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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 12:17:00 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461583100bnttzxll2mbiow1.htm/, Retrieved Mon, 06 May 2024 10:28:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294692, Retrieved Mon, 06 May 2024 10:28:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 11:17:00] [55e0f811d0de406b35493d0ca672d497] [Current]
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Dataseries X:
83.61
83.89
83.4
82.96
82.76
83.35
87.78
88.99
88.92
88.91
89.79
90.54
93.15
92.79
93.21
95.35
100.91
103.69
104.04
104.16
104.71
105.18
104.92
104.83
104.9
105.05
104.6
103.21
102.52
101.09
101.19
102.34
102.62
102.47
101.82
101.86
101.54
101.98
101.23
100.4
99.94
99.94
100
98.8
99.07
99.46
99.18
98.47
97.12
96.91
96.09
97.17
96.8
97.13
99.9
100.56
100.84
99.81
100.44
100.07
101.32
103.98
104.81
106.23
106.48
107.59
107.16
107.54
107.1
106.38
106.64
106.13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294692&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294692&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'Gwilym Jenkins' @ jenkins.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=294692&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=294692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294692&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
383.484.17-0.769999999999996
482.9683.68-0.720000000000013
582.7683.24-0.47999999999999
683.3583.040.309999999999988
787.7883.634.15000000000001
888.9988.060.929999999999993
988.9289.27-0.349999999999994
1088.9189.2-0.290000000000006
1189.7989.190.600000000000009
1290.5490.070.469999999999999
1393.1590.822.33
1492.7993.43-0.640000000000001
1593.2193.070.139999999999986
1695.3593.491.86
17100.9195.635.28
18103.69101.192.5
19104.04103.970.0700000000000074
20104.16104.32-0.160000000000011
21104.71104.440.269999999999996
22105.18104.990.190000000000012
23104.92105.46-0.540000000000006
24104.83105.2-0.370000000000005
25104.9105.11-0.209999999999994
26105.05105.18-0.13000000000001
27104.6105.33-0.730000000000004
28103.21104.88-1.67
29102.52103.49-0.969999999999999
30101.09102.8-1.70999999999999
31101.19101.37-0.180000000000007
32102.34101.470.870000000000005
33102.62102.620
34102.47102.9-0.430000000000007
35101.82102.75-0.930000000000007
36101.86102.1-0.239999999999995
37101.54102.14-0.599999999999994
38101.98101.820.159999999999997
39101.23102.26-1.03
40100.4101.51-1.11
4199.94100.68-0.740000000000009
4299.94100.22-0.280000000000001
43100100.22-0.219999999999999
4498.8100.28-1.48
4599.0799.08-0.0100000000000051
4699.4699.350.109999999999999
4799.1899.74-0.559999999999988
4898.4799.46-0.990000000000009
4997.1298.75-1.63
5096.9197.4-0.490000000000009
5196.0997.19-1.09999999999999
5297.1796.370.799999999999997
5396.897.45-0.650000000000006
5497.1397.080.0499999999999972
5599.997.412.49000000000001
56100.56100.180.379999999999995
57100.84100.840
5899.81101.12-1.31
59100.44100.090.349999999999994
60100.07100.72-0.650000000000006
61101.32100.350.969999999999999
62103.98101.62.38000000000001
63104.81104.260.549999999999997
64106.23105.091.14
65106.48106.51-0.0300000000000011
66107.59106.760.829999999999998
67107.16107.87-0.710000000000008
68107.54107.440.100000000000009
69107.1107.82-0.720000000000013
70106.38107.38-1
71106.64106.66-0.019999999999996
72106.13106.92-0.790000000000006

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 83.4 & 84.17 & -0.769999999999996 \tabularnewline
4 & 82.96 & 83.68 & -0.720000000000013 \tabularnewline
5 & 82.76 & 83.24 & -0.47999999999999 \tabularnewline
6 & 83.35 & 83.04 & 0.309999999999988 \tabularnewline
7 & 87.78 & 83.63 & 4.15000000000001 \tabularnewline
8 & 88.99 & 88.06 & 0.929999999999993 \tabularnewline
9 & 88.92 & 89.27 & -0.349999999999994 \tabularnewline
10 & 88.91 & 89.2 & -0.290000000000006 \tabularnewline
11 & 89.79 & 89.19 & 0.600000000000009 \tabularnewline
12 & 90.54 & 90.07 & 0.469999999999999 \tabularnewline
13 & 93.15 & 90.82 & 2.33 \tabularnewline
14 & 92.79 & 93.43 & -0.640000000000001 \tabularnewline
15 & 93.21 & 93.07 & 0.139999999999986 \tabularnewline
16 & 95.35 & 93.49 & 1.86 \tabularnewline
17 & 100.91 & 95.63 & 5.28 \tabularnewline
18 & 103.69 & 101.19 & 2.5 \tabularnewline
19 & 104.04 & 103.97 & 0.0700000000000074 \tabularnewline
20 & 104.16 & 104.32 & -0.160000000000011 \tabularnewline
21 & 104.71 & 104.44 & 0.269999999999996 \tabularnewline
22 & 105.18 & 104.99 & 0.190000000000012 \tabularnewline
23 & 104.92 & 105.46 & -0.540000000000006 \tabularnewline
24 & 104.83 & 105.2 & -0.370000000000005 \tabularnewline
25 & 104.9 & 105.11 & -0.209999999999994 \tabularnewline
26 & 105.05 & 105.18 & -0.13000000000001 \tabularnewline
27 & 104.6 & 105.33 & -0.730000000000004 \tabularnewline
28 & 103.21 & 104.88 & -1.67 \tabularnewline
29 & 102.52 & 103.49 & -0.969999999999999 \tabularnewline
30 & 101.09 & 102.8 & -1.70999999999999 \tabularnewline
31 & 101.19 & 101.37 & -0.180000000000007 \tabularnewline
32 & 102.34 & 101.47 & 0.870000000000005 \tabularnewline
33 & 102.62 & 102.62 & 0 \tabularnewline
34 & 102.47 & 102.9 & -0.430000000000007 \tabularnewline
35 & 101.82 & 102.75 & -0.930000000000007 \tabularnewline
36 & 101.86 & 102.1 & -0.239999999999995 \tabularnewline
37 & 101.54 & 102.14 & -0.599999999999994 \tabularnewline
38 & 101.98 & 101.82 & 0.159999999999997 \tabularnewline
39 & 101.23 & 102.26 & -1.03 \tabularnewline
40 & 100.4 & 101.51 & -1.11 \tabularnewline
41 & 99.94 & 100.68 & -0.740000000000009 \tabularnewline
42 & 99.94 & 100.22 & -0.280000000000001 \tabularnewline
43 & 100 & 100.22 & -0.219999999999999 \tabularnewline
44 & 98.8 & 100.28 & -1.48 \tabularnewline
45 & 99.07 & 99.08 & -0.0100000000000051 \tabularnewline
46 & 99.46 & 99.35 & 0.109999999999999 \tabularnewline
47 & 99.18 & 99.74 & -0.559999999999988 \tabularnewline
48 & 98.47 & 99.46 & -0.990000000000009 \tabularnewline
49 & 97.12 & 98.75 & -1.63 \tabularnewline
50 & 96.91 & 97.4 & -0.490000000000009 \tabularnewline
51 & 96.09 & 97.19 & -1.09999999999999 \tabularnewline
52 & 97.17 & 96.37 & 0.799999999999997 \tabularnewline
53 & 96.8 & 97.45 & -0.650000000000006 \tabularnewline
54 & 97.13 & 97.08 & 0.0499999999999972 \tabularnewline
55 & 99.9 & 97.41 & 2.49000000000001 \tabularnewline
56 & 100.56 & 100.18 & 0.379999999999995 \tabularnewline
57 & 100.84 & 100.84 & 0 \tabularnewline
58 & 99.81 & 101.12 & -1.31 \tabularnewline
59 & 100.44 & 100.09 & 0.349999999999994 \tabularnewline
60 & 100.07 & 100.72 & -0.650000000000006 \tabularnewline
61 & 101.32 & 100.35 & 0.969999999999999 \tabularnewline
62 & 103.98 & 101.6 & 2.38000000000001 \tabularnewline
63 & 104.81 & 104.26 & 0.549999999999997 \tabularnewline
64 & 106.23 & 105.09 & 1.14 \tabularnewline
65 & 106.48 & 106.51 & -0.0300000000000011 \tabularnewline
66 & 107.59 & 106.76 & 0.829999999999998 \tabularnewline
67 & 107.16 & 107.87 & -0.710000000000008 \tabularnewline
68 & 107.54 & 107.44 & 0.100000000000009 \tabularnewline
69 & 107.1 & 107.82 & -0.720000000000013 \tabularnewline
70 & 106.38 & 107.38 & -1 \tabularnewline
71 & 106.64 & 106.66 & -0.019999999999996 \tabularnewline
72 & 106.13 & 106.92 & -0.790000000000006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294692&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]83.4[/C][C]84.17[/C][C]-0.769999999999996[/C][/ROW]
[ROW][C]4[/C][C]82.96[/C][C]83.68[/C][C]-0.720000000000013[/C][/ROW]
[ROW][C]5[/C][C]82.76[/C][C]83.24[/C][C]-0.47999999999999[/C][/ROW]
[ROW][C]6[/C][C]83.35[/C][C]83.04[/C][C]0.309999999999988[/C][/ROW]
[ROW][C]7[/C][C]87.78[/C][C]83.63[/C][C]4.15000000000001[/C][/ROW]
[ROW][C]8[/C][C]88.99[/C][C]88.06[/C][C]0.929999999999993[/C][/ROW]
[ROW][C]9[/C][C]88.92[/C][C]89.27[/C][C]-0.349999999999994[/C][/ROW]
[ROW][C]10[/C][C]88.91[/C][C]89.2[/C][C]-0.290000000000006[/C][/ROW]
[ROW][C]11[/C][C]89.79[/C][C]89.19[/C][C]0.600000000000009[/C][/ROW]
[ROW][C]12[/C][C]90.54[/C][C]90.07[/C][C]0.469999999999999[/C][/ROW]
[ROW][C]13[/C][C]93.15[/C][C]90.82[/C][C]2.33[/C][/ROW]
[ROW][C]14[/C][C]92.79[/C][C]93.43[/C][C]-0.640000000000001[/C][/ROW]
[ROW][C]15[/C][C]93.21[/C][C]93.07[/C][C]0.139999999999986[/C][/ROW]
[ROW][C]16[/C][C]95.35[/C][C]93.49[/C][C]1.86[/C][/ROW]
[ROW][C]17[/C][C]100.91[/C][C]95.63[/C][C]5.28[/C][/ROW]
[ROW][C]18[/C][C]103.69[/C][C]101.19[/C][C]2.5[/C][/ROW]
[ROW][C]19[/C][C]104.04[/C][C]103.97[/C][C]0.0700000000000074[/C][/ROW]
[ROW][C]20[/C][C]104.16[/C][C]104.32[/C][C]-0.160000000000011[/C][/ROW]
[ROW][C]21[/C][C]104.71[/C][C]104.44[/C][C]0.269999999999996[/C][/ROW]
[ROW][C]22[/C][C]105.18[/C][C]104.99[/C][C]0.190000000000012[/C][/ROW]
[ROW][C]23[/C][C]104.92[/C][C]105.46[/C][C]-0.540000000000006[/C][/ROW]
[ROW][C]24[/C][C]104.83[/C][C]105.2[/C][C]-0.370000000000005[/C][/ROW]
[ROW][C]25[/C][C]104.9[/C][C]105.11[/C][C]-0.209999999999994[/C][/ROW]
[ROW][C]26[/C][C]105.05[/C][C]105.18[/C][C]-0.13000000000001[/C][/ROW]
[ROW][C]27[/C][C]104.6[/C][C]105.33[/C][C]-0.730000000000004[/C][/ROW]
[ROW][C]28[/C][C]103.21[/C][C]104.88[/C][C]-1.67[/C][/ROW]
[ROW][C]29[/C][C]102.52[/C][C]103.49[/C][C]-0.969999999999999[/C][/ROW]
[ROW][C]30[/C][C]101.09[/C][C]102.8[/C][C]-1.70999999999999[/C][/ROW]
[ROW][C]31[/C][C]101.19[/C][C]101.37[/C][C]-0.180000000000007[/C][/ROW]
[ROW][C]32[/C][C]102.34[/C][C]101.47[/C][C]0.870000000000005[/C][/ROW]
[ROW][C]33[/C][C]102.62[/C][C]102.62[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]102.47[/C][C]102.9[/C][C]-0.430000000000007[/C][/ROW]
[ROW][C]35[/C][C]101.82[/C][C]102.75[/C][C]-0.930000000000007[/C][/ROW]
[ROW][C]36[/C][C]101.86[/C][C]102.1[/C][C]-0.239999999999995[/C][/ROW]
[ROW][C]37[/C][C]101.54[/C][C]102.14[/C][C]-0.599999999999994[/C][/ROW]
[ROW][C]38[/C][C]101.98[/C][C]101.82[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]39[/C][C]101.23[/C][C]102.26[/C][C]-1.03[/C][/ROW]
[ROW][C]40[/C][C]100.4[/C][C]101.51[/C][C]-1.11[/C][/ROW]
[ROW][C]41[/C][C]99.94[/C][C]100.68[/C][C]-0.740000000000009[/C][/ROW]
[ROW][C]42[/C][C]99.94[/C][C]100.22[/C][C]-0.280000000000001[/C][/ROW]
[ROW][C]43[/C][C]100[/C][C]100.22[/C][C]-0.219999999999999[/C][/ROW]
[ROW][C]44[/C][C]98.8[/C][C]100.28[/C][C]-1.48[/C][/ROW]
[ROW][C]45[/C][C]99.07[/C][C]99.08[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]46[/C][C]99.46[/C][C]99.35[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]47[/C][C]99.18[/C][C]99.74[/C][C]-0.559999999999988[/C][/ROW]
[ROW][C]48[/C][C]98.47[/C][C]99.46[/C][C]-0.990000000000009[/C][/ROW]
[ROW][C]49[/C][C]97.12[/C][C]98.75[/C][C]-1.63[/C][/ROW]
[ROW][C]50[/C][C]96.91[/C][C]97.4[/C][C]-0.490000000000009[/C][/ROW]
[ROW][C]51[/C][C]96.09[/C][C]97.19[/C][C]-1.09999999999999[/C][/ROW]
[ROW][C]52[/C][C]97.17[/C][C]96.37[/C][C]0.799999999999997[/C][/ROW]
[ROW][C]53[/C][C]96.8[/C][C]97.45[/C][C]-0.650000000000006[/C][/ROW]
[ROW][C]54[/C][C]97.13[/C][C]97.08[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]55[/C][C]99.9[/C][C]97.41[/C][C]2.49000000000001[/C][/ROW]
[ROW][C]56[/C][C]100.56[/C][C]100.18[/C][C]0.379999999999995[/C][/ROW]
[ROW][C]57[/C][C]100.84[/C][C]100.84[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]99.81[/C][C]101.12[/C][C]-1.31[/C][/ROW]
[ROW][C]59[/C][C]100.44[/C][C]100.09[/C][C]0.349999999999994[/C][/ROW]
[ROW][C]60[/C][C]100.07[/C][C]100.72[/C][C]-0.650000000000006[/C][/ROW]
[ROW][C]61[/C][C]101.32[/C][C]100.35[/C][C]0.969999999999999[/C][/ROW]
[ROW][C]62[/C][C]103.98[/C][C]101.6[/C][C]2.38000000000001[/C][/ROW]
[ROW][C]63[/C][C]104.81[/C][C]104.26[/C][C]0.549999999999997[/C][/ROW]
[ROW][C]64[/C][C]106.23[/C][C]105.09[/C][C]1.14[/C][/ROW]
[ROW][C]65[/C][C]106.48[/C][C]106.51[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]66[/C][C]107.59[/C][C]106.76[/C][C]0.829999999999998[/C][/ROW]
[ROW][C]67[/C][C]107.16[/C][C]107.87[/C][C]-0.710000000000008[/C][/ROW]
[ROW][C]68[/C][C]107.54[/C][C]107.44[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]69[/C][C]107.1[/C][C]107.82[/C][C]-0.720000000000013[/C][/ROW]
[ROW][C]70[/C][C]106.38[/C][C]107.38[/C][C]-1[/C][/ROW]
[ROW][C]71[/C][C]106.64[/C][C]106.66[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]72[/C][C]106.13[/C][C]106.92[/C][C]-0.790000000000006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294692&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
383.484.17-0.769999999999996
482.9683.68-0.720000000000013
582.7683.24-0.47999999999999
683.3583.040.309999999999988
787.7883.634.15000000000001
888.9988.060.929999999999993
988.9289.27-0.349999999999994
1088.9189.2-0.290000000000006
1189.7989.190.600000000000009
1290.5490.070.469999999999999
1393.1590.822.33
1492.7993.43-0.640000000000001
1593.2193.070.139999999999986
1695.3593.491.86
17100.9195.635.28
18103.69101.192.5
19104.04103.970.0700000000000074
20104.16104.32-0.160000000000011
21104.71104.440.269999999999996
22105.18104.990.190000000000012
23104.92105.46-0.540000000000006
24104.83105.2-0.370000000000005
25104.9105.11-0.209999999999994
26105.05105.18-0.13000000000001
27104.6105.33-0.730000000000004
28103.21104.88-1.67
29102.52103.49-0.969999999999999
30101.09102.8-1.70999999999999
31101.19101.37-0.180000000000007
32102.34101.470.870000000000005
33102.62102.620
34102.47102.9-0.430000000000007
35101.82102.75-0.930000000000007
36101.86102.1-0.239999999999995
37101.54102.14-0.599999999999994
38101.98101.820.159999999999997
39101.23102.26-1.03
40100.4101.51-1.11
4199.94100.68-0.740000000000009
4299.94100.22-0.280000000000001
43100100.22-0.219999999999999
4498.8100.28-1.48
4599.0799.08-0.0100000000000051
4699.4699.350.109999999999999
4799.1899.74-0.559999999999988
4898.4799.46-0.990000000000009
4997.1298.75-1.63
5096.9197.4-0.490000000000009
5196.0997.19-1.09999999999999
5297.1796.370.799999999999997
5396.897.45-0.650000000000006
5497.1397.080.0499999999999972
5599.997.412.49000000000001
56100.56100.180.379999999999995
57100.84100.840
5899.81101.12-1.31
59100.44100.090.349999999999994
60100.07100.72-0.650000000000006
61101.32100.350.969999999999999
62103.98101.62.38000000000001
63104.81104.260.549999999999997
64106.23105.091.14
65106.48106.51-0.0300000000000011
66107.59106.760.829999999999998
67107.16107.87-0.710000000000008
68107.54107.440.100000000000009
69107.1107.82-0.720000000000013
70106.38107.38-1
71106.64106.66-0.019999999999996
72106.13106.92-0.790000000000006







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73106.41103.985855548153108.834144451847
74106.69103.261742039046110.118257960954
75106.97102.771258644514111.168741355486
76107.25102.401711096305112.098288903695
77107.53102.10944821839112.95055178161
78107.81101.872083030175113.747916969825
79108.09101.676316638315114.503683361685
80108.37101.513484078092115.226515921908
81108.65101.377566644458115.922433355542
82108.93101.264182154902116.595817845098
83109.21101.170022415601117.249977584399
84109.49101.092517289029117.887482710971

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.41 & 103.985855548153 & 108.834144451847 \tabularnewline
74 & 106.69 & 103.261742039046 & 110.118257960954 \tabularnewline
75 & 106.97 & 102.771258644514 & 111.168741355486 \tabularnewline
76 & 107.25 & 102.401711096305 & 112.098288903695 \tabularnewline
77 & 107.53 & 102.10944821839 & 112.95055178161 \tabularnewline
78 & 107.81 & 101.872083030175 & 113.747916969825 \tabularnewline
79 & 108.09 & 101.676316638315 & 114.503683361685 \tabularnewline
80 & 108.37 & 101.513484078092 & 115.226515921908 \tabularnewline
81 & 108.65 & 101.377566644458 & 115.922433355542 \tabularnewline
82 & 108.93 & 101.264182154902 & 116.595817845098 \tabularnewline
83 & 109.21 & 101.170022415601 & 117.249977584399 \tabularnewline
84 & 109.49 & 101.092517289029 & 117.887482710971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294692&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]106.41[/C][C]103.985855548153[/C][C]108.834144451847[/C][/ROW]
[ROW][C]74[/C][C]106.69[/C][C]103.261742039046[/C][C]110.118257960954[/C][/ROW]
[ROW][C]75[/C][C]106.97[/C][C]102.771258644514[/C][C]111.168741355486[/C][/ROW]
[ROW][C]76[/C][C]107.25[/C][C]102.401711096305[/C][C]112.098288903695[/C][/ROW]
[ROW][C]77[/C][C]107.53[/C][C]102.10944821839[/C][C]112.95055178161[/C][/ROW]
[ROW][C]78[/C][C]107.81[/C][C]101.872083030175[/C][C]113.747916969825[/C][/ROW]
[ROW][C]79[/C][C]108.09[/C][C]101.676316638315[/C][C]114.503683361685[/C][/ROW]
[ROW][C]80[/C][C]108.37[/C][C]101.513484078092[/C][C]115.226515921908[/C][/ROW]
[ROW][C]81[/C][C]108.65[/C][C]101.377566644458[/C][C]115.922433355542[/C][/ROW]
[ROW][C]82[/C][C]108.93[/C][C]101.264182154902[/C][C]116.595817845098[/C][/ROW]
[ROW][C]83[/C][C]109.21[/C][C]101.170022415601[/C][C]117.249977584399[/C][/ROW]
[ROW][C]84[/C][C]109.49[/C][C]101.092517289029[/C][C]117.887482710971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294692&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294692&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
73106.41103.985855548153108.834144451847
74106.69103.261742039046110.118257960954
75106.97102.771258644514111.168741355486
76107.25102.401711096305112.098288903695
77107.53102.10944821839112.95055178161
78107.81101.872083030175113.747916969825
79108.09101.676316638315114.503683361685
80108.37101.513484078092115.226515921908
81108.65101.377566644458115.922433355542
82108.93101.264182154902116.595817845098
83109.21101.170022415601117.249977584399
84109.49101.092517289029117.887482710971



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):
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')