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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 May 2012 14:34:42 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/27/t1338143852i6ucdc3g74r8xml.htm/, Retrieved Wed, 08 May 2024 19:26:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167731, Retrieved Wed, 08 May 2024 19:26:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-27 18:34:42] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
16,41
16,38
16,12
16,03
16,02
16,01
16,01
15,94
15,88
15,75
15,8
15,84
15,84
15,79
15,79
15,75
15,63
15,63
15,63
15,62
15,59
15,55
15,61
15,58
15,58
15,64
15,56
15,57
15,46
15,5
15,5
15,58
15,69
15,78
15,8
15,79
15,79
15,79
15,75
15,71
15,76
15,76
15,76
15,76
15,78
15,84
15,82
15,86
15,86
15,87
15,84
15,84
15,89
15,89
15,89
15,91
15,95
16,08
16,08
16,09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167731&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167731&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167731&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.651118695995578
beta0.0987662409783271
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.651118695995578 \tabularnewline
beta & 0.0987662409783271 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167731&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]0.651118695995578[/C][/ROW]
[ROW][C]beta[/C][C]0.0987662409783271[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167731&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167731&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
alpha0.651118695995578
beta0.0987662409783271
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.8416.0296741452991-0.189674145299144
1415.7915.844969684387-0.0549696843870127
1515.7915.7906887959299-0.000688795929887576
1615.7515.72670691331770.0232930866823153
1715.6315.595671360710.0343286392900222
1815.6315.59652888760590.0334711123941336
1915.6315.6464805412797-0.0164805412797406
2015.6215.57493123303640.0450687669635688
2115.5915.54635613699090.0436438630090841
2215.5515.43674326604740.113256733952602
2315.6115.56224001274620.0477599872537908
2415.5815.6423286451481-0.0623286451481064
2515.5815.54013781641620.039862183583768
2615.6415.56771845702510.0722815429748938
2715.5615.6392479887488-0.0792479887487723
2815.5715.55144672976990.0185532702300737
2915.4615.43983543367610.0201645663239223
3015.515.44892076344960.0510792365504216
3115.515.5117920214539-0.0117920214539264
3215.5815.48395223450110.0960477654988825
3315.6915.51053511588430.179464884115687
3415.7815.54484065340.235159346600016
3515.815.76589543278220.0341045672177689
3615.7915.8368422929549-0.0468422929548904
3715.7915.8195406847333-0.0295406847333037
3815.7915.8479324285317-0.0579324285317497
3915.7515.8081276170509-0.0581276170509106
4015.7115.7958737068586-0.0858737068585622
4115.7615.63778910677690.122210893223123
4215.7615.75162561130310.00837438869685592
4315.7615.7895314042989-0.0295314042988917
4415.7615.8113987314131-0.0513987314131139
4515.7815.7852313176801-0.00523131768008689
4615.8415.72098312019190.119016879808102
4715.8215.79107681963490.0289231803651422
4815.8615.82488163356470.0351183664352774
4915.8615.8667256192235-0.00672561922354475
5015.8715.9012778023946-0.0312778023946301
5115.8415.8816848112215-0.0416848112215469
5215.8415.874439032782-0.0344390327820108
5315.8915.82973103179520.0602689682048485
5415.8915.86682686215860.0231731378414395
5515.8915.9054017603756-0.0154017603755552
5615.9115.9340067035396-0.0240067035395501
5715.9515.94870988258960.00129011741036855
5816.0815.93940335438990.140596645610129
5916.0816.00085136663640.0791486333635874
6016.0916.08148555365830.00851444634173504

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.84 & 16.0296741452991 & -0.189674145299144 \tabularnewline
14 & 15.79 & 15.844969684387 & -0.0549696843870127 \tabularnewline
15 & 15.79 & 15.7906887959299 & -0.000688795929887576 \tabularnewline
16 & 15.75 & 15.7267069133177 & 0.0232930866823153 \tabularnewline
17 & 15.63 & 15.59567136071 & 0.0343286392900222 \tabularnewline
18 & 15.63 & 15.5965288876059 & 0.0334711123941336 \tabularnewline
19 & 15.63 & 15.6464805412797 & -0.0164805412797406 \tabularnewline
20 & 15.62 & 15.5749312330364 & 0.0450687669635688 \tabularnewline
21 & 15.59 & 15.5463561369909 & 0.0436438630090841 \tabularnewline
22 & 15.55 & 15.4367432660474 & 0.113256733952602 \tabularnewline
23 & 15.61 & 15.5622400127462 & 0.0477599872537908 \tabularnewline
24 & 15.58 & 15.6423286451481 & -0.0623286451481064 \tabularnewline
25 & 15.58 & 15.5401378164162 & 0.039862183583768 \tabularnewline
26 & 15.64 & 15.5677184570251 & 0.0722815429748938 \tabularnewline
27 & 15.56 & 15.6392479887488 & -0.0792479887487723 \tabularnewline
28 & 15.57 & 15.5514467297699 & 0.0185532702300737 \tabularnewline
29 & 15.46 & 15.4398354336761 & 0.0201645663239223 \tabularnewline
30 & 15.5 & 15.4489207634496 & 0.0510792365504216 \tabularnewline
31 & 15.5 & 15.5117920214539 & -0.0117920214539264 \tabularnewline
32 & 15.58 & 15.4839522345011 & 0.0960477654988825 \tabularnewline
33 & 15.69 & 15.5105351158843 & 0.179464884115687 \tabularnewline
34 & 15.78 & 15.5448406534 & 0.235159346600016 \tabularnewline
35 & 15.8 & 15.7658954327822 & 0.0341045672177689 \tabularnewline
36 & 15.79 & 15.8368422929549 & -0.0468422929548904 \tabularnewline
37 & 15.79 & 15.8195406847333 & -0.0295406847333037 \tabularnewline
38 & 15.79 & 15.8479324285317 & -0.0579324285317497 \tabularnewline
39 & 15.75 & 15.8081276170509 & -0.0581276170509106 \tabularnewline
40 & 15.71 & 15.7958737068586 & -0.0858737068585622 \tabularnewline
41 & 15.76 & 15.6377891067769 & 0.122210893223123 \tabularnewline
42 & 15.76 & 15.7516256113031 & 0.00837438869685592 \tabularnewline
43 & 15.76 & 15.7895314042989 & -0.0295314042988917 \tabularnewline
44 & 15.76 & 15.8113987314131 & -0.0513987314131139 \tabularnewline
45 & 15.78 & 15.7852313176801 & -0.00523131768008689 \tabularnewline
46 & 15.84 & 15.7209831201919 & 0.119016879808102 \tabularnewline
47 & 15.82 & 15.7910768196349 & 0.0289231803651422 \tabularnewline
48 & 15.86 & 15.8248816335647 & 0.0351183664352774 \tabularnewline
49 & 15.86 & 15.8667256192235 & -0.00672561922354475 \tabularnewline
50 & 15.87 & 15.9012778023946 & -0.0312778023946301 \tabularnewline
51 & 15.84 & 15.8816848112215 & -0.0416848112215469 \tabularnewline
52 & 15.84 & 15.874439032782 & -0.0344390327820108 \tabularnewline
53 & 15.89 & 15.8297310317952 & 0.0602689682048485 \tabularnewline
54 & 15.89 & 15.8668268621586 & 0.0231731378414395 \tabularnewline
55 & 15.89 & 15.9054017603756 & -0.0154017603755552 \tabularnewline
56 & 15.91 & 15.9340067035396 & -0.0240067035395501 \tabularnewline
57 & 15.95 & 15.9487098825896 & 0.00129011741036855 \tabularnewline
58 & 16.08 & 15.9394033543899 & 0.140596645610129 \tabularnewline
59 & 16.08 & 16.0008513666364 & 0.0791486333635874 \tabularnewline
60 & 16.09 & 16.0814855536583 & 0.00851444634173504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167731&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]15.84[/C][C]16.0296741452991[/C][C]-0.189674145299144[/C][/ROW]
[ROW][C]14[/C][C]15.79[/C][C]15.844969684387[/C][C]-0.0549696843870127[/C][/ROW]
[ROW][C]15[/C][C]15.79[/C][C]15.7906887959299[/C][C]-0.000688795929887576[/C][/ROW]
[ROW][C]16[/C][C]15.75[/C][C]15.7267069133177[/C][C]0.0232930866823153[/C][/ROW]
[ROW][C]17[/C][C]15.63[/C][C]15.59567136071[/C][C]0.0343286392900222[/C][/ROW]
[ROW][C]18[/C][C]15.63[/C][C]15.5965288876059[/C][C]0.0334711123941336[/C][/ROW]
[ROW][C]19[/C][C]15.63[/C][C]15.6464805412797[/C][C]-0.0164805412797406[/C][/ROW]
[ROW][C]20[/C][C]15.62[/C][C]15.5749312330364[/C][C]0.0450687669635688[/C][/ROW]
[ROW][C]21[/C][C]15.59[/C][C]15.5463561369909[/C][C]0.0436438630090841[/C][/ROW]
[ROW][C]22[/C][C]15.55[/C][C]15.4367432660474[/C][C]0.113256733952602[/C][/ROW]
[ROW][C]23[/C][C]15.61[/C][C]15.5622400127462[/C][C]0.0477599872537908[/C][/ROW]
[ROW][C]24[/C][C]15.58[/C][C]15.6423286451481[/C][C]-0.0623286451481064[/C][/ROW]
[ROW][C]25[/C][C]15.58[/C][C]15.5401378164162[/C][C]0.039862183583768[/C][/ROW]
[ROW][C]26[/C][C]15.64[/C][C]15.5677184570251[/C][C]0.0722815429748938[/C][/ROW]
[ROW][C]27[/C][C]15.56[/C][C]15.6392479887488[/C][C]-0.0792479887487723[/C][/ROW]
[ROW][C]28[/C][C]15.57[/C][C]15.5514467297699[/C][C]0.0185532702300737[/C][/ROW]
[ROW][C]29[/C][C]15.46[/C][C]15.4398354336761[/C][C]0.0201645663239223[/C][/ROW]
[ROW][C]30[/C][C]15.5[/C][C]15.4489207634496[/C][C]0.0510792365504216[/C][/ROW]
[ROW][C]31[/C][C]15.5[/C][C]15.5117920214539[/C][C]-0.0117920214539264[/C][/ROW]
[ROW][C]32[/C][C]15.58[/C][C]15.4839522345011[/C][C]0.0960477654988825[/C][/ROW]
[ROW][C]33[/C][C]15.69[/C][C]15.5105351158843[/C][C]0.179464884115687[/C][/ROW]
[ROW][C]34[/C][C]15.78[/C][C]15.5448406534[/C][C]0.235159346600016[/C][/ROW]
[ROW][C]35[/C][C]15.8[/C][C]15.7658954327822[/C][C]0.0341045672177689[/C][/ROW]
[ROW][C]36[/C][C]15.79[/C][C]15.8368422929549[/C][C]-0.0468422929548904[/C][/ROW]
[ROW][C]37[/C][C]15.79[/C][C]15.8195406847333[/C][C]-0.0295406847333037[/C][/ROW]
[ROW][C]38[/C][C]15.79[/C][C]15.8479324285317[/C][C]-0.0579324285317497[/C][/ROW]
[ROW][C]39[/C][C]15.75[/C][C]15.8081276170509[/C][C]-0.0581276170509106[/C][/ROW]
[ROW][C]40[/C][C]15.71[/C][C]15.7958737068586[/C][C]-0.0858737068585622[/C][/ROW]
[ROW][C]41[/C][C]15.76[/C][C]15.6377891067769[/C][C]0.122210893223123[/C][/ROW]
[ROW][C]42[/C][C]15.76[/C][C]15.7516256113031[/C][C]0.00837438869685592[/C][/ROW]
[ROW][C]43[/C][C]15.76[/C][C]15.7895314042989[/C][C]-0.0295314042988917[/C][/ROW]
[ROW][C]44[/C][C]15.76[/C][C]15.8113987314131[/C][C]-0.0513987314131139[/C][/ROW]
[ROW][C]45[/C][C]15.78[/C][C]15.7852313176801[/C][C]-0.00523131768008689[/C][/ROW]
[ROW][C]46[/C][C]15.84[/C][C]15.7209831201919[/C][C]0.119016879808102[/C][/ROW]
[ROW][C]47[/C][C]15.82[/C][C]15.7910768196349[/C][C]0.0289231803651422[/C][/ROW]
[ROW][C]48[/C][C]15.86[/C][C]15.8248816335647[/C][C]0.0351183664352774[/C][/ROW]
[ROW][C]49[/C][C]15.86[/C][C]15.8667256192235[/C][C]-0.00672561922354475[/C][/ROW]
[ROW][C]50[/C][C]15.87[/C][C]15.9012778023946[/C][C]-0.0312778023946301[/C][/ROW]
[ROW][C]51[/C][C]15.84[/C][C]15.8816848112215[/C][C]-0.0416848112215469[/C][/ROW]
[ROW][C]52[/C][C]15.84[/C][C]15.874439032782[/C][C]-0.0344390327820108[/C][/ROW]
[ROW][C]53[/C][C]15.89[/C][C]15.8297310317952[/C][C]0.0602689682048485[/C][/ROW]
[ROW][C]54[/C][C]15.89[/C][C]15.8668268621586[/C][C]0.0231731378414395[/C][/ROW]
[ROW][C]55[/C][C]15.89[/C][C]15.9054017603756[/C][C]-0.0154017603755552[/C][/ROW]
[ROW][C]56[/C][C]15.91[/C][C]15.9340067035396[/C][C]-0.0240067035395501[/C][/ROW]
[ROW][C]57[/C][C]15.95[/C][C]15.9487098825896[/C][C]0.00129011741036855[/C][/ROW]
[ROW][C]58[/C][C]16.08[/C][C]15.9394033543899[/C][C]0.140596645610129[/C][/ROW]
[ROW][C]59[/C][C]16.08[/C][C]16.0008513666364[/C][C]0.0791486333635874[/C][/ROW]
[ROW][C]60[/C][C]16.09[/C][C]16.0814855536583[/C][C]0.00851444634173504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167731&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167731&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
1315.8416.0296741452991-0.189674145299144
1415.7915.844969684387-0.0549696843870127
1515.7915.7906887959299-0.000688795929887576
1615.7515.72670691331770.0232930866823153
1715.6315.595671360710.0343286392900222
1815.6315.59652888760590.0334711123941336
1915.6315.6464805412797-0.0164805412797406
2015.6215.57493123303640.0450687669635688
2115.5915.54635613699090.0436438630090841
2215.5515.43674326604740.113256733952602
2315.6115.56224001274620.0477599872537908
2415.5815.6423286451481-0.0623286451481064
2515.5815.54013781641620.039862183583768
2615.6415.56771845702510.0722815429748938
2715.5615.6392479887488-0.0792479887487723
2815.5715.55144672976990.0185532702300737
2915.4615.43983543367610.0201645663239223
3015.515.44892076344960.0510792365504216
3115.515.5117920214539-0.0117920214539264
3215.5815.48395223450110.0960477654988825
3315.6915.51053511588430.179464884115687
3415.7815.54484065340.235159346600016
3515.815.76589543278220.0341045672177689
3615.7915.8368422929549-0.0468422929548904
3715.7915.8195406847333-0.0295406847333037
3815.7915.8479324285317-0.0579324285317497
3915.7515.8081276170509-0.0581276170509106
4015.7115.7958737068586-0.0858737068585622
4115.7615.63778910677690.122210893223123
4215.7615.75162561130310.00837438869685592
4315.7615.7895314042989-0.0295314042988917
4415.7615.8113987314131-0.0513987314131139
4515.7815.7852313176801-0.00523131768008689
4615.8415.72098312019190.119016879808102
4715.8215.79107681963490.0289231803651422
4815.8615.82488163356470.0351183664352774
4915.8615.8667256192235-0.00672561922354475
5015.8715.9012778023946-0.0312778023946301
5115.8415.8816848112215-0.0416848112215469
5215.8415.874439032782-0.0344390327820108
5315.8915.82973103179520.0602689682048485
5415.8915.86682686215860.0231731378414395
5515.8915.9054017603756-0.0154017603755552
5615.9115.9340067035396-0.0240067035395501
5715.9515.94870988258960.00129011741036855
5816.0815.93940335438990.140596645610129
5916.0816.00085136663640.0791486333635874
6016.0916.08148555365830.00851444634173504







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6116.101663042891115.957631081530616.2456950042517
6216.142715517208515.965618504322716.3198125300944
6316.152555619537615.942850621689716.3622606173856
6416.190358549659115.947963632971916.4327534663463
6516.218710053802715.943260842862316.4941592647431
6616.217339536923115.908310913762516.5263681600837
6716.239595626667115.896366622495316.582824630839
6816.288445020599315.910336262146216.6665537790524
6916.342367017661515.928663586482416.7560704488406
7016.395500964163715.945466938949416.845534989378
7116.349603294414915.862491289679816.8367152991499
7216.354606930880215.829664495766616.8795493659939

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 16.1016630428911 & 15.9576310815306 & 16.2456950042517 \tabularnewline
62 & 16.1427155172085 & 15.9656185043227 & 16.3198125300944 \tabularnewline
63 & 16.1525556195376 & 15.9428506216897 & 16.3622606173856 \tabularnewline
64 & 16.1903585496591 & 15.9479636329719 & 16.4327534663463 \tabularnewline
65 & 16.2187100538027 & 15.9432608428623 & 16.4941592647431 \tabularnewline
66 & 16.2173395369231 & 15.9083109137625 & 16.5263681600837 \tabularnewline
67 & 16.2395956266671 & 15.8963666224953 & 16.582824630839 \tabularnewline
68 & 16.2884450205993 & 15.9103362621462 & 16.6665537790524 \tabularnewline
69 & 16.3423670176615 & 15.9286635864824 & 16.7560704488406 \tabularnewline
70 & 16.3955009641637 & 15.9454669389494 & 16.845534989378 \tabularnewline
71 & 16.3496032944149 & 15.8624912896798 & 16.8367152991499 \tabularnewline
72 & 16.3546069308802 & 15.8296644957666 & 16.8795493659939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167731&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]61[/C][C]16.1016630428911[/C][C]15.9576310815306[/C][C]16.2456950042517[/C][/ROW]
[ROW][C]62[/C][C]16.1427155172085[/C][C]15.9656185043227[/C][C]16.3198125300944[/C][/ROW]
[ROW][C]63[/C][C]16.1525556195376[/C][C]15.9428506216897[/C][C]16.3622606173856[/C][/ROW]
[ROW][C]64[/C][C]16.1903585496591[/C][C]15.9479636329719[/C][C]16.4327534663463[/C][/ROW]
[ROW][C]65[/C][C]16.2187100538027[/C][C]15.9432608428623[/C][C]16.4941592647431[/C][/ROW]
[ROW][C]66[/C][C]16.2173395369231[/C][C]15.9083109137625[/C][C]16.5263681600837[/C][/ROW]
[ROW][C]67[/C][C]16.2395956266671[/C][C]15.8963666224953[/C][C]16.582824630839[/C][/ROW]
[ROW][C]68[/C][C]16.2884450205993[/C][C]15.9103362621462[/C][C]16.6665537790524[/C][/ROW]
[ROW][C]69[/C][C]16.3423670176615[/C][C]15.9286635864824[/C][C]16.7560704488406[/C][/ROW]
[ROW][C]70[/C][C]16.3955009641637[/C][C]15.9454669389494[/C][C]16.845534989378[/C][/ROW]
[ROW][C]71[/C][C]16.3496032944149[/C][C]15.8624912896798[/C][C]16.8367152991499[/C][/ROW]
[ROW][C]72[/C][C]16.3546069308802[/C][C]15.8296644957666[/C][C]16.8795493659939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167731&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167731&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
6116.101663042891115.957631081530616.2456950042517
6216.142715517208515.965618504322716.3198125300944
6316.152555619537615.942850621689716.3622606173856
6416.190358549659115.947963632971916.4327534663463
6516.218710053802715.943260842862316.4941592647431
6616.217339536923115.908310913762516.5263681600837
6716.239595626667115.896366622495316.582824630839
6816.288445020599315.910336262146216.6665537790524
6916.342367017661515.928663586482416.7560704488406
7016.395500964163715.945466938949416.845534989378
7116.349603294414915.862491289679816.8367152991499
7216.354606930880215.829664495766616.8795493659939



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')