0.0381338672041913
1824.4124.4271863168589-0.0171863168588686
1924.3924.4296879386052-0.0396879386051658
2024.3424.4348420457959-0.0948420457959074
2124.3124.3311939377969-0.021193937796923
2224.3424.22640518735020.113594812649808
2324.4124.33645451651550.0735454834844518
2424.3924.27735989651070.11264010348928
2524.5424.47706212489780.0629378751021861
2624.924.75952759483740.140472405162619
2725.6325.30768206393940.322317936060575
2826.725.99569957344020.704300426559801
2927.1227.2575933242282-0.137593324228156
3027.6827.7204855940434-0.0404855940434388
3127.8428.1345163666786-0.294516366678632
3227.8428.2270232579781-0.387023257978104
3327.7728.0671476931405-0.297147693140541
3427.827.8220312542149-0.0220312542148946
3527.8227.8827714164545-0.0627714164545132
3627.7227.7241164653918-0.00411646539183153
3727.8727.80136985427690.0686301457231373
3827.8328.0859048461654-0.25590484616545
3928.0728.089949613474-0.0199496134739654
4028.0528.1635299249979-0.113529924997913
4128.1528.03808752017710.111912479822934
4228.328.27169187525220.0283081247477597
4328.4128.3007337762180.109266223782036
4428.4328.4900427064986-0.0600427064985816
4528.4328.4690464910892-0.0390464910891595
4628.2928.3877671407844-0.0977671407843985
4728.1928.2509722313416-0.0609722313415944
4827.5327.9729714046749-0.442971404674864
4927.9227.33067160472580.589328395274212
5027.9828.0445153150532-0.0645153150531819
5127.9228.2181430066153-0.298143006615252
5227.8927.8905813711879-0.000581371187912794
5327.9527.79620333712250.153796662877468
5428.0228.00503540042170.0149645995782954
5527.9727.94922603551230.0207739644877023
5627.8127.9463620975084-0.136362097508439
5727.7827.71761866743760.0623813325623814
5827.5627.6432151301898-0.0832151301897817
5927.5227.43171085208430.0882891479156811
6027.1827.2679765424339-0.0879765424338537
6127.1827.0747411717990.105258828201027
6227.2627.22259314515230.0374068548477133
6327.3827.4532763777712-0.0732763777711547
6427.3127.3874688357421-0.0774688357421169
6527.4327.22513705420150.204862945798535
6627.427.5125351345432-0.112535134543251
6727.3227.31037106940460.00962893059541869
6827.3127.27345516447950.0365448355204698
6927.3427.25757499528790.0824250047120572
7027.327.25045867648330.049541323516717
7127.327.26722026855760.0327797314424174
7226.9427.1233045649752-0.18330456497522







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326.875411067883926.49983876100627.2509833747617
7426.92040546910126.28533112641527.5554798117871
7527.102483203651526.194692450843528.0102739564596
7627.125394271535425.925128505181628.3256600378892
7727.084138672752625.570774718021528.5975026274836
7827.135799740636425.289107789760728.9824916915121
7927.056210808520324.85668143215829.2557401848825
8027.016205209737424.445109165365829.5873012541091
8126.95703294428823.996395040239529.9176708483365
8226.830777345505123.463323600055130.1982310909552
8326.743271746722322.952371046663730.5341724467809
8426.499932814606222.269540819705930.7303248095064

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 26.8754110678839 & 26.499838761006 & 27.2509833747617 \tabularnewline
74 & 26.920405469101 & 26.285331126415 & 27.5554798117871 \tabularnewline
75 & 27.1024832036515 & 26.1946924508435 & 28.0102739564596 \tabularnewline
76 & 27.1253942715354 & 25.9251285051816 & 28.3256600378892 \tabularnewline
77 & 27.0841386727526 & 25.5707747180215 & 28.5975026274836 \tabularnewline
78 & 27.1357997406364 & 25.2891077897607 & 28.9824916915121 \tabularnewline
79 & 27.0562108085203 & 24.856681432158 & 29.2557401848825 \tabularnewline
80 & 27.0162052097374 & 24.4451091653658 & 29.5873012541091 \tabularnewline
81 & 26.957032944288 & 23.9963950402395 & 29.9176708483365 \tabularnewline
82 & 26.8307773455051 & 23.4633236000551 & 30.1982310909552 \tabularnewline
83 & 26.7432717467223 & 22.9523710466637 & 30.5341724467809 \tabularnewline
84 & 26.4999328146062 & 22.2695408197059 & 30.7303248095064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205248&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]26.8754110678839[/C][C]26.499838761006[/C][C]27.2509833747617[/C][/ROW]
[ROW][C]74[/C][C]26.920405469101[/C][C]26.285331126415[/C][C]27.5554798117871[/C][/ROW]
[ROW][C]75[/C][C]27.1024832036515[/C][C]26.1946924508435[/C][C]28.0102739564596[/C][/ROW]
[ROW][C]76[/C][C]27.1253942715354[/C][C]25.9251285051816[/C][C]28.3256600378892[/C][/ROW]
[ROW][C]77[/C][C]27.0841386727526[/C][C]25.5707747180215[/C][C]28.5975026274836[/C][/ROW]
[ROW][C]78[/C][C]27.1357997406364[/C][C]25.2891077897607[/C][C]28.9824916915121[/C][/ROW]
[ROW][C]79[/C][C]27.0562108085203[/C][C]24.856681432158[/C][C]29.2557401848825[/C][/ROW]
[ROW][C]80[/C][C]27.0162052097374[/C][C]24.4451091653658[/C][C]29.5873012541091[/C][/ROW]
[ROW][C]81[/C][C]26.957032944288[/C][C]23.9963950402395[/C][C]29.9176708483365[/C][/ROW]
[ROW][C]82[/C][C]26.8307773455051[/C][C]23.4633236000551[/C][C]30.1982310909552[/C][/ROW]
[ROW][C]83[/C][C]26.7432717467223[/C][C]22.9523710466637[/C][C]30.5341724467809[/C][/ROW]
[ROW][C]84[/C][C]26.4999328146062[/C][C]22.2695408197059[/C][C]30.7303248095064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205248&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205248&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
7326.875411067883926.49983876100627.2509833747617
7426.92040546910126.28533112641527.5554798117871
7527.102483203651526.194692450843528.0102739564596
7627.125394271535425.925128505181628.3256600378892
7727.084138672752625.570774718021528.5975026274836
7827.135799740636425.289107789760728.9824916915121
7927.056210808520324.85668143215829.2557401848825
8027.016205209737424.445109165365829.5873012541091
8126.95703294428823.996395040239529.9176708483365
8226.830777345505123.463323600055130.1982310909552
8326.743271746722322.952371046663730.5341724467809
8426.499932814606222.269540819705930.7303248095064



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')