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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 08:10:17 -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/15/t13582554251xvnlufjly2vnfk.htm/, Retrieved Sun, 28 Apr 2024 08:22:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205453, Retrieved Sun, 28 Apr 2024 08:22:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-15 13:10:17] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
32,98
32,7
32,74
32,87
32,95
32,94
32,94
32,97
32,87
32,96
32,97
32,99
32,99
33,04
33,23
33,03
33,05
33,03
33,04
33,11
33,14
33,08
33,09
33,07
33,07
33,02
33
33,08
33,35
33,36
33,36
33,35
33,41
33,47
33,47
33,48
33,48
33,55
33,68
33,72
33,79
33,83
33,83
33,84
33,91
34,06
34,16
34,16
34,16
34,29
34,48
34,48
34,39
34,29
34,29
34,25
34,2
34,1
34,09
34,06
34,06
34,04
34,19
34,21
34,17
34,08
34,08
34,08
34,3
34,28
34,45
34,41




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205453&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205453&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.384112312147484
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.384112312147484 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205453&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]0.384112312147484[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205453&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
beta0.384112312147484
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
332.7432.420.319999999999993
432.8732.58291593988720.287084060112797
532.9532.82318846199780.126811538002194
632.9432.9518983350668-0.0118983350668174
732.9432.93732803807360.00267196192640995
832.9732.93835437154710.0316456284528854
932.8732.9805098470615-0.110509847061515
1032.9632.83806165419160.121938345808353
1132.9732.9748996741395-0.00489967413953707
1232.9932.9830176489770.00698235102297673
1332.9933.0056996559727-0.0156996559726892
1433.0432.99966922481710.0403307751828947
1533.2333.06516077212330.164839227876698
1633.0333.3184775490756-0.288477549075623
1733.0533.00766977069760.0423302293024435
1833.0333.0439293329486-0.0139293329486421
1933.0433.01857890466310.021421095336926
2033.1133.03680701112170.0731929888783327
2133.1433.13492133931270.00507866068728902
2233.0833.1668721154119-0.0868721154119214
2333.0933.07350346629990.0164965337001064
2433.0733.0898399880019-0.0198399880018698
2533.0733.06221920433750.00778079566251222
2633.0233.0652079037498-0.0452079037497626
273332.99784299131310.00215700868689339
2833.0832.97867152490710.101328475092849
2933.3533.09759303976140.252406960238559
3033.3633.4645456608608-0.104545660860794
3133.3633.4343883853426-0.0743883853425658
3233.3533.4058148906517-0.0558148906517104
3333.4133.37437570395120.0356242960487663
3433.4733.44805943467510.0219405653248543
3533.4733.5164870759519-0.0464870759519016
3633.4833.498630817723-0.018630817723043
3733.4833.5014744912502-0.0214744912502454
3833.5533.49322587476390.0567741252360818
3933.6833.58503351527850.0949664847215033
4033.7233.7515113113014-0.0315113113014007
4133.7933.77940742865860.0105925713413839
4233.8333.8534761657281-0.023476165728141
4333.8333.8844586814299-0.0544586814299493
4433.8433.8635404313894-0.0235404313893852
4533.9133.86449826185950.0455017381405298
4634.0633.95197603970330.108023960296656
4734.1634.14346937286020.0165306271397654
4834.1634.2498189902721-0.0898189902721285
4934.1634.2153184102439-0.0553184102439488
5034.2934.19406992778080.0959300722191756
5134.4834.36091784962540.119082150374588
5234.4834.5966587697413-0.116658769741285
5334.3934.5518486999637-0.161848699963677
5434.2934.3996806216026-0.109680621602571
5534.2934.2575509444410.0324490555589705
5634.2534.2700150261988-0.0200150261987915
5734.234.2223270082079-0.0223270082078741
5834.134.1637509294618-0.0637509294618184
5934.0934.03926341254470.0507365874553187
6034.0634.04875196046260.011248039537378
6134.0634.02307247093650.0369275290635471
6234.0434.03725678950690.00274321049305115
6334.1934.01831049043210.171689509567862
6434.2134.2342585449237-0.0242585449237112
6534.1734.2449405391437-0.0749405391437321
6634.0834.1761549553797-0.0961549553796601
6734.0834.04922065314430.0307793468556596
6834.0834.06104337923150.0189566207685417
6934.334.06832485066540.231675149334635
7034.2834.3773141279434-0.0973141279433989
7134.4534.31993457325450.130065426745553
7234.4134.5398943050521-0.12989430505214

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 32.74 & 32.42 & 0.319999999999993 \tabularnewline
4 & 32.87 & 32.5829159398872 & 0.287084060112797 \tabularnewline
5 & 32.95 & 32.8231884619978 & 0.126811538002194 \tabularnewline
6 & 32.94 & 32.9518983350668 & -0.0118983350668174 \tabularnewline
7 & 32.94 & 32.9373280380736 & 0.00267196192640995 \tabularnewline
8 & 32.97 & 32.9383543715471 & 0.0316456284528854 \tabularnewline
9 & 32.87 & 32.9805098470615 & -0.110509847061515 \tabularnewline
10 & 32.96 & 32.8380616541916 & 0.121938345808353 \tabularnewline
11 & 32.97 & 32.9748996741395 & -0.00489967413953707 \tabularnewline
12 & 32.99 & 32.983017648977 & 0.00698235102297673 \tabularnewline
13 & 32.99 & 33.0056996559727 & -0.0156996559726892 \tabularnewline
14 & 33.04 & 32.9996692248171 & 0.0403307751828947 \tabularnewline
15 & 33.23 & 33.0651607721233 & 0.164839227876698 \tabularnewline
16 & 33.03 & 33.3184775490756 & -0.288477549075623 \tabularnewline
17 & 33.05 & 33.0076697706976 & 0.0423302293024435 \tabularnewline
18 & 33.03 & 33.0439293329486 & -0.0139293329486421 \tabularnewline
19 & 33.04 & 33.0185789046631 & 0.021421095336926 \tabularnewline
20 & 33.11 & 33.0368070111217 & 0.0731929888783327 \tabularnewline
21 & 33.14 & 33.1349213393127 & 0.00507866068728902 \tabularnewline
22 & 33.08 & 33.1668721154119 & -0.0868721154119214 \tabularnewline
23 & 33.09 & 33.0735034662999 & 0.0164965337001064 \tabularnewline
24 & 33.07 & 33.0898399880019 & -0.0198399880018698 \tabularnewline
25 & 33.07 & 33.0622192043375 & 0.00778079566251222 \tabularnewline
26 & 33.02 & 33.0652079037498 & -0.0452079037497626 \tabularnewline
27 & 33 & 32.9978429913131 & 0.00215700868689339 \tabularnewline
28 & 33.08 & 32.9786715249071 & 0.101328475092849 \tabularnewline
29 & 33.35 & 33.0975930397614 & 0.252406960238559 \tabularnewline
30 & 33.36 & 33.4645456608608 & -0.104545660860794 \tabularnewline
31 & 33.36 & 33.4343883853426 & -0.0743883853425658 \tabularnewline
32 & 33.35 & 33.4058148906517 & -0.0558148906517104 \tabularnewline
33 & 33.41 & 33.3743757039512 & 0.0356242960487663 \tabularnewline
34 & 33.47 & 33.4480594346751 & 0.0219405653248543 \tabularnewline
35 & 33.47 & 33.5164870759519 & -0.0464870759519016 \tabularnewline
36 & 33.48 & 33.498630817723 & -0.018630817723043 \tabularnewline
37 & 33.48 & 33.5014744912502 & -0.0214744912502454 \tabularnewline
38 & 33.55 & 33.4932258747639 & 0.0567741252360818 \tabularnewline
39 & 33.68 & 33.5850335152785 & 0.0949664847215033 \tabularnewline
40 & 33.72 & 33.7515113113014 & -0.0315113113014007 \tabularnewline
41 & 33.79 & 33.7794074286586 & 0.0105925713413839 \tabularnewline
42 & 33.83 & 33.8534761657281 & -0.023476165728141 \tabularnewline
43 & 33.83 & 33.8844586814299 & -0.0544586814299493 \tabularnewline
44 & 33.84 & 33.8635404313894 & -0.0235404313893852 \tabularnewline
45 & 33.91 & 33.8644982618595 & 0.0455017381405298 \tabularnewline
46 & 34.06 & 33.9519760397033 & 0.108023960296656 \tabularnewline
47 & 34.16 & 34.1434693728602 & 0.0165306271397654 \tabularnewline
48 & 34.16 & 34.2498189902721 & -0.0898189902721285 \tabularnewline
49 & 34.16 & 34.2153184102439 & -0.0553184102439488 \tabularnewline
50 & 34.29 & 34.1940699277808 & 0.0959300722191756 \tabularnewline
51 & 34.48 & 34.3609178496254 & 0.119082150374588 \tabularnewline
52 & 34.48 & 34.5966587697413 & -0.116658769741285 \tabularnewline
53 & 34.39 & 34.5518486999637 & -0.161848699963677 \tabularnewline
54 & 34.29 & 34.3996806216026 & -0.109680621602571 \tabularnewline
55 & 34.29 & 34.257550944441 & 0.0324490555589705 \tabularnewline
56 & 34.25 & 34.2700150261988 & -0.0200150261987915 \tabularnewline
57 & 34.2 & 34.2223270082079 & -0.0223270082078741 \tabularnewline
58 & 34.1 & 34.1637509294618 & -0.0637509294618184 \tabularnewline
59 & 34.09 & 34.0392634125447 & 0.0507365874553187 \tabularnewline
60 & 34.06 & 34.0487519604626 & 0.011248039537378 \tabularnewline
61 & 34.06 & 34.0230724709365 & 0.0369275290635471 \tabularnewline
62 & 34.04 & 34.0372567895069 & 0.00274321049305115 \tabularnewline
63 & 34.19 & 34.0183104904321 & 0.171689509567862 \tabularnewline
64 & 34.21 & 34.2342585449237 & -0.0242585449237112 \tabularnewline
65 & 34.17 & 34.2449405391437 & -0.0749405391437321 \tabularnewline
66 & 34.08 & 34.1761549553797 & -0.0961549553796601 \tabularnewline
67 & 34.08 & 34.0492206531443 & 0.0307793468556596 \tabularnewline
68 & 34.08 & 34.0610433792315 & 0.0189566207685417 \tabularnewline
69 & 34.3 & 34.0683248506654 & 0.231675149334635 \tabularnewline
70 & 34.28 & 34.3773141279434 & -0.0973141279433989 \tabularnewline
71 & 34.45 & 34.3199345732545 & 0.130065426745553 \tabularnewline
72 & 34.41 & 34.5398943050521 & -0.12989430505214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205453&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]32.74[/C][C]32.42[/C][C]0.319999999999993[/C][/ROW]
[ROW][C]4[/C][C]32.87[/C][C]32.5829159398872[/C][C]0.287084060112797[/C][/ROW]
[ROW][C]5[/C][C]32.95[/C][C]32.8231884619978[/C][C]0.126811538002194[/C][/ROW]
[ROW][C]6[/C][C]32.94[/C][C]32.9518983350668[/C][C]-0.0118983350668174[/C][/ROW]
[ROW][C]7[/C][C]32.94[/C][C]32.9373280380736[/C][C]0.00267196192640995[/C][/ROW]
[ROW][C]8[/C][C]32.97[/C][C]32.9383543715471[/C][C]0.0316456284528854[/C][/ROW]
[ROW][C]9[/C][C]32.87[/C][C]32.9805098470615[/C][C]-0.110509847061515[/C][/ROW]
[ROW][C]10[/C][C]32.96[/C][C]32.8380616541916[/C][C]0.121938345808353[/C][/ROW]
[ROW][C]11[/C][C]32.97[/C][C]32.9748996741395[/C][C]-0.00489967413953707[/C][/ROW]
[ROW][C]12[/C][C]32.99[/C][C]32.983017648977[/C][C]0.00698235102297673[/C][/ROW]
[ROW][C]13[/C][C]32.99[/C][C]33.0056996559727[/C][C]-0.0156996559726892[/C][/ROW]
[ROW][C]14[/C][C]33.04[/C][C]32.9996692248171[/C][C]0.0403307751828947[/C][/ROW]
[ROW][C]15[/C][C]33.23[/C][C]33.0651607721233[/C][C]0.164839227876698[/C][/ROW]
[ROW][C]16[/C][C]33.03[/C][C]33.3184775490756[/C][C]-0.288477549075623[/C][/ROW]
[ROW][C]17[/C][C]33.05[/C][C]33.0076697706976[/C][C]0.0423302293024435[/C][/ROW]
[ROW][C]18[/C][C]33.03[/C][C]33.0439293329486[/C][C]-0.0139293329486421[/C][/ROW]
[ROW][C]19[/C][C]33.04[/C][C]33.0185789046631[/C][C]0.021421095336926[/C][/ROW]
[ROW][C]20[/C][C]33.11[/C][C]33.0368070111217[/C][C]0.0731929888783327[/C][/ROW]
[ROW][C]21[/C][C]33.14[/C][C]33.1349213393127[/C][C]0.00507866068728902[/C][/ROW]
[ROW][C]22[/C][C]33.08[/C][C]33.1668721154119[/C][C]-0.0868721154119214[/C][/ROW]
[ROW][C]23[/C][C]33.09[/C][C]33.0735034662999[/C][C]0.0164965337001064[/C][/ROW]
[ROW][C]24[/C][C]33.07[/C][C]33.0898399880019[/C][C]-0.0198399880018698[/C][/ROW]
[ROW][C]25[/C][C]33.07[/C][C]33.0622192043375[/C][C]0.00778079566251222[/C][/ROW]
[ROW][C]26[/C][C]33.02[/C][C]33.0652079037498[/C][C]-0.0452079037497626[/C][/ROW]
[ROW][C]27[/C][C]33[/C][C]32.9978429913131[/C][C]0.00215700868689339[/C][/ROW]
[ROW][C]28[/C][C]33.08[/C][C]32.9786715249071[/C][C]0.101328475092849[/C][/ROW]
[ROW][C]29[/C][C]33.35[/C][C]33.0975930397614[/C][C]0.252406960238559[/C][/ROW]
[ROW][C]30[/C][C]33.36[/C][C]33.4645456608608[/C][C]-0.104545660860794[/C][/ROW]
[ROW][C]31[/C][C]33.36[/C][C]33.4343883853426[/C][C]-0.0743883853425658[/C][/ROW]
[ROW][C]32[/C][C]33.35[/C][C]33.4058148906517[/C][C]-0.0558148906517104[/C][/ROW]
[ROW][C]33[/C][C]33.41[/C][C]33.3743757039512[/C][C]0.0356242960487663[/C][/ROW]
[ROW][C]34[/C][C]33.47[/C][C]33.4480594346751[/C][C]0.0219405653248543[/C][/ROW]
[ROW][C]35[/C][C]33.47[/C][C]33.5164870759519[/C][C]-0.0464870759519016[/C][/ROW]
[ROW][C]36[/C][C]33.48[/C][C]33.498630817723[/C][C]-0.018630817723043[/C][/ROW]
[ROW][C]37[/C][C]33.48[/C][C]33.5014744912502[/C][C]-0.0214744912502454[/C][/ROW]
[ROW][C]38[/C][C]33.55[/C][C]33.4932258747639[/C][C]0.0567741252360818[/C][/ROW]
[ROW][C]39[/C][C]33.68[/C][C]33.5850335152785[/C][C]0.0949664847215033[/C][/ROW]
[ROW][C]40[/C][C]33.72[/C][C]33.7515113113014[/C][C]-0.0315113113014007[/C][/ROW]
[ROW][C]41[/C][C]33.79[/C][C]33.7794074286586[/C][C]0.0105925713413839[/C][/ROW]
[ROW][C]42[/C][C]33.83[/C][C]33.8534761657281[/C][C]-0.023476165728141[/C][/ROW]
[ROW][C]43[/C][C]33.83[/C][C]33.8844586814299[/C][C]-0.0544586814299493[/C][/ROW]
[ROW][C]44[/C][C]33.84[/C][C]33.8635404313894[/C][C]-0.0235404313893852[/C][/ROW]
[ROW][C]45[/C][C]33.91[/C][C]33.8644982618595[/C][C]0.0455017381405298[/C][/ROW]
[ROW][C]46[/C][C]34.06[/C][C]33.9519760397033[/C][C]0.108023960296656[/C][/ROW]
[ROW][C]47[/C][C]34.16[/C][C]34.1434693728602[/C][C]0.0165306271397654[/C][/ROW]
[ROW][C]48[/C][C]34.16[/C][C]34.2498189902721[/C][C]-0.0898189902721285[/C][/ROW]
[ROW][C]49[/C][C]34.16[/C][C]34.2153184102439[/C][C]-0.0553184102439488[/C][/ROW]
[ROW][C]50[/C][C]34.29[/C][C]34.1940699277808[/C][C]0.0959300722191756[/C][/ROW]
[ROW][C]51[/C][C]34.48[/C][C]34.3609178496254[/C][C]0.119082150374588[/C][/ROW]
[ROW][C]52[/C][C]34.48[/C][C]34.5966587697413[/C][C]-0.116658769741285[/C][/ROW]
[ROW][C]53[/C][C]34.39[/C][C]34.5518486999637[/C][C]-0.161848699963677[/C][/ROW]
[ROW][C]54[/C][C]34.29[/C][C]34.3996806216026[/C][C]-0.109680621602571[/C][/ROW]
[ROW][C]55[/C][C]34.29[/C][C]34.257550944441[/C][C]0.0324490555589705[/C][/ROW]
[ROW][C]56[/C][C]34.25[/C][C]34.2700150261988[/C][C]-0.0200150261987915[/C][/ROW]
[ROW][C]57[/C][C]34.2[/C][C]34.2223270082079[/C][C]-0.0223270082078741[/C][/ROW]
[ROW][C]58[/C][C]34.1[/C][C]34.1637509294618[/C][C]-0.0637509294618184[/C][/ROW]
[ROW][C]59[/C][C]34.09[/C][C]34.0392634125447[/C][C]0.0507365874553187[/C][/ROW]
[ROW][C]60[/C][C]34.06[/C][C]34.0487519604626[/C][C]0.011248039537378[/C][/ROW]
[ROW][C]61[/C][C]34.06[/C][C]34.0230724709365[/C][C]0.0369275290635471[/C][/ROW]
[ROW][C]62[/C][C]34.04[/C][C]34.0372567895069[/C][C]0.00274321049305115[/C][/ROW]
[ROW][C]63[/C][C]34.19[/C][C]34.0183104904321[/C][C]0.171689509567862[/C][/ROW]
[ROW][C]64[/C][C]34.21[/C][C]34.2342585449237[/C][C]-0.0242585449237112[/C][/ROW]
[ROW][C]65[/C][C]34.17[/C][C]34.2449405391437[/C][C]-0.0749405391437321[/C][/ROW]
[ROW][C]66[/C][C]34.08[/C][C]34.1761549553797[/C][C]-0.0961549553796601[/C][/ROW]
[ROW][C]67[/C][C]34.08[/C][C]34.0492206531443[/C][C]0.0307793468556596[/C][/ROW]
[ROW][C]68[/C][C]34.08[/C][C]34.0610433792315[/C][C]0.0189566207685417[/C][/ROW]
[ROW][C]69[/C][C]34.3[/C][C]34.0683248506654[/C][C]0.231675149334635[/C][/ROW]
[ROW][C]70[/C][C]34.28[/C][C]34.3773141279434[/C][C]-0.0973141279433989[/C][/ROW]
[ROW][C]71[/C][C]34.45[/C][C]34.3199345732545[/C][C]0.130065426745553[/C][/ROW]
[ROW][C]72[/C][C]34.41[/C][C]34.5398943050521[/C][C]-0.12989430505214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205453&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
332.7432.420.319999999999993
432.8732.58291593988720.287084060112797
532.9532.82318846199780.126811538002194
632.9432.9518983350668-0.0118983350668174
732.9432.93732803807360.00267196192640995
832.9732.93835437154710.0316456284528854
932.8732.9805098470615-0.110509847061515
1032.9632.83806165419160.121938345808353
1132.9732.9748996741395-0.00489967413953707
1232.9932.9830176489770.00698235102297673
1332.9933.0056996559727-0.0156996559726892
1433.0432.99966922481710.0403307751828947
1533.2333.06516077212330.164839227876698
1633.0333.3184775490756-0.288477549075623
1733.0533.00766977069760.0423302293024435
1833.0333.0439293329486-0.0139293329486421
1933.0433.01857890466310.021421095336926
2033.1133.03680701112170.0731929888783327
2133.1433.13492133931270.00507866068728902
2233.0833.1668721154119-0.0868721154119214
2333.0933.07350346629990.0164965337001064
2433.0733.0898399880019-0.0198399880018698
2533.0733.06221920433750.00778079566251222
2633.0233.0652079037498-0.0452079037497626
273332.99784299131310.00215700868689339
2833.0832.97867152490710.101328475092849
2933.3533.09759303976140.252406960238559
3033.3633.4645456608608-0.104545660860794
3133.3633.4343883853426-0.0743883853425658
3233.3533.4058148906517-0.0558148906517104
3333.4133.37437570395120.0356242960487663
3433.4733.44805943467510.0219405653248543
3533.4733.5164870759519-0.0464870759519016
3633.4833.498630817723-0.018630817723043
3733.4833.5014744912502-0.0214744912502454
3833.5533.49322587476390.0567741252360818
3933.6833.58503351527850.0949664847215033
4033.7233.7515113113014-0.0315113113014007
4133.7933.77940742865860.0105925713413839
4233.8333.8534761657281-0.023476165728141
4333.8333.8844586814299-0.0544586814299493
4433.8433.8635404313894-0.0235404313893852
4533.9133.86449826185950.0455017381405298
4634.0633.95197603970330.108023960296656
4734.1634.14346937286020.0165306271397654
4834.1634.2498189902721-0.0898189902721285
4934.1634.2153184102439-0.0553184102439488
5034.2934.19406992778080.0959300722191756
5134.4834.36091784962540.119082150374588
5234.4834.5966587697413-0.116658769741285
5334.3934.5518486999637-0.161848699963677
5434.2934.3996806216026-0.109680621602571
5534.2934.2575509444410.0324490555589705
5634.2534.2700150261988-0.0200150261987915
5734.234.2223270082079-0.0223270082078741
5834.134.1637509294618-0.0637509294618184
5934.0934.03926341254470.0507365874553187
6034.0634.04875196046260.011248039537378
6134.0634.02307247093650.0369275290635471
6234.0434.03725678950690.00274321049305115
6334.1934.01831049043210.171689509567862
6434.2134.2342585449237-0.0242585449237112
6534.1734.2449405391437-0.0749405391437321
6634.0834.1761549553797-0.0961549553796601
6734.0834.04922065314430.0307793468556596
6834.0834.06104337923150.0189566207685417
6934.334.06832485066540.231675149334635
7034.2834.3773141279434-0.0973141279433989
7134.4534.31993457325450.130065426745553
7234.4134.5398943050521-0.12989430505214







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7334.450000303203834.249926435372534.650074171035
7434.490000606407534.148362136433834.8316390763812
7534.530000909611334.038194060624335.0218077585983
7634.570001212815133.916309349471135.2236930761591
7734.610001516018833.78244718389335.4375558481447
7834.650001819222633.636944348027435.6630592904178
7934.690002122426333.480273658615635.8997305862371
8034.730002425630133.312917098901836.1470877523584
8134.770002728833933.135328099695936.4046773579719
8234.810003032037632.947921933403536.6720841306718
8334.850003335241432.751075621041436.9489310494414
8434.890003638445232.54513096817837.2348763087123

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 34.4500003032038 & 34.2499264353725 & 34.650074171035 \tabularnewline
74 & 34.4900006064075 & 34.1483621364338 & 34.8316390763812 \tabularnewline
75 & 34.5300009096113 & 34.0381940606243 & 35.0218077585983 \tabularnewline
76 & 34.5700012128151 & 33.9163093494711 & 35.2236930761591 \tabularnewline
77 & 34.6100015160188 & 33.782447183893 & 35.4375558481447 \tabularnewline
78 & 34.6500018192226 & 33.6369443480274 & 35.6630592904178 \tabularnewline
79 & 34.6900021224263 & 33.4802736586156 & 35.8997305862371 \tabularnewline
80 & 34.7300024256301 & 33.3129170989018 & 36.1470877523584 \tabularnewline
81 & 34.7700027288339 & 33.1353280996959 & 36.4046773579719 \tabularnewline
82 & 34.8100030320376 & 32.9479219334035 & 36.6720841306718 \tabularnewline
83 & 34.8500033352414 & 32.7510756210414 & 36.9489310494414 \tabularnewline
84 & 34.8900036384452 & 32.545130968178 & 37.2348763087123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205453&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]34.4500003032038[/C][C]34.2499264353725[/C][C]34.650074171035[/C][/ROW]
[ROW][C]74[/C][C]34.4900006064075[/C][C]34.1483621364338[/C][C]34.8316390763812[/C][/ROW]
[ROW][C]75[/C][C]34.5300009096113[/C][C]34.0381940606243[/C][C]35.0218077585983[/C][/ROW]
[ROW][C]76[/C][C]34.5700012128151[/C][C]33.9163093494711[/C][C]35.2236930761591[/C][/ROW]
[ROW][C]77[/C][C]34.6100015160188[/C][C]33.782447183893[/C][C]35.4375558481447[/C][/ROW]
[ROW][C]78[/C][C]34.6500018192226[/C][C]33.6369443480274[/C][C]35.6630592904178[/C][/ROW]
[ROW][C]79[/C][C]34.6900021224263[/C][C]33.4802736586156[/C][C]35.8997305862371[/C][/ROW]
[ROW][C]80[/C][C]34.7300024256301[/C][C]33.3129170989018[/C][C]36.1470877523584[/C][/ROW]
[ROW][C]81[/C][C]34.7700027288339[/C][C]33.1353280996959[/C][C]36.4046773579719[/C][/ROW]
[ROW][C]82[/C][C]34.8100030320376[/C][C]32.9479219334035[/C][C]36.6720841306718[/C][/ROW]
[ROW][C]83[/C][C]34.8500033352414[/C][C]32.7510756210414[/C][C]36.9489310494414[/C][/ROW]
[ROW][C]84[/C][C]34.8900036384452[/C][C]32.545130968178[/C][C]37.2348763087123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205453&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205453&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
7334.450000303203834.249926435372534.650074171035
7434.490000606407534.148362136433834.8316390763812
7534.530000909611334.038194060624335.0218077585983
7634.570001212815133.916309349471135.2236930761591
7734.610001516018833.78244718389335.4375558481447
7834.650001819222633.636944348027435.6630592904178
7934.690002122426333.480273658615635.8997305862371
8034.730002425630133.312917098901836.1470877523584
8134.770002728833933.135328099695936.4046773579719
8234.810003032037632.947921933403536.6720841306718
8334.850003335241432.751075621041436.9489310494414
8434.890003638445232.54513096817837.2348763087123



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')