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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 14:36:14 -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/2013/Jan/15/t1358278591gff311sfj0qcsk1.htm/, Retrieved Sun, 28 Apr 2024 13:43:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205519, Retrieved Sun, 28 Apr 2024 13:43:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean versus Median] [] [2012-10-22 19:08:21] [018035fb0d4285098cb1e31787361d70]
- RMPD    [Exponential Smoothing] [] [2013-01-15 19:36:14] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
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
7,27
7,3
7,32
7,34
7,35
7,36
7,39
7,41
7,43
7,46
7,47
7,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205519&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205519&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205519&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[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205519&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
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.156.158.88178419700125e-16
46.156.17-0.0199999999999996
56.166.17-0.00999999999999979
66.186.180
76.216.20.0100000000000007
86.226.23-0.00999999999999979
96.236.24-0.0099999999999989
106.266.250.00999999999999979
116.286.288.88178419700125e-16
126.286.3-0.0199999999999996
136.296.3-0.00999999999999979
146.326.310.0100000000000007
156.366.340.0200000000000005
166.376.38-0.00999999999999979
176.386.39-0.00999999999999979
186.386.4-0.0199999999999996
196.46.48.88178419700125e-16
206.416.42-0.00999999999999979
216.426.43-0.00999999999999979
226.436.44-0.00999999999999979
236.446.45-0.0099999999999989
246.476.460.00999999999999979
256.476.49-0.0199999999999996
266.486.49-0.0099999999999989
276.516.50.00999999999999979
286.546.530.0100000000000007
296.566.560
306.576.58-0.0099999999999989
316.66.590.00999999999999979
326.626.628.88178419700125e-16
336.656.640.0100000000000007
346.716.670.04
356.766.730.0300000000000002
366.786.788.88178419700125e-16
376.86.80
386.836.820.0100000000000007
396.866.850.0100000000000007
406.866.88-0.0199999999999996
416.876.88-0.00999999999999979
426.886.89-0.00999999999999979
436.96.98.88178419700125e-16
446.926.920
456.936.94-0.00999999999999979
466.946.95-0.0099999999999989
476.966.960
486.986.988.88178419700125e-16
496.997-0.00999999999999979
507.017.010
517.067.030.0300000000000002
527.077.08-0.0099999999999989
537.087.09-0.00999999999999979
547.087.1-0.0199999999999996
557.17.10
567.117.12-0.0099999999999989
577.227.130.0899999999999999
587.247.248.88178419700125e-16
597.257.26-0.00999999999999979
607.267.27-0.00999999999999979
617.277.28-0.00999999999999979
627.37.290.0100000000000007
637.327.328.88178419700125e-16
647.347.340
657.357.36-0.00999999999999979
667.367.37-0.0099999999999989
677.397.380.00999999999999979
687.417.418.88178419700125e-16
697.437.430
707.467.450.0100000000000007
717.477.48-0.00999999999999979
727.57.490.0100000000000007

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.15 & 6.15 & 8.88178419700125e-16 \tabularnewline
4 & 6.15 & 6.17 & -0.0199999999999996 \tabularnewline
5 & 6.16 & 6.17 & -0.00999999999999979 \tabularnewline
6 & 6.18 & 6.18 & 0 \tabularnewline
7 & 6.21 & 6.2 & 0.0100000000000007 \tabularnewline
8 & 6.22 & 6.23 & -0.00999999999999979 \tabularnewline
9 & 6.23 & 6.24 & -0.0099999999999989 \tabularnewline
10 & 6.26 & 6.25 & 0.00999999999999979 \tabularnewline
11 & 6.28 & 6.28 & 8.88178419700125e-16 \tabularnewline
12 & 6.28 & 6.3 & -0.0199999999999996 \tabularnewline
13 & 6.29 & 6.3 & -0.00999999999999979 \tabularnewline
14 & 6.32 & 6.31 & 0.0100000000000007 \tabularnewline
15 & 6.36 & 6.34 & 0.0200000000000005 \tabularnewline
16 & 6.37 & 6.38 & -0.00999999999999979 \tabularnewline
17 & 6.38 & 6.39 & -0.00999999999999979 \tabularnewline
18 & 6.38 & 6.4 & -0.0199999999999996 \tabularnewline
19 & 6.4 & 6.4 & 8.88178419700125e-16 \tabularnewline
20 & 6.41 & 6.42 & -0.00999999999999979 \tabularnewline
21 & 6.42 & 6.43 & -0.00999999999999979 \tabularnewline
22 & 6.43 & 6.44 & -0.00999999999999979 \tabularnewline
23 & 6.44 & 6.45 & -0.0099999999999989 \tabularnewline
24 & 6.47 & 6.46 & 0.00999999999999979 \tabularnewline
25 & 6.47 & 6.49 & -0.0199999999999996 \tabularnewline
26 & 6.48 & 6.49 & -0.0099999999999989 \tabularnewline
27 & 6.51 & 6.5 & 0.00999999999999979 \tabularnewline
28 & 6.54 & 6.53 & 0.0100000000000007 \tabularnewline
29 & 6.56 & 6.56 & 0 \tabularnewline
30 & 6.57 & 6.58 & -0.0099999999999989 \tabularnewline
31 & 6.6 & 6.59 & 0.00999999999999979 \tabularnewline
32 & 6.62 & 6.62 & 8.88178419700125e-16 \tabularnewline
33 & 6.65 & 6.64 & 0.0100000000000007 \tabularnewline
34 & 6.71 & 6.67 & 0.04 \tabularnewline
35 & 6.76 & 6.73 & 0.0300000000000002 \tabularnewline
36 & 6.78 & 6.78 & 8.88178419700125e-16 \tabularnewline
37 & 6.8 & 6.8 & 0 \tabularnewline
38 & 6.83 & 6.82 & 0.0100000000000007 \tabularnewline
39 & 6.86 & 6.85 & 0.0100000000000007 \tabularnewline
40 & 6.86 & 6.88 & -0.0199999999999996 \tabularnewline
41 & 6.87 & 6.88 & -0.00999999999999979 \tabularnewline
42 & 6.88 & 6.89 & -0.00999999999999979 \tabularnewline
43 & 6.9 & 6.9 & 8.88178419700125e-16 \tabularnewline
44 & 6.92 & 6.92 & 0 \tabularnewline
45 & 6.93 & 6.94 & -0.00999999999999979 \tabularnewline
46 & 6.94 & 6.95 & -0.0099999999999989 \tabularnewline
47 & 6.96 & 6.96 & 0 \tabularnewline
48 & 6.98 & 6.98 & 8.88178419700125e-16 \tabularnewline
49 & 6.99 & 7 & -0.00999999999999979 \tabularnewline
50 & 7.01 & 7.01 & 0 \tabularnewline
51 & 7.06 & 7.03 & 0.0300000000000002 \tabularnewline
52 & 7.07 & 7.08 & -0.0099999999999989 \tabularnewline
53 & 7.08 & 7.09 & -0.00999999999999979 \tabularnewline
54 & 7.08 & 7.1 & -0.0199999999999996 \tabularnewline
55 & 7.1 & 7.1 & 0 \tabularnewline
56 & 7.11 & 7.12 & -0.0099999999999989 \tabularnewline
57 & 7.22 & 7.13 & 0.0899999999999999 \tabularnewline
58 & 7.24 & 7.24 & 8.88178419700125e-16 \tabularnewline
59 & 7.25 & 7.26 & -0.00999999999999979 \tabularnewline
60 & 7.26 & 7.27 & -0.00999999999999979 \tabularnewline
61 & 7.27 & 7.28 & -0.00999999999999979 \tabularnewline
62 & 7.3 & 7.29 & 0.0100000000000007 \tabularnewline
63 & 7.32 & 7.32 & 8.88178419700125e-16 \tabularnewline
64 & 7.34 & 7.34 & 0 \tabularnewline
65 & 7.35 & 7.36 & -0.00999999999999979 \tabularnewline
66 & 7.36 & 7.37 & -0.0099999999999989 \tabularnewline
67 & 7.39 & 7.38 & 0.00999999999999979 \tabularnewline
68 & 7.41 & 7.41 & 8.88178419700125e-16 \tabularnewline
69 & 7.43 & 7.43 & 0 \tabularnewline
70 & 7.46 & 7.45 & 0.0100000000000007 \tabularnewline
71 & 7.47 & 7.48 & -0.00999999999999979 \tabularnewline
72 & 7.5 & 7.49 & 0.0100000000000007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205519&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]6.15[/C][C]6.15[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]4[/C][C]6.15[/C][C]6.17[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]5[/C][C]6.16[/C][C]6.17[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]6[/C][C]6.18[/C][C]6.18[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]6.21[/C][C]6.2[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]8[/C][C]6.22[/C][C]6.23[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]9[/C][C]6.23[/C][C]6.24[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]10[/C][C]6.26[/C][C]6.25[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]11[/C][C]6.28[/C][C]6.28[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]12[/C][C]6.28[/C][C]6.3[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]13[/C][C]6.29[/C][C]6.3[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]14[/C][C]6.32[/C][C]6.31[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]15[/C][C]6.36[/C][C]6.34[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]16[/C][C]6.37[/C][C]6.38[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]17[/C][C]6.38[/C][C]6.39[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]18[/C][C]6.38[/C][C]6.4[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]19[/C][C]6.4[/C][C]6.4[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]20[/C][C]6.41[/C][C]6.42[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]21[/C][C]6.42[/C][C]6.43[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]22[/C][C]6.43[/C][C]6.44[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]23[/C][C]6.44[/C][C]6.45[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]24[/C][C]6.47[/C][C]6.46[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]25[/C][C]6.47[/C][C]6.49[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]26[/C][C]6.48[/C][C]6.49[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]27[/C][C]6.51[/C][C]6.5[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]28[/C][C]6.54[/C][C]6.53[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]29[/C][C]6.56[/C][C]6.56[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]6.57[/C][C]6.58[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]31[/C][C]6.6[/C][C]6.59[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]32[/C][C]6.62[/C][C]6.62[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]33[/C][C]6.65[/C][C]6.64[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]34[/C][C]6.71[/C][C]6.67[/C][C]0.04[/C][/ROW]
[ROW][C]35[/C][C]6.76[/C][C]6.73[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]36[/C][C]6.78[/C][C]6.78[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]37[/C][C]6.8[/C][C]6.8[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]6.83[/C][C]6.82[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]39[/C][C]6.86[/C][C]6.85[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]40[/C][C]6.86[/C][C]6.88[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]41[/C][C]6.87[/C][C]6.88[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]42[/C][C]6.88[/C][C]6.89[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]6.9[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]44[/C][C]6.92[/C][C]6.92[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]6.93[/C][C]6.94[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]46[/C][C]6.94[/C][C]6.95[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]47[/C][C]6.96[/C][C]6.96[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]6.98[/C][C]6.98[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]49[/C][C]6.99[/C][C]7[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]50[/C][C]7.01[/C][C]7.01[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]7.06[/C][C]7.03[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]52[/C][C]7.07[/C][C]7.08[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]53[/C][C]7.08[/C][C]7.09[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]54[/C][C]7.08[/C][C]7.1[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]55[/C][C]7.1[/C][C]7.1[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]7.11[/C][C]7.12[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]57[/C][C]7.22[/C][C]7.13[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]58[/C][C]7.24[/C][C]7.24[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]59[/C][C]7.25[/C][C]7.26[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]60[/C][C]7.26[/C][C]7.27[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]61[/C][C]7.27[/C][C]7.28[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]62[/C][C]7.3[/C][C]7.29[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]63[/C][C]7.32[/C][C]7.32[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]64[/C][C]7.34[/C][C]7.34[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]7.35[/C][C]7.36[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]66[/C][C]7.36[/C][C]7.37[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]67[/C][C]7.39[/C][C]7.38[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]68[/C][C]7.41[/C][C]7.41[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]69[/C][C]7.43[/C][C]7.43[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]7.46[/C][C]7.45[/C][C]0.0100000000000007[/C][/ROW]
[ROW][C]71[/C][C]7.47[/C][C]7.48[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]72[/C][C]7.5[/C][C]7.49[/C][C]0.0100000000000007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205519&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
36.156.158.88178419700125e-16
46.156.17-0.0199999999999996
56.166.17-0.00999999999999979
66.186.180
76.216.20.0100000000000007
86.226.23-0.00999999999999979
96.236.24-0.0099999999999989
106.266.250.00999999999999979
116.286.288.88178419700125e-16
126.286.3-0.0199999999999996
136.296.3-0.00999999999999979
146.326.310.0100000000000007
156.366.340.0200000000000005
166.376.38-0.00999999999999979
176.386.39-0.00999999999999979
186.386.4-0.0199999999999996
196.46.48.88178419700125e-16
206.416.42-0.00999999999999979
216.426.43-0.00999999999999979
226.436.44-0.00999999999999979
236.446.45-0.0099999999999989
246.476.460.00999999999999979
256.476.49-0.0199999999999996
266.486.49-0.0099999999999989
276.516.50.00999999999999979
286.546.530.0100000000000007
296.566.560
306.576.58-0.0099999999999989
316.66.590.00999999999999979
326.626.628.88178419700125e-16
336.656.640.0100000000000007
346.716.670.04
356.766.730.0300000000000002
366.786.788.88178419700125e-16
376.86.80
386.836.820.0100000000000007
396.866.850.0100000000000007
406.866.88-0.0199999999999996
416.876.88-0.00999999999999979
426.886.89-0.00999999999999979
436.96.98.88178419700125e-16
446.926.920
456.936.94-0.00999999999999979
466.946.95-0.0099999999999989
476.966.960
486.986.988.88178419700125e-16
496.997-0.00999999999999979
507.017.010
517.067.030.0300000000000002
527.077.08-0.0099999999999989
537.087.09-0.00999999999999979
547.087.1-0.0199999999999996
557.17.10
567.117.12-0.0099999999999989
577.227.130.0899999999999999
587.247.248.88178419700125e-16
597.257.26-0.00999999999999979
607.267.27-0.00999999999999979
617.277.28-0.00999999999999979
627.37.290.0100000000000007
637.327.328.88178419700125e-16
647.347.340
657.357.36-0.00999999999999979
667.367.37-0.0099999999999989
677.397.380.00999999999999979
687.417.418.88178419700125e-16
697.437.430
707.467.450.0100000000000007
717.477.48-0.00999999999999979
727.57.490.0100000000000007







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.527.488092228416157.55190777158385
747.547.494875596681017.58512440331899
757.567.504734118460467.61526588153953
767.587.516184456832297.6438155431677
777.67.528652053727977.67134794627203
787.627.541842240790287.69815775920971
797.647.555579971498877.72442002850112
807.667.569751193362027.75024880663797
817.687.584276685248447.77572331475155
827.77.599098766734627.80090123326537
837.727.614173893759997.82582610624
847.739999999999997.629468236920927.85053176307906

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.52 & 7.48809222841615 & 7.55190777158385 \tabularnewline
74 & 7.54 & 7.49487559668101 & 7.58512440331899 \tabularnewline
75 & 7.56 & 7.50473411846046 & 7.61526588153953 \tabularnewline
76 & 7.58 & 7.51618445683229 & 7.6438155431677 \tabularnewline
77 & 7.6 & 7.52865205372797 & 7.67134794627203 \tabularnewline
78 & 7.62 & 7.54184224079028 & 7.69815775920971 \tabularnewline
79 & 7.64 & 7.55557997149887 & 7.72442002850112 \tabularnewline
80 & 7.66 & 7.56975119336202 & 7.75024880663797 \tabularnewline
81 & 7.68 & 7.58427668524844 & 7.77572331475155 \tabularnewline
82 & 7.7 & 7.59909876673462 & 7.80090123326537 \tabularnewline
83 & 7.72 & 7.61417389375999 & 7.82582610624 \tabularnewline
84 & 7.73999999999999 & 7.62946823692092 & 7.85053176307906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205519&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]7.52[/C][C]7.48809222841615[/C][C]7.55190777158385[/C][/ROW]
[ROW][C]74[/C][C]7.54[/C][C]7.49487559668101[/C][C]7.58512440331899[/C][/ROW]
[ROW][C]75[/C][C]7.56[/C][C]7.50473411846046[/C][C]7.61526588153953[/C][/ROW]
[ROW][C]76[/C][C]7.58[/C][C]7.51618445683229[/C][C]7.6438155431677[/C][/ROW]
[ROW][C]77[/C][C]7.6[/C][C]7.52865205372797[/C][C]7.67134794627203[/C][/ROW]
[ROW][C]78[/C][C]7.62[/C][C]7.54184224079028[/C][C]7.69815775920971[/C][/ROW]
[ROW][C]79[/C][C]7.64[/C][C]7.55557997149887[/C][C]7.72442002850112[/C][/ROW]
[ROW][C]80[/C][C]7.66[/C][C]7.56975119336202[/C][C]7.75024880663797[/C][/ROW]
[ROW][C]81[/C][C]7.68[/C][C]7.58427668524844[/C][C]7.77572331475155[/C][/ROW]
[ROW][C]82[/C][C]7.7[/C][C]7.59909876673462[/C][C]7.80090123326537[/C][/ROW]
[ROW][C]83[/C][C]7.72[/C][C]7.61417389375999[/C][C]7.82582610624[/C][/ROW]
[ROW][C]84[/C][C]7.73999999999999[/C][C]7.62946823692092[/C][C]7.85053176307906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205519&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205519&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
737.527.488092228416157.55190777158385
747.547.494875596681017.58512440331899
757.567.504734118460467.61526588153953
767.587.516184456832297.6438155431677
777.67.528652053727977.67134794627203
787.627.541842240790287.69815775920971
797.647.555579971498877.72442002850112
807.667.569751193362027.75024880663797
817.687.584276685248447.77572331475155
827.77.599098766734627.80090123326537
837.727.614173893759997.82582610624
847.739999999999997.629468236920927.85053176307906



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')