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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Dec 2011 10:42:40 -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/2011/Dec/27/t1325000838qv5j0mde4ddpc9w.htm/, Retrieved Sun, 19 May 2024 00:05:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160859, Retrieved Sun, 19 May 2024 00:05:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-27 15:42:40] [f824ea295e177f9d3dd7528a75f4b680] [Current]
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Dataseries X:
5,82
5,85
5,87
5,88
5,9
5,91
5,94
5,97
5,98
6
6,01
6,02
6,11
6,13
6,15
6,15
6,16
6,18
6,21
6,22
6,23
6,26
6,28
6,28
6,29
6,32
6,36
6,37
6,38
6,38
6,4
6,41
6,42
6,43
6,44
6,47
6,47
6,48
6,51
6,54
6,56
6,57
6,6
6,62
6,65
6,71
6,76
6,78
6,8
6,83
6,86
6,86
6,87
6,88
6,9
6,92
6,93
6,94
6,96
6,98
6,99
7,01
7,06
7,07
7,08
7,08
7,1
7,11
7,22
7,24
7,25
7,26




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160859&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160859&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160859&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0550600650237198
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0550600650237198 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160859&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]0.0550600650237198[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160859&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160859&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
beta0.0550600650237198
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35.875.88-0.0099999999999989
45.885.89944939934976-0.0194493993497629
55.95.90837851415689-0.00837851415689173
65.915.92791719262261-0.0179171926226118
75.945.936930670831770.00306932916823222
85.975.967099668295350.00290033170464898
95.985.9972593607476-0.0172593607475973
1066.00630905922257-0.00630905922256808
116.016.02596168201153-0.0159616820115351
126.026.03508283076209-0.0150828307620916
136.116.044252369119590.0657476308804119
146.136.13787243795102-0.00787243795102022
156.156.15743898100554-0.0074389810055413
166.156.17702939022767-0.0270293902276659
176.166.17554115024418-0.0155411502441796
186.186.18468545350119-0.00468545350119243
196.216.204427472126750.00557252787324991
206.226.2347342958738-0.0147342958737982
216.236.24392302458491-0.0139230245849076
226.266.253156421945940.00684357805406322
236.286.28353322979859-0.00353322979858728
246.286.30333868993613-0.0233386899361339
256.296.30205366015068-0.0120536601506824
266.326.311389984839010.00861001516098892
276.366.341864052833630.0181359471663693
286.376.38286261926388-0.0128626192638777
296.386.39215440261083-0.0121544026108333
306.386.40148518041276-0.021485180412756
316.46.40030220498218-0.000302204982182808
326.416.42028556555621-0.010285565556214
336.426.42971924164788-0.00971924164788351
346.436.43918409957077-0.00918409957076971
356.446.44867842245122-0.00867842245121775
366.476.458200587946750.0117994120532483
376.476.48885026434164-0.0188502643416451
386.486.48781236756128-0.00781236756127868
396.516.497382218095370.0126177819046331
406.546.528076953987490.0119230460125097
416.566.558733437676220.00126656232377975
426.576.57880317468012-0.00880317468012315
436.66.588318471309820.0116815286901781
446.626.618961657039080.00103834296092131
456.656.639018828270020.0109811717299761
466.716.669623452299510.040376547700486
476.766.731846587641340.0281534123586642
486.786.78339671635644-0.00339671635644212
496.86.80320969293299-0.003209692932991
506.836.823032967031390.0069670329686069
516.866.853416572319670.00658342768033293
526.866.88377905627583-0.0237790562758251
536.876.88246977989108-0.0124697798910764
546.886.89178319299944-0.0117831929994416
556.96.9011344096267-0.00113440962670452
566.926.9210719489589-0.00107194895889595
576.936.94101292737952-0.0110129273795172
586.946.9504065548819-0.0104065548818983
596.966.959833569293430.000166430706570964
606.986.979842732978950.000157267021045904
616.996.99985139211136-0.00985139211135966
627.017.009308973821130.000691026178865961
637.067.029347021767470.0306529782325251
647.077.08103477674213-0.0110347767421279
657.087.09042720121719-0.0104272012171851
667.087.09985307884015-0.0198530788401508
677.17.098759967028290.00124003297170816
687.117.11882824332435-0.00882824332434495
697.227.128342159672860.0916578403271382
707.247.24338884632121-0.00338884632120706
717.257.26320225622241-0.0132022562224066
727.267.27247533913634-0.0124753391363415

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.87 & 5.88 & -0.0099999999999989 \tabularnewline
4 & 5.88 & 5.89944939934976 & -0.0194493993497629 \tabularnewline
5 & 5.9 & 5.90837851415689 & -0.00837851415689173 \tabularnewline
6 & 5.91 & 5.92791719262261 & -0.0179171926226118 \tabularnewline
7 & 5.94 & 5.93693067083177 & 0.00306932916823222 \tabularnewline
8 & 5.97 & 5.96709966829535 & 0.00290033170464898 \tabularnewline
9 & 5.98 & 5.9972593607476 & -0.0172593607475973 \tabularnewline
10 & 6 & 6.00630905922257 & -0.00630905922256808 \tabularnewline
11 & 6.01 & 6.02596168201153 & -0.0159616820115351 \tabularnewline
12 & 6.02 & 6.03508283076209 & -0.0150828307620916 \tabularnewline
13 & 6.11 & 6.04425236911959 & 0.0657476308804119 \tabularnewline
14 & 6.13 & 6.13787243795102 & -0.00787243795102022 \tabularnewline
15 & 6.15 & 6.15743898100554 & -0.0074389810055413 \tabularnewline
16 & 6.15 & 6.17702939022767 & -0.0270293902276659 \tabularnewline
17 & 6.16 & 6.17554115024418 & -0.0155411502441796 \tabularnewline
18 & 6.18 & 6.18468545350119 & -0.00468545350119243 \tabularnewline
19 & 6.21 & 6.20442747212675 & 0.00557252787324991 \tabularnewline
20 & 6.22 & 6.2347342958738 & -0.0147342958737982 \tabularnewline
21 & 6.23 & 6.24392302458491 & -0.0139230245849076 \tabularnewline
22 & 6.26 & 6.25315642194594 & 0.00684357805406322 \tabularnewline
23 & 6.28 & 6.28353322979859 & -0.00353322979858728 \tabularnewline
24 & 6.28 & 6.30333868993613 & -0.0233386899361339 \tabularnewline
25 & 6.29 & 6.30205366015068 & -0.0120536601506824 \tabularnewline
26 & 6.32 & 6.31138998483901 & 0.00861001516098892 \tabularnewline
27 & 6.36 & 6.34186405283363 & 0.0181359471663693 \tabularnewline
28 & 6.37 & 6.38286261926388 & -0.0128626192638777 \tabularnewline
29 & 6.38 & 6.39215440261083 & -0.0121544026108333 \tabularnewline
30 & 6.38 & 6.40148518041276 & -0.021485180412756 \tabularnewline
31 & 6.4 & 6.40030220498218 & -0.000302204982182808 \tabularnewline
32 & 6.41 & 6.42028556555621 & -0.010285565556214 \tabularnewline
33 & 6.42 & 6.42971924164788 & -0.00971924164788351 \tabularnewline
34 & 6.43 & 6.43918409957077 & -0.00918409957076971 \tabularnewline
35 & 6.44 & 6.44867842245122 & -0.00867842245121775 \tabularnewline
36 & 6.47 & 6.45820058794675 & 0.0117994120532483 \tabularnewline
37 & 6.47 & 6.48885026434164 & -0.0188502643416451 \tabularnewline
38 & 6.48 & 6.48781236756128 & -0.00781236756127868 \tabularnewline
39 & 6.51 & 6.49738221809537 & 0.0126177819046331 \tabularnewline
40 & 6.54 & 6.52807695398749 & 0.0119230460125097 \tabularnewline
41 & 6.56 & 6.55873343767622 & 0.00126656232377975 \tabularnewline
42 & 6.57 & 6.57880317468012 & -0.00880317468012315 \tabularnewline
43 & 6.6 & 6.58831847130982 & 0.0116815286901781 \tabularnewline
44 & 6.62 & 6.61896165703908 & 0.00103834296092131 \tabularnewline
45 & 6.65 & 6.63901882827002 & 0.0109811717299761 \tabularnewline
46 & 6.71 & 6.66962345229951 & 0.040376547700486 \tabularnewline
47 & 6.76 & 6.73184658764134 & 0.0281534123586642 \tabularnewline
48 & 6.78 & 6.78339671635644 & -0.00339671635644212 \tabularnewline
49 & 6.8 & 6.80320969293299 & -0.003209692932991 \tabularnewline
50 & 6.83 & 6.82303296703139 & 0.0069670329686069 \tabularnewline
51 & 6.86 & 6.85341657231967 & 0.00658342768033293 \tabularnewline
52 & 6.86 & 6.88377905627583 & -0.0237790562758251 \tabularnewline
53 & 6.87 & 6.88246977989108 & -0.0124697798910764 \tabularnewline
54 & 6.88 & 6.89178319299944 & -0.0117831929994416 \tabularnewline
55 & 6.9 & 6.9011344096267 & -0.00113440962670452 \tabularnewline
56 & 6.92 & 6.9210719489589 & -0.00107194895889595 \tabularnewline
57 & 6.93 & 6.94101292737952 & -0.0110129273795172 \tabularnewline
58 & 6.94 & 6.9504065548819 & -0.0104065548818983 \tabularnewline
59 & 6.96 & 6.95983356929343 & 0.000166430706570964 \tabularnewline
60 & 6.98 & 6.97984273297895 & 0.000157267021045904 \tabularnewline
61 & 6.99 & 6.99985139211136 & -0.00985139211135966 \tabularnewline
62 & 7.01 & 7.00930897382113 & 0.000691026178865961 \tabularnewline
63 & 7.06 & 7.02934702176747 & 0.0306529782325251 \tabularnewline
64 & 7.07 & 7.08103477674213 & -0.0110347767421279 \tabularnewline
65 & 7.08 & 7.09042720121719 & -0.0104272012171851 \tabularnewline
66 & 7.08 & 7.09985307884015 & -0.0198530788401508 \tabularnewline
67 & 7.1 & 7.09875996702829 & 0.00124003297170816 \tabularnewline
68 & 7.11 & 7.11882824332435 & -0.00882824332434495 \tabularnewline
69 & 7.22 & 7.12834215967286 & 0.0916578403271382 \tabularnewline
70 & 7.24 & 7.24338884632121 & -0.00338884632120706 \tabularnewline
71 & 7.25 & 7.26320225622241 & -0.0132022562224066 \tabularnewline
72 & 7.26 & 7.27247533913634 & -0.0124753391363415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160859&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]5.87[/C][C]5.88[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]4[/C][C]5.88[/C][C]5.89944939934976[/C][C]-0.0194493993497629[/C][/ROW]
[ROW][C]5[/C][C]5.9[/C][C]5.90837851415689[/C][C]-0.00837851415689173[/C][/ROW]
[ROW][C]6[/C][C]5.91[/C][C]5.92791719262261[/C][C]-0.0179171926226118[/C][/ROW]
[ROW][C]7[/C][C]5.94[/C][C]5.93693067083177[/C][C]0.00306932916823222[/C][/ROW]
[ROW][C]8[/C][C]5.97[/C][C]5.96709966829535[/C][C]0.00290033170464898[/C][/ROW]
[ROW][C]9[/C][C]5.98[/C][C]5.9972593607476[/C][C]-0.0172593607475973[/C][/ROW]
[ROW][C]10[/C][C]6[/C][C]6.00630905922257[/C][C]-0.00630905922256808[/C][/ROW]
[ROW][C]11[/C][C]6.01[/C][C]6.02596168201153[/C][C]-0.0159616820115351[/C][/ROW]
[ROW][C]12[/C][C]6.02[/C][C]6.03508283076209[/C][C]-0.0150828307620916[/C][/ROW]
[ROW][C]13[/C][C]6.11[/C][C]6.04425236911959[/C][C]0.0657476308804119[/C][/ROW]
[ROW][C]14[/C][C]6.13[/C][C]6.13787243795102[/C][C]-0.00787243795102022[/C][/ROW]
[ROW][C]15[/C][C]6.15[/C][C]6.15743898100554[/C][C]-0.0074389810055413[/C][/ROW]
[ROW][C]16[/C][C]6.15[/C][C]6.17702939022767[/C][C]-0.0270293902276659[/C][/ROW]
[ROW][C]17[/C][C]6.16[/C][C]6.17554115024418[/C][C]-0.0155411502441796[/C][/ROW]
[ROW][C]18[/C][C]6.18[/C][C]6.18468545350119[/C][C]-0.00468545350119243[/C][/ROW]
[ROW][C]19[/C][C]6.21[/C][C]6.20442747212675[/C][C]0.00557252787324991[/C][/ROW]
[ROW][C]20[/C][C]6.22[/C][C]6.2347342958738[/C][C]-0.0147342958737982[/C][/ROW]
[ROW][C]21[/C][C]6.23[/C][C]6.24392302458491[/C][C]-0.0139230245849076[/C][/ROW]
[ROW][C]22[/C][C]6.26[/C][C]6.25315642194594[/C][C]0.00684357805406322[/C][/ROW]
[ROW][C]23[/C][C]6.28[/C][C]6.28353322979859[/C][C]-0.00353322979858728[/C][/ROW]
[ROW][C]24[/C][C]6.28[/C][C]6.30333868993613[/C][C]-0.0233386899361339[/C][/ROW]
[ROW][C]25[/C][C]6.29[/C][C]6.30205366015068[/C][C]-0.0120536601506824[/C][/ROW]
[ROW][C]26[/C][C]6.32[/C][C]6.31138998483901[/C][C]0.00861001516098892[/C][/ROW]
[ROW][C]27[/C][C]6.36[/C][C]6.34186405283363[/C][C]0.0181359471663693[/C][/ROW]
[ROW][C]28[/C][C]6.37[/C][C]6.38286261926388[/C][C]-0.0128626192638777[/C][/ROW]
[ROW][C]29[/C][C]6.38[/C][C]6.39215440261083[/C][C]-0.0121544026108333[/C][/ROW]
[ROW][C]30[/C][C]6.38[/C][C]6.40148518041276[/C][C]-0.021485180412756[/C][/ROW]
[ROW][C]31[/C][C]6.4[/C][C]6.40030220498218[/C][C]-0.000302204982182808[/C][/ROW]
[ROW][C]32[/C][C]6.41[/C][C]6.42028556555621[/C][C]-0.010285565556214[/C][/ROW]
[ROW][C]33[/C][C]6.42[/C][C]6.42971924164788[/C][C]-0.00971924164788351[/C][/ROW]
[ROW][C]34[/C][C]6.43[/C][C]6.43918409957077[/C][C]-0.00918409957076971[/C][/ROW]
[ROW][C]35[/C][C]6.44[/C][C]6.44867842245122[/C][C]-0.00867842245121775[/C][/ROW]
[ROW][C]36[/C][C]6.47[/C][C]6.45820058794675[/C][C]0.0117994120532483[/C][/ROW]
[ROW][C]37[/C][C]6.47[/C][C]6.48885026434164[/C][C]-0.0188502643416451[/C][/ROW]
[ROW][C]38[/C][C]6.48[/C][C]6.48781236756128[/C][C]-0.00781236756127868[/C][/ROW]
[ROW][C]39[/C][C]6.51[/C][C]6.49738221809537[/C][C]0.0126177819046331[/C][/ROW]
[ROW][C]40[/C][C]6.54[/C][C]6.52807695398749[/C][C]0.0119230460125097[/C][/ROW]
[ROW][C]41[/C][C]6.56[/C][C]6.55873343767622[/C][C]0.00126656232377975[/C][/ROW]
[ROW][C]42[/C][C]6.57[/C][C]6.57880317468012[/C][C]-0.00880317468012315[/C][/ROW]
[ROW][C]43[/C][C]6.6[/C][C]6.58831847130982[/C][C]0.0116815286901781[/C][/ROW]
[ROW][C]44[/C][C]6.62[/C][C]6.61896165703908[/C][C]0.00103834296092131[/C][/ROW]
[ROW][C]45[/C][C]6.65[/C][C]6.63901882827002[/C][C]0.0109811717299761[/C][/ROW]
[ROW][C]46[/C][C]6.71[/C][C]6.66962345229951[/C][C]0.040376547700486[/C][/ROW]
[ROW][C]47[/C][C]6.76[/C][C]6.73184658764134[/C][C]0.0281534123586642[/C][/ROW]
[ROW][C]48[/C][C]6.78[/C][C]6.78339671635644[/C][C]-0.00339671635644212[/C][/ROW]
[ROW][C]49[/C][C]6.8[/C][C]6.80320969293299[/C][C]-0.003209692932991[/C][/ROW]
[ROW][C]50[/C][C]6.83[/C][C]6.82303296703139[/C][C]0.0069670329686069[/C][/ROW]
[ROW][C]51[/C][C]6.86[/C][C]6.85341657231967[/C][C]0.00658342768033293[/C][/ROW]
[ROW][C]52[/C][C]6.86[/C][C]6.88377905627583[/C][C]-0.0237790562758251[/C][/ROW]
[ROW][C]53[/C][C]6.87[/C][C]6.88246977989108[/C][C]-0.0124697798910764[/C][/ROW]
[ROW][C]54[/C][C]6.88[/C][C]6.89178319299944[/C][C]-0.0117831929994416[/C][/ROW]
[ROW][C]55[/C][C]6.9[/C][C]6.9011344096267[/C][C]-0.00113440962670452[/C][/ROW]
[ROW][C]56[/C][C]6.92[/C][C]6.9210719489589[/C][C]-0.00107194895889595[/C][/ROW]
[ROW][C]57[/C][C]6.93[/C][C]6.94101292737952[/C][C]-0.0110129273795172[/C][/ROW]
[ROW][C]58[/C][C]6.94[/C][C]6.9504065548819[/C][C]-0.0104065548818983[/C][/ROW]
[ROW][C]59[/C][C]6.96[/C][C]6.95983356929343[/C][C]0.000166430706570964[/C][/ROW]
[ROW][C]60[/C][C]6.98[/C][C]6.97984273297895[/C][C]0.000157267021045904[/C][/ROW]
[ROW][C]61[/C][C]6.99[/C][C]6.99985139211136[/C][C]-0.00985139211135966[/C][/ROW]
[ROW][C]62[/C][C]7.01[/C][C]7.00930897382113[/C][C]0.000691026178865961[/C][/ROW]
[ROW][C]63[/C][C]7.06[/C][C]7.02934702176747[/C][C]0.0306529782325251[/C][/ROW]
[ROW][C]64[/C][C]7.07[/C][C]7.08103477674213[/C][C]-0.0110347767421279[/C][/ROW]
[ROW][C]65[/C][C]7.08[/C][C]7.09042720121719[/C][C]-0.0104272012171851[/C][/ROW]
[ROW][C]66[/C][C]7.08[/C][C]7.09985307884015[/C][C]-0.0198530788401508[/C][/ROW]
[ROW][C]67[/C][C]7.1[/C][C]7.09875996702829[/C][C]0.00124003297170816[/C][/ROW]
[ROW][C]68[/C][C]7.11[/C][C]7.11882824332435[/C][C]-0.00882824332434495[/C][/ROW]
[ROW][C]69[/C][C]7.22[/C][C]7.12834215967286[/C][C]0.0916578403271382[/C][/ROW]
[ROW][C]70[/C][C]7.24[/C][C]7.24338884632121[/C][C]-0.00338884632120706[/C][/ROW]
[ROW][C]71[/C][C]7.25[/C][C]7.26320225622241[/C][C]-0.0132022562224066[/C][/ROW]
[ROW][C]72[/C][C]7.26[/C][C]7.27247533913634[/C][C]-0.0124753391363415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160859&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160859&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
35.875.88-0.0099999999999989
45.885.89944939934976-0.0194493993497629
55.95.90837851415689-0.00837851415689173
65.915.92791719262261-0.0179171926226118
75.945.936930670831770.00306932916823222
85.975.967099668295350.00290033170464898
95.985.9972593607476-0.0172593607475973
1066.00630905922257-0.00630905922256808
116.016.02596168201153-0.0159616820115351
126.026.03508283076209-0.0150828307620916
136.116.044252369119590.0657476308804119
146.136.13787243795102-0.00787243795102022
156.156.15743898100554-0.0074389810055413
166.156.17702939022767-0.0270293902276659
176.166.17554115024418-0.0155411502441796
186.186.18468545350119-0.00468545350119243
196.216.204427472126750.00557252787324991
206.226.2347342958738-0.0147342958737982
216.236.24392302458491-0.0139230245849076
226.266.253156421945940.00684357805406322
236.286.28353322979859-0.00353322979858728
246.286.30333868993613-0.0233386899361339
256.296.30205366015068-0.0120536601506824
266.326.311389984839010.00861001516098892
276.366.341864052833630.0181359471663693
286.376.38286261926388-0.0128626192638777
296.386.39215440261083-0.0121544026108333
306.386.40148518041276-0.021485180412756
316.46.40030220498218-0.000302204982182808
326.416.42028556555621-0.010285565556214
336.426.42971924164788-0.00971924164788351
346.436.43918409957077-0.00918409957076971
356.446.44867842245122-0.00867842245121775
366.476.458200587946750.0117994120532483
376.476.48885026434164-0.0188502643416451
386.486.48781236756128-0.00781236756127868
396.516.497382218095370.0126177819046331
406.546.528076953987490.0119230460125097
416.566.558733437676220.00126656232377975
426.576.57880317468012-0.00880317468012315
436.66.588318471309820.0116815286901781
446.626.618961657039080.00103834296092131
456.656.639018828270020.0109811717299761
466.716.669623452299510.040376547700486
476.766.731846587641340.0281534123586642
486.786.78339671635644-0.00339671635644212
496.86.80320969293299-0.003209692932991
506.836.823032967031390.0069670329686069
516.866.853416572319670.00658342768033293
526.866.88377905627583-0.0237790562758251
536.876.88246977989108-0.0124697798910764
546.886.89178319299944-0.0117831929994416
556.96.9011344096267-0.00113440962670452
566.926.9210719489589-0.00107194895889595
576.936.94101292737952-0.0110129273795172
586.946.9504065548819-0.0104065548818983
596.966.959833569293430.000166430706570964
606.986.979842732978950.000157267021045904
616.996.99985139211136-0.00985139211135966
627.017.009308973821130.000691026178865961
637.067.029347021767470.0306529782325251
647.077.08103477674213-0.0110347767421279
657.087.09042720121719-0.0104272012171851
667.087.09985307884015-0.0198530788401508
677.17.098759967028290.00124003297170816
687.117.11882824332435-0.00882824332434495
697.227.128342159672860.0916578403271382
707.247.24338884632121-0.00338884632120706
717.257.26320225622241-0.0132022562224066
727.267.27247533913634-0.0124753391363415







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.28178844615237.244586306477987.31899058582662
747.30357689230467.249497318424647.35765646618456
757.32536533845697.257319803424957.39341087348885
767.34715378460927.266474330779267.42783323843915
777.36894223076157.276368313796247.46151614772677
787.390730676913817.286707343822257.49475401000537
797.412519123066117.29732217458417.52771607154812
807.434307569218417.308106258083097.56050888035372
817.456096015370717.318988220919397.59320380982203
827.477884461523017.329918054746417.62585086829962
837.499672907675317.340859516768867.65848629858176
847.521461353827617.351785646716977.69113706093826

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.2817884461523 & 7.24458630647798 & 7.31899058582662 \tabularnewline
74 & 7.3035768923046 & 7.24949731842464 & 7.35765646618456 \tabularnewline
75 & 7.3253653384569 & 7.25731980342495 & 7.39341087348885 \tabularnewline
76 & 7.3471537846092 & 7.26647433077926 & 7.42783323843915 \tabularnewline
77 & 7.3689422307615 & 7.27636831379624 & 7.46151614772677 \tabularnewline
78 & 7.39073067691381 & 7.28670734382225 & 7.49475401000537 \tabularnewline
79 & 7.41251912306611 & 7.2973221745841 & 7.52771607154812 \tabularnewline
80 & 7.43430756921841 & 7.30810625808309 & 7.56050888035372 \tabularnewline
81 & 7.45609601537071 & 7.31898822091939 & 7.59320380982203 \tabularnewline
82 & 7.47788446152301 & 7.32991805474641 & 7.62585086829962 \tabularnewline
83 & 7.49967290767531 & 7.34085951676886 & 7.65848629858176 \tabularnewline
84 & 7.52146135382761 & 7.35178564671697 & 7.69113706093826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160859&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]7.2817884461523[/C][C]7.24458630647798[/C][C]7.31899058582662[/C][/ROW]
[ROW][C]74[/C][C]7.3035768923046[/C][C]7.24949731842464[/C][C]7.35765646618456[/C][/ROW]
[ROW][C]75[/C][C]7.3253653384569[/C][C]7.25731980342495[/C][C]7.39341087348885[/C][/ROW]
[ROW][C]76[/C][C]7.3471537846092[/C][C]7.26647433077926[/C][C]7.42783323843915[/C][/ROW]
[ROW][C]77[/C][C]7.3689422307615[/C][C]7.27636831379624[/C][C]7.46151614772677[/C][/ROW]
[ROW][C]78[/C][C]7.39073067691381[/C][C]7.28670734382225[/C][C]7.49475401000537[/C][/ROW]
[ROW][C]79[/C][C]7.41251912306611[/C][C]7.2973221745841[/C][C]7.52771607154812[/C][/ROW]
[ROW][C]80[/C][C]7.43430756921841[/C][C]7.30810625808309[/C][C]7.56050888035372[/C][/ROW]
[ROW][C]81[/C][C]7.45609601537071[/C][C]7.31898822091939[/C][C]7.59320380982203[/C][/ROW]
[ROW][C]82[/C][C]7.47788446152301[/C][C]7.32991805474641[/C][C]7.62585086829962[/C][/ROW]
[ROW][C]83[/C][C]7.49967290767531[/C][C]7.34085951676886[/C][C]7.65848629858176[/C][/ROW]
[ROW][C]84[/C][C]7.52146135382761[/C][C]7.35178564671697[/C][C]7.69113706093826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160859&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160859&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
737.28178844615237.244586306477987.31899058582662
747.30357689230467.249497318424647.35765646618456
757.32536533845697.257319803424957.39341087348885
767.34715378460927.266474330779267.42783323843915
777.36894223076157.276368313796247.46151614772677
787.390730676913817.286707343822257.49475401000537
797.412519123066117.29732217458417.52771607154812
807.434307569218417.308106258083097.56050888035372
817.456096015370717.318988220919397.59320380982203
827.477884461523017.329918054746417.62585086829962
837.499672907675317.340859516768867.65848629858176
847.521461353827617.351785646716977.69113706093826



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')