Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 07 Jan 2016 23:00:03 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/07/t1452207730kewa2hgv0tbsr3o.htm/, Retrieved Sun, 28 Apr 2024 16:04:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287397, Retrieved Sun, 28 Apr 2024 16:04:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Saghar Najafi Zadeh] [2015-11-29 15:14:08] [a726dea3093235710caf789b0c5edf8a]
- R PD    [Exponential Smoothing] [Saghar Najafi Zadeh] [2016-01-07 23:00:03] [c23f68ac64e5ceef3ca8a84a34b0ff7e] [Current]
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Dataseries X:
88.83
89.01
88.21
87.78
87.93
88.11
88.2
88.12
88.38
87.65
88.24
87.83
87.75
87.88
87.61
88.05
87.77
87.79
88.34
88.48
88.75
87.95
89.09
88.73
89.24
89.77
89.84
90.97
91.53
92.2
92.27
92.42
92.07
91.73
92.1
91.68
92.63
93.02
92.66
93.23
93.79
93.92
94.04
94.23
94.37
94.29
94.38
94
94.11
93.98
93.42
93.3
93.32
93.75
93.82
94.06
94.09
93.64
93.9
93.18
93.54
93.55
93.8
93.39
93.27
93.58
93.47
93.75
93.3
92.65
92.96
92.84
93.29
93.57
93.54
94.38
93.98
94.48
94.63
95.45
95.59
94.76
95.66
95.03
96.45
97.15
97.5
98.54
99.54
100.33
100.28
101.81
101.91
101.92
102.68
101.9
102.14
102.3
102.06
102.4
102.99
102.99
102.83
103.01
102.6
102.18
102.6
101.44




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287397&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287397&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.870709591524665
beta0.230775607021298
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.870709591524665 \tabularnewline
beta & 0.230775607021298 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287397&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]0.870709591524665[/C][/ROW]
[ROW][C]beta[/C][C]0.230775607021298[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287397&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
alpha0.870709591524665
beta0.230775607021298
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1387.7587.8920032051282-0.142003205128248
1487.8887.85097666886070.029023331139328
1587.6187.55511315041930.0548868495806971
1688.0588.00529812867480.0447018713252163
1787.7787.71559727718830.0544027228117159
1887.7987.72027465353290.0697253464671093
1988.3488.21438742753310.125612572466878
2088.4888.3853188181510.0946811818490403
2188.7588.8683430482063-0.118343048206313
2287.9588.0937720259144-0.143772025914387
2389.0988.56983707530330.520162924696677
2488.7388.7531007634731-0.0231007634730815
2589.2488.75783806167180.482161938328147
2689.7789.52153576365590.24846423634412
2789.8489.7033251553340.13667484466599
2890.9790.52308096957780.446919030422166
2991.5390.96534367414820.564656325851843
3092.291.89930942697540.300690573024625
3192.2793.1311859374105-0.861185937410511
3292.4292.7700518380881-0.35005183808812
3392.0793.0800853406571-1.01008534065707
3491.7391.58837720718710.141622792812868
3592.192.5187246791566-0.418724679156583
3691.6891.7455384375117-0.0655384375116483
3792.6391.70141039933360.928589600666356
3893.0292.83606653007650.183933469923517
3992.6692.9467128033225-0.286712803322544
4093.2393.3523553704631-0.12235537046314
4193.7993.11420137456650.675798625433544
4293.9293.933178002033-0.0131780020329586
4394.0494.5008448019261-0.460844801926086
4494.2394.3941184235835-0.164118423583503
4594.3794.657813238166-0.287813238166024
4694.2993.96613477062210.323865229377873
4794.3895.0415700582595-0.661570058259528
489494.1126577463367-0.11265774633668
4994.1194.1566237464028-0.046623746402787
5093.9894.1505074781958-0.170507478195816
5193.4293.6250998361233-0.205099836123296
5293.393.8728638930079-0.572863893007934
5393.3293.00492739609360.315072603906344
5493.7593.00754052344870.742459476551275
5593.8293.9139079641592-0.0939079641592286
5694.0693.97741149896640.0825885010336123
5794.0994.3018673882554-0.211867388255371
5893.6493.63260384962410.00739615037589658
5993.994.1186923009669-0.21869230096685
6093.1893.5489713618187-0.36897136181868
6193.5493.2294012835990.310598716401003
6293.5593.4411859022790.108814097720952
6393.893.13352108401860.666478915981415
6493.3994.2467698207905-0.85676982079049
6593.2793.3435288065781-0.0735288065780679
6693.5893.08204840867580.49795159132421
6793.4793.637263571124-0.167263571123968
6893.7593.61485237792470.135147622075266
6993.393.9127002310713-0.612700231071273
7092.6592.8079321552998-0.157932155299804
7192.9692.9727715606812-0.012771560681216
7292.8492.45623051957840.383769480421591
7393.2992.92450802289360.365491977106416
7493.5793.21359710303130.35640289696866
7593.5493.2989582582850.241041741715009
7694.3893.86469391222620.51530608777378
7793.9894.5529616216655-0.572961621665513
7894.4894.1257154365710.354284563428962
7994.6394.6361723788697-0.00617237886966393
8095.4594.99183310577040.458166894229578
8195.5995.7378638093856-0.147863809385584
8294.7695.4536503904778-0.693650390477785
8395.6695.42017620134760.239823798652409
8495.0395.4749709955443-0.444970995544296
8596.4595.35289689491261.09710310508737
8697.1596.55844432169430.591555678305724
8797.597.16150407464620.338495925353755
8898.5498.1949999775910.345000022409039
8999.5498.90750314178650.632496858213514
90100.33100.2051934717590.124806528240796
91100.28100.978575298795-0.698575298795404
92101.81101.1615955847050.648404415294578
93101.91102.403346822353-0.493346822353061
94101.92102.086765067-0.166765066999744
95102.68103.077627813295-0.39762781329469
96101.9102.805644954864-0.905644954863945
97102.14102.706060838069-0.566060838069347
98102.3102.2881471369570.011852863043373
99102.06102.127285358443-0.0672853584425184
100102.4102.500316895231-0.100316895231174
101102.99102.4647799748180.525220025181895
102102.99103.184398841075-0.194398841075369
103102.83103.090224453405-0.260224453405471
104103.01103.433988493544-0.423988493544201
105102.6102.983810307407-0.383810307406947
106102.18102.216267893296-0.03626789329644
107102.6102.728570310982-0.128570310981729
108101.44102.116903546308-0.676903546308083

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 87.75 & 87.8920032051282 & -0.142003205128248 \tabularnewline
14 & 87.88 & 87.8509766688607 & 0.029023331139328 \tabularnewline
15 & 87.61 & 87.5551131504193 & 0.0548868495806971 \tabularnewline
16 & 88.05 & 88.0052981286748 & 0.0447018713252163 \tabularnewline
17 & 87.77 & 87.7155972771883 & 0.0544027228117159 \tabularnewline
18 & 87.79 & 87.7202746535329 & 0.0697253464671093 \tabularnewline
19 & 88.34 & 88.2143874275331 & 0.125612572466878 \tabularnewline
20 & 88.48 & 88.385318818151 & 0.0946811818490403 \tabularnewline
21 & 88.75 & 88.8683430482063 & -0.118343048206313 \tabularnewline
22 & 87.95 & 88.0937720259144 & -0.143772025914387 \tabularnewline
23 & 89.09 & 88.5698370753033 & 0.520162924696677 \tabularnewline
24 & 88.73 & 88.7531007634731 & -0.0231007634730815 \tabularnewline
25 & 89.24 & 88.7578380616718 & 0.482161938328147 \tabularnewline
26 & 89.77 & 89.5215357636559 & 0.24846423634412 \tabularnewline
27 & 89.84 & 89.703325155334 & 0.13667484466599 \tabularnewline
28 & 90.97 & 90.5230809695778 & 0.446919030422166 \tabularnewline
29 & 91.53 & 90.9653436741482 & 0.564656325851843 \tabularnewline
30 & 92.2 & 91.8993094269754 & 0.300690573024625 \tabularnewline
31 & 92.27 & 93.1311859374105 & -0.861185937410511 \tabularnewline
32 & 92.42 & 92.7700518380881 & -0.35005183808812 \tabularnewline
33 & 92.07 & 93.0800853406571 & -1.01008534065707 \tabularnewline
34 & 91.73 & 91.5883772071871 & 0.141622792812868 \tabularnewline
35 & 92.1 & 92.5187246791566 & -0.418724679156583 \tabularnewline
36 & 91.68 & 91.7455384375117 & -0.0655384375116483 \tabularnewline
37 & 92.63 & 91.7014103993336 & 0.928589600666356 \tabularnewline
38 & 93.02 & 92.8360665300765 & 0.183933469923517 \tabularnewline
39 & 92.66 & 92.9467128033225 & -0.286712803322544 \tabularnewline
40 & 93.23 & 93.3523553704631 & -0.12235537046314 \tabularnewline
41 & 93.79 & 93.1142013745665 & 0.675798625433544 \tabularnewline
42 & 93.92 & 93.933178002033 & -0.0131780020329586 \tabularnewline
43 & 94.04 & 94.5008448019261 & -0.460844801926086 \tabularnewline
44 & 94.23 & 94.3941184235835 & -0.164118423583503 \tabularnewline
45 & 94.37 & 94.657813238166 & -0.287813238166024 \tabularnewline
46 & 94.29 & 93.9661347706221 & 0.323865229377873 \tabularnewline
47 & 94.38 & 95.0415700582595 & -0.661570058259528 \tabularnewline
48 & 94 & 94.1126577463367 & -0.11265774633668 \tabularnewline
49 & 94.11 & 94.1566237464028 & -0.046623746402787 \tabularnewline
50 & 93.98 & 94.1505074781958 & -0.170507478195816 \tabularnewline
51 & 93.42 & 93.6250998361233 & -0.205099836123296 \tabularnewline
52 & 93.3 & 93.8728638930079 & -0.572863893007934 \tabularnewline
53 & 93.32 & 93.0049273960936 & 0.315072603906344 \tabularnewline
54 & 93.75 & 93.0075405234487 & 0.742459476551275 \tabularnewline
55 & 93.82 & 93.9139079641592 & -0.0939079641592286 \tabularnewline
56 & 94.06 & 93.9774114989664 & 0.0825885010336123 \tabularnewline
57 & 94.09 & 94.3018673882554 & -0.211867388255371 \tabularnewline
58 & 93.64 & 93.6326038496241 & 0.00739615037589658 \tabularnewline
59 & 93.9 & 94.1186923009669 & -0.21869230096685 \tabularnewline
60 & 93.18 & 93.5489713618187 & -0.36897136181868 \tabularnewline
61 & 93.54 & 93.229401283599 & 0.310598716401003 \tabularnewline
62 & 93.55 & 93.441185902279 & 0.108814097720952 \tabularnewline
63 & 93.8 & 93.1335210840186 & 0.666478915981415 \tabularnewline
64 & 93.39 & 94.2467698207905 & -0.85676982079049 \tabularnewline
65 & 93.27 & 93.3435288065781 & -0.0735288065780679 \tabularnewline
66 & 93.58 & 93.0820484086758 & 0.49795159132421 \tabularnewline
67 & 93.47 & 93.637263571124 & -0.167263571123968 \tabularnewline
68 & 93.75 & 93.6148523779247 & 0.135147622075266 \tabularnewline
69 & 93.3 & 93.9127002310713 & -0.612700231071273 \tabularnewline
70 & 92.65 & 92.8079321552998 & -0.157932155299804 \tabularnewline
71 & 92.96 & 92.9727715606812 & -0.012771560681216 \tabularnewline
72 & 92.84 & 92.4562305195784 & 0.383769480421591 \tabularnewline
73 & 93.29 & 92.9245080228936 & 0.365491977106416 \tabularnewline
74 & 93.57 & 93.2135971030313 & 0.35640289696866 \tabularnewline
75 & 93.54 & 93.298958258285 & 0.241041741715009 \tabularnewline
76 & 94.38 & 93.8646939122262 & 0.51530608777378 \tabularnewline
77 & 93.98 & 94.5529616216655 & -0.572961621665513 \tabularnewline
78 & 94.48 & 94.125715436571 & 0.354284563428962 \tabularnewline
79 & 94.63 & 94.6361723788697 & -0.00617237886966393 \tabularnewline
80 & 95.45 & 94.9918331057704 & 0.458166894229578 \tabularnewline
81 & 95.59 & 95.7378638093856 & -0.147863809385584 \tabularnewline
82 & 94.76 & 95.4536503904778 & -0.693650390477785 \tabularnewline
83 & 95.66 & 95.4201762013476 & 0.239823798652409 \tabularnewline
84 & 95.03 & 95.4749709955443 & -0.444970995544296 \tabularnewline
85 & 96.45 & 95.3528968949126 & 1.09710310508737 \tabularnewline
86 & 97.15 & 96.5584443216943 & 0.591555678305724 \tabularnewline
87 & 97.5 & 97.1615040746462 & 0.338495925353755 \tabularnewline
88 & 98.54 & 98.194999977591 & 0.345000022409039 \tabularnewline
89 & 99.54 & 98.9075031417865 & 0.632496858213514 \tabularnewline
90 & 100.33 & 100.205193471759 & 0.124806528240796 \tabularnewline
91 & 100.28 & 100.978575298795 & -0.698575298795404 \tabularnewline
92 & 101.81 & 101.161595584705 & 0.648404415294578 \tabularnewline
93 & 101.91 & 102.403346822353 & -0.493346822353061 \tabularnewline
94 & 101.92 & 102.086765067 & -0.166765066999744 \tabularnewline
95 & 102.68 & 103.077627813295 & -0.39762781329469 \tabularnewline
96 & 101.9 & 102.805644954864 & -0.905644954863945 \tabularnewline
97 & 102.14 & 102.706060838069 & -0.566060838069347 \tabularnewline
98 & 102.3 & 102.288147136957 & 0.011852863043373 \tabularnewline
99 & 102.06 & 102.127285358443 & -0.0672853584425184 \tabularnewline
100 & 102.4 & 102.500316895231 & -0.100316895231174 \tabularnewline
101 & 102.99 & 102.464779974818 & 0.525220025181895 \tabularnewline
102 & 102.99 & 103.184398841075 & -0.194398841075369 \tabularnewline
103 & 102.83 & 103.090224453405 & -0.260224453405471 \tabularnewline
104 & 103.01 & 103.433988493544 & -0.423988493544201 \tabularnewline
105 & 102.6 & 102.983810307407 & -0.383810307406947 \tabularnewline
106 & 102.18 & 102.216267893296 & -0.03626789329644 \tabularnewline
107 & 102.6 & 102.728570310982 & -0.128570310981729 \tabularnewline
108 & 101.44 & 102.116903546308 & -0.676903546308083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287397&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]87.75[/C][C]87.8920032051282[/C][C]-0.142003205128248[/C][/ROW]
[ROW][C]14[/C][C]87.88[/C][C]87.8509766688607[/C][C]0.029023331139328[/C][/ROW]
[ROW][C]15[/C][C]87.61[/C][C]87.5551131504193[/C][C]0.0548868495806971[/C][/ROW]
[ROW][C]16[/C][C]88.05[/C][C]88.0052981286748[/C][C]0.0447018713252163[/C][/ROW]
[ROW][C]17[/C][C]87.77[/C][C]87.7155972771883[/C][C]0.0544027228117159[/C][/ROW]
[ROW][C]18[/C][C]87.79[/C][C]87.7202746535329[/C][C]0.0697253464671093[/C][/ROW]
[ROW][C]19[/C][C]88.34[/C][C]88.2143874275331[/C][C]0.125612572466878[/C][/ROW]
[ROW][C]20[/C][C]88.48[/C][C]88.385318818151[/C][C]0.0946811818490403[/C][/ROW]
[ROW][C]21[/C][C]88.75[/C][C]88.8683430482063[/C][C]-0.118343048206313[/C][/ROW]
[ROW][C]22[/C][C]87.95[/C][C]88.0937720259144[/C][C]-0.143772025914387[/C][/ROW]
[ROW][C]23[/C][C]89.09[/C][C]88.5698370753033[/C][C]0.520162924696677[/C][/ROW]
[ROW][C]24[/C][C]88.73[/C][C]88.7531007634731[/C][C]-0.0231007634730815[/C][/ROW]
[ROW][C]25[/C][C]89.24[/C][C]88.7578380616718[/C][C]0.482161938328147[/C][/ROW]
[ROW][C]26[/C][C]89.77[/C][C]89.5215357636559[/C][C]0.24846423634412[/C][/ROW]
[ROW][C]27[/C][C]89.84[/C][C]89.703325155334[/C][C]0.13667484466599[/C][/ROW]
[ROW][C]28[/C][C]90.97[/C][C]90.5230809695778[/C][C]0.446919030422166[/C][/ROW]
[ROW][C]29[/C][C]91.53[/C][C]90.9653436741482[/C][C]0.564656325851843[/C][/ROW]
[ROW][C]30[/C][C]92.2[/C][C]91.8993094269754[/C][C]0.300690573024625[/C][/ROW]
[ROW][C]31[/C][C]92.27[/C][C]93.1311859374105[/C][C]-0.861185937410511[/C][/ROW]
[ROW][C]32[/C][C]92.42[/C][C]92.7700518380881[/C][C]-0.35005183808812[/C][/ROW]
[ROW][C]33[/C][C]92.07[/C][C]93.0800853406571[/C][C]-1.01008534065707[/C][/ROW]
[ROW][C]34[/C][C]91.73[/C][C]91.5883772071871[/C][C]0.141622792812868[/C][/ROW]
[ROW][C]35[/C][C]92.1[/C][C]92.5187246791566[/C][C]-0.418724679156583[/C][/ROW]
[ROW][C]36[/C][C]91.68[/C][C]91.7455384375117[/C][C]-0.0655384375116483[/C][/ROW]
[ROW][C]37[/C][C]92.63[/C][C]91.7014103993336[/C][C]0.928589600666356[/C][/ROW]
[ROW][C]38[/C][C]93.02[/C][C]92.8360665300765[/C][C]0.183933469923517[/C][/ROW]
[ROW][C]39[/C][C]92.66[/C][C]92.9467128033225[/C][C]-0.286712803322544[/C][/ROW]
[ROW][C]40[/C][C]93.23[/C][C]93.3523553704631[/C][C]-0.12235537046314[/C][/ROW]
[ROW][C]41[/C][C]93.79[/C][C]93.1142013745665[/C][C]0.675798625433544[/C][/ROW]
[ROW][C]42[/C][C]93.92[/C][C]93.933178002033[/C][C]-0.0131780020329586[/C][/ROW]
[ROW][C]43[/C][C]94.04[/C][C]94.5008448019261[/C][C]-0.460844801926086[/C][/ROW]
[ROW][C]44[/C][C]94.23[/C][C]94.3941184235835[/C][C]-0.164118423583503[/C][/ROW]
[ROW][C]45[/C][C]94.37[/C][C]94.657813238166[/C][C]-0.287813238166024[/C][/ROW]
[ROW][C]46[/C][C]94.29[/C][C]93.9661347706221[/C][C]0.323865229377873[/C][/ROW]
[ROW][C]47[/C][C]94.38[/C][C]95.0415700582595[/C][C]-0.661570058259528[/C][/ROW]
[ROW][C]48[/C][C]94[/C][C]94.1126577463367[/C][C]-0.11265774633668[/C][/ROW]
[ROW][C]49[/C][C]94.11[/C][C]94.1566237464028[/C][C]-0.046623746402787[/C][/ROW]
[ROW][C]50[/C][C]93.98[/C][C]94.1505074781958[/C][C]-0.170507478195816[/C][/ROW]
[ROW][C]51[/C][C]93.42[/C][C]93.6250998361233[/C][C]-0.205099836123296[/C][/ROW]
[ROW][C]52[/C][C]93.3[/C][C]93.8728638930079[/C][C]-0.572863893007934[/C][/ROW]
[ROW][C]53[/C][C]93.32[/C][C]93.0049273960936[/C][C]0.315072603906344[/C][/ROW]
[ROW][C]54[/C][C]93.75[/C][C]93.0075405234487[/C][C]0.742459476551275[/C][/ROW]
[ROW][C]55[/C][C]93.82[/C][C]93.9139079641592[/C][C]-0.0939079641592286[/C][/ROW]
[ROW][C]56[/C][C]94.06[/C][C]93.9774114989664[/C][C]0.0825885010336123[/C][/ROW]
[ROW][C]57[/C][C]94.09[/C][C]94.3018673882554[/C][C]-0.211867388255371[/C][/ROW]
[ROW][C]58[/C][C]93.64[/C][C]93.6326038496241[/C][C]0.00739615037589658[/C][/ROW]
[ROW][C]59[/C][C]93.9[/C][C]94.1186923009669[/C][C]-0.21869230096685[/C][/ROW]
[ROW][C]60[/C][C]93.18[/C][C]93.5489713618187[/C][C]-0.36897136181868[/C][/ROW]
[ROW][C]61[/C][C]93.54[/C][C]93.229401283599[/C][C]0.310598716401003[/C][/ROW]
[ROW][C]62[/C][C]93.55[/C][C]93.441185902279[/C][C]0.108814097720952[/C][/ROW]
[ROW][C]63[/C][C]93.8[/C][C]93.1335210840186[/C][C]0.666478915981415[/C][/ROW]
[ROW][C]64[/C][C]93.39[/C][C]94.2467698207905[/C][C]-0.85676982079049[/C][/ROW]
[ROW][C]65[/C][C]93.27[/C][C]93.3435288065781[/C][C]-0.0735288065780679[/C][/ROW]
[ROW][C]66[/C][C]93.58[/C][C]93.0820484086758[/C][C]0.49795159132421[/C][/ROW]
[ROW][C]67[/C][C]93.47[/C][C]93.637263571124[/C][C]-0.167263571123968[/C][/ROW]
[ROW][C]68[/C][C]93.75[/C][C]93.6148523779247[/C][C]0.135147622075266[/C][/ROW]
[ROW][C]69[/C][C]93.3[/C][C]93.9127002310713[/C][C]-0.612700231071273[/C][/ROW]
[ROW][C]70[/C][C]92.65[/C][C]92.8079321552998[/C][C]-0.157932155299804[/C][/ROW]
[ROW][C]71[/C][C]92.96[/C][C]92.9727715606812[/C][C]-0.012771560681216[/C][/ROW]
[ROW][C]72[/C][C]92.84[/C][C]92.4562305195784[/C][C]0.383769480421591[/C][/ROW]
[ROW][C]73[/C][C]93.29[/C][C]92.9245080228936[/C][C]0.365491977106416[/C][/ROW]
[ROW][C]74[/C][C]93.57[/C][C]93.2135971030313[/C][C]0.35640289696866[/C][/ROW]
[ROW][C]75[/C][C]93.54[/C][C]93.298958258285[/C][C]0.241041741715009[/C][/ROW]
[ROW][C]76[/C][C]94.38[/C][C]93.8646939122262[/C][C]0.51530608777378[/C][/ROW]
[ROW][C]77[/C][C]93.98[/C][C]94.5529616216655[/C][C]-0.572961621665513[/C][/ROW]
[ROW][C]78[/C][C]94.48[/C][C]94.125715436571[/C][C]0.354284563428962[/C][/ROW]
[ROW][C]79[/C][C]94.63[/C][C]94.6361723788697[/C][C]-0.00617237886966393[/C][/ROW]
[ROW][C]80[/C][C]95.45[/C][C]94.9918331057704[/C][C]0.458166894229578[/C][/ROW]
[ROW][C]81[/C][C]95.59[/C][C]95.7378638093856[/C][C]-0.147863809385584[/C][/ROW]
[ROW][C]82[/C][C]94.76[/C][C]95.4536503904778[/C][C]-0.693650390477785[/C][/ROW]
[ROW][C]83[/C][C]95.66[/C][C]95.4201762013476[/C][C]0.239823798652409[/C][/ROW]
[ROW][C]84[/C][C]95.03[/C][C]95.4749709955443[/C][C]-0.444970995544296[/C][/ROW]
[ROW][C]85[/C][C]96.45[/C][C]95.3528968949126[/C][C]1.09710310508737[/C][/ROW]
[ROW][C]86[/C][C]97.15[/C][C]96.5584443216943[/C][C]0.591555678305724[/C][/ROW]
[ROW][C]87[/C][C]97.5[/C][C]97.1615040746462[/C][C]0.338495925353755[/C][/ROW]
[ROW][C]88[/C][C]98.54[/C][C]98.194999977591[/C][C]0.345000022409039[/C][/ROW]
[ROW][C]89[/C][C]99.54[/C][C]98.9075031417865[/C][C]0.632496858213514[/C][/ROW]
[ROW][C]90[/C][C]100.33[/C][C]100.205193471759[/C][C]0.124806528240796[/C][/ROW]
[ROW][C]91[/C][C]100.28[/C][C]100.978575298795[/C][C]-0.698575298795404[/C][/ROW]
[ROW][C]92[/C][C]101.81[/C][C]101.161595584705[/C][C]0.648404415294578[/C][/ROW]
[ROW][C]93[/C][C]101.91[/C][C]102.403346822353[/C][C]-0.493346822353061[/C][/ROW]
[ROW][C]94[/C][C]101.92[/C][C]102.086765067[/C][C]-0.166765066999744[/C][/ROW]
[ROW][C]95[/C][C]102.68[/C][C]103.077627813295[/C][C]-0.39762781329469[/C][/ROW]
[ROW][C]96[/C][C]101.9[/C][C]102.805644954864[/C][C]-0.905644954863945[/C][/ROW]
[ROW][C]97[/C][C]102.14[/C][C]102.706060838069[/C][C]-0.566060838069347[/C][/ROW]
[ROW][C]98[/C][C]102.3[/C][C]102.288147136957[/C][C]0.011852863043373[/C][/ROW]
[ROW][C]99[/C][C]102.06[/C][C]102.127285358443[/C][C]-0.0672853584425184[/C][/ROW]
[ROW][C]100[/C][C]102.4[/C][C]102.500316895231[/C][C]-0.100316895231174[/C][/ROW]
[ROW][C]101[/C][C]102.99[/C][C]102.464779974818[/C][C]0.525220025181895[/C][/ROW]
[ROW][C]102[/C][C]102.99[/C][C]103.184398841075[/C][C]-0.194398841075369[/C][/ROW]
[ROW][C]103[/C][C]102.83[/C][C]103.090224453405[/C][C]-0.260224453405471[/C][/ROW]
[ROW][C]104[/C][C]103.01[/C][C]103.433988493544[/C][C]-0.423988493544201[/C][/ROW]
[ROW][C]105[/C][C]102.6[/C][C]102.983810307407[/C][C]-0.383810307406947[/C][/ROW]
[ROW][C]106[/C][C]102.18[/C][C]102.216267893296[/C][C]-0.03626789329644[/C][/ROW]
[ROW][C]107[/C][C]102.6[/C][C]102.728570310982[/C][C]-0.128570310981729[/C][/ROW]
[ROW][C]108[/C][C]101.44[/C][C]102.116903546308[/C][C]-0.676903546308083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287397&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
1387.7587.8920032051282-0.142003205128248
1487.8887.85097666886070.029023331139328
1587.6187.55511315041930.0548868495806971
1688.0588.00529812867480.0447018713252163
1787.7787.71559727718830.0544027228117159
1887.7987.72027465353290.0697253464671093
1988.3488.21438742753310.125612572466878
2088.4888.3853188181510.0946811818490403
2188.7588.8683430482063-0.118343048206313
2287.9588.0937720259144-0.143772025914387
2389.0988.56983707530330.520162924696677
2488.7388.7531007634731-0.0231007634730815
2589.2488.75783806167180.482161938328147
2689.7789.52153576365590.24846423634412
2789.8489.7033251553340.13667484466599
2890.9790.52308096957780.446919030422166
2991.5390.96534367414820.564656325851843
3092.291.89930942697540.300690573024625
3192.2793.1311859374105-0.861185937410511
3292.4292.7700518380881-0.35005183808812
3392.0793.0800853406571-1.01008534065707
3491.7391.58837720718710.141622792812868
3592.192.5187246791566-0.418724679156583
3691.6891.7455384375117-0.0655384375116483
3792.6391.70141039933360.928589600666356
3893.0292.83606653007650.183933469923517
3992.6692.9467128033225-0.286712803322544
4093.2393.3523553704631-0.12235537046314
4193.7993.11420137456650.675798625433544
4293.9293.933178002033-0.0131780020329586
4394.0494.5008448019261-0.460844801926086
4494.2394.3941184235835-0.164118423583503
4594.3794.657813238166-0.287813238166024
4694.2993.96613477062210.323865229377873
4794.3895.0415700582595-0.661570058259528
489494.1126577463367-0.11265774633668
4994.1194.1566237464028-0.046623746402787
5093.9894.1505074781958-0.170507478195816
5193.4293.6250998361233-0.205099836123296
5293.393.8728638930079-0.572863893007934
5393.3293.00492739609360.315072603906344
5493.7593.00754052344870.742459476551275
5593.8293.9139079641592-0.0939079641592286
5694.0693.97741149896640.0825885010336123
5794.0994.3018673882554-0.211867388255371
5893.6493.63260384962410.00739615037589658
5993.994.1186923009669-0.21869230096685
6093.1893.5489713618187-0.36897136181868
6193.5493.2294012835990.310598716401003
6293.5593.4411859022790.108814097720952
6393.893.13352108401860.666478915981415
6493.3994.2467698207905-0.85676982079049
6593.2793.3435288065781-0.0735288065780679
6693.5893.08204840867580.49795159132421
6793.4793.637263571124-0.167263571123968
6893.7593.61485237792470.135147622075266
6993.393.9127002310713-0.612700231071273
7092.6592.8079321552998-0.157932155299804
7192.9692.9727715606812-0.012771560681216
7292.8492.45623051957840.383769480421591
7393.2992.92450802289360.365491977106416
7493.5793.21359710303130.35640289696866
7593.5493.2989582582850.241041741715009
7694.3893.86469391222620.51530608777378
7793.9894.5529616216655-0.572961621665513
7894.4894.1257154365710.354284563428962
7994.6394.6361723788697-0.00617237886966393
8095.4594.99183310577040.458166894229578
8195.5995.7378638093856-0.147863809385584
8294.7695.4536503904778-0.693650390477785
8395.6695.42017620134760.239823798652409
8495.0395.4749709955443-0.444970995544296
8596.4595.35289689491261.09710310508737
8697.1596.55844432169430.591555678305724
8797.597.16150407464620.338495925353755
8898.5498.1949999775910.345000022409039
8999.5498.90750314178650.632496858213514
90100.33100.2051934717590.124806528240796
91100.28100.978575298795-0.698575298795404
92101.81101.1615955847050.648404415294578
93101.91102.403346822353-0.493346822353061
94101.92102.086765067-0.166765066999744
95102.68103.077627813295-0.39762781329469
96101.9102.805644954864-0.905644954863945
97102.14102.706060838069-0.566060838069347
98102.3102.2881471369570.011852863043373
99102.06102.127285358443-0.0672853584425184
100102.4102.500316895231-0.100316895231174
101102.99102.4647799748180.525220025181895
102102.99103.184398841075-0.194398841075369
103102.83103.090224453405-0.260224453405471
104103.01103.433988493544-0.423988493544201
105102.6102.983810307407-0.383810307406947
106102.18102.216267893296-0.03626789329644
107102.6102.728570310982-0.128570310981729
108101.44102.116903546308-0.676903546308083







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109101.798081590082100.968785109611102.627378070552
110101.599194476783100.383651281127102.814737672438
111101.06683207505899.4570767079846102.676587442132
112101.15675077055999.1357188339181103.1777827072
113100.97216599951998.520053707178103.424278291859
114100.71862333540897.8148839617305103.622362709086
115100.4014578815697.0255655181455103.777350244975
116100.61917246852396.7509388168355104.48740612021
117100.29709914999395.9168040061995104.677394293786
11899.739539598740394.8279769828423104.651102214638
119100.10963626521794.6481206215571105.571151908876
12099.403006668915493.3733599854571105.432653352374

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.798081590082 & 100.968785109611 & 102.627378070552 \tabularnewline
110 & 101.599194476783 & 100.383651281127 & 102.814737672438 \tabularnewline
111 & 101.066832075058 & 99.4570767079846 & 102.676587442132 \tabularnewline
112 & 101.156750770559 & 99.1357188339181 & 103.1777827072 \tabularnewline
113 & 100.972165999519 & 98.520053707178 & 103.424278291859 \tabularnewline
114 & 100.718623335408 & 97.8148839617305 & 103.622362709086 \tabularnewline
115 & 100.40145788156 & 97.0255655181455 & 103.777350244975 \tabularnewline
116 & 100.619172468523 & 96.7509388168355 & 104.48740612021 \tabularnewline
117 & 100.297099149993 & 95.9168040061995 & 104.677394293786 \tabularnewline
118 & 99.7395395987403 & 94.8279769828423 & 104.651102214638 \tabularnewline
119 & 100.109636265217 & 94.6481206215571 & 105.571151908876 \tabularnewline
120 & 99.4030066689154 & 93.3733599854571 & 105.432653352374 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287397&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]109[/C][C]101.798081590082[/C][C]100.968785109611[/C][C]102.627378070552[/C][/ROW]
[ROW][C]110[/C][C]101.599194476783[/C][C]100.383651281127[/C][C]102.814737672438[/C][/ROW]
[ROW][C]111[/C][C]101.066832075058[/C][C]99.4570767079846[/C][C]102.676587442132[/C][/ROW]
[ROW][C]112[/C][C]101.156750770559[/C][C]99.1357188339181[/C][C]103.1777827072[/C][/ROW]
[ROW][C]113[/C][C]100.972165999519[/C][C]98.520053707178[/C][C]103.424278291859[/C][/ROW]
[ROW][C]114[/C][C]100.718623335408[/C][C]97.8148839617305[/C][C]103.622362709086[/C][/ROW]
[ROW][C]115[/C][C]100.40145788156[/C][C]97.0255655181455[/C][C]103.777350244975[/C][/ROW]
[ROW][C]116[/C][C]100.619172468523[/C][C]96.7509388168355[/C][C]104.48740612021[/C][/ROW]
[ROW][C]117[/C][C]100.297099149993[/C][C]95.9168040061995[/C][C]104.677394293786[/C][/ROW]
[ROW][C]118[/C][C]99.7395395987403[/C][C]94.8279769828423[/C][C]104.651102214638[/C][/ROW]
[ROW][C]119[/C][C]100.109636265217[/C][C]94.6481206215571[/C][C]105.571151908876[/C][/ROW]
[ROW][C]120[/C][C]99.4030066689154[/C][C]93.3733599854571[/C][C]105.432653352374[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287397&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
109101.798081590082100.968785109611102.627378070552
110101.599194476783100.383651281127102.814737672438
111101.06683207505899.4570767079846102.676587442132
112101.15675077055999.1357188339181103.1777827072
113100.97216599951998.520053707178103.424278291859
114100.71862333540897.8148839617305103.622362709086
115100.4014578815697.0255655181455103.777350244975
116100.61917246852396.7509388168355104.48740612021
117100.29709914999395.9168040061995104.677394293786
11899.739539598740394.8279769828423104.651102214638
119100.10963626521794.6481206215571105.571151908876
12099.403006668915493.3733599854571105.432653352374



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')