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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 10:48:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/25/t1264441784arxa7rbghz2ljjr.htm/, Retrieved Mon, 06 May 2024 06:33:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72478, Retrieved Mon, 06 May 2024 06:33:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2010-01-25 13:50:04] [830dacb160eeaee72e8ff2204da365bc]
-    D  [(Partial) Autocorrelation Function] [Autocorrelation F...] [2010-01-25 14:02:55] [830dacb160eeaee72e8ff2204da365bc]
- RMP       [Exponential Smoothing] [Exponential smoot...] [2010-01-25 17:48:59] [3588db8f96a346e7899895ad48978494] [Current]
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Dataseries X:
8,2
8,21
8,22
8,2
8,18
8,2
8,19
8,24
8,31
8,27
8,36
8,32
8,29
8,27
8,27
8,43
8,46
8,48
8,46
8,46
8,43
8,4
8,38
8,3
8,39
8,53
8,52
8,54
8,62
8,52
8,49
8,44
8,31
8,26
8,21
8,03
7,89
7,83
7,85
7,84
7,88
8,01
8,08
8,11
8,11
8,07
8,06
7,95
7,95
8,07
8,17
8,21
8,2
8,19
8,18
8,16
8,17
8,17
8,19
8,01
8,04
8,13
8,14
8,17
8,25
8,27
8,27
8,26
8,24
8,21
8,25
8,06
8,16
8,32
8,43
8,39
8,41




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72478&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72478&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72478&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.731983554074229
beta0.0105744478801132
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.731983554074229 \tabularnewline
beta & 0.0105744478801132 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72478&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]0.731983554074229[/C][/ROW]
[ROW][C]beta[/C][C]0.0105744478801132[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72478&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72478&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
alpha0.731983554074229
beta0.0105744478801132
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.298.186006944444450.103993055555552
148.278.237800514821160.0321994851788414
158.278.263541606775490.00645839322451103
168.438.43424063279812-0.00424063279812081
178.468.47124199053114-0.0112419905311434
188.488.49928145292143-0.0192814529214296
198.468.352536916405310.107463083594688
208.468.49189909505162-0.0318990950516191
218.438.5506702082702-0.120670208270198
228.48.4264449669418-0.0264449669417992
238.388.49140302675327-0.111403026753266
248.38.361227555371-0.0612275553710102
258.398.305594298685840.0844057013141626
268.538.322601811398720.20739818860128
278.528.469835952423180.0501640475768159
288.548.67014709500729-0.13014709500729
298.628.612623768768230.007376231231774
308.528.65179412092145-0.131794120921455
318.498.455448263512410.0345517364875914
328.448.5023113035444-0.0623113035444032
338.318.51301578594351-0.203015785943512
348.268.35111819292922-0.0911181929292244
358.218.34281510871978-0.132815108719781
368.038.20709721161844-0.17709721161844
377.898.10146752619301-0.211467526193014
387.837.92836070374696-0.0983607037469643
397.857.800772348290620.0492276517093826
407.847.9431937847836-0.103193784783596
417.887.93358905066529-0.0535890506652912
428.017.881692684207540.128307315792455
438.087.913192303488580.166807696511417
448.118.024799424291840.0852005757081642
458.118.100806631308070.00919336869192833
468.078.1209131821462-0.0509131821461999
478.068.12785538262013-0.0678553826201291
487.958.0253127512322-0.075312751232203
497.957.98325779817257-0.033257798172567
508.077.970573445903860.0994265540961425
518.178.02851054546360.141489454536407
528.218.19952111724030.0104788827597098
538.28.28920411853051-0.089204118530514
548.198.26249998137135-0.0724999813713545
558.188.158287039257540.0217129607424589
568.168.141648411708420.0183515882915781
578.178.147667907649060.0223320923509380
588.178.160699771754740.00930022824526056
598.198.20706000895451-0.0170600089545108
608.018.13997682976858-0.129976829768578
618.048.06903374319487-0.0290337431948728
628.138.094889267692350.0351107323076523
638.148.116410316816870.0235896831831326
648.178.164483149219840.00551685078015929
658.258.222254875368490.0277451246315117
668.278.2849754035192-0.0149754035191947
678.278.247908142186090.0220918578139084
688.268.230436908681870.0295630913181295
698.248.24560761236589-0.00560761236588725
708.218.23435678726281-0.024356787262807
718.258.248416618458820.00158338154117921
728.068.16426178826803-0.104261788268026
738.168.138940397929210.0210596020707889
748.328.218787241759050.101212758240948
758.438.286249747159140.143750252840855
768.398.41900809662625-0.0290080966262494
778.418.45877221035183-0.0487722103518315

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.29 & 8.18600694444445 & 0.103993055555552 \tabularnewline
14 & 8.27 & 8.23780051482116 & 0.0321994851788414 \tabularnewline
15 & 8.27 & 8.26354160677549 & 0.00645839322451103 \tabularnewline
16 & 8.43 & 8.43424063279812 & -0.00424063279812081 \tabularnewline
17 & 8.46 & 8.47124199053114 & -0.0112419905311434 \tabularnewline
18 & 8.48 & 8.49928145292143 & -0.0192814529214296 \tabularnewline
19 & 8.46 & 8.35253691640531 & 0.107463083594688 \tabularnewline
20 & 8.46 & 8.49189909505162 & -0.0318990950516191 \tabularnewline
21 & 8.43 & 8.5506702082702 & -0.120670208270198 \tabularnewline
22 & 8.4 & 8.4264449669418 & -0.0264449669417992 \tabularnewline
23 & 8.38 & 8.49140302675327 & -0.111403026753266 \tabularnewline
24 & 8.3 & 8.361227555371 & -0.0612275553710102 \tabularnewline
25 & 8.39 & 8.30559429868584 & 0.0844057013141626 \tabularnewline
26 & 8.53 & 8.32260181139872 & 0.20739818860128 \tabularnewline
27 & 8.52 & 8.46983595242318 & 0.0501640475768159 \tabularnewline
28 & 8.54 & 8.67014709500729 & -0.13014709500729 \tabularnewline
29 & 8.62 & 8.61262376876823 & 0.007376231231774 \tabularnewline
30 & 8.52 & 8.65179412092145 & -0.131794120921455 \tabularnewline
31 & 8.49 & 8.45544826351241 & 0.0345517364875914 \tabularnewline
32 & 8.44 & 8.5023113035444 & -0.0623113035444032 \tabularnewline
33 & 8.31 & 8.51301578594351 & -0.203015785943512 \tabularnewline
34 & 8.26 & 8.35111819292922 & -0.0911181929292244 \tabularnewline
35 & 8.21 & 8.34281510871978 & -0.132815108719781 \tabularnewline
36 & 8.03 & 8.20709721161844 & -0.17709721161844 \tabularnewline
37 & 7.89 & 8.10146752619301 & -0.211467526193014 \tabularnewline
38 & 7.83 & 7.92836070374696 & -0.0983607037469643 \tabularnewline
39 & 7.85 & 7.80077234829062 & 0.0492276517093826 \tabularnewline
40 & 7.84 & 7.9431937847836 & -0.103193784783596 \tabularnewline
41 & 7.88 & 7.93358905066529 & -0.0535890506652912 \tabularnewline
42 & 8.01 & 7.88169268420754 & 0.128307315792455 \tabularnewline
43 & 8.08 & 7.91319230348858 & 0.166807696511417 \tabularnewline
44 & 8.11 & 8.02479942429184 & 0.0852005757081642 \tabularnewline
45 & 8.11 & 8.10080663130807 & 0.00919336869192833 \tabularnewline
46 & 8.07 & 8.1209131821462 & -0.0509131821461999 \tabularnewline
47 & 8.06 & 8.12785538262013 & -0.0678553826201291 \tabularnewline
48 & 7.95 & 8.0253127512322 & -0.075312751232203 \tabularnewline
49 & 7.95 & 7.98325779817257 & -0.033257798172567 \tabularnewline
50 & 8.07 & 7.97057344590386 & 0.0994265540961425 \tabularnewline
51 & 8.17 & 8.0285105454636 & 0.141489454536407 \tabularnewline
52 & 8.21 & 8.1995211172403 & 0.0104788827597098 \tabularnewline
53 & 8.2 & 8.28920411853051 & -0.089204118530514 \tabularnewline
54 & 8.19 & 8.26249998137135 & -0.0724999813713545 \tabularnewline
55 & 8.18 & 8.15828703925754 & 0.0217129607424589 \tabularnewline
56 & 8.16 & 8.14164841170842 & 0.0183515882915781 \tabularnewline
57 & 8.17 & 8.14766790764906 & 0.0223320923509380 \tabularnewline
58 & 8.17 & 8.16069977175474 & 0.00930022824526056 \tabularnewline
59 & 8.19 & 8.20706000895451 & -0.0170600089545108 \tabularnewline
60 & 8.01 & 8.13997682976858 & -0.129976829768578 \tabularnewline
61 & 8.04 & 8.06903374319487 & -0.0290337431948728 \tabularnewline
62 & 8.13 & 8.09488926769235 & 0.0351107323076523 \tabularnewline
63 & 8.14 & 8.11641031681687 & 0.0235896831831326 \tabularnewline
64 & 8.17 & 8.16448314921984 & 0.00551685078015929 \tabularnewline
65 & 8.25 & 8.22225487536849 & 0.0277451246315117 \tabularnewline
66 & 8.27 & 8.2849754035192 & -0.0149754035191947 \tabularnewline
67 & 8.27 & 8.24790814218609 & 0.0220918578139084 \tabularnewline
68 & 8.26 & 8.23043690868187 & 0.0295630913181295 \tabularnewline
69 & 8.24 & 8.24560761236589 & -0.00560761236588725 \tabularnewline
70 & 8.21 & 8.23435678726281 & -0.024356787262807 \tabularnewline
71 & 8.25 & 8.24841661845882 & 0.00158338154117921 \tabularnewline
72 & 8.06 & 8.16426178826803 & -0.104261788268026 \tabularnewline
73 & 8.16 & 8.13894039792921 & 0.0210596020707889 \tabularnewline
74 & 8.32 & 8.21878724175905 & 0.101212758240948 \tabularnewline
75 & 8.43 & 8.28624974715914 & 0.143750252840855 \tabularnewline
76 & 8.39 & 8.41900809662625 & -0.0290080966262494 \tabularnewline
77 & 8.41 & 8.45877221035183 & -0.0487722103518315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72478&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]8.29[/C][C]8.18600694444445[/C][C]0.103993055555552[/C][/ROW]
[ROW][C]14[/C][C]8.27[/C][C]8.23780051482116[/C][C]0.0321994851788414[/C][/ROW]
[ROW][C]15[/C][C]8.27[/C][C]8.26354160677549[/C][C]0.00645839322451103[/C][/ROW]
[ROW][C]16[/C][C]8.43[/C][C]8.43424063279812[/C][C]-0.00424063279812081[/C][/ROW]
[ROW][C]17[/C][C]8.46[/C][C]8.47124199053114[/C][C]-0.0112419905311434[/C][/ROW]
[ROW][C]18[/C][C]8.48[/C][C]8.49928145292143[/C][C]-0.0192814529214296[/C][/ROW]
[ROW][C]19[/C][C]8.46[/C][C]8.35253691640531[/C][C]0.107463083594688[/C][/ROW]
[ROW][C]20[/C][C]8.46[/C][C]8.49189909505162[/C][C]-0.0318990950516191[/C][/ROW]
[ROW][C]21[/C][C]8.43[/C][C]8.5506702082702[/C][C]-0.120670208270198[/C][/ROW]
[ROW][C]22[/C][C]8.4[/C][C]8.4264449669418[/C][C]-0.0264449669417992[/C][/ROW]
[ROW][C]23[/C][C]8.38[/C][C]8.49140302675327[/C][C]-0.111403026753266[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]8.361227555371[/C][C]-0.0612275553710102[/C][/ROW]
[ROW][C]25[/C][C]8.39[/C][C]8.30559429868584[/C][C]0.0844057013141626[/C][/ROW]
[ROW][C]26[/C][C]8.53[/C][C]8.32260181139872[/C][C]0.20739818860128[/C][/ROW]
[ROW][C]27[/C][C]8.52[/C][C]8.46983595242318[/C][C]0.0501640475768159[/C][/ROW]
[ROW][C]28[/C][C]8.54[/C][C]8.67014709500729[/C][C]-0.13014709500729[/C][/ROW]
[ROW][C]29[/C][C]8.62[/C][C]8.61262376876823[/C][C]0.007376231231774[/C][/ROW]
[ROW][C]30[/C][C]8.52[/C][C]8.65179412092145[/C][C]-0.131794120921455[/C][/ROW]
[ROW][C]31[/C][C]8.49[/C][C]8.45544826351241[/C][C]0.0345517364875914[/C][/ROW]
[ROW][C]32[/C][C]8.44[/C][C]8.5023113035444[/C][C]-0.0623113035444032[/C][/ROW]
[ROW][C]33[/C][C]8.31[/C][C]8.51301578594351[/C][C]-0.203015785943512[/C][/ROW]
[ROW][C]34[/C][C]8.26[/C][C]8.35111819292922[/C][C]-0.0911181929292244[/C][/ROW]
[ROW][C]35[/C][C]8.21[/C][C]8.34281510871978[/C][C]-0.132815108719781[/C][/ROW]
[ROW][C]36[/C][C]8.03[/C][C]8.20709721161844[/C][C]-0.17709721161844[/C][/ROW]
[ROW][C]37[/C][C]7.89[/C][C]8.10146752619301[/C][C]-0.211467526193014[/C][/ROW]
[ROW][C]38[/C][C]7.83[/C][C]7.92836070374696[/C][C]-0.0983607037469643[/C][/ROW]
[ROW][C]39[/C][C]7.85[/C][C]7.80077234829062[/C][C]0.0492276517093826[/C][/ROW]
[ROW][C]40[/C][C]7.84[/C][C]7.9431937847836[/C][C]-0.103193784783596[/C][/ROW]
[ROW][C]41[/C][C]7.88[/C][C]7.93358905066529[/C][C]-0.0535890506652912[/C][/ROW]
[ROW][C]42[/C][C]8.01[/C][C]7.88169268420754[/C][C]0.128307315792455[/C][/ROW]
[ROW][C]43[/C][C]8.08[/C][C]7.91319230348858[/C][C]0.166807696511417[/C][/ROW]
[ROW][C]44[/C][C]8.11[/C][C]8.02479942429184[/C][C]0.0852005757081642[/C][/ROW]
[ROW][C]45[/C][C]8.11[/C][C]8.10080663130807[/C][C]0.00919336869192833[/C][/ROW]
[ROW][C]46[/C][C]8.07[/C][C]8.1209131821462[/C][C]-0.0509131821461999[/C][/ROW]
[ROW][C]47[/C][C]8.06[/C][C]8.12785538262013[/C][C]-0.0678553826201291[/C][/ROW]
[ROW][C]48[/C][C]7.95[/C][C]8.0253127512322[/C][C]-0.075312751232203[/C][/ROW]
[ROW][C]49[/C][C]7.95[/C][C]7.98325779817257[/C][C]-0.033257798172567[/C][/ROW]
[ROW][C]50[/C][C]8.07[/C][C]7.97057344590386[/C][C]0.0994265540961425[/C][/ROW]
[ROW][C]51[/C][C]8.17[/C][C]8.0285105454636[/C][C]0.141489454536407[/C][/ROW]
[ROW][C]52[/C][C]8.21[/C][C]8.1995211172403[/C][C]0.0104788827597098[/C][/ROW]
[ROW][C]53[/C][C]8.2[/C][C]8.28920411853051[/C][C]-0.089204118530514[/C][/ROW]
[ROW][C]54[/C][C]8.19[/C][C]8.26249998137135[/C][C]-0.0724999813713545[/C][/ROW]
[ROW][C]55[/C][C]8.18[/C][C]8.15828703925754[/C][C]0.0217129607424589[/C][/ROW]
[ROW][C]56[/C][C]8.16[/C][C]8.14164841170842[/C][C]0.0183515882915781[/C][/ROW]
[ROW][C]57[/C][C]8.17[/C][C]8.14766790764906[/C][C]0.0223320923509380[/C][/ROW]
[ROW][C]58[/C][C]8.17[/C][C]8.16069977175474[/C][C]0.00930022824526056[/C][/ROW]
[ROW][C]59[/C][C]8.19[/C][C]8.20706000895451[/C][C]-0.0170600089545108[/C][/ROW]
[ROW][C]60[/C][C]8.01[/C][C]8.13997682976858[/C][C]-0.129976829768578[/C][/ROW]
[ROW][C]61[/C][C]8.04[/C][C]8.06903374319487[/C][C]-0.0290337431948728[/C][/ROW]
[ROW][C]62[/C][C]8.13[/C][C]8.09488926769235[/C][C]0.0351107323076523[/C][/ROW]
[ROW][C]63[/C][C]8.14[/C][C]8.11641031681687[/C][C]0.0235896831831326[/C][/ROW]
[ROW][C]64[/C][C]8.17[/C][C]8.16448314921984[/C][C]0.00551685078015929[/C][/ROW]
[ROW][C]65[/C][C]8.25[/C][C]8.22225487536849[/C][C]0.0277451246315117[/C][/ROW]
[ROW][C]66[/C][C]8.27[/C][C]8.2849754035192[/C][C]-0.0149754035191947[/C][/ROW]
[ROW][C]67[/C][C]8.27[/C][C]8.24790814218609[/C][C]0.0220918578139084[/C][/ROW]
[ROW][C]68[/C][C]8.26[/C][C]8.23043690868187[/C][C]0.0295630913181295[/C][/ROW]
[ROW][C]69[/C][C]8.24[/C][C]8.24560761236589[/C][C]-0.00560761236588725[/C][/ROW]
[ROW][C]70[/C][C]8.21[/C][C]8.23435678726281[/C][C]-0.024356787262807[/C][/ROW]
[ROW][C]71[/C][C]8.25[/C][C]8.24841661845882[/C][C]0.00158338154117921[/C][/ROW]
[ROW][C]72[/C][C]8.06[/C][C]8.16426178826803[/C][C]-0.104261788268026[/C][/ROW]
[ROW][C]73[/C][C]8.16[/C][C]8.13894039792921[/C][C]0.0210596020707889[/C][/ROW]
[ROW][C]74[/C][C]8.32[/C][C]8.21878724175905[/C][C]0.101212758240948[/C][/ROW]
[ROW][C]75[/C][C]8.43[/C][C]8.28624974715914[/C][C]0.143750252840855[/C][/ROW]
[ROW][C]76[/C][C]8.39[/C][C]8.41900809662625[/C][C]-0.0290080966262494[/C][/ROW]
[ROW][C]77[/C][C]8.41[/C][C]8.45877221035183[/C][C]-0.0487722103518315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72478&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72478&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
138.298.186006944444450.103993055555552
148.278.237800514821160.0321994851788414
158.278.263541606775490.00645839322451103
168.438.43424063279812-0.00424063279812081
178.468.47124199053114-0.0112419905311434
188.488.49928145292143-0.0192814529214296
198.468.352536916405310.107463083594688
208.468.49189909505162-0.0318990950516191
218.438.5506702082702-0.120670208270198
228.48.4264449669418-0.0264449669417992
238.388.49140302675327-0.111403026753266
248.38.361227555371-0.0612275553710102
258.398.305594298685840.0844057013141626
268.538.322601811398720.20739818860128
278.528.469835952423180.0501640475768159
288.548.67014709500729-0.13014709500729
298.628.612623768768230.007376231231774
308.528.65179412092145-0.131794120921455
318.498.455448263512410.0345517364875914
328.448.5023113035444-0.0623113035444032
338.318.51301578594351-0.203015785943512
348.268.35111819292922-0.0911181929292244
358.218.34281510871978-0.132815108719781
368.038.20709721161844-0.17709721161844
377.898.10146752619301-0.211467526193014
387.837.92836070374696-0.0983607037469643
397.857.800772348290620.0492276517093826
407.847.9431937847836-0.103193784783596
417.887.93358905066529-0.0535890506652912
428.017.881692684207540.128307315792455
438.087.913192303488580.166807696511417
448.118.024799424291840.0852005757081642
458.118.100806631308070.00919336869192833
468.078.1209131821462-0.0509131821461999
478.068.12785538262013-0.0678553826201291
487.958.0253127512322-0.075312751232203
497.957.98325779817257-0.033257798172567
508.077.970573445903860.0994265540961425
518.178.02851054546360.141489454536407
528.218.19952111724030.0104788827597098
538.28.28920411853051-0.089204118530514
548.198.26249998137135-0.0724999813713545
558.188.158287039257540.0217129607424589
568.168.141648411708420.0183515882915781
578.178.147667907649060.0223320923509380
588.178.160699771754740.00930022824526056
598.198.20706000895451-0.0170600089545108
608.018.13997682976858-0.129976829768578
618.048.06903374319487-0.0290337431948728
628.138.094889267692350.0351107323076523
638.148.116410316816870.0235896831831326
648.178.164483149219840.00551685078015929
658.258.222254875368490.0277451246315117
668.278.2849754035192-0.0149754035191947
678.278.247908142186090.0220918578139084
688.268.230436908681870.0295630913181295
698.248.24560761236589-0.00560761236588725
708.218.23435678726281-0.024356787262807
718.258.248416618458820.00158338154117921
728.068.16426178826803-0.104261788268026
738.168.138940397929210.0210596020707889
748.328.218787241759050.101212758240948
758.438.286249747159140.143750252840855
768.398.41900809662625-0.0290080966262494
778.418.45877221035183-0.0487722103518315







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
788.454747773090238.283809537001388.62568600917908
798.439407080456068.22678359097398.65203056993821
808.408426569676388.160366143094188.65648699625858
818.392961607734238.113320654538938.67260256092952
828.381264138194128.072706992822088.68982128356615
838.420767421074468.085263584610968.75627125753795
848.307735371650447.94680809234648.66866265095448
858.393777145332118.008643346205778.77891094445845
868.480985118790098.07264095952028.88932927805997
878.486272926436028.055549430717578.91699642215447
888.46690433148478.014505307868558.91930335510085
898.522227274748168.04875616253368.99569838696272

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
78 & 8.45474777309023 & 8.28380953700138 & 8.62568600917908 \tabularnewline
79 & 8.43940708045606 & 8.2267835909739 & 8.65203056993821 \tabularnewline
80 & 8.40842656967638 & 8.16036614309418 & 8.65648699625858 \tabularnewline
81 & 8.39296160773423 & 8.11332065453893 & 8.67260256092952 \tabularnewline
82 & 8.38126413819412 & 8.07270699282208 & 8.68982128356615 \tabularnewline
83 & 8.42076742107446 & 8.08526358461096 & 8.75627125753795 \tabularnewline
84 & 8.30773537165044 & 7.9468080923464 & 8.66866265095448 \tabularnewline
85 & 8.39377714533211 & 8.00864334620577 & 8.77891094445845 \tabularnewline
86 & 8.48098511879009 & 8.0726409595202 & 8.88932927805997 \tabularnewline
87 & 8.48627292643602 & 8.05554943071757 & 8.91699642215447 \tabularnewline
88 & 8.4669043314847 & 8.01450530786855 & 8.91930335510085 \tabularnewline
89 & 8.52222727474816 & 8.0487561625336 & 8.99569838696272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72478&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]78[/C][C]8.45474777309023[/C][C]8.28380953700138[/C][C]8.62568600917908[/C][/ROW]
[ROW][C]79[/C][C]8.43940708045606[/C][C]8.2267835909739[/C][C]8.65203056993821[/C][/ROW]
[ROW][C]80[/C][C]8.40842656967638[/C][C]8.16036614309418[/C][C]8.65648699625858[/C][/ROW]
[ROW][C]81[/C][C]8.39296160773423[/C][C]8.11332065453893[/C][C]8.67260256092952[/C][/ROW]
[ROW][C]82[/C][C]8.38126413819412[/C][C]8.07270699282208[/C][C]8.68982128356615[/C][/ROW]
[ROW][C]83[/C][C]8.42076742107446[/C][C]8.08526358461096[/C][C]8.75627125753795[/C][/ROW]
[ROW][C]84[/C][C]8.30773537165044[/C][C]7.9468080923464[/C][C]8.66866265095448[/C][/ROW]
[ROW][C]85[/C][C]8.39377714533211[/C][C]8.00864334620577[/C][C]8.77891094445845[/C][/ROW]
[ROW][C]86[/C][C]8.48098511879009[/C][C]8.0726409595202[/C][C]8.88932927805997[/C][/ROW]
[ROW][C]87[/C][C]8.48627292643602[/C][C]8.05554943071757[/C][C]8.91699642215447[/C][/ROW]
[ROW][C]88[/C][C]8.4669043314847[/C][C]8.01450530786855[/C][C]8.91930335510085[/C][/ROW]
[ROW][C]89[/C][C]8.52222727474816[/C][C]8.0487561625336[/C][C]8.99569838696272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72478&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72478&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
788.454747773090238.283809537001388.62568600917908
798.439407080456068.22678359097398.65203056993821
808.408426569676388.160366143094188.65648699625858
818.392961607734238.113320654538938.67260256092952
828.381264138194128.072706992822088.68982128356615
838.420767421074468.085263584610968.75627125753795
848.307735371650447.94680809234648.66866265095448
858.393777145332118.008643346205778.77891094445845
868.480985118790098.07264095952028.88932927805997
878.486272926436028.055549430717578.91699642215447
888.46690433148478.014505307868558.91930335510085
898.522227274748168.04875616253368.99569838696272



Parameters (Session):
par1 = additive ; par2 = 12 ;
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')