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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 22 May 2012 10:57:15 -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/22/t13376986719vjleqi1i9styjf.htm/, Retrieved Fri, 03 May 2024 15:20:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167075, Retrieved Fri, 03 May 2024 15:20:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact90

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave10oef2] [2012-05-22 14:57:15] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10,92
10,98
11,15
11,19
11,33
11,38
11,4
11,45
11,56
11,61
11,82
11,77
11,85
11,82
11,92
11,86
11,87
11,94
11,86
11,92
11,83
11,91
11,93
11,99
11,96
12,12
11,85
12,01
12,1
12,21
12,31
12,31
12,39
12,35
12,41
12,51
12,27
12,51
12,44
12,47
12,51
12,58
12,5
12,52
12,59
12,51
12,67
12,64
12,54
12,6
12,67
12,62
12,72
12,85
12,85
12,82
12,79
12,94
12,71
12,56

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167075&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167075&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.63720661066149
beta0.0384080284877684
gamma0.182987595170336

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.63720661066149 \tabularnewline
beta & 0.0384080284877684 \tabularnewline
gamma & 0.182987595170336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167075&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]0.63720661066149[/C][/ROW]
[ROW][C]beta[/C][C]0.0384080284877684[/C][/ROW]
[ROW][C]gamma[/C][C]0.182987595170336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167075&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.63720661066149
beta0.0384080284877684
gamma0.182987595170336






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311.8511.53219551282050.31780448717949
1411.8211.71567983288730.104320167112656
1511.9211.90360031568760.0163996843124288
1611.8611.8829819823765-0.0229819823765265
1711.8711.9133735997976-0.0433735997976274
1811.9411.9930433581688-0.0530433581688143
1911.8611.9327533074094-0.0727533074093731
2011.9211.91062339319060.00937660680939167
2111.8312.0077233515771-0.177723351577095
2211.9111.9283357383719-0.0183357383718956
2311.9312.1196455531877-0.189645553187717
2411.9911.94173759810860.0482624018913977
2511.9612.0710386527622-0.111038652762163
2612.1211.95459397373950.165406026260534
2711.8512.1646022280797-0.314602228079691
2812.0111.91135218661580.0986478133842468
2912.112.00176944836010.0982305516398636
3012.2112.15837002997980.0516299700202403
3112.3112.15337346201730.156626537982714
3212.3112.27837546703060.0316245329694489
3312.3912.3732927287820.0167072712179657
3412.3512.4291990002649-0.0791990002649374
3512.4112.569684282872-0.159684282871956
3612.5112.42672566871760.0832743312823911
3712.2712.5686818630047-0.29868186300469
3812.5112.34735036190590.162649638094125
3912.4412.5199970337116-0.0799970337116029
4012.4712.44567593292370.0243240670762539
4112.5112.4888895809650.0211104190349634
4212.5812.5915512887833-0.0115512887832718
4312.512.5500155338746-0.0500155338746442
4412.5212.5267380025619-0.00673800256186752
4512.5912.58697384375540.0030261562445606
4612.5112.6182144371985-0.10821443719847
4712.6712.7245765394072-0.0545765394072468
4812.6412.6570036828195-0.0170036828194835
4912.5412.699532257599-0.159532257599045
5012.612.59072660413540.00927339586463738
5112.6712.63901123194890.030988768051138
5212.6212.6345316209449-0.0145316209449291
5312.7212.6440169466420.0759830533579695
5412.8512.77206262411120.0779373758887569
5512.8512.77977332310950.0702266768904956
5612.8212.8337079643225-0.0137079643225064
5712.7912.8877001170889-0.0977001170888965
5812.9412.84245661595040.0975433840495743
5912.7113.0836097379521-0.373609737952123
6012.5612.8075531186854-0.247553118685399

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11.85 & 11.5321955128205 & 0.31780448717949 \tabularnewline
14 & 11.82 & 11.7156798328873 & 0.104320167112656 \tabularnewline
15 & 11.92 & 11.9036003156876 & 0.0163996843124288 \tabularnewline
16 & 11.86 & 11.8829819823765 & -0.0229819823765265 \tabularnewline
17 & 11.87 & 11.9133735997976 & -0.0433735997976274 \tabularnewline
18 & 11.94 & 11.9930433581688 & -0.0530433581688143 \tabularnewline
19 & 11.86 & 11.9327533074094 & -0.0727533074093731 \tabularnewline
20 & 11.92 & 11.9106233931906 & 0.00937660680939167 \tabularnewline
21 & 11.83 & 12.0077233515771 & -0.177723351577095 \tabularnewline
22 & 11.91 & 11.9283357383719 & -0.0183357383718956 \tabularnewline
23 & 11.93 & 12.1196455531877 & -0.189645553187717 \tabularnewline
24 & 11.99 & 11.9417375981086 & 0.0482624018913977 \tabularnewline
25 & 11.96 & 12.0710386527622 & -0.111038652762163 \tabularnewline
26 & 12.12 & 11.9545939737395 & 0.165406026260534 \tabularnewline
27 & 11.85 & 12.1646022280797 & -0.314602228079691 \tabularnewline
28 & 12.01 & 11.9113521866158 & 0.0986478133842468 \tabularnewline
29 & 12.1 & 12.0017694483601 & 0.0982305516398636 \tabularnewline
30 & 12.21 & 12.1583700299798 & 0.0516299700202403 \tabularnewline
31 & 12.31 & 12.1533734620173 & 0.156626537982714 \tabularnewline
32 & 12.31 & 12.2783754670306 & 0.0316245329694489 \tabularnewline
33 & 12.39 & 12.373292728782 & 0.0167072712179657 \tabularnewline
34 & 12.35 & 12.4291990002649 & -0.0791990002649374 \tabularnewline
35 & 12.41 & 12.569684282872 & -0.159684282871956 \tabularnewline
36 & 12.51 & 12.4267256687176 & 0.0832743312823911 \tabularnewline
37 & 12.27 & 12.5686818630047 & -0.29868186300469 \tabularnewline
38 & 12.51 & 12.3473503619059 & 0.162649638094125 \tabularnewline
39 & 12.44 & 12.5199970337116 & -0.0799970337116029 \tabularnewline
40 & 12.47 & 12.4456759329237 & 0.0243240670762539 \tabularnewline
41 & 12.51 & 12.488889580965 & 0.0211104190349634 \tabularnewline
42 & 12.58 & 12.5915512887833 & -0.0115512887832718 \tabularnewline
43 & 12.5 & 12.5500155338746 & -0.0500155338746442 \tabularnewline
44 & 12.52 & 12.5267380025619 & -0.00673800256186752 \tabularnewline
45 & 12.59 & 12.5869738437554 & 0.0030261562445606 \tabularnewline
46 & 12.51 & 12.6182144371985 & -0.10821443719847 \tabularnewline
47 & 12.67 & 12.7245765394072 & -0.0545765394072468 \tabularnewline
48 & 12.64 & 12.6570036828195 & -0.0170036828194835 \tabularnewline
49 & 12.54 & 12.699532257599 & -0.159532257599045 \tabularnewline
50 & 12.6 & 12.5907266041354 & 0.00927339586463738 \tabularnewline
51 & 12.67 & 12.6390112319489 & 0.030988768051138 \tabularnewline
52 & 12.62 & 12.6345316209449 & -0.0145316209449291 \tabularnewline
53 & 12.72 & 12.644016946642 & 0.0759830533579695 \tabularnewline
54 & 12.85 & 12.7720626241112 & 0.0779373758887569 \tabularnewline
55 & 12.85 & 12.7797733231095 & 0.0702266768904956 \tabularnewline
56 & 12.82 & 12.8337079643225 & -0.0137079643225064 \tabularnewline
57 & 12.79 & 12.8877001170889 & -0.0977001170888965 \tabularnewline
58 & 12.94 & 12.8424566159504 & 0.0975433840495743 \tabularnewline
59 & 12.71 & 13.0836097379521 & -0.373609737952123 \tabularnewline
60 & 12.56 & 12.8075531186854 & -0.247553118685399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167075&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]11.85[/C][C]11.5321955128205[/C][C]0.31780448717949[/C][/ROW]
[ROW][C]14[/C][C]11.82[/C][C]11.7156798328873[/C][C]0.104320167112656[/C][/ROW]
[ROW][C]15[/C][C]11.92[/C][C]11.9036003156876[/C][C]0.0163996843124288[/C][/ROW]
[ROW][C]16[/C][C]11.86[/C][C]11.8829819823765[/C][C]-0.0229819823765265[/C][/ROW]
[ROW][C]17[/C][C]11.87[/C][C]11.9133735997976[/C][C]-0.0433735997976274[/C][/ROW]
[ROW][C]18[/C][C]11.94[/C][C]11.9930433581688[/C][C]-0.0530433581688143[/C][/ROW]
[ROW][C]19[/C][C]11.86[/C][C]11.9327533074094[/C][C]-0.0727533074093731[/C][/ROW]
[ROW][C]20[/C][C]11.92[/C][C]11.9106233931906[/C][C]0.00937660680939167[/C][/ROW]
[ROW][C]21[/C][C]11.83[/C][C]12.0077233515771[/C][C]-0.177723351577095[/C][/ROW]
[ROW][C]22[/C][C]11.91[/C][C]11.9283357383719[/C][C]-0.0183357383718956[/C][/ROW]
[ROW][C]23[/C][C]11.93[/C][C]12.1196455531877[/C][C]-0.189645553187717[/C][/ROW]
[ROW][C]24[/C][C]11.99[/C][C]11.9417375981086[/C][C]0.0482624018913977[/C][/ROW]
[ROW][C]25[/C][C]11.96[/C][C]12.0710386527622[/C][C]-0.111038652762163[/C][/ROW]
[ROW][C]26[/C][C]12.12[/C][C]11.9545939737395[/C][C]0.165406026260534[/C][/ROW]
[ROW][C]27[/C][C]11.85[/C][C]12.1646022280797[/C][C]-0.314602228079691[/C][/ROW]
[ROW][C]28[/C][C]12.01[/C][C]11.9113521866158[/C][C]0.0986478133842468[/C][/ROW]
[ROW][C]29[/C][C]12.1[/C][C]12.0017694483601[/C][C]0.0982305516398636[/C][/ROW]
[ROW][C]30[/C][C]12.21[/C][C]12.1583700299798[/C][C]0.0516299700202403[/C][/ROW]
[ROW][C]31[/C][C]12.31[/C][C]12.1533734620173[/C][C]0.156626537982714[/C][/ROW]
[ROW][C]32[/C][C]12.31[/C][C]12.2783754670306[/C][C]0.0316245329694489[/C][/ROW]
[ROW][C]33[/C][C]12.39[/C][C]12.373292728782[/C][C]0.0167072712179657[/C][/ROW]
[ROW][C]34[/C][C]12.35[/C][C]12.4291990002649[/C][C]-0.0791990002649374[/C][/ROW]
[ROW][C]35[/C][C]12.41[/C][C]12.569684282872[/C][C]-0.159684282871956[/C][/ROW]
[ROW][C]36[/C][C]12.51[/C][C]12.4267256687176[/C][C]0.0832743312823911[/C][/ROW]
[ROW][C]37[/C][C]12.27[/C][C]12.5686818630047[/C][C]-0.29868186300469[/C][/ROW]
[ROW][C]38[/C][C]12.51[/C][C]12.3473503619059[/C][C]0.162649638094125[/C][/ROW]
[ROW][C]39[/C][C]12.44[/C][C]12.5199970337116[/C][C]-0.0799970337116029[/C][/ROW]
[ROW][C]40[/C][C]12.47[/C][C]12.4456759329237[/C][C]0.0243240670762539[/C][/ROW]
[ROW][C]41[/C][C]12.51[/C][C]12.488889580965[/C][C]0.0211104190349634[/C][/ROW]
[ROW][C]42[/C][C]12.58[/C][C]12.5915512887833[/C][C]-0.0115512887832718[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]12.5500155338746[/C][C]-0.0500155338746442[/C][/ROW]
[ROW][C]44[/C][C]12.52[/C][C]12.5267380025619[/C][C]-0.00673800256186752[/C][/ROW]
[ROW][C]45[/C][C]12.59[/C][C]12.5869738437554[/C][C]0.0030261562445606[/C][/ROW]
[ROW][C]46[/C][C]12.51[/C][C]12.6182144371985[/C][C]-0.10821443719847[/C][/ROW]
[ROW][C]47[/C][C]12.67[/C][C]12.7245765394072[/C][C]-0.0545765394072468[/C][/ROW]
[ROW][C]48[/C][C]12.64[/C][C]12.6570036828195[/C][C]-0.0170036828194835[/C][/ROW]
[ROW][C]49[/C][C]12.54[/C][C]12.699532257599[/C][C]-0.159532257599045[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]12.5907266041354[/C][C]0.00927339586463738[/C][/ROW]
[ROW][C]51[/C][C]12.67[/C][C]12.6390112319489[/C][C]0.030988768051138[/C][/ROW]
[ROW][C]52[/C][C]12.62[/C][C]12.6345316209449[/C][C]-0.0145316209449291[/C][/ROW]
[ROW][C]53[/C][C]12.72[/C][C]12.644016946642[/C][C]0.0759830533579695[/C][/ROW]
[ROW][C]54[/C][C]12.85[/C][C]12.7720626241112[/C][C]0.0779373758887569[/C][/ROW]
[ROW][C]55[/C][C]12.85[/C][C]12.7797733231095[/C][C]0.0702266768904956[/C][/ROW]
[ROW][C]56[/C][C]12.82[/C][C]12.8337079643225[/C][C]-0.0137079643225064[/C][/ROW]
[ROW][C]57[/C][C]12.79[/C][C]12.8877001170889[/C][C]-0.0977001170888965[/C][/ROW]
[ROW][C]58[/C][C]12.94[/C][C]12.8424566159504[/C][C]0.0975433840495743[/C][/ROW]
[ROW][C]59[/C][C]12.71[/C][C]13.0836097379521[/C][C]-0.373609737952123[/C][/ROW]
[ROW][C]60[/C][C]12.56[/C][C]12.8075531186854[/C][C]-0.247553118685399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167075&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167075&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311.8511.53219551282050.31780448717949
1411.8211.71567983288730.104320167112656
1511.9211.90360031568760.0163996843124288
1611.8611.8829819823765-0.0229819823765265
1711.8711.9133735997976-0.0433735997976274
1811.9411.9930433581688-0.0530433581688143
1911.8611.9327533074094-0.0727533074093731
2011.9211.91062339319060.00937660680939167
2111.8312.0077233515771-0.177723351577095
2211.9111.9283357383719-0.0183357383718956
2311.9312.1196455531877-0.189645553187717
2411.9911.94173759810860.0482624018913977
2511.9612.0710386527622-0.111038652762163
2612.1211.95459397373950.165406026260534
2711.8512.1646022280797-0.314602228079691
2812.0111.91135218661580.0986478133842468
2912.112.00176944836010.0982305516398636
3012.2112.15837002997980.0516299700202403
3112.3112.15337346201730.156626537982714
3212.3112.27837546703060.0316245329694489
3312.3912.3732927287820.0167072712179657
3412.3512.4291990002649-0.0791990002649374
3512.4112.569684282872-0.159684282871956
3612.5112.42672566871760.0832743312823911
3712.2712.5686818630047-0.29868186300469
3812.5112.34735036190590.162649638094125
3912.4412.5199970337116-0.0799970337116029
4012.4712.44567593292370.0243240670762539
4112.5112.4888895809650.0211104190349634
4212.5812.5915512887833-0.0115512887832718
4312.512.5500155338746-0.0500155338746442
4412.5212.5267380025619-0.00673800256186752
4512.5912.58697384375540.0030261562445606
4612.5112.6182144371985-0.10821443719847
4712.6712.7245765394072-0.0545765394072468
4812.6412.6570036828195-0.0170036828194835
4912.5412.699532257599-0.159532257599045
5012.612.59072660413540.00927339586463738
5112.6712.63901123194890.030988768051138
5212.6212.6345316209449-0.0145316209449291
5312.7212.6440169466420.0759830533579695
5412.8512.77206262411120.0779373758887569
5512.8512.77977332310950.0702266768904956
5612.8212.8337079643225-0.0137079643225064
5712.7912.8877001170889-0.0977001170888965
5812.9412.84245661595040.0975433840495743
5912.7113.0836097379521-0.373609737952123
6012.5612.8075531186854-0.247553118685399






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6112.680381599202512.42442559415212.9363376042531
6212.675011302590712.368096567862312.9819260373191
6312.709175416371412.35556418065713.0627866520859
6412.671516138549212.273867156988413.0691651201099
6512.686214252479512.246297720559813.1261307843992
6612.754057342923212.273094855084413.235019830762
6712.697771091253212.176620179696713.2189220028097
6812.685843117828912.125106896504413.2465793391534
6912.727788032858712.127884784242913.3276912814745
7012.744946277700212.106155899622713.3837366557777
7112.877463568008312.199959834215213.5549673018015
7212.841783447451812.125657148980713.557909745923

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 12.6803815992025 & 12.424425594152 & 12.9363376042531 \tabularnewline
62 & 12.6750113025907 & 12.3680965678623 & 12.9819260373191 \tabularnewline
63 & 12.7091754163714 & 12.355564180657 & 13.0627866520859 \tabularnewline
64 & 12.6715161385492 & 12.2738671569884 & 13.0691651201099 \tabularnewline
65 & 12.6862142524795 & 12.2462977205598 & 13.1261307843992 \tabularnewline
66 & 12.7540573429232 & 12.2730948550844 & 13.235019830762 \tabularnewline
67 & 12.6977710912532 & 12.1766201796967 & 13.2189220028097 \tabularnewline
68 & 12.6858431178289 & 12.1251068965044 & 13.2465793391534 \tabularnewline
69 & 12.7277880328587 & 12.1278847842429 & 13.3276912814745 \tabularnewline
70 & 12.7449462777002 & 12.1061558996227 & 13.3837366557777 \tabularnewline
71 & 12.8774635680083 & 12.1999598342152 & 13.5549673018015 \tabularnewline
72 & 12.8417834474518 & 12.1256571489807 & 13.557909745923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167075&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]12.6803815992025[/C][C]12.424425594152[/C][C]12.9363376042531[/C][/ROW]
[ROW][C]62[/C][C]12.6750113025907[/C][C]12.3680965678623[/C][C]12.9819260373191[/C][/ROW]
[ROW][C]63[/C][C]12.7091754163714[/C][C]12.355564180657[/C][C]13.0627866520859[/C][/ROW]
[ROW][C]64[/C][C]12.6715161385492[/C][C]12.2738671569884[/C][C]13.0691651201099[/C][/ROW]
[ROW][C]65[/C][C]12.6862142524795[/C][C]12.2462977205598[/C][C]13.1261307843992[/C][/ROW]
[ROW][C]66[/C][C]12.7540573429232[/C][C]12.2730948550844[/C][C]13.235019830762[/C][/ROW]
[ROW][C]67[/C][C]12.6977710912532[/C][C]12.1766201796967[/C][C]13.2189220028097[/C][/ROW]
[ROW][C]68[/C][C]12.6858431178289[/C][C]12.1251068965044[/C][C]13.2465793391534[/C][/ROW]
[ROW][C]69[/C][C]12.7277880328587[/C][C]12.1278847842429[/C][C]13.3276912814745[/C][/ROW]
[ROW][C]70[/C][C]12.7449462777002[/C][C]12.1061558996227[/C][C]13.3837366557777[/C][/ROW]
[ROW][C]71[/C][C]12.8774635680083[/C][C]12.1999598342152[/C][C]13.5549673018015[/C][/ROW]
[ROW][C]72[/C][C]12.8417834474518[/C][C]12.1256571489807[/C][C]13.557909745923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167075&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167075&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6112.680381599202512.42442559415212.9363376042531
6212.675011302590712.368096567862312.9819260373191
6312.709175416371412.35556418065713.0627866520859
6412.671516138549212.273867156988413.0691651201099
6512.686214252479512.246297720559813.1261307843992
6612.754057342923212.273094855084413.235019830762
6712.697771091253212.176620179696713.2189220028097
6812.685843117828912.125106896504413.2465793391534
6912.727788032858712.127884784242913.3276912814745
7012.744946277700212.106155899622713.3837366557777
7112.877463568008312.199959834215213.5549673018015
7212.841783447451812.125657148980713.557909745923


Figures (Output of Computation)

Input Parameters & R Code

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')