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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 10:16:54 -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/t1211991563nien4mvkqlmxv88.htm/, Retrieved Tue, 14 May 2024 18:46:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13453, Retrieved Tue, 14 May 2024 18:46:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-28 16:16:54] [b64702de7eac3a2282df81a39c87ddc7] [Current]
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Dataseries X:
20.66
20.66
20.67
20.71
20.73
20.73
20.74
20.74
20.75
20.75
20.77
20.78
20.78
20.8
20.84
20.85
20.86
20.86
20.86
20.86
20.9
20.92
20.95
20.95
20.95
20.96
21.1
21.18
21.19
21.19
21.19
21.19
21.19
21.21
21.22
21.22
21.22
21.23
21.41
21.42
21.43
21.44
21.44
21.44
21.48
21.53
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.57
21.6
21.61
21.6
21.6
21.71
21.75
21.84
21.85
21.92
21.92
21.93
22
22
21.99
22.01
22.01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13453&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13453&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.957264156086689
beta0.000728381616693922
gamma0.0436617754682502

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.957264156086689 \tabularnewline
beta & 0.000728381616693922 \tabularnewline
gamma & 0.0436617754682502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13453&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]0.957264156086689[/C][/ROW]
[ROW][C]beta[/C][C]0.000728381616693922[/C][/ROW]
[ROW][C]gamma[/C][C]0.0436617754682502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13453&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
alpha0.957264156086689
beta0.000728381616693922
gamma0.0436617754682502







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.7820.68431096620980.0956890337901655
1420.820.8035987033585-0.00359870335853785
1520.8420.8466009164802-0.00660091648018124
1620.8520.8546382827958-0.00463828279578848
1720.8620.8632994673315-0.00329946733154429
1820.8620.8632377301432-0.00323773014320139
1920.8620.8636470812610-0.00364708126102542
2020.8620.8640757840295-0.00407578402951358
2120.920.9003471252069-0.000347125206889842
2220.9220.91310806252310.0068919374769223
2320.9520.93988730633270.0101126936672671
2420.9520.93977017311960.0102298268803942
2520.9520.9860023929698-0.0360023929698094
2620.9620.9790976480829-0.0190976480829228
2721.121.00744212755150.0925578724484808
2821.1821.11039494817670.0696050518233235
2921.1921.1901405564534-0.000140556453377627
3021.1921.1929577864363-0.00295778643629774
3121.1921.1934960734358-0.00349607343584069
3221.1921.1939370234997-0.00393702349964897
3321.1921.230790213948-0.0407902139479859
3421.2121.20484404031210.00515595968786542
3521.2221.2300589066462-0.0100589066461723
3621.2221.21031991215320.0096800878468315
3721.2221.2562222506461-0.036222250646091
3821.2321.2493084655983-0.0193084655983071
3921.4121.27807627060420.131923729395847
4021.4221.41868858856730.00131141143273794
4121.4321.4328956824652-0.00289568246520133
4221.4421.43292204241880.00707795758118479
4321.4421.4429234571782-0.00292345717816644
4421.4421.4437742090780-0.00377420907803128
4521.4821.4810105358994-0.00101053589935063
4621.5321.49322296805350.036777031946535
4721.5421.5487940549371-0.00879405493711616
4821.5421.52996172519120.0100382748087569
4921.5421.5764832131057-0.0364832131056687
5021.5421.5695812629633-0.0295812629633403
5121.5421.5893029495434-0.0493029495433639
5221.5421.5561103661355-0.0161103661354751
5321.5421.5535373732239-0.0135373732239437
5421.5421.543243287304-0.00324328730401646
5521.5421.5431954985783-0.00319549857825407
5621.5421.5436361267929-0.00363612679290881
5721.5721.5810351530419-0.0110351530418917
5821.621.58361349010290.0163865098970604
5921.6121.6194851074222-0.00948510742223618
6021.621.59983103154480.000168968455238172
6121.621.6367606437960-0.0367606437960362
6221.7121.62952349281090.0804765071890543
6321.7521.7547601494398-0.00476014943981085
6421.8421.76422984587550.0757701541245268
6521.8521.84960928845650.00039071154353465
6621.9221.85252185689990.067478143100054
6721.9221.9200367206734-3.67206734281922e-05
6821.9321.92337197979810.00662802020194775
692221.97113078334570.0288692166542965
702222.0120269381526-0.0120269381526299
7121.9922.0208334448575-0.0308334448574996
7222.0121.98038586398920.0296141360108244
7322.0122.0459357368618-0.0359357368617808

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 20.78 & 20.6843109662098 & 0.0956890337901655 \tabularnewline
14 & 20.8 & 20.8035987033585 & -0.00359870335853785 \tabularnewline
15 & 20.84 & 20.8466009164802 & -0.00660091648018124 \tabularnewline
16 & 20.85 & 20.8546382827958 & -0.00463828279578848 \tabularnewline
17 & 20.86 & 20.8632994673315 & -0.00329946733154429 \tabularnewline
18 & 20.86 & 20.8632377301432 & -0.00323773014320139 \tabularnewline
19 & 20.86 & 20.8636470812610 & -0.00364708126102542 \tabularnewline
20 & 20.86 & 20.8640757840295 & -0.00407578402951358 \tabularnewline
21 & 20.9 & 20.9003471252069 & -0.000347125206889842 \tabularnewline
22 & 20.92 & 20.9131080625231 & 0.0068919374769223 \tabularnewline
23 & 20.95 & 20.9398873063327 & 0.0101126936672671 \tabularnewline
24 & 20.95 & 20.9397701731196 & 0.0102298268803942 \tabularnewline
25 & 20.95 & 20.9860023929698 & -0.0360023929698094 \tabularnewline
26 & 20.96 & 20.9790976480829 & -0.0190976480829228 \tabularnewline
27 & 21.1 & 21.0074421275515 & 0.0925578724484808 \tabularnewline
28 & 21.18 & 21.1103949481767 & 0.0696050518233235 \tabularnewline
29 & 21.19 & 21.1901405564534 & -0.000140556453377627 \tabularnewline
30 & 21.19 & 21.1929577864363 & -0.00295778643629774 \tabularnewline
31 & 21.19 & 21.1934960734358 & -0.00349607343584069 \tabularnewline
32 & 21.19 & 21.1939370234997 & -0.00393702349964897 \tabularnewline
33 & 21.19 & 21.230790213948 & -0.0407902139479859 \tabularnewline
34 & 21.21 & 21.2048440403121 & 0.00515595968786542 \tabularnewline
35 & 21.22 & 21.2300589066462 & -0.0100589066461723 \tabularnewline
36 & 21.22 & 21.2103199121532 & 0.0096800878468315 \tabularnewline
37 & 21.22 & 21.2562222506461 & -0.036222250646091 \tabularnewline
38 & 21.23 & 21.2493084655983 & -0.0193084655983071 \tabularnewline
39 & 21.41 & 21.2780762706042 & 0.131923729395847 \tabularnewline
40 & 21.42 & 21.4186885885673 & 0.00131141143273794 \tabularnewline
41 & 21.43 & 21.4328956824652 & -0.00289568246520133 \tabularnewline
42 & 21.44 & 21.4329220424188 & 0.00707795758118479 \tabularnewline
43 & 21.44 & 21.4429234571782 & -0.00292345717816644 \tabularnewline
44 & 21.44 & 21.4437742090780 & -0.00377420907803128 \tabularnewline
45 & 21.48 & 21.4810105358994 & -0.00101053589935063 \tabularnewline
46 & 21.53 & 21.4932229680535 & 0.036777031946535 \tabularnewline
47 & 21.54 & 21.5487940549371 & -0.00879405493711616 \tabularnewline
48 & 21.54 & 21.5299617251912 & 0.0100382748087569 \tabularnewline
49 & 21.54 & 21.5764832131057 & -0.0364832131056687 \tabularnewline
50 & 21.54 & 21.5695812629633 & -0.0295812629633403 \tabularnewline
51 & 21.54 & 21.5893029495434 & -0.0493029495433639 \tabularnewline
52 & 21.54 & 21.5561103661355 & -0.0161103661354751 \tabularnewline
53 & 21.54 & 21.5535373732239 & -0.0135373732239437 \tabularnewline
54 & 21.54 & 21.543243287304 & -0.00324328730401646 \tabularnewline
55 & 21.54 & 21.5431954985783 & -0.00319549857825407 \tabularnewline
56 & 21.54 & 21.5436361267929 & -0.00363612679290881 \tabularnewline
57 & 21.57 & 21.5810351530419 & -0.0110351530418917 \tabularnewline
58 & 21.6 & 21.5836134901029 & 0.0163865098970604 \tabularnewline
59 & 21.61 & 21.6194851074222 & -0.00948510742223618 \tabularnewline
60 & 21.6 & 21.5998310315448 & 0.000168968455238172 \tabularnewline
61 & 21.6 & 21.6367606437960 & -0.0367606437960362 \tabularnewline
62 & 21.71 & 21.6295234928109 & 0.0804765071890543 \tabularnewline
63 & 21.75 & 21.7547601494398 & -0.00476014943981085 \tabularnewline
64 & 21.84 & 21.7642298458755 & 0.0757701541245268 \tabularnewline
65 & 21.85 & 21.8496092884565 & 0.00039071154353465 \tabularnewline
66 & 21.92 & 21.8525218568999 & 0.067478143100054 \tabularnewline
67 & 21.92 & 21.9200367206734 & -3.67206734281922e-05 \tabularnewline
68 & 21.93 & 21.9233719797981 & 0.00662802020194775 \tabularnewline
69 & 22 & 21.9711307833457 & 0.0288692166542965 \tabularnewline
70 & 22 & 22.0120269381526 & -0.0120269381526299 \tabularnewline
71 & 21.99 & 22.0208334448575 & -0.0308334448574996 \tabularnewline
72 & 22.01 & 21.9803858639892 & 0.0296141360108244 \tabularnewline
73 & 22.01 & 22.0459357368618 & -0.0359357368617808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13453&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]20.78[/C][C]20.6843109662098[/C][C]0.0956890337901655[/C][/ROW]
[ROW][C]14[/C][C]20.8[/C][C]20.8035987033585[/C][C]-0.00359870335853785[/C][/ROW]
[ROW][C]15[/C][C]20.84[/C][C]20.8466009164802[/C][C]-0.00660091648018124[/C][/ROW]
[ROW][C]16[/C][C]20.85[/C][C]20.8546382827958[/C][C]-0.00463828279578848[/C][/ROW]
[ROW][C]17[/C][C]20.86[/C][C]20.8632994673315[/C][C]-0.00329946733154429[/C][/ROW]
[ROW][C]18[/C][C]20.86[/C][C]20.8632377301432[/C][C]-0.00323773014320139[/C][/ROW]
[ROW][C]19[/C][C]20.86[/C][C]20.8636470812610[/C][C]-0.00364708126102542[/C][/ROW]
[ROW][C]20[/C][C]20.86[/C][C]20.8640757840295[/C][C]-0.00407578402951358[/C][/ROW]
[ROW][C]21[/C][C]20.9[/C][C]20.9003471252069[/C][C]-0.000347125206889842[/C][/ROW]
[ROW][C]22[/C][C]20.92[/C][C]20.9131080625231[/C][C]0.0068919374769223[/C][/ROW]
[ROW][C]23[/C][C]20.95[/C][C]20.9398873063327[/C][C]0.0101126936672671[/C][/ROW]
[ROW][C]24[/C][C]20.95[/C][C]20.9397701731196[/C][C]0.0102298268803942[/C][/ROW]
[ROW][C]25[/C][C]20.95[/C][C]20.9860023929698[/C][C]-0.0360023929698094[/C][/ROW]
[ROW][C]26[/C][C]20.96[/C][C]20.9790976480829[/C][C]-0.0190976480829228[/C][/ROW]
[ROW][C]27[/C][C]21.1[/C][C]21.0074421275515[/C][C]0.0925578724484808[/C][/ROW]
[ROW][C]28[/C][C]21.18[/C][C]21.1103949481767[/C][C]0.0696050518233235[/C][/ROW]
[ROW][C]29[/C][C]21.19[/C][C]21.1901405564534[/C][C]-0.000140556453377627[/C][/ROW]
[ROW][C]30[/C][C]21.19[/C][C]21.1929577864363[/C][C]-0.00295778643629774[/C][/ROW]
[ROW][C]31[/C][C]21.19[/C][C]21.1934960734358[/C][C]-0.00349607343584069[/C][/ROW]
[ROW][C]32[/C][C]21.19[/C][C]21.1939370234997[/C][C]-0.00393702349964897[/C][/ROW]
[ROW][C]33[/C][C]21.19[/C][C]21.230790213948[/C][C]-0.0407902139479859[/C][/ROW]
[ROW][C]34[/C][C]21.21[/C][C]21.2048440403121[/C][C]0.00515595968786542[/C][/ROW]
[ROW][C]35[/C][C]21.22[/C][C]21.2300589066462[/C][C]-0.0100589066461723[/C][/ROW]
[ROW][C]36[/C][C]21.22[/C][C]21.2103199121532[/C][C]0.0096800878468315[/C][/ROW]
[ROW][C]37[/C][C]21.22[/C][C]21.2562222506461[/C][C]-0.036222250646091[/C][/ROW]
[ROW][C]38[/C][C]21.23[/C][C]21.2493084655983[/C][C]-0.0193084655983071[/C][/ROW]
[ROW][C]39[/C][C]21.41[/C][C]21.2780762706042[/C][C]0.131923729395847[/C][/ROW]
[ROW][C]40[/C][C]21.42[/C][C]21.4186885885673[/C][C]0.00131141143273794[/C][/ROW]
[ROW][C]41[/C][C]21.43[/C][C]21.4328956824652[/C][C]-0.00289568246520133[/C][/ROW]
[ROW][C]42[/C][C]21.44[/C][C]21.4329220424188[/C][C]0.00707795758118479[/C][/ROW]
[ROW][C]43[/C][C]21.44[/C][C]21.4429234571782[/C][C]-0.00292345717816644[/C][/ROW]
[ROW][C]44[/C][C]21.44[/C][C]21.4437742090780[/C][C]-0.00377420907803128[/C][/ROW]
[ROW][C]45[/C][C]21.48[/C][C]21.4810105358994[/C][C]-0.00101053589935063[/C][/ROW]
[ROW][C]46[/C][C]21.53[/C][C]21.4932229680535[/C][C]0.036777031946535[/C][/ROW]
[ROW][C]47[/C][C]21.54[/C][C]21.5487940549371[/C][C]-0.00879405493711616[/C][/ROW]
[ROW][C]48[/C][C]21.54[/C][C]21.5299617251912[/C][C]0.0100382748087569[/C][/ROW]
[ROW][C]49[/C][C]21.54[/C][C]21.5764832131057[/C][C]-0.0364832131056687[/C][/ROW]
[ROW][C]50[/C][C]21.54[/C][C]21.5695812629633[/C][C]-0.0295812629633403[/C][/ROW]
[ROW][C]51[/C][C]21.54[/C][C]21.5893029495434[/C][C]-0.0493029495433639[/C][/ROW]
[ROW][C]52[/C][C]21.54[/C][C]21.5561103661355[/C][C]-0.0161103661354751[/C][/ROW]
[ROW][C]53[/C][C]21.54[/C][C]21.5535373732239[/C][C]-0.0135373732239437[/C][/ROW]
[ROW][C]54[/C][C]21.54[/C][C]21.543243287304[/C][C]-0.00324328730401646[/C][/ROW]
[ROW][C]55[/C][C]21.54[/C][C]21.5431954985783[/C][C]-0.00319549857825407[/C][/ROW]
[ROW][C]56[/C][C]21.54[/C][C]21.5436361267929[/C][C]-0.00363612679290881[/C][/ROW]
[ROW][C]57[/C][C]21.57[/C][C]21.5810351530419[/C][C]-0.0110351530418917[/C][/ROW]
[ROW][C]58[/C][C]21.6[/C][C]21.5836134901029[/C][C]0.0163865098970604[/C][/ROW]
[ROW][C]59[/C][C]21.61[/C][C]21.6194851074222[/C][C]-0.00948510742223618[/C][/ROW]
[ROW][C]60[/C][C]21.6[/C][C]21.5998310315448[/C][C]0.000168968455238172[/C][/ROW]
[ROW][C]61[/C][C]21.6[/C][C]21.6367606437960[/C][C]-0.0367606437960362[/C][/ROW]
[ROW][C]62[/C][C]21.71[/C][C]21.6295234928109[/C][C]0.0804765071890543[/C][/ROW]
[ROW][C]63[/C][C]21.75[/C][C]21.7547601494398[/C][C]-0.00476014943981085[/C][/ROW]
[ROW][C]64[/C][C]21.84[/C][C]21.7642298458755[/C][C]0.0757701541245268[/C][/ROW]
[ROW][C]65[/C][C]21.85[/C][C]21.8496092884565[/C][C]0.00039071154353465[/C][/ROW]
[ROW][C]66[/C][C]21.92[/C][C]21.8525218568999[/C][C]0.067478143100054[/C][/ROW]
[ROW][C]67[/C][C]21.92[/C][C]21.9200367206734[/C][C]-3.67206734281922e-05[/C][/ROW]
[ROW][C]68[/C][C]21.93[/C][C]21.9233719797981[/C][C]0.00662802020194775[/C][/ROW]
[ROW][C]69[/C][C]22[/C][C]21.9711307833457[/C][C]0.0288692166542965[/C][/ROW]
[ROW][C]70[/C][C]22[/C][C]22.0120269381526[/C][C]-0.0120269381526299[/C][/ROW]
[ROW][C]71[/C][C]21.99[/C][C]22.0208334448575[/C][C]-0.0308334448574996[/C][/ROW]
[ROW][C]72[/C][C]22.01[/C][C]21.9803858639892[/C][C]0.0296141360108244[/C][/ROW]
[ROW][C]73[/C][C]22.01[/C][C]22.0459357368618[/C][C]-0.0359357368617808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13453&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
1320.7820.68431096620980.0956890337901655
1420.820.8035987033585-0.00359870335853785
1520.8420.8466009164802-0.00660091648018124
1620.8520.8546382827958-0.00463828279578848
1720.8620.8632994673315-0.00329946733154429
1820.8620.8632377301432-0.00323773014320139
1920.8620.8636470812610-0.00364708126102542
2020.8620.8640757840295-0.00407578402951358
2120.920.9003471252069-0.000347125206889842
2220.9220.91310806252310.0068919374769223
2320.9520.93988730633270.0101126936672671
2420.9520.93977017311960.0102298268803942
2520.9520.9860023929698-0.0360023929698094
2620.9620.9790976480829-0.0190976480829228
2721.121.00744212755150.0925578724484808
2821.1821.11039494817670.0696050518233235
2921.1921.1901405564534-0.000140556453377627
3021.1921.1929577864363-0.00295778643629774
3121.1921.1934960734358-0.00349607343584069
3221.1921.1939370234997-0.00393702349964897
3321.1921.230790213948-0.0407902139479859
3421.2121.20484404031210.00515595968786542
3521.2221.2300589066462-0.0100589066461723
3621.2221.21031991215320.0096800878468315
3721.2221.2562222506461-0.036222250646091
3821.2321.2493084655983-0.0193084655983071
3921.4121.27807627060420.131923729395847
4021.4221.41868858856730.00131141143273794
4121.4321.4328956824652-0.00289568246520133
4221.4421.43292204241880.00707795758118479
4321.4421.4429234571782-0.00292345717816644
4421.4421.4437742090780-0.00377420907803128
4521.4821.4810105358994-0.00101053589935063
4621.5321.49322296805350.036777031946535
4721.5421.5487940549371-0.00879405493711616
4821.5421.52996172519120.0100382748087569
4921.5421.5764832131057-0.0364832131056687
5021.5421.5695812629633-0.0295812629633403
5121.5421.5893029495434-0.0493029495433639
5221.5421.5561103661355-0.0161103661354751
5321.5421.5535373732239-0.0135373732239437
5421.5421.543243287304-0.00324328730401646
5521.5421.5431954985783-0.00319549857825407
5621.5421.5436361267929-0.00363612679290881
5721.5721.5810351530419-0.0110351530418917
5821.621.58361349010290.0163865098970604
5921.6121.6194851074222-0.00948510742223618
6021.621.59983103154480.000168968455238172
6121.621.6367606437960-0.0367606437960362
6221.7121.62952349281090.0804765071890543
6321.7521.7547601494398-0.00476014943981085
6421.8421.76422984587550.0757701541245268
6521.8521.84960928845650.00039071154353465
6621.9221.85252185689990.067478143100054
6721.9221.9200367206734-3.67206734281922e-05
6821.9321.92337197979810.00662802020194775
692221.97113078334570.0288692166542965
702222.0120269381526-0.0120269381526299
7121.9922.0208334448575-0.0308334448574996
7222.0121.98038586398920.0296141360108244
7322.0122.0459357368618-0.0359357368617808







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7422.040049140949021.974088951334422.1060093305635
7522.088641973504221.995352001636222.1819319453721
7622.102853321152121.988631367214922.2170752750893
7722.115535927394121.983651933300022.2474199214882
7822.118053075447121.970647347619022.2654588032753
7922.120700392813621.959256635479422.2821441501477
8022.123941694981221.949581426790122.2983019631722
8122.165592276696321.978923774710622.3522607786821
8222.178707056803121.980679734235722.3767343793706
8322.198985291655621.990144805926122.4078257773851
8422.187891544742321.969035477647222.4067476118374
8522.225102054911418.517464095812325.9327400140105

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 22.0400491409490 & 21.9740889513344 & 22.1060093305635 \tabularnewline
75 & 22.0886419735042 & 21.9953520016362 & 22.1819319453721 \tabularnewline
76 & 22.1028533211521 & 21.9886313672149 & 22.2170752750893 \tabularnewline
77 & 22.1155359273941 & 21.9836519333000 & 22.2474199214882 \tabularnewline
78 & 22.1180530754471 & 21.9706473476190 & 22.2654588032753 \tabularnewline
79 & 22.1207003928136 & 21.9592566354794 & 22.2821441501477 \tabularnewline
80 & 22.1239416949812 & 21.9495814267901 & 22.2983019631722 \tabularnewline
81 & 22.1655922766963 & 21.9789237747106 & 22.3522607786821 \tabularnewline
82 & 22.1787070568031 & 21.9806797342357 & 22.3767343793706 \tabularnewline
83 & 22.1989852916556 & 21.9901448059261 & 22.4078257773851 \tabularnewline
84 & 22.1878915447423 & 21.9690354776472 & 22.4067476118374 \tabularnewline
85 & 22.2251020549114 & 18.5174640958123 & 25.9327400140105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13453&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]74[/C][C]22.0400491409490[/C][C]21.9740889513344[/C][C]22.1060093305635[/C][/ROW]
[ROW][C]75[/C][C]22.0886419735042[/C][C]21.9953520016362[/C][C]22.1819319453721[/C][/ROW]
[ROW][C]76[/C][C]22.1028533211521[/C][C]21.9886313672149[/C][C]22.2170752750893[/C][/ROW]
[ROW][C]77[/C][C]22.1155359273941[/C][C]21.9836519333000[/C][C]22.2474199214882[/C][/ROW]
[ROW][C]78[/C][C]22.1180530754471[/C][C]21.9706473476190[/C][C]22.2654588032753[/C][/ROW]
[ROW][C]79[/C][C]22.1207003928136[/C][C]21.9592566354794[/C][C]22.2821441501477[/C][/ROW]
[ROW][C]80[/C][C]22.1239416949812[/C][C]21.9495814267901[/C][C]22.2983019631722[/C][/ROW]
[ROW][C]81[/C][C]22.1655922766963[/C][C]21.9789237747106[/C][C]22.3522607786821[/C][/ROW]
[ROW][C]82[/C][C]22.1787070568031[/C][C]21.9806797342357[/C][C]22.3767343793706[/C][/ROW]
[ROW][C]83[/C][C]22.1989852916556[/C][C]21.9901448059261[/C][C]22.4078257773851[/C][/ROW]
[ROW][C]84[/C][C]22.1878915447423[/C][C]21.9690354776472[/C][C]22.4067476118374[/C][/ROW]
[ROW][C]85[/C][C]22.2251020549114[/C][C]18.5174640958123[/C][C]25.9327400140105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13453&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13453&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
7422.040049140949021.974088951334422.1060093305635
7522.088641973504221.995352001636222.1819319453721
7622.102853321152121.988631367214922.2170752750893
7722.115535927394121.983651933300022.2474199214882
7822.118053075447121.970647347619022.2654588032753
7922.120700392813621.959256635479422.2821441501477
8022.123941694981221.949581426790122.2983019631722
8122.165592276696321.978923774710622.3522607786821
8222.178707056803121.980679734235722.3767343793706
8322.198985291655621.990144805926122.4078257773851
8422.187891544742321.969035477647222.4067476118374
8522.225102054911418.517464095812325.9327400140105



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')