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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 12:33:40 -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/28/t121199973749jn8196mprxx2i.htm/, Retrieved Tue, 14 May 2024 07:49:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13465, Retrieved Tue, 14 May 2024 07:49:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsExponentional smooting - Blue Jeans (D) - Alexia Versluys
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponentional smo...] [2008-05-28 18:33:40] [e8c1fcf34dff5578299591fe58b62c2d] [Current]
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Dataseries X:
44,13
44,13
44,17
44,14
44,15
44,14
44,14
44,14
44,19
44,29
44,29
44,29
44,29
44,27
44,26
44,33
44,32
44,34
44,34
44,34
44,37
44,47
44,51
44,51
44,51
44,52
44,7
44,84
44,9
44,95
44,94
44,94
44,91
45,28
45,36
45,34
45,34
45,34
45,44
45,62
45,75
45,77
45,77
45,77
46,09
46,25
46,35
46,34
46,34
46,28
46,59
46,42
46,29
46,29
46,29
46,3
46,52
46,66
46,67
46,72
46,72
46,72
46,76
46,89
47,04
47,02
47,02
47,18
47,22
47,8
47,88
47,91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13465&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13465&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0607904611895088
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0607904611895088 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13465&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]0.0607904611895088[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13465&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
beta0.0607904611895088
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
344.1744.130.0399999999999991
444.1444.1724316184476-0.0324316184475819
544.1544.1404600854050.00953991459496706
644.1444.151040021213-0.0110400212129633
744.1444.1403688932319-0.000368893231886602
844.1444.1403464680422-0.000346468042188519
944.1944.14032540609010.0496745939098773
1044.2944.19334514756330.0966548524367
1144.2944.2992208406191-0.00922084061913608
1244.2944.2986603014653-0.00866030146534058
1344.2944.2981338377452-0.0081338377452198
1444.2744.2976393779974-0.0276393779974455
1544.2644.275959167462-0.0159591674620003
1644.3344.26498900231180.0650109976882192
1744.3244.3389410508436-0.0189410508436367
1844.3444.32778961562740.0122103843725654
1944.3444.3485318905248-0.00853189052475045
2044.3444.3480132329649-0.0080132329649274
2144.3744.34752610483740.0224738951626193
2244.4744.3788923032890.0911076967109707
2344.5144.484430782190.0255692178099949
2444.5144.5259851467329-0.0159851467329304
2544.5144.5250134022909-0.0150134022908546
2644.5244.5241007306416-0.0041007306415608
2744.744.53385144533470.166148554665348
2844.8444.72395169259870.116048307401272
2944.944.87100632272590.0289936772740802
3044.9544.9327688617390.0172311382610175
3144.9444.9838163505807-0.0438163505806983
3244.9444.9711527344213-0.031152734421255
3344.9144.9692589453285-0.0592589453284731
3445.2844.93565656671230.344343433287655
3545.3645.32658936282950.0334106371705118
3645.3445.4086204108717-0.0686204108717092
3745.3445.3844489444478-0.044448944447808
3845.3445.3817468726154-0.0417468726154411
3945.4445.37920906097590.0607909390240664
4045.6245.48290457019530.137095429804653
4145.7545.67123866460010.0787613353998609
4245.7745.806026602503-0.0360266025030000
4345.7745.8238365287218-0.053836528721753
4445.7745.8205637813119-0.0505637813119151
4546.0945.81748998572650.272510014273522
4646.2546.15405599517290.0959440048270679
4746.3546.31988847547470.0301115245252674
4846.3446.4217189689377-0.0817189689377429
4946.3446.4067512351281-0.0667512351280877
5046.2846.4026933967597-0.122693396759686
5146.5946.33523480858580.254765191414251
5246.4246.6607221020669-0.240722102066862
5346.2946.4760884944637-0.186088494463711
5446.2946.3347760890632-0.0447760890631983
5546.2946.3320541299588-0.0420541299587782
5646.346.3294976400037-0.0294976400036688
5746.5246.33770446486380.18229553513617
5846.6646.56878629451760.0912137054824385
5946.6746.7143312177406-0.0443312177406341
6046.7246.7216363025691-0.00163630256909642
6146.7246.7715368309813-0.05153683098127
6246.7246.7684038832577-0.0484038832576701
6346.7646.7654613888711-0.00546138887107617
6446.8946.80512938852290.084870611477136
6547.0446.9402887121360.0997112878640039
6647.0247.0963502073110-0.0763502073110445
6747.0247.0717088429967-0.0517088429966961
6847.1847.06856543858340.111434561416644
6947.2247.2353395969643-0.0153395969643242
7047.847.27440709579040.525592904209603
7147.8847.8863581308352-0.00635813083523118
7247.9147.9659716171295-0.0559716171294653

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 44.17 & 44.13 & 0.0399999999999991 \tabularnewline
4 & 44.14 & 44.1724316184476 & -0.0324316184475819 \tabularnewline
5 & 44.15 & 44.140460085405 & 0.00953991459496706 \tabularnewline
6 & 44.14 & 44.151040021213 & -0.0110400212129633 \tabularnewline
7 & 44.14 & 44.1403688932319 & -0.000368893231886602 \tabularnewline
8 & 44.14 & 44.1403464680422 & -0.000346468042188519 \tabularnewline
9 & 44.19 & 44.1403254060901 & 0.0496745939098773 \tabularnewline
10 & 44.29 & 44.1933451475633 & 0.0966548524367 \tabularnewline
11 & 44.29 & 44.2992208406191 & -0.00922084061913608 \tabularnewline
12 & 44.29 & 44.2986603014653 & -0.00866030146534058 \tabularnewline
13 & 44.29 & 44.2981338377452 & -0.0081338377452198 \tabularnewline
14 & 44.27 & 44.2976393779974 & -0.0276393779974455 \tabularnewline
15 & 44.26 & 44.275959167462 & -0.0159591674620003 \tabularnewline
16 & 44.33 & 44.2649890023118 & 0.0650109976882192 \tabularnewline
17 & 44.32 & 44.3389410508436 & -0.0189410508436367 \tabularnewline
18 & 44.34 & 44.3277896156274 & 0.0122103843725654 \tabularnewline
19 & 44.34 & 44.3485318905248 & -0.00853189052475045 \tabularnewline
20 & 44.34 & 44.3480132329649 & -0.0080132329649274 \tabularnewline
21 & 44.37 & 44.3475261048374 & 0.0224738951626193 \tabularnewline
22 & 44.47 & 44.378892303289 & 0.0911076967109707 \tabularnewline
23 & 44.51 & 44.48443078219 & 0.0255692178099949 \tabularnewline
24 & 44.51 & 44.5259851467329 & -0.0159851467329304 \tabularnewline
25 & 44.51 & 44.5250134022909 & -0.0150134022908546 \tabularnewline
26 & 44.52 & 44.5241007306416 & -0.0041007306415608 \tabularnewline
27 & 44.7 & 44.5338514453347 & 0.166148554665348 \tabularnewline
28 & 44.84 & 44.7239516925987 & 0.116048307401272 \tabularnewline
29 & 44.9 & 44.8710063227259 & 0.0289936772740802 \tabularnewline
30 & 44.95 & 44.932768861739 & 0.0172311382610175 \tabularnewline
31 & 44.94 & 44.9838163505807 & -0.0438163505806983 \tabularnewline
32 & 44.94 & 44.9711527344213 & -0.031152734421255 \tabularnewline
33 & 44.91 & 44.9692589453285 & -0.0592589453284731 \tabularnewline
34 & 45.28 & 44.9356565667123 & 0.344343433287655 \tabularnewline
35 & 45.36 & 45.3265893628295 & 0.0334106371705118 \tabularnewline
36 & 45.34 & 45.4086204108717 & -0.0686204108717092 \tabularnewline
37 & 45.34 & 45.3844489444478 & -0.044448944447808 \tabularnewline
38 & 45.34 & 45.3817468726154 & -0.0417468726154411 \tabularnewline
39 & 45.44 & 45.3792090609759 & 0.0607909390240664 \tabularnewline
40 & 45.62 & 45.4829045701953 & 0.137095429804653 \tabularnewline
41 & 45.75 & 45.6712386646001 & 0.0787613353998609 \tabularnewline
42 & 45.77 & 45.806026602503 & -0.0360266025030000 \tabularnewline
43 & 45.77 & 45.8238365287218 & -0.053836528721753 \tabularnewline
44 & 45.77 & 45.8205637813119 & -0.0505637813119151 \tabularnewline
45 & 46.09 & 45.8174899857265 & 0.272510014273522 \tabularnewline
46 & 46.25 & 46.1540559951729 & 0.0959440048270679 \tabularnewline
47 & 46.35 & 46.3198884754747 & 0.0301115245252674 \tabularnewline
48 & 46.34 & 46.4217189689377 & -0.0817189689377429 \tabularnewline
49 & 46.34 & 46.4067512351281 & -0.0667512351280877 \tabularnewline
50 & 46.28 & 46.4026933967597 & -0.122693396759686 \tabularnewline
51 & 46.59 & 46.3352348085858 & 0.254765191414251 \tabularnewline
52 & 46.42 & 46.6607221020669 & -0.240722102066862 \tabularnewline
53 & 46.29 & 46.4760884944637 & -0.186088494463711 \tabularnewline
54 & 46.29 & 46.3347760890632 & -0.0447760890631983 \tabularnewline
55 & 46.29 & 46.3320541299588 & -0.0420541299587782 \tabularnewline
56 & 46.3 & 46.3294976400037 & -0.0294976400036688 \tabularnewline
57 & 46.52 & 46.3377044648638 & 0.18229553513617 \tabularnewline
58 & 46.66 & 46.5687862945176 & 0.0912137054824385 \tabularnewline
59 & 46.67 & 46.7143312177406 & -0.0443312177406341 \tabularnewline
60 & 46.72 & 46.7216363025691 & -0.00163630256909642 \tabularnewline
61 & 46.72 & 46.7715368309813 & -0.05153683098127 \tabularnewline
62 & 46.72 & 46.7684038832577 & -0.0484038832576701 \tabularnewline
63 & 46.76 & 46.7654613888711 & -0.00546138887107617 \tabularnewline
64 & 46.89 & 46.8051293885229 & 0.084870611477136 \tabularnewline
65 & 47.04 & 46.940288712136 & 0.0997112878640039 \tabularnewline
66 & 47.02 & 47.0963502073110 & -0.0763502073110445 \tabularnewline
67 & 47.02 & 47.0717088429967 & -0.0517088429966961 \tabularnewline
68 & 47.18 & 47.0685654385834 & 0.111434561416644 \tabularnewline
69 & 47.22 & 47.2353395969643 & -0.0153395969643242 \tabularnewline
70 & 47.8 & 47.2744070957904 & 0.525592904209603 \tabularnewline
71 & 47.88 & 47.8863581308352 & -0.00635813083523118 \tabularnewline
72 & 47.91 & 47.9659716171295 & -0.0559716171294653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13465&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]44.17[/C][C]44.13[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]44.14[/C][C]44.1724316184476[/C][C]-0.0324316184475819[/C][/ROW]
[ROW][C]5[/C][C]44.15[/C][C]44.140460085405[/C][C]0.00953991459496706[/C][/ROW]
[ROW][C]6[/C][C]44.14[/C][C]44.151040021213[/C][C]-0.0110400212129633[/C][/ROW]
[ROW][C]7[/C][C]44.14[/C][C]44.1403688932319[/C][C]-0.000368893231886602[/C][/ROW]
[ROW][C]8[/C][C]44.14[/C][C]44.1403464680422[/C][C]-0.000346468042188519[/C][/ROW]
[ROW][C]9[/C][C]44.19[/C][C]44.1403254060901[/C][C]0.0496745939098773[/C][/ROW]
[ROW][C]10[/C][C]44.29[/C][C]44.1933451475633[/C][C]0.0966548524367[/C][/ROW]
[ROW][C]11[/C][C]44.29[/C][C]44.2992208406191[/C][C]-0.00922084061913608[/C][/ROW]
[ROW][C]12[/C][C]44.29[/C][C]44.2986603014653[/C][C]-0.00866030146534058[/C][/ROW]
[ROW][C]13[/C][C]44.29[/C][C]44.2981338377452[/C][C]-0.0081338377452198[/C][/ROW]
[ROW][C]14[/C][C]44.27[/C][C]44.2976393779974[/C][C]-0.0276393779974455[/C][/ROW]
[ROW][C]15[/C][C]44.26[/C][C]44.275959167462[/C][C]-0.0159591674620003[/C][/ROW]
[ROW][C]16[/C][C]44.33[/C][C]44.2649890023118[/C][C]0.0650109976882192[/C][/ROW]
[ROW][C]17[/C][C]44.32[/C][C]44.3389410508436[/C][C]-0.0189410508436367[/C][/ROW]
[ROW][C]18[/C][C]44.34[/C][C]44.3277896156274[/C][C]0.0122103843725654[/C][/ROW]
[ROW][C]19[/C][C]44.34[/C][C]44.3485318905248[/C][C]-0.00853189052475045[/C][/ROW]
[ROW][C]20[/C][C]44.34[/C][C]44.3480132329649[/C][C]-0.0080132329649274[/C][/ROW]
[ROW][C]21[/C][C]44.37[/C][C]44.3475261048374[/C][C]0.0224738951626193[/C][/ROW]
[ROW][C]22[/C][C]44.47[/C][C]44.378892303289[/C][C]0.0911076967109707[/C][/ROW]
[ROW][C]23[/C][C]44.51[/C][C]44.48443078219[/C][C]0.0255692178099949[/C][/ROW]
[ROW][C]24[/C][C]44.51[/C][C]44.5259851467329[/C][C]-0.0159851467329304[/C][/ROW]
[ROW][C]25[/C][C]44.51[/C][C]44.5250134022909[/C][C]-0.0150134022908546[/C][/ROW]
[ROW][C]26[/C][C]44.52[/C][C]44.5241007306416[/C][C]-0.0041007306415608[/C][/ROW]
[ROW][C]27[/C][C]44.7[/C][C]44.5338514453347[/C][C]0.166148554665348[/C][/ROW]
[ROW][C]28[/C][C]44.84[/C][C]44.7239516925987[/C][C]0.116048307401272[/C][/ROW]
[ROW][C]29[/C][C]44.9[/C][C]44.8710063227259[/C][C]0.0289936772740802[/C][/ROW]
[ROW][C]30[/C][C]44.95[/C][C]44.932768861739[/C][C]0.0172311382610175[/C][/ROW]
[ROW][C]31[/C][C]44.94[/C][C]44.9838163505807[/C][C]-0.0438163505806983[/C][/ROW]
[ROW][C]32[/C][C]44.94[/C][C]44.9711527344213[/C][C]-0.031152734421255[/C][/ROW]
[ROW][C]33[/C][C]44.91[/C][C]44.9692589453285[/C][C]-0.0592589453284731[/C][/ROW]
[ROW][C]34[/C][C]45.28[/C][C]44.9356565667123[/C][C]0.344343433287655[/C][/ROW]
[ROW][C]35[/C][C]45.36[/C][C]45.3265893628295[/C][C]0.0334106371705118[/C][/ROW]
[ROW][C]36[/C][C]45.34[/C][C]45.4086204108717[/C][C]-0.0686204108717092[/C][/ROW]
[ROW][C]37[/C][C]45.34[/C][C]45.3844489444478[/C][C]-0.044448944447808[/C][/ROW]
[ROW][C]38[/C][C]45.34[/C][C]45.3817468726154[/C][C]-0.0417468726154411[/C][/ROW]
[ROW][C]39[/C][C]45.44[/C][C]45.3792090609759[/C][C]0.0607909390240664[/C][/ROW]
[ROW][C]40[/C][C]45.62[/C][C]45.4829045701953[/C][C]0.137095429804653[/C][/ROW]
[ROW][C]41[/C][C]45.75[/C][C]45.6712386646001[/C][C]0.0787613353998609[/C][/ROW]
[ROW][C]42[/C][C]45.77[/C][C]45.806026602503[/C][C]-0.0360266025030000[/C][/ROW]
[ROW][C]43[/C][C]45.77[/C][C]45.8238365287218[/C][C]-0.053836528721753[/C][/ROW]
[ROW][C]44[/C][C]45.77[/C][C]45.8205637813119[/C][C]-0.0505637813119151[/C][/ROW]
[ROW][C]45[/C][C]46.09[/C][C]45.8174899857265[/C][C]0.272510014273522[/C][/ROW]
[ROW][C]46[/C][C]46.25[/C][C]46.1540559951729[/C][C]0.0959440048270679[/C][/ROW]
[ROW][C]47[/C][C]46.35[/C][C]46.3198884754747[/C][C]0.0301115245252674[/C][/ROW]
[ROW][C]48[/C][C]46.34[/C][C]46.4217189689377[/C][C]-0.0817189689377429[/C][/ROW]
[ROW][C]49[/C][C]46.34[/C][C]46.4067512351281[/C][C]-0.0667512351280877[/C][/ROW]
[ROW][C]50[/C][C]46.28[/C][C]46.4026933967597[/C][C]-0.122693396759686[/C][/ROW]
[ROW][C]51[/C][C]46.59[/C][C]46.3352348085858[/C][C]0.254765191414251[/C][/ROW]
[ROW][C]52[/C][C]46.42[/C][C]46.6607221020669[/C][C]-0.240722102066862[/C][/ROW]
[ROW][C]53[/C][C]46.29[/C][C]46.4760884944637[/C][C]-0.186088494463711[/C][/ROW]
[ROW][C]54[/C][C]46.29[/C][C]46.3347760890632[/C][C]-0.0447760890631983[/C][/ROW]
[ROW][C]55[/C][C]46.29[/C][C]46.3320541299588[/C][C]-0.0420541299587782[/C][/ROW]
[ROW][C]56[/C][C]46.3[/C][C]46.3294976400037[/C][C]-0.0294976400036688[/C][/ROW]
[ROW][C]57[/C][C]46.52[/C][C]46.3377044648638[/C][C]0.18229553513617[/C][/ROW]
[ROW][C]58[/C][C]46.66[/C][C]46.5687862945176[/C][C]0.0912137054824385[/C][/ROW]
[ROW][C]59[/C][C]46.67[/C][C]46.7143312177406[/C][C]-0.0443312177406341[/C][/ROW]
[ROW][C]60[/C][C]46.72[/C][C]46.7216363025691[/C][C]-0.00163630256909642[/C][/ROW]
[ROW][C]61[/C][C]46.72[/C][C]46.7715368309813[/C][C]-0.05153683098127[/C][/ROW]
[ROW][C]62[/C][C]46.72[/C][C]46.7684038832577[/C][C]-0.0484038832576701[/C][/ROW]
[ROW][C]63[/C][C]46.76[/C][C]46.7654613888711[/C][C]-0.00546138887107617[/C][/ROW]
[ROW][C]64[/C][C]46.89[/C][C]46.8051293885229[/C][C]0.084870611477136[/C][/ROW]
[ROW][C]65[/C][C]47.04[/C][C]46.940288712136[/C][C]0.0997112878640039[/C][/ROW]
[ROW][C]66[/C][C]47.02[/C][C]47.0963502073110[/C][C]-0.0763502073110445[/C][/ROW]
[ROW][C]67[/C][C]47.02[/C][C]47.0717088429967[/C][C]-0.0517088429966961[/C][/ROW]
[ROW][C]68[/C][C]47.18[/C][C]47.0685654385834[/C][C]0.111434561416644[/C][/ROW]
[ROW][C]69[/C][C]47.22[/C][C]47.2353395969643[/C][C]-0.0153395969643242[/C][/ROW]
[ROW][C]70[/C][C]47.8[/C][C]47.2744070957904[/C][C]0.525592904209603[/C][/ROW]
[ROW][C]71[/C][C]47.88[/C][C]47.8863581308352[/C][C]-0.00635813083523118[/C][/ROW]
[ROW][C]72[/C][C]47.91[/C][C]47.9659716171295[/C][C]-0.0559716171294653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13465&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13465&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
344.1744.130.0399999999999991
444.1444.1724316184476-0.0324316184475819
544.1544.1404600854050.00953991459496706
644.1444.151040021213-0.0110400212129633
744.1444.1403688932319-0.000368893231886602
844.1444.1403464680422-0.000346468042188519
944.1944.14032540609010.0496745939098773
1044.2944.19334514756330.0966548524367
1144.2944.2992208406191-0.00922084061913608
1244.2944.2986603014653-0.00866030146534058
1344.2944.2981338377452-0.0081338377452198
1444.2744.2976393779974-0.0276393779974455
1544.2644.275959167462-0.0159591674620003
1644.3344.26498900231180.0650109976882192
1744.3244.3389410508436-0.0189410508436367
1844.3444.32778961562740.0122103843725654
1944.3444.3485318905248-0.00853189052475045
2044.3444.3480132329649-0.0080132329649274
2144.3744.34752610483740.0224738951626193
2244.4744.3788923032890.0911076967109707
2344.5144.484430782190.0255692178099949
2444.5144.5259851467329-0.0159851467329304
2544.5144.5250134022909-0.0150134022908546
2644.5244.5241007306416-0.0041007306415608
2744.744.53385144533470.166148554665348
2844.8444.72395169259870.116048307401272
2944.944.87100632272590.0289936772740802
3044.9544.9327688617390.0172311382610175
3144.9444.9838163505807-0.0438163505806983
3244.9444.9711527344213-0.031152734421255
3344.9144.9692589453285-0.0592589453284731
3445.2844.93565656671230.344343433287655
3545.3645.32658936282950.0334106371705118
3645.3445.4086204108717-0.0686204108717092
3745.3445.3844489444478-0.044448944447808
3845.3445.3817468726154-0.0417468726154411
3945.4445.37920906097590.0607909390240664
4045.6245.48290457019530.137095429804653
4145.7545.67123866460010.0787613353998609
4245.7745.806026602503-0.0360266025030000
4345.7745.8238365287218-0.053836528721753
4445.7745.8205637813119-0.0505637813119151
4546.0945.81748998572650.272510014273522
4646.2546.15405599517290.0959440048270679
4746.3546.31988847547470.0301115245252674
4846.3446.4217189689377-0.0817189689377429
4946.3446.4067512351281-0.0667512351280877
5046.2846.4026933967597-0.122693396759686
5146.5946.33523480858580.254765191414251
5246.4246.6607221020669-0.240722102066862
5346.2946.4760884944637-0.186088494463711
5446.2946.3347760890632-0.0447760890631983
5546.2946.3320541299588-0.0420541299587782
5646.346.3294976400037-0.0294976400036688
5746.5246.33770446486380.18229553513617
5846.6646.56878629451760.0912137054824385
5946.6746.7143312177406-0.0443312177406341
6046.7246.7216363025691-0.00163630256909642
6146.7246.7715368309813-0.05153683098127
6246.7246.7684038832577-0.0484038832576701
6346.7646.7654613888711-0.00546138887107617
6446.8946.80512938852290.084870611477136
6547.0446.9402887121360.0997112878640039
6647.0247.0963502073110-0.0763502073110445
6747.0247.0717088429967-0.0517088429966961
6847.1847.06856543858340.111434561416644
6947.2247.2353395969643-0.0153395969643242
7047.847.27440709579040.525592904209603
7147.8847.8863581308352-0.00635813083523118
7247.9147.9659716171295-0.0559716171294653







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7347.992569076710647.774326311688948.2108118417324
7448.075138153421347.756976697464948.3932996093776
7548.157707230131947.756281703475948.5591327567879
7648.240276306842547.763066542269548.7174860714156
7748.322845383553247.773901979685548.8717887874209
7848.405414460263847.787091253579549.0237376669481
7948.487983536974447.80166336973349.1743037042159
8048.570552613685147.817010150714949.3240950766553
8148.653121690395747.832726521425249.4735168593662
8248.735690767106347.848530481695549.6228510525171
8348.81825984381747.864219126418349.7723005612157
8448.900828920527647.879642738022849.9220151030324

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 47.9925690767106 & 47.7743263116889 & 48.2108118417324 \tabularnewline
74 & 48.0751381534213 & 47.7569766974649 & 48.3932996093776 \tabularnewline
75 & 48.1577072301319 & 47.7562817034759 & 48.5591327567879 \tabularnewline
76 & 48.2402763068425 & 47.7630665422695 & 48.7174860714156 \tabularnewline
77 & 48.3228453835532 & 47.7739019796855 & 48.8717887874209 \tabularnewline
78 & 48.4054144602638 & 47.7870912535795 & 49.0237376669481 \tabularnewline
79 & 48.4879835369744 & 47.801663369733 & 49.1743037042159 \tabularnewline
80 & 48.5705526136851 & 47.8170101507149 & 49.3240950766553 \tabularnewline
81 & 48.6531216903957 & 47.8327265214252 & 49.4735168593662 \tabularnewline
82 & 48.7356907671063 & 47.8485304816955 & 49.6228510525171 \tabularnewline
83 & 48.818259843817 & 47.8642191264183 & 49.7723005612157 \tabularnewline
84 & 48.9008289205276 & 47.8796427380228 & 49.9220151030324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13465&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]47.9925690767106[/C][C]47.7743263116889[/C][C]48.2108118417324[/C][/ROW]
[ROW][C]74[/C][C]48.0751381534213[/C][C]47.7569766974649[/C][C]48.3932996093776[/C][/ROW]
[ROW][C]75[/C][C]48.1577072301319[/C][C]47.7562817034759[/C][C]48.5591327567879[/C][/ROW]
[ROW][C]76[/C][C]48.2402763068425[/C][C]47.7630665422695[/C][C]48.7174860714156[/C][/ROW]
[ROW][C]77[/C][C]48.3228453835532[/C][C]47.7739019796855[/C][C]48.8717887874209[/C][/ROW]
[ROW][C]78[/C][C]48.4054144602638[/C][C]47.7870912535795[/C][C]49.0237376669481[/C][/ROW]
[ROW][C]79[/C][C]48.4879835369744[/C][C]47.801663369733[/C][C]49.1743037042159[/C][/ROW]
[ROW][C]80[/C][C]48.5705526136851[/C][C]47.8170101507149[/C][C]49.3240950766553[/C][/ROW]
[ROW][C]81[/C][C]48.6531216903957[/C][C]47.8327265214252[/C][C]49.4735168593662[/C][/ROW]
[ROW][C]82[/C][C]48.7356907671063[/C][C]47.8485304816955[/C][C]49.6228510525171[/C][/ROW]
[ROW][C]83[/C][C]48.818259843817[/C][C]47.8642191264183[/C][C]49.7723005612157[/C][/ROW]
[ROW][C]84[/C][C]48.9008289205276[/C][C]47.8796427380228[/C][C]49.9220151030324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13465&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13465&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
7347.992569076710647.774326311688948.2108118417324
7448.075138153421347.756976697464948.3932996093776
7548.157707230131947.756281703475948.5591327567879
7648.240276306842547.763066542269548.7174860714156
7748.322845383553247.773901979685548.8717887874209
7848.405414460263847.787091253579549.0237376669481
7948.487983536974447.80166336973349.1743037042159
8048.570552613685147.817010150714949.3240950766553
8148.653121690395747.832726521425249.4735168593662
8248.735690767106347.848530481695549.6228510525171
8348.81825984381747.864219126418349.7723005612157
8448.900828920527647.879642738022849.9220151030324



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=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')