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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Dec 2014 18:47:06 +0000
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/Dec/01/t1417459639d8cdryq7ag5ncv3.htm/, Retrieved Thu, 16 May 2024 14:07:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=262193, Retrieved Thu, 16 May 2024 14:07:45 +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)
-       [Exponential Smoothing] [] [2014-12-01 18:47:06] [18123dc03e4972c6afb0cd442b9891ee] [Current]
- R P     [Exponential Smoothing] [] [2014-12-31 12:22:29] [71f2a5ac3ba156c8901e0764f5884b00]
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Dataseries X:
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8
8
8.8
8.7
8.5
8.1
7.8
7.7
7.5
7.2
6.9
6.6
6.5
6.6
7.7
8
7.7
7.3
7
7
7.3
7.3
7.1
7.1
7
7
7.5
7.8
7.9
8.1
8.3
8.4
8.6
8.5
8.4
8.3
8
8
8.7
8.7
8.6
8.5
8.5
8.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262193&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262193&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262193&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]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262193&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
beta1
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.86.9-0.0999999999999996
46.46.5-0.0999999999999996
56.160.0999999999999988
66.55.80.700000000000001
77.76.90.8
87.98.9-1
97.58.1-0.600000000000001
106.97.1-0.199999999999999
116.66.30.299999999999999
126.96.30.600000000000001
137.77.20.499999999999999
1488.5-0.5
1588.3-0.300000000000001
167.78-0.3
177.37.4-0.100000000000001
187.46.90.500000000000001
198.17.50.599999999999999
208.38.8-0.499999999999998
218.18.5-0.400000000000002
227.97.91.77635683940025e-15
237.97.70.199999999999999
248.37.90.4
258.68.7-0.100000000000001
268.78.9-0.199999999999999
278.58.8-0.299999999999999
288.38.30
2988.1-0.100000000000001
3087.70.300000000000001
318.880.800000000000001
328.79.6-0.900000000000002
338.58.6-0.0999999999999979
348.18.3-0.200000000000001
357.87.70.100000000000001
367.77.50.2
377.57.6-0.100000000000001
387.27.3-0.0999999999999996
396.96.90
406.66.6-8.88178419700125e-16
416.56.30.200000000000001
426.66.40.199999999999999
437.76.71
4488.8-0.800000000000001
457.78.3-0.600000000000001
467.37.4-0.100000000000001
4776.90.100000000000001
4876.70.3
497.370.3
507.37.6-0.3
517.17.3-0.2
527.16.90.2
5377.1-0.0999999999999996
5476.90.0999999999999996
557.570.5
567.88-0.2
577.98.1-0.199999999999999
588.180.0999999999999996
598.38.31.77635683940025e-15
608.48.5-0.100000000000001
618.68.50.0999999999999996
628.58.8-0.299999999999999
638.48.40
648.38.30
6588.2-0.200000000000001
6687.70.300000000000001
678.780.699999999999999
688.79.4-0.699999999999999
698.68.7-0.0999999999999996
708.58.50
718.58.40.0999999999999996
728.68.50.0999999999999996

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.8 & 6.9 & -0.0999999999999996 \tabularnewline
4 & 6.4 & 6.5 & -0.0999999999999996 \tabularnewline
5 & 6.1 & 6 & 0.0999999999999988 \tabularnewline
6 & 6.5 & 5.8 & 0.700000000000001 \tabularnewline
7 & 7.7 & 6.9 & 0.8 \tabularnewline
8 & 7.9 & 8.9 & -1 \tabularnewline
9 & 7.5 & 8.1 & -0.600000000000001 \tabularnewline
10 & 6.9 & 7.1 & -0.199999999999999 \tabularnewline
11 & 6.6 & 6.3 & 0.299999999999999 \tabularnewline
12 & 6.9 & 6.3 & 0.600000000000001 \tabularnewline
13 & 7.7 & 7.2 & 0.499999999999999 \tabularnewline
14 & 8 & 8.5 & -0.5 \tabularnewline
15 & 8 & 8.3 & -0.300000000000001 \tabularnewline
16 & 7.7 & 8 & -0.3 \tabularnewline
17 & 7.3 & 7.4 & -0.100000000000001 \tabularnewline
18 & 7.4 & 6.9 & 0.500000000000001 \tabularnewline
19 & 8.1 & 7.5 & 0.599999999999999 \tabularnewline
20 & 8.3 & 8.8 & -0.499999999999998 \tabularnewline
21 & 8.1 & 8.5 & -0.400000000000002 \tabularnewline
22 & 7.9 & 7.9 & 1.77635683940025e-15 \tabularnewline
23 & 7.9 & 7.7 & 0.199999999999999 \tabularnewline
24 & 8.3 & 7.9 & 0.4 \tabularnewline
25 & 8.6 & 8.7 & -0.100000000000001 \tabularnewline
26 & 8.7 & 8.9 & -0.199999999999999 \tabularnewline
27 & 8.5 & 8.8 & -0.299999999999999 \tabularnewline
28 & 8.3 & 8.3 & 0 \tabularnewline
29 & 8 & 8.1 & -0.100000000000001 \tabularnewline
30 & 8 & 7.7 & 0.300000000000001 \tabularnewline
31 & 8.8 & 8 & 0.800000000000001 \tabularnewline
32 & 8.7 & 9.6 & -0.900000000000002 \tabularnewline
33 & 8.5 & 8.6 & -0.0999999999999979 \tabularnewline
34 & 8.1 & 8.3 & -0.200000000000001 \tabularnewline
35 & 7.8 & 7.7 & 0.100000000000001 \tabularnewline
36 & 7.7 & 7.5 & 0.2 \tabularnewline
37 & 7.5 & 7.6 & -0.100000000000001 \tabularnewline
38 & 7.2 & 7.3 & -0.0999999999999996 \tabularnewline
39 & 6.9 & 6.9 & 0 \tabularnewline
40 & 6.6 & 6.6 & -8.88178419700125e-16 \tabularnewline
41 & 6.5 & 6.3 & 0.200000000000001 \tabularnewline
42 & 6.6 & 6.4 & 0.199999999999999 \tabularnewline
43 & 7.7 & 6.7 & 1 \tabularnewline
44 & 8 & 8.8 & -0.800000000000001 \tabularnewline
45 & 7.7 & 8.3 & -0.600000000000001 \tabularnewline
46 & 7.3 & 7.4 & -0.100000000000001 \tabularnewline
47 & 7 & 6.9 & 0.100000000000001 \tabularnewline
48 & 7 & 6.7 & 0.3 \tabularnewline
49 & 7.3 & 7 & 0.3 \tabularnewline
50 & 7.3 & 7.6 & -0.3 \tabularnewline
51 & 7.1 & 7.3 & -0.2 \tabularnewline
52 & 7.1 & 6.9 & 0.2 \tabularnewline
53 & 7 & 7.1 & -0.0999999999999996 \tabularnewline
54 & 7 & 6.9 & 0.0999999999999996 \tabularnewline
55 & 7.5 & 7 & 0.5 \tabularnewline
56 & 7.8 & 8 & -0.2 \tabularnewline
57 & 7.9 & 8.1 & -0.199999999999999 \tabularnewline
58 & 8.1 & 8 & 0.0999999999999996 \tabularnewline
59 & 8.3 & 8.3 & 1.77635683940025e-15 \tabularnewline
60 & 8.4 & 8.5 & -0.100000000000001 \tabularnewline
61 & 8.6 & 8.5 & 0.0999999999999996 \tabularnewline
62 & 8.5 & 8.8 & -0.299999999999999 \tabularnewline
63 & 8.4 & 8.4 & 0 \tabularnewline
64 & 8.3 & 8.3 & 0 \tabularnewline
65 & 8 & 8.2 & -0.200000000000001 \tabularnewline
66 & 8 & 7.7 & 0.300000000000001 \tabularnewline
67 & 8.7 & 8 & 0.699999999999999 \tabularnewline
68 & 8.7 & 9.4 & -0.699999999999999 \tabularnewline
69 & 8.6 & 8.7 & -0.0999999999999996 \tabularnewline
70 & 8.5 & 8.5 & 0 \tabularnewline
71 & 8.5 & 8.4 & 0.0999999999999996 \tabularnewline
72 & 8.6 & 8.5 & 0.0999999999999996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262193&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]6.8[/C][C]6.9[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]6.4[/C][C]6.5[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]5[/C][C]6.1[/C][C]6[/C][C]0.0999999999999988[/C][/ROW]
[ROW][C]6[/C][C]6.5[/C][C]5.8[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]7[/C][C]7.7[/C][C]6.9[/C][C]0.8[/C][/ROW]
[ROW][C]8[/C][C]7.9[/C][C]8.9[/C][C]-1[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]8.1[/C][C]-0.600000000000001[/C][/ROW]
[ROW][C]10[/C][C]6.9[/C][C]7.1[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]11[/C][C]6.6[/C][C]6.3[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]12[/C][C]6.9[/C][C]6.3[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]13[/C][C]7.7[/C][C]7.2[/C][C]0.499999999999999[/C][/ROW]
[ROW][C]14[/C][C]8[/C][C]8.5[/C][C]-0.5[/C][/ROW]
[ROW][C]15[/C][C]8[/C][C]8.3[/C][C]-0.300000000000001[/C][/ROW]
[ROW][C]16[/C][C]7.7[/C][C]8[/C][C]-0.3[/C][/ROW]
[ROW][C]17[/C][C]7.3[/C][C]7.4[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]18[/C][C]7.4[/C][C]6.9[/C][C]0.500000000000001[/C][/ROW]
[ROW][C]19[/C][C]8.1[/C][C]7.5[/C][C]0.599999999999999[/C][/ROW]
[ROW][C]20[/C][C]8.3[/C][C]8.8[/C][C]-0.499999999999998[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]8.5[/C][C]-0.400000000000002[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.9[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]23[/C][C]7.9[/C][C]7.7[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]7.9[/C][C]0.4[/C][/ROW]
[ROW][C]25[/C][C]8.6[/C][C]8.7[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.9[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]27[/C][C]8.5[/C][C]8.8[/C][C]-0.299999999999999[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.3[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]8.1[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.7[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]31[/C][C]8.8[/C][C]8[/C][C]0.800000000000001[/C][/ROW]
[ROW][C]32[/C][C]8.7[/C][C]9.6[/C][C]-0.900000000000002[/C][/ROW]
[ROW][C]33[/C][C]8.5[/C][C]8.6[/C][C]-0.0999999999999979[/C][/ROW]
[ROW][C]34[/C][C]8.1[/C][C]8.3[/C][C]-0.200000000000001[/C][/ROW]
[ROW][C]35[/C][C]7.8[/C][C]7.7[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]36[/C][C]7.7[/C][C]7.5[/C][C]0.2[/C][/ROW]
[ROW][C]37[/C][C]7.5[/C][C]7.6[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.3[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]39[/C][C]6.9[/C][C]6.9[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]6.6[/C][C]6.6[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]41[/C][C]6.5[/C][C]6.3[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]42[/C][C]6.6[/C][C]6.4[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]43[/C][C]7.7[/C][C]6.7[/C][C]1[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]8.8[/C][C]-0.800000000000001[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]8.3[/C][C]-0.600000000000001[/C][/ROW]
[ROW][C]46[/C][C]7.3[/C][C]7.4[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]6.9[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]48[/C][C]7[/C][C]6.7[/C][C]0.3[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7[/C][C]0.3[/C][/ROW]
[ROW][C]50[/C][C]7.3[/C][C]7.6[/C][C]-0.3[/C][/ROW]
[ROW][C]51[/C][C]7.1[/C][C]7.3[/C][C]-0.2[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]6.9[/C][C]0.2[/C][/ROW]
[ROW][C]53[/C][C]7[/C][C]7.1[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]54[/C][C]7[/C][C]6.9[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7[/C][C]0.5[/C][/ROW]
[ROW][C]56[/C][C]7.8[/C][C]8[/C][C]-0.2[/C][/ROW]
[ROW][C]57[/C][C]7.9[/C][C]8.1[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]58[/C][C]8.1[/C][C]8[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]59[/C][C]8.3[/C][C]8.3[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]60[/C][C]8.4[/C][C]8.5[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]61[/C][C]8.6[/C][C]8.5[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]62[/C][C]8.5[/C][C]8.8[/C][C]-0.299999999999999[/C][/ROW]
[ROW][C]63[/C][C]8.4[/C][C]8.4[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]8.3[/C][C]8.3[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]8[/C][C]8.2[/C][C]-0.200000000000001[/C][/ROW]
[ROW][C]66[/C][C]8[/C][C]7.7[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]67[/C][C]8.7[/C][C]8[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]68[/C][C]8.7[/C][C]9.4[/C][C]-0.699999999999999[/C][/ROW]
[ROW][C]69[/C][C]8.6[/C][C]8.7[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]70[/C][C]8.5[/C][C]8.5[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]8.5[/C][C]8.4[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]72[/C][C]8.6[/C][C]8.5[/C][C]0.0999999999999996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262193&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
36.86.9-0.0999999999999996
46.46.5-0.0999999999999996
56.160.0999999999999988
66.55.80.700000000000001
77.76.90.8
87.98.9-1
97.58.1-0.600000000000001
106.97.1-0.199999999999999
116.66.30.299999999999999
126.96.30.600000000000001
137.77.20.499999999999999
1488.5-0.5
1588.3-0.300000000000001
167.78-0.3
177.37.4-0.100000000000001
187.46.90.500000000000001
198.17.50.599999999999999
208.38.8-0.499999999999998
218.18.5-0.400000000000002
227.97.91.77635683940025e-15
237.97.70.199999999999999
248.37.90.4
258.68.7-0.100000000000001
268.78.9-0.199999999999999
278.58.8-0.299999999999999
288.38.30
2988.1-0.100000000000001
3087.70.300000000000001
318.880.800000000000001
328.79.6-0.900000000000002
338.58.6-0.0999999999999979
348.18.3-0.200000000000001
357.87.70.100000000000001
367.77.50.2
377.57.6-0.100000000000001
387.27.3-0.0999999999999996
396.96.90
406.66.6-8.88178419700125e-16
416.56.30.200000000000001
426.66.40.199999999999999
437.76.71
4488.8-0.800000000000001
457.78.3-0.600000000000001
467.37.4-0.100000000000001
4776.90.100000000000001
4876.70.3
497.370.3
507.37.6-0.3
517.17.3-0.2
527.16.90.2
5377.1-0.0999999999999996
5476.90.0999999999999996
557.570.5
567.88-0.2
577.98.1-0.199999999999999
588.180.0999999999999996
598.38.31.77635683940025e-15
608.48.5-0.100000000000001
618.68.50.0999999999999996
628.58.8-0.299999999999999
638.48.40
648.38.30
6588.2-0.200000000000001
6687.70.300000000000001
678.780.699999999999999
688.79.4-0.699999999999999
698.68.7-0.0999999999999996
708.58.50
718.58.40.0999999999999996
728.68.50.0999999999999996







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.77.92498806314199.4750119368581
748.87.0670206258115110.5329793741885
758.96.000170861616911.7998291383831
7694.7550847984704713.2449152015295
779.13.3523576463918514.8476423536081
789.21.806857318649816.5931426813502
799.30.12993509738579318.4700649026142
809.4-1.6693845566770420.469384556677
819.5-3.5837073548622522.5837073548622
829.6-5.6068322925891324.8068322925891
839.7-7.7334624257463527.1334624257463
849.8-9.9590049465340529.559004946534

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.7 & 7.9249880631419 & 9.4750119368581 \tabularnewline
74 & 8.8 & 7.06702062581151 & 10.5329793741885 \tabularnewline
75 & 8.9 & 6.0001708616169 & 11.7998291383831 \tabularnewline
76 & 9 & 4.75508479847047 & 13.2449152015295 \tabularnewline
77 & 9.1 & 3.35235764639185 & 14.8476423536081 \tabularnewline
78 & 9.2 & 1.8068573186498 & 16.5931426813502 \tabularnewline
79 & 9.3 & 0.129935097385793 & 18.4700649026142 \tabularnewline
80 & 9.4 & -1.66938455667704 & 20.469384556677 \tabularnewline
81 & 9.5 & -3.58370735486225 & 22.5837073548622 \tabularnewline
82 & 9.6 & -5.60683229258913 & 24.8068322925891 \tabularnewline
83 & 9.7 & -7.73346242574635 & 27.1334624257463 \tabularnewline
84 & 9.8 & -9.95900494653405 & 29.559004946534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262193&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]8.7[/C][C]7.9249880631419[/C][C]9.4750119368581[/C][/ROW]
[ROW][C]74[/C][C]8.8[/C][C]7.06702062581151[/C][C]10.5329793741885[/C][/ROW]
[ROW][C]75[/C][C]8.9[/C][C]6.0001708616169[/C][C]11.7998291383831[/C][/ROW]
[ROW][C]76[/C][C]9[/C][C]4.75508479847047[/C][C]13.2449152015295[/C][/ROW]
[ROW][C]77[/C][C]9.1[/C][C]3.35235764639185[/C][C]14.8476423536081[/C][/ROW]
[ROW][C]78[/C][C]9.2[/C][C]1.8068573186498[/C][C]16.5931426813502[/C][/ROW]
[ROW][C]79[/C][C]9.3[/C][C]0.129935097385793[/C][C]18.4700649026142[/C][/ROW]
[ROW][C]80[/C][C]9.4[/C][C]-1.66938455667704[/C][C]20.469384556677[/C][/ROW]
[ROW][C]81[/C][C]9.5[/C][C]-3.58370735486225[/C][C]22.5837073548622[/C][/ROW]
[ROW][C]82[/C][C]9.6[/C][C]-5.60683229258913[/C][C]24.8068322925891[/C][/ROW]
[ROW][C]83[/C][C]9.7[/C][C]-7.73346242574635[/C][C]27.1334624257463[/C][/ROW]
[ROW][C]84[/C][C]9.8[/C][C]-9.95900494653405[/C][C]29.559004946534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262193&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
738.77.92498806314199.4750119368581
748.87.0670206258115110.5329793741885
758.96.000170861616911.7998291383831
7694.7550847984704713.2449152015295
779.13.3523576463918514.8476423536081
789.21.806857318649816.5931426813502
799.30.12993509738579318.4700649026142
809.4-1.6693845566770420.469384556677
819.5-3.5837073548622522.5837073548622
829.6-5.6068322925891324.8068322925891
839.7-7.7334624257463527.1334624257463
849.8-9.9590049465340529.559004946534



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')