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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Jan 2014 04:10:05 -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/2014/Jan/13/t1389604229c8m3vqc7g1jgvc0.htm/, Retrieved Sun, 19 May 2024 11:33:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233122, Retrieved Sun, 19 May 2024 11:33:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2014-01-13 09:07:58] [33591c51b6fd6c0de3aee2101c04ad72]
-   PD    [Exponential Smoothing] [] [2014-01-13 09:10:05] [e0c7fa3260b5bc60bc725c9d38409993] [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
7.51
7.52
7.58
7.59
7.63
7.64
7.64
7.66
7.67
7.68
7.69
7.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233122&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]5 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=233122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233122&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.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=233122&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=233122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233122&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
737.517.52-0.00999999999999979
747.527.53-0.00999999999999979
757.587.540.0400000000000009
767.597.6-0.00999999999999979
777.637.610.0200000000000005
787.647.65-0.00999999999999979
797.647.66-0.0199999999999996
807.667.668.88178419700125e-16
817.677.68-0.00999999999999979
827.687.69-0.00999999999999979
837.697.7-0.0099999999999989
847.77.71-0.00999999999999979

\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
73 & 7.51 & 7.52 & -0.00999999999999979 \tabularnewline
74 & 7.52 & 7.53 & -0.00999999999999979 \tabularnewline
75 & 7.58 & 7.54 & 0.0400000000000009 \tabularnewline
76 & 7.59 & 7.6 & -0.00999999999999979 \tabularnewline
77 & 7.63 & 7.61 & 0.0200000000000005 \tabularnewline
78 & 7.64 & 7.65 & -0.00999999999999979 \tabularnewline
79 & 7.64 & 7.66 & -0.0199999999999996 \tabularnewline
80 & 7.66 & 7.66 & 8.88178419700125e-16 \tabularnewline
81 & 7.67 & 7.68 & -0.00999999999999979 \tabularnewline
82 & 7.68 & 7.69 & -0.00999999999999979 \tabularnewline
83 & 7.69 & 7.7 & -0.0099999999999989 \tabularnewline
84 & 7.7 & 7.71 & -0.00999999999999979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233122&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]
[ROW][C]73[/C][C]7.51[/C][C]7.52[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]74[/C][C]7.52[/C][C]7.53[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]75[/C][C]7.58[/C][C]7.54[/C][C]0.0400000000000009[/C][/ROW]
[ROW][C]76[/C][C]7.59[/C][C]7.6[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]77[/C][C]7.63[/C][C]7.61[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]78[/C][C]7.64[/C][C]7.65[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]79[/C][C]7.64[/C][C]7.66[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]80[/C][C]7.66[/C][C]7.66[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]81[/C][C]7.67[/C][C]7.68[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]82[/C][C]7.68[/C][C]7.69[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]83[/C][C]7.69[/C][C]7.7[/C][C]-0.0099999999999989[/C][/ROW]
[ROW][C]84[/C][C]7.7[/C][C]7.71[/C][C]-0.00999999999999979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233122&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233122&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
737.517.52-0.00999999999999979
747.527.53-0.00999999999999979
757.587.540.0400000000000009
767.597.6-0.00999999999999979
777.637.610.0200000000000005
787.647.65-0.00999999999999979
797.647.66-0.0199999999999996
807.667.668.88178419700125e-16
817.677.68-0.00999999999999979
827.687.69-0.00999999999999979
837.697.7-0.0099999999999989
847.77.71-0.00999999999999979







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
857.727.688112502148647.75188749785136
867.747.694904268068467.78509573193154
877.767.70476923359527.8152307664048
887.787.716225004297287.84377499570272
897.87.728697387171987.87130261282802
907.827.741891901090077.89810809890992
917.847.755633610753197.9243663892468
927.867.769808536136937.95019146386307
937.887.784337506445927.97566249355407
947.97.799162877905978.00083712209402
957.927.814241134123778.02575886587622
967.947.82953846719048.05046153280959

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 7.72 & 7.68811250214864 & 7.75188749785136 \tabularnewline
86 & 7.74 & 7.69490426806846 & 7.78509573193154 \tabularnewline
87 & 7.76 & 7.7047692335952 & 7.8152307664048 \tabularnewline
88 & 7.78 & 7.71622500429728 & 7.84377499570272 \tabularnewline
89 & 7.8 & 7.72869738717198 & 7.87130261282802 \tabularnewline
90 & 7.82 & 7.74189190109007 & 7.89810809890992 \tabularnewline
91 & 7.84 & 7.75563361075319 & 7.9243663892468 \tabularnewline
92 & 7.86 & 7.76980853613693 & 7.95019146386307 \tabularnewline
93 & 7.88 & 7.78433750644592 & 7.97566249355407 \tabularnewline
94 & 7.9 & 7.79916287790597 & 8.00083712209402 \tabularnewline
95 & 7.92 & 7.81424113412377 & 8.02575886587622 \tabularnewline
96 & 7.94 & 7.8295384671904 & 8.05046153280959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233122&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]85[/C][C]7.72[/C][C]7.68811250214864[/C][C]7.75188749785136[/C][/ROW]
[ROW][C]86[/C][C]7.74[/C][C]7.69490426806846[/C][C]7.78509573193154[/C][/ROW]
[ROW][C]87[/C][C]7.76[/C][C]7.7047692335952[/C][C]7.8152307664048[/C][/ROW]
[ROW][C]88[/C][C]7.78[/C][C]7.71622500429728[/C][C]7.84377499570272[/C][/ROW]
[ROW][C]89[/C][C]7.8[/C][C]7.72869738717198[/C][C]7.87130261282802[/C][/ROW]
[ROW][C]90[/C][C]7.82[/C][C]7.74189190109007[/C][C]7.89810809890992[/C][/ROW]
[ROW][C]91[/C][C]7.84[/C][C]7.75563361075319[/C][C]7.9243663892468[/C][/ROW]
[ROW][C]92[/C][C]7.86[/C][C]7.76980853613693[/C][C]7.95019146386307[/C][/ROW]
[ROW][C]93[/C][C]7.88[/C][C]7.78433750644592[/C][C]7.97566249355407[/C][/ROW]
[ROW][C]94[/C][C]7.9[/C][C]7.79916287790597[/C][C]8.00083712209402[/C][/ROW]
[ROW][C]95[/C][C]7.92[/C][C]7.81424113412377[/C][C]8.02575886587622[/C][/ROW]
[ROW][C]96[/C][C]7.94[/C][C]7.8295384671904[/C][C]8.05046153280959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233122&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233122&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
857.727.688112502148647.75188749785136
867.747.694904268068467.78509573193154
877.767.70476923359527.8152307664048
887.787.716225004297287.84377499570272
897.87.728697387171987.87130261282802
907.827.741891901090077.89810809890992
917.847.755633610753197.9243663892468
927.867.769808536136937.95019146386307
937.887.784337506445927.97566249355407
947.97.799162877905978.00083712209402
957.927.814241134123778.02575886587622
967.947.82953846719048.05046153280959



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')