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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 07:12:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/19/t1324296781gt3wju36bzrx9ya.htm/, Retrieved Fri, 31 May 2024 09:21:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157310, Retrieved Fri, 31 May 2024 09:21:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-19 12:12:17] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
99,96
100,21
100,37
101,11
101,04
101,02
101,02
101,11
100,96
101,27
101,01
101,07
101,07
101,07
101,24
101,29
101,67
101,66
101,66
101,66
101,8
102,32
102,38
102,4
102,39
102,78
102,81
102,82
102,96
102,98
102,98
103,03
103,26
103,47
103,58
103,52
103,52
103,52
103,54
103,74
103,94
103,9
103,9
103,9
103,87
104,51
104,82
104,87
104,87
105,13
105,22
105,02
104,7
104,76
104,76
104,57
104,64
104,72
104,49
104,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157310&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]1 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=157310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157310&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.1215772421127
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.1215772421127 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157310&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]0.1215772421127[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157310&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
beta0.1215772421127
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3100.37100.46-0.0899999999999892
4101.11100.609058048210.500941951790139
5101.04101.409961189167-0.369961189167043
6101.02101.294982328099-0.274982328099398
7101.02101.241550735019-0.221550735019335
8101.11101.214615207668-0.104615207667635
9100.96101.291896379236-0.331896379236369
10101.27101.1015453327820.168454667218384
11101.01101.432025586643-0.422025586643031
12101.07101.120716879718-0.0507168797179958
13101.07101.174550861353-0.104550861353317
14101.07101.161839855969-0.091839855969468
15101.24101.1506742195650.0893257804353311
16101.29101.3315342016-0.0415342015995463
17101.67101.3764845879160.293515412084261
18101.66101.792169382235-0.132169382234522
19101.66101.766100593251-0.106100593250702
20101.66101.753201175737-0.0932011757367661
21101.8101.7418700338290.0581299661709807
22102.32101.88893731480.431062685199805
23102.38102.461344727244-0.0813447272444847
24102.4102.511455059646-0.111455059645678
25102.39102.517904660874-0.127904660874464
26102.78102.4923543649520.287645635048023
27102.81102.917325527967-0.107325527966879
28102.82102.934277186268-0.114277186268382
29102.96102.9303836811250.0296163188745311
30102.98103.073984351496-0.0939843514957488
31102.98103.082557993239-0.102557993239159
32103.03103.070089275265-0.0400892752645348
33103.26103.115215331740.144784668260428
34103.47103.3628178524070.107182147593122
35103.58103.585848762315-0.00584876231496878
36103.52103.695137685923-0.175137685922934
37103.52103.613844929078-0.0938449290784291
38103.52103.602435521415-0.0824355214148085
39103.54103.592413238069-0.0524132380690645
40103.74103.6060409811340.133959018865554
41103.94103.8223273492040.117672650795768
42103.9104.03663366556-0.136633665560069
43103.9103.980022121322-0.0800221213215337
44103.9103.970293252503-0.070293252503248
45103.87103.961747192725-0.0917471927247817
46104.51103.9205928220620.589407177938284
47104.82104.6322513212370.1877486787631
48104.87104.965077287811-0.0950772878111934
49104.87105.003518053372-0.13351805337156
50105.13104.987285296670.142714703329602
51105.22105.26463615671-0.0446361567101405
52105.02105.349209415879-0.329209415878807
53104.7105.109185043019-0.409185043018724
54104.76104.7394374539750.0205625460252605
55104.76104.801937391611-0.041937391611313
56104.57104.796838759198-0.226838759197818
57104.64104.579260328450.0607396715497401
58104.72104.6566448902040.0633551097958787
59104.49104.744347429727-0.254347429726849
60104.42104.483424570682-0.0634245706822014

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 100.37 & 100.46 & -0.0899999999999892 \tabularnewline
4 & 101.11 & 100.60905804821 & 0.500941951790139 \tabularnewline
5 & 101.04 & 101.409961189167 & -0.369961189167043 \tabularnewline
6 & 101.02 & 101.294982328099 & -0.274982328099398 \tabularnewline
7 & 101.02 & 101.241550735019 & -0.221550735019335 \tabularnewline
8 & 101.11 & 101.214615207668 & -0.104615207667635 \tabularnewline
9 & 100.96 & 101.291896379236 & -0.331896379236369 \tabularnewline
10 & 101.27 & 101.101545332782 & 0.168454667218384 \tabularnewline
11 & 101.01 & 101.432025586643 & -0.422025586643031 \tabularnewline
12 & 101.07 & 101.120716879718 & -0.0507168797179958 \tabularnewline
13 & 101.07 & 101.174550861353 & -0.104550861353317 \tabularnewline
14 & 101.07 & 101.161839855969 & -0.091839855969468 \tabularnewline
15 & 101.24 & 101.150674219565 & 0.0893257804353311 \tabularnewline
16 & 101.29 & 101.3315342016 & -0.0415342015995463 \tabularnewline
17 & 101.67 & 101.376484587916 & 0.293515412084261 \tabularnewline
18 & 101.66 & 101.792169382235 & -0.132169382234522 \tabularnewline
19 & 101.66 & 101.766100593251 & -0.106100593250702 \tabularnewline
20 & 101.66 & 101.753201175737 & -0.0932011757367661 \tabularnewline
21 & 101.8 & 101.741870033829 & 0.0581299661709807 \tabularnewline
22 & 102.32 & 101.8889373148 & 0.431062685199805 \tabularnewline
23 & 102.38 & 102.461344727244 & -0.0813447272444847 \tabularnewline
24 & 102.4 & 102.511455059646 & -0.111455059645678 \tabularnewline
25 & 102.39 & 102.517904660874 & -0.127904660874464 \tabularnewline
26 & 102.78 & 102.492354364952 & 0.287645635048023 \tabularnewline
27 & 102.81 & 102.917325527967 & -0.107325527966879 \tabularnewline
28 & 102.82 & 102.934277186268 & -0.114277186268382 \tabularnewline
29 & 102.96 & 102.930383681125 & 0.0296163188745311 \tabularnewline
30 & 102.98 & 103.073984351496 & -0.0939843514957488 \tabularnewline
31 & 102.98 & 103.082557993239 & -0.102557993239159 \tabularnewline
32 & 103.03 & 103.070089275265 & -0.0400892752645348 \tabularnewline
33 & 103.26 & 103.11521533174 & 0.144784668260428 \tabularnewline
34 & 103.47 & 103.362817852407 & 0.107182147593122 \tabularnewline
35 & 103.58 & 103.585848762315 & -0.00584876231496878 \tabularnewline
36 & 103.52 & 103.695137685923 & -0.175137685922934 \tabularnewline
37 & 103.52 & 103.613844929078 & -0.0938449290784291 \tabularnewline
38 & 103.52 & 103.602435521415 & -0.0824355214148085 \tabularnewline
39 & 103.54 & 103.592413238069 & -0.0524132380690645 \tabularnewline
40 & 103.74 & 103.606040981134 & 0.133959018865554 \tabularnewline
41 & 103.94 & 103.822327349204 & 0.117672650795768 \tabularnewline
42 & 103.9 & 104.03663366556 & -0.136633665560069 \tabularnewline
43 & 103.9 & 103.980022121322 & -0.0800221213215337 \tabularnewline
44 & 103.9 & 103.970293252503 & -0.070293252503248 \tabularnewline
45 & 103.87 & 103.961747192725 & -0.0917471927247817 \tabularnewline
46 & 104.51 & 103.920592822062 & 0.589407177938284 \tabularnewline
47 & 104.82 & 104.632251321237 & 0.1877486787631 \tabularnewline
48 & 104.87 & 104.965077287811 & -0.0950772878111934 \tabularnewline
49 & 104.87 & 105.003518053372 & -0.13351805337156 \tabularnewline
50 & 105.13 & 104.98728529667 & 0.142714703329602 \tabularnewline
51 & 105.22 & 105.26463615671 & -0.0446361567101405 \tabularnewline
52 & 105.02 & 105.349209415879 & -0.329209415878807 \tabularnewline
53 & 104.7 & 105.109185043019 & -0.409185043018724 \tabularnewline
54 & 104.76 & 104.739437453975 & 0.0205625460252605 \tabularnewline
55 & 104.76 & 104.801937391611 & -0.041937391611313 \tabularnewline
56 & 104.57 & 104.796838759198 & -0.226838759197818 \tabularnewline
57 & 104.64 & 104.57926032845 & 0.0607396715497401 \tabularnewline
58 & 104.72 & 104.656644890204 & 0.0633551097958787 \tabularnewline
59 & 104.49 & 104.744347429727 & -0.254347429726849 \tabularnewline
60 & 104.42 & 104.483424570682 & -0.0634245706822014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157310&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]100.37[/C][C]100.46[/C][C]-0.0899999999999892[/C][/ROW]
[ROW][C]4[/C][C]101.11[/C][C]100.60905804821[/C][C]0.500941951790139[/C][/ROW]
[ROW][C]5[/C][C]101.04[/C][C]101.409961189167[/C][C]-0.369961189167043[/C][/ROW]
[ROW][C]6[/C][C]101.02[/C][C]101.294982328099[/C][C]-0.274982328099398[/C][/ROW]
[ROW][C]7[/C][C]101.02[/C][C]101.241550735019[/C][C]-0.221550735019335[/C][/ROW]
[ROW][C]8[/C][C]101.11[/C][C]101.214615207668[/C][C]-0.104615207667635[/C][/ROW]
[ROW][C]9[/C][C]100.96[/C][C]101.291896379236[/C][C]-0.331896379236369[/C][/ROW]
[ROW][C]10[/C][C]101.27[/C][C]101.101545332782[/C][C]0.168454667218384[/C][/ROW]
[ROW][C]11[/C][C]101.01[/C][C]101.432025586643[/C][C]-0.422025586643031[/C][/ROW]
[ROW][C]12[/C][C]101.07[/C][C]101.120716879718[/C][C]-0.0507168797179958[/C][/ROW]
[ROW][C]13[/C][C]101.07[/C][C]101.174550861353[/C][C]-0.104550861353317[/C][/ROW]
[ROW][C]14[/C][C]101.07[/C][C]101.161839855969[/C][C]-0.091839855969468[/C][/ROW]
[ROW][C]15[/C][C]101.24[/C][C]101.150674219565[/C][C]0.0893257804353311[/C][/ROW]
[ROW][C]16[/C][C]101.29[/C][C]101.3315342016[/C][C]-0.0415342015995463[/C][/ROW]
[ROW][C]17[/C][C]101.67[/C][C]101.376484587916[/C][C]0.293515412084261[/C][/ROW]
[ROW][C]18[/C][C]101.66[/C][C]101.792169382235[/C][C]-0.132169382234522[/C][/ROW]
[ROW][C]19[/C][C]101.66[/C][C]101.766100593251[/C][C]-0.106100593250702[/C][/ROW]
[ROW][C]20[/C][C]101.66[/C][C]101.753201175737[/C][C]-0.0932011757367661[/C][/ROW]
[ROW][C]21[/C][C]101.8[/C][C]101.741870033829[/C][C]0.0581299661709807[/C][/ROW]
[ROW][C]22[/C][C]102.32[/C][C]101.8889373148[/C][C]0.431062685199805[/C][/ROW]
[ROW][C]23[/C][C]102.38[/C][C]102.461344727244[/C][C]-0.0813447272444847[/C][/ROW]
[ROW][C]24[/C][C]102.4[/C][C]102.511455059646[/C][C]-0.111455059645678[/C][/ROW]
[ROW][C]25[/C][C]102.39[/C][C]102.517904660874[/C][C]-0.127904660874464[/C][/ROW]
[ROW][C]26[/C][C]102.78[/C][C]102.492354364952[/C][C]0.287645635048023[/C][/ROW]
[ROW][C]27[/C][C]102.81[/C][C]102.917325527967[/C][C]-0.107325527966879[/C][/ROW]
[ROW][C]28[/C][C]102.82[/C][C]102.934277186268[/C][C]-0.114277186268382[/C][/ROW]
[ROW][C]29[/C][C]102.96[/C][C]102.930383681125[/C][C]0.0296163188745311[/C][/ROW]
[ROW][C]30[/C][C]102.98[/C][C]103.073984351496[/C][C]-0.0939843514957488[/C][/ROW]
[ROW][C]31[/C][C]102.98[/C][C]103.082557993239[/C][C]-0.102557993239159[/C][/ROW]
[ROW][C]32[/C][C]103.03[/C][C]103.070089275265[/C][C]-0.0400892752645348[/C][/ROW]
[ROW][C]33[/C][C]103.26[/C][C]103.11521533174[/C][C]0.144784668260428[/C][/ROW]
[ROW][C]34[/C][C]103.47[/C][C]103.362817852407[/C][C]0.107182147593122[/C][/ROW]
[ROW][C]35[/C][C]103.58[/C][C]103.585848762315[/C][C]-0.00584876231496878[/C][/ROW]
[ROW][C]36[/C][C]103.52[/C][C]103.695137685923[/C][C]-0.175137685922934[/C][/ROW]
[ROW][C]37[/C][C]103.52[/C][C]103.613844929078[/C][C]-0.0938449290784291[/C][/ROW]
[ROW][C]38[/C][C]103.52[/C][C]103.602435521415[/C][C]-0.0824355214148085[/C][/ROW]
[ROW][C]39[/C][C]103.54[/C][C]103.592413238069[/C][C]-0.0524132380690645[/C][/ROW]
[ROW][C]40[/C][C]103.74[/C][C]103.606040981134[/C][C]0.133959018865554[/C][/ROW]
[ROW][C]41[/C][C]103.94[/C][C]103.822327349204[/C][C]0.117672650795768[/C][/ROW]
[ROW][C]42[/C][C]103.9[/C][C]104.03663366556[/C][C]-0.136633665560069[/C][/ROW]
[ROW][C]43[/C][C]103.9[/C][C]103.980022121322[/C][C]-0.0800221213215337[/C][/ROW]
[ROW][C]44[/C][C]103.9[/C][C]103.970293252503[/C][C]-0.070293252503248[/C][/ROW]
[ROW][C]45[/C][C]103.87[/C][C]103.961747192725[/C][C]-0.0917471927247817[/C][/ROW]
[ROW][C]46[/C][C]104.51[/C][C]103.920592822062[/C][C]0.589407177938284[/C][/ROW]
[ROW][C]47[/C][C]104.82[/C][C]104.632251321237[/C][C]0.1877486787631[/C][/ROW]
[ROW][C]48[/C][C]104.87[/C][C]104.965077287811[/C][C]-0.0950772878111934[/C][/ROW]
[ROW][C]49[/C][C]104.87[/C][C]105.003518053372[/C][C]-0.13351805337156[/C][/ROW]
[ROW][C]50[/C][C]105.13[/C][C]104.98728529667[/C][C]0.142714703329602[/C][/ROW]
[ROW][C]51[/C][C]105.22[/C][C]105.26463615671[/C][C]-0.0446361567101405[/C][/ROW]
[ROW][C]52[/C][C]105.02[/C][C]105.349209415879[/C][C]-0.329209415878807[/C][/ROW]
[ROW][C]53[/C][C]104.7[/C][C]105.109185043019[/C][C]-0.409185043018724[/C][/ROW]
[ROW][C]54[/C][C]104.76[/C][C]104.739437453975[/C][C]0.0205625460252605[/C][/ROW]
[ROW][C]55[/C][C]104.76[/C][C]104.801937391611[/C][C]-0.041937391611313[/C][/ROW]
[ROW][C]56[/C][C]104.57[/C][C]104.796838759198[/C][C]-0.226838759197818[/C][/ROW]
[ROW][C]57[/C][C]104.64[/C][C]104.57926032845[/C][C]0.0607396715497401[/C][/ROW]
[ROW][C]58[/C][C]104.72[/C][C]104.656644890204[/C][C]0.0633551097958787[/C][/ROW]
[ROW][C]59[/C][C]104.49[/C][C]104.744347429727[/C][C]-0.254347429726849[/C][/ROW]
[ROW][C]60[/C][C]104.42[/C][C]104.483424570682[/C][C]-0.0634245706822014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157310&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
3100.37100.46-0.0899999999999892
4101.11100.609058048210.500941951790139
5101.04101.409961189167-0.369961189167043
6101.02101.294982328099-0.274982328099398
7101.02101.241550735019-0.221550735019335
8101.11101.214615207668-0.104615207667635
9100.96101.291896379236-0.331896379236369
10101.27101.1015453327820.168454667218384
11101.01101.432025586643-0.422025586643031
12101.07101.120716879718-0.0507168797179958
13101.07101.174550861353-0.104550861353317
14101.07101.161839855969-0.091839855969468
15101.24101.1506742195650.0893257804353311
16101.29101.3315342016-0.0415342015995463
17101.67101.3764845879160.293515412084261
18101.66101.792169382235-0.132169382234522
19101.66101.766100593251-0.106100593250702
20101.66101.753201175737-0.0932011757367661
21101.8101.7418700338290.0581299661709807
22102.32101.88893731480.431062685199805
23102.38102.461344727244-0.0813447272444847
24102.4102.511455059646-0.111455059645678
25102.39102.517904660874-0.127904660874464
26102.78102.4923543649520.287645635048023
27102.81102.917325527967-0.107325527966879
28102.82102.934277186268-0.114277186268382
29102.96102.9303836811250.0296163188745311
30102.98103.073984351496-0.0939843514957488
31102.98103.082557993239-0.102557993239159
32103.03103.070089275265-0.0400892752645348
33103.26103.115215331740.144784668260428
34103.47103.3628178524070.107182147593122
35103.58103.585848762315-0.00584876231496878
36103.52103.695137685923-0.175137685922934
37103.52103.613844929078-0.0938449290784291
38103.52103.602435521415-0.0824355214148085
39103.54103.592413238069-0.0524132380690645
40103.74103.6060409811340.133959018865554
41103.94103.8223273492040.117672650795768
42103.9104.03663366556-0.136633665560069
43103.9103.980022121322-0.0800221213215337
44103.9103.970293252503-0.070293252503248
45103.87103.961747192725-0.0917471927247817
46104.51103.9205928220620.589407177938284
47104.82104.6322513212370.1877486787631
48104.87104.965077287811-0.0950772878111934
49104.87105.003518053372-0.13351805337156
50105.13104.987285296670.142714703329602
51105.22105.26463615671-0.0446361567101405
52105.02105.349209415879-0.329209415878807
53104.7105.109185043019-0.409185043018724
54104.76104.7394374539750.0205625460252605
55104.76104.801937391611-0.041937391611313
56104.57104.796838759198-0.226838759197818
57104.64104.579260328450.0607396715497401
58104.72104.6566448902040.0633551097958787
59104.49104.744347429727-0.254347429726849
60104.42104.483424570682-0.0634245706822014







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61104.405713586296104.014999484102104.796427688491
62104.391427172593103.804323423738104.978530921448
63104.377140758889103.615161247371105.139120270408
64104.362854345186103.432834844855105.292873845517
65104.348567931482103.252130899017105.445004963947
66104.334281517779103.070620435587105.597942599971
67104.319995104075102.887010584399105.752979623752
68104.305708690372102.700559804974105.91085757577
69104.291422276668102.510824867985106.072019685352
70104.277135862965102.317536397421106.236735328508
71104.262849449261102.120531869136106.405167029386
72104.248563035558101.919717045104106.577409026012

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 104.405713586296 & 104.014999484102 & 104.796427688491 \tabularnewline
62 & 104.391427172593 & 103.804323423738 & 104.978530921448 \tabularnewline
63 & 104.377140758889 & 103.615161247371 & 105.139120270408 \tabularnewline
64 & 104.362854345186 & 103.432834844855 & 105.292873845517 \tabularnewline
65 & 104.348567931482 & 103.252130899017 & 105.445004963947 \tabularnewline
66 & 104.334281517779 & 103.070620435587 & 105.597942599971 \tabularnewline
67 & 104.319995104075 & 102.887010584399 & 105.752979623752 \tabularnewline
68 & 104.305708690372 & 102.700559804974 & 105.91085757577 \tabularnewline
69 & 104.291422276668 & 102.510824867985 & 106.072019685352 \tabularnewline
70 & 104.277135862965 & 102.317536397421 & 106.236735328508 \tabularnewline
71 & 104.262849449261 & 102.120531869136 & 106.405167029386 \tabularnewline
72 & 104.248563035558 & 101.919717045104 & 106.577409026012 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157310&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]61[/C][C]104.405713586296[/C][C]104.014999484102[/C][C]104.796427688491[/C][/ROW]
[ROW][C]62[/C][C]104.391427172593[/C][C]103.804323423738[/C][C]104.978530921448[/C][/ROW]
[ROW][C]63[/C][C]104.377140758889[/C][C]103.615161247371[/C][C]105.139120270408[/C][/ROW]
[ROW][C]64[/C][C]104.362854345186[/C][C]103.432834844855[/C][C]105.292873845517[/C][/ROW]
[ROW][C]65[/C][C]104.348567931482[/C][C]103.252130899017[/C][C]105.445004963947[/C][/ROW]
[ROW][C]66[/C][C]104.334281517779[/C][C]103.070620435587[/C][C]105.597942599971[/C][/ROW]
[ROW][C]67[/C][C]104.319995104075[/C][C]102.887010584399[/C][C]105.752979623752[/C][/ROW]
[ROW][C]68[/C][C]104.305708690372[/C][C]102.700559804974[/C][C]105.91085757577[/C][/ROW]
[ROW][C]69[/C][C]104.291422276668[/C][C]102.510824867985[/C][C]106.072019685352[/C][/ROW]
[ROW][C]70[/C][C]104.277135862965[/C][C]102.317536397421[/C][C]106.236735328508[/C][/ROW]
[ROW][C]71[/C][C]104.262849449261[/C][C]102.120531869136[/C][C]106.405167029386[/C][/ROW]
[ROW][C]72[/C][C]104.248563035558[/C][C]101.919717045104[/C][C]106.577409026012[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157310&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157310&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
61104.405713586296104.014999484102104.796427688491
62104.391427172593103.804323423738104.978530921448
63104.377140758889103.615161247371105.139120270408
64104.362854345186103.432834844855105.292873845517
65104.348567931482103.252130899017105.445004963947
66104.334281517779103.070620435587105.597942599971
67104.319995104075102.887010584399105.752979623752
68104.305708690372102.700559804974105.91085757577
69104.291422276668102.510824867985106.072019685352
70104.277135862965102.317536397421106.236735328508
71104.262849449261102.120531869136106.405167029386
72104.248563035558101.919717045104106.577409026012



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')