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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 11:37:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/01/t12123418472clq5t3yml7vs9y.htm/, Retrieved Sat, 18 May 2024 17:59:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13718, Retrieved Sat, 18 May 2024 17:59:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact232
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Aankoop nieuwe en...] [2008-06-01 17:37:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
102.8
103.1
103.1
103.3
103.5
103.3
103.5
103.8
103.9
103.9
104.2
104.6
104.9
105.2
105.2
105.6
105.6
106.2
106.3
106.4
106.9
107.2
107.3
107.3
107.4
107.55
107.87
108.37
108.38
107.92
108.03
108.14
108.3
108.64
108.66
109.04
109.03
109.03
109.54
109.75
109.83
109.65
109.82
109.95
110.12
110.15
110.2
109.99
110.14
110.14
110.81
110.97
110.99
109.73
109.81
110.02
110.18
110.21
110.25
110.36
110.51
110.64
110.95
111.18
111.19
111.69
111.7
111.83
111.77
111.73
112.01
111.86
112.04




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13718&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13718&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13718&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13718&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]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13718&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13718&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2103.1102.80.299999999999997
3103.1103.10
4103.3103.10.200000000000003
5103.5103.30.200000000000003
6103.3103.5-0.200000000000003
7103.5103.30.200000000000003
8103.8103.50.299999999999997
9103.9103.80.100000000000009
10103.9103.90
11104.2103.90.299999999999997
12104.6104.20.399999999999991
13104.9104.60.300000000000011
14105.2104.90.299999999999997
15105.2105.20
16105.6105.20.399999999999991
17105.6105.60
18106.2105.60.600000000000009
19106.3106.20.0999999999999943
20106.4106.30.100000000000009
21106.9106.40.5
22107.2106.90.299999999999997
23107.3107.20.0999999999999943
24107.3107.30
25107.4107.30.100000000000009
26107.55107.40.149999999999991
27107.87107.550.320000000000007
28108.37107.870.5
29108.38108.370.0099999999999909
30107.92108.38-0.459999999999994
31108.03107.920.109999999999999
32108.14108.030.109999999999999
33108.3108.140.159999999999997
34108.64108.30.340000000000003
35108.66108.640.019999999999996
36109.04108.660.38000000000001
37109.03109.04-0.0100000000000051
38109.03109.030
39109.54109.030.510000000000005
40109.75109.540.209999999999994
41109.83109.750.0799999999999983
42109.65109.83-0.179999999999993
43109.82109.650.169999999999987
44109.95109.820.130000000000010
45110.12109.950.170000000000002
46110.15110.120.0300000000000011
47110.2110.150.0499999999999972
48109.99110.2-0.210000000000008
49110.14109.990.150000000000006
50110.14110.140
51110.81110.140.670000000000002
52110.97110.810.159999999999997
53110.99110.970.019999999999996
54109.73110.99-1.25999999999999
55109.81109.730.0799999999999983
56110.02109.810.209999999999994
57110.18110.020.160000000000011
58110.21110.180.0299999999999869
59110.25110.210.0400000000000063
60110.36110.250.109999999999999
61110.51110.360.150000000000006
62110.64110.510.129999999999995
63110.95110.640.310000000000002
64111.18110.950.230000000000004
65111.19111.180.0099999999999909
66111.69111.190.5
67111.7111.690.0100000000000051
68111.83111.70.129999999999995
69111.77111.83-0.0600000000000023
70111.73111.77-0.039999999999992
71112.01111.730.280000000000001
72111.86112.01-0.150000000000006
73112.04111.860.180000000000007

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 103.1 & 102.8 & 0.299999999999997 \tabularnewline
3 & 103.1 & 103.1 & 0 \tabularnewline
4 & 103.3 & 103.1 & 0.200000000000003 \tabularnewline
5 & 103.5 & 103.3 & 0.200000000000003 \tabularnewline
6 & 103.3 & 103.5 & -0.200000000000003 \tabularnewline
7 & 103.5 & 103.3 & 0.200000000000003 \tabularnewline
8 & 103.8 & 103.5 & 0.299999999999997 \tabularnewline
9 & 103.9 & 103.8 & 0.100000000000009 \tabularnewline
10 & 103.9 & 103.9 & 0 \tabularnewline
11 & 104.2 & 103.9 & 0.299999999999997 \tabularnewline
12 & 104.6 & 104.2 & 0.399999999999991 \tabularnewline
13 & 104.9 & 104.6 & 0.300000000000011 \tabularnewline
14 & 105.2 & 104.9 & 0.299999999999997 \tabularnewline
15 & 105.2 & 105.2 & 0 \tabularnewline
16 & 105.6 & 105.2 & 0.399999999999991 \tabularnewline
17 & 105.6 & 105.6 & 0 \tabularnewline
18 & 106.2 & 105.6 & 0.600000000000009 \tabularnewline
19 & 106.3 & 106.2 & 0.0999999999999943 \tabularnewline
20 & 106.4 & 106.3 & 0.100000000000009 \tabularnewline
21 & 106.9 & 106.4 & 0.5 \tabularnewline
22 & 107.2 & 106.9 & 0.299999999999997 \tabularnewline
23 & 107.3 & 107.2 & 0.0999999999999943 \tabularnewline
24 & 107.3 & 107.3 & 0 \tabularnewline
25 & 107.4 & 107.3 & 0.100000000000009 \tabularnewline
26 & 107.55 & 107.4 & 0.149999999999991 \tabularnewline
27 & 107.87 & 107.55 & 0.320000000000007 \tabularnewline
28 & 108.37 & 107.87 & 0.5 \tabularnewline
29 & 108.38 & 108.37 & 0.0099999999999909 \tabularnewline
30 & 107.92 & 108.38 & -0.459999999999994 \tabularnewline
31 & 108.03 & 107.92 & 0.109999999999999 \tabularnewline
32 & 108.14 & 108.03 & 0.109999999999999 \tabularnewline
33 & 108.3 & 108.14 & 0.159999999999997 \tabularnewline
34 & 108.64 & 108.3 & 0.340000000000003 \tabularnewline
35 & 108.66 & 108.64 & 0.019999999999996 \tabularnewline
36 & 109.04 & 108.66 & 0.38000000000001 \tabularnewline
37 & 109.03 & 109.04 & -0.0100000000000051 \tabularnewline
38 & 109.03 & 109.03 & 0 \tabularnewline
39 & 109.54 & 109.03 & 0.510000000000005 \tabularnewline
40 & 109.75 & 109.54 & 0.209999999999994 \tabularnewline
41 & 109.83 & 109.75 & 0.0799999999999983 \tabularnewline
42 & 109.65 & 109.83 & -0.179999999999993 \tabularnewline
43 & 109.82 & 109.65 & 0.169999999999987 \tabularnewline
44 & 109.95 & 109.82 & 0.130000000000010 \tabularnewline
45 & 110.12 & 109.95 & 0.170000000000002 \tabularnewline
46 & 110.15 & 110.12 & 0.0300000000000011 \tabularnewline
47 & 110.2 & 110.15 & 0.0499999999999972 \tabularnewline
48 & 109.99 & 110.2 & -0.210000000000008 \tabularnewline
49 & 110.14 & 109.99 & 0.150000000000006 \tabularnewline
50 & 110.14 & 110.14 & 0 \tabularnewline
51 & 110.81 & 110.14 & 0.670000000000002 \tabularnewline
52 & 110.97 & 110.81 & 0.159999999999997 \tabularnewline
53 & 110.99 & 110.97 & 0.019999999999996 \tabularnewline
54 & 109.73 & 110.99 & -1.25999999999999 \tabularnewline
55 & 109.81 & 109.73 & 0.0799999999999983 \tabularnewline
56 & 110.02 & 109.81 & 0.209999999999994 \tabularnewline
57 & 110.18 & 110.02 & 0.160000000000011 \tabularnewline
58 & 110.21 & 110.18 & 0.0299999999999869 \tabularnewline
59 & 110.25 & 110.21 & 0.0400000000000063 \tabularnewline
60 & 110.36 & 110.25 & 0.109999999999999 \tabularnewline
61 & 110.51 & 110.36 & 0.150000000000006 \tabularnewline
62 & 110.64 & 110.51 & 0.129999999999995 \tabularnewline
63 & 110.95 & 110.64 & 0.310000000000002 \tabularnewline
64 & 111.18 & 110.95 & 0.230000000000004 \tabularnewline
65 & 111.19 & 111.18 & 0.0099999999999909 \tabularnewline
66 & 111.69 & 111.19 & 0.5 \tabularnewline
67 & 111.7 & 111.69 & 0.0100000000000051 \tabularnewline
68 & 111.83 & 111.7 & 0.129999999999995 \tabularnewline
69 & 111.77 & 111.83 & -0.0600000000000023 \tabularnewline
70 & 111.73 & 111.77 & -0.039999999999992 \tabularnewline
71 & 112.01 & 111.73 & 0.280000000000001 \tabularnewline
72 & 111.86 & 112.01 & -0.150000000000006 \tabularnewline
73 & 112.04 & 111.86 & 0.180000000000007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13718&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]2[/C][C]103.1[/C][C]102.8[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]3[/C][C]103.1[/C][C]103.1[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]103.3[/C][C]103.1[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]5[/C][C]103.5[/C][C]103.3[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]6[/C][C]103.3[/C][C]103.5[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]7[/C][C]103.5[/C][C]103.3[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]8[/C][C]103.8[/C][C]103.5[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]9[/C][C]103.9[/C][C]103.8[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]10[/C][C]103.9[/C][C]103.9[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]104.2[/C][C]103.9[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]12[/C][C]104.6[/C][C]104.2[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]13[/C][C]104.9[/C][C]104.6[/C][C]0.300000000000011[/C][/ROW]
[ROW][C]14[/C][C]105.2[/C][C]104.9[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]15[/C][C]105.2[/C][C]105.2[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]105.6[/C][C]105.2[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]17[/C][C]105.6[/C][C]105.6[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]106.2[/C][C]105.6[/C][C]0.600000000000009[/C][/ROW]
[ROW][C]19[/C][C]106.3[/C][C]106.2[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]20[/C][C]106.4[/C][C]106.3[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]21[/C][C]106.9[/C][C]106.4[/C][C]0.5[/C][/ROW]
[ROW][C]22[/C][C]107.2[/C][C]106.9[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]23[/C][C]107.3[/C][C]107.2[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]24[/C][C]107.3[/C][C]107.3[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]107.4[/C][C]107.3[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]26[/C][C]107.55[/C][C]107.4[/C][C]0.149999999999991[/C][/ROW]
[ROW][C]27[/C][C]107.87[/C][C]107.55[/C][C]0.320000000000007[/C][/ROW]
[ROW][C]28[/C][C]108.37[/C][C]107.87[/C][C]0.5[/C][/ROW]
[ROW][C]29[/C][C]108.38[/C][C]108.37[/C][C]0.0099999999999909[/C][/ROW]
[ROW][C]30[/C][C]107.92[/C][C]108.38[/C][C]-0.459999999999994[/C][/ROW]
[ROW][C]31[/C][C]108.03[/C][C]107.92[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]32[/C][C]108.14[/C][C]108.03[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]33[/C][C]108.3[/C][C]108.14[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]34[/C][C]108.64[/C][C]108.3[/C][C]0.340000000000003[/C][/ROW]
[ROW][C]35[/C][C]108.66[/C][C]108.64[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]36[/C][C]109.04[/C][C]108.66[/C][C]0.38000000000001[/C][/ROW]
[ROW][C]37[/C][C]109.03[/C][C]109.04[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]38[/C][C]109.03[/C][C]109.03[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]109.54[/C][C]109.03[/C][C]0.510000000000005[/C][/ROW]
[ROW][C]40[/C][C]109.75[/C][C]109.54[/C][C]0.209999999999994[/C][/ROW]
[ROW][C]41[/C][C]109.83[/C][C]109.75[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]42[/C][C]109.65[/C][C]109.83[/C][C]-0.179999999999993[/C][/ROW]
[ROW][C]43[/C][C]109.82[/C][C]109.65[/C][C]0.169999999999987[/C][/ROW]
[ROW][C]44[/C][C]109.95[/C][C]109.82[/C][C]0.130000000000010[/C][/ROW]
[ROW][C]45[/C][C]110.12[/C][C]109.95[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]46[/C][C]110.15[/C][C]110.12[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]47[/C][C]110.2[/C][C]110.15[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]48[/C][C]109.99[/C][C]110.2[/C][C]-0.210000000000008[/C][/ROW]
[ROW][C]49[/C][C]110.14[/C][C]109.99[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]50[/C][C]110.14[/C][C]110.14[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]110.81[/C][C]110.14[/C][C]0.670000000000002[/C][/ROW]
[ROW][C]52[/C][C]110.97[/C][C]110.81[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]53[/C][C]110.99[/C][C]110.97[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]54[/C][C]109.73[/C][C]110.99[/C][C]-1.25999999999999[/C][/ROW]
[ROW][C]55[/C][C]109.81[/C][C]109.73[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]56[/C][C]110.02[/C][C]109.81[/C][C]0.209999999999994[/C][/ROW]
[ROW][C]57[/C][C]110.18[/C][C]110.02[/C][C]0.160000000000011[/C][/ROW]
[ROW][C]58[/C][C]110.21[/C][C]110.18[/C][C]0.0299999999999869[/C][/ROW]
[ROW][C]59[/C][C]110.25[/C][C]110.21[/C][C]0.0400000000000063[/C][/ROW]
[ROW][C]60[/C][C]110.36[/C][C]110.25[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]61[/C][C]110.51[/C][C]110.36[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]62[/C][C]110.64[/C][C]110.51[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]63[/C][C]110.95[/C][C]110.64[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]64[/C][C]111.18[/C][C]110.95[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]65[/C][C]111.19[/C][C]111.18[/C][C]0.0099999999999909[/C][/ROW]
[ROW][C]66[/C][C]111.69[/C][C]111.19[/C][C]0.5[/C][/ROW]
[ROW][C]67[/C][C]111.7[/C][C]111.69[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]68[/C][C]111.83[/C][C]111.7[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]69[/C][C]111.77[/C][C]111.83[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]70[/C][C]111.73[/C][C]111.77[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]71[/C][C]112.01[/C][C]111.73[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]72[/C][C]111.86[/C][C]112.01[/C][C]-0.150000000000006[/C][/ROW]
[ROW][C]73[/C][C]112.04[/C][C]111.86[/C][C]0.180000000000007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13718&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13718&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
2103.1102.80.299999999999997
3103.1103.10
4103.3103.10.200000000000003
5103.5103.30.200000000000003
6103.3103.5-0.200000000000003
7103.5103.30.200000000000003
8103.8103.50.299999999999997
9103.9103.80.100000000000009
10103.9103.90
11104.2103.90.299999999999997
12104.6104.20.399999999999991
13104.9104.60.300000000000011
14105.2104.90.299999999999997
15105.2105.20
16105.6105.20.399999999999991
17105.6105.60
18106.2105.60.600000000000009
19106.3106.20.0999999999999943
20106.4106.30.100000000000009
21106.9106.40.5
22107.2106.90.299999999999997
23107.3107.20.0999999999999943
24107.3107.30
25107.4107.30.100000000000009
26107.55107.40.149999999999991
27107.87107.550.320000000000007
28108.37107.870.5
29108.38108.370.0099999999999909
30107.92108.38-0.459999999999994
31108.03107.920.109999999999999
32108.14108.030.109999999999999
33108.3108.140.159999999999997
34108.64108.30.340000000000003
35108.66108.640.019999999999996
36109.04108.660.38000000000001
37109.03109.04-0.0100000000000051
38109.03109.030
39109.54109.030.510000000000005
40109.75109.540.209999999999994
41109.83109.750.0799999999999983
42109.65109.83-0.179999999999993
43109.82109.650.169999999999987
44109.95109.820.130000000000010
45110.12109.950.170000000000002
46110.15110.120.0300000000000011
47110.2110.150.0499999999999972
48109.99110.2-0.210000000000008
49110.14109.990.150000000000006
50110.14110.140
51110.81110.140.670000000000002
52110.97110.810.159999999999997
53110.99110.970.019999999999996
54109.73110.99-1.25999999999999
55109.81109.730.0799999999999983
56110.02109.810.209999999999994
57110.18110.020.160000000000011
58110.21110.180.0299999999999869
59110.25110.210.0400000000000063
60110.36110.250.109999999999999
61110.51110.360.150000000000006
62110.64110.510.129999999999995
63110.95110.640.310000000000002
64111.18110.950.230000000000004
65111.19111.180.0099999999999909
66111.69111.190.5
67111.7111.690.0100000000000051
68111.83111.70.129999999999995
69111.77111.83-0.0600000000000023
70111.73111.77-0.039999999999992
71112.01111.730.280000000000001
72111.86112.01-0.150000000000006
73112.04111.860.180000000000007







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74112.04111.539710105102112.540289894898
75112.04111.332483245517112.747516754483
76112.04111.173472483523112.906527516477
77112.04111.039420210204113.040579789796
78112.04110.921317786552113.158682213448
79112.04110.814545034029113.265454965971
80112.04110.716357354661113.363642645339
81112.04110.624966491034113.455033508966
82112.04110.539130315306113.540869684694
83112.04110.457944441756113.622055558244
84112.04110.380726132217113.699273867783
85112.04110.306944967047113.773055032953

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 112.04 & 111.539710105102 & 112.540289894898 \tabularnewline
75 & 112.04 & 111.332483245517 & 112.747516754483 \tabularnewline
76 & 112.04 & 111.173472483523 & 112.906527516477 \tabularnewline
77 & 112.04 & 111.039420210204 & 113.040579789796 \tabularnewline
78 & 112.04 & 110.921317786552 & 113.158682213448 \tabularnewline
79 & 112.04 & 110.814545034029 & 113.265454965971 \tabularnewline
80 & 112.04 & 110.716357354661 & 113.363642645339 \tabularnewline
81 & 112.04 & 110.624966491034 & 113.455033508966 \tabularnewline
82 & 112.04 & 110.539130315306 & 113.540869684694 \tabularnewline
83 & 112.04 & 110.457944441756 & 113.622055558244 \tabularnewline
84 & 112.04 & 110.380726132217 & 113.699273867783 \tabularnewline
85 & 112.04 & 110.306944967047 & 113.773055032953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13718&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]74[/C][C]112.04[/C][C]111.539710105102[/C][C]112.540289894898[/C][/ROW]
[ROW][C]75[/C][C]112.04[/C][C]111.332483245517[/C][C]112.747516754483[/C][/ROW]
[ROW][C]76[/C][C]112.04[/C][C]111.173472483523[/C][C]112.906527516477[/C][/ROW]
[ROW][C]77[/C][C]112.04[/C][C]111.039420210204[/C][C]113.040579789796[/C][/ROW]
[ROW][C]78[/C][C]112.04[/C][C]110.921317786552[/C][C]113.158682213448[/C][/ROW]
[ROW][C]79[/C][C]112.04[/C][C]110.814545034029[/C][C]113.265454965971[/C][/ROW]
[ROW][C]80[/C][C]112.04[/C][C]110.716357354661[/C][C]113.363642645339[/C][/ROW]
[ROW][C]81[/C][C]112.04[/C][C]110.624966491034[/C][C]113.455033508966[/C][/ROW]
[ROW][C]82[/C][C]112.04[/C][C]110.539130315306[/C][C]113.540869684694[/C][/ROW]
[ROW][C]83[/C][C]112.04[/C][C]110.457944441756[/C][C]113.622055558244[/C][/ROW]
[ROW][C]84[/C][C]112.04[/C][C]110.380726132217[/C][C]113.699273867783[/C][/ROW]
[ROW][C]85[/C][C]112.04[/C][C]110.306944967047[/C][C]113.773055032953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13718&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13718&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
74112.04111.539710105102112.540289894898
75112.04111.332483245517112.747516754483
76112.04111.173472483523112.906527516477
77112.04111.039420210204113.040579789796
78112.04110.921317786552113.158682213448
79112.04110.814545034029113.265454965971
80112.04110.716357354661113.363642645339
81112.04110.624966491034113.455033508966
82112.04110.539130315306113.540869684694
83112.04110.457944441756113.622055558244
84112.04110.380726132217113.699273867783
85112.04110.306944967047113.773055032953



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')